MSU LIBRARIES RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. CHARACTERISTICS OF ASPHALT PAVING MIXTURES UNDER STATIC AND CYCLIC LOADING BY Karim Chatti A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Civil and Environmental Engineering 1987 ."-o (“D . a I I" I) '1‘ OJ. ABSTRACT CHARACTERISTICS OF ASPHADT PAVING MIXTURES UNDER.STATIC AND CYCLIC LOADING BY Karim Chatti In this study, the elastic and plastic characteristics of asphalt paving mixtures were evaluated using static and repeated load unconfined triaxial tests. The objective of the study is to quantify relationships between structural properties, and mix and test variables. The structural properties investigated were: a) resilient and total moduli; b) cumulative plastic strain: c) unconfined compressive strength; and d) secondary creep compliance. The mix variables included in the study were: a) percent air voids in the asphalt mix: b) asphalt kinematic viscosity; c) aggregate angularity; and d) aggregate gradation. The test variables were: a) test temperature; b) applied load; and c) number of load repetitions. I ”In ‘ u.- '- ”In . ‘n-V I . may I . u.‘ ‘ ‘0' U A“ U g... O I.”- AI‘I. o h rout-v. s 0...... . o . 0’s. :9. ho. ". (I) Four types of tests were used: a) unconfined b) unconfined c) unconfined d) unconfined The results development of multiple linear these structural variables. triaxial constant peak cyclic load; triaxial variable peak cyclic load: triaxial compressive: and creep tests. of the investigation has led to the five statistical equations, using a regression analysis, relating each of properties to the above test and mix TONY PARENTS iv a“ :u I. T‘ It: ‘ u s fl ..‘ 5'. O ‘ a I. 'u I:‘ O \ Q .U \‘i \. .I ‘i ACKNOWLEDGEMENTS The writer wishes to express his sincere appreciation to his major professor, Dr. Gilbert Y. Baladi, Associate Professor of Civil Engineering, for his continual support, both morally and materially, and guidance throughout the writer's undergraduate studies as well as during the preparation of this thesis. Thanks are also due to the other members of the committee: Dr. ZR. W. Iqles, Associate Professor of Civil Engineering: and Dr. R. S. Harichandran, Assistant Professor of Civil Engineering. The writer also wishes to express his appreciation to: Mr. J. Defoe, Transportation Engineer, Mr J. Sweeny, and Mr. J. Chernach, Research Technicians, from the Michigan Department of Transportation for their cooperation and valuable suggestions during the experimental phase of the study: and to his friend, Mr. ‘Wadood Hamad for his encouragement and help. Thanks are also extended. to the Federal Highway Administration, the Michigan Department of Transportation, and the Division of Engineering Research at. .Michigan State. ‘University for ‘the financial assistance which made this research possible. .- .0 W: 4 fl honouv. Last, but not least, the writer is indebted to Miss Margaret Anne Soeters for her continuing support, assistance, and encouragement during the course of his graduate studies, without which he would not have completed this work. vi uno- " . wie. \. -‘ ‘ I ”a '0 .I n nuc- 0“ . .\....... 0 fit 00-.- n 00.?“ ' “em-‘- I O f C-. -. F.) Al Al 'I'IAIAIAI ‘- A. I I ‘ : a, t t : ,‘.‘u 41;“..‘1 1. d.. 1. c.‘ 1 . I 4.3 'I C . 5.4 I 1 Q TABLE OF CONTENTS Page LIST OF TABLES ................ ...................... ix LIST OF FIGUES ................... ..... ... ........... xii CHAPTER 1 INTRODUCTION AND RESEARCH OBJECTIVES ............ 1 2 LITERATURE REVIEW ...... .......... . .............. 7 2.1 General ................ .................... 7 2.1.1 Theoretical Considerations ........... 8 2.1.2 Laboratory Evaluation ........... ..... 13 2.1.3 Practical Applications ............... 14 2.2 Stability and Stiffness of Asphalt Mixtures 17 2.2.1 Definition of Stability ...... ........ 17 2.2.2 Effects of Mix Variables ............. 21 2.2.3 Effects of Specimen Variables ........ 30 2.2.4 Comparison of Marshall Test Results Others ................. ....... ....... 34 2.3 Resilient Characteristics of Asphalt Mixes . 40 2.3.1 Asphalt Binder and Mix Stiffness ..... 44 2.3.2 Mix and Sample Variables ............. 46 2.3.3 Test Variables .................. ..... 54 2.3.4 Test Type .......... .................. 56 2.3.5 Resilient Poisson's Ratio ............ 63 2.4 Plastic Characteristics ...-. ............. .. 65 2.4.1 Effects of Test Variables ............ 68 2.4.2 Sample and Mix Variables ............. 74 2.5 Strength of Asphaltic Concrete Mixes ....... 75 3 LABORATORY INVESTIGATION.............. ...... 81 3.1 General ............................. ....... 81 3.2 Test Types ................................. 82 3.3 Test Materials .............. ...... .. ....... 83 3.3.1 Aggregate and Mineral Filler ... ...... 83 3.3.2 Asphalt Type ......................... 90 3.4 Test Procedures ............................ 90 3.4.1 Preliminary Test (Marshall Stability- Flow) ................................ 90 3.4.2 Basic Tests .......................... 103 3.4.2.1 Unconfined Compressive Tests . 103 3.4.2.2 Creep Tests .................. 104 3.4.2.3 Unconfined Triaxial Constant Peak Cyclic Load (TXCCL) Tests 105 vii .‘d I... Q A - ‘ . - lac fist ”a“. ... .. Q a Q\w 0 e .4. 9.! D U I " w I ..l‘ l‘ ‘.I DRd -... «Ia I... ... I. . I I .\4 to. and our CHAPTER Page 3.4.2.4 Unconfined Triaxial Variable Peak Cyclic Load (TXVCL) Tests 106 3.5 Specimen Preparation Procedure ...... ....... 108 3.6 Mix, Specimen, and Test Variables .......... 110 3 O 6. 1 Mix variables I O O I O O O O O O O O O ........... 110 3.6.2 Specimen Variables ....... ............ 111 3.6.3 Test Variables .. ..................... 112 3.7 Test Matrices ............ .................. 112 3.8 Specimen Designation Number ................ 116 4 TEST “SULTS ......OOOOOO ........ 0.... ........... 118 4.1 General .............. ...................... 118 4.2 Unconfined Triaxial Constant Peak Cyclic mad (TXCCL) Tests ......OOOOOOOOOO ......... 118 4.3 Unconfined Triaxial Variable Peak Cyclic Load (TXVCL) Tests ......................... 121 4.4 Unconfined Static Compression Tests ........ 121 4.5 Static Creep Tests ........... .............. 125 5 ANALYSIS AND DISCUSSION . ........................ 131 5.1 Introduction .............. ................. 131 5.2 Analysis Methods .............. ...... . ...... 133 5.2.1 Separation of Variables ...... ........ 134 5.2.2 General Equation ..................... 146 5.2.3 Stepwise Correlation ......... ........ 147 5.3 Resilient and Total Characteristics ........ 149 5.4 Plastic Defamation O O O O O O O O O O O O O 00000000000 178 5.5 Unconfined Compressive Strength ............ 184 5.6 Creep Characteristics . ..................... 191 5 CONCLUSIONS AND RECOMMENDATIONS ................. 197 6.1 Conclusions ............... ................. 197 6.2 Recommendations ........... ................. 198 LISTOFREFERENCES.............. .................... 199 APPENDICES APPENDIX A .00... OOOOOOOOOOOOOOOO O 000000000000000 217 APPENDIX B .... ....... . .......................... 233 APPENDIXCOOOOOOOOOOOOO 00000000000 0...... ....... 256 APPENDIXDOOOOOOOOOOO OOOOOOOOOOOOOOO O ........... 302 APPENDIXE.....OOOOOOOOOOOOO ..... O OOOOOOOOOOOOOO 323 viii “on. 0 ob. TABLE 2.1 3.1 13-:2 13 -:3 3 4 3 5 3-6 3.7 3-8 3.9 3-10 3‘11 55 “ 3L ES __ :2 LIST OF TABLES SUMMARY OF EXISTING INFORMATION FROM SELECTED REFERENCES CONCERNING FACTORS AFFECTING STABILITY AND FLOW OF COMPACTED BITUMINOUS AGGREGATE MIXTURES............... ....... ... ..... SUMMARY OF EXISTING INFORMATION FROM SELECTED REFERENCES CONCERNING FACTORS AFFECTING REILIENT AND DYNAMIC MODULI, PERMANENT DEFORMATION, AND STRENGTH OF COMPACTED BITUMINOUS AGGREGATE MIXTURES............ ....... PERCENT PASSING BY WEIGHT FOR GRADATIONS A AND BCOOOOOOOIOOOOCOOOOOOOOO OOOOOOOOOOOOOOOOOOOO SPECIFIC GRAVITY OF THE COARSE AGGREGATE ........ SPECIFIC GRAVITY OF THE FINE AGGREGATE.......... ASPHALT PROPERTIES...................... ........ MARSHALL MIX DESIGN RESULTS FOR ASPHALT PENETRATIONOF 75-100.000.00...0.00.0000...OO... MARSHALL MIX DESIGN RESULTS FOR ASPHALT PENETRATIONOF120-150000000000000000.00.0000oo- MARSHALL MIX DESIGN RESULTS FOR ASPHALT PENETRATION OF 200-250........ ........... .. ..... ASPHALT MIX DESIGN FOR THREE PERCENT AIR VOIDS...00.000.000.000.......0...0.00.00.00.0000 ASPHALT MIX DESIGN FOR FIVE PERCENT AIR VOIDS... ASPHALT MIX DESIGN FOR SEVEN PERCENT AIR VOIDS......OOOOO00.0.0.0.........OOOOOOOOOO ..... LOAD AND TEMPERATURE VARIABLES FOR THE BASIC TESTS-......OOCOOOOOOOCOO......0.0.00.0... ...... REGRESSION COEFFICIENTS, COEFFICIENTS OF CORRELATION, AND STANDARD ERRORS OF EQUATION 5.1FORMERAGGREGATESCCOOOOC00.000.000.000... REGRESSION COEFFICIENT MATRIX FOR RESILIENT MODULUS VERSUS SPECIMEN VARIABLES (TXCCL)....... ix Page 38 77 86 88 89 91 94 96 98 100 101 102 113 139 154 ,ad " QII'.‘ I i I 9 Iain“ gov-1 Ol-U‘l v-‘Q *9.- ...-I I' .- 6.501 .u‘ou uv-h4 OA‘R * Cu I‘!.- an.-.. 'F RIO! ‘0'... ‘On.« " .- 0—5... '3 In" so...“ ' .- 0“.“ I! ‘9‘. Il'.‘ ‘_.d ...- " .- .“l . "fitn. ."'v. .‘1\ 4m. TABLE 5.3 5.4 5.5 5.:5 5-7 55- s: 55..59 55 - 3Lc> ES - 3L1. ES __.3_2 Es ‘_ 3‘3 53 ‘_ 3L4! 3‘15 REGRESSION COEFFICIENT MATRIX FOR RESILIENT MODULUS VERSUS SPECIMEN VARIABLES AND TEST TEMPERATURE (TXCCL)..................... ........ REGRESSION COEFFICIENT MATRIX FOR RESILIENT MODULUS VERSUS SPECIMEN VARIABLES AND CYCLIC mAD (TXVCL)0000000000000...000000.000... ....... REGRESSION COEFFICIENT MATRIX FOR RESILIENT MODULUS VERSUS SPECIMEN VARIABLES, CYCLIC LOAD AND TEST TEMPERATURE (TXVCL)....... ........ REGRESSION COEFFICIENT MATRIX FOR RESILIENT MODULUS VERSUS SPECIMEN VARIABLES, CYCLIC LOAD AND TEST TEMPERATURE (TXCCL+TXVCL).. ....... PARTIAL CORRELATION MATRIX FOR RESILIENT MOOULUS AND SPECIMEN VARIABLES (TXCCL).. ........ REGRESSION COEFFICIENT MATRIX FOR TOTAL MODULUS VERSUS SPECIMEN VARIABLES (TXCCL) ....... REGRESSION COEFFICIENT MATRIX FOR TOTAL MODULUS VERSUS SPECIMEN VARIABLES AND TEST TEMPERATURE (TXCCL).................... ......... REGRESSION COEFFICIENT MATRIX FOR TOTAL MODULUS VERSUS SPECIMEN VARIABLES AND CYCLIC IDAD (TXVCL)000000000000...0000000000000... ..... REGRESSION COEFFICIENT MATRIX FOR TOTAL MODULUS VERSUS SPECIMEN VARIABLES, CYCLIC LOAD AND TEST TEMPERATURE (TXVCL) ............... REGRESSION COEFFICIENT MATRIX FOR RESILIENT MODULUS VERSUS SPECIMEN VARIABLES, CYCLIC LOAD AND TEST TEMPERATURE (TXCCL+TXVCL)......... REGRESSION COEFFICIENT MATRIX FOR CUMULATIVE STRAIN VERSUS SPECIMEN VARIABLES (TXCCL)........ REGRESSION COEFFICIENT MATRIX FOR CUMULATIVE STRAIN VERSUS SPECIMEN VARIABLES AND TEST mmm...’......OCOOOOIOOOOOI00.0.0.0...OO. REGRESSION COEFFICIENT MATRIX FOR UNCONFINED COMPRESSIVE STRENGTH VERSUS SPECIMEN VMABESOOOCOOOCOOOOOOOOOC0.000.000....00...... Page 155 156 157 158 159 168 169 170 171 172 181 182 187 Qt. '1. . u. ML q'nO'F . ,I' \ .-..-- A. -0!- val. yuan-- n‘nv‘l .l .- Iguuoate .~~ .- "\ 1. ‘u UUI‘O ...-4- I\ \ afloal ”IA H "\‘ \- bo 'VI 1 ”-‘A |\ Ania-It "O M ‘01 it‘bva‘n WAR"‘ '0 iv.” "\‘AA‘V‘ '0 UV.!. TABLE Page 5J5 REGRESSION COEFFICIENT MATRIX FOR UNCONFINED A.1 COMPRESSIVE STRENGTH VERSUS SPECIMEN VARIABLES AND TEST TEMPERATURE........... ....... 188 UNCONFINED TRIAXIAL CONSTANT PEAK CYCLIC LOAD TESTSOOOOO0.0000000000000000..0...... ........... 217 UNCONFINED TRIAXIAL VARIABLE PEAK CYCLIC LOAD TESTS...‘......OOOOOOOOOOOOOO...00.0.00... ...... 233 UNCONFINED TRIAXIAL TESTS (virgin specimens)... 256 UNCONFINED TRIAXIAL TESTS (after TXVCL). ........ 279 UNCONFINED TRIAXIAL CREEP TESTS ................. 302 xi a." u , I ”...w . I :v- ... 0.. cu 1:" . Ac 1 l I'.‘ \ ... don-4 . I .0“ v.- v'. in.“ ‘a-c . w‘ 045-. ..‘l u. .0." . a -¢‘- l- v. 4.5. . . ‘- "' 1.1:. ‘ A Ipqi \ I "1 It»... ...- | s I--. . l . “.d .. V ' .3: "“A. '01-. ‘ I- . a n. I' x 0‘.- ‘.Q. It _ "be. I | .f- t “O. I.‘ I. a..." c 1.- a x;- FIGURE 2.1 2.2 3.1 3. .3 3. -3 -55 4-1 <1 - :3 4-3 4.4 4-5 4‘6 4‘7 4‘8 4‘9 4‘10 ES ‘ 3L LIST OF FIGURES Page FITURES OF THE CYCLIC STRESS-STRAIN CURVES OF “PmLTMIXESOQCOCCCOOOOOIOCOOOO0.00.00... ...... lo STRESS-STRAIN CURVE OF ASPHALT CONCRETE. ........ 41 GRADATIONS A AND B FOR ALL THREE TYPES OF AGGREGATES ALONG WITH THE STRAIGHT LINE GmATIONOOOOOOOOOOOOOOO00......0.00.00.00.00... 84 GRAIN SIZE DISTRIBUTION CURVES.. ...... .......... 85 MARSHALL MIX DESIGN MATRIX...... ....... . ........ 93 SCHEMATIC DIAGRAMS OF THE UNCONFINED TRIAXIAL TEST SETUPSCOOOOOOOOOOOIOOO00...... 000000000000 107 PARTIAL FACTORIAL EXPERIMENT MATRIX FOR THE UNCONFINED TRIAXIAL TESTS............... ........ 115 RESILIENT MODULUS VERSUS NUMBER OF LOAD REPETITIONS FOR THREE AIR VOIDS....... .......... 119 TOTAL MODULUS VERSUS NUMBER OF LOAD REPETITIONS FOR THREE AIR VOIDS............ ..... 120 CUMULATIVE PERMANENT STRAIN VERSUS NUMBER OF LOAD REPETITIONS FOR THREE AIR VOIDS............ 122 RESILIENT MODULUS VERSUS NUMBER OF LOAD REPETITIONS FOR THREE CYCLIC LOADS...... ........ 123 TOTAL MODULUS VERSUS NUMBER OF LOAD REPETITIONS FOR THREE CYCLIC LOADS.............. 124 STATIC STRESS-STRAIN CURVES FOR THREE AIR VOIDS........................................... 126 CREEP TEST FOR SAMPLE 12117613...... ............ 127 CREEP TEST FOR SAMPLE 21117613..... ..... ........ 128 CREEP TEST FOR SAMPLE 11317513.................. 129 CREEP TEST FOR SAMPLE 11117513.................. 130 PARTIAL FACTORIAL EXPERIMENT MATRIX FOR THE UNCONFINED TRIAXIAL CONSTANT PEAK CYCLIC LOAD TESTS.......COOOOOOO............OOOOOOCOOOOOOOOI 135 xii U! 07 FIGURE Page 5.2 RESILIENT MODULUS VERSUS PERCENT AIR VOIDS FORTHREE AGGREGATE TYPES............... ........ 137 5.3 REGRESSION COEFFICIENT A1 VERSUS AGGREGATE ANGUMRITYOOOOOOOOIOOOOOOOOOC.....OOOOOOO. ...... 140 5.4 REGRESSION COEFFICIENT B VERSUS AGGREGATE MGUmITYOOOOOCOOOOOOOO}.......OOOOOOOOOOC ..... 141 5. 5 RATIO OF MEASURED TO CALCULATED RESILIENT MODULUS VERSUS KINEMATIC VISCOSITY. . . . . . . . ...... 143 5 . 6 CALCULATED VERSUS MEASURED RESILIENT MODULUS (SEPARATION OF VARIABLES METHOD). . . . . . . . . . . . . . . . 145 5 - 7 CALCULATED VERSUS MEASURED RESILIENT MODULUS . . . . 167 5 - 8 CALCULATED VERSUS MEASURED TOTAL MODULUS ........ 176 5 - 9 CALCULATED MODULUS USING THE ASPHALT INSTITUTE EQUATION VERSUS MEASURED RESILIENT MODULUSOOOOOOOOOOOOOOOO......OOOOOOOOOOOO...COO. 179 5 - 10 CALCULATED VERSUS MEASURED CUMULATIVE PLASTIC SmINOOOOOOOOOOOO......OOOOIOOO ........ 185 5 - 11 CALCULATED VERSUS MEASURED UNCONFINED COMPRESSIVE STRENGTH................ ...... . ..... 190 ~12 CONSTANT-STRESS CREEPTEST...................... 192 ‘ 13 CALCULATED VERSUS MEASURED SECONDARY CREEP COMPLIMCEOOOO......O.........COOOOOOOOOOO...... 196 ‘ l STANDARDIZED SCATTERPLOTS OF WEIGHTED RESIDUALS VERSUS INDEPENDENT VARIABLES AND RESILIENT MoDUmSOOCOOCOOCOOOOOOO......OOOOOOOOOO.... ..... 323 xiii CHAPTERI INTRODUCTION AND RESEARCH OBJECTIVES W9! Over the years, Americans alone have invested better than one trillion dollars in their highway systems and are just beginning to realize that the conditions of the highway infrastructures are a major problem that requires the infusion of funds for maintaining, rehabilitating, and rehuilding the systems. Public and legislative attentions have been focused on the SCOpe of public programs to Jrebuild and upgrade existing facilities and on the financing aspects of these programs. Financing alone cannot ScDive the problem because the needs far exceed the a“"ailable resources. Innovation in structural and nl'El‘t-fierial mix design is the key to bridging the gap and to a""-‘-Ce1erate the search for a better solution. In recognition of this need , the Federal Iij-ghway Administration initiated and sponsored this areSearch study to identify, evaluate, and document a l aJ'Dcaratory test procedure whereby asphalt mix design can be g)‘tamined from the structural viewpoint. The results of the study should help the highway engineer to assess the a‘hll'ructural properties of asphalt concrete mixes that are l‘Qeded in the design of flexible pavement. As stated by Yoder and Witczak (Y4)*, the classical definition of flexible pavements includes those PaVements that have an asphalt concrete surface. An aSphalt: pavement may consist of thin wearing surface course built over a base course and subbase course, and they rest upon the compacted subgrade. Thus, the term pavement herein implies all the layers (courses) in the pavement structure- The load carrying-capacity of a flexible pavement is brought about by the load distribution characteristics of the layered system. The highest quality layer is placed at or near the surface. Hence, the strength of the pavement is the result of building up thick layers and, thereby, distributing the load over the relatively weak subgrade (Y4) *. The structural design of flexible pavements is a dynamic Precess, continually changing as new data become available- This process involves the design of the supporting foundation (subgrade), subbase and base courses, and the asPhalt course. In Practice, the design of the asphalt course is accomplished in two steps: a) the design of the asphalt mix (proportioning of the different material in the mix): and ‘—7——‘\ * Figures in brackets indicate reference number. b) the structural design of the asphalt course which involves thickness design and evaluation of the mix performance under the anticipated traffic loads and environmental conditions. In general, a typical asphalt mix consists of four major components: asphalt, coarse and fine aggregates, mineral fillers, and air. Also, certain types of additives or modifiers could be added to the mix to alter some of its properties. Asphalt mix design involves the proportioning of these components to meet certain specificat :ions. In the early stages of development, asphalt mix design consisted of rule-of-thumb procedures based on judgement and past experience. Later, more refined design procedures were introduced (e.g. , Marshall, Hveem, and Hubbard-field methods) with the objective being to select and proportion materials in the blend to obtain the desired properties in the finished products. These PrOperties are dependent upon the properties of the constituent materials in the mix, the test type and procedure, and temperature. During the same time, pavement structural design has 3V°1ved slowly from a "trial and error approach" to one based on experience and mix design test data. These ampirical methods were thought for many years to be the only way . Beginning in the early 19605 , new analytical pavement design techniques started to emerge. Elastic and viscoelastic layered pavement models and the finite element model were developed, and are slowly being tried across the country. These new structural models provide the pavement engineer with a better understanding of pavement behavior and performance. One drawback (as percieved by some engineers) is that the models require new types of data to be collected prior to their use. Since the required data cannot be obtained from existing asphalt mix design methods and tests, new tests were developed and implemented. Most of the tests, l71‘3'9-7ever justified, are time consuming, require new training Of personnel, and are quite costly. Thus, the need to develop new and simplified testing procedure(s), or to improve and/or supplement existing ones, has been reCOgnized in recent years. Several standard test procedures were developed and are ha 1119 used in the USA and most of the world. These tests can be divided into two categories: a) those to establish the asphalt mix design (proportioning of the different components in the mix): and b) those to evaluate the structural properties of the mix that are required as input to the analytcal and semi-empirical pavement design methods. The first category includes: Marshall stability and flow, Hveem stabilometer, and, to a much lesser extent, Hubbard-field method. These tests are termed asphalt mix design methods and are being used to establish the proportioning of the different components (asphalt content, aggregates, mineral filler, and percent air voids) in the mix. The second category includes: unconfined compression and triaxial tests , indirect tensile tests, and flexural tests. Currently, these last tests are employed to evaluate the structural Properties of the asphalt mix that are needed as input to the analytical and semi-empirical pavement design methods. The work presented in this thesis is a part of a cc>lllprehensive research study undertaken at Michigan State UniVersity to tailor the asphalt mix design procedure to obtain its structural properties. This part includes the e"a~luation of these properties using unconfined compression a I ‘6 triaxial tests . W The objective of this study is to quantify relationships be . . tWeen the structural properties of asphalt mixes and the \x and test variables. An important aspect of the study is that the analysis must be undertaken in a manner that is consistent with established statistical and analytical pro(zedures (e.g., that recognize both the inherent assumptions and limitations of different statistical procedures) . During the laboratory phase of this study, several tests were employed. These are: unconfined compression; creep; and constant and variable peak cyclic load triaxial tests. The presentation herein is organized in several chapters as follows: Chapter 2. A literature review which contains a summary of existing information concerning the structural properties of asphalt mixes. cl'la-pter 3. A description of the laboratory investigation and test procedures. chapter 4. Test results. chapter 5. Analysis and discussion of the results. c‘1'133-pter 6. A summary of the findings of the study, conclusions, and recommendations. All test results are tabulated in the appendices. I“: should be noted that, in an effort to establish the background of this study, the literature review contains Information pretaining to the asphalt mix design, and to the S‘zl‘uctural properties of asphalt mixes obtained from both E biaxial and indirect tensile tests. ——-—.—. .9 FM LITERATURE REVIEW w Its stated in the introduction, the process of asphalt mix design is largely an exercise in selecting and I?1=<31Jortioning materials to obtain the desired properties 59f! ‘the finished products (6). This exercise includes consideration of the following: a) aggregate type, proportion, and gradation: b) mineral filler type and proportion: c) asphalt type and content; d) percent air voids: e) method and procedure of compaction: and f) test method and procedure. The overall objectives of the exercise are to obtain an a‘sphalt mix having sufficient: a) asphalt to ensure a durable mix; b) stability or strength to satisfy traffic demands without excessive distortion or displacement: c) percent air voids in the compacted mix to avoid loss of stability, flushing, and bleeding due to additional compaction under traffic loading: and d) workability without causing any segregation. After establishing an acceptable asphalt mix design, its structural properties are then evaluated. These include: fatigue properties: resilient, viscoelastic, and plastic characteristics: durability: and moisture susceptibility. Knowledge of the structural properties permits the use of mechanistic pavement design methods such as elastic layers, viscoelastic layers, and others. The scenario above implies that the acceptability of a given asphalt concrete mix as a structural layer in a Pavement section should be based upon its response under the anticipated traffic loading and its structural Properties, and their variation with time, temperature and load. Laboratory evaluation of these properties and their relevance to pavement design and performance are major issues facing the pavement engineer today. There are three primary areas of concern: a) theoretical considerations: 1:) laboratory evaluations; and c) practical applications. 2 ‘ 1 - 1 Theoretical Considerations The mechanical response of most asphalt mixes a uhjected to static and quasi-static loadings is Q Q1“Flex and differs considerably from that of the §§uStituent materials in the mixes. The response depends upon several variables which can be divided into three c(”III-non groups: a) asphalt mix variables: including type of asphalt and the percent asphalt content, aggregate type proportion and gradation, type and proportion of the mineral filler, and type and concentration of modifier (if any): 13) specimen variables: including compaction procedure, density or the percent air voids, sample size, and the amount of induced moisture: and c) test variables: including temperature, load intensity and frequency, and loading and relaxation periods. The pertinent features of the mechanical response (Stress-strain) of asphalt mixes under cyclic loading (See figure 2.1) include: a) time-independent elastic strain that is immediately recoverable upon unloading: b) time-dependent elastic (viscoelastic) strain that is recoverable after removal of the load: and c) plastic strain during a load-unload cycle which is dependent upon load configuration, load intensity and rate, load period, and test temperature. Further, fatigue life, the dependency of the shear gtrength of the material on the radial stress, stress I)“‘i~story, age of the mix, test temperature, and other ‘qrialriables play a major role in determining pavement response and performance when subjected to traffic loading. In order to obtain an analytical assessment of the met=hanica1 response, a constitutive model should be used .mmtz BAémmm< ho mm>mDU zH vwsflmumsm lo» mam. cwmuum cflmuum Ofiummam :flmuum owummam ‘rtezas 11 that can account for the pertinent features of the stress-strain properties of asphal mixes. Laboratory observations suggest that several different models can be constructed: a) linear or nonlinear elastic: b) elasto-plastic: c) elastic-viscoelastic-plastic: d) elastic-viscoelastic: and e) viscoelastic-plastic. The model to be selected for the analysis depends upon the desired degree of accuracy, the desired mathematical simplicity and the anticipated load intensity. For example: mathematically, the linear elastic model is the simplest. However, it does not account for the viscoelastic and plastic deformation of the sample. In gPel'meral, the elastic-viscoelastic-plastic model (El and 82) is appropriate because of its ability to accurately model the actual pavement response when subjected to traffic 1°leading. Yet, it is mathematically simple enough to be used on a disktop microcomputer. The basic premise of this model is the assumption that, at each loading increment, tli'le material is capable of undergoing a small p l astic (permanent) strain , a smal l viscoelastic (recoverable with time upon unloading) strain , and a s‘lllall elastic (immidiately recoverable upon removal of the load) strain. Mathematically, for each loading cycle, 12 the total strain is assumed to be the sum of the plastic, viscoelastic and elastic components, i.e. , eT a eE + eVE + eP (2.1) ‘vwlameem:e: total strain: elastic strain: viscoelastic strain: and plastic strain. on 00 ’Ug‘lnt'l'i Since the elastic strain is time independent, then the total strain rate is the sum of the components of the viscoelastic and plastic strain rates. That is: ----- = —---—— + ----- ‘ (2 . 2) where: the strain rate is the first derivative of strain with respect to time. It should be noted that equation 2.2 assumes that the s'tlress is applied and removed instantly. That is, the s“:1':ess intensity is either zero or a prespecified value. If the stress increases gradually with time (as is the case er moving wheel load in the field and most laboratory tLasts) then strain rates in equation 2.2 should be expressed as partial derivatives. All strain rates (including the e1~astic one) would then be stress-dependent. Equation 2 - 2 represents the strain rates during the period of Constant stress . 13 2 . 1 . 2 laboratory Evaluation Irrespective of the theory and/or constitutive model employed, the laboratory test results play a significant role in calibrating and verifying the theoretical model. There are three different types of tests that are commonly used to directly determine structural properties such as elastic and/or resilient moduli and Poisson ' s ratios , creep and permanent de formation, and fatigue properties of asphalt mixes. These tests are based upon theoretical and/or empirical relationships between particular components of the load and defamation, and the type of specimen used in the test. Measurement of the load and deformation during a test can be used to estimate the structural properties of the Specimen. The three types of tests are: 1) indirect tensile: 2) triaxial: and 3) flexural. In each of the tests, difficulties are encountered in LC>aperly defined relative to a predetermined tiefc>rmation or strain level (M16). The determination of fatigue properties is n"53*: as straightforward as that of elastic properties. Definitions of fatigue failure vary although certain standards have been developed. It is necessary to 4 "Q‘ o. ‘ ‘ r.‘ .‘v, 16 critically examine the established standards to determine if they are sufficient to describe fatigue failure in real pavements. Variations in testing procedures and specimen types will yield even greater variation in fatigue parameters than in elastic properties. This is because fatigue failure is dependent upon the stress distribution within the specimen, which may be quite di :8 ferent from field conditions . Thus , the process leading to the selection of an appropriate test should address both the laboratory fatigue life and its relation to di. fferent field conditions. To summarize, asphalt mix design should not be treated as a subject in itself, it cannot be divorced from the structural properties of the mix and its performance in the field. It is the objective of this chapter, therefore, to discuss previous work in this field and the attempts that have been made to relate asphalt mix design Procedures to those employed to evaluate the structural lz’l‘eperties of the mix. In general, these procedures can be divided into two groups. The first includes all t1‘editional tests such as Marshall, Hveem, and triaxial. The second includes newly developed experimental test Procedures such as those used for determining the dynamic arid resilient moduli, permanent deformation, creep, and fatigue characteristics of the asphalt mix. In the following sections , the effects of .0 re": “...“! Iv . I In I' ...: Iv :I-pnuu ..IOUU. II . . u- .... I A -4. '.' I ' I ‘0 . 0-: b ...-.q. - lie e; . ""h- 4 ‘“"O.. ‘M. ‘ Q ':«t ”P- Q I Q ~ I, a. i wt so-’ ... 'ec ‘ i I .‘ I l‘z “ - ‘- A: V ‘A ‘U I.- c I ou‘ . ‘ s A ‘- t u \i‘ - Ah 17 different mix variables upon the structural properties of the mix are reviewed and summarized. The review is arranged, when possible, by test type and test procedure. this review is to establish the The purpose of background for this study and discuss the appropriateness of each test procedure to provide evaluating the effects of a simple and practical tool for asphalt mix variables on its structural properties. At each section of this review, the collected the end of information is summarized. OF ASPHALTIC S 2 - 2.1 Definition of Stability The stability of asphalt mixes is generally defined as the load or pressure which the mixture can support Without undergoing excessive deformation (M 19). SeVeral test methods and procedures have been developed to evaluate these properties (C1, C6, D5, F2, GB, 32. H5, H14, L2, M3, M7, M8, M10, M19, and others). D‘~-'le to the lack of a standard definition of stability, CcDrisiderable difference of opinion exists as to whether any of these tests provide a measure of this property. Monismith and Vallerga (M 19) defined stability as "the lead to cause a certain amount of deformation, said deformation depends upon the expected field conditions, triaxial compression test and that: only a form of Will . I"’e' n" . . | . ...n' ‘ o ...-g. 0.0! U‘ "_-c I § ”Q. I l ‘e.... v 3...... ...... it“... F i I 1 l 3. ll \ R! "I 'Q an 18 properly measure this property." They evaluated the stability of asphalt mixes using open-system triaxial compression tests. The tests were performed at a constant lateral pressure with deformations allowed to develop freely. They examined the effects of the density of the asphalt mix upon stability utilizing one penetration graded asphalt (85-100) and one gradation of crushed granite aggregate. They compacted the samples using a krneeading compactor with a 3000 psi double-plunger. Sample bl.¢anding, proportioning, mixing, (and curing were carefully controlled. For constant asphalt content, they obtained sessxleral curves of stress versus the mix density at 0.5, 1.0 and 2.0 percent strain levels. They concluded that: a) The relationship between density and stability of asphaltic mixtures depends upon the criterion used to determine stability. If stability is determined at a particular strain level, then an increase in density will result in an increase or decrease in stability depending upon the composition of the mix and the range of densities considered. Vb) Current methods for determining the stability of asphalt mixes show considerable variation in the magnitude of the strain at which stability is determined. C) For a given value of strain, say 2 percent, the stability of specimens produced by a kneading RA. Vu- as. ... () .‘..-.__a., .=."-Ubl C Q':: “' Viv... . A 'n l"“‘lonn H ... “ 3:... . \ h *5 ‘a‘ 19 compactor at higher asphalt contents were considerably lower than that for specimens produced by static compaction. d) For specimens produced by static compaction, stability is independent of the asphalt content. It is clear that one can almost obtain any value of stability he chooses. The value to be selected shall be based upon a predetermined deformation level. This deformation is dependent upon the pavement structure in question. An estimate of this deformation can be made utilizing mechanistic pavement design methods. This implies that present practice of accepting or rejecting an asphalt mix design based solely upon its stability is not valid. Both stability and deformation should be considered. Given that stability is a measure of the a~E>plied load (stress) and deformation is a measure of 3‘train: and the ratio of stress to strain can be Ciefined as a type of modulus, then one can deduce that a t3?I>e of mix modulus should be specified. Further, the sPecified modulus should be compatible to that required as il'lput to the structural pavement design method being used. Since most mechanistic pavement design methods use elastic theory: and the theory is based on a small strain Value, one can conclude that the specified modulus should be based on a small deformation. Thus asphalt mix stability -='. be V“ ' o .... . 6.2.. . UV“-- VA “-3 LC. . n‘n:' «a... IV“.... I. :‘ u‘ d. 3.: u ‘ :- I“..u‘~ I O Q‘O.~:. tb~'~-.' . a h ,' ‘6... “ ‘t‘."' I ‘o - .~ Q ‘ ‘ ‘3 ”' :~. 8V“": “I. U U \ ‘ \.¢“e . . “‘3 :r . ‘ :3» ‘.~-., 3‘s 20 can be defined using two concepts: a) design stability: the magnitude of the applied load at which a small strain is induced into the sample; and b) maximum stability (strength): the maximum load that the mix can withstand before yielding or fracturing. The design stability and the resulting strain can be used to calculate the modulus for pavement design purpose while the strength can be utilized to estimate the relative factor of safety of the pavement. The higher the factor of safety the longer the expected life of the pavement. The two definitions do not imply that new tests be conducted, indeed design and maximum stabilities can be obtained from the same test. For example: design stability could be specified as a certain percent (say 30 or 50) of the maximum stability. Corresponding deformation can then . be obtained from the load deformation record and consequently the modulus can be had. In this study (see chapter 6), the deformations at fifty percent of maximum stability are utilized to c3a1culate a modulus value from the Marshall and indirect terisile tests. Nevertheless, other investigators studied the Variations of stability due to variations in the mix, s'Elmple, and test variables. Their findings are slllllmarized in the next two subsections. I. . " ...o=v_ ...... vc .... 0 Q. ' no...bcl- . a o opp-q ’ \ .- voiuawvi C. ”an: Ma's.) ‘9‘, fl . a. d. J .. 'I I :1” ‘ -~ ""“Ouil 4 0A (‘A I " vIv' h ‘ u .6" “.Ia .. ’ ‘2 runs \ fl 3, .. a. M "I g E '0 .. u: 2:.“; ‘hb‘ ‘ . ‘- 3‘. 4-..?» . I v A. v".: Q q I-" "'u/ an 5» or (o S]. 21 2..:a.2 Effects of Mix'Variables Hveem and Vellegra (H14) studied the effects of different types of mineral aggregates, compaction type maxi! efforts, and asphalt content upon stability, density, tensile strength, and percent air voids of asphalt mixes utilizing the Hveem method. Three types of aggregates (crushed granite, crushed quartzite and uncrushed screened gravel) were selected, and the asphalt content was varied from 3 to 8%. The specimens were compacted using a kneading type compactor (the foot pressure varied from 200 to 600 psi) and double-plunger compaction at 2000 psi. They concluded that: a) There is no general relationship between density and stabilometer values. b) There is a general correlation between the density of a paving mixture and the cohesive or tensile resistance of the mix. c) There is a high degree of correlation between pavement performance and stabilometer results. Heithaus and Izatt (H5) studied the effects of asphalt content and viscos ity , compaction effort , temperature, aggregate type, and the percent of filler coritent upon the Marshall stability of asphalt mixes. They concluded that, in general, Marshall stability can be increased by: a) reducing the asphalt content: “I I ‘1‘ .a '1 ‘ "C C . ..." ;;4 .-2' and-d I ‘!-:~¢ I ‘ Iv-oo '05... - An. I s A? ...... '::’s q, I“. I ‘1 ‘ I I R '. .1 ‘ Q :‘I.. .- -‘.".I| e '1 ”' A—J .‘w l0] 1" A). 22 b) increasing filler content; c) using more active fillers; d) using higher viscosity asphalt; and c) using more angular aggregates. They added that the first three variables have more jJIljpaCt on stability than the other two. It should be noted however, that increasing the stability by decreasing the asphalt content may lead to a brittle and low durability mix. For this reason, Foster (F5) cautioned that increasing Marshall stability boasars} no relation to the load-carrying capacity of the mix. He added that stability should be increased by only two means: a) increasing compaction effort; and b) increasing the angularity of the fine aggregate. Cammpen et a1. (C1, C2), on the other hand, emphasized that: a) Changes in stability can be produced by minor reduction in asphalt content provided that the asphalt content is higher than the optimum. b) The use of high filler content in rounded coarse and fine aggregates has to be limited in order to provide for an adequate residual voids in the mix and a desirable ratio of asphalt film thickness to asphalt surface area. It is clear, at this point, that different conclusions Were drawn by the different investigators. The real . oun- -:c , . .uvov' I ..:v}"‘:‘ ...-1' bba Qn'FA“.' vinb' 0" . unuvac~ O antUUOU l ovflicv.‘ '0'... b. . . “.1" a: ' “...". . ...9 I. ' : .Vg»! ‘" '4. ..u u. u. 23 question is whether it is possible to estimate the resilient characteristics of asphalt mixes by using only mix composition. Dukats (05) indicated that the composition of asphalt mix is inadequate to characterize its properties. He strongly emphasized that the physico- chemical interactions of the binder-aggregate matrix also had to be considered. The effects of coarse to fine aggregate ratio and the gradation of the fine aggregate on the percent air voids of asphalt mixes were also evaluated by Campen et al. ((21 and C2) using Marshall test method. They found that: a) When a well-graded coarse aggregate is combined with a well graded fine aggregate, the percent air voids decreases until the percent of the coarse aggregates reaches 70-80 percent. After this, the percent air voids increase appreciably. b) When the amounts of coarse and fine aggregates are kept constant but the amount of material passing sieve number 40 is either more or less than 55 percent by weight of the fine aggregate, the percent air voids increases. Li and Kett (L3) studied the effects of coarse a‘ggregate shape, angularity, and surface texture upon the s‘tI-ability of asphalt concrete mixture utilizing both the I"‘alrshall and Hveem test methods. Throughout their testing Program, a single dense graded asphalt concrete paving 1;; 3'3. 3.:$:r‘ 6.00'. ‘ Ov:"'" .0... 'i O aacn' ‘1 ova-bond A‘ I "U. 1 a) ‘ v“ ‘ e N. l v .I ' . 5... w :‘:le u e 24 mix was used. The aggregates in the mix consisted of nine different combinations of coarse and fine crushed traprock, coarse gravel and sand, coarse and fine crushed shale, and limestone dust for mineral filler. These combinations resulted in diffrent aggregate angularity, shape, and surface texture. They concluded that: a) Stability increases with increasing aggregate angularity. b) Surface texture has no influence on the stability. c) Particle shape has no harmful effect on stability as long as ’the dimension ratio (the width to the thickness or the length to the width of the particle) is less than three. d) The maximum percentage of flat-shaped particles that could be contained in a mixture without reducing its stability is 30 percent. A similar conclusion was made by Wedding and Gaynor (W1). They studied the effects of crushed coarse and fine gravel upon the percent air voids and stability of asphalt Inixes. They found that as the percent crushed gravel j~11c:reases, the angularity, stability, and the percent a35-1:- voids increase. The deformation (flow value) however, aDpears to be unaffected. Stephens and Sinha ($19) studied the effects of aQgregate shape on the characteristics of asphalt Illixes. Their test results indicated that the percent ' "A’ 3" TV: not __,..;;. ‘..-n...¢ 0" I . . 1‘.‘ “‘6’ m.v~~‘ . ...-'0: .‘b-- u‘ a :9 <" ....=.. V'.-..... .. . \ " 1' 'u..‘. I o _ I: ‘Fnol‘ WO".-.. . . slé: ' o....‘ I. . " ‘ 6. u I‘ I ' ,‘.‘. Sec“ei s... l I 3.” :-,.: cu““‘ Q... ~ V 1 ‘ P. "\ Owing. ... 'v .1 l 9" i 25 air voids, the asphalt content, and the stability are si. gnificantly influenced by the aggregate shape . Ra lcheff and Tunnicliff (K2), on the other hand, reported that all mixture characteristics are influenced by the shape of the fine aggregate, the filler concentration, and the gradation of the combined aggregates. Mixes containing higher percentages of coarse aggregate and larger particle sizes yielded lower optimum asphalt contents . Further , mixes containing crushed coarse and fine aggregates produced higher Marshall stability. 8 inilar findings were also reported by Nichols and Kalcheff (Nl). Gietz and Lamb (Gl) evaluated the effects of mineral filler concentration and composition on the temperature-consistency relationships of asphalt mixes. The selected mineral filler were 1 imestone , 5 il ica , and Portland cement . The asphalt cements empl oyed were Obtained from two di f f erent sources with one Penetration grade of 8 5-100 . The mineral fil ler °°ncentrations utilized in their study were based on vOlumetric filler asphalt ratios (F/A) of 0.18, 0.45, and 0.72. The F/A is defined as follows: V W /G F(l-A/100)(G ) F/A - --2- - --s--:- = ............. 2-- (2.3) va wa/ca A(Gf) where: V a absolute volume of filler; Vf a absolute volume of asphalt: W2 - weight of filler: -‘ _\ (”A '1': and. I . :.' :v:u u. '..4 '3:"":‘ .-..‘b-fll . . 2:": ~ Ohinu.- I .QII-c.. . no. I _“b‘ .A to." ‘ .‘F ‘ hul \I‘ ¢ a I.. I u a“ " , 6 -~ W.» _‘x “In.” \ ~§us ‘ i‘q‘ “ s... 4‘. .4 tr .- 0. 26 Gf a specific gravity of filler: Wa = weight of asphalt: Ga - specific gravity of asphalt: F = percent filler in mix by weight of total aggregate (F - l to 100): and A a percent asphalt in mix by weight of total mix (A a 1 to 100), in this study A = 6. Marshall specimens were prepared utilizing two d:i.:fferent methods: a pre-mixed binder having a pre- designated F/A ratio of 0.326 which gave six percent asphalt content by total weight of mix: and the c<:>nventional Marshall test method that produced control specimens with a compatible asphalt content. In both methods, the following materials were used: crushed Limestone coarse aggregate (larger than 3/16 inches); wrahshed gravel fine aggregate (passing 3/16 inches, retained on number 200 sieve): the designated mineral filler: arm: an asphalt content of six percent by total weight of tdie mix. The samples were mixed and compacted at 275°F uSing the standard Marshall compaction procedure. Gietz and Lamb concluded: a) Pre-mixing of filler and asphalt to form a binder that is then mixed with coarser aggregate fractions is believed to result in a higher stability and more uniform density. b) The stiffness of the mix increases with increasing F/A. c) As the mineral filler content increases, the 26: A'- V: wa-veaqe ‘0'. id“ b I‘|A “a ":5 3M lilacs; A, d b Down-“v |;A:-IA 'bv‘uae i run. 'I". On" HI- a. l. ..ifa-_’_e: ‘9!- Due: L1 'I' "I .O :f is") ‘ 3'“ c '3‘!» (4 our-‘ ‘e‘ . .332 4 "9 H‘ o In . ‘Ag . O"‘v.": \u 27 temperature related variation in mixture consistency decreases with the Portland cement filler producing the greatest effect. Similarly, Bolk et al. (310) reported that the type, nature, and concentration of filler materials are very important. They also noted that the Marshall test does not adequately characterize the mechanical behavior of asphalt mixes. The latter was noted because different asphalt mixes showed similar stability and flow but drastically different creep and fatigue characteristics . Several other investigators studied the effects of mix variables upon Marshall stability, flow, and stiffness of asphalt mixes. As noted above, Heithaus and Izatt (H5) reported that Marshall stability can be increased by using large quantities of filler and active filler and by reducing the asphalt content. Metcalf (M10) , however, POinted out that Marshall stability alone cannot adequately measure the resistance capacity of a paving mixture subjected to traffic loading. He analysed the stress Conditions in a Marshall specimen and showed that the bearing capacity of a paving mixture is related to Marshall 8liability and flow. Bearing capacities calculated from these combinations were found to agree with field Performance tests. He also demonstrated the importance of the flow value, especially in the evaluation of in- V... II. (”var-O "d. ‘V . ’51-.-- 1' ..vv—b. 2:1: 5 ‘ . .‘ 'n I nu-oital l "““A .‘ MD". 0 .. ..A Cu ...: ".v.-‘ (7‘ i 28 place properties of mixtures. Again, this implies that some type of modulus (stability and flow) value should be specified and stability cannot be solely used to clearacterize the mix. Hawever, Metcalff did not recommend a strain or flow level at which the values of l><:>th stability and flow can be adequately considered for closesign. Fink and Lettier (F2) studied the effects of the Viscosity of the bituminous binder and asphalt content c>ln. the Marshall stability of dense-graded asphalt concrete mixes. The tests were conducted at temperatures above the softening point of the asphalt and at a high deformation rate. A variety of asphalt types and grades were incorporated into the mixes. When these mixes were czcmmacted and tested at equivalent binder viscosities, nearly identical stabilities were obtained. It was cOncluded that: a) Marshall stability values are strongly influenced by the viscous resistance of the binder which can be altered over a very wide range by either increasing asphalt viscosity or decreasing asphalt content. b) The flowvalue,which isinfluencedalmost entirely by asphalt content, reflects an excess in the asphalt binder content that reduces aggregate friction and interlocking. c) Neither density nor flow-value are influenced by f' () I. .IA":~ ‘ v'hd I u 'r. Var: 04] () I :0 “' vAA ‘ u .- --.e "I “-‘ ‘ n u."~.e: .... A “"t: 29 the consistency or source of the asphat binder if compaction and testing are carried out at an equiviscous temperature above the softening point of the binder. A different direction was taken by Tunnicliff (T3). He showed that the viscosity of filler-asphalt systems and the Marshall stability of paving mixes are functions of the filler characteristics and concentration. He noted that an increase in the filler concentration produces an increase ix: Ibinder viscosity, shearing resistance, and internal stability of the mixtures. He added that the aggregate matrix (arrangement of aggregate particles in the paving mixture) is a function of the filler concentration. To summarize, the stability of asphalt mixes can be altered by changing any one, or a combination of, the variables characterizing the mix. However, The problem addressed in the research here is not to increase the stability but to improve the performance of the mix under the anticipated traffic loading and environmental conditions. In addition, the relationship, if any, between stability and structural properties of the mix should be addressed prior to the selection of the asphalt mix. If no relationship can be found, then the idea of accepting asphalt mixes based upon stability should perhaps be abandoned. L2.3 Hf .ee «can V: v I...‘ All. I “='e:e: I.“ iazete: .0- . I 'Una. ‘~‘I.; n "1“I.h ‘1 "m . 1.. ...-'2 18 '~ 30 2.2.3 Effects of Specimen Variables Lee (L2) examined the effects of specimen thickness upon Marshall stability and flow utilizing four-inch diameter' laboratory' prepared. specimens and four-inch diameter field cores. He noted that the Corps of Engineers thickness correction factors are not adequate for thin specimens. He recommended that both stability and flow values be corrected for all specimens with thicknesses other than the standard 2.5 inches. His correction equations are: st/s - b + at (2.4) Ft/F - 0.35 + O.26(t) (2.5) where: S - stability of a standard 2.5 inch specimen: St - stability of specimen with thickness t: t = thickness of specimen, inches; a,b - regression coefficients: F = flow of a standard 2.5 inch specimen: and Ft 8 flow of specimen with thickness t; In addition, Lee modified Metcalf's (M9) equation which relates stability and flow to the bearing capacity of asphalt mixtures to account for specimen thickness. The modified equation is: B = 3(120 - F)/[l40(F)(t)] (2.6) where: 120, 140 - regression constants: B a corrected bearing capacity (psi): and all ather parameters are as before. Again, the findings above implie that stability alone . 5 .332» ch: :cu'h I. ’0. ”lb . at: it '3 On ‘ “ 'av:-: uo-sau.‘ ' vv 3“ r- ...u v‘ . I . :znn: ...sg‘. - ‘ a CIA-u ‘ 3‘... i 0'. '- “e u: A ‘ Q n1.“ “‘0‘. ’Qq ‘ n u‘ .‘ ‘5' ‘. “ “‘“v 4. 0"...- ”‘Io . ‘ "n “.. ‘IQ'. flu...es 3'?“ c .vh. ‘ 333:9: 31 cannot be used to assess the load-carrying capacity of the asphalt mix. Stability and deformation are required for such an assessement. The effects of aggregate and specimen sizes on the Marshall test results were also investigated by Mamlouk and Wood (M3). Cold mixes were made using emulsified asphalt and large aggregates. The test results showed that the stability of the asphalt mixes increases as the particle size increases. The flow, on the other hand, decreases. No correlations was found between test results of six-inch diameter samples and the standard four-inch diameter ones. Consequently, they recommended continued use of the standard sample size of four- inches. In this regard, it is concluded that test results are generally independent of the specimen and aggregate sizes if the diameter to maximum aggregate size ratio is four or better (W10). Consequaently, Marshall type specimens are adequate if and only if the maximum aggregate size is limited to one inch or less. Pignataro (P7) studied the effects of test temperature on the stability of asphalt concrete mixtures utilizing the Marshall test method. The mixtures were prepared using the Asphalt Institute specifications for mix number IV b. This produced the following percentages by total weight of blend: coarse aggregate, 57: fine aggregate, 37: and mineral filler, 6. Three penetration graded asphalts were used (52, I,» ‘ ..A‘I F ‘ L‘s-nun O... A" ...qu I I ~ a:-nn 1 nuhung' o ....v I ‘I‘ h ()_ (I. 5 II (n r) 32 76, and 108). Marshall specimens were compacted by a mechanical compactor and tested in a specially designed, water bath that maintained the test temperature at (30, 40, so, 60, 70 or 80 0C). An optimum asphalt content of about 6 percent was selected using the Army Corps of Engineers criterion for 100 psi tire pressure. The reason of this selection was to limit the variables to test temperature and asphalt penetration. Pignataro concluded: a) Stability increases as the test temperature decreases. b) Stability increases as the penetration decreases. c) The optimum asphalt content is unaffected by the asphalt penetration or the test temperature. It should be noted that the first and third findings above are more or less similar. That is, the lower the temperature, the lower the penetration of the same asphalt binder and the higher the stability. Thus, the effects of the penetration of the asphalt binder can also be expressed in term of the test temperature. Gilmore et al. (62) investigated the effects of moisture. and ‘various additives on the ‘tensile strength, resilient. modulus, and fatigue life of asphalt. mixtures using indirect tension tests. The tests were conducted at constant temperature of 55°F using dry and moisture-conditioned Marshall samples that were subjected to Av :29 ... "a" 3'? .‘o. l the :a. 3”“:- i'. ..‘t hwgnn a bolbcloi a an: AA. 'n. Vi. :-- a and " 'E. . U ‘50. ‘ .A” Q A1 fuvov. ‘.-‘a' II‘... a. . ‘::.\‘ . 6..“— (1 (“D LL 33 one or more cycles of freezing followed by soaking in warm water. Six different chemical additives were added to the basic mix disigns: a) two inorganic solids (Type II Portland cement and dry hydrated lime); b) two commercial organic liquids (Pave Bond Special and Pave Bond LP): (n one commercial liquid metalloamine complex bonding additive: and d) one experimental organic liquid additive (EA-1). The inorganic solids were added to the aggregate portion of the mix as a percent by weight of the aggregate whereas the liquid materials were added to the mix as a percent by weight of the asphalt cement. The test results showed that: a) The wet strength of treated samples are 200 to 250 percent higher than the wet stength of untreated samples. b) A combination of additive types (inorganic and organic) produces significantly higher wet tensile strength. c) The resilient moduli of wet-treated samples are 250 to 500 percent higher than the moduli of the untreated samples. d) The fatigue lives of wet-treated samples are higher than the untreated ones. To summarize, it was found that: a) the standard four-inch Marshall type sample is adequate to characterize the behavior of asphalt a\ 1 'A . " >..e” ::. “A: o y'- . a‘ ‘ 1‘ t: F :‘Vw' U ‘. 1‘..l. I)". run: cze: 34 mixes: b) a change in one or more of the test or specimen variables affect the stability and flow values of the test: and c) the presence of moisture in asphalt mixes decreases the values of their structural properties (e.g. stability, durability). 2.2.4 Comparison of Marshall Test Results With Others .As noted above, Marshall tests and the Marshall mix design method are mainly used to proportion the different constituent in the asphalt mix. The final mix design is. solely selected based on a pre-selected criterion that do not possess any relationship to the structural properties of the compacted mix. To obtain the structural properties, other tests (e.g., cyclic load triaxial or indirect tensile) have to be employed. These tests require a large investment that is not available to most pavement engineers: complex: time consuming; and require new training of personnel. Since the Marshall test is simple, easy' to perform: and. widely' used, researchers compared the results from the latter tests to those from Marshall, Their findings and conclusions are discussed below. Goetz (G3) and Mclaughlin and Goetz (M8) compared Marshall and triaxial test results using asphalt mixes '. A a ‘uvae I‘ 35 compacted to nearly equal densities. The mixes were made using gravel and crushed limestone (three different gradations) and three 'penetration graded asphalts (54, 185, and 266). The results showed that: a) The optimum asphalt content at maximum stability is the same from both tests provided that a confining pressure of 10 psi is applied to the triaxial samples. b) As the asphalt content increases, the angle of internal friction decreases. c) The -cohesion of the mix increases as the asphalt content increases to the optimum value. Further increase in the asphalt content results in a decrease in the cohesion of the mix. d) Both triaxial and Marshall stabilities decrease as the asphalt penetration increases, although the angle of internal friction is independent of the asphalt penetration. e) For both tests, increasing aggregate angularity increases stability. f) The design asphalt content based on the Army Corps of Engineers criterion is the same for both tests. Campen et al. (Cl) at Omaha Testing laboratories (OTL) compared results obtained from the Marshall test to those from the OTL test. They also compared the Army fl .::: < in“; a ‘ . Junie ' | . . one. ”4‘ eon-veld‘ Corps 36 of Engineers criterion for an acceptable design asphalt content to that obtained by the OTL Method. They concluded that: a) b) C) d) In general, data from both test methods reveal the relative stability of asphalt concrete mixtures. For all asphalt contents (below or above the optimum), the Mashall test method produced higher densities and lower percent air voids than the OTL method. This implies that the compaction effort of the Marshall test is higher than that of the OTL method. For both methods, higher percent asphalt contents result in a higher flow value. However, the flow value varies considerably between mixtures and is a function of the maximum size, angularity and surface texture of the aggregate particles. The design asphalt contents determined using the Army Corps of Engineers criterion are significantly less than those obtained by the OTL method. These low asphalt contents may produce lean mixtures which may adversely affect durability of the mix. Bonnaure et al. (811 through 8 13) developed a new method to predict the stiffness and fatigue life of asphalt paving mixtures where the stiffness of an asphalt mix is related to the test temperature, time of loading, hjvfl‘fies no.“' .5 zany “ ..uu. O. ... A N a. \. I $035 .1 a\. (1‘ e In“ ‘V.~J~6 s ‘V‘ ‘v, ”i ‘Y ‘ ' h afl 37 hardness and temperature of the bitumen binder, percent of aggregate by volume, and the percent air voids in the mix. In summary, it appears that differences in opinion exist in the literature concerning: a) the effects of the sample and mix variables upon its stability, flow, density, and stiffness: b) the usefulness of the results obtained from Marshall and other tests to assess the structural properties of the asphalt mixes: and c) the validity of the different criteria to select the design asphalt content. Table 2.1 summarizes the effects of several factors on stability and flow of asphalt mixes. In the research program here, the Marshall test and mix design method was used. For each combination of material type in the mix, the asphalt contents that resulted in three percent air voids were designated as the design asphalt content. Marshall type test specimens were then made using the design asphalt content and compacted at three, five, and sevent percent air voids by varying the compaction effort. The compacted specimens were then tested to extract the structural properties, strength, fatigue life, and Marshall stability and flow. The data obtained from each type of test were then Correlated to the specimen and test variables. Comparison T. T \..2 5 he ...... .2 ... Te 38 13532.1. mammmmmmm mmnmmmmm mm ‘IYEEG' m MIN mammm NJER 'EHI‘ m CNSIREIIIIY CNFIm MU TRIAXIAL mm - mm - mm W m - 'IDSIPGIC MY m we - mes HIS I'm MY - [NEIHMDED - mm m mes: Cl. mm mm m - m HUGH} [-5 mm. mm m m - 1'5 13 W m m - m . I2 mm m W W P7 CHEN]? G1 mar: m m - mm mm 1mm m - W m mums: - MID sun: m m mm W m m m m *Chdn'lan'rglanratnzy ”832.1 HE EL‘EE it" (a! mm]...- 39 m 'IYEECF Fm Q-PNIZIN EFFECI‘CFCI-NEEIINFPCICR um ‘IESI‘ FPCJIR CNSIPBIIIIY CNFIEN G3 ML 253mm. 1mm m - M]. AND MIG-NIL mm m m - MCINIENI' m m m I3 mam ME m m - PhD mm mm mews om mm - 3mm 2636-37 a g; ..3 a. . . .....- .c«...“ .I'A(. ‘3} m (t I'- le‘e I b‘h. 4". 40 between Marshall test results and others were then made. 3,; BBfiILIEEI QEABAQIEBJ§IIC§ OF ASPHALT MIXES The field of flexible pavement design has evolved from empirical rule-of-thumb procedures based on past experiences ‘to rational methods based upon soil classification systems and later on road test data. Beginning in the late 19505 wheel loads imposed by heavy trucks and aircraft necessitated a more rational approach. At the same time, the growth of truck traffic results in severe breakup of some highways. To solve the problem, pavement engineers evaluated the basic fundamentals involved in the. design. of’ pavement structures. Analytical (mechanistic) design methods started to emerge and provided a better understanding of pavement response under traffic loading. This development gave rise to the problem of material characterization under simulated field conditions. Consequently, new tests such as the resilient modulus and permanent deformation-creep were developed (K7b) . These tests enabled pavement engineers to obtain material properties necessary for mechanistic design models. In order to understand these properties, an extensive knowledge of the basic stress- strain responses of the material must be obtained. The basic stress-strain curve of a material Subjected to cyclic load“ is shown in figure 2.2. As STRESS 41 Load l l l ' Unload l l l I l l I I . . . . STRAIN plastic Viscoelastic elastic strain strain strain FIGURE 2.2 STRESS-STRAIN CURVE OF ASPHALT MIXES. ”.043 uh. J va‘Ifl“ .::UV:e o I. \ 3.3.3 393378! If () K). I at) 42 noted in the figure and section 2.1.1, the total strain response can be divided into three parts: a) elastic strain which is stress dependent and immediately recoverable upon unloading; b) viscoelastic strain which is time and stress dependent and completely recoverable: and c) plastic strain which is stress-dependent. Each of these parts can be analysed seperately to derive the respective structural properties of the material. The following definitions of properties are relevant. a) Resilient modulus is the ratio of the applied axial stress to the elastic part of the axial strain. b) Resilient Poisson's ratio is the ratio of the radial strain (not shown in the figure) to the axial elastic strain. c) Viscoelastic modulus is the ratio of the applied axial stress to the viscoelastic part of the axial strain. d) Total modulus is the ratio of the applied axial stress to the total axial strain. e) Elasto-viscoelastic modulus is the ratio of the applied axial stress to the sum of the axial elastic and viscoelastic strains. f) Stiffness is a general term describes any one of the above modulus. g) Fatigue life is the time or the number of load repetitions a material can withstand prior to the g\ “'1 \ l N s..“‘ i..‘.‘ \. a. “I SV- 25:» ‘u AA. A ~ ....Sc‘ 0 I‘:v~ ,. h.“ 43 initiation of a microcrack. It should be noted that the cyclic plastic strain is ultimately responsible for fatigue damage and that elastic and viscoelastic strain possess no relationship to fatigue life. h) Permanent deformation is the sum (cumulative) plastic axial deformation over the number of load repetitions. i) Creep is the total axial strain under a constant applied stress. Where the above terms are generally accepted, one can find several terms describing the modulus of a material (e.g., stiffness modulus, ‘mix modulus, complex modulus, dynamic modulus, elastic modulus, elastic stiffness, flexural stiffness). To add to this confusion, in some of the literature terms are not defined to mean any specific modulus as defined above . Consequently, in the sections below, efforts have been made, when possible, to clarify such terms. In addition, many tests have been developed for measuring the characteristics of asphalt mixes. Some are arbitrary in the sense that their usefulness lies in the correlation of their results with field performance. Nevertheless, many of the test procedures have been standardized. Recently, a great deal of effort has been expended in developing a set of test methods to Ah;ya Veil. . :6 3i .k’Av Haul SIZE )1 I). 44 characterize material' response to load. The majority of these tests, however, have not been standardized. As a result, descrepancies in test conditions and test results can be found. This, however, should not deter the engineer from realizing the wealth of information that may be obtained from these tests. The stiffness of asphalt can be characterized through measurement of a total or resilient modulus using one of the following tests: a) unconfined cyclic load: b) confined triaxial cyclic load: c) cyclic load flexural: or c) indirect tensile cyclic load. Because these tests require very expensive equipment, efforts have been made to correlate the stiffness of asphalt mixes to the mix, sample, and test variables thereby eliminating the need for such test. For example: some investigators correlated the stiffness to Marshal stability and flow. The following sections summarize the findings and conclusions found in the literature that are pertinent to this study. 2.3.1 Asphalt Binder and Mix Stiffness Van der Poel (811) showed that the stiffness modulus of asphalt mixes depends on the stiffness I ‘ . .A‘“ ' ,uuuoh n‘ .&D vs "" Lie a w. 'Ia 'bgn—u ..R‘. not“ -‘:- ....” (I: I... “ vvuv .. EA. n w. u. ~O‘ "'ae. I’13. 'O“b 0‘. . ..e v: "'5 “a “"5 \n. "‘ . . ‘ ‘.I- . F ‘ vVuy. e ~ a~~ a 0.. SOJ‘ b.. ‘6‘. V5“ ‘- .: u. 2“»: 45 modulus of the asphalt binder and the volume concentration of the aggregate in the mix. The latter is defined as the ratio of the volume filled by aggregates to the volume filled by aggregates and asphalt. Van der Poel's work was extended by Heukelom and Klomp (812) who derived a statistical equation relating mixture stiffness to the asphalt stiffness and the volume concentration of aggregates. They noted that the method is not suitable for mixes with percent air voids higher than three. This shortcoming was later eliminated by Van Draat and Sommer (Y4) by introducing a correction to the value of the volume concentration of the aggregate. More complicated methods of predicting mix stiffness for a wide range of mixes (open mixes, wearing course asphalt concretes) were later developed (B11). FinalLy, Bonnaure et al. (B11) developed nomographs for the higher range of stiffness values. Other researchers correlated the resilient modulus to the stiffness of the asphalt mix using a flexural type test. Yoder (Y2 and Y3) reported that the values of the dynamic modulus determined- from flexural testing are half of those obtained from triaxial tests. However, if the hypothetical flexural stiffness at zero stress is employed, then compatible values from both tests can be :Eound. Deacon and Monismith (DZ), on the other hand, found a good agreement between the flexural stiffness and :e :i '0 .i nAIIRc 'U-bvu A 0'. Ho 2X. 15:2; .0." ‘ “ Uh... me; :'.x ::.'.:e: 0‘. Ir ..e .. e i. I p “e tn ‘ 1 u 6‘. . 4.9.: V- we! (7‘ f) 46 the mix stiffness as determined by Van Der Poel's method. It should be noted however that the stiffness of a composite material such as an asphalt mix is a function of the properties of the constituent materials in the mix. For example, the stiffness of asphalt mixes made using hard aggregate is Imnfli different than the stiiffness of mixes made using softem' aggregates. Consequently, any statistical derivation relating the mix stiffness to the asphalt stiffness and volume concentration of aggregates without due consideration of the properties of the aggregates is limited. In addition, the load intensity and frequency should be considered. Due to these facts, other researchers have directed their efforts to relate the stiffness of asphalt mixes to the mix, sample, and test variables. 2.3.2 Mix and Sample variables Efforts have also been made to correlate the resilient or dynamic modulus of asphalt mixes to the mix and sample variables. Shook and Kallas ($15) at the Asphalt Institute (AI) used data from several different tests to develop such correlations. These tests include: a) Marshall stability and flow at 40, 70, 100, and 140°F: b) Hveem tests at the same temperatures: c) direct and indirect tensile tests: and O 5...‘ 1*" d) The 47 dynamic modulus tests on four-inch diameter and eight-inch high cylindrical specimens. test results were statistically analysed to develop the correlation equations shown below (also known a) 13) Log E Log E Log E Log E Where: as the AI equations) where: equations 2.7 and 2.8 relates the dynamic modulus to the mix and test variables: equation 2.9 relates the dynamic modulus to Marshall stability and flow: and equation 2.10 relates the dynamic modulus to the ultimate tensile strength without a temperature correction factor. - 1.54536 + 0.020108(X1) - 0.031880§(X2)1 4 + 0.068142(X3) - 0.00127003(X4) ' (x5) ° (2.7) R2 = 0.968, and S.E. = 0.0888904 = 3.12197 + 0.0238132(x1)0-90.0345875(x2) - 9.02594((X4) ° /(X6) ' (2.8) R2 8 0.971, and S.E. = 0.0849186 = -0.124262 + l.25469(k) - 0.0616215(V) (2.9) R2 = 0.900, and S.E. = 0.151416 = 0.0983861 + 0.00351866(U) - 0.052137(V) (2.10) R2 = 0.744, and S.E. = 0.284357 Log 8 logarithm to base 1 ; E a dynamic modulus, 10 psi (4 Hz loading frequency): x1 8 percent passing #200 sieve; F—n‘ U 94 9.44 U (I) II. ’II '6 ‘2'. -..! O 93'; ‘Q‘ "2‘; ... ‘h ‘0 pg. V ‘Q ‘- ...e ,1 0 {i cl . ..‘Gh ‘e 48 X2 = percent air voids in mix: 6 X3 = asphalt viscocity at 70 F, 10 poises: X4 = percent asphalt by total weight of mix: X5 = test temperature, F: X6 = the Logarithmic value of the viscosity (in poises) of the asphalt at the test temperature: K a the logarithmic value of Marshall stability (lbs) divided by 100 times the Marshall flow (0.01 in.): V - percent air voids for the modulus specimen minus percent air voids for the Marshall test specimen: U s ultimate tensile strength in psi with a load rate of 2 in/min: standard error of the estimate: and R = coefficient of multiple correlation. (a m to II It should be noted that the values of R2 reported above may be artificially high because they represent the variance of the logarithmic values of the modulus. The variance could be much greater for the actual values of the modulus. Nevertheless, Shook and Kalls noted that: a) for a constant asphalt content, the dynamic modulus decreases as the percent air voids increases: and b) the dynamic modulus of the mix increases as the asphalt viscosity increases, or penetration decreases. Later, Witczak (W7) utilized an expanded data base to modify the AI equations and to include the test frequency as one of the variables. Log E = 5.553833 + 0.028829(P /f ) - 0.03476(V) + 0.070377(n) + 0.000689(T )(P ) - 0.00189(T )(Pac /£ ) + 0.9317§9(1/£ ) (2.11) Where: Log E a Dynamic modulus, psi: P200 - Percent aggregate passing sieve #200; 49 f - Loading frequency, Hz: V a percent air voids: o n a Asphalt viscosity at 70 F, megapoises: Pac = percent asphaltoby weight of total mix: and T = Temperature in F. Miller et al. (M11) compared nearly 1200 laboratory measured dynamic modulus values with those predicted using the AI equation. They observed that for all mixes made using crushed aggregate, the measured and predicted moduli showed a good agreement. However, very poor agreement was noted for mixes made using slag and sand. Consequently, they modified the AI equation to obtain a higher correlation for all mixes. The modified equation has the following form: Log E = c1 + 02(9ac - popt + 4.0) (2.12) Where: 5 E = dynamic modulus (10 ), (psi): c1 = 0.553833 + 0.028829(P2 /f) - 0.03476(V) + 0.070377n(10 ,70) + ?8.931757/f); c2 = 0.000005Texp(1.3 + 0.49825Log f) - (0.00189T(exp(l.3 + 0.49825Log f)/f): P200 8 percent passing the #200 sieve: f a loading frequency (Hz): V a volume of voids (percent): n(10,70) a viscosity of the asphalt cement at 70°F: T a temperature of pavement: Pac = asphalt content in percent by total weight: and Popt = optimum asphalt content. These findings by Miller support the contention that the modulus of the asphalt mix depends upon the constituent material in the mix. The original AI equations were obtained using crushed and natural gravel. Consequently, 50 when similar aggregates were used, calculated and measured moduli showed a relatively good agreement. However, when slag (different aggregate hardness) is used, the predicted and observed values did not show good agreement and therefore they had to modify the equations. In any event, when the AI equations failed to predict the modulus to within reasonable limits, researchers developed alternative equations. For example, Terrel et al. correlated the resilient modulus to the asphalt content, test temperature, and percent air voids in the mix. Yeagger and Wood (Y4) correlated the dynamic modulus to the slope of the lines representing the logarithmic values of the kinematic viscosity against the inverse values of the temperature, loading rate, and test temperature. Their correlations, however, were limited to a specific aggregate type, gradation, asphalt type, and asphalt content. From the scenario above, one can conclude that: a) the properties of the constituent materials in the asphalt mix should be evaluated first and then used to estimate the properties of the mix: or b) the effects of the specimen and test variables on the behavior of the constituent materials in the mix should be evaluated first and then extrapolated to those of the mix. In this regard, Hicks & Monismith (H6) evaluated factors influencing the resilient response of granular materials . They 51 concluded that: a) For a given stress level, the modulus increases with increasing density, increasing particle angularity or surface roughness, decreasing amounts of fines, and decreasing the degree of saturation. b) Poisson's ratio is slightly affected by density, decreasing with increasing percent fine content and the degree of saturation. c) For a granular base layer, a small change in the values of the modulus and Poisson's ratio can cause a signficant change in the response of the pavement structure: d) A reasonable estimate of the resilient characteristics of granular materials can be made after the application of 50 to 100 load repititions. e) For untreated granular materials, the resilient properties are significantly affected by the stress level. In all cases the modulus increased considerably with increasing confining pressure, and slightly with increasing axial stress. Further, there have been extensive efforts to evaluate the effects of aggregate angularity and gradation and the percent fine content on the resilient characteristics of aggregates and asphalt mixes. In - general, the results showed that the effect of aggregate 52 gradation is insignificant (Y3, 512, Y3, W10) introduced. a correlation equation between the strength of granular materials and the particle angularity and the percent fine content. He concluded that the higher the percent fine content, the lower the strength: and the greater the particle angularity the higher the strength. Similar findings were also reported by Hicks and Monismith (H6) and Barksdale and Hicks (B7). Unfortunately, no attempt was made to integrate these findings into a more precise equation to predict the modulus of asphalt mix given the moduli of the constituent materials. Although, from the engineering viewpoint, the approach is a logic one, it is not the objective of this research to explore such an equation due to limitaion on both time and funding. Nevertheless, the effects of various environmental conditions on the resilient characteristics of asphalt mixes were evaluated by Schmidt (84 through S7). They used hot asphalt-treated mixes (ATM) containing lime (L-ATM) or cement (C-ATM) and. emulsion-treated. mixes (ETM) containing lime (L-ETM) or cement (C-ETM). He noted that: a) ETM are less susceptible to temperature change than hot ATM made with the same asphalts and aggregates: b) C-ETM have lower temperature susceptibilities than ETM and greatly lower than ATM: c) dry,hot C-ATM and L-ATM have almost thesame value 53 of resilient modulus: d) the susceptibility to temperature change ofthe dry and wet ATM and dry and wet ETM is the same with ETM showing less temperature susceptibility than ATM: e) freeze-thaw cycles significantly decrease the resilient modulus of water-saturated ATM and ETM; and f) cement and lime ATM retard the effects of freeze-thaw cycles on the resilient modulus. Similarly, Yeagger' and. ‘Wood (Y1) reported. that moisture exposure reduces the resilient modulus, and that the reduction is probably a function of aggregate and asphalt types and asphalt content. To this end, it is evident from the above that treated mixes are less susceptible to environmental changes (temperature and freeze—thaw cycles) than untreated mixes. This implies that the service life of asphalt mixes may be improved by addition of modifiers. The trade-off, however, is with the extra cost involved. Baum (B8) measured the dynamic modulus of 23 asphalt pavement sections utilizing static and repeated load plate tests. He concluded that, in general, the dynamic and static moduli increase with time (age of pavement): and that the static plate load test data were not consistent due to the viscoelastic properties of the asphalt surface. The last finding is expected for tWO reasons 3 (T :‘In IeMV "I."‘| “05.4 n ’ 3‘ In " I; n 4;“ ‘9‘ee: "53;”. ‘ .V“‘ |.-‘. w- “. .:“|: V'Ifl““ v.‘~E Vb. . . we 3: 54 a) Under static load pavement deflection is dependent upon the time of loading: the longer the time of loading, the higher the deflection. b) At any time, pavement deflection under static loading is a manifestation of three mechanisms: elastic, viscoelastic, and viscoplastic. The last two components are time dependent. Since the load in a static plate load test is constant until the deformation rate drops to a prespecified value, and since this rate varies from one pavement section to another, pavement deflections are collected at different times. Consequently, inconsistent results (modulus values) should be expected. Finally, Francken and Verstraeten (F4) concluded that, for different temperature and loading frequency, the moduli of asphalt mixes can be correlated to the volumetric composition of the mix and the characteristics of the bitumen. 2.3.3 Test variables The effects of test variables were investigated by several researchers. These variables include applied stress, test temperature, load frequency, relaxation period, number of load repetitions, and confining pressure. Kim et al. (K11) and Kennedy (K8 and K9) reported that the resilient modulus decreases as the 55 number of load applications increases and it is independent of the magnitude of the applied stress. Brown and Cooper (814) stated that, for a stiff asphalt binder and relatively moderate stress levels, the resilient modulus is independent of stress level. Yeagger and Wood (Y1) found that a constant value of the resilient modulus can be obtained for a stress levels up to 70 psi and test temperatures between 40 and 100°F. They recommended that a single stress level of 50 psi be employed. The value of the resilient modulus of granular materials and asphalt mixes however was found to increase with increasing confining pressure (A2, BB, B15, B16, F1, F4, G4, H12, H13, K1, K5, M20, P3, $2, $11, and Y4). Kalcheff (K1) showed that the application of 5 psi confining pressure increases the resilient modulus by a factor of 2.5 over that obtained from unconfined tests. Van Quintous (V5) reported that for a 10 psi confining pressure, the value of the factor is about 9. The effects of load duration and frequency upon the resilient response of asphalt mixes were also evaluated by several investigators. Generally, it has been found that longer load durations and lower frequencies result in lower values of the resilient modulus (813, B14, Y1, and ‘Y4). .Also, since the response of viscoelastic materials, such as asphalt mixes, to load is temperature dependent, higher test temperatures result in 56 higher deflections and lower values of the modulus (Y1 through Y4, V5, Bll through B14, 812, and 57). To summarize, the resilient characteristics of asphalt mixes are dependent upon the test variables and reasonably consistent results are reported in the literature. The concern is to conduct laboratory tests such that the test variables and their variations are equal to those experienced. in the field. Variation between laboratory and field conditions result ix: different material characteristics that, later, have to be modified to field conditions. 2.3.4 Test Type Other investigators developed simple tests and test procedure to measure the resilient modulus. Schmidt ($10) developed a new apparatus to conduct cyclic load indirect tensile test using Marshall type specimens. He also derived analytical equations for the analysis of the test data assuming elastic material and plane-stress conditions. Kennedy ( K8 and K9) and Cowher and Kennedy (C8) used the indirect tensile test to study the resilient modulus of asphalt mixes. They reported that the cyclic load indirect tensile tests yielded similar modulus values to those obtained from cyclic load triaxial and flexural tests. 57 Von Quintus et al. (V5) compared stiffness moduli of asphalt: mixes obtained from. indirect ‘tensile, ‘unconfined compression, and confined compression tests. Cored specimens recovered from 31 flexible pavement sections located in different states were used in this analysis. These specimens varied from dense-graded hot mix asphalt with three to eight percent air voids to open-graded asphalt base course with fifteen to twenty percent air voids. The aggregate types were basalt, granite, limestone, chert, limerock, sand, and shell. Asphalt types ranged from an AC-S to an AC-40 with asphalt contents from 4 to 8%. The test temperature varied from 10 to 100°F. The loading frequency was 1 Hz. with a loading time of 0.15 second. and a relaxation period of 0.85 seconds. They observed that: a) For all tests at low temperatures, the dynamic moduli were very consistent but varied considerably at the higher temperatures. b) For all temperatures higher than 90°F, the confined compression tests yielded higher dynamic moduli than the unconfined compression tests. However, the moduli from the indirect tensile tests were very similar to those from the confined compression tests c) At low temperatures, the calculated modulus values using Witczak regression equation were lower than those measured from the unconfined compression tests. 58 It should be noted that, for the indirect tensile test, it is very common to obtain a value of Poisson's ratio higher than the limiting value of 0.5 (K8 and K9). Therefore, to calculate the value of the resilient modulus, it is recommended that a value of Poisson's ratio around 0.35 be assumed. The assumption of Poisson's ratio practically determine the value of the resilient modulus. This implies that, for the same specimen, the value of the resilient modulus could differ by as much as fifty percent for assumed values of Poisson's ratio of 0.2 to 0.4 (a typical range). Consequently, any reported agreement between the values of the resilient modulus obtained from the indirect tensile and other tests should be reviewed cautiously. Kallas (K3) compared the dynamic modulus values obtained from. various testing' ‘modes (compression, tension- compression, and tension). He found that, for several loading frequencies and test temperatures, similar values were obtained. However, differences were found in the phase lag (time difference between peak load and peak deformation). The values of the phase lag obtained from tension and tension-compression tests were greater than those from compression tests. Since the resilient modulus is calculated as the ratio of the applied cyclic stress to the instanteneous recoverable strain, the finding above (concerning time lag) implies that unless the 59 time lag is measured from the different tests, correlation between resilient modulus values is not valid. Alternative methods for determining the resilient modulus of asphalt mixes using simple tests have also been developed. Nijboer (N2) related the Marshall stability-flow quotient to the resilient modulus. Shook and Kallas ($15) examined the same relationship and developed a correction factor to account for differences in the percent air voids. Brown and Cooper (B14) at the Transport and Road Research Laboratory (TRRL) in the United Kingdom (UK) used laboratory and core triaxial samples to study the stress- strain characteristics of bituminous materials. The samples were tested in tension and compression. They observed that: a) The method of compaction has a significant influence on resistance to permanent deformation. b) For the same stress levels, the repeated load test with a square wave form results in higher permanent deformation than in the creep test. c) Shear strains and strain rates exhibit similar behavior for both repeated load extension and compression tests. d) Volumetric strain depends only on the mean normal stress while shear strain and strain rates depend on the deviator and mean normal stresses. 60 e) For moderate values of stress level, the resilient modulus is independent of the stress level (linear behavior). Kallas (K3) measured the dynamic modulus (also referred to as the complex modulus) of asphalt in tension, and ix: tension compression. These values were compared to the dynamic modulus in compression. It was concluded that: a) For high temperatures (70 to 100 0F and low frequency of loading (1 Hz), there were large differences between the modulus in tension or tension compression and the modulus in compression. These differences were smaller for low temperatures (40 to 70°F) and loading frequencies from 1 to 16 Hz. b) The viscoelastic response of asphalt concrete is high for dynamic tension loading, intermediate for dynamic tension compression loading, and low for dynamic compression loading. Hofstra and Valkering (H11) used a laboratory test track (LTT) to study the modulus of asphalt layers at different temperatures. The stress and strain, due to a wheel load moving at a constant speed, were measured at different depths. The data were used to calculate the modulus of the asphalt layer which was then compared to that predicted by the theory of elasticity. They noted that: a) The shapes of the measured stress and strain signals 61 agree with those predicted by the theory of elasticity. b) The condition at the interface between the asphalt layer and the sand subgrade is between slip and complete friction. Hills and Heukelom (H8) studied the characteristics of the stress-strain curve of asphalt mixes loaded in tension and compression at a constant deformation rate. They observed that: a) The characteristics of the stress-strain curves can be described by using two complimentary parameters, the stiffness modulus and the strain ratio. b) The initial value of the strain ratio of asphalt mixes can be determined either directly or indirectly by combining the results of tension and compression tests. Bonnaure et al. (B11) studied the effects of several factors upon the elastic modulus of asphalt mixes utilizing a two-point bending apparatus for testing trapezoidal specimens. Some of their test specimens were fabricated in the laboratory while others were obtained from the field. They concluded that: a) Test temperature, time of loading,asphalt content, percent air voids, hardness and temperature susceptiblity of the bitumen binder, and volume 62 concentration of the aggregate significantly affect the test results. b) Accurate estimiates of the stiffness modulus and phase angle of the mix can be obtained using the above-noted variables with the aid of nomographs or a computer. c) The simplest way to estimate the stifness modulus is by using the Van Der Poel nomograph. Kennedy (K8, K9) found no relationship between the resilient and static moduli. They noted however that the resilient moduli were generally larger than the static moduli. Ratios between the resilient modulus and the mean total modulus of elasticity were found to range from 0.9 to 10.7. Further, for limestone mixes the ratio was found to be approximately twice that for gravel mixes. Goetz (G3) compared the results obtained from triaxial tests to those from Marshall tests. He concluded that, for a research purpose, the triaxial test method appears to be superior to Marshall test: and the Marshall test method is adequate for mix design. Similar findings were also reported by McLaughlin and Goetz (M8). Mamlouk et al. (M4) studied the distribution of internal stresses and the resulting deformations of asphalt mixes using the results from unconfined compression tests and a nonlinear plane-stress finite element computer program. They found that measured deformations agree 63 with those predicted by the finite element model. However, the stress-strain relations obtained from an unconfined compression test cannot account for the influence of hydrostatic pressure on the shear strength of asphalt concrete mix. In summary, several laboratory tests have been developed to estimate the resilient response of asphalt mixes. Each of these tests possesses certain advantages and disadvantages. Some are very simple while others are very complex. A problem that is shared between all laboratory test is how to simulate the expected field conditions. Nevertheless, the effects of the different test and specimen variables on the resilient modulus were evaluated. It was found that the required tests are expensive, time consuming, and require new training of personnel. Thus, correlations to ‘the results from simpler tests were developed. These correlations were found relatively accurate for certain materials and were modified for others. No attempt was made to correlate the characteristics of the constituent materials in an asphalt mix to those of the mix. 2.3.6 Resilient Poisson's Ratio The resilient Poisson's ratio for isotropic linear elastic material under uniaxial stress is defined as the ratio of recoverable radial strain to the recoverable 64 axial strain. This definition applies only for zero or constant confining pressure. For variable confining pressure, the definition is more complex. The range of Poisson's ratio is theoretically between -1.0 and 0.5. Although values higher than 0.5 were measured (K8 and K9). The difference can be attributed to several factors: a) Asphalt mixes are not perfectly elastic material. b) Laboratory test conditions do not duplicate those dictated by the theory of elasticity. c) The test specimen experiences volume change during shear which is not permissible in the theory of . elasticity. In general, because of the problems associated with laboratory measurements of Poisson's ratio and since pavement response is relatively insensitive to variations in this parameter, estimated values of Poisson's ratio are used by pavement engineers (Y3) . A typical range of Poisson's ratio for asphalt concrete mixes is between 0.2 to 0.4. The reader is reminded again that assuming a value of Poisson's ratio to calculate the resilient modulus for the indirect tensile test may result in a fifty percent error. Nevertheless, researchers have evaluated the effects of mix, sample, and test variables on the value of Poisson's ratio. Their findings are summarized below. a) Higher test temperature yield higher values of Poisson's ratio (Y3). 65 b) Poisson's ratio is independent of asphalt content and aggregate gradation (Y3). c) Higher particle angularity yield higher values of Poisson's ratio (K8, K9, H6). d) Increasing number of load applications yields higher values of Poisson's ratio (A1). The finding in item d above impacts the calculation of the resilient modulus from the indirect tensile test. Since Poisson's ratio is not constant throughout the test then what value shall be assumed for what number of load applications. Given the uncertainty of the value of Poisson's ratio from the indirect tensile test, it fellows that the validity of the correlation to another test is very much questionable. To this end, the findings in the literature concerning the resilient characteristics of asphalt mixes are presented. It should be noted that there are an ovewhelmig number of available references in this field. Only few of these were summarized and presented. 2eA_ELA§IIQ_§EABAQIEBI§IIQ§ In general, the plastic characteristics of any material can be divided into two categories: permanent deformation and creep. The basic difference is that the former is the cumulative plastic deformation under cyclic load (e.g., a moving wheel load) while the latter is a measure of the OAOa bib 0 "-‘a' uni». a-IL :‘ :bcaln . Q Khan is». a \ '- bue S 3§ccA ‘.~‘c' R“ . by 1“. ‘J . I an... 66 total deformation (elastic, viscoelastic, anxi plastic) under a constant static load (e.g., a parked vehicle). Theoretically, permanent deformation of a: comacted asphalt mix is a manifestation of two different mechanisms: material densification that results in a volume change: and repetitive shear deformation that results in a plastic flow with no volume change (L2b). The portion of deformation due to densification can be minimized by proper compaction specifications (B1, 82, B3, L2b). To control or minimize plastic flow in a pavement section, the applied shear stress should be minimized by proper design. In practice, the seperation of the two components of permanent deformation is not possible. Therefore, the term permanent deformation refers to the sum of both deformations. Permanent deformation represents a basic concern in the structural design of pavement system. It causes two different distress modes in the pavement: ruts and fatigue cracking. Ruts in flexible pavements are simply a surface distortion that can be found in the wheel paths. This surface distortion can be caused by any one layer or a combination of layers in the pavement system. Water tends to accumulate in the rutted area of the pavement causing a safety' problem (hydroplaning). Fatigue cracking (also known as alligator cracking) is the result of cyclic plastic strain induced by traffic loading. 67 These cracks cause slow disintegration of the asphalt course which shortens the pavement life. Concentrated efforts to control both ruts and fatigue cracking resulted in the development of two pavement design methods that are based upon limiting permanent deformations: a) The empirical method based on correlations of excessive deformations to preselected failure conditions of the pavement: and b) The quasi-elastic or viscoelastic method that used to predict the cumulative permanent deformations in pavement systems. The second method is preferred because it can be used in more advanced theoretical and rational pavement design methods. It should be noted, however, that neither method is perfected to the point where permanent deformations can be accurately predicted. In the following paragraphs, the effects of several factors upon the plastic characteristics of asphalt mixes are summarized. It should be noted that the effects of the factors on permanent deformation and/or creep, are more or less similar. Therefore, only the effects on permanent deformation are addressed. 68 2.4.1 Effects of Test Variables Monismith et al. (M13 to M16, M18) found that, for asphalt mixes, the functional relationship between the permanent strain and the number of load cycles (in the logarithmic space) can be described by a third-degree polynomial. Allen and Deen (A4) confirmed this finding and expanded the relationship to include the effects of the test temperature and the applied deviatoric stress. Comparisons of predicted permanent deformation with actual rut depths measured from full-depth asphalt pavements showed a reasonable agreement. Haas (H1) and Morris et al. (M20) introduced a polynomial function between the ratio of the logarithmic value of the permanent deformation to the logarithmic value of the number of load repetitions and the applied stress, the test temperature, and the percent air voids in the mix. They concluded that the permanent deformation is a function of the tensile properties of the asphalt mixes. Consequently, they recommended that tensile tests be employed to characterize the permanent deformation. A similar conclusion was also reached by Vallejo et al. (V1). A different approach was proposed by Brown and Cooper (314) at the TRRL. They stated that the permanent deformation of asphalt mixes can be better expressed by using the percent air voids or the voids in the ab ‘4‘ v n‘U 69 mineral aggregate (VMA) as the independent variable rather than the number of load cycles. Yhis implies that the permanent deformation is independent of the number of load applications. This is true if the permanent defromation term includes only creep. For this case, time becomes important. In general, permanent defromation is a function of several variables including time of loading, percent air voids, temperature and others. Other investigators (H1, M19, C5, A3) examined the effects of confining pressure (lateral stress in the asphalt course) on the cumulative permanent deformation. One conclusion was that higher confining pressures result in lower permanent deformations. Disagreement was found concerning the sensitivity of the permanent deformation and rut to the confining pressure. Some researchers concluded that unconfined tests are satisfactory to characterize the permanent deformation (i.e., permanent deformations are not sensitive to the confining pressure), where others suggested that confining pressure be included in the permanent deformation prediction equation. Theoretically, permanent deformation of any material is a function of material properties, applied stresses, service life, and environmental conditions. For example, the performance and service life of two similar pavement sections are drastically different if one section is 70 subjected to a high number of trucks (high axle loads), while the other is subjected only tx: automobile traffic. Further, even if the traffic characteristics are the same, pavements located in different geographical areas (e.g. presence/absence of freeze-thaw cycles) then the will perform differently. The above imply that to properly model permanent deformations of asphalt mixes, all factors involved should be included in the model. Thus, the differences in opinion are mainly related to the fact that each study did not include all the possible independent variables and/or their ranges. It is extremely difficult to pinpoint the exact reason because several authors neglected to note the range of their variables. Further, in some of the literature, the effects of the variables expressed only qualitatively (e.g., significantly affecting the results: decreases with increasing: and so forth). Nevertheless, the effects of cyclic stress level and test temperature on permanent deformations of asphalt mixes were also investigated. Researchers reported that higher stress levels and/or test temperatures result in higher permanent deformations (H1, M19, K2). Allen and Deen (A4) found that the permanent deformation at the first load application (initial response) is a function of the stress level and test temperature. The increment of permanent deformation between any subsequent cycles, however, is 71 independent of load and temperature. Haas and Meyer (H1) , on the other hand, reported that the accumulated permanent deformation (in percent) per the logarithmic value of the number of load application increases with increasing axial stress and increas ing temperature . Again, the difference could be attributed to the total number of independent variables included in the study or to the type of test used, recall that permanent deformation is affected by the stress level as well as the stress distribution in the sample. Hence, different tests may yield different stress distribution and consequently the results may not compare. Monismith and Vallerga (M19) examined the effects of the relaxation period during load-unload cycles on permanent deformation. They found that, relative to other variables, the effect of relaxation period is statistically insignificant. Allen and Deen (A4) studied the effects of the load duration on permanent deformation. They showed that regardless of the load frequency, equivalent loading time (number of load cycles multiplied by load ‘ duration) yields an equivalent permanent” deformation. In practice, the above findings imply that spacing between equally loaded truck axles (relaxation period) does not affect the permanent deformation. Traffic speed (loading period), on the other hand, inversely affects permanent 72 deformation. That is, the higher the speed the lower the permanent deformation. The finding by Allen and Deen (A4) however, was disputed by Brown and Cooper (B14). They examined the behavior of asphalt mixes under static and cyclic load (stationary and moving vehicle) using a square wave. In both tests, the peak cyclic load was equal to the static load in the creep test. Thus, The equivalent loading time for the creep test is much higher than that of the cyclic test. They found that the permanent deformation recorded from the cyclic test is significantly higher than that measured from the creep test. Brown and Cooper attributed this to the shape of the loading wave. Consequently, they recommended the use of sinusoidal wave form. Again, the differences in the findings are actually related to the variables involved. Allen and Deen used a sinusoidal wave form while Brown and Cooper used a square wave form. In general, the sinusoidal wave form simulates traffic better than the other form. Finally, Francken and Verstraeten (F4) developed a correlation between creep and permanent deformation. To summarize, the effects of test variables on permanent deformation of asphalt mixes vary. Results appear to depend upon the number of independent variables 73 under consideration. Ideally, the effects of the independent variables can be separated by holding all variables but one to constant values. Then the test results from two different investigations can be compared if and only if the constant values in both investigations are equal. To illustrate, assume that one set of tests was conducted while holding all independent variables but the percent air voids constant. For another series of tests, assume that the percent air voids was varied, say, from three to ten percent. Then the findings can be compared provided that, in both sets, the same independent variables were held constant at exactly the same level. Any other ‘values may lead to drastically different results. Nevertheless, the most significant finding is that reported by Allen and Deen (A4). That is, regardless of the applied stress level and other mix variables, the permanent deformation at the first load cycle is dependent on the stress level and mix variables. The increment of permanent deformation between any subsequent cycles is load independent. These findings imply that, in the field, the permanent deformation of a pavement system under the first application of axle load plays a major role in the extent of future ruts of that pavement. Thus, measurements of the permanent deformation of a newly-constructed pavement is crucial to the prediction of its future performance. 74 2.4.2 Sample and Mix Variables The effects of sample and mix variables upon the permanent deformation of asphalt mixes have been extensively studied. Since the findings are similar and consistent, a summary with illustrative citations is presented below. a) Lower percent air voids results in lower permanent deformation (H1, 814). b) The effects of the percent fine content depend upon the type of the aggregate in the mix (K1, K2, B4). c) The percent of coarse aggregate and top size aggregate in the mix cause no significant effects on permanent deformation (K1). d) Softer asphalt binder causes higher permanent deformation (H1). e) Higher asphalt contents cause higher permanent deformation (K1). These findings bear a direct impact on this study in selecting the specimen and test variables and their ranges. It was decided to use percent air voids from. three to seven: ‘three viscosity' graded asphalts: three types of aggregate with one top size and a constant percent _fine content: two proportions of fine and coarse aggregates (two gradations): three levels of cyclic load: and two test temperatures (see Chapter 3 for detail). 75 N MIXES In practice, the unconfined compression and the triaxial test are rarely used. to characterize the strength. of asphalt mixes. The Marshall stability-flow or the Hveem stabilometer tests are preferred because of their simplicity and convenience. Nevertheless, among these tests the triaxial one is generally considered a better research tool for modeling the strength of asphalt concrete mixes as a function of the specimen and test variables (M8, G3, H6, H7, Y2). In the triaxial tests, several field conditions can be better approximated than in the other tests. Further, triaxial specimen could be tested under any environmental conditions (e. g., dry, moist, hot, aged) while the Marshall specimen can only be conditioned in a water bath whose temperature is 140°F. Researchers studied the strength characteristics of asphalt concrete mixes utilizing one or more test methods and procedures. Some correlated Marshall stability and flow to strength. Others used the unconfined compression, the triaxial, and the indirect tensile tests to evaluate the effects of specimen and test variables upon the strength of asphalt mixes. The volume of existing information in this area is overwhelming. The findings and conclusions, however, are parallel to those concerning the effects of the same variables upon stiffness and modulus presented in sections 2.2 and 2.3 above. 76 Therefore, to avoid unnecessary duplication, the reader is referred to these sections and to table 2.2. One piece of information is of interest to be noted. Hargett and Johnson (H5) measured the strength of asphalt mixes utilizing four-inch by eight-inch cylindrical specimens (triaxial type samples) tested in compression and tension. They showed that, for a wide variety of mixes, the compressive strength ranges from 200 to 365 psi and the tensile strength ranges from 20 to 30 psi. This information impacts- this study in determining the magnitudes of the cyclic load. In general, the magnitude of the cyclic load should range from 5 to about 40 percent of the strength of the material being tested. Thus, it was decided, for the triaxial test to use cyclic loads of 200, 500 and 900 pounds (16, 40, and 72 psi). mmmmmmmmmmm mus—r momma, Emma-mm, HDSHEGIH mun-WWW Emma mm mm EFFEIII‘CFCIMNFPCICRQ‘I mm “1551' m MIIIELB RELIEF. 8m G4 1mm 10.10513 W m m - Y1 AEHS. VS S7 SIRS - I‘DEFFEEI‘ - - EVEL mm mm mm - - m4 mam. mm mm m 11mm: - m :m - mums" - - 3:5 mm. (mm was - mes - sues 039cm 1mm - 5mm. - r: max. sue - murmur2 - - Y4 me. 815 V5 mm m m - - mm m mes: - - WEN. nmss m - - ammo mm m ms: - - Y4 mm CDFINIIG m m - - cs m m1 815 mam - mm - - m sues name: names - - 113mm mama m (1an mmommmm mm m m rams mums. SIREIGIH mm mm sumr - — mm m W V5 mam! mums 1mm roe-rmf/ - - mm m m m - SVNLEI‘FEEP- - Bll mm m m - - Hm 1120 max. mm - :oEmmf’ - - 57 mm m 313$ mm - - mm new name: mm - - CCNIENI' momma: mes: €959 mmm.m m - - mm m m - - mm mm. m m’ - - Imam mum Emma mm: mm mmmmmm mm 1531' m mums muss. sneer}: mm W W - - 9mm B7 mm mm m m3 - - mes H]. mm m - Dom-1:12 - :21 mm. IQ mm. m - m - W m - '11- 1421 mm mm - - MINIMAL - \71 mom came m - mass: - W m - m - A4 mam. m - m3 - mm. KL mam. Hiram - - mm - mm. 'IIPSIZE - - mm - mm mm m - m - CINIENI' MZJCINHNE). m 'IYECF mm mm mammmm um 'IESI‘ FPCIIZR MIIJIIB HERVLIIF. SW GB MU WEN. m - - mes MIG-NI. 18 W PER-NI m - - m mam CINIENI' TDAEE CPI'. lfirnnhzflestreleelsadxehesofbmhrsdffieas ' m2. gtptnanmdmmxehecfm 'firtetpaahnesofcio, 7031:1100 4flrtarpaatureslestim60 . SthmmoFcrhiga'. 6firfiec1difia'sofs'xrtszedmatimadlmtmpaamre. 7¢mmm amdgmmarm mmmmymmm, a’dtiatofcnsted 9Wimaaseselictdasas). mflrgmularnataaals. CHAPTER 3 LABORATORY INVESTIGATION 111_§EEEBAL Recall that (see Chapter 1) the objective of this study is to quantify relationships between structural properties and. material mix: design. parameters. The structural properties required for the analytical and mechanistic mix design a) b) C) are: resilient characteristics; creep and permanent deformation; and compressive strength. The mix design parameters are: a) b) c) d) e) f) asphalt type and content: percent air voids in the asphalt mix; aggregate type, angularity, and proportion: mineral filler type and proportion; percent voids in mineral aggregate: and Marshall stability and flow. To accomplish the objective of the study, several tests and materials were selected and an experiment design £213: throughout the remaining parts of this thesis, the term sample indicates any sample that is being prepared for the test in question. The term specimen implies that all preparatory work on the sample are done and the specimen is ready for testing. 81 82 matrix was established. These are presented in the following sections. .1LZ_IE§ILIIEE§ In order to properly characterize the structural properties of the asphalt mixes, several tests were selected. These can be divided into two categories: the preliminary test to establish the asphalt mix design: and basic tests to determine the structural properties. The Marshall stability-flow test was employed to establish the mix design. -Four basic tests were then used to assess the structural properties ofythe mixes. These tests and the measured asphalt mix properties are: a) Unconfined triaxial compressive tests to determine the unconfined compressive strength. b) Unconfined creep tests to evaluate the creep characteristics: c) Unconfined triaxial constant peak cyclic load (TXCCL) tests to assess the resilient, viscoelastic, and plastic characteristics. d) Unconfined triaxial variable peak cyclic load (TXVCL) tests to evaluate the dependency of the properties on the load intensity. The Marshall tests were conducted first to establish the asphalt mix design. For all the test materials, the design. asphalt content *was then selected as that which 83 corresponds to the three percent air voids. The test specimens for the other tests were then fabricated using the design asphalt content. The percent air voids of the specimens was varied by using different compaction efforts. 243.12511MAIEBLAL5 Several different materials were selected for this study. These include: three types of aggregate ; three types of asphalt, and one type of mineral filler (fly ash). 3.3.1 Aggregate and Mineral Filler The primary aggregates used in this study are coarse and fine crushed limestone (L) and coarse and fine natural and rounded gravel (N). The third type of aggregate (50/50) was made by mixing fifty percent by weight per sieve size of L and N. The fly ash mineral filler (passing sieve number 200) was obtained from the Michigan Department of Transportation (MDOT). All three. aggregates were sieved and separated into different size fractions. Each size fraction was then stored in a different storage bag. Later (before making an asphalt mix), the aggregates were washed, dryed to a constant weight and then recombined in accordance with the grain size distribution curves shown in figures 3.1 and 3.2. Note that figure 3.1 shows the two gradation curves along 84 C] lNlVl id 1N3383d 00. oo Om On 00 On. Ow. On. On o. .ZOHBdng MZHA BmUngm mme mBHZ UZOAd 33:52:22 2. «3.32.4.0 mm9<0mm00< m0 mmmwe mmmmfi Adda mom m DZAN d mZOHBQQQmw a..m mmDOHh mmNG u>m_m .2.-. 21$” .273 .273 .27.: v e o. 2 onovom 8.8... .4 :00» “w o u. ...-Incl .....M.x..u.n. “fins 3&8 \\ \NNN 1 WV _ _ _) _ u - . -1 _ _ ..-U...n.......u. , \ _ 1 : ....u......m.. .../bu _ 1 \e\ _ 1 1\\\. . 1 . LAN ...... .. ... .. m, . ,2 - v I I. c. t .8 r .0 .7. .c. .7.8 .l .0 6 :0 s In o. On On 0v 0m 00 On 0m 00 oo— lNiDBJrl UNISSVA 85 .mm>mDU ZOHBDmHmBmHQ MNHm 2Husu mo ucmfiOfiww ~.om soHELoch: mo ucmfiowmmoo om e.euoeo .ae e.equo .ee Ne.ouo2 m~.o .ww< mcwm\.ww< mmumoo < m>m=u Ce qm.e msaspoz mmmcmcfim mw.~ aboum>usu mo ucmfiofimwmoo m.mm n quEucch: wo ucmwOfiuwmoo co .5: m.qu3c: .EE o.~u0ma .EE N~.ouo~m a m>MDU ow oo~ aquram Xq Burssed Juaoiaa MBJMMHWKRWAHDB. SIRE mmmm NJERSIEdIEh) SIZECnm) WA WE 3/4:: 3/8" 4.0 8.0 16.0 30.0 50.0 100.0 313.0 0.750 0.375 0.1% 0.® 0.046 0.024 0.012 0.03 0.(II3 19.01) 9.50) 4.750 2.360 1.180 0.60) 0.300 0.150 0.075 100.001 70.71 49. 36.312 27.54 20.40 15.11 11.1.9 8.29:3 100.001 78.46 61.; 43. 31.42 22.65 16.20 11.59 8.83 1W~mem$.m, 9:333.ij 3858,9133ij zmfirewwmlveigt 41.55, gmiatimA 53.13,grijmB *mya‘ 87 with the straight line gradation curve in the Federal Highway Administration 0.45 power gradation chart whereas figure 3.2 shows the regular aggregate grading chart. table 3.1 lists the percent passing by total weight for gradations A and B. It can be seen that, for both curves, the percent fine content (passing sieve number 200) and the top size of the aggregate were the same (8.29% and less than 0.75 inches respectively). Also, curve A has a higher percent of coarse aggregate than curve B. The three aggregates possess different angularities. For computational purposes, the angularity of the aggregate was given a scale from one to four (W10). A value of one means a perfectly spherical and smooth aggregate, while a value of 4 designates highly angular and rough aggregate. The limestone was assigned an angularity value of 4: the natural gravel two: and a value of three for the 50/50 mix. These values were later used to analyze the effects of angularity upon the structural properties of the asphalt mixes. It should be noted that neither the limestone dust, nor the material passing sieve number 200 of the natural aggregate was used. Rather, fly ash was utilized as the mineral filler. For each aggregate, two specific gravity tests of the coarse and fine portions were determined utilizing AASHTO test procedures T 85 and T 84 respectively. The specific gravity of the mineral filler was determined in 88 MBJWMQEMW album A B mm 1 2 AVG. 1 2 AVG. Gs (8.1K) 2.665 2.676 2.671 2.757 2.699 2.728 mm Ge (s3) 2.688 2.699 2.694 2.768 2.716 2.742 Gs (AER) 2.728 2.740 2.734 2.789 2.747 2.768 Gs (mm) 2.688 2.704 2.694 2.623 2.703 2.663 mm Gs (s3) 2.712 2.732 2.72 2.- 2.732 2.693 G5 (24:19.) 2.763 2.783 2.773 2.702 2.784 2.743 Gs (BIK) 2.663 2.726 2&5 2.697 2.726 2.712 swsomxmmn' as ($3) 2&6 2.747 2.717 2.72 2.748 2.735 as (7433.) 2.725 2.785 2.755 2.767 2.787 2.777 89 MBJWMG'BEFMM mm A B sum mm 1 2 AVG. 1 2 AVG. mm Gs (8.1110 2.794 2.810 2.802 2.809 2.803 2.806 mm m 05 (81:10 2.720 2.746 2.733 2.72 2.750 2.736 50/50 MIX 5: m <2 (mm) 2.765 2.776 2.771 2.788 2.770 2.777 90 accordance with AASHTO standard test T100. The data from each test and the average values are listed in tables 3.2 and 3.3. 3.3.2 Asphalt Type Three viscosity graded asphalt cements (AC10, AC5, and AC2.5) were obtained from a local Marathon refinery and utilized in this study. The three asphalts were then tested in accordance with the proper AASHTO test procedures to determine their properties. The test results are listed in table 3.4. §e$_IE§ILBBQ§EDQBE§ As noted in section 3.1, five tests were employed in this study. These can be divided into two different categories: priliminary tests to establish the asphalt mix design and select the design asphalt content: and basic tests to determine the structural properties of the asphalt mixes. The test procedures and the preliminary test results are presented in the following subsections. 3.4.1 Preliminary Test (Marshall Stability-Flow) The asphalt mix designs, for all materials, were determined using Marshall stability and flow. The sample preparation, the test procedure, and all the supporting data were obtained according to the following 91 MBAMH Wm 75-100 120-150 200-250 Vigrsitchah 150-10 ADC-5 ACE-2.5 mm 863-296 863-297 863-298 W4Q2mg.,60$c. 35 52 84 W2C, 103g.,5sc. 96 154 272 mwc,1mg.,538c. 157 233‘ *** Womb/2c. 1.24 1.020 1.015 nae: Rain: (c.0.c.) , c. 288 310 314 Site-011312211: (HB),C. 42.0 37.5 35.0 W113: in Tridflcxoetiylae, % 99.60 99.70 99.60 W,Zc,cnynfin,cn. 150:- ]50+ 95 Visrsiiaficne) 77F Kym 793 40/ 162 memhm) 140F {me 1026 594 271 WWMF, cs 2'70 212 159 1/8"‘IhmEflm, 163C, Sl‘r,50g. OngeinWeigt, 1:31:21: 0.47 0.43 0.34 mac, 1mg,553:. 48 73 123 %cfcngirallea:ratim 50 47 45 sztility, 25C, Smytnimcn 150+- 150+ 106 Vimsityexs.) 140F7F1i£ 3(33 1614 727 Viszsinzadn.)275F,cs 419 335 237 W(cne)77F,Kp3is 4554 1742 634 WIfithtrm. 92 AASHTO test standards. a) T 245-82 for sample preparation and Marshall test: b) T 209-82 for maximum specific gravity: c) T 166-82 for specific gravity: and d) T 269-80 for percent air voids. Figure 3.3 depicts the full factorial matrix utilized in this test. There are eighteen cells in the matrix for eighteen possible combinations of the variables (3 asphalts: 3 aggregates, 2 gradations). Each cell, represents a total of 12 samples: one triplicate for each of the following percent asphalt content by total weigh of mix 3.5, 4.2, 4.9 and 5.6. Thus, a total of 216 samples were tested. The test results are summarized in tables 3.5 through 3.7. Also, for each asphalt content, the average values for stability, flow, density, percent air voids, and percent voids in mineral aggregates were calculated. These ‘values are also listed in the tables. For each combination of the variables (asphalt, aggregate, and gradation), the stability: density: percent air voids: and the percent fine in mineral aggregate were then related to the asphalt content. The asphalt content at the three percent air voids was then selected as the design asphalt content and used throughout the rest of the testing program. These data are listed in tables 3.8 through 3.10. It should be noted that 93 .me842 Zmemo xHE Addmmmdz m.m mmDUHm e. z e 2 s . 2 sees me 2 e a e 1 2;: e m 1.. .... N 1 eve m e e e 1 2 ...... II $.40. 212 22422 “miles 2222222 222212112 .. 94 TABLE 3.5 MARSHALL MIX DESIGN RESULTS FOR ASPHALT PENETRATION OF 75-100. S = MISMU. SflllU" (PMS). AS = WALL SMIIUTY ADJUSTED 70 "IE SAHPLE REIGN. : Flflll (IIIM'). , = SPECIFIC GIAVHY. : AIR VIJIDS [I PEECEM. VHA : V'IIBS IN MINERAL AGGREGHES 1N PEECINL 95 TABLE 3.5 (CONTINUED). S = MISIMU. STAIILITT (PMS). AS = msmu STABILITY ADJUSTED TO THE SMPLE MIGHT. F: FLDH (IIIOD'). SE = SPECIFIC GRLVTTT. AV : AIR VII'IDS TN PERCENT. VHA : VOIDS TN HIKRAL AGGREGATE$_IILPIRCENL 96 TABLE 3.6 MARSHALL MIX DESIGN RESULTS FOR ASPHALT PENETRATION OF 120-150. 2452 2.47 3.08 15.20 S = HAD-WALL STUTUTT (MS). AS = MARSHALL STAITLTTT ADJUSTED TD TIE SAflPlE ’ETSITT. F = noun/100'). $6 = S'ECTTTC GRAVITY. AV : All VOIDS TN PERCENT. VITA : VDTDS TIT HIDERAl AGGRESATES ITLPEITCENT. 97 TABLE 3.6 (CONTINUED). NATURAL SRAVEL IT HETEHT S = TIAlSIIALL STABILITY (PDUNDS). AS = RAISIALI. STADTLITY ADJUSTED TD TIC SAMPLE HEIGHT. F = FLDII (l/IDD'). SE = SPECIFIC GRAVITY. AV = ATI VOIDS TN PERCENT. VNA = VOIDS TN NTNERAL AGENEGATES TN. PERCENT. 98 TABLE 3.7 MARSHALL MIX DESIGN RESULTS FOR ASPHALT PENETRATION OF 200-250. S : NARSNALL STADTLTTY (KINDS). AS = MARSHALL STAITLTTY ADJUSTED TO THE SANPLE HEIGHT. F : FLDIT (T/TTIT'T. SD 7 SPECIFIC GRAVITY. AV : ATR VOIDS TN PERCENT. VIIA = VOIDS TN TITNERAL AGGREGATES TN PERCENT. 99 TABLE 3 . 7 (CONTINUED) . '1” (IF A 4- ((1 no I: as ~4 ch '44 T T 24 T 3. u‘ v- S = NARSITALL STAITLITT (POUNDS). AS = NAISTIALL STAITLTTT ADJUSTED TO TNE SATIPLE HEIGHT. FLOW (HWY). 55 = SPECTFTC SRAVTH. Av = ATE VOIDS TN PERCTNT. A : \‘UTDS TN HTNEEAL AGGREGATES TN PERCENT. ‘H u § 100 maamm-Immmmmm. mm mm mm mm 50%MD( 10x mm 11:51:11 A B A B A B HEN mm %A.C. 4.310 4.460 3.990 4.280 4.160 4.400 1m. 5. G. 2.546 2.543 2.539 2.520 2.541 2.60 75 31138.6. 2.470 2.467 2.463 2.445 2.46 2.454 - 611148.055) 2242. 2380. 2177. 1984. 1884. 2302. 100 V.M.A 13.39 13.75 12.60 13.21 13.01 13.54 m (0.01") 11.34 10.38 7.38 9.42 10.38 8.95 %A.C. 4.250 4.480 4.030 4.320 4.140 4.380 MAX. 8. G. 2.547 2.541 2.537 2.517 2.541 2.60 125 ms. G. 2.471 2.46 2.460 2.442 2.46 2.454 - 51118. (lbs) m. 2392. 1m 1896. 2238. m. 150 V.M.A. 13.26 13.79 12.70 13.31 12.96 13.49 m (0.01") 9.90 9.76 7.42 8.34 9.99 9.68 %A.C. 4.070 4.240 3.990 4.380 3.860 4.200 mx. 5. G. 2.553 2.549 2.537 2.516 2.551 2.535 200 ms. G. 2.477 2.473 2.461 2.441 2.474 2.459 - SJPB. (lbs) 2173. 648. 1584. 1942. 196. 1935. 250 V.M.A. 12.85 13.23 12.61 13.31 12.33 13.08 m (0.01") 8.85 8.85 6.63 7.86 6.39 7.08 A.c. a-mmmmm. MAX. S. G. IWWWQW. V.M.A. amm WWW. 101 MBJMHDE-‘RRMMNI‘AIR‘UHB. mm mm m mum 50%MIX 111x W A 8 A B A B EN m %A.C. 4.310 4.460 3.990 4.280 4.160 4.400 mx. 8. 6* 2.546 2.543 2.69 2.60 2.541 2.60 75 HJEKS.G. 2.419 2.416 2.412 2.394 2.414 2.403 - 8048.915) 100 V.M.A 15.18 15.6 14.40 15.01 14.81 15.33 new (0.01") %A.C. 4.60 4.480 4.030 4.320 4.140 4.380 mx. 8. G, 2.547 2.541 2.67 2.517 2.541 2.60 16 EIKS.G. 2.420 2.363 2.410 2.392 2.414 2.408 - 81148. 913) 150 mu. 15.08 17.38 14.6 15.13 14.80 15.32 m (0.01") %A.C. 4.070 4.240 3.990 4.380 3.860 4.200 MAX. 8. 6* 2.56 2.549 2.67 2.516 2.551 2.65 200 HIKS.G. 2.426 2.422 2.410 2m 2.423 2.409 - 81148. 913) 60 VJLA. 14.73 15.12 14.48 15.20 14.22 14.97 m (0.08") A.C. =mmpsammm. mx. 8. G. xmmmm. SIPB. amm. V.M.A. smmmmm. 4 all-WES. 102 mmmmm—anmmmmm mm mm mm RINED 50%MIX MIX A6846 1158821 A B A B A 8 BEN m %A.C. 4.310 4.460 3.990 4.280 4.160 4.400 144x. 5. G. 2.546 2.543 2.69 2.60 2.541 2.60 75 811886. 2.36 2.36 2.36 2.344 2.36 2.36 — 8128.913) 100 mu 16.96 17.30 16.20 16.80 16.60 17.11 m (0.01") %A.C. 4.60 4.480 4.030 4.320 4.140 4.380 1441:. s. 6* 2.547 2.541 2.67 2.517 2.541 2.60 16 3138.6. 2.36 2.36 2.36 2.341 2.363 2.36 - 8128. 91:5) 150 was. 16.87 17.38 16.32 16.92 16.6 17.10 51076.01") %A.C. 4.070 4.240 3.990 4.330 3.860 4.200 MAX. 8.6,. 2.63 2.549 2.67 2.516 2.61 2.65 200 81886. 2.374 2.371 2.360 2.340 2.372 2.36 - SJPB. plus) 60 V.M.A. 16.6 16.90 16.28 16.98 16.02 16.58 m (0.01") A0. =mmmmm MAX. 8. G. smmmm. 81148. =mamLsxA88m. v.8.A. amm 111mm. * amm. 103 the selected design asphalt contents are slightly lower than those determined by the Asphalt Institute criterion (0.2 percent) and slightly higher than the Corps of Engineers criterion. 3.4.2 Basic Tests As noted above, four basic tests were conducted on the asphalt mixes to determine their structural properties. For all tests, the sample preparation procedure outlined in section 3.5 was employed. The test procedures are presented in the following sections. 3.4.2.1 Unconfined Compressive Tests These tests were conducted to determine the unconfined compressive strength of the asphlt mixes using The AASHTO T 208-82 test procedure with two modifications: a) Both vertical and radial deformations were measured. b) After two trial tests, it was noticed that the radial deformation at mid-height of the specimens was much larger than that measured near the bottom. This indicated possible friction between the end platens and the specimen surfaces. Subsequently, all the test specimens were capped and a low viscosity oil was used to lubricate the capped surfaces and thus minimize the end friction. This resulted in more uniform radial deformations. 104 Nevertheless, cylindrical specimens (four inch- diameter and eight inch-high) were prepared using the sample preparation procedure outlined in Section 3.5. The specimens were placed on the bottom platen of a triaxial apparatus which was placed under the loading frame (Wykeham Farrance with 10,000 pound capacity). The tests were conducted using a strain rate of 0.16 inches per minute. For each combination of specimen and test conditions, four specimens were made. One of these was used in each of the following tests: a) unconfined compression; b) creep; c) triaxial constant peak cyclic load; and d) variable peak cyclic load. In addition, after terminating .the last test, the same specimen was then tested to determine its unconfined compressive strength. The data from the last test was used in conjunction with those from the tests in item a to analyse the effects of cyclic load on the unconfined compressive strength. A total of 46 specimens were tested; 42 at 77°F and 4 at 40°F. 3.4.2.2 Creep Tests Creep tests were conducted using a constant static load to determine the creep characteristics of the asphalt mixes. In all tests, cylindrical specimens (four inch- diameter and eight inch-high) were prepared using the sample procedure outlined in Section 3.5. Each specimen was placed on the bottom platen of a triaxial apparatus. 105 Three LVDT(s) were mounted to monitor the vertical and radial deformations of the specimen; one LVDT for the vertical deformation and two for the radial deformations at mid-height and one-third-height. A constant static load (900 pounds) was then applied using the stress- controlled mode of an MTS hydraulic system. The test data were continuously collected. using strip chart recorders. The test was terminated either after twenty four hours or at failure. A total of 21 specimens were tested; 20 at 77°F and 1 at 40°F. 3.4.2.3 Unconfined Triaxial Constant Peak Cyclic Load (TXCCL) Tests The tests were conducted in a temperature controlled chamber using cylindrical specimens (four inch-diameter and eight inch-high) and an MTS hydraulic system. The tests were conducted at 77 and 40°F. The objectives of the tests were to determine the resilient and permanent deformation chracteristics of the asphalt mixes. The test specimens 'were jprepared and. conditioned as outlined in Section 3.5. After conditioning, each specimen was placed on the bottom platen of a triaxial apparatus and three LVDT(s) were mounted as in the creep test. The sustained and cyclic loads were then applied as follows: a) The test specimen was first subjected to a sustained 106 load of 50 pounds and the deformations were measured until the specimen came to rest (5 to 10 minutes). b) A repeated haversine wave form load was then applied with a peak load of 500 pounds. The load frequency was set at two cycles per second with 0.1 second loading time and 0.4 second relaxation period. It should be noted that one specimen was tested for each combination of the test material and test conditions. Early in the testing program, several apparatus related problems were observed which led to inconsistent results. All tests were then repeated using a new apparatus (see figure 3.4). A total of 27 specimens were tested using the new apparatus; 23 at 77°F and 4 at 40°F. 3.4.2.4 Unconfined Triaxial Variable Peak Cyclic Load (TXVCL) Tests The tests were conducted to determine the resilient characteristics of the asphalt mixes as a function of the specimen variables, load intensity, and test temperature. Basically, the test procedure is the same as that of the TXCCL tests. The only difference was that after ‘the application. of the sustained load, the specimen was subjected to 200, 500, and 900 pounds peak cyclic loads, each being applied for only 1000 cycles. Again, for each combination of the test material and test condition, one specimen was tested. The total number '\\_I\\m (a) Old set up. (b) New set up. J J l I -L. :1: \ l \ ‘\ . \ ~\ ‘\ FIGURE 3.4 SCHEMATIC DIAGRAMS OF THE UNCONFINED TRIAXIAL TEST TRIAXIAL TEST SET UPS. 108 of test specimens was 23. It should be noted that after terminating the cyclic test, each specimen was then sheared to failure, in order to determine its unconfined compressive strength. For all tests, each aggregate fraction (size) was washed and oven dried, to a constant weight, at 230°F for a twenty four hour period. After drying, all aggregate fractions were brought back to room temperature. Each fraction, starting with top size, was then weighed to the nearest 0.1 gram in accordance with the specific gradation curve. The proper amount of fly ash was then added. The aggregate mix was placed in an oven to bring its temperature to the compaction temperature as specified in the AASHTO T 245-82 test procedure. The proper weight of asphalt was then added to the aggregate mix to yield the design asphalt content. The aggregate and asphalt were mixed according to AASHTO T245-82 procedure. All test specimens were made using a California Kneading compactor model CS-1000. For all four types of triaxial tests, cylindrical samples (4 inch-diameter and about 8.5 inch-high) were compacted in four layers. The weight of the material per layer, the number of tampings, and the foot pressure of the compactor were varied between the layers to yield an 109 asphalt mix sample with uniform density near the target values of the percent air voids. Three values of percent air voids were targeted: three, five, and seven percent. About twenty trial samples were made prior to the start of the testing program. These samples were later sawed to three Marshall size specimens. The density of each specimen was then determined and compared to those from the other two specimens. From these trials, the proper weight of the asphalt mix, the number of tampings, and the foot pressure per layer were determined to yield samples with uniform density near the target air voids. After compaction, the sample was allowed to cool to room temperature. The density was then determined and the excess upper part of the sample was sawed to yield an eight inch-high specimen. After sawing, the specimen was air-dried and its density was again determined. Next, both ends of the specimen were capped using gypsum plater. The capped specimen was stored over night in the temperature controlled chamber which was set at the desired test temperature of either 77 or 40°F. It should be noted that the actual percent air voids of the compacted specimen was different than the target value. However, uniform specimens, were obtained. The uniformity of the specimens were checked using the indirect tensile tests outlined in reference 32b. 110 V AB S This study was designed to evaluate the effects of several variables on the structural properties of asphalt mixes. These variables can be divided into three categories: mix or material variables (aggregate type, gradation, and asphalt type); specimen variable (percent air voids); and test variables (load level and temperature). 3.6.1 Mix variables Three mix variables were included in this study: a) Asphalt type: three viscosity graded asphalts were used (AC10, AC5, and AC2.5). The properties of the asphalt are listed in table 3.4 . The kinematic viscosity of the asphalts was used as an independent variable to assess the effects of asphalt type on the structural properties. b) Aggregate type: three aggregate types were used in the mixes (crushed limestone, rounded natural aggregate, and a combination of 50 percent by weight per size fraction thereof). The angularity of the aggregates was used to assess the effects of aggregate type on the structural properties. Based upon a previous study (W10), the angularity factor of the limestone, natural aggregate, and the 50/50 mix were assigned the following values: four, two, and three 111 respectively. c) Gradation: for each aggregate type, two gradations were used: A and B as shown in figures 3.1 and 3.2. Both gradations had the same top size and percent passing sieve number 200. Gradation A had a higher percent of coarse aggregate relative to gradation B. In the analysis, the gradation factor was assigned one value for each gradation curve; the ratio of coarse (+ No.4 sieve) to fine (- No.4, + No.200 sieves) aggregates. Since only two gradations were employed, a meaningful relationship between aggregate gradation and structural properties cannot be found. Consequently, the effects of this variable was assessed only qualitatively. The total number of possible combinations of these variables was eighteen (3 asphalt x 3 aggregates x 2 gradations). 3.6.2 Specimen variables Only one specimen variable was used: the percent air voids. For each combination of mix variables, the test specimens were compacted to yield three target air voids: three, five, and seven percent. For most specimens, near target air voids were achieved. The air voids in the specimens were varied by varying the compaction efforts. 112 3.6.3 Test variables 2n1 all tests, except the Marshall tests, the load and the test temperatures were varied. The values of these test parameters for the particular test are listed in table 3.11. Since only two test temperatures were employed, a meaningful relationship between test temperature and structural properties cannot be found. Consequently, the reader should be cautioned in interpreting the form of the relationship. Due to the large number of variables, a partial factorial test matrix was established for each of the basic tests. A full factorial matrix was utilized in the Marshall tests. These matrices are presented in the next section. It should be noted that throughout the remaining parts of this thesis, the term specimen variables is used to indicate specimen and mix variables as outlined above. §;1_IE§I_§BIBI£E§ As noted above, a full factorial experiment matrix was established and the tests were conducted to establish the asphalt mix design. This matrix is shown in figure 3.3. Each cell in the matrix represents 12 specimens: triplicate for each of the following percent asphalt contents: 3.5, 4.2, 4.9 and 5.6. Thus the total number of specimens in the matrix was 216. The tests were used to 113 12118111101)me KR'JIEESIC'IESIS. 'Iést'llpe Lcai Cycliclcai (118) (1135) WW I] E' ST' .1 WW 77,40tofailme - can 77,40 900 - arslthcliclcai 77,40 - 500 vadaaleqcliclcm 77,40 - 200,500,900 114 establish the asphalt mix design. The design asphalt content for each cell was selected as the asphalt content for which the percent air voids in the mix was three. For the basic tests, a total of six independent variables were considered. Each had either two or three values. These are: three viscosity graded asphalts; three aggregate types; ‘two gradations; three values of percent air voids; two test temperatures; and three loads. Thus , the possible number of combinations of the values of the variables is 324. This implied that, for each of the four basic tests and for a full factorial study, 324 specimens were required (no duplicates or triplicates). Time and funds for such a study were not available. Consequently, for each test, a basic partial factorial experiment matrix was established based on the cocept of seperation of variables. This matrix (common to all four tests) is shown in figure 3.5. It should be noted that, for each test, one' single specimen is represented by each designated cell in the matrix. Tests corresponding to the designated cells of the matrix were conducted. Data from three cells that have all variables, but one, constant (e.g. cells 1, 4, and 5 in figure 3.5) were analysed to infer the effects of the independent variable (asphalt type in this case) on test results (i.e. cell 1 corresponds to asphalt type 1; 2 to asphalt type 2: 3 to asphalt type 3: with all other 115 .mEmmB A4HX¢H¢B szHEZOUZD mmm. mom meQRZ BZMZHmmmxm Q¢Hm§¢m AdHBy—dm .n.mm~50H.m 116 variables are invariant). 26§_fi2EQIHEE_DE§1§EAIIQE_EQ!§EB In order to establish the data base subroutine and to systematically store the data on a computer so that any one set or sets of data could be recalled for analysis, a specimen designation numbering system was established. This numbering system applies to the overall experimental investigation. The designation number consisted of eight digits. The first leftmost digit is designated as digit one, the last (rightmost) digit is digit number eight. Each digit designates one independent variable as follow: 1. For aggregate type, (limestone = 1, gravel = 2, 50% mix by weight = 3). 2. For gradation type, (gradation A = 1, B = 2). 3. For asphalt viscosity, (high = 1, medium = 2, low =3). 4. For test temperature, (77°F = 1, 40°F = 2). 5. For test type, (Marshall = l, indirect at 140°F = 2; indirect at 77°F = 3; indirect variable cyclic load= 4; indirect constant cyclic load = 5; unconfined a 6: triaxial creep = 7; triaxial variable cyclic load = 8; triaxial constant cyclic load a 9: and beam = 0). 6. For percent asphalt contents (Marshall tests only): and for percent air voids ( basic test only ), 117 (3.5% = l, 4.2% = 2, 4.9% = 3, and 5.6% = 4); (design asphalt content at 3% air voids 5, at 5% air voids a 6, at 7% air voids = 7). 7. For sample number (triplicate) by order of test, (SN = 1 to 3) . 8. For mix design (Marshall tests only), or for load level (beam tests only), (Marshall mix design = 0): for all constant peak cyclic load (3): and for beam tests at 100 pounds cyclic load = l, at 200 pounds = 2, at 500 pounds = 5). The designation number can be illustrated with three examples: Example 1” .A designation number of 11110521 implies (from left to right): limestone: gradation A; high viscosity asphalt; 77°F; beam test: 3% air voids; second beam of a triplicate: and 100 pounds cyclic load. Example 2. A designation number of 32325715 indicates: 50/50 mix, gradation B: low viscosity asphalt; 40°F; indirect constant cyclic load test: 7% air voids; first specimen of a triplicate; and 500 pounds cyclic load. Example 3. A designation number of 21217613 indicates: natural gravel, gradation A; medium viscosity asphalt: 77°F: triaxial creep test: 5% air voids. CHAPTER 4 TEST RESULTS 261_§EEEEAL Recall that for' each cell of the partial factorial matrix of figure 3.2, four tests were conducted. a) TXCCL test (500 pounds): b) TXVCL test (200, 500, and 900 pounds); c) unconfined compression tests using virgin and item b specimens; and d) static creep test at 900 pounds (70 psi). The test results are tabulated in the appendices. Typical data are presented in the following sections. 4 Ihvll' hi" 1;. . 4- 0 T ' " CL C V- 03.0 _ C IE§I§ These tests were jperformed to study the effects of specimen variables (percent air voids, asphalt type, and aggregate type and gradation), and the test temperature on the resilient and total characteristics of compacted asphalt mixes. Typical plots of resilient and total moduli versus the number of load applications for three values of the percent air voids are shown in figures 4.1 and 4.2 respectively. The percent air voids (AV) and the specimen designation numbers are indicated in the figures. 118 119 .mo_o> ~=< uumIp mo... MZOEEQum 93.. no 666232 mzwmu> MDJDQOS ._.zu_.=mmm :4 6630: Z .mcozsoaom too; :0 806832 40$: coco 89 con 8: p P b P — h _ — LPb — p b b L p P oofi .. on. 1 4 4 l I I e e e .. com 23:: 6888 n 53.6")... 4 - 28:: .863. 1 «86.7.2: .. 23:: .658. u an??? o Omm (191) an “snlnpow 1116112588 120 .mo_o> 63 6661.? 60.6 MZOEEQMK 9.40.. “.0 ”$6232 m3mmw> MDTSOOZ 450... Nd manor. 2 .mcozzmaom too; 6o ..onEoz 3+2 coon 89 com 8: C P p p _ p b p h P p p h — - h b 00F < < 4 I I I 02 C O O 1 .. com 23:: 2668 1 «3:72 4 . 28:: .663 1 «86.124 .. 28:: oasow .. «6:612 o com (18)!) 3 “snlnpow 10101 121 Figure 4.3 depicts typical the total cumulative plastic strain versus the number of load applications for three values of the percent air voids. The percent air voids (AV), the specimen designationnumbers, and the corresponding coefficients of correlation (R2) are indicated in the figure. All TXCCL test results data are tabulated in appendix A. 4. Us 041' T! QA 1314-; f PEAK YC C _0-_0 TXV L TESTS These tests were jperformed to study the effects of specimen variables, test temperature, and cyclic load on the resilient and total characteristics of compacted asphalt mixes. Figures 4.4 and 4.5 show, respectively, typical plots of the resilient and total moduli versus the number of load applications for three values of the cyclic load. The specimen designation number, the percent air voids, and the magnitudes of the cyclic load are indicated in the figures. All TXVCL test results are tabulated in appendix B. 4 ON These tests were jperformed to study the effects of specimen variables and the test temperature on the static total stress-strain characteristics of compacted asphalt mixes. Figure. 4.6 shows typical plots of the stress-strain I 122 vo+m— L b p 0000 |P .mo_o> a? mmmxh mo“. mzofifiudwm 0(0... 60 mumIDZ mama”; 231.5 .Fzmzs‘mun. u>fi53§30 mat $50.... 2 .mcozswqom 68.. Co .3852 COD P own —T-||Pb|~ L - cop _ 5.0 H I) 885.18. 23:: 29:8 1 58.8.24 a 8.3m». 28:: .868 1 x8346 a N864». 28:: 4.858 1 «231% o .. no.0 o pd r md 1T1Ul'fr CO C. v— r "tilt I O o. n (z) 'a 'ugohs wauouuad 8701010an 123 .woo HES. 60... szEBan 95.. 8.0 666562 mama“; 96.500: Eugmwm «.6 #50: z .wcozzoaom 68.. .o .3832 $2.813 28:8 .868. 1 com a T 08 - «v.52. cow I onm can (191) am ‘smnpow 4U9!I!3°a 124 6940.6 030>o wmth 60.6 szFanfim 940.. ....O mmmZDZ mama”; 94.500} 1.5.0.. 66 6630.... 2 5:02:33. 603 _o .3832 82 com 8: . 1 . . 8 . A _ 02 A . 2 t I 4 4 . 1 08 £24813 n .8 . 2 :4. .868 1 com 4 T 08 I avcaoa 8N I own (191) 3 'smnpow 10101 125 curves of three specimens. The percent air voids (AV), the specimen designation number, and the unconfined compressive strength (qu) are indicated in the figure. All data pretaining to this test are listed in appendix C. $6§_§IAIIQ_§BEEE_IE§I§_ These tests were jperformed to study the effects of specimen variables and the test temperature on the creep characteristics of compacted asphalt mixes. Figures 4.7 through 4.10 show typical plots of axial strain as a function of time for' different mixes. The percent of air voids, the specimen designation numbers, and the constant axial stress are indicated in the figures. All creep data are listed in appendix D. Axial stress, psi 126 0—0 AV-1.321% - Sample 11116513 (qu=493.4psi) 600 _ s—a AV=3.169% - Sample 11116613 (05248.3031) H Min-7.2042 - Sample 11116713 (qU-165.5psi) 500 -1 o I r I I I I r T r I I I I 0.0 0.5 1.0 1.5 Axial Strain, 2 FIGURE 4.6 STATIC STRESS-STRAIN CURVES FOR THREE AIR VOIDS. 127 606 F .mponprg m._n_s_U xfimm QmZHmZOUz: mmB mom XHMde BZHZHmmmxm BZQBmZOO AdedeB QdeOBoflh AdHEmdm ~.nmmDUHh 136 the regression coefficients of the three equations reflect the effects of the second independent variable (aggregate type in this case). These differences can be correlated to the aggregate type to yield one equation for all eight cells. Both avenues "a" and "b" are compatible and give equivalent results. The advantage of this method is that the effect of each of the independent variables was assessed separately. The disadvantage, however, is that the interaction. (if any) between these variables cannot be infered. Stated differently, this procedure assumes that the variables are truly independent of each other and a collection of two or more variables does not increase or decrease the effects of any individual one. Avenue "b" was utilized for assessing the effects of percent air voids and aggregate angularity; avenue "a" was used for evaluating the effects of the kinematic viscosity of the asphalt. Examination of the values of the resilient modulus revealed that they are independent of aggregate gradation (see figure 5.2). Hence, data from certain cells (e.g., 1, 2, 3; and 13, 14, 15) were combined in one analysis. This increased the number of observations in the analysis. Nevertheless, using the separation of variables method, the analysis was-conducted as follows: 137 3.0 Kinematic Viscosity =- 270 centistokes '0‘) o. O 0 2.0—4 05' 2 :3 ‘O o 2 4n! c .2 '65 0 0: Closed symbols = Grad A \ Open Symbols - Grad B \ \ a 50/50 Mix a Naturai Gravel a Limestone 1.0 i i I I l i i i i 0 2 4 6 8 10 Air Voids. % FIGURE 5.2 RESILIENT MODULUS VERSUS PERCENT AIR VOIDS FOR THREE AGGREGATE WPES. a) b) 138 Step 1. The values of the resilient modulus (dependent variable) from cells 1, 2, 3, 13, 14, and 15; 6, 7, 8, and 18; and 11, 12, and 19 were utilized to study the effects of the percent air voids. Figure 5.2 shows plots of the logarithmic values of the resilient modulus (MR) as a function of the percent air voids (AV). It can be noted that the logarithmic values of MR can be related to AV using equation 5.1. 1n(MR) = 1n(A1) + BIAV (5.1) MR a resilient modulus; AV 2 percent air voids; ln(A1),B1 - regression coefficients; ln a natural logarithm (base e). where: The intercept (A1) represents the logarithm of the resilient modulus at the theoretical zero percent air voids; the slope (Bl) indicates the rate at which the logarithmic value of MR decreases with increasing AV. The values of the regression coefficients are listed in table 5.1 along with the coefficients of correlation and the standard errors for the three aggregates. Step 2. To infer the effects of the aggregate angularity, the values of the intercept (A1) and slope (Bl) were plotted against,and statistically correlated to, the aggregate angularity (see figures 139 TABLE 5.1 REGRESSION COEFFICIENTS, COEFFICIENTS OF CORRELATION, AND STANDARD ERRORS OF EQUATION 5.1 FOR THREE AGGREGATES. Aggregate Type ln(A1) A1 81 R SE Limestone 12.433 251003 -.07327 0.993 0.010 Gravel 12.485 264448 -.04757 0.910 0.029 50/50 Mix 12.469 260102 -.03743 0.999 0.004 ln 8 Natural logarithm (base e): A2, B1 3 Regression coefficients; R 2 Correlation coefficient: SE = Standard error. 140 280 260 - 0 Regression Coefficient AV ksi 24o .,.,,,, 1 2 3 4 5 Aggregate Angularity, ANG FIGURE 5.3 REGRESSION COEFFICIENT A‘ VERSUS AGGREGATE ANGULARITY. 141 —.02 m.- E o .2 -.04- .2 E . o a C .9 g —.06-4 0" Q) I . -08 I F I I I I r - I 2 3 4 5 Aggregate Angularity, ANG FIGURE 5.4 REGRESSION COEFFICIENT B, VERSUS AGGREGATE ANGULARI'IY. C) 142 5.3 and 5.4). Equation 5.2 was found to relate the intercepts to angularity. A1 = 278685 - 6722.5 ANG (5.2) R2 = .960; S.E. = 1940 where: A = regression coefficient from equation 5.1: ANS = aggregate angularity. No linear correlation was found however between the values of the slope and aggregate angularity. Since the objective herein is to obtain a simple equation, it was concluded that the proper value of B1 can be assigned to the corresponding angularity. Step 3. Equation 5.2 was substituted into equation 5.1 which resulted in equation 5.3. MR = (278685 - 6722.5ANG) eBlAV (5.3) with B1 = -0.07327 for limestone = -0.04757 for gravel - -0.03743 for 50/50 mix. where: all terms in the equation have been previously defined. This last equation was then used along with the proper values of B1 to calculate the values of the resilient modulus of cells 1 through 19. Figure 5.5 shows a plot of the values of the ratio of measured to calculated resilient modulus versus the kinematic viscosity of the asphalt. It can be noted that a 143 .>:moom_> o:<§mz_x m3mmw> 94.5005 HZMDEME Duh/«430.20 OH ommamfifi ...O GEE oh “#50; 8 56083 26832 com com co. _ . one a 9 road m. m. U 1- W o o. 18., m. n S peiomomg o3, pemsoew )0 01103 0.... 144 range of values was obtained for each value of the kinematic viscosity. Equation 5.4 represents the best fit line of the data. MR/MRcal with R2 = 0.457 SE = 0.0378 where MR/MR a ratio of measured to prgdicted MR: E9 = kinematic viscosity (10 cs). = 0.7948 + 0.7527KV (5.4) Finally, when equation equation 5.4 was multiplied by 5.3, equation 5.5 which expresses the resilient modulus in terms of the aggregate angularity, the kinematic viscosity of the asphalt, and the percent air voids of the specimens, was obtained. B AV MR = (278685 - 6722.5 ANG)(.79483 + .7527KV) e 1 (5.5) where: MR resilient modulus (psi); o = kinematic viscosity of the asphalt at 275 F (135 C) (10 centistokes), (AASHTO T201): AV = air voids in percent (AV = 1 to 100): ANG = aggregate angularity: b = regression coefficient that depends on aggregate type -.07327 for limestone (ANG=4) -.04757 for gravel (ANG=2) -.03743 for 50/50 mix (ANG=3). Figure 5.6 depicts the calculated values of the resilient modulus (using equation 5.5) plotted against the measured values. The straight line in the figure represents equality between predicted and measured data. Finally, the 145 300 o Excluded data for s ecimens / 12119613 and 12219 13 / '2 TT = 77°F / .. R = 0.969 /' 3 1 46/ a 8 / 2 0 :c; 200 F O 0 L: o '0 C 2 .9. 3 - 2 O C U O 100 i I x 100 200 300 Measured Resilient Modulus, ksi FIGURE 5.6 CALCULATED VERSUS MEASURED RESILIENT MODULUS. 146 correlation coefficient (R) of the equation is 0.969. It should be noted that during the statistical analysis, data obtained from two test specimens (12119613 and 12219713) were excluded from the data base because, statistically, they represent a different population. That is, the two data points (see figure 5.6) did not follow the general trend of the other seventeen data points. The deviation from the general trend could be attributed to error in the backcalculation of the percent air voids. Unfortunately, the percent air voids of these two specimens were not rechecked immediately after the tests because the data analysis phase was lacking the testing phase. Nevertheless, when these two observations were included in the calculation of the coefficient of correlation (R), a value of 0.860 was obtained. Due to this, the method of separation of variables was abandoned because of two reasons: a) the method was based on the assumption of no interaction between the variables: and b) the method did not fully account for the effects of the aggregate angularity (the values of the slope B 1 need to be assigned). 5.2.2 General Equation Unlike the separation of variables, the SPSS/PC+ program in this procedure utilizes the entire data base 147 to correlate the dependent and all independent variables based on a user-specified equation form. The outcome of the analysis includes a tabulation of the regression coefficient(s) for each independent variable, and the coefficients of correlation and standard error of the entire equation. The disadvantages in this method are: a) Seperate analysis of the resulting equation should be conducted to determine the most significant variable. b) All variables, important or not, were included in the correlation equation. Item b above implies that the user of the computer program should possess prior knowledge, and/or estimates, of the variables that affect the test results. In addition, the inclusion of one or more variables in the equation may or may not mean that said variable(s) do affect the test results. It simply means that the two sets of number are statistically' related. The jphysical meaning of the correlation still has to be examined. Due to these shortcomings, this method was not used in the analysis. 5.2.3 Stepwise Correlations In this procedure, all available data and the identified variables were entered to the memory of a microcomputer and the SPSS/PC+ computer program was used to correlate the dependent and independent variables. Unlike 148 the general equation method, the correlation was done using a stepwise procedure. That is, the most significant variable affecting the test results was analysed first and the regression coefficients and the coefficients of correlation and standard errors were determined. The second-most significant variable was then included along with the first one and new values of the regression coefficients and the coefficient of correlation and standard. errors 'were determined, The least significant variable was included last. Again, from each step, a new set of ‘values of the regression coefficients and. the coefficient of correlation and standard error were determined. Variables that did not have a significant level (higher than 0.05 percent relative to the previous variable) were not included in the final equation. The advantages of this method are: a) In each step, the variables in the equation are listed in the order of their significance. b) the interaction between variables can be assessed by comparing the regression constants of the equations from two consecutive steps. c) The method produced the simplest possible equation. Like ' the general equation method and any other statistical analysis, the physical meaning of the final correlation equation still has to be assessed. This method was utilized in all statistical analyses which are presented 149 in the following sections. 5 TIC As noted in Chapter 2, the pertinent features of the stress-strain relationship of a compacted asphalt mix under cyclic loads include: a) time-independent elastic strain that is recoverable upon unloading: b) time-dependent elastic (viscoelastic) strain that is recoverable after removal of the load (during the relaxation period): and c) plastic strain during a load-unload cycle which is dependent upon load configuration, load intensity and rate, loading period, and test temperature. Thus, the e1astic-viscoelastic-plastic model was employed and the measured total strain was separated into three components: elastic (resilient), viscoelastic, and plastic. The term "resilient characteristics" refers to two resilient parameters: resilient modulus and Poisson's ratio. Presently, there are no standard definitions of these two terms. In general, the resilient and total moduli and Poisson's ratios were calculated using equations 5.5 through 5.9. e a a /L (5.5) 150 eR = DR/Co (5.6) oPA = QPA/Ao (5.7) E or HR = OPA/eA (5.8) U = eRAV/eA (5.9) where: eA = elastic or total axial strain: DA = elastic or total axial deformation: L0 = original specimen length: eR = elastic or total radial strain: D = elastic or total radial deformation: CE = original specimen circumference: °PA = axial cyclic stress: QPA = axial cyclic load: A0 a original specimen cross-sectional area: eRAV - average radial strain =- (2e 3 + $1} )/3: eR1/2’ eR1/3 = radial strain at mid-height one-t 148- height of the specimen: E = total modulus: MR = resilient modulus: U a resilient or total Poisson's ratio. The viscoelastic properties are time dependent. For example: a longer loading period will produce higher viscoelastic deformation. Also, longer relaxation period results in higher viscoelastic recovery. Since only one relaxation and loading period were utilized and since the rate of recovery (recovery versus time) were not recorded, calculation of the viscoelastic properties becomes tedious and misleading. Consequently, only the resilient, total, and plastic deformations are considered. In addition, no attempt was made to correlate Poisson's ratio to the specimen and test variables because of the inconsistencies in the recorded signals which could be due to sample rocking and/or lateral movement. Nevertheless, 151 Poisson's ratio was calculated and it was found that, for all tests, its values range from -0.248 to 0.481; and, for one specimen, the values varied from one load application to another. For most tests, specimen deformations were recorded at cycle numbers 100, 500, 1000, 5000, and 10000. Some specimens were tested up to 150000 cycles. For all tests, the resilient modulus (MR) was found to be independent of the number of load cycles (see figure 4.1). Since it is a common practice to disregard the test results from the first few hundred cycles (100 to 500 cycles) to allow for sample conditioning, the values of MR at cycle number 1000 was selected for the analysis. It should be noted that the values of MR obtained at different load cycles were analyzed for variation within one test. It was found that, for 38 specimens, these values vary by five percent; ten percent for 11 specimens, twenty five percent for 5 specimens, and thirty five percent for one specimen. These variations could be attributed to the operator's error in reading the data from the strip chart and/or the variation of the applied load between the different cycles. Further, the variations were found to be erratic and not related to the number of load applications. The values of the resilient modulus, at cycle number 1000, were statistically correlated to the different specimen and test variables using, for each variable, 152 several transformations (arithmetic, semi-logarithmic, and logarithmic). In the final analysis only one form was accepted based on: a) physical interpretation between the modulus and the variable in question: b) highest coefficient of correlation. c) examination of the residuals in order to satisfy linearity and the basic assumptions of independence, constant variance, and normality. It should be noted that selecting the equation form based only on the highest value of the coefficient of correlation could be misleading. Variations in the logarithmic values of the dependent and/or independent variables are naturally less than those in the arithmetic values. The verification of the assumptions mentioned in item c is illustrated through a set of typical residual plots in appendix E. Recall that two types of unconfined triaxial cyclic loadtests were used: a) constant peak (TXCCL) , and b) variable peak (TXVCL) . Data from the first type were utilized to infer the effects of specimen variables and test temperature upon the test results. The second type was used to evaluate the effects of specimen variables, test temperature, and magnitude of cyclic load. The MR values calculated from equation 5.8 were statistically correlated to the test and specimen variables using the stepwise correlation procedure 153 described in section 5.2.3. The analysis was conducted in five phases, as follows: phase 1 TXCCL test results at 77°F: 17 specimens; phase 2 TXCCL test results at 77 and 40°F: 20 specimens: phase 3 : TXVCL test results at 77°F: 16 specimens: phase 4 : TXVCL test results at 77 and 40°F: 18 specimens, and phase 5 TXCCL and TXVCL tests at 77 and 40°F; 38 specimens. Tables 5.2 through 5.6 summarize the results of the stepwise regression analysis for phases 1 through 5, respectively. Each table presents the regression coefficients, coefficients of correlation, and standard errors of the resulting equation from each step of the analysis. The variables in the tables are listed in the order of significance. For example: The percent air voids in table 5.3 is the most significant variable: the kinematic viscosity is the least significant. It should be noted that the magnitudes of the regression coefficients for each variable do not necessarily show the relative importance of that variable: this can be determined using two methods: a) examination of the partial correlation coefficients matrix: and b) a sensitivity analysis of the resulting equation. The partial correlation coefficients (PCC) matrix TABLE 5.2 REGRESSION COEFFICIENT MATRIX FOR RESILIENT 154 MODULUS VERSUS SPECIMEN VARIABLES(TXCCL). MR Intercept Slopes R SE ln(§ I A3 ID(- ) (10 Y) (10 9I (lOKY) ln(MR) 12.600 -2.932 - - .441 .117 12.838 -2.653 -9.006 - .743 .082 11.239 -2.141 -8.648 2.759 .876 .059 ln = Natural logarithm (base e): MR = Resilient modulus (psi); AV = Percent air voids (%): KV a Asphalt kinematic viscosity (centistokes): ANG a Aggregate angularity: GRAD = Aggregate gradation: R a Coefficient of multiple correlation: SE = Standard error. 155 TABLE 5.3 REGRESSION COEFFICIENT MATRIX FOR RESILIENT MODULUS VERSUS SPECIMEN VARIABLES AND TEST TEMPERATURE (TXCCL). MR Intercept Slopes R SE 1n(- ) AN§ 1n<8 I T! (loKYI (10 2) (10 Yi (10 3) 1n(MR) 9.550 4.799 - - - .359 .130 10.049 4.404 -9.103 - - .631 .102 10.712 3.671 -9.119 -l.703 - .751 .086 11.593 2.782 -8.936 -2.073 -4.773 .904 .055 In a Natural logarithm (base e): MR 8 Resilient modulus (psi): AV - Percent air voids (%): KV = Asphalt kinematic viscosity (centistokes): ANG a Aggregate angularity: GRAD = Aggregate gradatiog: T3 = Test temperature ( F): R = Coefficient of multiple correlation: SE = Standard error. 156 TABLE 5.4 REGRESSION COEFFICIENT MATRIX FOR RESILIENT MODULUS VERSUS SPECIMEN VARIABLES AND CYCLIC LOAD (TXVCL). MR Intercept Slopes R2 SE ln( ) ln(C ) ln(A ) (10KY) (10 E) (10 3) ln(MR) 9.341 5.262 - - .455 .121 8.249 5.374 1.683 - .872' .059 8.540 5.007 1.694 -6.156 .889 .056 In a Natural logarithm (base e): MR 8 Resilient modulus (psi): AV - Percent air voids (%): RV = Asphalt kinematic viscosity (centistokes): ANG 3 Aggregate angularity: GRAD 2 Aggregate gradation: C5 8 Cyclic load (pounds): R = Coefficient of multiple correlation: SE = Standard error. 157 TABLE 5.5 REGRESSION COEFFICIENT MATRIX FOR RESILIENT MODULUS VERSUS SPECIMEN VARIABLES, CYCLIC LOAD AND TEST TEMPERATURE (TXVCL) . MR Intercept Slopes R2 SE ln( ) ln(C ) TT ln(A ) (logy) (10 E) (10 3) (10 3) ln(MR) 8.867 6.183 - - - .423 .145 7.770 6.301 1.686 - - .728 .101 8.771 5.375 1.692 -6.859 - .912 .058 9.104 4.978 1.703 -7.091 -6.652 .926 .054 1n a Natural logarithm (base e): MR a Resilient modulus (psi): AV 8 Percent air voids (%): RV = Asphalt kinematic viscosity (centistokes): ANG 8 Aggregate angularity: GRAD 2 Aggregate gradation: CL = Cyclic load (pound ): T3 = Test temperature ( F): R = Coefficient of multiple correlation: SE = Standard error. 158 TABLE 5.6 REGRESSION COEFFICIENT MATRIX FOR RESILIENT MODULUS VERSUS SPECIMEN VARIABLES, CYCLIC LOAD AND TEST TEMPERATURE (TXCCL+TXVCL). MR Intercept Slopes R2 SE ln(_ ) ln(g ) TT ln(A ) (loKY) (10 E) (10 3) (10 341) ln(MR) 9.088 5.740 - - - .386 .144 8.055 5.810 1.618 - - .602 .117 8.919 4.994 1.619 -5.781 - .750 .093 9.387 4.447 1.631 -6.144 -9.534 .780 .088 ln a Natural logarithm (base e): MR = Resilient modulus (psi): AV = Percent air voids (%): KV = Asphalt kinematic viscosity (centistokes): ANG = Aggregate angularity: GRAD = Aggregate gradation: CL = Cyclic load (pounds): T3 = Test temperature ( F): R = Coefficient of multiple correlation: SE = Standard error. 159 TABLE 5.7 PARTIAL CORRELATION MATRIX FOR RESILIENT MODULUS AND SPECIMEN VARIABLES (TXCCL). ln(AV) ANG ln(KV) GRAD ln(MR) ln(AV) 1.000 .114 -.308 .069 -.664 ANG .114 1.000 -.092 .203 -.622 ln(KV) GRAD -.308 .069 -.092 .203 1.000 .051 .051 1.000 .582 -.128 ln(MR) -.664 -.622 .582 -.128 1.000 160 corresponding to table 5.2 is shown in table 5.7. The values of the PCC indicate that the percent air voids (AV) has the highest. (in absolute value) partial. coefficient of correlation (R = -0.664), followed by aggregate angularity (ANG) (R = -0.622), and the kinematic viscosity of the asphalt (KV) (R = 0.582). The numerical value of R indicates the strength of the linear relationship between the corresponding independent variable and the dependent variable (MR), with all else constant. A negative value of R indicates that increasing values of the independent variable results in. decreasing ‘values of the dependent one. The value of R between any two independent variables (e.g., R - -0.308 between ln(AV) and ln(KV)) indicates some interactions. The lower the absolute value of R, the lower the degree of interaction. For example: There is a little interaction between the AV and RV, and no significant interaction between the other variables. Comparison of the order of the variables and the values of the regression coefficients in tables 5.2 through 5.6 indicates that: a) The order of significance of the independent variables changes from one phase of the analysis to another. For example, while the percent air voids (AV) is the most significant variable affecting the resilient modulus (MR) (table 5.2): it is the least significant in tables 5.4 and 5.5. 161 b) The effects of the independent variables (as seen from the values of the regression coefficients) on the resilient modulus change from the TXCCL to the TXVCL tests. c) The kinematic viscosity of the asphalt is the most significant variable affecting the resilient modulus when test results at different temperatures and/or cyclic loads are included (tables 5.3, 5.4, 5.5, and 5.6). It is the least significant, however, when the tests are conducted using one temperature and a single value of the cyclic load (table 5.2). The finding in item c was expected because the effects of kinematic viscosity are magnified when the test temperature and the magnitude of the cyclic load are varied. Lower temperatures cause the hardness and stiffness of asphalt concrete to increase. Hence, the stiffness of the mix increases. Items a and b indicate that failure to include all variables in the analysis of the resilient modulus may lead to an inaccurate assessement of their significance and effects. That is, laboratory tests should be designed such that all possible variables affecting the resilient modulus are included and the respective data are collected. Further,' it is necessary' in the :multiple regression analysis to include all the variables in order to obtain an accurate assessement of their effects. Nevertheless, the values of the regression coefficients in tables 5.2 through 5.5 were 162 used to generate the following respective equations. ln(MR) = 11.23906 - 0.214121n(AV) - 0.08648ANG + 0.275901n(KV) (5.10) R2 = 0.876: SE = 0.05884 ln(MR) = 11.59293 + 0.278161n(KV) - 0.08936ANG - 0.207301n(AV) - 0.004773TT (5.11) R2 = 0.904; SE = 0.05532 ln(MR) = 8.53974 + 0.500741n(KV) + 0.169381n(CL) - 0.06156ln(AV) (5.12) R2 = 0.889: SE = 0.056 ln(MR) = 9.10392 + 0.49783ln(KV) + 0.17027ln(CL) 0.007091TT - 0.066521n(AV) (5.13) R2 = 0.926: SE = 0.05383 where ln a natural logarithm (base e) MR - resilient modulus (psi): AV = percent air voids (%): ANG = aggregate angularity: RV = asphalt kinematic xiscosity (centistokes): TT 2 test temperature ( F): CL = cyclic load (pounds): R = coefficient of multiple correlation: and SE = standard error. It should be noted that regardless of the values of R2 of equations 5.10 through 5.13, the equations are limited to a specific number of variables. Therefore, it is recommended that the reader be cautious when using these equations. Since the statistical matrix in table 5.6 is more general (includes more variables) than those in the other tables, it is used in the discussion below. Equation 5.14 163 represents the general equation relating the resilient modulus to all the independent variables of the TXCCL and TXVCL tests. ln(MR) = 9.38675 + 0.444691n(KV) + 0.163llln(CL) - 0.0061443TT - 0.09534ln(AV) (5.14) with R2 SE 0.780 0.08835 where ln = natural logarithm (base e) MR - resilient modulus (psi): AV 8 percent air voids (%): ANG - aggregate angularity: RV = asphalt kinematic xiscosity (centistokes): TT 2 test temperature ( F): CL = cyclic load (pounds). Examination of table 5.6 and equation 5.14 has indicated that: a) The most significant variable affecting the resilient modulus (MR) is the kinematic viscosity of the asphalt (KV). The value of MR increases by 26.6 percent as KV increases from 159 to 270 centistokes. b) The value of the regression coefficient corresponding to KV increases from 0.5740 to 0.5810 as the cyclic load is included in the analysis: decreases from 0.5810 to 0.4994 as the test temperature is included: and it decreases from 0.4994 to 0.4447 as the percent air voids is included. c) The regression coefficient corresponding to the cyclic load (CL) changes only when the percent air 164 voids is included in the analysis. Further, increasing CL from 200 to 900 pounds (15.9 to 71.6 psi) causes an increase of 27.8 percent in the value of MR. d) The regression coefficient corresponding to the test temperature (TT) decreases as the percent air voids is included in the analysis. The value of MR increases by 25.5 percent for a decrease in the test temperature from 77 to 40°F. e) The effect of the percent air voids (AV) on MR, relative to the other variables, is insignificant. Increasing AV from three to seven percent yields a decrease of 7.8 percent in the value of MR. f) The effects of the aggregate angularity and gradation are insignificant. The observations in items a and b indicate that KV is the most significant variable affecting MR and its effects slightly increase as the CL is included in the analysis. This was expected because at higher loads, more energy is delivered to the specimen causing an increase in the temperature (heat due to friction) and consequently a decrease in the value of the RV. Lower KV causes lower asphalt stiffness and hence, lower mix stiffness. Further, for a constant. percent asphalt content, the higher’ the percent air voids the lower the percent of voids filled with asphalt. Hence, in any cross-section through the specimen, 165 less asphalt binder and more voids can be found. Consequently, the effects of the binder decreases as the percent air voids increases. The finding in item c implies that the resilient modulus is stress-dependent. MR increases with increasing CL. It was reported (see chapter 2) that MR is either independent of stress level (Y1, K8, K9, K11, 814) or decreases with increasing stress level(B14). The finding in this research (increasing MR with increasing CL) could be related to the test procedure. Recall that in the TXVCL tests, the specimens were subjected to 1000 cycles of 200 pounds load followed by 1000 cycles for each of the 500 and 900 pounds loads. Under the 200 pounds cyclic load, the test specimen experienced plastic deformation and hence higher density. Consequently, when the 500 pounds cyclic load was applied, the measured resilient deformations were slightly less than those for virgin samples subjected immediately to 500 pounds cyclic load. That is the specimen experienced densification and work hardening due to its stress history and consequently showed higher MR. In addition, it was reported (see chapter 2) that the value of MR increases by two to four folds due to a decrease in temperature from 77 to 40°F. The finding in this research (item d) indicates an increase of only 25.5 percent. No explanation can be offered herein for this dicrepancy. One point that should be pointed, however, is that during the 166 tests, the temperature was carefully controlled to within 11°F. Nevertheless, equation 5.14 was based on 70 independent observations from a total of 77 observations of: 23 specimens (observations) from the TXCCL and 18 specimens (54 observations; one observation at each of the 200, 500, and 900 pounds cyclic load). Three specimens (12119613, 12219713, and 11329513) from the TXCCL and four observations at the 500 and 900 pounds cyclic loads of specimens 11218513 and at the 200 pounds for specimens 11318513 and 12118713 were excluded. Statistically, these seven observations showed significantly different population (results) than the other seventy, since the corresponding residuals were significantly' higher’ than the other seventy. Figure 5.7 shows a plot of the values of the resilient modulus calculated using equation 5.14 versus the measured values. Similarly, the values of the total modulus (calculated using equation 5.8) were statistically correlated to the specimen and test variables using five phases. tables 5.8 through 5.11 summarize the regression coefficients, coefficients of correlation, and standard errors of the resulting equations from each phase of the analysis. Table 5.12 shows the statistical matrix of the last phase (all specimens from TXCCL and TXVCL at 77 and 40°F). Equation 5.15 is the corresponding equation. Calculated Resilient Modulus, ksi 167 400 e TXCCL Test /. o TXVCL Test -I TI = 77°F AND 40°F R2 = 0.780 ECO—I o o 0 o _ a e . 0 e o 200—) '. o ‘35 Q; °.° o no a I oo IOO . I I 100 200 300 Measured Resilient Modulus, ksi 400 FIGURE 5.7 CALCULATED VERSUS MEASURED RESILIENT MODULUS. 168 TABLE 5.8 REGRESSION COEFFICIENT MATRIX FOR TOTAL MODULUS VERSUS SPECIMEN VARIABLES(TXCCL). E Intercept Slopes R SE ln(A ) ln(- ) A15 (10 Y) (IOKY) (10 ) ln(E) 12.639 -4.492 - - .539 .147 9.905 -3.593 4.745 - .744 .113 10.254 -3.380 4.518 -8.253 .876 .082 ln Natural logarithm (base e); E = Total modulus (psi): AV - Percent air voids (%): KV - Asphalt kinematic viscosity (centistokes): ANG 8 Aggregate angularity: GRAD a Aggregate gradation: R = Coefficient of multiple correlation; SE = Standard error. 169 TABLE 5.9 REGRESSION COEFFICIENT MATRIX FOR TOTAL MODULUS VERSUS SPECIMEN VARIABLES AND TEST TEMPERATURE (TXCCL). E Intercept Slopes R SE ln(_ ) TT ln(A ) ANg (IOKY) (10 3) (10 YI (10 2) ln(E) 7.772 7.723 - - - .425 .183 8.960 4.404 -7.589 '- - .608 .155 10.437 4.942 -9.076 -3.201 - .796 .115 10.891 4.588 -8.911 -3.l95 -8.809 .912 .078 ln a Natural logarithm (base e): E - Total modulus (psi): AV = Percent air voids (%): . RV = Asphalt kinematic viscosity (centistokes): ANG = Aggregate angularity: GRAD = Aggregate gradatiog: T3 = Test temperature ( F): R = Coefficient of multiple correlation; SE = Standard error. 170 TABLE 5.10 REGRESSION COEFFICIENT MATRIX FOR TOTAL . MODULUS VERSUS SPECIMEN VARIABLES AND CYCLIC LOAD (TXVCL). E Intercept Slopes R SE ln( ) ln(C ) ln(A ) (logy) (10 EI) (10 Y) ln(E) 8.085 7.237 - - .662 .109 7.470 7.300 9.474 - .764 .092 7.968 6.671 9.661 -1.056 .803 .085 ln Natural logarithm (base e): E a Total modulus (psi): AV - Percent air voids (%): RV = ANG 8 Aggregate angularity: GRAD = Aggregate gradation: CL = Cyclic load (pounds): R = Coefficient of multiple correlation: SE = Standard error. Asphalt kinematic viscosity (centistokes): 171 TABLE 5.11 REGRESSION COEFFICIENT MATRIX FOR TOTAL MODULUS VERSUS SPECIMEN VARIABLES, CYCLIC LOAD AND TEST TEMPERATURE (TXVCL). E Intercept Slopes R2 SE ln(_ ) TT ln(g ) ln(A ) (loKY) (10 3) (10 E) (10 Y) ln(E) 7.415 8.539 - - - .536 .160 8.827 7.237 -9.638 - - .777 .112 8.143 7.308 -9.664 1.058 - .856 .091 8.701 6.642 -10.050 1.076 -1.116 .883 .083 ln = Natural logarithm (base e): E - Total modulus (psi): AV 2 Percent air voids (%): RV = Asphalt kinematic viscosity (centistokes): ANG = Aggregate angularity: GRAD = Aggregate gradation: CL = Cyclic load (poundg): T3 = Test temperature ( F): R = Coefficient of multiple correlation: SE = Standard error. 172 TABLE 5.12 REGRESSION COEFFICIENT MATRIX FOR TOTAL MODULUS VERSUS SPECIMEN VARIABLES, CYCLIC LOAD AND TEST TEMPERATURE (TXCCL+TXVCL). E Intercept Slopes R SE ln(_ ) TT ln(g ) ln(A ) ANG (loKY) (10 3) (10 E3 (10 Y) (10 2) ln(E) 7.552 8.242 - - - - .484 .169 8.874 6.994 -8.837 - - - .695 .131 8.250 7.036 -8.841 9.785 - - .743 .121 9.012 6.144 -9.433 9.979 -l.553 - .791 .110 9.284 5.861 -9.531 10.162 -l.629 -3.617 .811 .106 ln a Natural logarithm (base e): E a Total modulus (psi): AV = Percent air voids (%): RV = Asphalt kinematic viscosity (centistokes): ANG = Aggregate angularity: GRAD= Aggregate gradation: CL = Cyclic load (pounds): T3 = Test temperature ( F): R = Coefficient of multiple correlation; SE = Standard error. 173 ln(E) = 9.284 + 0.58611n(KV) - 0.009531TT R where: 2 + 0.101621n(CL) — 0.16291n(AV) - 0.03617ANG (5.15) = 0.811: SE = 0.106 E = Total modulus (psi): all other variables have been defined previously. Comparison of the statistical matrices of the resilient and total moduli (tables 5.7 and 5.13) and their corresponding equations (5.14 and 5.15) has indicated that: a) The test temperature (TT) possesses higher effects b) C) d) e) and significance on the total modulus than on the resilient one. Decreasing TT from 77°F to 44°F results in a 42.3 percent increase in the value of the total modulus. The effects of RV on the total modulus is also higher than on the resilient modulus. Increasing KV from 159 to 270 centistokes yields an increase of 36.4 percent in the values of the total modulus compared to 26.6 percent for the resilient one. The effects of the cyclic load (CL) on the total modulus is lower than on the resilient. Increasing the CL from 200 to 900 pounds causes an increase of 16.5 percent in the values of the total modulus and 27.8 percent in the values of MR. The effect of the percent air voids(AV) on the total modulus is slightly higher than that on the f) 174 resilient. Increasing AV from three to seven percent causes a decrease of 12.9 percent in the values of the total modulus and 7.8 percent in the values of MR. Higher aggregate angularity results in lower values of the total modulus. The resilient modulus however is not affected. The above observations were expected because the values of the total modulus were calculated using the sum of the resilient and viscoelastic deformations while the values of MR the the and (in All were based on the resilient deformation. The effects of test temperature, cyclic load, and percent air voids on viscoelastic response is different than their effects on resilient response. The findings in items a, b, c, d, e imply respectively that the viscoelastic deformation proportion): a) b) C) d) decreases more than the elastic deformation with decreasing test temperature: decreases more than the elastic deformation with increasing kinematic viscosity of the asphalt: increases more than the elastic deformation with increasing cyclic load magnitudes: and increases more than the elastic deformation with increasing percent air voids. these findings were expected. The above implications (a through d) show that although the 175 resilient and total moduli depend on the same test and specimen variables, the corresponding relationships are different (in magnitude). Therefore, no explicit correlation between the resilient and total moduli can be obtained: the correlation would depend on the mix and test variables. For this reason, correlating E, by itself, to the mix and test variables is necessary. Further, from a practical point of view, the main reason behind comparing MR and E is that field testing permits only the measurement of the total modulus, whereas the analytical models for the design of asphalt pavements require the resilient modulus to be input. Figure 5.8 shows a plot of the values of the total modulus calculated using equation 5.15 versus the measured values. Recall the existing (modified) Asphalt Institue equation (equation 2.12) reported in chapter 2. Log E = C1 + C2(Pac - Popt + 4.0) (2.12) Where: E = dynamic modulus (105), (psi): C1 = 0.553833 + 0.028829(P200/f) - 0.03476(V) + 0.070377n(10 ,70) + (0.931757/f): C = 0.000005Texp(1.3 + 0.49825Log f) - (0.00189T(exp(1.3 + 0.49825Log f)/f): P200 = percent passing the #200 sieve: 176 400 e TXCCL Test / o TXVCL Test 9;) .- 5: TT = 77°F AND 40°F / g); R2 = 0.811 ' 3 300— E o _ O .00 g 4 ,2 “e '8 Q” o :5 ZOO-d 0° <9 o' 3 O O 0 g 000 .9 o o q 06’ 0 0 o e O 4 100 I I I I W 100 200 300 Measured Total Modulus, ksi 400 FIGURE 5.8 CALCULATED VERSUS MEASURED TOTAL MODULUS. f V n(10, T Pac Popt 177 = loading frequency (Hz): = volume of voids (percent): 70) viscosity of the asphalt cement at 70°F; temperature of pavement: = asphalt content in percent by total weight: and optimum asphalt content. Comparison of equations 5.14 and 5.15 with equation 2.12 shows: a) b) d) The magnitude of the dynamic modulus reported in equation 2.12 is about twice as high as the values reported in this research: Decreasing the test temperature from 77 to 40°F causes an increase in the value of the dynamic modulus by a factor of 4, as compared to 25.5 and 40 percent increase for the resilient and total moduli in this investigation: Increasing the percent air voids from three to seven causes a decrease of 27.4 percent in the value of the dynamic modulus, as compared to 7.8 and 12.9 percent for MR and E of this investigation Increasing the viscosity of the asphalt (at 70°F) from 162 to 793 poises causes an increase of 10.8 percent in the dynamic modulus value, as compared to MR and E increasing by 26.6 and 36.4 percent, respectively, for an increase in RV from 159 to 270 178 centistokes. A plot of the values of the resilient modulus calculated from equation 2.12 versus the measured values at 77°F is shown in figure 5.9. §IA_ELA§IIQ_DEEQBHAIIQE The cumulative plastic (permanent) strain (ep) measured from the TXCCL tests was statistically correlated to the number of load repetitions (N), test temperature (TT), and the mix variables using the SPSS/PC+ program and the stepwise procedure. The correlations were conducted in two phases. In the first phase, the measured plastic strain at 77°F ‘were 'used: the «corresponding statistical matrix is presented in table 5.13. In the second, measured plastic strain at 77 and 40°F were used: the statistical matrix is summarized in table 5.14. It should be noted that (in the first phase) the results from two tests (specimens 12219713 and 21219613) were excluded because they were statistically different from the results of the other 24 tests. Examination of the values of the regression coefficients listed in tables 5.13 and 5.14 indicated that: a) The value of the regression coefficient of ln(N) varies from 0.2853 to 0.3364. This was expected and consistent with that reported by Bonnaure etal (Bll) (from 0.14 to 0.3). b) AV and KV are the most important specimen variables 179 .mDDDQOE Hzm_.__mmm ommamfii m3mmm> 20.233. Ebb-Hm; 5X... o «mo... ..ooxp e I I T III I I COP com com 00¢ com com uogianbg anmsul )(Dudsv eu; Bugsn sninpow peiomoiog l$>I 180 affecting plastic deformation. It should be noted that, in this study, the effects of the magnitude of cyclic load was not assessed because all the TXVCL tests were conducted for only 1000 cycles for each cyclic load. Also, the statistical matrix in table 5.14 was obtained using measured results from 26 tests. Equations 5.16 and 5.17 express the cumulative plastic strain as a function of TT, N, AV, KV and ANG. first phase) the results from two tests (specimens 12219713 and 21219613) were excluded because they were statistically different from the results of the other 24 tests. Examination of the values of the regression coefficients listed in Tables 5.13 and 5.14 indicated that: a) The value of the regression coefficient of ln(N) varies from 0.2853 to 0.3364. This was expected and consistent with that reported by Bonnaure et al (0.14 to 0.3) (Bll). b) AV and KV are the most important specimen variables affecting plastic deformation. It should be noted that, in this study, the effects of the magnitude of cyclic load was not assessed because all the TXVCL tests were conducted for only 1000 cycles for each cyclic load. Also, the statistical matrix in Table 5.14 was obtained using measured results from 26 tests. Equations 5.16 and 5.17 express the cumulative plastic strain as a function of TT, N, AV, KV and ANG. 181 TABLE 5.13 REGRESSION COEFFICIENT MATRIX FOR STRAIN VERSUS SPECIMEN VARIABLES(TXCCL) . TIVE ep Intercept Slopes R SE ln(N) A21 ln(KV) ANG1 (10 ) (10 ) (10 ) ln(e ) 0.531 3.064 - - - .353 0.740 p -1.329 3.236 3.572 - - .669 0.532 8.355 3.306 3.055 -1.721 - .790 0.426 9.128 3.364 3.171 -1.771 -1.819 .817 0.400 Samples 12219713 and 21219613 are not included. a Natural logarithm (base e):_ Axial cumulative strain (10 Number of load repetitions: Percent air voids (%): Aggregate angularity: Aggregate gradatio : Test temperature ( F): 4): Asphalt kinematic viscosity (centistokes): R = Coefficient of multiple correlation: Standard error. 182 TABLE 5.14 REGRESSION COEFFICIENT MATRIX FOR CUMULATIVE STRAIN VERSUS SPECIMEN VARIABLES AND TEST TEMPERATURE (TXCCL) . ep Intercept Slopes R2 SE TT ln(N Ay ln(_ ) AN9 (10 2)(10 l)(10 1) (loKY) (10 1) ln(e ) -1.463 5.471 - - - - .491 0.851 p -4.160 6.300 2.853 - - - .704 0.652 -6.051 6.700 2.955 3.105 - - .836 0.487 0.662 6.810 2.987 2.759 -12.074 - .875 0.427 1.908 6.844 3.022 2.744 -13.434 -1.652 .888 0.406 Samples 12219713 and 21219613 are not included 2 Natural logarithm (base e):_ Axial cumulative strain (10 Number of load repetitions; Percent air voids (%): Asphalt kinematic viscosity (centistokes): Aggregate angularity: Aggregate gradatiog: Test temperature ( F): Coefficient of multiple correlation: Standard error. 4 ) o I where: F < H" “II“ N 183 9.1285 + 3.3641n(N) + 0.3171AV - l.77lln(KV) - 0.1819ANG (5.16) = 0.817; SE 3 0.4003 1.9076 + 0.06844TT + 0.30221n(N) + 0.2744AV — 1.3434ln(KV) - 0.1652ANG (5.17) = 0.888; SE = 0.4062 natural logarithm (base e): test temperature ( F): number of load repetitions: percent air voids (%): asphalt kinematic viscosity (centistokes): and aggregate angularity. The difference between the two equations is that equation 5.17 accounts for the effects of the test temperature. A sensitivity analysis of equation 5.17 has indicated that: a) b) C) d) e) Increasing TT from 40 to 77°F causes an increase in the plastic strain by a factor of about 12.5. Increasing the value of AV from three to seven percent causes an increase in plastic strain by a factor of three. Increasing KV from 159 to 270 centistokes causes a decrease of 51 percent in the plastic strain. Increasing aggregate angularity from 2 to 4 yields a decrease in the plastic strain by about twenty-eight percent. There is a little interaction between the independent variables TT, N, AV, KV, and ANG. 184 The above observations imply that the plastic (permanent) deformation of flexible pavement can be improved by either decreasing the percent air voids in the asphalt course, using higher viscosity asphalt, and using crushed aggregate. This, however, should not imply that the fatigue life of the pavement is improved. Lower temperatures and percent air voids, and higher viscosity and aggregate angularity yield stiffer and more brittle asphalt mixes. Consequently, the magnitude of plastic strain that causes fatigue is substantially reduced. That is, the pavement engineer should be cautious in using the above results: decreasing permanent deformation may not improve the fatigue life of the pavement system. Figure 5.11 shows the calculated versus measured values of the cumulative plastic strain at load cycles 100 to 10000. §I§_EHQQHIIHED_§QHEB§§§I¥E_§IBE!§IH As discussed in chapters 3 and 4, unconfined static compression tests were performed on virgin specimens as well as specimens that have already been tested under variable peak cyclic load tests (TXVCL). No differences were observed between the measured unconfined compressive strengths of both types of specimens. Results obtained from both specimen types were included in one statistical analysis. The correlations were conducted in two phases (77°F, and77and 185 100 E: o N = 100 .- - a N = 500 / .9: A N - 1000 g 80- . N - 5000 03 v N = 10000 / .3 TXCCL Test // 8 50_ TT - 77°F AND 40°F / o“. R1 = 0.888 4) q .3 v / v °v 2 a 3 :8: v 0 0 0 v '8 o ‘5 '5 2 O o T T Y I T 60 80 100 Measured Cumulative Plastic Strain, 10“ FIGURE 5.10 CALCULATED VERSUS MEASURED CUMULATIVE PLASTIC STRAIN. 186 40°F).The statistical matrices corresponding to the two phases are summarized in Tables 5.15 and 5.16, respectively. It should be noted that results from two specimens (21216613 and 21218613) at 77°F were statistically different relative to the other 38 specimens and consequently they were excluded from the analysis. Also, the unconfined compressive strength of only two specimens were included in the analysis because all other specimens did not fail when the capacity of the load cell (10000 pounds) was reached. Equations 5.18 and 5.19 express the unconfined strength as a function of TT, AV, RV and GRAD. ln(Su) - 4.239 - 0.14239AV + 0.003055KV + 2.267GRAD (5.18) R2 - 0.804: SE - 0.158 ln(Su) = 6.290 + 0.003056KV - 0.02664TT - 0.1424ln(AV) + 2.267GRAD (5.19) R2 = 0.858: SE - 0.156 where: ln = natural logarithm (base e): S a unconfined compressive strength (psi); GRAB - aggregate gradation quantified here by the percent passing sieve No. 4 (GRAD = 0 to 1): all other terms in the equation have been defined previously. The difference between the two equations is that equation 5.19 accounts for the effects of the test temperature. Examination of the values of the regression coefficients listed in Tables 5.15 and 5.16 and in equations 5.18 and 5.19 indicated that: 187 TABLE 5.15 REGRESSION COEFFICIENT MATRIX FOR UNCONFINED * COMPRESSIVE STRENGTH VERSUS SPECIMEN VARIABLES . SU Intercept Slopes R SE Ayl KY3 GRAD (10 ) (10 ) 6.169 -1.337 - - .508 .244 5.230 -1.143 3.482 - .685 .198 4.239 -1.424 3.055 2.267 .804 .158 Samples 21216613 and 21218613 are not included. Natural logarithm (base e): Unconfined compressive strength (psi): Percent air voids (%): Asphalt kinematic viscosity (centistokes): Aggregate angularity: Aggregate gradation: Coefficient of multiple correlation: Standard error. 2 TABLE 5.16 REGRESSION COEFFICIENT MATRIX FOR UNCONFINED 188 COMPRESSIVE STRENGTH ¥ERSUS SPECIMEN VARIABLES AND TEST TEMPERATURE . SU Intercept Slopes R2 SE K23 T22 Ayl GRAD (10 ) (10 ) (10 ) 1n(sU) 4.300 5.252 - - - .315 .329 6.093 4.652 -2.190 - - .518 .279 7.480 3.482 -2.922 -1.143 - .772 .195 6.290 3.056 -2.664 -l.424 2.267 .858 .156 * Samples 21216613 and 21218613 are not included. In a Natural logarithm (base e): S a Unconfined compressive strength (psi): A9 = Percent air voids (%): RV = Asphalt kinematic viscosity (centistokes): ANG = Aggregate angularity: GRAD = Aggregate gradatiog: T3 = Test temperature ( F): R = Coefficient of multiple correlation: SE = Standard error. 189 a) TT is the most important variable affecting the strength of asphalt concrete mixes. Decreasing TT from 77 to 40°F causes an increase in the strength by 170 percent. b) The regression coefficients corresponding to the specimen variables remained unchanged when TT was included in the analysis. c) Increasing AV from three to seven percent causes a decrease in strength by 57 percent. d) Increasing KV from 159 to 270 centistokes yields a 40 percent increase in the strength. e) Increasing the percent passing sieve #4 from 49.8 to 61.4 percent causes a 30 percent increase in the strength value. The above observations suggest that the strength of asphalt concrete could be correlated to the resilient and/or total moduli, since all three quantities depend mainly on the test temperature, the percent air voids, and the kinematic viscosity of the asphalt. However, because the relative effects of these varibles on the strength are different than those on MR, and those on E, an explicit correlation between the strength on one hand, and the resilient and total moduli on the other cannot be obtained. Such a correlation would be dependent on the mix and specimen variables. Figure 5.12 shows the calculated versus measured values of the unconfined compressive strength. 190 .Ipozmmbm m>_mmmmn_500 szlzooz: amm3m 35530.20 :6 “$50.... 6d .5985 o>_mmo.ano noeccoocn omSmooE 00m 0mm own odes own owm om: o o 1.00— i com I com 1 00¢ 1 com some .. .m loom 1.9. oz... 8R .1. t con 15d 'UlDUSJlS GAISSGJOUJOQ pauguoaun palolnoiag 191 It should be noted that the total axial strain at failure did not correlate well to the mix and test variables. é;§_£BEEE_§EABAQIEBI§IIQ§ Material creep can be defined as the total deformation with respect to time under a constant applied load. In this study, triaxial specimens were subjected to a constant stress of 71.6 psi (900 pounds load) and the resulting time- dependent deformations were measured. The creep strain (ec) is defined by the ratio of the measured deformations to the original specomen length. Knowing the creep strain and the applied stress, the creep compliance (J(t)) can then be calculated using equation 5.20. J(t) = ec/oo (5.20) where J(t) = creep compliance: ec = axial time-dependent strain: oo = applied stress 8 applied load/cross-sectional area. Figure 5.12 shows a typical plot of the axial creep strain versus time. The curve consists of three regions: a) primary, creep rate decreases: b) secondary, creep rate is constant; and c) tertiary, creep rate increases. The characteristics of the creep curve in the secondary region is used herein to study the effects of mix and test 192 E S .7. ( ) ’1 Time I a I 1 ‘ I I .._, l 1 l 1 5 \ I ' / I l g 1 , / 03 I I 1 l 0 I f II 1 III ( ) t, Time I b FIGURE 5.12 (Afib) CONSTANT-STRESS CREEP TEST: (8) Basic Creep Curve; (b) True Strain Rate versus Time. 193 variables upon the axial creep strain. The strain in the secondary creep is given by (A6): e = ei+ ec (5.21) where the pseudo-instantaneous strain ei is governed by: ei = F(o,T) (5.22) and the creep strain ec by the creep law: ..... = e = G(o,T) (5.23) where: o = applied stress: and T a temperature. Both ei and eC were statistically correlated to the specimen variables and test temperature using the SPSS/PC+ program and the stepwise procedure. Test results from 16 specimens at 77°F and one specimen at 40°F were included in the analysis. Results obtained from four tests were not included because two specimens were failed upon loading and the other two showed statistically different results from the other 16 tests. Examination of the secondary creep data have indicated that both ei and ec are independent of temperature. Consequently, results at 77 and 40°F were together used in the statistical analysis. Further, it was found that both ei and ec are a function of the percent air voids. (see equations 5.24 and 5.25). ei = 25.117 + 5.741AV (5.24) 194 R2 = 0.539; SE = 11.229 ln(ec) = -4.732 + 0.906Av (5.25) R2 = 0.529; SE = 1.825 where: _4 ec = secondary creep rate (10 /min)£ e. = pseudo-instantaneous strain (10 in/in): A? = percent air voids (%): R = coefficient of multiple correlation: and SE = standard error. Examination of the equations indicates that the only variable affecting the secondary creep rate (eC and the ) pseudo-instantaneous strain (ei) is the percent air voids (AV): it increases by a factor of 37.5 and 21 respectively as the percent air voids (AV) increases from 3 to 7. Combining equations 5.24 and 5.25, and dividing by the applied stress (71.6 psi), one can obtain the secondary creep compliance a function of time and percent air voids. Jt = (0.3508 + 0.0802AV) + t*exp(-9.0031 + 0.906AV) (5.26) where: _4 = secodary creep compliance (10 /psi): E = time (min): exp = exponential: and AV = percent air voids(%). J Equation 5.26 states that for a constant static load, both the initial and future creep strains depend only on the percent air voids. This implies that in the field, compaction is the most important factor to control, when dealing with static loads. 195 Figure 5.13 shows the calculated versus the measured values of the secondary creep compliance. 196 A“ 10 3 ,/ q, ..TT=77°F AND 40°F // o / c / 8 ... / E . / o —1 o / Q. / .. 6— 138 ' // o.\ . . . I 82 . 8 .' - / $ ‘ 0 . 9 e U 2_ . (D ' e E .‘ § " 1:!“ o o O T I T I T I T I T 0 2 4 6 8 IO Measured Seconda Creep Compliance (J1) 1 "/p51 FIGURE 5.13 CALCULATED VERSUS MEASURED SECONDARY CREEP COMPLIANCE. CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS £51.99N9LHSIQNE On the basis of the test results of this study and in the range of the test and sample variables, the following conclusions concerning the structural properties of asphalt concrete mixes obtained from unconfined triaxial tests were drawn: a) b) C) d) The resilient modulus was found to be a function of several variables. These include the stress level, the test temperature, the kinematic viscosity of the asphalt, and the percent air voids. Equation 5.14 was found to model the resilient modulus. The total modulus was found to be a function of the above variables as well as the aggregate angularity. Equation 5.15 was found to model the total modulus. The cumulative plastic strain was found to be a function of the number of load repetitions, test temperature, percent air voids, kinematic viscosity of the asphalt, and aggregate angularity. Equation 5.17 was found to model the cumulative plastic strain. The unconfined compressive strength was found to be a function of the test temperature, percent air voids, and aggregate gradation. Equation 5.19 was found to 197 198 model the unconfined compressive strength. e) The secondary creep compliance was found to be a function of the percent air voids. Equation 5.26 was found to model the secondary creep compliance for a stress of 72 psi. f) The asphalt institute equation (2.12) was found to overpredict the values of the resilient modulus, measured in this investigation, by a factor of two. .§12_BEQQ!MEEDAIIQE§ The results in this investigation has led to the development of five statistical equations relating each of the structural properties of asphalt concrete mixes obtained from triaxial testing to the test and specimen variables. Due to variations in the results, it is recommended that triplicates be employed for each combination of the variables. 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Yoder, E.J., "Selection of Soil Strength Values for the Design of Flexible Pavements," Highway Research Board Record no. 276, 1969, pp. 1-13. Young, M.A., and Baladi, G.Y., "Repeated Load Triaxial Testing, State of the Art," Michgan State University, Division of Engineering Research, 1977. D.c., 1975, pp. 26-38. Yoder, E.J-. and Witczak. M-W-..Eriueiele§_2f_£axement Design, second edition, John Wiley & Sons, Inc., 1975. APPENDIX A 217 TABLE A.1 UNCONFINED TRIAXIAL CONSTANT PEAK CYCLIC LOAD TESTS. SAMPLE HA wn A.C. SL CL wnw WBA GMM A.V. NUMBER (8r) (8:) (t) (lbs) (lbs) (8r) (8:) (%) 11119513 4200 189 4.31 50 500 2455.5 4075.1 2.546 1.17 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 4.5 6.0 14.7 5.2 5.8 5.2 3.9 4.6 5.2 500 4.2 5.6 38.5 5.0 5.5 12.0 4.4 5.2 13.8 1000 4.2 5.5 59.1 5.0 5.5 15.4 3.9 4.4 21.0 5000 3.8 5.1 146.6 5.0 5.6 33.6 3.8 4.4 47.6 10000 3.7 5.2 203.8 4.9 5.6 46.2 3.7 4.4 63.2 WWWWWW SAMPLE WA 88 A.C. SL 0L wnw WBA GMM A.V. NUMBER (8:) (Sr) (3) (lbs) (lbs) (8r) (8:) (t) 11119613 4200 189 4.31 50 500 2353.6 3960.3 2.546 3.19 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 102 5.9 9.4 49.0 5 4 6.4 20.7 4.0 5.0 10.3 500 6.1 10.1 98.5 5.4 6.6 40.0 4.1 5.2 18.6 1000 6.1 10.1 126.5 5.6 7.1 52.6 4.1 5.4 24.2 5000 5.9 10.8 223.0 6 1 8.6 78.9 4.4 6.2 34.8 10000 6.1 11.1 272.7 6 5 9.5 104.7 4.7 6.8 ' 39.8 VA - TOTAL WEIGHT 0? DRY AGGREGATES; VB - WEIGHT 0F BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; "BU - WEIGHT 0F SAMPLE IN WATER; CL - CYCLIC LOAD; NBA - WEIGHT 0F SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 218 TABLE A.1 (CONTINUED). SAMPLE WA wn A.C. SL CL waw wnA GMM A.v. NUMBER (8:) (Sr) (3) (lbs} (1b8) (3r) (Sr) (%) 11119713 4200 189 4.31 50 500 2159.8 3754.9 2.546 7.54 DEPORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 108 8.5 14.6 66.5 4.0 5.6 26.0 3.4 4.8 22.0 500 8.8 15.7 181.5 4.0 5.2 74.0 3.2 4.6 52.0 1000 8.6 15.8 276.5 3.6 4.4 120.0 3.2 4.6 78.0 5000 8.9 17.2 679.5 - - 412.0 2.8 3.8 224.0 10000 9.7 17.8 1050.0 - - 720.0 3.2 3.8 390.0 WNWWWWHWW SAMPLE WA wn A.C. SL CL wnw wnA CMM A.V. NUMBER (at) (Sr) (%> (1b8) (lbs) (at) (at) (t) 11219613 4200 186 4.25 50 500 2317.3 3925.2 2.547 4.15 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 6.3 11.3 48.0 2.8 4.0 15.0 2.5 3.7 15.0 500 6.7 12.3 139.0 2.9 4.0 35.0 2.5 3.8 36.0 1000 6.9 12.6 199.0 2.9 3.9 50.0 2.5 3.7 51.0 5005 7.1 13.5 423.0 2.9 3.9 115.0 2.6 4.0 109.0 10000 7.4 14.0 587.0 2.9 3.8 164.0 2.6 4.1 156.0 WA - TOTAL WEIGHT OP DRY AGGREGATES; VB WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBU - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; UBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 219 TABLE A.1 (CONTINUED). SAMPLE WA wn A.C. SL CL wnw wRA CMM A.v. NUMBER (81') (81') 6) (lbs) (lbs) (81') (gr) (‘3) 11119523 4200 189 4.31 50 500 2352.0 3974.2 2.546 3.78 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. 'ro'r. PLA. ELA. 'ro'r. PLA. ELA. 'ro'r. PLA. 100 16.9 18.8 27.1 2.5 2.8 4.1 2.5 2.8 3.7 500 16.8 18.7 47.5 2.5 2.9 9.1 2.5 2.8 8.9 1000 16.8 18.9 59.1 2.5 2.9 12.3 2.5 2.9 12.1 5000 17.0 19.1 90.0 2.6 3.1 21.3 2.6 3.1 21.2 10000 16.9 19.0 104.3 2.7 3.3 25.8 2.5 3.1 25.9 131900 16.7 19.2 167.3 - - 38.2 - - 38.4 361700 16.9 19.4 196.2 - - 45.3 - - 45.4 “WWW SAMPLE WA wn A.C. SL CL wnw WBA CMM A.v. NUMBER (Sr) (81’) (t) (lbs)<1bs) (81‘) (at) (t) 11119623 4200 189 4.31 50 500 2283.1 3889.6 2.546 4.90 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 18.5 21.2 44.1 2.9 3.0 1.6 2.5 2.7 0.9 600 18.5 21.6 83.9 3.0 3.1 2.1 2.5 2.7 0.5 1000 18.4 21.4 99.3 3.1 3.3 2.0 2.5 2.7 0.7 5000 18.2 21.9 160.0 3.2 3.4 1.4 2.6 2.8 0.3 10000 17.9 21.4 192.8 3.1 3.2 1.2 2.6 2.8 0.6 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE A.1 (CONTINUED). 220 SAMPLE NUMBER WA (St) W3 A.C. (8r) (%) SL CL (lbs) (lbs) WBW (3r) WBA (gr) GMM A.V. (%) 11119723 4200 189 4.31 50 500 2190.0 3755.6 2.546 5.78 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 19.2 23.3 84.3 3.8 4.0 8.5 2.7 2.9 7.8 500 19.2 23.8 172.1 3.9 4.1 21.0 2.5 2.8 19.5 1000 19.3 23.9 229.5 3.8 4.1 32.0 2.7 3.0 29.4 5000 19.2 23.9 431.2 3.8 4.1 85.3 2.6 3.0 77.8 10000 19.0 23.8 569.3 3.9 4.2 34.5 2.5 3.0 21.5 *WWWW SAMPLE NUMBER WA (St) 93 A.C. (at) (t) SL CL (lbs) (lbs) (Sr WBW ) WBA GMM A.V. (gr) (3) 11219513 4200 186 4.25 50 500 2365.0 3991.4 2.547 3.65 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 19.5 22.7 48.2 - 3.0 5.5 3.1 3.7 6.3 500 19.0 22.2 87.2 - 2.5 11.9 2.7 3.5 13.0 1000 18.7 22.1 108.3 - 2.4 15.4 2.8 3.4 17.6 5000 18.9 22.4 162.5 - 2.5 27.9 3.0 3.9 32.7 10000 18.8 22.4 194.7 - 2.7 36.2 3.1 4.0 40.0 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT 0F SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT 0F SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 221 TABLE A.1 (CONTINUED). SAMPLE WA W8 A.C. SL CL waw WBA CMM A.V. NUMBER (8:) (3r) (%) (lbs) (lbs) (at) (Sr) (%) 11319513 4200 178 4.07 50 500 2304.8 3921.8 2.553 5.00 DEFORMATION (inches x 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 18.4 24.1 40.1 2.2 2.7 19.9 - 2.3 4.2 500 18.9 25.2 86.3 8.0 3.0 30.7 - 2.3 14.1 1000 19.4 25.4 114.7 2.0 3.1 36.8 - 2.4 23.4 5000 19.4 26.4 209.2 2.3 3.3 51.6 - 2.6 41.7 10000 19.6 26.0 272.3 2.3 3.1 67.8 - 3.0 64.2 “WWW SAMPLE WA WB A.C. SL CL wnw wnA CMM A.V. NUMBER (8!) (at) (t) (lbs) (lbs) (8:) (at) (t) 12119513 4200 196 4.46 50 500 2410.3 4044.1 2.543 2.66 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 125 17.3 19.7 38.9 - - 6.9 1.3 1.7 2.7 500 16.0 18.2 61.2 - - 8.7 1.0 1.4 4.2 1000 15.3 17.6 74.7 - - 9.8 0.9 1.2 5.3 5000 14.2 16.2 118.3 - - 12.2 0.5 0.9 9.3 10000 14.6 16.7 147.8 - - 13.8 0.7 1.1 12.3 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WEA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE A.1 (CONTINUED). 222 SAMPLE NUMBER WA (St) VB A.C. (at) (t) SL (lbs) (lbs) CL WBW (Er) wBA (gr) CMM A.V. (%) 12119613 4200 196 4.46 50 500 2294.7 3920.8 2.543 5.18 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. T0T. PLA. ELA. TOT. PLA. ELA. T0T. PLA. 100 15.5 17.4 31.5 - - 1.0 1.5 2.2 1.4 500 15.0 17.9 51.4 - - 2.6 1.4 2.2 4.8 1000 15.5 17.7 62.7 - - 3.7 1.4 2.2 6.6 5100 15.3 17.5 93.8 - - 5.1 1.5 2.3 11.9 9600 14.8 17.5 108.0 - - 6.1 1.5 2.4 14.3 WWW SAMPLE NUMBER WA (Sr) VB A.C. (at) (5) SL (lbs) (lbs) CL VBV (8r) WBA (3r) GMM A.V. (t) 12119713 4200 196 4.46 50 500 2245.4 3865.3 2.543 6.17 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 18.3 22.1 45.5 -1.9 -2.5 9.6 1.3 2.5 2.7 500 19.8 23.6 90.5 -2.8 -3.3 14.2 2.1 3.5 6.3 1040 19.8 25.0 111.3 -3.2 -4.0 18.6 3.0 4.2 8.5 5000 24.5 28.6 168.6 -4.3 -5.8 33.6 4.5 5.7 13.8 10000 24.8 29.6 202.2 -6.3 -6.0 46.0 5.5 6.2 19.4 WA - TOTAL WEIGHT 0P DRY ACCRECATES; VB - WEIGHT 0? BITUMEN; A.C. WBW WBA GMM - PERCENT ASPHALT CONTENT; - WEIGHT OF SAMPLE IN WATER; - WEIGHT OF SAMPLE IN AIR; - MAXIMUM SPECIFIC GRAVITY; SL - CL - A.V.- SUSTAINED LOAD; CYCLIC LOAD; PERCENT AIR VOIDS; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 223 TABLE A.1 (CONTINUED). SAMPLE WA NUMBER (gr) VB A.C. SL CL (st) (8) (lbs) (lbs) 21119523 4200 175 3.99 50 WBW (3r) VBA (8r) CMM A.V. (%) 500 2413.8 4049.8 2.539 2.50 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 13.5 15.4 30.0 0.4 0.7 4.4 0.3 0.5 5.1 510 13.3 14.9 53.5 0.4 0.6 10.6 0.3 0.4 11.4 1000 13.3 15.1 66.6 0.4 0.6 14.4 0.3 0.5 15.1 5155 13.2 15.0 107.5 0.5 0.7 26.8 0.4 0.7 27.3 9300 13.1 15.0 124.9 0.6 0.8 32.4 0.4 0.7 32.6 WNW SAMPLE WA NUMBER (gr) VB A.C. SL CL (Sr) (t) (lbs) (lbs) 21119613 4200 175 3.99 50 WBW (8r) WBA CMM (8r) A.V. (%) 500 2299.3 3910.2 2.539 4.40 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 110 14.8 17.3 31.4 - - 8.0 0.9 1.4 5.7 500 14.8 17.0 53.3 - - 13.7 0.9 1.4 7.3 1000 14.8 17.3 67.7 - - 17.4 0.7 1.3 8.3 5000 14.8 17.3 115.4 - - 29.4 0.6 1.2 12.2 10000 14.8 17.3 144.3 - - 36.8 0.5 1.1 14.5 WA - TOTAL WEIGHT 0F DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 224 TABLE A.1 (CONTINUED). SAMPLE WA NB A.C. SL CL WBW WBA CMM A.V. NUMBER (8:) (8:) (t) (lbs) (lbs) (at) (Sr) (%) 21119713 4200 175 3.99 50 500 2173.0 3750.9 2.539 6.37 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TCT. PLA. ELA. T0T. PLA. ELA. TOT. PLA. 117 16.4 20.6 91.1 2.6 3.4 17.4 1.5 2.1 19.6 500 16.3 21.0 187.3 2.7 3.5 35.2 1.5 2.2 40.9 1000 16.1 20.7 256.1 2.8 3.6 50.8 1.4 2.2 56.8 5000 16.5 21.9 499.8 2.8 3.9 123.8 1.5 2.4 123.1 10000 16.4 22.1 670.4 2.8 4.0 188.2 1.4 2.4 175.1 WWW SAMPLE VA VB A.C. SL CL VBV WBA CMM A.V. NUMBER (8r) (8:) C‘) (lbs) (lbs) (Br) (at) <%) 21219613 4200 176 4.03 50 500 2247.4 3850.7 2.537 5.33 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 15.7 17.0 17.7 -0.9 -1.0 -1. 500 15.2 17.7 34.2 -0.9 -1.0 -2. 1000 15.5 17.6 42.8 -0.9 -0.9 -2. 5000 15.5 17.2 74.3 -0.8 -0.9 -4. 10000 16.0 17.7 93.3 -0.7 -0.8 -5. -1.0 -1.3 -2.7 -0.9 -1.1 -3.8 -1.2 -5.3 -1.1 -1.4 -14.5 -1.0 -1.3 -22.2 P'F‘O\h‘¥‘ I H ..A WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 225 TABLE A.1 (CONTINUED). SAMPLE WA VB A.C. SL CL wa VBA CMM A.V. NUMBER (at) (at) (8) (lbs) (lbs) (8r) (gr) (%) 21319613 4200 175 3.99 50 500 2288.0 3899.6 2.537 4.62 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 17.5 22.7 105.1 2.6 4.3 34.1 1.9 3.7 34.7 520 18.6 24.3 239.6 2.9 5.0 78.8 2.8 4.7 79.4 1000 18.0 25.1 324.6 3.1 5.4 110.6 2.7 5.3 116.3 5000 18.5 26.3 653.0 3.6 6.6 259.0 3.2 6.4 273.0 9000 18.7 27.9 855.9 4.0 7.1 365.3 3.4 6.8 378.2 SAMPLE WA VB A.C. SL CL VBV VBA CMM A.V. NUMBER (8r) (8:) (8) (lbs) (lbs) (at) (Sr) (1) 12219713 4200 197 4.48 50 500 2058.2 3592.5 2.541 7.85 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 18.5 22.1 47.1 2.9 3.7 10.7 3.1 4.1 9.4 580 17.8 21.6 107.4 3.9 4.8 12.9 3.2 4.1 19.9 1000 17.8 21.7 135.4 3.9 4.8 15.2 3.3 4.2 25.1 5000 17.6 21.9 162.0 4.3 5.1 33.9 3.6 4.7 50.8 10000 17.6 21.6 235.0 4.1 5.0 52.0 3.7 4.9 70.5 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 226 TABLE A.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA CMM A.V. NUMBER (at) (Sr) (t) (lbs) (lbs) (8r) (8:) ($) 31119713 4200 182 4.16 50 500 2111.5 3644.9 2.541 6.45 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 14.3 16.3 31.9 - - 5.1 - - 6.2 500 14.4 16.3 73.1 - - 12.8 - - 15.2 1000 14.2 16.1 105.8 - - 19.2 - - 22.6 5000 14.4 16.3 232.3 - - 46.2 - - 53.2 10000 14.3 16.4 313.9 - - 64.3 - - 74.5 SAMPLE VA VB A.C. SL CL VBV VBA CMM A.V. NUMBER (8:) (gr) (t) (lbs) (lbs) (8:) (Sr) (%) 31119513 4200 182 4.16 50 500 2404.5 4033.9 2.541 2.57 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 13.4 14.6 24.3 2.1 2.4 5.7 1.6 2.0 5.0 500 13.4 14.6 48.8 1.8 2.2 9.0 1.5 1.9 8.3 1000 13.5 14.9 65.6 1.9 2.2 11.4 1.6 1.9 10.4 5000 13.4 15.1 119.7 2.3 2.5 19.7 1.8 2.1 18.3 10000 13.5 15.1 153.5 2.4 2.6 26.3 1.9 2.3 23.5 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT 0F SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; CMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEPORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 227 TABLE A.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (8:) (at) (t) (lbs) (lbs) (8r) (3:) (%) 32119613 4200 193 4.40 50 500 2233.4 3848.7 2.530 5.82 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 13.7 16.3 47.2 1.0 1.5 9.3 0.6 0.9 9.0 500 13.7 16.7 107.2 1.0 1.4 16.9 0.6 0.9 19.7 1000 13.8 16.8 148.5 1.0 1.3 24.6 0.7 0.9 27.3 5000 13.9 17.2 292.6 1.0 1.4 57.1 0.7 1.0 56.4 10200 14.1 17.9 379.5 1.0 1.3 77.8 0.7 1.0 75.3 WWW SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (8:) (st) (t) (lbs) (lbs) (8:) (8r) (%) 22119613 4200 188 4.28 50 500 2315.1 3947.7 2.520 4.05 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 15.1 17.4 44.4 1.4 1.9 7.6 1.3 1.8 13.1 500 15.1 18.0 80.8 1.5 1.9 13.4 1.2 1.6 21.9 1000 15.1 18.2 103.2 1.5 2.0 16.3 1.3 1.7 26.1 5000 15.1 18.7 176.7 1.6 2.2 23.1 1.4 1.9 37.4 10000 15.0 18.9 218.0 1.7 2.3 28.0 1.4 2.0 44.2 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEPORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OP THE SAMPLE. 228 TABLE A.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (8!) (8r) (5) (lbs) (lbs) (8r) (Er) (%) 12319713 4200 186 4.24 50 500 2089.0 3640.7 2.549 7.95 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 22.4 31.1 313.9 1.6 3.3 68.7 2.0 3.9 50.6 500 22.5 32.2 604.8 1.9 3.8 173.1 2.3 4.2 182.1 1000 23.0 32.4 853.6 2.3 4.5 279 9 2.5 4.4 292.3 3000 21.5 31.1 1696.8 3.7 6.4 748 7 5.9 9.3 722.1 5000 25.2 36.0 2686.4 3.4 6.6 1487.9 6.2 11.5 1519.6 SAMPLE WA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (Sr) (8:) (9) (lbs) (lbs) (8:) (8r) (3) 11329513 4200 178 4.07 50 500 2288.3 3908.8 2.553 5.52 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 14.6 15.1 8.7 1.5 1.5 -1.4 1.0 1.0 -0.7 500 14.5 14.9 11.6 1.6 1.7 -2.0 1.1 1.2 -0.7 1000 14.2 14.7 13.3 1.7 1.8 -2.4 1.2 1.2 -0.6 5200 13.9 14.2 18.6 2.0 2.1 -2.7 1.3 1.4 -0.2 10000 13.6 13.9 19.1 2.1 2.1 -2.6 1.4 1.5 0.1 36000 12.6 12.8 24.7 2.1 2.2 -1.3 1.4 1.5 1.5 188000 11.6 11.6 30.3 1.9 2.0 0.5 1.3 1.4 3.7 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 229 TABLE A.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (Ct) (at) (%) (lbs) (lbs) (Sr) (8r) (%) 22129613 4200 188 4.28 50 500 2253.9 3881.4 2.520 5.36 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 12.8 13.6 11.4 0.3 0.3 1.6 -0.3 -0.4 0.6 500 12.5 13.2 14.3 - - 2.5 -0.4 -0.4 1.3 1000 12.5 13.0 16.2 - - 2.9 -0.4 -0.5 1.4 6100 12.0 12.4 23.2 - - 3.8 - - 0.5 11000 12.0 12.4 26.1 0.4 0.4 4.4 - - 0.2 25000 12.0 12.1 30.4 0.3 0.3 5.4 - - -0.4 189200 11.9 12.2 39.7 -0.3 -0.3 10.9 -0.3 -0.3 -3.0 SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (8:) (3:) ($) (lbs) (lbs) (Br) (Br) (%) 11129513 4200 189 4.31 50 500 2370.0 3997.2 2.546 3.52 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 14.7 14.9 6.6 1.8 1.9 5.9 0.4 0.6 4.1 500 14.5 14.7 7.8 1.8 1.9 8.1 0.5 0.7 5.5 1000 14.2 14.5 8.8 1.8 1.8 8.8 0.4 0.4 6.6 5000 14.3 14.4 13.1 1.5 1.6 10.5 0.4 0.4 7.8 10000 14.1 14.3 14.8 1.2 1.2 11.5 0.3 0.3 8.6 40000 13.8 14.0 18.6 1.0 1.1 12.5 0.3 0.4 9.5 161500 13.3 13.4 - - - 18.2 - - 13.7 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT 0F BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 230 TABLE A.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (Er) (at) (t) (lbs) (lbs) (St) (St) (%) 21119513 4200 175 3.99 50 500 2455.0 4087.6 2.539 1.39 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 15.5 17.8 32.8 1.1 1.4 8.6 0.5 0.7 3.7 500 14.9 16.3 51.7 1.2 1.3 14.9 0.4 0.6 6.8 1000 14.5 16.2 64.0 1.4 1.6 20.4 0.4 0.7 8.9 5000 14.3 15.1 99.4 1.8 2.0 34.6 - - 16.0 10000 14.1 15.2 116.3 2.2 2.5 42.2 - - 20.3 MWWWWWWW SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (81:) (81‘) (’3) (lbs) (lbs) (81') (81') (t) 12119623 4200 196 4.46 50 500 2319.7 3947.2 2.543 4.63 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 14.9 17.0 35.6 2.7 2.7 -0.8 2.0 2.2 4.2 500 14.9 16.9 58.5 2.6 2.6 -0.7 2.0 2.2 10.4 1000 14.9 16.9 71.7 2.6 2.6 -1.3 2.0 2.3 14.3 5000 15.2 17.2 106.8 2.5 2.5 -6.5 1.9 2.2 25.9 10000 14.8 17.3 124.3 2.4 2.6 -10.2 1.9 2.2 33.0 15600 14.7 17.4 130.9 2.4 2.5 -13.2 1.9 2.2 38.9 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE A.1 (CONTINUED). 231 SAMPLE NUMBER VA (8:) VB A.C. (8r) (1) SL CL (1bs) (1bs) VBV (Er) VBA (8r) GMM A.V. (%) 32119623 4200 193 4.40 50 500 2305.1 3925.4 2.530 4.24 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 14.4 16.7 31.0 1.4 2.0 6.1 1.3 1.8 6.5 500 14.2 16.6 55.9 1.4 1.9 10.8 1.3 1.9 11.3 1000 14.3 16.7 70.5 1.4 1.9 13.8 1.3 1.9 13.7 5000 14.3 16.8 113.6 1.4 1.9 23.3 1.3 2.0 20.6 10000 14.3 16.9 136.4 1.5 2.0 28.7 1.4 2.1 24.6 *WHWWWWWWW SAMPLE NUMBER VA (8:) VB A.C. (Sr) (b) 31119723 4200 182 4.16 50 SL CL (1bs) (1bs) VBV (8r) VBA GMM A.V. (at) (t) 500 2156.0 3736.5 2.541 6.96 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 110 15.9 17.2 75.9 2.4 2.5 4.1 0.7 0.8 7.8 510 15.9 20.6 155.2 2.3 2.5 12.4 1.4 1.5 19.2 1000 15.9 20.6 206.4 2.3 2.4 20.2 1.1 1.5 29.1 5000 16.5 21.6 424.1 2.2 2.5 72.2 1.5 1.7 85.0 10050 16.5 22.2 601.1 2.1 2.5 125.0 1.7 2.0 29.6 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB VEIGHT 0F BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW‘ - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 232 TABLE A.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (81:) (Sr) (’3) (lbs) (lbs) (81:) (at) (is) 32129613 4200 193 4.40 50 500 2198.0 3817.0 2.530 6.81 DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) CYCLE NUMBER ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 100 15.1 15.9 6.5 0.5 0.8 0.3 0.3 0.5 0.3 500 14.5 15.3 9.2 0.5 0.8 0.4 0.3 0.5 0.2 1000_ 14.5 15.1 11.2 0.6 0.8 0.3 0.3 0.5 0.0 5300 13.7 14.1 18.6 0.6 0.8 0.9 0.2 0.4 0.0 10000 13.3 13.7 22.1 0.5 0.6 1.2 0.3 0.4 0.1 33800 12.0 12.4 29.3 0.2 0.3 2.6 0.3 0.4 0.7 149500 11.2 11.6 38.4 0.8 0.8 4.1 - - 1.7 WA - TOTAL WEIGHT 0F DRY AGGREGATES; WB - WEIGHT 0F BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT 0F SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. APPENDIX B 233 TABLE B.1 UNCONFINED TRIAXIAL VARIABLE PEAK CYCLIC LOAD TESTS. SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (8:) (3r) (%) (lbs) (lbs) (Sr) (Er) (%) 11118513 4200 189 4.31 50 VAR 2463.4 4079.3 2.546 0.85 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 1.8 2.3 6.2 1.3 1.5 - 1.0 1.1 - 500 1.7 2.2 14.3 1.4 1.5 9.8 1.1 1.1 5.4 1000 1.7 2.1 20.7 1.4 1.5 19.2 1.1 1.2 11.8 500 100 3.5 4.8 5.4 3.2 3.4 11.6 2.5 2.8 12.4 500 3.4 4.7 13.7 3.3 3.7 20.0 2.5 3.0 23.0 1000 3.4 4.6 24.1 3.5 3.7 47.0 2.7 3.0 44.4 900 100 5.6 7.8 12.3 5.3 6.1 24.4 4.5 4.9 25.4 500 6.0 7.9 34.1 6.3 6.7 77.0 4.8 5.4 77.2 1000 5.6 7.9 53.1 6.4 6.8 127.4 4.7 5.5 125.4 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. 234 TABLE B.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (8:) (8r) (3) (lbs) (lbs) (31') (Sr) (b) 11118613 4200 189 4.31 50 VAR 2373.2 3995.1 2.546 3.25 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. FLA. 200 100 2.7 4.2 14.2 - - 0.6 1.0 1.0 - 500 2.5 3.9 29.6 - - 3.2 0.8 0.8 - 1000 2.5 3.7 40.8 - - 5.6 1.0 1.1 - 500 100 5.6 8.6 30.5 - - 9.3 3.0 3.1 6.4 500 5.4 9.2 69.1 4.5 4.5 16.0 3.0 3.6 13.0 1036 5.7 9.5 96.9 4.6 5.1 21.4 3.4 3.9 18.5 900 100 9.5 15.6 42.2 7.6 8.9 16.0 5.9 7.2 9.6 500 9.4 16.5 109.5 8.5 10.3 46.5 6.7 8.3 26.8 1000 9.4 17.0 160.7 8.9 11.8 71.9 6.8 9.0 40.8 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; VBV - VEIGHT OF SAMPLE IN VATER; CL - CYCLIC LOAD; VBA - VEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 235 SAMPLE WA NUMBER (gr) VB A.C. (Sr) (b) SL (lbs) (lbs) CL VBV (gr) VBA GMM A.V. (%) (Sr) 11118713 4200 189 4.31 50 VAR 2178.8 3777.6 2.546 7.20 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 2.8 4.2 20.0 1.2 1.5 5.0 1.2 1.3 2.0 500 2.6 4.2 42.0 1.3 1.5 6.0 1.2 1.4 - 1000 2.8 4.3 55.5 1.2 1.5 6.0 1.0 1.4 - 500 100 6.3 10.2 24.0 3.2 4.2 4.0 2.8 4.0 3.0 500 6.6 10.8 52.5 3.8 4.6 9.0 2.8 4.0 5.0 1000 6.1 11.1 90.5 3.8 4.6 14.0 3.0 4.4 6.0 900 100 10.7 19.0 47.5 6.2 8.2 10.0 5.6 7.4 8.0 500 11.2 20.2 140.5 6.6 8.4 32.0 5.2 7.6 19.0 1000 11.2 20.2. 230.0 6.4 8.6 56.0 5.4 7.8 30.0 WA - TOTAL WEIGHT 0F DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 236 SAMPLE WA VB A.C. SL NUMBER (gr) (gr) (b) CL (1bs) (1bs) VBV (8r) VBA GMM A.V. (8r) (%) 11218613 4200 186 4.25 50 VAR 2329.1 3943.1 2.547 4.08 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 2.6 4.5 12.5 0.9 1.3 2.3 0.6 0.9 2.0 500 2.9 4.7 20.5 0.9 1.4 3.4 0.6 0.9 2.4 1000 2.7 4.7 30.0 1.0 1.4 4.0 0.7 1.1 0.4 500 107 6.0 11.5 37.5 2.6 4.0 8.5 1.9 3.0 6.2 500 6.3 12.3 94.5 2.9 4.5 19.4 2.3 3.5 13.5 1000 6.6 12.7 141.5 2.8 4.8 26.8 2.3 3.9 18.3 900 104 11.2 21.7 68.5 5.4 9.3 15.0 4.3 7.3 15.0 500 10.9 23.4 194.5 6.7 11.7 53.0 5.2 8.4 40.0 1000 11.3 24.3 297.5 7.1 13.4 88.0 5.4 9.5 61.0 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 237 SAMPLE VA NUMBER (3:) VB A.C. SL CL (8:) (3) (lbs) (lbs) VBV (gr) VBA GMM A.V. (3:) (s) 11218513 4200 186 4.25 50 VAR 2340.8 3962.1 2.547 4.05 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 110 9.3 10.5 12.4 0.3 0.7 - 0.5 0.6 - 500 8.5 9.5 28.1 - 0.8 - 1.2 1.4 - 1000 8.6 9.6 35.7 - 0.5 - 1.3 1.5 - 500 100 19.9 23.3 25.2 — 1.0 2.5 2.2 2.8 3.3 500 20.4 23.7 57.4 0.5 1.2 4.6 2.4 3.1 4.8 1000 20.2 23.8 78.6 0.5 1.2 6.1 2.5 3.2 5.9 900 100 34.0 40.3 38.3 0.8 2.4 4.3 4.4 6 3 7.4 500 32.8 41.1 93.8 0.7 2.0 11.0 4.2 - 13.3 1000 33.5 43.6 134.7 1.0 2.5 18.2 4.3 6.1 19.8 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; _ SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 238 SAMPLE VA NUMBER (gr) ( VB A.C. at) (t) SL (1bs) (1bs) CL VBV (Er) VBA GMM A.V. (8r) (%) 11318513 4200 178 4.07 50 VAR 2328.7 3944.4 2.553 4.38 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 150 5.8 7.6 54.7 - 0.3 3.1 1.0 1.6 5.8 500 5.8 7.6 74.0 - 0.2 4.9 0.9 1.6 9.4 1005 7.3 9.2 85.8 - 0.3 6.3 1.1 1.8 10.6 500 150 18.0 23.4 64.2 1.9 3.0 - 2.0 3.6 - 500 17.5 24.0 112.6 1.5 2.9 15.7 2.1 4.0 7.8 1000 17.5 24.5 152.7 1.4 2.8 28.2 2.3 4.0 14.8 900 119 31.0 42.6 75.5 2.7 5.0 25.3 3.4 6.3 15.0 510 30.7 42.6 192.8 3.0 5.5 65.4 3.4 6.5 42.0 1002 30.3 43.5 296.8 3.0 5.9 99.6 3.2 6.9 69.0 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; VBV - VEIGHT OF SAMPLE IN VATER; CL - CYCLIC LOAD; VBA - VEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. 239 TABLE B.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (at) (Sr) (b) (lbs) (lbs) (8:) (8r) (%) 12118513 4200 196 4.46 50 VAR 2433.5 4069.6 2.543 2.19 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. #UHHPOI UINGO‘#\O 200 100 6.3 7.0 16.5 0.6 0.6 3.5 - - 500 6.2 7.4 24.2 0.7 0.7 7.0 - - 1000 6.4 7.3 32.2 0.7 0.7 9.4 - - 500 100 14.2 16.5 18.6 1.2 1.6 5.6 - - 500 14.3 16.4 30.8 1.3 1.8 11.5 - - 1005 14.3 16.3 46.4 1.4 1.8 15.5 - - 900 100 22.8 26.6 25.6 1.8 2.8 7.9 - - 500 22.4 26.5 63.5 1.9 2.9 17.3 - - 1000 22.8 26.4 91.9 1.9 3.0 24.6 - - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT 0F SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 240 SAMPLE WA NUMBER (gr) WB A.C. (8r) (3) SL CL (1bs) (1bs) VBV (8r) VBA GMM A.V. (t) (8:) 12118613 4200 196 4.46 50 VAR 2304.8 3932.1 2.543 4.98 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (lbs .) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 6.2 7.2 16.1 0.3 0.5 - 0.4 0.6 - 500 5.9 7.0 24.8 0.4 0.5 0.3 0.3 0.5 - 1000 6.1 6.9 29.1 0.4 0.5 0.5 0.2 0.4 - 500 100 12.7 15.6 13.9 1.3 1.7 2.2 0.2 0.9 3.6 500 13.3 15.9 27.4 1.4 1.8 3.8 0.3 0.9 5.1 1000 13.6 16.1 35.8 1.5 2.0 5.2 0.3 0.9 6.0 900 100 21.8 26.9 22.5 2.8 3.9 5.5 0.5 1.6 3.8 500 21.9 27.7 46.7 2.9 4.4 11.9 0.6 1.8 8.3 1000 22.0 28.2 63.0 3.3 4.6 16.6 0.7 1.9 10.9 WA TOTAL WEIGHT OF DRY AGGREGATES; WB WEIGHT 0F BITUMEN; A.C. WBW WBA GMM PERCENT ASPHALT CONTENT; WEIGHT OF SAMPLE IN WATER; WEIGHT OF SAMPLE IN AIR; MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. SL CL A.V. SUSTAINED LOAD; CYCLIC LOAD; PERCENT AIR VOIDS; TABLE B.1 (CONTINUED). 241 SAMPLE WA NUMBER (3:) WB A.C. SL (Er) (i) CL (1bs) (lbs) VBV (8r) WBA GMM A.V. (8r) (%) 12118713 4200 196 4.46 50 VAR 2193.6 3801.0 2.543 7.01 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 5.5 7.2 37.3 1.8 2.3 - -0.9 -l.0 - 500 5.4 7.3 58.9 1.9 2.4 5.9 -1.0 —1.1 2.1 1000 5.7 7.2 72.1 1.8 2.4 9.1_-1.1 -1.2 3.2 500 107 13.5 17.5 36.7 3.9 5.3 10.5 -1.2 -1.2 2.9 500 13.7 18.0 82.6 4.0 5.5 28.4 -1.1 -1.2 8.9 1000 13.8 18.4 113.4 4.2 5.6 40.7 -1.1 -1.2 13.7 900 100 23.3 31.0 49.9 6.6 9.4 23.2 -1.4 -1.2 4.7 500 23.5 32.2 130.7 6.8 10.0 60.5 -1.4 -1.6 18.9 1000 24.6 33.2 220.7 8.4 11.1 94.4 -1.7 -2.0 36.7 WA - TOTAL WEIGHT 0F DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. 242 TABLE B.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (8:) (gr) (%) (lbs) (lbs) (at) (Sr) (%) 21118513 4200 175 3.99 50 VAR 2414.5 4050.1 2.539 2.47 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. OOOUO“ 200 100 6.9 7.5 12.8 1.9 1.9 2.1 1.2 1.3 2. 500 6.9 7.4 21.8 1.8 1.9 0.3 1.1 1.2 3. 1000 6.9 7.4 27.8 1.7 1.7 -0.5 1.0 1.1 4. 500 100 14.4 15.8 17.6 1.8 2.1 0.7 - - 3. 500 14.4 16.0 38.2 1.5 1.8 1.9 - - 6. 1000 14.4 16.1 52.5 1.4 1.7 2.9 - - 8. 900 100 22.3 25.8 29.4 1.6 2.2 4.0 - - - 520 22.4 25.9 67.5 1.3 1.9 10.9 - - - 1000 22.3 26.2 93.9 1.3 2.1 15.8 - - - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 243 SAMPLE WA WB A.C. SL CL NUMBER (8r) (8!) (i) (1b8) (1bs) VBV (Sr) VBA GMM A.V. (8r) (%) 21118613 4200 175 3.99 50 VAR 2301.3 3917.6 2.539 4.54 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 170 7.0 7.6 13.4 - - 0.5 0.3 0.4 -O.4 500 6.9 7.7 20.8 - - 1.3 0.3 0.4 -1.8 1000 6.9 7.4 27.7 - - 2.0 0.3 0.4 -3.3 500 104 14.8 16.9 30.7 - 0.4 2.8 0.3 0.8 0.8 500 14.8 16.7 53.1 - 0.5 6.3 0.4 0.8 1.4 1000 14.8 17.0 69.9 - 0.5 8.7 0.4 0.8 1.4 900 100 23.9 27.7 34.0 - 0.9 4.9 0.6 1.4 3.5 500 24.0 28.3 79.5 - 0.9 16.5 0.6 1.6 8.0 1000 23.5 28.7 115.7 - 0.8 22.4 0.4 1.7 11.6 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; VBV - VEIGHT OF SAMPLE IN VATER; CL - CYCLIC LOAD; VBA - VEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 244 SAMPLE WA NUMBER (gr) (8:) (%) WB A.C. SL CL WBW (1bs) (1bs) (gr) VBA (Er) GMM A.V. (b) 21118713 4200 175 3.99 50 VAR 2196.3 3778.4 2.539 5.94 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 120 7.7 8.9 28.6 0.6 0.8 7.1 0.4 0.7 8.0 500 7.9 9.3 57.9 0.6 0.9 15.7 0.4 0.7 17.3 1000 7.8 9.1 79.3 0.7 1.0 23.0 0.5 0.8 25.1 500 100 15.7 19.4 43.0 1.7 2.8 12.2 1.6 2.5 12.8 505 16.1 19.9 107.7 2.0 3.0 36.0 1.6 2.6 38.7 1000 15.5 20.2 156.3 2.1 3.2 54.7 1.6 2.7 58.4 900 110 26.2 34.3 69.2 3.0 5.2 21.1 3.0 5.2 22.8 500 26.3 34.8 181.3 3.3 5.9 66.6 3.0 5.8 69.8 1000 26.1 35.4 283.7 3.5 6.1 114.9 3.2 6.1 116.6 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. 245 TABLE B.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (8:) (81') (3) (lbs) (lbs) (8:) (Sr) (15) 21218613 4200 176 4.03 50 VAR 2214.7 3806.6 2.537 5.75 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. #‘O#£DNC\O\HUI 200 100 7.9 8.4 5.7 2.0 2.2 2.3 1.4 1.5 1. 500 7.7 8.1 9.8 2.0 2.1 3.3 1.3 1.4 2. 1000 7.6 8.1 12.9 1.9 2.1 4.2 1.2 1.3 2. 500 100 15.9 17.6 9.8 3.0 3.5 2.1 1.8 2.1 1. 500 15.9 17.4 19.7 2.8 3.1 5.2 1.7 1.9 3. 1000 15.5 17.3 27.1 2.6 3.1 7.3 1.6 1.9 5. 900 100 24.7 28.6 18.3 4.3 5.2 3.6 2.4 3.1 3. 500 24.9 28.8 39.5 4.0 4.7 7.7 2.6 3.3 7 1000 25.7 28.7 55.9 4.0 4.8 11.2 2.5 3.3 11 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 246 SAMPLE WA NUMBER (gr) VB A.C. (8r) (%) SL (1bs) (1bs) CL VBV (Sr) VBA (gr) GMM A.V. (%) 21318613 4200 175 3.99 50 VAR 2257.1 3861.0 2.537 5.11 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 8.4 9.9 6.8 2.5 3.2 2.1 2.3 2.9 1.3 500 8.4 9.9 16.1 2.7 3.4 5.3 2.3 2.9 3.4 1000 8.4 9.9 24.0 2.9 3.5 8.3 2.5 3.1 5.2 500 100 19.3 23.5 44.1 5.7 7.9 23.9 4.7 6.8 13.1 516 19.4 24.4 110.1 6.4 8.8 47.2 5.5 8.0 32.8 1026 19.6 24.4 161.2 6.7 9.3 75.5 5.7 8.5 55.6 900 100 31.4 45.3 78.3 12.2 17.3 43.2 8.8 13.9 31.8 507 31.4 45.3 236.9 11.5 17.2 113.9 10.0 16.1 94.2 1010 31.6 45.3 383.0 10.6 18.8 182.7 9.6 17.7 152.4 WA A.C. WBW WBA GMM TOTAL WEIGHT OF PERCENT ASPHALT CONTENT; WEIGHT OF SAMPLE IN WATER; WEIGHT OF SAMPLE IN AIR; - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. DRY AGGREGATES; WB SL CL A.V. WEIGHT OF BITUMEN; SUSTAINED LOAD; CYCLIC LOAD; PERCENT AIR VOIDS; 247 TABLE B.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (Sr) (81') (1:) (lbs) (lbs) (8r) (31') ($1) 12218713 4200 197 4.48 50 VAR 2116.2 3652.8 2.541 6.45 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (lbs .) NUMB . ELA. TOT . PLA. ELA. TOT . PLA. ELA. TOT . PLA. 200 100 8.0 8.9 16.9 2.8 3.2 3.1 1.9 2.0 1.2 500 7.8 8.8 33.9 2.9 3.2 5.7 1.9 2.0 2.4 1000 7.6 8.6 48.3 2.9 3.2 8.1 2.0 2.1 3.1 500 100 16.6 19.8 23.4 4.2 5.0 4.6 2.4 2.8 2.6 500 16.8 19.9 56.8 4.2 5.0 11.2 2.5 3.0 5.8 1000 16.8 19.7 81.6 4.3 5.1 16.1 2.5 3.0 '8.3 900 100 27.7 33.7 40.7 5.0 6.6 9.0 2.7 3.6 6.2 500 28.0 33.9 101.2 5.1 6.7 19.5 2.6 3.6 14.2 1000 27.6 33.9 150.9 5.1 6.7 30.0 2.7 3.6 20.4 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 248 SAMPLE WA NUMBER (3:) VB A.C. SL (8:) (t) CL (lbs) (1bs) VBV (Er) WBA GMM A.V. (Sr) (b) 31118513 4200 182 4.16 50 VAR 2382.1 4007.7 2.541 2.98 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 6.4 6.9 4.3 0.9 1.0 0.2 0.7 0.8 0.2 500 6.4 6.9 9.3 0.8 1.0 0.2 0.7 0.8 0.4 1000 6.4 7.0 13.6 0.9 1.0 0.4 0.7 0.8 0.6 500 100 14.0 15.4 15.6 1.6 1.9 3.0 1.4 1.8 3.3 500 14.0 15.6 34.5 1.6 1.9 5.9 1.4 1.8 6.7 1000 14.0 15.6 48.3 1.6 1.9 7.3 1.4 1.8 9.0 900 100 22.5 25.8 27.8 2.3 2.9 5.5 2.0 2.8 6.7 500 22.5 25.8 65.0 2.5 3.1 11.7 2.2 3.0 14.9 1000 22.2 25.9 94.4 2.4 3.2 16.4 2.2 3.1 21.0 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT 0F SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 249 SAMPLE WA NUMBER (gr) VB A.C. (Sr) (b) SL (1bs) (lbs) CL VBV (8r) VBA GMM A.V. (t) (Er) 31118713 4200 182 4.16 50 VAR 2121.2 3661.0 2.541 6.43 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (lbs .) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT . PLA. 200 100 7.0 7.8 12.7 0.6 0.8 1.9 0.3 0.4 2.4 500 7.1 7.7 29.6 0.6 0.8 3.5 0.2 0.4 4.1 1000 7.0 7.8 42.5 0.6 0.8 4.6 0.3 0.4 5.8 500 100 15.3 17.4 22.6 1.6 2.1 3.5 0.8 1.2 4.6 500 15.3 17.3 54.9 1.6 2.1 9.3 0.8 1.3 11.3 1000 15.1 17.4 80.3 1.7 2.2 14.3 0.9 1.4 16.8 900 100 25.8 29.6 40.5 3.0 4.1 9.0 1.7 2.6 10.1 500 25.6 29.3 102.0 3.2 4.3 25.2 1.9 2.8 27.8 1000 25.9 30.1 152.6 3.3 4.4 40.2 2.0 3.0 43.0 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 250 SAMPLE VA NUMBER (gr) (3:) (%) WB A.C. SL CL (1bs) (1bs) VBV (Sr) VBA GMM A.V. (8r) (%) 12318713 4200 186 4.24 50 VAR 2095.1 3651.4 2.549 7.96 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 8.3 10.3 43.4 1.7 2.2 3.9 1.3 1.7 3.3 500 8.7 10.5 95.0 1.7 2.2 8.6 1.3 1.7 8.3 1000 8.7 10.7 127.4 1.7 2.2 15.6 1.3 1.7 16.6 500 105 19.5 26.0 80.0 4.0 5.6 14.5 3.1 4.5 14.4 500 20.4 26.8 189.8 4.2 5.8 42.2 3.1 4.7 39.7 1000 20.5 27.1 277.8 4.3 5.9 70.0 3.3 4.9 63.1 900 100 32.9 46.5 114.0 7.2 10.6 34.1 5.5 9.4 33.2 500 34.1 47.7 343.8 7.6 11.5 118.8 6.1 10.2 109.4 1000 34.6 48.5 555.0 7.8 12.0 211.3 6.5 10.8 188.3 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; VBV - VEIGHT OF SAMPLE IN VATER; CL - CYCLIC LOAD; VBA - VEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. 251 TABLE B.1 (CONTINUED). SAMPLE VA VB A.C. SL CL VBV VBA GMM A.V. NUMBER (81') (Sr) (1:) (lbs) (lbs) (gr) (8r) (1:) 22118613 4200 188 4.28 50 VAR 2264.8 3898.6 2.520 5.31 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. Q§HHHOOOO ##ONNNMU'Ik 200 100 6.7 7.2 5.8 0.8 0.9 1.0 0.5 0.6 500 6.6 7.1 11.9 0.8 0.9 1.5 0.5 0.6 1000 6.5 7.0 16.4 0.8 0.9 2.0 0.6 0.6 500 100 13.9 15.3 10.1 1.6 1.8 1.6 1.0 1.2 500 13.9 15.4 20.2 1.6 1.8 3.1 1.1 1.3 1000 14.0 15.4 27.2 1.6 1.9 4.3 1.1 1.3 900 110 22.1 25.0 17.6 2.5 3.0 2.9 1.7 2.0 520 21.8 25.4 35.7 2.5 2.9 6.3 1.6 1.9 1000 22.2 25.3 49.1 2.4 2.9 8.6 1.6 1.9 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 252 SAMPLE VA NUMBER (gr) ( VB A.C. 8r) (3) SL (1bs) (1bs) CL VBV (8r) VBA (Sr) GMM A.V. (%) 32118613 4200 193 4.40 50 VAR 2246.0 3865.8 2.530 5.67 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (1bs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 7.3 8.1 24.1 0.9 1.0 3.7 0.7 0.9 4.1 500 7.0 8.0 50.5 0.8 1.0 7.5 0.7 1.0 8.1 1000 7.0 7.8 68.9 0.8 1.1 10.4 0.7 0.9 10.9 500 100 14.4 17.4 32.6 1.9 2.6 7.4 1.4 2.3 7.8 500 14.6 17.4 81.8 1.9 2.7 19.4 1.6 2.4 18.8 1000 14.4 17.8 114.8 2.0 2.8 28.3 1.7 2.5 26.6 900 100 23.2 29.2 48.2 3.8 5.3 13.0 2.9 4.6 14.0 500 23.8 30.0 129.8 4.0 6.0 43.5 3.0 4.9 37.7 1000 23.7 30.2 186.2 4.2 6.1 68.1 3.2 5.0 55.4 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT 0F SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 253 SAMPLE WA NUMBER (8r) WB A.C. SL (Sr) (3) CL (1bs) (1bs) VBV (Sr) WBA (Sr) GMM A.V. (%) 11128513 4200 189 4.31 50' VAR 2353.6 3977.2 2.546 3.79 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (lbs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 5.1 5.1 0.0 -0.4 -0.4 -0.7 -0.4 -0.5 0.0 500 5.1 5.1 0.0 -0.5 -O.4 -1.6 -0.5 -0.5 -0.3 1000 4.9 5.1 0.0 -0.5 -0.5 -2.4 -0.4 -0.3 -0.3 500 100 11.0 11.2 2.0 -0.6 -0.6 -0.4 -0.6 -0.5 -0.1 500 11.0 11.2 2.4 -0.6 -0.6 -1.2 -0.7 -0.7 -0.2 1000 11.0 11.3 2.9 -0.6 -O.5 -1.5 -0.8 -0.8 -0.4 900 100 17.9 18.7 4.1 -1.0 -0.9 -0.1 -1.0 -0.9 -0.1 500 17.9 18.4 5.2 -1.3 -1.2 -0.2 -0.9 -0.9 -0.4 1000 17.9 18.4 5.8 -1.1 -1.0 -0.3 -1.2 -1.1 -0.4 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 254 SAMPLE VA NUMBER (gr) (Sr) (b) WB A.C. SL CL (1bs) (1bs) VBV (8r) VBA GMM A.V. (Sr) (%) 21118513 4200 175 3.99 50 VAR 2450.3 4080.2 2.539 1.40 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (lbs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 8.5 9.5 20.7 -0.7 -O.8 -1.8 1.4 1.6 6.0 500 8.2 9.4 39.9 -0.8 -1.0 -2.8 1.2 1.5 14.3 1000 7.9 8.9 53.9 -0.9 -1.1 -3.2 1.2 1.6 21.9 500 100 16.3 18.8 21.0 -2.0 -2.4 1.8 2.9 3.8 5.4 500 16.3 19.1 50.7 -2.3 -2.7 2.1 3.0 3.8 15.0 1000 16.3 19.4 74.8 -2.3 -2.7 1.8 2.9 3.8 23.9 900 100 24.8 29.8 29.8 -2.8 -3.4 3.0 4.4 5.6 9.4 500 24.8 29.9 80.6 -3.2 -3.6 4.3 4.3 5.5 28.3 1000 24.8 30.2 121.4 -3.3 -3.5 4.3 4.2 5.5 44.0 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; WBW - WEIGHT OF SAMPLE IN WATER; CL - CYCLIC LOAD; WBA - WEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. TABLE B.1 (CONTINUED). 255 SAMPLE WA NUMBER (gr) WB A.C. (8:) (3) SL (1bs) (1bs) CL VBV (Sr) VBA (Sr) GMM A.V. (%) 22128613 4200 188 4.28 50 VAR 2198.5 3825.7 2.520 6.70 DEFORMATION (inches X 0.0001) CYCLIC VERTICAL RADIAL (1/2) RADIAL (1/3) LOAD CYCLE (lbs.) NUMB. ELA. TOT. PLA. ELA. TOT. PLA. ELA. TOT. PLA. 200 100 5.8 6.3 13.9 1.0 1.0 -O.9 0.9 1.1 -0.9 500 5.6 6.0 18.2 1.0 1.0 -1.9 0.9 0.9 -3.0 1000 5.6 6.0 20.5 1.0 1.0 -2.2 0.9 0.9 -3.4 500 100 11.5 12.5 9.1 1.8 1.7 2.4 2.1 2.1 1.8 500 11.5 12.3 13.2 1.7 1.5 2.6 1.8 2.0 2.4 1000 11.6 12.3 15.7 1.5 1.3 2.2 1.7 1.9 2.2 900 100 18.1 19.2 7.3 1.5 1.4 -O.2 2.4 2.4 0.4 500 18.3 19.2 11.7 1.5 1.5 -O.6 2.3 2.3 0.2 1000 18.2 19.2 14.5 1.4 1.4 -O.9 2.2 2.2 0.1 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; SL - SUSTAINED LOAD; VBV - VEIGHT OF SAMPLE IN VATER; CL - CYCLIC LOAD; VBA - VEIGHT OF SAMPLE IN AIR; A.V. - PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELAS AND TOTAL - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLAS - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION. NOTE: LONGITUDINAL DEFORMATION IS ALONG THE SAMPLE LENGTH. APPENDIX C 256 TABLE C.1 UNCONFINED TRIAXIAL TESTS (virgin specimens). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (81') (Sr) (’3) (Sr) (Sr) (1:) (P81) 11116513 4200 189 4.31 2451.4 4072.3 2.546 1.32 493.4 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 3.0 1.0 - 800 11.0 1.6 - 1600 26.5 2.0 - 2400 50.5 2.0 - 3200 96.5 2.0 - 4000 157.5 6.0 - 4400 222.5 12.0 - 4800 279.0 22.0 - 5200 364.0 32.0 - 5600 450.5 50.0 - 6000 700.5 84.0 - 6200 1017.5 164.0 - 6000 1284.0 288.0 - VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 257 TABLE C.l (CONTINUED). SAMPLE VA NUMBER (31') ( VB A.C. VBV Sr) (b) (Sr) VBA (Er) GMM A.V. CU (%) (psi) 11116613 4200 189 4.31 2382.0 4007.6 2.546 3.17 248.3 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 200 26.1 44.0 - 400 68.1 45.0 - 800 136.6 66.0 - 1200 217.1 82.0 - 1600 313.1 110.0 - 2000 416.1 137.0 - 2400 499.1 176.0 - 2600 584.6 209.0 - 2800 700.1 242.0 - 3000 826.6 330.0 - 3120 1037.1 491.0 - 3000 1311.1 725.0 - 2880 1342.6 846.0 - VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 258 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8:) (Sr) (%) (St) (St) (%) (psi) 11116713 4200 189 4.31 2166.8 3757.0 2.546 7.20 165.5 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 50 10.3 24.0 14.0 400 95.3 28.0 22.0 800 203.3 40.0 44.0 1200 339.8 62.0 78.0 1600 503.3 92.0 122.0 2000 863.8 138.0 218.0 2080 1163.3 182.0 314.0 2000 1572.3 ‘258.0 456.0 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 259 TABLE C.1 (CONTINUED). SAMPLE VA NUMBER (gr) ( VB A.C. VBV at) (t) (at) VBA (Sr) GMM A.V. CU (s) (psi) 11216513 4200 186 4.25 2329.3 3945.1 2.547 4.14 288.9 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 420 63.9 -29.2 39.3 1220 190.1 -4.9 53.1 2020 327.3 29.2 64.9 2820 491.9 81.6 84.6 3220 618.1 126.3 103.3 3630 974.7 306.1 182.0 3350 1293.0 583.1 293.1 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 260 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (St) (Sr) (b) (at) (Sr) (%) (psi) 11216613 4200 186 4.25 2311.5 3915.9 2.547 4.17 167.1 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 50.0 18.0 26.0 800 161.0 50.0 66.0 1200 293.5 94.0 120.0 1600 442.5 148.0 174.0 2000 683.0 278.0 294.0 2100 946.5 426.0 408.0 1920 1450.5 824.0 654.0 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT 0F SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 261 TABLE C.1 (CONTINUED). SAMPLE NUMBER VA (Sr) VBV (8r) VB A.C. GMM A.V. CU (Sr) (3) (3) (psi) 11316513 4200 178 4.07 2411.3 4040.5 2.553 2.86 222.8 VBA (8r) DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 91.3 16.5 -12.8 1200 272.3 19.4 21.3 2000 508.1 10.7 92.9 2400 667.2 48.5 119.6 2800 1056.6 198.6 217.9 2680 1314.4 342.1 318.8 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; . RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 262 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8:) (Sr) (S) (8r) (8:) (t) (psi) 12116513 4200 196 4.46 2401.0 4045.0 2.543 3.25 432.9 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 45.2 13.5 3.5 1200 132.2 37.2 8.3 2000 241.9 66.1 17.3 2800 351.7 101.4 26.3 3600 483.4 134.7 40.2 4200 614.3 - - 4800 720.6 - - 5200 908.7 - - 5440 1276.8 - - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 263 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (at) (Sr) (s) (at) (Sr) (%) (psi) 12116613 4200 196 4.46 2323.0 3952.8 2.543 4.63 370.0 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 49.9 -21.9 31.4 1200 147.4 46.9 -13.1 2000 241.6 126.9 -41.3 2800 360.2 187.5 -4O.6 3600 500.0 268.8 -28.8 4400 736.4 443.8 0.0 4650 974.4 737.5 82.5 4400 1275.0 987.5 203.1 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 264 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV NUMBER (8:) (Sr) (8) (8r) VBA (Sr) GMM A.V. CU (%) (Psi) 12116713 4200 196 4.46 2218.8 3834.2 2.543 6.66 247.5 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 78.6 10.0 -21.0 1200 236.7 82.1 -28.0 2000 447.5 220.6 -66.4 2800 743.3 339.3 14.0 3110 1120.3 512.6 183.8 2930 1485.0 29.1 426.3 WA TOTAL WEIGHT 0F DRY AGGREGATES; WB - WEIGHT 0F BITUMEN; A.C. WBW WBA GMM PERCENT ASPHALT CONTENT; WEIGHT OF SAMPLE IN WATER; WEIGHT OF SAMPLE IN AIR; MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. CU - UNCONFINED COMPR- ESSIVE STRENGTH; A.V.- PERCENT AIR VOIDS; 265 TABLE C.1 (CONTINUED). SAMPLE VA NUMBER (gr) ( VB A.C. VBV 8r) (%) (8r) VBA (Er) GMM A.V. CU (%) (psi) 21116513 4200 175 3.99 2385.6 4015.7 2.539 2.97 343.0 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 40.6 5.5 5.1 1200 127.6 34.6 37.3 2000 247.0 72.5 68.2 2800 375.2 132.6 115.6 3200 452.7 168.6 147.9 3600 547.2 224.9 189.4 4000 674.1 317.3 235.4 4200 772.3 399.5 304.6 4310 950.5 599.1 424.3 4200 1097.4 788.4 525.7 4000 1203.7 918.2 597.1 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 266 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (Sr) (8:) ($) (Er) (8r) (%) (Psi) 21116613 4200 175 3.99 2324.6 3938.5 2.539 3.88 334.2 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 20.0 0.0 0.0 1200 57.2 7.4 23.7 2000 125.7 20.3 29.6 2800 217.2 31.3 76.9 3560 348.7 46.1 165.6 4000 477.3 - - 4200 591.6 - - VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 267 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8:) (Sr) (is) (81') (gr) (1:) (Psi) 21116713 4200 175 3.99 2194.9 3778.1 2.539 6.01 154.4 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 72.5 20.3 13.2 800 171.4 60.9 36.2 1200 356.1 115.0 105.3 1600 560.5 196.0 197.5 1940 1081.3 520.8 480.6 1820 1490.1 784.5 744.0 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 268 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8:) (81') (1;) (at) (Sr) (b) (Psi) 21216613 4200 176 4.03 2217.8 3817.4 2.537 5.93 340.6 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 27.4 -47.4 -33.0 800 57.8 -54.1 -46.1 1200 95.7 -54.1 -46.1 1600 133.7 -47.4 -46.1 2000 186.9 -33.8 -39.6 2400 255.3 -20.3 -33.0 2800 331.2 0.0 -13.2 3200 414.8 20.3 6.6 3600 513.5 60.9 39.6 4000 680.7 128.5 105.5 4280 946.5 263.8 211.0 4120 1242.8 460.0 336.2 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 269 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8r) (8:) (%) (8:) (Sr) (%) (psi) 21316613 4200 175 3.99 2260.3 3863.0 2.537 4.99 148.0 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 158.4 62.1 37.9 800 319.4 77.6 47.4 1200 480.4 95.4 61.6 1600 757.4 137.5 90.1 1860 1362.7 297.5 208.6 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 270 TABLE C.1 (CONTINUED). SAMPLE WA NUMBER (3:) ( VB A.C. VBV 8r) (%) (Sr) VBA (Sr) GMM A.V. CU (%) (Psi) ‘ 12216713 4200 197 4.48 2130.2 3665.8 2.541 6.05 235.6 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 50.0 6.9 3.9 1200 178.1 31.0 22.2 2000 421.2 53.7 59.5 2400 599.7 72.2 88.9 2800 842.5 110.1 150.0 2960 1342.5 227.0 352.9 2920 1599.3 491.9 527.9 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE C.1 (CONTINUED). 271 SAMPLE WA NUMBER (gr) VB A.C. (Sr) (1) VBV (Sr) VBA (gr) GMM A.V. CU (%) (ps1) 31116513 4200 182 4.16 2385.3 4012.4 2.541 2.95 301.4 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 41.0 4.9 3.0 1200 143.9 11.2 9.9 2000 297.2 18.8 21.3 2800 482.0 29.1 38.7 3200 622.7 43.8 55.6 3600 831.6 77.8 93.8 3788 1142.5 192.7 189.1 3640 366.5 352.9 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 272 TABLE C.1 (CONTINUED). SAMPLE NUMBER VA (Sr) VBV (8r) VB A.C. GMM A.V. CU (Sr) (1) (t) (psi) 31116713 4200 182 4.16 2136.7 3677.9 2.541 6.08 226.0 VBA (Er) DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 70.3 0.0 0.4 1200 272 3 8.5 9.2 2000 632.9 41.3 49.0 2400 856.7 76.3 88.1 2720 1198.6 104.1 114.8 2840 1590.3 219.9 223.2 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OP SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 273 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV WBA GMM A.V. CU NUMBER (8:) (Sr) (i) (8r) (8:) (t) (Psi) 11126513 4200 189 4.31 2339.1 3961.9 2.546 4.11 0.0 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 800 85.1 25.4 35.2 2000 127.6 25.4 35.2 3200 204.2 23.3 35.2 4400 263.8 22.2 35.2 5600 331.9 21.4 35.2 7200 425.5 20.6 37.0 8400 612.7 20.1 41.2 9400 625.5 20.1 45.8 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 274 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (at) (Sr) (3) (St) (Sr) (b) (Ps1) 12316713 4200 186 4.24 2063.5 3621.4 2.549 8.81 122.6 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 142.3 11.7 1.1 800 398.3 25.6 4.2 1200 739.7 74.6 38.1 1540 1589.7 405.6 306.1 1440 1589.7 547.8 418.9 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.v.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 275 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8t) (at) (t) (St) (Rt) (%) (psi) 22116613 4200 188 4.28 2273.5 3907.4 2.520 5.10 331.0 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 800 97.6 44.6 32.0 1600 188.3 62.4 42.3 2400 334.7 93.6 65.2 3200 474.2 132.2 92.7 3800 697.3 199.0 138.9 4160 1087.8 368.3 248.3 4000 1394.6 567.3 359.2 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 276 TABLE C.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (St) (Sr) (3) (Sr) (Er) (%) (Psi) 32116613 4200 193 4.40 2336.0 3969.9 2.530 3.96 248.3 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 800 158.9 40.1 33.0 1600 325.0 55.4 52.9 2400 570.6 75.2 92.6 2800 787.3 97.4 131.2 . 3120 1220.7 200.5 279.5 3000 1538.5 364.7 478.2 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 277 TABLE C.1 (CONTINUED). SAMPLE WA NUMBER (gr) ( VB A.C. VBV VBA Sr) (b) (Er) (8r) GMM A.V. CU (%) (psi) 21116513 4200 175 3.99 2477.1 4121.7 2.539 1.29 341.4 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 360 46.4 - 46.7 1160 151.7 - 86.7 1960 257.0 - 133.3 2760 428.0 - 200.0 3160 546.4 - 280.0 3560 717.5 - 386.7 4000 947.8 - - 4290 1401.7 - - VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 278 TABLE C.1 (CONTINUED). SAMPLE NUMBER VA (8:) VBV (Sr) VB A.C. GMM A.V. CU (8r) (t) (t) (psi) 22126613 4200 188 4.28 2190.1 3817.6 2.520 6.92 639.0 VBA (Sr) DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 800 53.0 8.7 2.0 1600 106.1 13.0 9.3 2400 168.5 22.5 18.9 3200 243.4 34.6 32.6 4000 324.5 46.3 45.5 4800 420.0 62.4 65.6 5600 530.4 82.3 83.3 6400 674.0 114.8 113.9 7200 861.2 167.2 170.2 7800 1085.8 233.9 254.7 8030 1410.4 368.1 403.6 7840 1619.4 447.0 500.2 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 279 TABLE C.2 UNCONFINED TRIAXIAL TESTS (after TXVCL). SAMPLE WA NUMBER (3:) ( VB A.C. VBV Sr) (b) (Sr) VBA (Er) GMM A.V. CU (b) (Psi) 11118513 4200 189 4.31 2463.4 4079.3 2.546 0.85 467.9 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 2.0 2.0 - 800 4.5 8.0 - 1600 13.0 20.0 - 2400 48.5 30.0 - 3200 98.5 48.0 - 4000 161.5 72.0 - 4400 218.5 86.0 - 4800 285.0 104.0 - 5200 405.0 132.0 - 5600 670.0 184.0 - 5880 1086.5 244.0 - 5720 1534.5 264.0 - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 280 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (St) (8r) (1) (St) (Rt) (%) (Psi) 11118613 4200 189 4.31 2373.2 3995.1 2.546 3.25 270.6 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 200 6.8 -15.2 - 400 28.8 -13.2 - 800 58.3 0.0 - 1200 103.3 13.2 - 1600 152.8 32.5 - 2000 207.3 58.8 - 2400 265.8 87.2 - 2800 349.8 121.7 - 3000 406.3 147.1 - 3200 482.3 187.7 - 3400 704.3 281.0 - 3240 930.8 405.8 - VA - TOTAL VEIGHT OF DRY AGGREGATES; WB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 281 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (81') (at) (’3) (81:) (Sr) (‘3) (Ps1) 11118713 4200 189 4.31 2178.8 3777.6 2.546 7.20 206.9 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 40 -31.5 - 0.0 400 36.0 - 14.0 800 92.0 - 24.0 1200 137.0 - 34.0 1600 220.5 - 48.0 2000 337.0 - 64.0 2400 508.5 - 96.0 2600 842.0 - 144.0 2480 1194.0 - 228.0 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 282 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (St) (St) (S) (gr) (Er) (%) (ps1) 11218513 4200 186 4.25 2340.8 3962.1 2.547 4.05 289.7 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 32.9 9.7 7.9 1200 128.4 29.2 19.7 2000 225.0 58.3 32.5 2800 344.6 92.3 64.9 3200 451.0 121.5 86.6 3600 614.5 204.1 126.9 3640 762.7 291.6 160.3 3600 1075.4 447.0 196.7 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 283 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV WBA GMM A.V. CU NUMBER (8:) (Sr) (3) (8:) (Sr) (%) (psi) 11218613 4200 186 4.25 2329.1 3943.1 2.547 4.08 219.6 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 20.9 0.0 32.0 800 70.4 0.0 54.0 1200 106.9 2.0 70.0 1600 154.4 8.0 104 O 2000 225.9 10.0 140.0 2400 296.4 16.0 186.0 2760 591.9 138.0 326.0 2520 929.9 456.0 544.0 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; WBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 284 TABLE C.2 (CONTINUED). SAMPLE WA NUMBER (31') ( VB A.C. VBV 8r) (3) (8r) VBA (Er) GMM A.V. CU (%) (Psi) 11318513 4200 178 4.07 2328.7 3944.4 2.553 4.38 219.2 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 58.7 -4.8 37.9 1200 179.2 17.4 65.4 2000 305.3 16.4 140.1 2400 393.0 46.4 168.1 2755 628.6 215.7 218.3 2480 869.7 525.2 324.0 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 285 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (Sr) (Er) (t) (St) (St) (%) (ps1) 12118513 4200 196 4.46 2433.5 4069.6 2.543 2.19 406.6 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 14.9 - 3.6 1200 84.0 - 15.5 2000 181.7 - 29.7 2800 301.7 - 50.9 3600 470.9 - 75.8 4200 656.9 - - 4600 799.5 - - 4800 923.4 - - 5000 1134.1 - - 5110 1425.4 - - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 286 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (Sr) (8:) ($) (at) (Sr) (%) (psi) 12118613 4200 196 4.46 2304.8 3932.1 2.543 4.98 378.8 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 37.0 6.3 4.6 1200 110.1 -25 O 85.2 2000 191.3 -20.0 119.2 2800 288.8 6.3 142.1 3600 398.5 50.6 170.3 4400 585.3 141.9 235.8 4760 845.3 339.4 336.7 4580 1084.9 506.3 429.0 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 287 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8r) (8:) (%) (gr) (Er) (s) (ps1) 12118713 4200 196 4.46 2193.6 3801.0 2.543 7.01 226.8 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 62.5 -7.7 15.3 1200 253.6 6.4 54.1 2000 424.3 48.1 88.0 2600 676.4 100.7 190.6 2850 1046.3 208.5 409.0 2720 1440.7 442.7 623.8 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.v.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 288 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV WBA GMM A.V. CU NUMBER (8r) (Sr) (3) (8:) (8r) (%) (ps1) 21118513 4200 175 3.99 2414.5 4050.1 2.539 2.47 316.7 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 32.5 16.2 10.6 1200 107.6 50.8 38.2 2000 210.7 110.9 84.3 2800 338.9 207.8 159.4 3200 . 422.7 281.7 217.9 3600 539.0 378.7 305.5 3840 647.2 512.7 429.9 3980 861.7 808.3 655.6 3840 1029.9 1131.6 939.0 3680 1150.0 - - VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; WBA - VEIGHT OF SAMPLE IN AIR; A.v.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 289 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8:) (Sr) (8) (8:) (8r) (%) (ps1) 21118613 4200 175 3.99 2301.3 3917.6 2.539 4.54 270.6 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 18.3 -O.6 0.0 800 45.4 -O.9 0.0 1200 65.4 0.9 2.4 1600 88.3 2.8 8.9 2000 128.3 10.1 17.7 2400 156.9 20.3 17.7 2800 228.4 24.9 23.7 3200 316.9 33.2 76.9 3400 468.4 40.5 106.5 3240 657.0 120.7 153.8 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE C.2 (CONTINUED). 290 SAMPLE WA NUMBER (31') VB A.C. (as) ($) VBV (Sr) WBA (8r) GMM A.V. CU (8) (ps1) 21118713 4200 175 3.99 2196.3 3778.4 2.539 5.94 181.4 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 63.7 23.7 16.5 800 129.6 44.0 36.2 1200 195.6 71.0 56.0 1600 314.3 91.3 75.7 2000 479.1 145.4 115.2 2280 868.1 388.9 319.3 2140 1237.4 713.5 628.8 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 291 TABLE C.2 (CONTINUED). SAMPLE WA NUMBER (gr) ( VB A.C. VBV Sr) (t) (as) VBA GMM A.V. CU (8r) (%) (Psi) 21218613 4200 176 4.03 2214.7 3806.6 2.537 5.75 331.8 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 20.3 0.0 13.2 800 43.1 23.7 26.4 1200 88.7 33.8 46.1 1600 134.3 54.1 65.9 2400 240.6 67.6 79.1 2800 309.0 94.7 112.1 3540 521.7 202.9 217.5 4170 - VA TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. WBW WBA GMM PERCENT ASPHALT CONTENT; WEIGHT OF SAMPLE IN WATER; WEIGHT OF SAMPLE IN AIR; - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. CU - UNCONFINED COMPR- ESSIVE STRENGTH; A.V.- PERCENT AIR VOIDS; 292 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8r) (8:) (1;) (81') (gr) (1:) (psi) 21318613 4200 175 3.99 2257.1 3861.0 2.537 5.11 167.1 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 51.6 48.8 42.7 800 103.2 79.8 61.6 1200 180.4 110.9 94.8 1600 289.9 155.2 147.0 2000 470.3 292.7 265.5 2100 637.7 421.4 - 2040 843.8 550.0 - VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE C.2 (CONTINUED). 293 SAMPLE WA NUMB ER (Sr) VB A.C. VBV VBA GMM A.V. CU (Sr) (b) (at) (Sr) (b) (Psi) 12218713 4200 197 4.48 2116.2 3652.8 2.541 6.45 235.5 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 71.4 -48.2 -3s.5 1200 199.9 -53.0 -42.8 2000 285.6 -48.2 -38.9 2400 428.4 -34.4 -28.9 2800 646.7 0.0 -16.7 2960 985.3 86.0 51.7 VA TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. WBW WBA GMM PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WEIGHT OF SAMPLE IN WATER; WEIGHT OF SAMPLE IN AIR; ESSIVE STRENGTH; A.V.- PERCENT AIR VOIDS; - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE C.2 (CONTINUED). 294 SAMPLE WA NUMBER (3:) VB A.C. VBV (at) (s) (8:) VBA (Sr) GMM A.V. CU (%) (psi) 31118513 4200 182 4.16 2382.1 4007.7 2.541 2.98 312.9 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 16.1 -1.3 0.0 1200 111.1 9.8 2.0 2000 184.6 29.5 18.4 2800 331.6 55.4 45.7 3200 442.9 70.6 63.5 3600 582.0 106.4 95.3 3932 960.0 237.4 186.6 3820 1211.0 388.9 266.5 393;? TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; PERCENT ASPHALT CONTENT; WEIGHT OF SAMPLE IN WATER; WEIGHT OF SAMPLE IN AIR; MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. CU - UNCONFINED COMPR- ESSIVE STRENGTH; A.V.- PERCENT AIR VOIDS; 295 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV WBA GMM A.V. CU NUMBER (8:) (8:) (t) (8:) (8r) (%) (Psi) 31118713 4200 182 4.16 2121.2 3661.0 2.541 6.43 226.8 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 52.1 1.5 3.6 1200 165.3 3.1 4.4 2000 372.3 10.4 14.3 2400 568.1 28.1 29.5 2710 838.5 72.5 64.6 2850 1227.1 180.4 120.4 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; WBA - VEIGHT OF SAMPLE IN AIR; A.v.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 296 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8:) (8r) (%) (at) (Sr) (%) (P31) 11128513 4200 189 4.31 2353.6 3977.2 2.546 3.79 0.0 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 800 68.1 0 8 1.1 1600 110.6 4 O 7 O 2400 212.7 4 5 9 5 3200 263.8 6 7 11 6 4000 331.9 5 1 6 O 4800 314.9 3 5 2 5 5920 323.4 2 1 1.1 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 297 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (81’) (Sr) (b) (81') (Sr) (1;) (Psi) 12318713 4200 186 4.24 2095.1 3651.4 2.549 7.96 140.1 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 51.4 11.7 6.3 800 104.8 25.6 25.4 1200 190.1 60.6 55.0 1600 410.6 165.5 205.2 1760 787.6 378.8 444.3 1700 1036.5 502.3 478.1 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 298 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV WBA GMM A.V. CU NUMBER (at) (Sr) (t) (8r) (8:) (%) (psi) 22118613 4200 188 4.28 2264.8 3898.6 2.520 5.31 343.8 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 800 83.7 - - 1600 170.8 - - 2400 254.5 - - 3200 404.4 - - 4000 652.0 - - 4320 1011.1 - - 4080 1359.7 - - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 299 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8r) (8:) (1;) (Sr) (8r) (15) (P81) 32118613 4200 193 4.40 2246.0 3865.8 2.530 5.67 259.4 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 800 141.8 127.4 107.9 1600 289.0 162.5 140.3 2400 463.1 211.9 198.6 2800 603.6 283.3 261.2 3200 898.2 368.9 366.9 3260 1092.3 452.3 436.0 3080 1507.4 336.0 284.9 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.v.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 300 TABLE C.2 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. CU NUMBER (8t) (at) (t) (at) (Sr) (%) (psi) 21118513 4200 175 3.99 2450.3 4080.2 2.539 1.40 311.2 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 400 31.3 14.6 24.1 1200 117.5 24.3 48.2 2000 227.1 37.0 90.3 2800 407.2 48.6 174.7 3200 522.4 58.4 265.0 3600 714.5 - - 3800 875.9 - - 3910 1114.0 - - VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- VBV - VEIGHT OF SAMPLE IN VATER; ESSIVE STRENGTH; VBA - VEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 301 TABLE C.2 (CONTINUED). SAMPLE NUMBER VA (8r) VBV (Er) VBA (8:) VB A.C. GMM A.V. CU (8r) (%) (%) (Ps1) 22128613 4200 188 4.28 2198.5 3825.7 2.520 6.70 655.7 DEFORMATION (inches X 0.0001) AXIAL LOAD VERTICAL RADIAL (1/2) RADIAL (1/3) 800 55.7 0.7 2.5 1600 108.5 6.0 9.6 2400 175.3 14.0 18.9 3200 236.6 23.3 29.6 4000 311.7 33.9 45.5 4800 403.6 47.2 64.8 5600 501.3 67.2 92.1 6400 615.1 85.8 116.1 7200 762.6 116.4 160.0 8000 1027.0 179.0 274.5 8240 1280.3 252.2 430.7 8040 1503.0 - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; CU - UNCONFINED COMPR- WBW - WEIGHT OF SAMPLE IN WATER; ESSIVE STRENGTH; WBA - WEIGHT OF SAMPLE IN AIR; A.V.- PERCENT AIR VOIDS; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. APPENDIX D 302 TABLE D.1 UNCONFINED TRIAXIAL CREEP TESTS SAMPLE VA VB A.C. VBV NUMBER (8:) (8:) (t) (Sr) GMM A.V. (%) 11117513 4200 189 4.31 2445.1 4063.6 2.546 1.39 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 25.5 - 2.8 2 36.5 - 4.6 5 87.5 - 7.6 10 105.0 - 7.6 20 127.5 - 10.0 30 142.5 - 10.0 60 170.0 - 10.0 100 193.5 - 12.6 200 225.3 - - 400 264.9 - - 600 287.2 - - 800 307.7 - - 950 314.5 - 25.0 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; WBW - WEIGHT OF SAMPLE IN WATER; WBA - WEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE D.1 (CONTINUED). 303 SAMPLE WA NUMBER (3:) WB A.C. (Sr) (3) VBV (8r) VBA (8r) GMM A.V. (%) 11117613 4200 189 4.31 2371.3 3989.3 2.546 3.16 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 367.0 110.0 0.0 2 436.5 133.0 -4.0 5 556.0 181.0 -5.0 7 605.5 203.0 -10.0 10 667.0 235.0 -10.0 20 815.5 322.0 -10.0 30 947.5 417.0 4.0 40 1111.8 - - 45 1210.6 - - 50 1352.1 - - 56 1557.5 1102.0 278.0 60 1807.0 1451.0 482.0 62 2531.0 1566.0 522.0 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; VBV - VEIGHT OF SAMPLE IN VATER; VBA - VEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 304 TABLE D.1 (CONTINUED). SAMPLE VA VB A.C. WBW VBA GMM A.V. NUMBER (Sr) (Er) (s) (Er) (8r) (%) 11117713 4200 189 4.31 2136.5 3720.3 2.546 7.74 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; VBV - VEIGHT OF SAMPLE IN VATER; WBA - WEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 305 TABLE D.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. NUMBER (8r) (8:) (%) (8r) (8:) (%) 11217513 4200 186 4.25 2389.1 4016.6 2.547 3.10 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 176.0 20.4 37.7 2 190.4 22.3 42.2 5 213.5 29.2 48.5 10 238.4 38.9 57.3 20 263.5 47.6 63.7 60 333.7 70.0 92.1 99 348.8 - - 960 1410.1 1211.2 990.2 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; - VEIGHT OP SAMPLE IN VATER; VBA - VEIGHT OF SAMPLE IN AIR; - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 306 TABLE D.1 (CONTINUED). SAMPLE NUMBER VA VB A.C. VBV VBA (8r) (8:) (i) (St) (St) GMM A.V. (%) 11217613 4200 186 4.25 2340.3 3948.6 2.547 3.61 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 509.0 158.0 180.0 2 625.0 212.0 220.0 5 861.0 330.0 316.0 8 1081.1 - - 10 1266.0 632.0 516.0 11 1383.9 - - 12 1533.8 - - 13 1715.1 - - 14 2021.3 - - 15 2639.5 1990.0 1534.0 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; VBV - VEIGHT OF SAMPLE IN VATER; VBA - VEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 307 TABLE D.1 (CONTINUED). SAMPLE VA VB A.C. VBV WBA GMM A.V. NUMBER (8:) (Sr) (V) (St) (St) (%) 11317513 4200 178 4.07 2377.5 3997.7 2.553 3.35 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 395.4 114.9 45.4 2 436.6 137.1 54.2 5 506.8 175.2 75.2 10 564.5 220.2 95.3 20 644.8 295.3 127.9 30 708.4 - - 35 754.1 - - 40 806.3 - - 45 863.5 - - 50 940.3 - - 55 1045.3 - - 60 1208.4 - - 65 1584.1 - - VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; VBV - VEIGHT OF SAMPLE IN VATER; VBA - VEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 308 TABLE D.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. NUMBER (8:) (8r) (1) (at) (Sr) (%) 12117513 4200 196 4.46 2371.0 4002.7 2.543 3.54 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 193.0 40.7 15.7 2 218.3 50.1 23.0 5 253.4 62.7 27.0 10 283.5 72.7 32.0 20 313.6 85.2 38.0 30 331.5 - - 50 361.9 - - 70 376.4 - - 100 397.6 128.3 55.0 200 425.1 - - 300 451.0 166.6 81.7 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; VBV - VEIGHT OF SAMPLE IN WATER; WBA - VEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE D.1 (CONTINUED). 309 SAMPLE WA NUMBER (gr) WB A.C. (8!) (5) VBV (8r) WBA GMM A.V. (8r) (%) 12117613 4200 196 4.46 2320.0 3947.1 2.543 4.61 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 238.2 46.4 25.6 2 262.8 56.3 32.0 5 309.6 57.3 44.1 10 342.2 63.2 54.1 20 378.5 73.3 68.1 50 433.7 95.4 91.1 100 485.1 121.5 118.2 150 518.3 - - 200 547.7 157.5 154.8 300 610.6 - - 400 673.1 264 6 240.7 450 721.3 - - 500 777.7 - - 550 855.8 - - 600 973.4 - - 630 1082.5 - - 650 1205.9 - - 660 1285.5 - - 670 1383.1 - - 680 1527.0 - - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; WBW - WEIGHT OF SAMPLE IN WATER; WBA - WEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE D.1 (CONTINUED). 310 SAMPLE NUMBER VA (Sr) VB A.C. (at) (t) VBV (8r) VBA (8r) GMM A.V. (%) 12117713 4200 196 4.46 2153.6 3758.7 2.543 7.91 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 475.4 177.6 68.6 2 573.2 231.0 91.5 5 752.7 341.2 132.2 10 953.4 499.9 194.3 15 1128.0 - - 20 1294.1 - - 25 1473.5 - - 28 1597.1 - - 30 1687.6 - - 33 1836.1 - - 35 1949.0 - - 38 2137.2 - - 40 2291.1 - - 42 2471.9 - - 44 2716.3 - - VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; VBV - VEIGHT OF SAMPLE IN VATER; VBA - VEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 311 TABLE D.1 (CONTINUED). SAMPLE VA WB A.C. WBW VBA GMM A.V. NUMBER (8r) (8:) (3) (8:) (8r) (%) 21117513 4200 175 3.99 2463.4 4100.8 2.539 1.36 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 314.1 48.6 64.4 2 393.9 57.7 98.0 5 521.9 75.2 137.0 10 639.8 97.8 174.0 22 800.4 135.4 224.0 30 863.3 - - 50 970.8 - - 70 1052.4 - - 90 1229.4 318 4 352 0 100 1175.1 - - 120 1241.0 - - 160 1368.1 - - 179 1430.1 - - 189 1542.6 496.4 394 0 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; WBW - WEIGHT OF SAMPLE IN WATER; WBA - WEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 312 TABLE D.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. NUMBER (Sr) (8r) (’3) (8:) (Sr) (is) 21117613 4200 175 3.99 2257.2 3864.0 2.539 5.29 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 437.9 150.1 125.2 2 561.5 219.0 184.0 4 744.0 - - s 798.4 369.5 297.0 8 1043.4 - - 10 1200.0 - - 12 1371.1 - - 14 1585.1 - - 16 1873.8 - - 17 2065.4 - - 18 2316.7 - - VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; VBV - VEIGHT OF SAMPLE IN VATER; VBA - VEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE D.1 (CONTINUED). 313 SAMPLE NUMBER VA (Er) VB A.C. (8r) (%) VBV VBA GMM (gr) (Er) A.V. (%) 21117713 4200 175 3.99 2162.7 3730.8 2.539 6.29 TIME (min) DEFORMATION (inches X 0.0001) VERTICAL RADIAL (1/2) RADIAL (1/3) OO‘ON‘IGUIéUNH P‘P‘ 582. 761. 907. 1045. 1182. 1315. 1473. 1651. 1889. 2031. 2194. N§O§ON¥~OOOH 191.7 224.6 WA A.C. WBW WBA GMM TOTAL WEIGHT OF DRY AGGREGATES; WB - PERCENT ASPHALT CONTENT; WEIGHT OF SAMPLE IN WATER; WEIGHT OF SAMPLE IN AIR; MAXIMUM SPECIFIC GRAVITY; A.V.- WEIGHT OF BITUMEN; PERCENT AIR VOIDS; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE D.1 (CONTINUED). 314 SAMPLE WA NUMBER (gr) VB A.C. (Sr) (s) VBV (8r) VBA (Sr) GMM A.V. (%) 21217613 4200 176 4.03 2304.5 3913.6 2.537 4.13 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 136.7 24.0 12.8 2 163.1 32.6 18.1 5 205.7 42.6 25.7 10 243.4 52.6 32.4 20 286.0 65.2 41.0 50 351.3 85.2 58.1 110 424.0 110.3 79.0 180 476.7 132.9 102.0 400 594.6 - - 600 678.6 - - 800 754.7 - - 1000 833.8 - - 1227 915.8 206.8 363.0 1301 945.9 438.7 367.6 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; WBW - WEIGHT OF SAMPLE IN WATER; WBA - WEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 315 TABLE D.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. NUMBER (8r) (8:) (%) (St) (St) (%) 21317613 4200 175 3.99 2250.0 3858.4 2.537 5.44 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 441.4 84.6 63.8 2 537.0 - - 5 723.7 - - 7 836.9 - - 10 999.0 - - 12 1116.3 - - 14 1250.6 - - 16 1410.7 - - 18 1628.7 - - 20 2004.9 - - VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; VBV - VEIGHT OF SAMPLE IN VATER; WBA - VEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE D.1 (CONTINUED). 316 SAMPLE WA NUMBER (gr) VB A.C. (8r) (%) VBV (Sr) WBA GMM A.V. (3) 31117513 4200 182 4.16 2417.5 4051.4 2.541 2.42 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 211.0 41.1 19.4 2 258.6 47.9 22.2 5 339.2 58.0 26.2 10 418.7 69.5 30.4 20 506.4 84.8 38.0 50 645.5 120.0 59.0 100 790.1 168.8 89.6 150 874.0 - ' - 200 942.6 - - 300 1070.7 - - 400 1206.1 - - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; WBW - WEIGHT OF SAMPLE IN WATER; WBA - WEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 317 TABLE D.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. NUMBER (8r) (8:) 0) (Sr) (81:) (1:) 31117713 4200 182 4.16 2146.5 3701.7 2.541 6.33 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 406.6 106.2 109.8 2 513.7 138.5 153.4 5 727.0 213.3 267.4 10 966.4 317.1 471.0 15 1172.2 - - 20 1376.3 557.1 590.5 25 1602.4 - - 29 1808.9 - - 33 2330.9 - - 50 - - - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; WBW - WEIGHT OF SAMPLE IN WATER; WBA - WEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 318 TABLE D.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. NUMBER (8:) (813)“) (8:) (8r) (1:) 12217713 4200 197 4.48 2107.2 3676.3 2.541 7.79 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; VBV - VEIGHT OF SAMPLE IN VATER; VBA - VEIGHT OP SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION]CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. TABLE D.1 (CONTINUED). 319 SAMPLE NUMBER VA (Er) VB A.C. (8:) (t) VBV (Sr) VBA (8r) GMM A.V. (%) 12317713 4200 186 4.24 2101.0 3660.0 2.549 7.90 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 653.5 - - 2 816.7 - - 5 1156.2 - - 7 1365.0 - - 8 1477.2 - - 9 1589.3 - - 10 1713.1 - - 11 1840.7 - - 12 1979.9 - - 13 2132.6 - - 14 2240.9 - - 15 2370.5 - - 20 2311.4 - - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; WBW - WEIGHT OF SAMPLE IN WATER; WBA - WEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 320 TABLE D.1 (CONTINUED). SAMPLE VA VB A.C. VBV VBA GMM A.V. NUMBER (at) (Sr) (%) (8t) (Sr) (b) 32117613 4200 193 4.40 2325.1 3957.8 2.530 4.19 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 280.5 34.0 35.6 2 357.6 38.0 42.6 5 464.5 - - 10 567.6 - - 20 707.4 - - 30 812.3 - - 40 912.9 - - 50 1022.8 - - 60 1132.4 - - 70 1332.2 - - 80 1544.5 - - 84 1644.3 - - 104 1700.0 573.2 527.4 WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - WEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; WBW - WEIGHT OF SAMPLE IN WATER; WBA - WEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 321 TABLE D.1 (CONTINUED). SAMPLE VA VB A.C. WBW VBA GMM A.V. NUMBER (8r) (8:) (t) (gr) (8r) (%) 22117613 4200 188 4.28 2250.4 3880.4 2.520 5.53 DEFORMATION (inches X 0.0001) TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 145.6 21.7 19.7 2 171.6 - - 5 213.7 - - 10 260.3 - - 20 322.3 - - 50 451.9 - - 100 609.5 - - 150 763.7 - - 200 936.4 - - 250 1171.8 - - 994 1505.6 761.9 659.0 VA - TOTAL VEIGHT OF DRY AGGREGATES; VB - VEIGHT OF BITUMEN; A.C. - PERCENT ASPHALT CONTENT; A.V.- PERCENT AIR VOIDS; VBV - VEIGHT OF SAMPLE IN VATER; VBA - VEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. 322 TABLE D.1 (CONTINUED). SAMPLE VA VB A.C. WBW NUMBER (8:) (St) (a) (Sr) VBA (8r) GMM A.V. (%) 11127513 4200 189 4.31 2457.9 4092.6 2.546 1.67 DEFORMATION (inches X 0.0001) WEIGHT OF BITUMEN; PERCENT AIR VOIDS; TIME (min) VERTICAL RADIAL (1/2) RADIAL (1/3) 1 68.3 - - 2 72.2 - - 5 80.6 - - 10 87.0 - - 20 96.3 - - 50 111.6 - - 100 125.3 - - 150 132.2 - - 200 139.1 - - 300 148.9 - - 400 156.3 - - 500 162.7 - - 600 168.6 - - 800 178.4 - - 1000 185.3 - - 1200 191.7 - - WA - TOTAL WEIGHT OF DRY AGGREGATES; WB - A.C. - PERCENT ASPHALT CONTENT; A.V.- WBW - WEIGHT OF SAMPLE IN WATER; WBA - WEIGHT OF SAMPLE IN AIR; GMM - MAXIMUM SPECIFIC GRAVITY; ELA. AND TOT. - ELASTIC AND TOTAL DEFORMATION/CYCLE; PLA. - CUMULATIVE PLASTIC (PERMANENT) DEFORMATION; RADIAL (1/2) AND (1/3) - RADIAL DEFORMATIONS AT THE MIDDLE AND ONE THIRD THE HEIGHT OF THE SAMPLE. APPENDIX E 323 Figure E.1 presents a typical output from the SPSS/PC+ program. It shows plots of standardized weighted residuals versus the indepen- dent and dependent variables, also standardized. FIGURE B.1 (a) (b) (C) (d) (e) (f) (9) STANDARDIZED SCATTERPLOTS OF WEIGHTED RESIDUALS VERSUS INDEPENDENT VARIABLES AND RESILIENT MODULUS. Natural Logarithm of the Percent Air Voids: Aggregate Angularity; Natural Logarithm of the Kinematic Viscosity Of the Asphalt: Aggregate Gradation: Natural Logarithm of the Cyclic Load: Test Temperature; and Natural Logarithm of the Resilient Modulus. 324 - Residual Down Across - ln(AV) 000 .. N 124. s . l x \I O a a m M c s 000* +.I||+.I|u+.lnu+.lnu+.Inu+.luu+ .”t H. 0.03000 0 0 ”00* +l|+||+l|+|l+|l+|l+ 3 2 1 o 1 2 a“. 3 Out 1 O 1 2 2 Down - Residual Out ++-----+-----+-----+-----+-----+-——-—++ ACI’OSS - ANG 000 126 Max N (m Symbols 000* + | | + l l + I | + | | + I | + | I + 00000**00* 000* 000 ** 000 0 .*****:o +||+ll+l|+ll+ll+ll+ 3 2 1 0 1 2 1.3 Out ++-----+--—--+-----+-----+-—---+-----++ -1 3 Out 1 2 O -2 -3 325 000 .0 N 240 S 1 1 X ) O a C m M < S 000* ++ll+l|+l|+|l+|l+ll+ + . . . l. a. u+ d. .1. S. e. R . + .A m“ 000***** 00 00000 O. 0.? _ . _ - 00 000 00 _ + _ . \l. W . . 7\+ n. 0000000 0 l. . .- . 8+ c0~++lll+ll+lll+ll+lll+llll+ r+c3 2 1 O 1 2 3 CU . . . AAU Out ++-----+-----+-----+-----+-----+-----++ 3 Out -2 -1 0 1 2 -3 Down - Residual Out ++-----+-----+-----+-----+-----+-----++ Across - GRAD 000 o. N 24.9 S a a m m M < S 000* +Il+|l+l|+|l+l|+ll+ 00000**000000 00 0 00****0000 00 +|l+l|+ll+ll+ll+|l+ 3 2 1 o 1 2 3 _ 3 Out -2 -1 O 1 2 -3 326 - Residual Out ++---—-+-----+-----+-----+—--—-+----_++ Down LNCL ACIOSS - 000 .4 N 248 S l x ) O a e m M < S ..* +||+|l+|l+|l+|l+||+ 0 000* 0 0 0 000**00* 00 000000 +ll+ll+ll+|l+ll+|l+ 3 Out 0 1 2 -1 -2 -3 Down - Residual Across - TT 000 .o N 363 S 1 1 x ) O a f m M ,. S 000* +||+|l+||+ll+ll+ll+ 0000**** 0000 000 +||+||+|I+|l+l|+|l+ 3 2 1 0 1 2 3 - 3 Out 0 1 2 -1 -2 -3 327 Across - ln(MRcal) Down - Residual Out ++ ----- + ----- + ----- + ----- + ----- + ----- ++ 3 + + Symbols: | I l I Max N 2 + + I . I 0 100 I - .. I : 2.0 1 + . : .: . . + i: 4.0 l O O O : O O. O O O O I I 0 0:0 : 0* 0 0 I 0 + .: . .: . + (g) I O: O O * O I I . . . I -1 + . . + I . | I . . . | “'2 + . + I - - I l . I ‘3 + , + Out ++ ----- + ----- + ----- + ----- + ----- + ————— ++