OVERDUE FINES ARE 25¢ PER DAY PER ITEM Return to book drop to remove ' this checkout from your record. . 42 ‘Q .’.§I ‘ 4..., ‘Jl. (It. .03 i all! ‘ a. ’1 '9. ‘ HI. 0 I my .11'." PERMANENT DEFORMATION OF COHESIONLESS SUBGRADE MATERIAL UNDER CYCLIC LOADING By Rodney Ward Lentz A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil Engineering 1979 ABSTRACT PERMAMENT DEFORMATION OF COHESIONLESS SUBGRADE MATERIAL UNDER CYCLIC LOADING By Rodney Ward Lentz The trend toward ever increasing axle loads on highway and air- port pavements has led to the development of numerous methods of pavement design. All of these methods agree that, for flexible pave- ments, subgrades should not undergo significant volume change or permanent deformation under the application of traffic loads. Thus,para- meters for characterizing permanent deformation of subgrade materials are required in each of these methods. Consequently, there exists a need for research in material characterization, particularly in development of simplified test procedures which will reduce the manpower, time and money required. In this research study, a very simple and economical test procedure was developed to evaluate parameters of cohesionless sub- grade soils. By this procedure, permanent strain in sand subjected to cyclic loading can be characterized using stress and strain para- meters from the universally accepted static triaxial test. To develop the procedure duplicate samples were tested using both static triaxial apparatus and a closed-loop electro-hydraulically actuated cyclic triaxial system. The dynamic test results were normalized Rodney Ward Lentz with respect to parametersobtained from the corresponding static tri- axial test. The normalized cyclic principal stress difference showed a unique relationship to the normalized accumulated permanent strain. This relationship was found to be independent of moisture content, density, and confining pressure. Based on this finding a constitutive equation was developed which allows prediction of permanent strain after any number of load repetitions using only parameters obtained from a static triaxial test. To my parents ii ACKNOWLEDGMENTS The writer wishes to express his appreciation to his major professor, Dr. Gilbert Y. Baladi, Assistant Professor of Civil Engineering, for his guidance and numerous helpful suggestions during the conducting of the research and preparation of this dissertation. Thanks also to members of the writer's doctoral committee: Dr. G. C. Blomquist, Associate Professor of Civil Engineering; Dr. L. E. Vallejo, Assistant Professor of Civil Engineering; and Dr. G. L. Cloud, Professor of Metallurgy, Mechanics, and Material Science. The writer also owes his appreciation to: his friend Dr. Amir Al-Khafaji for his constant encouragement; Mr. Greg Orsolini for his assistance in the laboratory; and to Ms. Ann Greenfield for her dedication in the typing of this dissertation. Special appreciation is also due his wife Nancy, and daughter Sheri, who make it all worth- while. TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS CHAPTER 1. INTRODUCTION 1. 2. Statement of the Problem Purpose and Scope II. REVIEW OF LITERATURE l. 2. 3. Design Methodologies Previous Studies of Dynamic Properties of Sand .l Effect of Number of Load Repetitions Effect of Confining Pressure Effect of Stress Level Effect of Stress History Effect of Load Duration and Frequency Effect of Density Effect of Moisture Content Effect of Fines Content Cyclic Triaxial Testing NNNNNNNN mummbwm III. LABORATORY INVESTIGATION 1 2. 01014:- Test Materials Test Variables 2.l Number of Load Repetitions 2.2 Confining Pressure 2.3 Cyclic Principal Stress Difference 2.4 Stress History 2.5 Load Duration and Frequency Sample Variables 3.l Density 3.2 Moisture Content Equipment Sample Preparation Testing Procedure 6.1 Cyclic Triaxial Test 6.2 Static Triaxial Test iv Page vi vii xii IV. TEST RESULTS 1 Static Traixial Tests l. l Highway Subgrade Sand l.2 Stamp Sand Cyclic Triaxial Tests 2.l Highway Subgrade Sand 2.2 Stamp Sand V. DISCUSSION 1. 2. 0301b General Effect of Test Variables 2.l Number of Load Repetitions 2.2 Confining Pressure 2.3 Stress Level 2.4 Stress History Effect of Sample Variables 3.l Density 3.2 Moisture Content Normalizing Effect of Static Stress-Strain Development of Constitutive Relationship Implementation VI. CONCLUSIONS AND RECOMMENDATIONS l. 2. Conclusions Recommendations LIST OF REFERENCES APPENDICES A. Description of Equipment Calibration Information Data Table of Conversion Factors 159 T75 177 217 Table 4.l 5.1 5.2 5.3 LIST OF TABLES RESULTS OF CYCLIC TRIAXIAL TESTS ON HIGHWAY SUBGRADE SAND REGRESSION PARAMETERS FOR LEAST SQUARES FIT OF EQUATIONS 5.1 AND 5.2 COMPARISON OF MEASURED AND CALCULATED PERMANENT STRAIN RUT DEPTH COMPUTATION vi Page 75 95 T35 T47 2.10 LIST OF FIGURES MODULAR STRUCTURE OF VESYS. LOAD HISTORY USED IN "INCREMENTAL STATIC- DYNAMIC" TEST. RELATIONSHIP BETWEEN PERMANENT STRAIN AND NUMBER OF STRESS APPLICATIONS FOR NON-COHESIVE SOILS. INFLUENCE OF NUMBER OF LOAD REPETITIONS AND DEVIATOR STRESS RATIO ON PLASTIC STRAIN IN A PORPHYRITIC GRANITE GNEISS-THREE PERCENT FINES. VARIATION OF RESILIENT STRAIN DURING DRAINED AND UNDRAINED TESTS,(1 kN/m2 = 0.15 psi). VARIATION OF PERMANENT STRAIN DURING DRAINED AND UNDRAINED TESTS,(1 kN/m2 = 0.15 psi). MODES OF APPLICATION OF CONFINING STRESS. PERMANENT STRAIN VERSUS DEVIATOR STRESS FOR VARIOUS CELL PRESSURES,(1 kN/m2 = 0.15 psi). RELATIONSHIP BETWEEN PERMANENT STRAIN AND APPLIED STRESSES. MODE OF APPLICATION OF DEVIATOR STRESS. SUMMARY OF PLASTIC STRESS-STRAIN CHARACTERISTICS AT 100,000 LOAD REPETITIONS AND A CONFINING PRESSURE 0F 10 PSI. EFFECT OF DURATION OF STRESS APPLICATION 0N DEFORMATION 0F SILTY SAND. EFFECT OF INTERVAL BETWEEN STRESS APPLICATION 0N DEFORMATION 0F SILTY SAND. EFFECT OF DENSITY ON THE PLASTIC STRAIN ACCUMULATION WITH LOAD REPETITIONS. vii Page 13 13 15 15 17 19 19 19 20 23 24 26 Figure 2. A wwmm hbhbhwwwww b 01th 15 .16 .17 .18 V03 d INFLUENCE OF FINES AND DEVIATOR STRESS RATIO ON THE PLASTIC STRAINS IN A CRUSHED GRANITE GNEISS BASE AFTER 100,000 LOAD REPETITIONS. THE VARIATION OF STRESSES ON A PAVEMENT ELEMENT DUE TO THE PASSAGE OF A ROLLING WHEEL LOAD. IN SITU STRESSES BENEATH A ROLLING WHEEL. STRESSES ON SAMPLE DURING CYCLIC TRIAXIAL TEST. GRAIN SIZE DISTRIBUTION OF HIGHWAY SUBGRADE SAND. MOISTURE - DENSITY RELATIONSHIP FOR HIGHWAY SUBGRADE SAND. GRAIN SIZE DISTRIBUTION OF STAMP SAND. MOISTURE-DENSITY RELATIONSHIP FOR STAMP SAND. COMPACTION MOLD AND HAMMER. MTS CYCLIC TRIAXIAL EQUIPMENT. TYPICAL OUTPUT FROM STRIP CHART RECORDER. STATIC STRESS-STRAIN FOR HIGHWAY SUBGRADE SAND. STATIC STRESS-STRAIN FOR HIGHWAY SUBGRADE SAND- STATIC STRESS—STRAIN FOR HIGHWAY SUBGRADE SAND- STATIC STRESS-STRAIN FOR HIGHWAY SUBGRADE SAND. MOHR CIRCLES FOR STATIC TRIAXIAL TESTS OF HIGHWAY SUBGRADE SAND. STATIC STRESS-STRAIN FOR STAMP SAND. STATIC STRESS-STRAIN FOR STAMP SAND. EFFECT OF CYCLIC PRINCIPAL STRESS DIFFERENCE AND NUMBER OF LOAD CYCLES 0N PERMANENT STRAIN AT CONSTANT CONFINING PRESSURE FOR HIGHWAY SUBGRADE SAND MATERIALS. EFFECT OF CYCLIC PRINCIPAL STRESS DIFFERENCE AND NUMBER OF LOAD CYCLES 0N PERMANENT STRAIN AT CONSTANT CONFINING PRESSURE FOR HIGHWAY SUBGRADE SAND MATERIALS. viii Page 28 29 29 31 33 34 36 37 42 42 49 56 57 58 59 60 62 63 65 66 Figure 4.10 EFFECT OF NUMBER OF CONFINING MATERIAL. EFFECT OF NUMBER OF CONFINING MATERIAL. EFFECT OF NUMBER OF CYCLIC PRINCIPAL STRESS DIFFERENCE LOAD CYCLES 0N PERMANENT STRAIN AT PRESSURE IN HIGHWAY SUBGRADE SAND CYCLIC PRINCIPAL STRESS DIFFERENCE LOAD CYCLES 0N PERMANENT STRAIN AT PRESSURE IN HIGHWAY SUBGRADE SAND CYCLIC PRINCIPAL STRESS DIFFERENCE LOAD CYCLES 0N PERMANENT STRAIN IN SUBGRADE SAND. EFFECT OF NUMBER OF CYCLIC PRINCIPAL STRESS DIFFERENCE LOAD CYCLES 0N PERMANENT STRAIN IN SUBGRADE SAND- EFFECT OF NUMBER OF CYCLIC PRINCIPAL STRESS DIFFERENCE LOAD CYCLES 0N PERMANENT STRAIN IN SUBGRADE SAND- PERMANENT STRAIN HIGHWAY SUBGRADE SAND- PERMANENT STRAIN HIGHWAY SUBGRADE SAND. EFFECT OF STRESS HISTORY 0N PERMANENT STRAIN HIGHWAY SUBGRADE SAND. EFFECT OF STRESS HISTORY 0N PERMANENT STRAIN HIGHWAY SUBGRADE SAND. EFFECT OF STRESS HISTORY 0N PERMANENT STRAIN HIGHWAY SUBGRADE SAND. EFFECT OF STRESS HISTORY 0N PERMANENT STRAIN HIGHWAY SUBGRADE SAND. AND CONSTANT AND CONSTANT AND HIGHWAY AND HIGHWAY AND HIGHWAY VERSUS NUMBER OF LOAD CYCLES FOR VERSUS NUMBER OF LOAD CYCLES FOR FOR FOR FOR FOR EFFECT OF DEGREE 0F SATURATION 0N PERMANENT STRAIN AT N = 10,000 CYCLES. PERMANENT STRAIN VERSUS NUMBER OF LOAD CYCLES FOR STAMP SAND. PERMANENT STRAIN VERSUS NUMBER OF LOAD CYCLES FOR STAMP SAND. ix Page 67 68 70 71 72 73 74 79 80 81 82 83 85 86 Figure 4.24 5.10 5.11 5.12 5.13 PERMANENT STRAIN VERSUS NUMBER OF LOAD CYCLES FOR STAMP SAND. LOG-LOG PLOT. TYPICAL PLOT 0F PERMANENT STRAIN VERSUS NUMBER OF LOAD CYCLES FOR HIGHWAY SUBGRADE SAND MATERIALS. EFFECT OF CONFINING PRESSURE AND CYCLIC PRINCIPAL STRESS DIFFERENCE 0N PERMANENT STRAIN DURING FIRST LOAD CYCLE. EFFECT OF CONFINING PRESSURE AND CYCLIC PRINCIPAL STRESS DIFFERENCE ON THE RATE OF CHANGE OF PERMANENT STRAIN DURING CYCLIC LOADING. EFFECT OF CONFINING PRESSURE AND NUMBER OF LOAD CYCLES ON THE CUMULATIVE PERMANENT STRAIN IN HIGHWAY SUBGRADE SAND. EFFECT OF CONFINING PRESSURE AND CYCLIC PRINCIPAL STRESS DIFFERENCE RATIO 0N PERMANENT STRAIN DURING FIRST LOAD CYCLE. EFFECT OF CONFINING PRESSURE AND CYCLIC PRINCIPAL STRESS DIFFERENCE RATIO 0N RATE OF CHANGE OF PERMANENT STRAIN. PERMANENT STRAIN VERSUS NUMBER OF LOAD CYCLES AT ONE STRESS RATIO AND DIFFERENT CONFINING PRESSURE FOR HIGHWAY SUBGRADE SAND MATERIALS. CYCLIC PRINCIPAL STRESS DIFFERENCE VERSUS PERMANENT STRAIN AT 10,000 LOAD APPLICATIONS. CYCLIC PRINCIPAL STRESS DIFFERENCE RATIO VERSUS PERMANENT STRAIN AT 10,000 LOAD APPLICATIONS. COMPARISON OF STRESS HISTORIES. EFFECT OF PARTICLE INTERLOCKING DUE TO DENSITY INCREASE. EFFECT OF DENSITY 0N PERMANENT STRAIN. NORMALIZED CYCLIC PRINCIPAL STRESS DIFFERENCE VERSUS PERMANENT STRAIN. STATIC STRESS-STRAIN FOR HIGHWAY SUBGRADE SAND. NORMALIZED CYCLIC PRINCIPAL STRESS DIFFERENCE VERSUS NORMALIZED PERMANENT STRAIN. Page 87 92 101 102 103 105 106 108 110 110 113 115 118 123 124 126 Figure 5.16 5.23 5.24 A.5 A.6 A.7 NORMALIZED CYCLIC PRINCIPAL STRESS DIFFERENCE NORMALIZED PARAMETER a, NORMALIZED CYCLIC PRINCIPAL STRESS DIFFERENCE VERSUS PARAMETER b. RELATIONSHIP BETWEEN CONFINING PRESSURE AND REGRESSION CONSTANTS n AND m. COMPARISON OF MEASURED AND CALCULATED PERMANENT STRAIN IN FIRST LOAD CYCLE. COMPARISON OF MEASURED AND CALCULATED CHANGE IN PERMANENT STRAIN FROM N = 1 TO N = 10000. COMPARISON OF MEASURED AND CALCULATED PERMANENT STRAIN AT 10000 CYCLES. VERTICAL STRESS DUE TO TIRE USING ONE-LAYER ELASTIC EQUATION. STATIC STRESS STRAIN FOR HIGHWAY SUBGRADE SAND. PERMANENT STRAIN VERSUS NUMBER OF LOAD CYCLES FOR HIGHWAY SUBGRADE SAND- SCHEMATIC 0F CYCLIC TRIAXIAL TEST EQUIPMENT. SCHEMATIC 0F MTS ELECTROHYDRAULIC CLOSED LOOP TEST SYSTEM. MTS 406.11 CONTROLLER. GAIN AND STABILITY ADJUSTMENT. MTS 436.11 CONTROL UNIT. CONTROL BOX. SPLIT SAMPLE MOLD AND COMPACTION HAMMER. C.l through C.39 PERMANENT STRAIN VERSUS NUMBER OF LOAD CYCLES FOR HIGHWAY SUBGRADE SAND. xi Page 129 130 133 139 140 141 144 146 149 160 161 164 166 171 173 173 178 - 216 Yd Ep,€ E .9ssd LIST OF SYMBOLS Regression parameters indicating permanent strain during first load cycle Regression parameters indicating rate of change of permanent strain with increasing load cycles. Crack Index Uniformity coefficient Specific gravity regression constants Number of load cycles Patched area Present Serviceability Index Rut Depth Correlation coefficient Degree of saturation Static strength Slope Variance Moisture content Permanent deformation response parameter Dry unit weight Permanent deformation Permanent strain Static strain at 95% of static strength Permanent deformation response parameter xii Cyclic principal stress difference Major principal stress Minor principal stress = confining pressure Angle of internal friction xiii CHAPTER I INTRODUCTION 1. Statement of the Problem The serviceability of a pavement structure depends on several parameters. These include the amount of permanent deformation and cracking which have occurred as the consequence of traffic loading (1,55,56)*. Thus, an important factor in any overall pavement design system, whether it be empirical or rational, is the consideration of permanent deformation (l,5,l9,27,36,40,56). Permanent deformation in pavements is the result of two different mechanisms: densification (volume change) and shear deformation (plastic flow with no volume change) (6,56). The portion of deforma— tion due to densification can be minimized by proper control of compac- tion during construction (1,36,42,56). The limitation of plastic flow is basic to structural design of pavement systems. General practice is to design pavement layers of such thickness and strength that the stresses transmitted to the subgrade will be low enough, relative to the strength of the soil, so that permanent defor- mation in the subgrade will be minimized (56). This approach is fundamental to most currently applied empirical design procedures (e.g. CBR, elastic layer analysis, etc.). The major disadvantage to empiri- cal design procedures is that they do not have the capacity to predict *Figures in brackets indicate reference numbers in the List of References. 2 the amount of deformation after a given number of load applications (19,24,27,56). A more rational design method should have the capability of pre- dicting cumulative deformations in any pavement system (19,27,36,56). The most likely method to gain acceptance in the future will be one that uses either linear or nonlinear elastic and/or viscoelastic theory coupled with laboratory determined constitutive relationships to predict permanent deformation (5,27,36,56). The success of such a design method will depend upon the availability of reliable procedures for the determination of constitutive deformation relationships for pavement and subgrade materials (5,8,24,36,39,40,57). 2. Purpose and Scope The objectives of the current research study are: 1) Develop a simplified testing procedure for determining material parameters needed to characterize the permanent deformation behavior of cohesionless subgrade soils subjected to cyclic loading. 2) Develop a constitutive relationship to relate cumulative plastic strain in cohesionless subgrade materials under cyclic loading to total strain under static loading. The accomplishment of these objectives involves an investigation of the factors which affect the cumulative permanent deformation of cohesionless subgrade materials subjected to repeated loading. Repeated load triaxial tests were used to evaluate dynamic properties of sand material which had been obtained from the subgrade of highway U.S. 27 in northern Michigan. Triaxial tests were also conducted to obtain static stress-strain behavior. Test procedures are described in Chapter III. The applicability of the results to other materials was assessed by testing samples of a stamp sand obtained from the Michigan Department of Transportation, Division of Testing and Research. The scope of the studies presented in this dissertation includes a detailed description of the cyclic triaxial test system and experi- mental techniques employed to evaluate dynamic properties of subgrade sand. Also included is a discussion of the experimental results and comparison of results of the present study to those reported by other investigators. CHAPTER II REVIEW OF LITERATURE 1. Design Methodologies Permanent deformation in pavements is the result of two differ- ent mechanisms: densification (volume change) and repetitive shear deformation (plastic flow with no volume change) (6,56). Yoder and Witczak (56) described two design methodologies based on limiting permanent deformation. The first of these methodologies is an empirical correlation of excessive deformations related to some predefined failure conditions of the pavement. They further subdivided this category into two procedures. One procedure is based on laboratory or field index tests to categorize the strength of subgrade material. Examples of such tests may be California Bearing Ratio (CBR) or Stabilometer. The other procedure is based on a limiting subgrade strain criterion where strains are calculated using elastic layer theory. The procedure using an index test to categorize material strength is the most widely accepted design pro- cedure for control of repetitive shear deformations (27,55,56). It is assumed that if the pavement layers are constructed with proper quality control the primary source of deformation will be the subgrade (1,36,56). Deformation is controlled by adjustment of the pavement thickness to reduce the stresses on the subgrade to a level such that actual accumulated permanent deformation will not exceed the allowable within the design life of the pavement. The procedure limiting vertical subgrade strain as computed using elastic layer theory is based on the same design philosophy and assumptions (56). However, Chou (13,15) used linear layered elastic computer program and results of laboratory repeated load tests to show that airfield pavements having the same subgrade elastic strains may have different amounts of permanent strain. Both of the above procedures are based on empirical relationships derived from experience and observation. Hence, they are applicable only to a defined range of pavement materials, traffic loads and environmental conditions for which experience is available (19,24,27, 56). Neither procedure predicts the amount of deformation anticipated after a given number of load applications. The second design methodology described by Yoder and Witczak (56) is based on prediction of accumulated deformations in a pavement system using quasi-elastic or viscoelastic approaches. However, these approaches are not presently refined to the point where deformations can be pre- dicted with a level of confidence needed for adequate design solutions. Despite this shortcoming, this methodology is the most preferred for use in a more advanced or rational design method (5,9,12,24,27,35,36,56). Many investigators have suggested that research should be directed towards developing better material characterization techniques for use in such rational design methods (9,24,27,36,39,40). The quasi-elastic approach, as described by Yoder and Witczak (56), uses the results of plastic strains determined by laboratory repeated load tests on pavement material together with elastic theory to predict permanent deformation. The fundamental concept of the analysis is the 6 assumption that plastic strain, ep, is functionally related to the elastic state of stress and number of load repetitions. Thus, elastic theory is used to calculate the expected stress state within the pave- ment, then permanent strain is computed using the laboratory determined constitutive deformation relationship. The laboratory test conditions must simulate the insitu conditions with respect to time, temperature, stress state, moisture, density, etc. Each pavement layer may be sub- divided into convenient thicknesses, Azj, for which the average stress state may be determined. The total deformation of the pavement may be found from n (p = p “t Z ‘3' (2.1) where a? = (a?) (Azj) is the permanent deformation within the jth layer (5,35,56). To take into account change in material proper- ties with time this procedure can be used at different number of load repetitions and the results of all the time increments summed to find cumulative permanent deformation (5). Barksdale (5) tested several unstabilized base materials using repeated load triaxial apparatus. He reported that the plastic stess- strain curves obtained from the tests could be described by hyperbolic functions. The hyperbolic expression used was similar to that develop- ed by Konder (29) and Konder and Zelasko (30,31) and extended by Duncan and Chang (17) for static stress-strain conditions. The expres- sion is of the form _ Od/KC'; ep ' l-[ode(l-sin¢)17t2(Ccos ¢ + 03 sin¢)j (2.2) 7 where - axial permanent strain 0') 'C I relationship defining the initial tangent modulus as a function of confining pressure, 03, (K and n are constants) 7C 0 00 II C = cohesion ¢ = angle of internal friction Rf = a constant relating compressive strength to an asymptotic stress difference Barksdale (5) also recommended that stresses within the pavement struc- ture be calculated using nonlinear elastic or nonlinear viscoelastic theory which gives special attention to the nonlinear, anisotropic material behavior. One pavement design method employing a viscoelastic approach has been developed under the direction of the Office of Research, Federal Highway Administration, (FHWA) (27). The procedure is based on a mechanistic structural subsystem known as VESYS IIM computer program. This computer program predicts the performance of a pavement in terms of its present serviceability index, PSI, derived from the American Association of State Highway Officials (AASHO) Road Test analysis (1, 27). Inputs to the program must be in the form of statistical distri- butions describing material properties, geometry of the pavement section being analysed, traffic, and environment. Program outputs are presented in terms of means and variances of the damage indicators - cracking, rutting, roughness - and serviceability. The VESYS IIM computer program consists of a set of models shown diagramatically in Figure 2.1. These models are: STR ESS olpsi) FIGURE 2.1 MATERIAL RESPONSE PROPERTIES PAVEMENT SYSTEM OEOMETRY MATERIAL DISTRESS PROPERTIES TRAFFIC CONDITIONS ENVIRONMENT DESIGN CRITERIA PRIMARY RESPONSE MODE L Pavement Syn-m Primary Row. DAMAGE RESPONSE MODEL Damn Indicators: racking Roughness Rimi PE R FORMANCE MODE L Snv inability Index .1: 1.: 10.: I USER l INCREMENTAL STATIC SERIES 100.: MODULAR STRUCTURE OF VESYS, (27). __..‘L_- II DYNAMIC SERIES —'* 1‘— 1000 Creep —I> 1000: 1 Tim. t FIGURE 2.2 LOAD HISTORY USED IN "INCREMENTAL STATIC-DYNAMIC" TEST, (27). Primary Response Model The Primary Response Model represents the pavement system by a three layer semi-infinite continuum such that the upper two layers are finite in thickness while the third layer is infinite in extent. Each layer is infinite in the horizontal directions and may have elastic or viscoelastic behavior. The model constitutes a closed form probabilistic solution to the three layer linear viscoelastic boundary value problem. It is valid for a single stationary circu- lar loading at the pavement surface. Stochastic inputs to the model are in terms of the means and variances of the creep compliances for viscoelastic materials, and elastic or resilient moduli for elastic materials. The output from the Primary Response Model, in the form of statistical estimates of stresses, strains and deflec- tions, is used as input to the Damage Model. Damage Model The Damage Model consists of three separate models each designed to predict distress accumulation in the pavement. 8.1 The Rut Depth Model uses the results from the Primary Response model along with laboratory determined permanent deformation characteristics of the pavement and subgrade materials to compute the mean and variance of the rut depth accumulated over any incremental analysis period. 8.2 The Roughness Model uses the rut depth output from the Rut Depth Model, along with the assumption that rut depth at any time along the wheel path will vary due to material lO variability and non-uniform construction practices, to compute the roughness in terms of slope variance as defined by AASHO (1). 8.3 The Fatigue Cracking Model is a phenomenological model which predicts the extent of cracking of the asphalt layer based on Miner's hypothesis. This cracking is due to fatigue resulting from tensile strain at the bottom of the asphalt concrete layer. A crack index is computed after any number of load applications using the viscoelastic radial strain amplitude at the bottom of the asphalt concrete layer along with labora- tory determined fatigue properties of the asphalt concrete. The radial strain amplitude is found at the peak of a haversine load pulse of specified duration applied to the pavement surface. From this crack index the expected area of cracking is computed in square yards cracked per 1000 square yards. The output from the above three parts of the Damage Model, i.e., rut depth, slope variance, and crack index, is used as input to the Performance Model. Performance Model The Performance Model computes a Serviceability Index, Pavement Reliability and Expected Life of the Pavement. The serviceability index, PSI, is defined according to the AASHO Interim Guide 1972 (l) as PSI = a + b log10 (l + SV) + c/C + P + dR2 (2.3) 11 where a = 5.03, b = 0.01, c = 1.91, d = 1.38 are multiple regressions constants SV = Slope Variance (Roughness) C = Crack Index R = Rut depth P = Patched area The expected value and variance of the PSI is then calculated at anytime. The reliability of the serviceability index at any time is defined as the probability that the PSI is above some unaccept- able level, PSIf, which has been established beforehand. The distribution of PSI's is obtained assuming a Gaussian distribu- tion. The expected life of the pavement is the time for the Serviceability Index to reach the unacceptable level, PSIf. Two categories of mechanical properties are required for the VESYS IIM structural analysis, primary response properties, and distress properties. The primary response properties define the response of layer materials to the given loads and environments. These properties are in the form of elastic or viscoelastic characteristics which may exhibit non-linear behavior because of previous load histories, plastic effects, and stress dependencies. The distress properties are those properties defining the capability of the materials to withstand the imposed loads. The Rut Depth Model in the current version of VESYS IIM (27) assumes a permanent deformation accumulative damage law of the form F(N) = u]. Nai (2.4) where N = Number of axle load repetitions 12 a1 and “i = Permanent deformation response parameters for material in layer i. One method for determining a1 and pi for equation 2.4 is to use the results of the Dynamic Series of an "Incremental Static-Dynamic" test described by the load program shown in Figure 2.2. For more detailed information the reader is referred to reference 27. A sensitivity analysis of the VESYS IIM structural model (41) determined that calculated responses of the system were: a) insensi— tive to variations of the parameter p for base and subgrade; b) insensi- tive to variations of parameter a for base materials; c) sensitive to variations of a for subgrade material. Researchers have indicated that one of the most urgent research needs in material characterization is the development of simplified tests which decrease the total number of tests, shorten the amount of time required for each test, and simplify the test methods and instru- mentation requirements (9,24,27,36,40). 2. Previous Studies of Dynamic Properties of Sand 2.1 Effect of Number of Load Repetitions The permanent deformation of granular materials subjected to repeated applications of load is large during the first few cycles. Each subsequent load application results in a smaller increment of permanent deformation. After a large number of load applications the rate of change in permanent deformation becomes very small (5,6,8,25,38,40). Figure 2.3 shows a typical relationship between permanent strain and number of stress applications for non-cohesive soil (40). 13 MJHBER OE STRESS APPLICATICWS KREASING I CELL PRESS ‘ \L E b in - mcneaswo 5 oewnon z STRESS ( z a U Q FIGURE 2.3 RELATIONSHIP BETWEEN PERMANENT STRAIN AND NUMBER OF STRESS APPLICATIONS FOR NON-COHESIVE SOILS, (40)- 2 o , ._ v I 1 n IASEE 100‘» TIIOC I. b I'OJ‘ 3'5“ 7"IJIPCF 03'I0'5I cuuuunvs rusnc STRAIN, .' mncum 100,000 1 000,000 IUMIIR 0' [GAO REPETITIONS, IILOG SCALE) FIGURE 2.4 INFLUENCE OF NUMBER OF LOAD REPETITIONS AND DEVIATOR STRESS RATIO 0N PLASTIC STRAIN IN A PORPHYRITIC GRANITE GNEISS-THREE PERCENT FINES, (5). l4 Barksdale (5) tested samples of unstabilized base course materials up to 100,000 load repetitions using repeated load tri- axial apparatus. He reported that accumulated plastic strain can be approximated as a linear function of logarithm of load appli- cations. The results of tests on a granite gneiss are shown in Figure 2.4. For very low principal stress differences, it was found that the rate of accumulation of plastic strain tends to decrease as the number of load applications increases. However, as the deviator stress increases a critical value is reached beyond which the rate of permanent strain accumulation tends to increase with increasing numbers of load repetitions. Morgan (38) tested dry sand samples under cyclic loading. He reported that permanent deformation continued to build up even after one million cycles. Similar tests on well graded crushed granite samples of 5 mm maximum particle size were conducted by Brown (8). He reported the establishment of an equilibrium situation after approximately 10,000 cycles of deviator stress. Brown reported that both resilient and permanent strains changed very little after 10,000 cycles of deviator stress. Results reported by Brown (8) are shown in Figures 2.5 and 2.6. In studies on plastic strain in sands Barksdale and Hicks (6) found that at lower values of deviator stress, the rate of accumulation of plastic strain tended to decrease as the number of load applications increased. At higher values of deviator stress, the reverse was found to be true, i.e., the rate of accumulation of plastic strain increased with increasing number of stress applications. 15 mm “or mml arc-r1000 smu (IN/m2) 0 around 125 I anon-nod 125 0 around 205 r O undmmod 230 i i j o armed 375 i . I i ‘ . i l i/ a ‘ N 1 1' v ' v 7 .2 A A A ' 2 mo 1 i v 1 i mo — i 2‘ c coo am . . L 10 102 03 0‘ 105 ‘06 Number 01 st!!- cycles FIGURE 2.5 VARIATION OF RESILIENT STRAIN DURING DRAINED AND UNDRAINED TESTS (1 kN/m2 = 0.15 psi), (8). "no"! inn PM '0 O a N U fi 0' 0 VI .1 7 i l T i *1. mu m down-3 I ' bone «as A 1 .. _ - 2 WOOMG I: i Y . / J i “V gunman/n? L / i 1 xi” 1 !/ i /1 0pm duo-Z i / j— ,_m1M71 , Z/ ’r‘ "'— —us , ’5’ 275 M 05 14.0 In 1 A Y ‘ IO 0 2 10 J 1 n‘ Imam d In“ cm 05 0‘ FIGURE 2.6 VARIATION OF PERMANENT STRAIN DURING DRAINED AND UNDRAINED TESTS (1 kN/m2 = 0.15 psi), (8). 2.2 2.3 16 Effect of Confining Pressure The effect of confining pressure on permanent strain in granular materials has been investigated by several researchers (2,5,6,8,ll,38,40). All tend to agree that for a given dynamic deviator stress, increasing confining pressure results in a decrease in permanent strain. The effect of cycling both confining pressure and deviator stress on permanent strain has been investigated by Allen and Thompson (2). They concluded that the permanent deformation in the constant confining pressure tests was always greater than that in the cycled confining pressure tests. The constant con- fining pressure was equal to the peak cyclic confining pressure. Brown and Hyde (ll) conducted similar tests using constant con- fining pressure equal to the mean of the cyclic confining pressure. They concluded that there was no effect on permanent strain due to cycling the confining pressure. They explained that the apparent discrepency with the work of Allen & Thompson was due to the difference in the level of constant confining pressure used for comparison with cyclic confining pressure tests. This differ- ence in approach is illustrated in Figure 2.7. Effect of Stress Level Repeated load triaxial tests on well graded crushed granite of 5 mm. maximum particle size were conducted by Brown (8). He concluded that permanent strain appears to be proportional to deviator stress at a particular cell pressure. Brown expressed 17 Level of constant 03 taken by Brown & Hyde (11) Level of constant 03 taken by Allen 8 Thompson (2) _ __1_ Cyclic 03 Confining Stress Time FIGURE 2.7 MODES OF APPLICATION OF CONFINING STRESS,(11). 2.4 18 this relationship as cp = 0.01 q/o3 (2.5) where q = effective deviator stress 03 = confining pressure Permanent strain versus deviator stress at various cell pressures and versus applied stresses are shown in Figures 2.8 and 2.9 respectively. In all tests the dynamic deviator stress was equal to twice the mean value of deviator stress, qm (see Figure 2.10). Barksdale (5) conducted repeated load triaxial tests on several unstabilized base course materials. A summary comparison plot of his data is shown in Figure 2.11 for a confining pressure of 10 psi. The curves exhibit a typical nonlinear response. At a given confining pressure, and for small values of deviator stress, plastic strain is almost proportional to the deviator stress. As the deviator stress increases the plastic strain increases at an increasing rate. The plastic strains became very large as the apparent yield stress of the material is reached. Morgan (38) tested poorly graded clean sand and reported that at a constant confining pressure the permanent axial strain after any number of load cycles depends directly on the magnitude of the deviator stress. Effect of Stress History The importance of the stress history on permanent strain accumulation was investigated by Kalcheff and Hicks (26). They 19 Form ml sIa n I'M 4)-a— .__.. -. v—u—J 1 I 1 l 1 J on no no 400 am Dynamic m at- Iql TEN/m2) FIGURE 2.8 PERMANENT STRAIN VERSUS DEVIATOR STRESS FOR VARIOUS CELL PRESSURES (1 kN/m2 = 0.15 psi),(8). V I. I Permanent 51min 1%) FIGURE 2.9 RELATIONSHIP BETWEEN PERMANENT STRAIN AND APPLIED STRESSES. (8)- Dcv‘olor sires: Tim q - Dynamic dov‘ubr cm. qm - Moon dancer sins; FIGURE 2.10 MODE OF APPLICATION OF DEVIATOR STRESS, (8). 20 .Amv .Hmm op mo mmzmmmma wszHuzou < oz< mzomhmhmmmm o<04 ooo.oop h< muHhmHmmhum<22=m cu .r: n. IDZU¢A5CH '50— ..ezarouizzse 2 :0:: —s_l g 8— :33: .2 c. .52.; 9:: r 3.: N. .6 v. 1\\ - 1-14:3»...35. . .o ‘0 91% «can. o 0 any I \ 51$ tacvfioa a... ow... so... 6 5 25a 6‘ I vr‘oa‘a . pr 5 cu PP.N muse“; ‘ou‘o - 1.. 1 mm: um: noumo' 2.5 21 tested a crushed stone material in repetitive triaxial loading and found the stress sequence to have a significant effect on permanent deformation. They presented data which indicated that for different sequences of applied stresses, total permanent deformation was greatly reduced when the lowest stress level was applied first. Brown and Hyde (11) extended the work of Brown (8) using the same material. They also found that permanent strain was significantly affected by loading sequence. Brown and Hyde stated: "The permanent strain resulting from a succes- sive increase in the stress level is considerably smaller than the strain that occurs when the highest stress level is applied immediately." Morgan (38) used cyclic triaxial loading to investigate the effect of preloading sand samples. He applied a preload of 100 cycles of peak deviator stress equal to 50 psi (representing 40% of static failure load). This was followed by 300,000 cycles at a deviator stress of 20 psi. Permanent deformation was found to be greatly affected by the preloading. Morgan concluded that the effect of preloading appears to be in reducing the time taken to reach a stable condition rather than in a significant reduction in the rate of strain after a large number of load cycles. Effect of Load Duration and Frequency The results of repeated load triaxial tests on silty sand were reported by Seed and Chan (44). It was found that, with intervals between stress applications up to two minutes, 2.6 22 increased durations of stress application resulted in increased deformation. The effect of stress duration was significantly influenced by the interval between load applications. The effect of increased interval between stress applications was to increase the deformation for a given load duration. This effect was more pronounced at shorter load durations. The authors hypothesized that this unexpected effect of rest interval may be due to the adsorbed water film being displaced due to the high stress intensities at the contact points between particles as the devia- tor stress is applied. Displacement of the adsorbed water results in essentially true mineral contact between particles and hence high frictional resistance to slipping of particles with respect to one another. If the interval between load applications is brief the water film may not have time to regain its original position before the next load application so that high frictional resistance is available immediately upon commencement of the load. If the interval between load applications is increased so that the water film has time to become re-established, frictional resistance will be reduced which will allow larger deformations to occur. Figures 2.12 and 2.13 show the test results reported by Seed and Chan (44). Morgan (38) and Brown (9), on the other hand, reported that duration and frequency had no effect on deformation of coarser clean sand. Effect of Density Barksdale (5) performed repeated load triaxial tests on specimens of base material compacted to 95,100 and 105 per cent Number 0/ Stress App/morons 100 I (.1 lam-cl um" mu mics-hon in: N I. Mi” 0""! Witt!" u‘D-m An‘al Sham worn»! A u G 7 Number of Stress AID/icon,” n1 IO m m D.” (”.000 ’ m "Traitor-n- wen curator-1‘ 2‘10 ’ _‘,____ - .— ~ \ 1 1‘ 3 x \ . C I s M“' K Q / h 1 t 4 .. \ I/V 1 '5 arm»: ohm" unconn- - loam ' D . ’m.‘ 5»- Numur of Sn": App/pennant 000 0.000 00.000 ° 1 I >—- L1 mm no! true. "nu not-coho“ - 20-»- 1““— 1 1 {0. ml!» If!“ 1 . :1 1_ \ Mu "II-i: :11“ HOMO/1' run “In“. ~/ — a 8 J 11.0! Shem - ”Iron! 1 FIGURE 2.12 EFFECT OF DURATION OF STRESS APPLICATION 0N DEFORMATION 0F SILTY SAND. 24 am a! 5mm Marion: I 0 no ’ IOI Dom-c- annon ”untitl- . A Au’ol Strain queen! I. km "on “lief-In . Main \l MW of Stress lpph’corbn: 0! I0 I” m 0” 00,090 I '—-————-—- ->---‘ -———~ I.) Dam-en d In“ opinion-m ‘ I K ‘J \ . I s - I E \\: "'W‘A .._ W“ ' 3‘ a ‘ \ If E VP’Wd'tfl R ‘ a : (”OHM ‘ 7 FIGURE 2.13 EFFECT OF INTERVAL BETWEEN STRESS APPLICATION ON DEFORMATION 0F SILTY SAND, (44). 2.7 25 of maximum density determined by AASHO T-l80 specification. The material was composed of 21% soil and 79% aggregate. Barksdale stated that too few tests were conducted to make detailed comparisons. However, the results indicated that a significant increase in plastic strain was experienced by samples compacted to 90% of maximum density when compared to those compacted to 100%. When samples compacted to 105% of maximum density were compared to those at 100% only a small decrease in plastic strain was observed due to the higher density. Similar results were report- ed by Kalcheff (25) and are shown in Figure 2.14. Effect of Moisture Content The effect of moisture content on plastic strain accumula- tion in granular materials has not been well documented. Haynes and Yoder (20) have reported that, for an untreated gravel used in the AASHO Test Road, the total deformations after 1000 load cycles increased markedly once the saturation exceeded about 85 per cent. Total deformation of samples compacted at saturations between 70 and 85 per cent showed only slight dependence on degree of saturation. Morgan (38) reported results of repeated load triaxial tests on two sands tested under drained conditions. He found that the behavior of saturated sand samples was only slightly different from that of air-dried. There was a tendency, however, for the saturated samples to show larger permanent and recoverable strains even though they were tested at higher densities. Whether this effect was due to lubrication of particles or reduction in effective stress was not concluded. 26 1.0 l l 0.8 Density Effects 0.6 - / Plastic Strain, Percent l I 102 103 101+ Load Repetitions FIGURE 2.14 EFFECT OF DENSITY ON THE PLASTIC STRAIN ACCUMULATION WITH LOAD REPETITIONS,(25). 105 2.8 27 Shackel (46) contrasted the above findings to that of Shackel, et al (47) who have reported that for a repetitively loaded Sydney breccia (a) there is no evidence to support the concept of a moisture content below which the deformations are indepen- dent of moisture changes, and (b) the peak total and resilient strains were a minimum at a degree of saturation around 25 per cent. Effect of Fines Content The effect of per cent fines (passing No. 200 sieve) on the permanent strain occurring in a crushed biotite granite gneiss was reported by Barksdale (5). As the per cent fines increased, the permanent strain increased significantly. This effect became even greater at higher levels of deviator stress. These results are shown in Figure 2.15. The type of fines present, as well as the quantity, is also important as reported by Kalcheff (25). Fines which were plastic in nature caused a larger increase in permanent strain than the same quantity of non- plastic fines. Cyclic Triaxial Testing Many investigators have used the cyclic triaxial test to study both the resilient properties and permanent strain in pavement materials (5,8,9,l3,37,38,40,45). They found this procedure to be a reasonable means of reproducing the insitu conditions associated with soils and pavement materials. The variation of stresses on an element within the pavement system due to the passage of a wheel load is shown in Figure 2.16 (40). 28 nasnc sum, .' mncum 1 Gunman to. nu no: ”.10 H In.“ IOAO nuumous ________f 1 In 1-1101: ousnv ‘ 1 a, - 10 PSI . 1 1 1 PINES IPERCEIT) FIGURE 2.15 INFLUENCE OF FINES AND DEVIATOR STRESS RATIO ON THE PLASTIC STRAINS IN A CRUSHED GRANITE GNEISS BASE AFTER 100,000 LOAD REPETITIONS, (5). 29 elsewhere / S HEAR STRESS VERTICAL [RADIAL VERTICAL STRESS H GRIZON TAL STRESS ‘ TIME \ ,’7TIME TIRE Bottom of $1111 layers FIGURE 2.16 THE VARIATION OF STRESSES ON A PAVEMENT ELEMENT DUE TO THE PASSAGE OF A ROLLING WHEEL LOAD, (40)- d) W (a) PrInCTpal Stress - Element Rotates W (b) No Rolallon — Shear Stress Reversal FIGURE 2.17 IN SITU STRESSES BENEATH A ROLLING WHEEL, (40). 30 The insitu stresses on soil elements in the vicinity of a rolling wheel load are shown in Figure 2.17 (40). None of the various testing techniques presently available are capable of completely reproducing the stress patterns shown in the figures. First, there is the practical problem of simultaneously applying both normal and shear stresses directly to a sample. The repeated load triaxial test is capable of pulsing both major and minor principal stresses, but cannot reproduce the shear reversal shown in Figure 2.16. Conversely, the direct shear apparatus can apply the shear stresses correctly but has not been developed to the stage where the normal stress pattern can be applied. The stress state that a sample is subjected to during a cyclic triaxial test is shown in Figure 2.18. During the test the cyclic axial load and sample deformation are recorded. The axial stress and strain in the sample are determined with a knowledge of the cross- sectional area and length of the sample. Both resilient strain and permanent strain can be determined using this procedure. Vertical stress / 31 / \ All around con- fining pressure approximating in situ horizontal stress Cyclic principal stress difference to simulate traffic load Axial stress due to sustained ver- tical stress plus 80d FIGURE 2.18 STRESSES 0N SAMPLE DURING CYCLIC TRIAXIAL TEST. CHAPTER III LABORATORY INVESTIGATION 1. Test Materials The primary material used in this investigation was a clean uniform sand which is a typical subgrade soil encountered in the northern part of Michigan's lower peninsula. The material was obtained from test site 2-N at a depth of two to three feet beneath the roadway of U.S. 27 near Grayling, Michigan as part of a previous research project (3). The soil is of the Grayling soil series as defined by the Michigan Department of Transportation (MDOT) soil manual (18). The grain size distribution of this material is shown in Figure 3.1. Also shown are the specific gravity, absorption capacity, and coefficient of uniformity. Moisture-density relation- ships at three different compactive efforts are shown in Figure 3.2. The top two curves were obtained using AASHTO standard methods T-99 and T-l80 (49). These methods require that samples be compacted in layers (three for T-99 and five for T-180) into a 1/30 cubic foot cylindrical mold by applying twenty-five hammer blows per layer. For T-99 method the hammer weighs 5.5 pounds and is dropped twelve inches. The T-180 method requires a hammer which weighs ten pounds and drops eighteen inches. The resulting compactive effort applied is 12,375 foot-pounds per cubic foot for the T-99 method and 56,250 foot-pounds per cubic foot for method T-180. The bottom curve in Figure 3.2 was obtained using a compactive effort of 4,950 foot-pounds per cubic _32 Percent Finer 100 80 60 4D 20 AJ 33 C 1.8 U G = 2.62 5 Absorption Capacity = 0.44% 1 lunnljn 1 llllllll 1111 1 IILIIIII 1 llJlll 10 1 0.1 0.01 0.001 Grain Diameter, (mm) FIGURE 3.1 GRAIN SIZE DISTRIBUTION OF HIGHWAY SUBGRADE SAND. Dry Density, (pcf) 34 115- S = 60% S = 100% 110. 0 0 ° 0 2249 105 “a A. A A A u ,n a CI 9 a F 100:— 95 __ 0 AASHTO Method T-180 £3 AASHTO Method T-99 (3 T-99 Reduced to 10 blows/layer 90 I I I l J 0 5 10 15 20 20 Water Con ent, (%) FIGURE 3.2 MOISTURE -DENSITY RELATIONSHIP FOR HIGHWAY SUBGRADE SAND. 35 foot. The procedure used was the same as for method T-99 with the exception that only ten blows were applied to each layer. To assess the applicability of the research findings to other materials a second sand was used. This was a stamp sand obtained from MDOT Testing and Research Division. Stamp sand is a material that is the product of stamp-mill crushing of rock, composed of hard, durable particles of rock, uniformly graded in size from coarse to fine, approximately all of which will pass number 4 U.S. Standard sieve and be retained on number 100 (18). The grain size distri- bution of the samples obtained is shown in Figure 3.3. Also shown in the figure are specific gravity, absorption capacity, and coeffi- cient of uniformity. Moisture-density relationships for stamp sand at three different compactive efforts are shown in Figure 3.4. The procedures used to obtain these relationships were identical to those used for the highway subgrade sand. 2. Test Variables Cyclic triaxial apparatus was used to test compacted samples of highway subgrade sand. The purpose of these tests was to investi- gate the factors which affect permanent deformation and to provide data for the development of a constitutive relationship. The review of literature in Chapter 11 provides the background needed to select the test variables to be controlled during the research program. Variables suggested in the literature as being of interest in study of permanent strain included number of load repetitions, confining pressure, cyclic principal stress difference, Percent Finer 100 80 6O 4O 20 36 . Cu = 3.25 G = 2.71 ' S r Absorption Capacity = 1.8% 1. 1.— 1. 14 1 llllllll l IIIIIIII I IIIJIIII l IIULJII I IILUJ 10 1 0.1 0.01 0.001 Grain Diameter, (mm) FIGURE 3.3 GRAIN SIZE DISTRIBUTION OF STAMP SAND. Dry Density, (pcf) 37 S =100% S = 60% 115 '— 110 105 100 951- 90 J 1 I L 0 5 10 15 20 Water Content, (%) o AASHTO Method T-180 A AASHTO Method T-99 El T-99 Reduced to 10 blows/layer FIGURE 3.4 MOISTURE-DENSITY-RELATIONSHIP FOR STAMP SAND. 25 38 stress history, load duration and frequency. 2.1 2.2 Number of Load Repetitions All previous investigators agree that permanent deformation is strongly dependent on number of load applications. This dependency relationship must be established in order to meet the research objective. This requires that all tests be carried out to a sufficiently large number of load cycles for reliable determination of the relationship between permanent strain and number of cycles. Barksdale and Hicks (6) stated that during its design life, a typical highway pavement will be subjected to between 100,000 and one million or more equivalent 18,000 pound single axle loads. At the frequency selected for testing, the application of 100,000 repetitions would require a test duration of 27.8 hours. This length of test is impractical for the large number of tests required. Ten thousand cycles was established as the minimum length of test with some special tests carried out longer. One sample was tested to 100,000 cycles as veri- fication that the relationship retained its validity beyond ten thousand cycles. Confining Pressure Confining pressure has been reported by all researchers to be the most important parameter controlling both resilient and permanent deformation behavior of granular soils. However, the confining pressure which exists in a highway subgrade is very difficult to determine (l3). Radial (i.e., confining) stresses 2.3 2.4 2.5 39 computed by linear layered elastic programs always show tension in the granular material at the bottom of the stiffer pavement layers. Since cohesionless material cannot take tension the computed stresses cannot represent true field conditions (13). Hicks and Monismith (22) indicated that the range of confining pressure encountered in field pavements is from zero to ten psi. For the current research, confining pressures of five, twenty- five and fifty psi were selected to cover a wide range of possibi- lities. Cyclic Principal Stress Difference Permanent deformation is strongly dependent on the level of cyclic principal stress difference. At each confining pressure samples were tested at several levels of ad, ranging from approximately 25 to 90 per cent of the static strength of the samples. Stress History Previous researchers have reported that stress history has a significant effect on permanent strain. To evaluate this effect several samples were each subjected to cyclic loading at more than one level of ad. Comparison of the permanent strain in these samples with that of samples tested at only one level of ad should show the stress history effect. Load Duration and Frequency The effect of frequency and duration of load on cohesionless soil has been reported to be negligible for the range of 40 conditions that generally exist under highway traffic loading. Duration and shape of the stress pulse acting on a soil element beneath a pavement depends on both depth of the element and vehicle speed. For convenience, all testing was done with sinu- soidal loading at a frequency of one cycle per second. Sample Variables Sample variables suggested in the literature as being of interest in study of permanent strain in cohesionless soils included density, moisture content, and amount and type of fines. 3.1 3.2 Density Researchers have reported that density has a significant effect on both resilient and permanent deformation behavior of cohesion- less soils. For this research project two levels of density were selected for study. These densities correspond to 99 per cent of maximum density as determined by AASHTO Standard Method T-180 and 99 per cent of maximum density as determined by AASHTO Standard Method T-99. These two densities also correspond closely to the insitu densities of site 2-N as reported by Baladi and Boker (3). They report dry unit weights of 107.2 and 103.9 pounds per cubic foot at the top and bottom, respectively, of the layer from which the sample material was taken. Moisture Content The effect of moisture content on permanent deformation of cohesionless material is left unclear by the literature review. To determine the effect of moisture on the material used in the 41 current research two series of samples were tested over the widest range of moisture contents that could be obtained under drained conditions. Each series was at one of the levels of density given in paragraph(3.l)above. These two series of samples were all tested at a confining pressure of five psi and a cyclic principal stress difference of ten psi. Samples that were tested at other stress conditions for use in developing the constitutive equation were all tested at a moisture content of two per cent. This moisture content was selected because it was well above the absorption capacity and the sand was easy to handle during compaction. Also, Baladi and Boker (3) reported insitu moisture contents at site 2-N of 2.7 to 3.1 per cent. 4. Equipment Equipment used to compact the triaxial samples are shown in Figure 3.5. Samples were formed by the split aluminum mold (referred to as MSU mold). The mold has an inside diameter of 2.181 inches without the rubber membrane and 2.171 inches with a 0.005 inch thick rubber membrane installed. The length of the mold is 5.5 inches. Unless specifically noted all samples were tested with a single membrane. Compaction was accomplished using a hammer having a contact face of two inches and a two pound weight dropping six inches to produce one foot-pound of energy per blow. The testing equipment is shown in Figure 3.6. The loading equipment consists of an MTS electrohydraulic closed loop system composed of: 1) An MTS hydraulic power supply, Model 506.02, 6.0 gal per min. SQEEDOM 4.4322: 3.65 we: m.m $50: $22? oz< so: zoCuEzoo m.m $150: 3) 4) 6) 43 An MTS hydraulic control unit, Model 436.11 with a function generator. An MTS Model 406.11 controller(servovalvecontroller with AC and DC feedback signal conditioning). An MTS actuator, Model 204.52, capacity of 5.5 Kips with a Model 252.23A-01 servovalve. An aluminum triaxial cell, nine inches in diameter and nineteen inches in height with a stainless steel top plate. (manufactured in-house). A Kendall pressure regulator, Model 10 with a range of 2 to 150 psi. Instrumentation equipment consisted of: l) 4) A Strainsert load cell Model FLSU-ZSGKT, S/N 0-3138-1. Maximum capacity 5,000 pounds, Non-linearity - 0.05% of full range. Calibrated for 20 mv per pound. A Schaevitz Linear Variable Differential Transformer (LVDT), Model GCA 121-250, S/N 1347, Repeatability 0.000025 inch, Linearity t 0.22 per cent of full range. Calibrated for 0.01 inch per volt output. Two ACCO Helicoid pressure gages, six inch diameter, specified accuracy 2 0.25 per cent. One gage has range of zero to thirty psi and was used for confining pressures of five and twenty-five psi. Second gage has range of zero to three hundred psi and was used for confining pressure of fifty psi. A Sanborn Model 150 strip chart recorder with two DC Coupling Preamplifiers, Model 150-1300. 44 5) A Simpson Model 460 digital voltmeter. 6) A Tektronix Model 013 dual beam storage oscilloscope with two 5A18N dual trace amplifiers. Calibration data for the load cell and LVDT are given in Appendix B. 5. Sample Preparation The development of the sample preparation technique was based on the objectives of a method that would allow good control of the sample density and also produce samples which closely resemble the soil fabric of undisturbed sand. With respect to the latter objective, Silver (48) recommended that moist rodding or tamping is a reasonable method of modeling insitu soil strength. Since tamping with a falling weight hammer also allows for good control of sample density this method was selected for compacting the test specimens. For reference purposes it was thought desireable to produce samples having densities approximately that produced by AASHTO T-99 and T-180 compactive effort. Moisture versus dry density curves for T99, T180 and a reduced compactive effort of 4950 foot-pounds per cubic foot are given in Figure 3.2. When the same compactive effort in terms of foot-pounds per cubic foot was applied to sand in the MSU mold it was found that the resulting densities were much higher than those found previously using the AASHTO standard methods. This is believed to be due to the smaller size of the MSU mold and the fact that the banner used has a tamping face which covered the entire top area of the sample. This resulted in a more efficient use of the energy input to the sample since the hammer does not shear through the sample and cause shear displacement of the sand as is typical in 45 the AASHTO standard methods. When T-99 compactive effort was applied to sand in the MSU mold,the resulting density was approximately the same as that obtained for T-180 compactive effort applied to the AASHTO standard mold. The reduced compactive effort of 4950 foot-pounds per cubic foot applied to sand in the MSU mold yielded samples approxi- mately equal to T-99 density. In order to produce samples having a uniform density throughout their length, the amount of sand placed in each layer was reduced from that of the preceding layer while maintaining the same number of hammer blows. Since some of the energy applied to upper layers is transmitted through to lower layers,this method is thought to make the energy applied per unit mass of sand more evenly distributed through- out the sample length than if the same amount of sand were placed in each layer. Samples were compacted using six layers and applying twenty-five blows per layer to produce T-180 density and ten blows per layer to produce T-99 density. Accurate measurement of permanent strain requires that the sample cap make perfect contact with the top of the sample. To ensure this contact and to ensure a level sample top,the sample forming mold was slightly overfilled and then excess sand was struck off with a straight edge to produce a smooth top surface. The top cap was then placed on the sample and subjected to additional hammer blows to ensure perfect contact with the sample. These hammer blows were included as part of the desired compactive effort. For samples compacted to approximately T-99 and T-180 densities the number of blows applied to seat the sample cap were five and ten, respectively. 46 The following procedure was found satisfactory for the prepar- ation of sand samples. 1) 5) 7) Weigh out appropriate amount of dry sand in an evaporating dish allowing for approximately twenty-five grams in excess of sand needed for sample. Record weight to nearest 0.1 gram. Add water to bring sand to desired water content. Mix thoroughly, place dish in a plastic bag, and allow sand to sit overnight before using. Mount sample base on compaction pedestal. Place rubber membrane over sample base and secure with O-rings. Place the split mold around the sample base and draw the membrane up through the mold. Tighten the mold firmly into place so as to obtain a tight seal between mold and O-rings. Care must be taken to avoid puncturing the membrane. Stretch the membrane tightly over the rim of the mold. Apply vacuum to the mold to remove all membrane wrinkles. The membrane now should fit smoothly around the inside peri- meter of the mold. The vacuum is maintained throughout the compaction procedure. Determine the inside diameter of the membrane lined mold to the nearest 0.001 inch using vernier caliper. Compact sample in six layers. Place appropriate amount of moist sand for each layer in the mold and compact using the appropriate number of blows for the desired compactive effort desired. Trim off excess sand level with top of mold. Return all excess sand to evaporating dish and oven dry it. Weight of dry 47 sand incorporated into the sample is determined by sub— tracting the weight of dried excess sand from the original weight of dry sand in step (1). 8) Place sample cap on top of sample and apply additional hammer blows to seat cap in good contact with sample. Roll the rubber membrane off the rim of the mold and over the sample cap. Seal the membrane to the sample cap with rubber bands. 9) Determine the height of the sample to nearest 0.01 inch by measuring the total height of sample plus base and cap then subtract thickness of base and cap from total. Calculate sample volume using diameter from step (5) and sample height. Dry unit weight can be calculated from sample weight found in step (7) divided by computed volume. 10) Remove compacted sample assembly from compaction pedestal and place on triaxial cell base in preparation for the repeated load testing. 6. Testing Procedure After a sample had been prepared in the forming mold, as previously described, a vacuum was applied to the inside of the sample. This was to confine the sand and give i t strength so the mold could be removed and the triaxial cell assembled. To prevent the sample from being overconsoli- dated by this vacuum,a valve was installed in the vacuum line so air could be leaked into the line and reduce the vacuum to a value lower than the confining pressure used during testing. Using this procedure the samples never experienced confinement greater than the confining pressure used during testing. The procedure above applies to both 48 cyclic triaxial tests and static triaxial tests. Procedures specific to the test type are outlined in the following two sections. 6.1 Cyclic Triaxial Test The testing procedure was developed to yield the best possible measure of permanent deformation. Strain was calculated as the change in distance between the sample cap and sample base divided by the original sample length. One of the most impor- tant questions was what to use as a reference point for zero deformation. During preparation great care was taken to ensure perfect contact between the top cap and the top of the sample. However, there was still some doubt about using the LVDT output with the sample unloaded as the zero reading just in case the contact was not perfect. Equipment characteristics are such that before applying the cyclic principal stress difference, °d’ it is necessary to apply a static stress equal to one-half the cyclic stress to be used. The MTS system will then apply a cyclic principal stress difference of plus and minus one-half °d about this static value. This is illustrated in Figure 3.7. The function generator was set so that on the first cycle of cyclic loading the sample was first unloaded before being put into compression to the full value of 0d: The LVDT output corres— ponding to this first unloaded condition was selected as the best value to use as the point of zero permanent deformation. At this point the sample had been subjected to a static load of only one-half ad. This was felt to be a large enough load to have seated the top cap firmly on the top of the sample without 49 .mmomoumm HmH m.m mmszm umcpaa< was; ucsaum vgoumm coo; _ 1'— 11V]- mmpuxu two; we gangsz or m P A, . . cowmecoemu pcmcmELma ocmN me new: wave; vcoomm pamEmompamwo ‘U D U D \N P901 [PDIlJBA + auawaoeldsgg 50 causing significant permanent deformation in the sample. The attenuator setting of the strip chart recorder was always set to as small a setting as possible to give maximum resolution in the voltage readings. A special voltage offset was built into the control panel which allowed periodic adjust- ments of the recording stylus during the test. This enabled lower attenuator settings to be used and hence better resolution of deformation readings than would otherwise have been possible. Based on the preceding considerations the following proce- dure was found satisfactory for the determination of permanent strain in sand samples. 1) Start MTS hydraulic pump to allow fluid and servo- valve to warm up. Turn on recording equipment to allow for warm up. 2) Remove vacuum line from sample mold and connect it to the sample base after adjusting the vacuum to five inches of mercury. Maintain vacuum on inside of sample until confining pressure is applied in step 6. 3) Remove split mold from sample and install LVDT on the LVDT position to the center of its range. 4) Adjust the stylus of the load channel on the strip chart recorder to the zero position while no load is applied to the sample. 5) Put the loading plate of the triaxial cell in place and carefully adjust it so that it is exactly parallel with top of the sample cap. Tighten loading plate in place. 10) 11) 12) 13) 51 Assemble triaxial cell around sample. Apply 2.5 psi confining pressure and then disconnect the vacuum line from sample base. This opens the sample interior to atmospheric pressure. Increase confining pressure to desired level for testing. Adjust the stylus on the strip chart recorder channel which is recording the LVDT output to the zero position. Apply required initial static stress (one-half ad) to the sample by moving the actuator of the MTS closed loop system (using set point dial as described in Appendix A). The digital voltmeter is used to observe the load cell output as this load is being applied. Adjust the span dial (see Appendix A) to the proper setting for the desired cyclic principal stress difference. Set the function generator to the desired frequency and wave form. A sinusoidal wave form with a frequency of one hertz was used for all tests in this investigation. Engage Run control button to conduct the cyclic test. Record output on strip chart recorder for the desired number of cycles. Record all cycles from one to one hundred. Record segments of about ten cycles before and after cycles 200, 400, 800, 1500, 3000, 5000, and 10,000. Between recordings the recorder paper should be stopped for economical reasons. At completion of test remove static load of one-half od using set point control dial, release confining pressure 52 dismantle cell, and determine moisture content of sample. 6.2 Static Triaxial Test Static triaxial tests were performed on samples of the test sand which had been prepared identically to samples tested cycli- cally. In these tests samples were confined at the same pressure as for dynamic tests. Conventional triaxial equipment utilizing the same sample size was not available. Therefore, the static tests were conducted in the same triaxial cell as the dynamic tests in order to provide the best possible correspondence between static and dynamic test and sample variables; The testing procedure for the static tests was the same as steps one through six for the cyclic tests. Using the dynamic triaxial cell precluded loading the samples at a constant strain rate as is normally done in conventionaltriaxial tests. Load was applied gradually in increments of approximately ten per cent of the estimated sample strength, as suggested by Bishop and Henkel (7). This was accomplished by moving the MTS hydraulic actuator up slowly using the set point control dial. The size of the load incre- ments was reduced as the failure stress was approached to allow for a reliable determination of strength. Each increment of load was maintained until the rate of strain decreased to less than 0.02 per cent per minute at which time the deformation reading was recorded. Both load and deformation readings were read from the digital voltmeter. From this data static stress- strain curves were plotted. Only peak sample strength could be 53 determined because the load control mode does not allow the load to decrease to the ultimate strength level as the sample deforms. This procedure of using incremental loading to conduct static tri- axial tests was also used by Khosla and Wu (28) to study stress- strain behavior of sand. CHAPTER IV TEST RESULTS 1. Static Triaxial Tests Static triaxial tests were performed on samples of each test material to provide reference data for use with results of cyclic tri- axial tests. A static triaxial test was conducted at each density and confining pressure used in the dynamic test program. Also, in each static test the samples were prepared identically to those tested dynamically using the same mold and compaction procedure. Conventional triaxial equipment utilizing the same size specimens as the dynamic triaxial cell werelnyt available. Thus, to provide the best possible correspondence between static and dynamic test conditions the static tests were performed in the dynamic triaxial cell. Using this equip- ment precluded loading the samples at a constant deformation rate as is usually done in conventional triaxial tests. Instead, the axial load was applied gradually in small increments using the load control mode of the MTS controller. After application of each load increment and the deformation rate had become very small (less than 0.02% strain per minute) the deformation output from the LVDT was recorded. From those data stress-strain curves were obtained. Because the load control mode was used, once the peak strength of a sample was reached the sample underwent large rapid deformation. This meant that the post- peak part of the stress-strain curve could not be obtained. 54 1.1 55 Highway Subgrade Sand Samples of highway subgrade sand were tested at two levels of compactive effort and three levels of confining pressure. Samples were prepared moist as described in Chapter III. The lower compactive effort applied approximately 4,950 foot pounds of energy per cubic foot of sample. This compactive effort produced samples having dry densities of approximately 98 to 99 per cent of maximum dry density as determined by AASHTO method T-99. The higher compactive effort applied approximately 12,375 foot pounds of energy per cubic foot of sample. This compactive effort pro- duced samples having dry densities of approximately 98 to 99 per cent of maximum dry density as determined by AASHTO method T-180. The stress-strain curve resulting from a static triaxial test of highway subgrade sand compacted to a density of 99 per cent of T-99 maximum density and subjected to a confining pressure of five psi is shown in Figure 4.1. Samples compacted to 99 per cent of T-180 maximum density were tested at three different confining pressures. The stress-strain curves resulting from static triaxial tests at confining pressures of five, twenty-five and fifty psi are shown in Figures 4.2, 4.3 and 4.4 respectively. The stress condi- tions at failure for each of these latter three samples are plotted as Mohr circles in Figure 4.5. The failure envelope constructed tangent to the three circles is slightly curved. This indicates that the angle of internal friction, ¢’, decreases somewhat as the confining pressure is increased. This is consistent with results expected for uniformly graded sand (32). 56 .oz<31wHI ace z~<3IwHI gem zH<3IGHI mom z~<3IwHI do mhmmh 4cm mcspwm» Ego: owF» thm<< &mm RN _E. .9 u» 3 oe om (15d) ‘ssauzs JPBUS 61 1.2 Stamp Sand Samples of stamp sand were prepared using a procedure identical to that used for the highway subgrade sand. The com- pactive effort was approximately 12,375 foot pounds per cubic foot. This produced samples with dry densities of appoximately 94 per cent of maximum dry density as determined by AASHTO method T-99. Stress-strain curves resulting from static triaxial tests at confining pressures of five and twenty-five psi are shown in Figures 4.6 and 4.7 respectively. 2. Cyclic Triaxial Tests Cyclic triaxial tests were performed on samples of each test material to study permanent deformation characterisitcs. Several para- meters were selected to evaluate their influence on permanent deforma- tion. These included number of load repetitions, confining pressure, cyclic principal stress difference, stress history, density and moisture content. All samples were tested to at least ten thousand cycles at a single level of confining pressure and cyclic principal stress difference. To determine stress history effects several samples were subsequently tested for additional cycles at higher levels of Gd. All testing was done with the sample drainage line open. Due to the permeable nature of both sands tested, there should have been no build up of pore water pressure during testing. Therefore, total stresses and effective stresses should be equal. However, this is probably not strictly true. Since the samples were only partially saturated, the existence of slight negative pore pressure due to Principal Stress Difference, (psi) 30 20 10 62 Strain (x10'”) 93.4 pcf w = 7.15% 03 = 5.0 psi Sd = 29.0 psi 6 = 56.8 x 10'” .9SSd L L 1 I 4 I O 20 40 60 80 FIGURE 4.6 STATIC STRESS-STRAIN FOR STAMP SAND. 63 .oz<3zw~z mom mmammmmm wszHmzou hzu o<04 do mmmzzz oz< muzmmmumua mmmmhm 4u mo hummmm m.¢ mmswmu mmFuzu one; we consaz oooop coop cor or F -dddd‘ 1 d 1 .d ‘1. d «4 d d d 'l I'll-I 11. 66 cm cm 18 iuaueuaad ‘ULPJ a e.¢_ a d o - d 4 N.N_ . a 1 n. can o.m . me o ow: 2:92 ea 38.2.2032 . n. Few.o mmme.o moo.o mm._ o.ec_ mm .- mem.o N_me.o Nom.N me._ ~.Nop (m nv o a: .88; 3: cm; 4.2: m2 o .. . omm.o omwm.m mm©.w mm.~ m.oo_ mu AV . mm: :84 SW2 3; :2 8 o . o t3 E: . as ATS 5 $2 5 :03 52.32 O m.» a m 333 u 333 (%z-01 x) 67 .4<3IwHI 2H mmzmmmma wszHuzoo hzu o<04 do mumznz oz< uuzmmmmufio mmmgpm 4U no Humumm op.v mazemm mmpuau vac; mo consaz 82: 82 2: 2 _ qddfiq- 1N - Jud-Add d 1 dqaq-fi-Jq q quad u d -O o o o o o. o o o o o o o o n m .VN . “HM 1m11 . d 2 4 mm a o 4 a nv 4 o I a Q 4. 8 4 4 q 4 u on o o 1 m: o .2. 9mm .. mo 0 om: 85% Sam 332222 03.0 am: on; 8; .22 2. 0 1 2: was :35 E: N: :2 E a o :2 £34 8:: 3; we: 8 G 0 8WD 3%.: SEN mm; :2 m: o o o Are 5 ATS S is aesz 0 0 Ta Rum u us we a m TS: » 29:8 L mmp (%z-01 x) ‘u1euas quauewuad .4<3I¢HI zH wmzmmmmm oszHmzou hzu o<04 no mmmzzz oz< muzmmmmumo mmmmhm 4Q no Humumm —p.e mmame mmpuxu ago; $o gangsz ooocp coop oop op p 68 nq.“4 q 4‘ q _q.. . 1 . ..fl1+ u x4 4 Aqquq JIIIIIIIJWIIIIIJVO .8 a 11 8 o .2. 98 ... mo 1 8, o 8: 8:92 Nam 332.332 0 a: $35 8: mm; :2 U. 0 . o 82 8%; 30.2 mm; :2 3 a .23 0.2: u no mmflo 82% 3m”: max ES 8 4 35 o 83 3 mm; S mm _ e m2 m: o 1 2: A:-o_ xv A:-o_ xv A$uav gmne=z N; a m A&v2 u» mpaEmm L , 15 QUBUPWJBd ‘ULPJ (%z-Ol X) 69 at confining pressures of five, twenty-five and fifty psi are presented in Figures 4.9, 4.10 and 4.11 respectively. For comparison purposes, these same data have a1so been pTotted on 109-109 sca1e. These p1ots are shown in Figures 4.12 through 4.14. A p10t of a samp1e tested for 100,000 cyc1es is shown in Figure 4.15. The same resu1ts p1otted on 1og-1og sca1e is shown in Figure 4.16. A summary of a11 test resu1ts on highway sub- grade sand is given in Tab1e 4.1. The effect of stress history on permanent strain was investi~ gated for severa1 samp1es. A11 tests were done at a confining pressure of five psi using samp1es compacted to 99 percent of maximum AASHTO T-180 density. After app1ication of the nomina1 ten thousand repetitions of a given 0d, the magnitude of Gd was increased. Additiona1 repetitions at this higher 1eve1 were then app1ied. The resu1ts of one samp1e tested initia11y at a 0d of ten psi for ten thousand cyc1es, then at ad of fifteen psi for another ten thousand cyc1es, then at ad of twenty psi for another ten thousand cyc1es is shown in Figure 4.17. Other samp1es were a1so tested using various 1oad histories. The resu1ts of these tests are shown in Figures 4.18 through 4.20. Severa1 samp1es were tested to determine the effect of moisture content on the cumu1ative permanent strain. The test resu1ts were p1otted in Figure 4.21 as cumu1ative permanent strain against degree of saturation. A11 tests were carried up to 10,000 1oad app1ications under ten psi cyc1ic stress and five psi con- fining pressure. 70 .az<31m~z 2H zHu o<04 no mmmzaz oz< muzmmummmo mmmmhm 4u mo Hummmw NP.¢ mazwmu mm_uzu two; we Lanszz oooop coop cop op P —J+-¢d 4 1 duaqqd q - qqiq-d q u qua! J «1 q . 39° 23.8 mama .8 o _ _ . ow Nmm.o mmo.- Pomm.m . QHMEFXOLQQ 1 mem.o mmm.mp mnpw.m mu.Ameh thm<< & mp . < m. 35.0 3.53 ommmép mo 0 .78 o.m c .U AN-o_ xv A.-o_ xv 202532 . N; m < mpasmm u . .U .I o F 0 We 0 . 3 1c \1‘ .m KJIIIIKUIIII|AUIIIIIfiWIi flw AV “V O my av . o.o_ ; nu .IIIiIIIIuiIIIII- o.o~ . 4 3 11; E u H d 4 O 0 F1513 T . . a . q q a 4 4w: o o o o o o o o o o 2mg N.m_ u no ,c.Om . 15 zuauewuad ‘ULPJ (%z-Ol x) 71 .oz<320HI zH zHu a<04 no mmmzzz oz< muzmmmmmHo mmmmkm 4u no humumu mp.¢ mmstu mmpuxu vac; mo gmnszz 802 SS 2: S F 14‘ d G q d 1‘ d 1 q I I 1 ‘1‘ I 1 d d. d ‘1 -1d d 1 d. d I L a: :3: at: 2. 0 L _ mm: 82 8:: E a . m opa.o Fm¢.m_ memo.F~ mg 4w wma o mm H o 5.0 was: 82x8 2 o . .A~-o_ xv A.-op xv tapas: . AV 1 m < 223 l$i 1011... 1% G G G . my my «a 59 Ar 1 m .55 2m u U0 [A1111 om cap (%z-Ol X) ‘ULPJIS nuauemuad 72 .oz¢m mo<2zw~z 2H 22um Hzngmmm zo mud: 33 “.0 $9.52 oz< muzmmmta mmwmhm 45822; 8.65 .5 But: 34‘ ”:53... mmpuxu two; we consaz oooop coop cop op _ _Id14q4 1 d _Idl-_ d 41 I -¢dqdd d J 4 ‘11... q d d K90 85m mmom.m 3. 0 om:— o._._._m<< .Ncmm L P Sod mmud ERdP m._ B m mead 3mg: 82.8 mo Aw .35 0.8 u o mmmd mood: 23.: m2 0 1 ATS xv T725 L22:2 N2 m < m_asmm AV can o.~¢_ u to ooF (%z-0[ X) ‘uteuns 1U8UPWJ3d .oz<3szz med mm4u>u o zHu o zHQ no mhgsmmm F.¢ m4m -233 A5 3 u . a pm 595m pm 595% . 85395 ”2983 we 23:8 smasaz mmm m\ w “5:2.ng “5:228 ufiuo five to 9.2.5.80 “.25 >5 @3me 3:33: 333 A.n.o=ouv P.e mom00000: 000000 00 000000 00.0 002000 000000 0000 00 000202 000.00 0000 000 00 0 -1 q _d#-1.d ‘ I -‘qu-qJ + -deI-# d 4 _llid.-+d d O 000 0.0 u 0 000.0 u 3 0 100 000 0.000 n 0 mm 00050m 100 om (%z-Ol x) UtPJQS 1uauemuad 80 .oz<3zw~z mom zHzOPmH: mmmmhm no hummum mp.¢ mmauHu oooop coop 000000 u000 00 000532 cor o— F q .III‘- I I I -IIII-d‘JIW I 00a mn.0~ u _IIIIq I I I l—ddfifid I I I we .000 0.0 n ma I 000.0 u z .. 03 0.02 u 00 1 000 000500 J om ow om ow oop oNF (%z_0[ x) ‘ugequ quauemJad 81 .0200 00<00020 >0o00H: 000000 00 000000 00.0 003000 000000 umo0 we Lwnszz oooom oooop ooo~ 000 OF 1‘ Al‘qul-fi I [-‘dj ‘ I J! dual. - wmQ m H U0 000 o.0 n 00 000.0 n 3 000 0.000 n 00 m> 000500 NF mp om . 15 1U8UPwJ8d ‘ULPJ (%Z_Ol X) 82 .oz<3zo~z mo; z~mOHmHI mmmmhm no pummum om.e mmzmuu 0mpu00 umo0 mo Lmnsaz oooom oooo0 ooo0 oo0 00 ‘ dIGIIqI I d1 .III1-II1 I 11 -III“1-‘I I I -IIIIdd I I‘ .000 0.0 fi~¢.~ u 3 to. 0.00: n 00 1 00 000500 . NP mp om 0N (%Z—Ol x) ‘ULPdls quauewJad 83 20 - A 18 r- A A A 16 0. f ‘2’: z“ 0 A E? 14 F' £5 £5 C) C) ‘__ x v 12 _ 0 ° .5. C) c, x) C) E 10 0 o .4.) U) *E 8 _ 0 yd = 99% AASHTO T180 0) g 6 _ 15 Yd = 99% AASHTO T99 S. 33 o = 5.0 psi 4 h- 3 ‘ 0d = Approx. 10 ps1 2 0 0 1 I 1 I J J A I l J 0 TO 20 30 4O 50 Degree of Saturation FIGURE 4.2] EFFECT OF DEGREE OF SATURATION ON PERMANENT STRAIN AT N = 10,000 CYCLES. 84 2.2 Stamp Sand Samples of stamp sand were tested in cyclic triaxial apparatus to provide information on the generality of the constitutive equation for permanent strain developed for the highway subgrade sand. The stamp sand samples were compacted and tested under comparable conditions to the highway subgrade sand. The stamp sand has a different mineral composition than the subgrade sand which was evident from the color and the higher specific gravity. The uniformity coefficient is nearly the same for the two sands, however, the stamp sand has a smaller particle size with approxi- mately 7.5 per cent passing the number two hundred sieve (see Figure 3.3). The angularity of the stamp sand particles is greater than the subgrade sand particles. Hence, for the same compactive effort the stamp sand compacts to a lower density than the sub- grade sand. Plots of permanent strain versus logarithm of number of load repetitions for stamp sand samples are given in Figures 4.22 and 4.23. The same results are also plotted on log-log scale in Figure 4.24. 85 .0200 02000 0O0 000u>u o 000020 @000 0c 005522 2Hu o<00 0o mmmzzz mammm> 000000 0000 00 000532 ooP op zHo o<00 0o mmmzzz mammm> zH 200000 020202000 00 0000 0000000 0.0 000000 000000 0000 00 000002 000 000 000 000 000 000 000 000 _ . _ 0 fix . _ . .o 000 0 n we m. 000 000000 000 u 0 u 00 )Lul 40 d n). . n) .l .0 .0 000 , w .. U c m. . 1. 40 S . 000“ a m... U 4 1 MAI . m. % 0T 0.: ( O l O n100 . 0 nVI. 000 0 00 u o L 93 to slide over one another causing further rearrangement of particles. Also,partial reversal of the sliding which took place during the load application will occur. Part of the energy input during the load cycle is lost as heat generated by particle movements during loading and unloading. Thus, all the strain is not recovered, which results in a net permanent strain due to the first load cycle. When this new arrangement of grains is subjected to a second application of load, elastic compression, crushing and sliding will again occur. This time the compression will be commencing from a more stable condition of the soil skeleton than existed during the first application of load. Thus, less sliding will occur to reach an equilibrium condition than took place during the first load application. Hence, the net permanent strain during the second cycle is much less than for the first cycle. Each subsequent load - unload cycle results in further rearrangement of particles into a more and more stable structure. This process is manifested by a large permanent strain during the first cycle of load followed by smaller increments of permanent strain due to each succeeding load cycle as shown in Figure 5.l. Further study of Figure 5.1 suggested that the permanent strain versus N relationship can be described by a logarithmic function. Typical plots of permanent strain versus logarithm of N for various samples and loading conditions are shown in Figures 4.8 through 4.ll. Examination of these figures indicated that 94 the relationship between permanent strain and logarithm of N is linear and can be expressed by the following equation. cp = a + b ln N (5.l) where ep = accumulated permanent strain N = number of load repetitions a,b==parameters obtained from least squares fitting technique. The straight lines shown in Figures 4.8 through 4.ll were deter- mined for each sample using least squares fitting technique. The regression parameters a and b and the correlation coefficient, r2, are shown in each of the figures and are also tabulated in Table 5.l. Parameter a represents the permanent strain during the first load cycle. Parameter b is the slope of the straight line which represents the rate of change in permanent strain with increasing load repetitions. One sand sample was tested for 100,000 cycles to check if the relationship between permanent strain and logarithm of N remained linear at larger numbers of load application. The results of this shown in Figure 4.15. By inspection of this figure it can be seen that equation 5.l fits the data well. This agrees with results reported by Barksdale (5) which indicated that permanent strain versus logarithm of N is linear up to 100,000 cycles (see Figure 2.4). Thus, it seems reasonable that equation 5.l can be used to predict permanent strain at large numbers of load repetitions. It should be noted however that this conclusion is based on limited data. 95 000.0 000.00 0000.0 000.0 0000.0 000.0 000.0 000.0 00.00 0.0 000 000.0 000.00 0000.0 000.0 0000.0 000.0 000.0 000.0 00.00 0.0 00 000.0 000.00 0000.0 000.0 0000.0 000.0 u 000.0 00.00 0.0 00 000.0 000.00 0000.0 000.0 0000.0 000.0 u 000.0 00.0 0.0 00 000.0 000.00 0000.0 000.0 0000.0 000.0 u 000.0 00.0 0.0 0 000.0 000.00 0000.0 000.0 0000.0 000.0 n 000.0 00.0 0.0 0 000.0 000.0 0000.0 000.0 0000.0 000.0 u 000.0 00.0 0.0 0 000.0 000.00 0000.0 000.0 0000.0 000.0 000.0 000.0 00.00 0.0 00 000.0 000.00 0000.0 000.0 0000.0 000.0 000.0 000.0 00.0 0.0 00 000.0 000.00 0000.0 000.0 0000.0 000.0 000.0 000.0 00.0 0.0 0 000.0 000.00 0000.0 000.0 0000.0 000.0 n 000.0 00.0 0.0 00 000.0 000.0 000.0 000.0 0000.0 00.0 a 000.0 00.0 0.0 0 :0 a: E 80 E 30 E 3 E 80 3 N0 $.00. x0 1 -000 .0 N.» 0.1000 .0 $60.0 x0 03? m3? 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u ou oz< mmzmmmmm wszHuzoo me Hummmm ~.m mmeHu Asuop xv m Lmuwsmgmm oe om om OF 1 — d fl - — q d 00 00 0 9m Pma o.om " mo AV E 0.8 n 3 n. .za 3. u S o om_ H oe=m<< gmm .xocaa< n a» a a c.m~ D O Pma 0.0m u mo 0 . om oop omp (gsd) ‘aouauaggtg ssaqu ledtougud alloxg 102 .wzHo<04 0H40>u wszzo 2Hu oz< mmzmmmma wszHuzou no Hummmm m.m mmswmm Asuop xv .n memEmLma NP op m o e N o O O ‘ O N OP «- (DWI/l NLO II or- 0.0.0. COO m'uéo om.-. op=m<< saw ».m.me.xocaa< u > a o . I o no nVIl o.mm 0 12: .ma 0.9m n ma I o ~h<4322u mIH zo mm40>u ou o<04 HmmHu wszao zHu oz< umzmmmma wszHmzou no Hummmm m.m mmzwfiu A:-o_ xv .m Lmqumme d. O we ow T» mm cm om op NP w ‘4. q. . d . _.4 . _ . _ . A. II D .ma o.om .ma o.m~ .ma o.m om. . oezm<< ems spaces.xocaa< " II D n» aunssaud butugguog aouaua;;;a ssauqs tedioutud otloxg mVII. m.~lllk o.m~ 106 .zHu oz< Nazmmmma oszHazou do Numaau m.m mmsza Azuop xv Na cmumsmcma e. m. N. >(. m e m N _ o _ _ _ _ _ N _ _ o nuo\o _. .ma o.om .0 av .8 o.mN No a . .93 o.m u mo 0 ow.» oezm<< Nam »_woas.xocaa< u a. o 0 80 IN . c .. \Il o om Au o.mN n. u .._N aunssaJd bugutguog aouauaggta ssauqs [edtoulud ottofig 2.3 107 permanent strains were calculated. The computed strains are plotted versus logarithm of N in Figure 5.7. From this figure it can be seen that at a constant value of od/o3 an increase in confining pressure results in increased permanent strain. This observation is in contrast to the effect of confining pressure noted when 0d was held constant. The explanation for this contrast may be had by referring to the Mohr-Coulomb failure enve- lope shown in Figure 4.5 and noting that the angle of internal friction decreases with increasing confining pressure. Because of this, the ratio of principal stress difference to confining pressure at failure decreases as confining pressure increases. This decrease means that at high confining pressures a constant ratio of od/o3 represents a larger per cent of the sample strength than at lower confining pressures. Thus, it is reasonable that if a sample is loaded closer to the peak strength then accumulated permanent deformation should be greater. Stress Level The effect of cyclic principal stress difference on permanent strain can clearly be seen from the results presented in Figures 4.8 through 4.11. Examination of these figures indicated that. for any confining pressure, higher cyclic principal stress difference causes a higher rate of accumulation of permanent strain. Also, the permanent strain during the first load cycle is seen to increase as the stress level increases. These obser- vations could be noticed also by examining the values of para- meters a and b of equation 5.1 that are listed in Table 5.1. The 108 .m4<3IwHI mo; mmzmmuam wszHmzou hzmmmmuHo oz< lou o<04 no mmmzaz mammm> zHeHmzmo No HUNLNN N..m mmaoHd ANN-O_ xv mapaxu coco. n z a. =.NLNm Neacmscaa om om oe om ON o. oo _ _ _ _ _ _ cal Im mm-p oexm<< Nam n W» AV om: 2:92 N2. u N o a o dxd 0 o lop xm u z .wma m u me 4 4 0 00 sim—' n. (gsd) ‘aouaqaggtg ssauns [edtoutud alloflg 3.2 119 causes the effect of density on permanent strain to become more pronounced as stress level increases. Similar results were reported by Barksdale (5). Moisture Content From the review of literature it appears that the effect of moisture on permanent strain in granular materials is not well defined. Conflicting results have been reported by various inves- tigators (21,38,46,47). The mechanism for permanent deformation to take place is sliding of particles with respect to each other. Resistance to sliding occurs at particle to particle contact points where chemical bonds can form. The degree to which these bonds can form depends on the amount of contamination of the mineral surface due to water and other materials which reduce the amount of actual solid—to-solid contact. The effect of such contamina- tion on frictional resistance decreases as the roughness of the surface increases. The mineralogical composition of the particles has been shown by some researchers to affect the degree to which frictional characteristics are influenced by water (23,33). Based on the above discussion it appears that the effect of moisture on interparticle sliding depends on a complex set of factors which will vary from one material to another. Some change in behavior may be expected between sand in the dry condition and that which has enough water to completely coat all particles. Once all particles are coated with water there should be no more influence due to increasing moisture. 120 For soils with poor drainage characteristics a possible effect of water at high degrees of saturation is increase in pore pressure during cyclic loading. This would cause a decrease in effective stress with resultant loss in shear resis- tance. Since the sand samples in this research program were prepared at low degrees of saturation and tested under drained conditions, excess pore pressure development was not likely. In this research project the effect of degree of saturation on the permanent deformation behavior was studied on two series of samples compacted at different compactive efforts. The densities of the two series of samples were equivalent to 99% of maximum dry density using AASHTO T-99 and 99% of maximum dry density using AASHTO T-180. The degree of saturation was varied from zero to approximately 47%. Higher degrees of saturation were attempted but were not attained due to the high permeability of the sand. All samples were tested for 10,000 cycles at a cyclic principal stress difference of ten psi and a confining pressure of five psi. Plots of permanent strain versus logarithm of N for both series of tests are presented in Figures C.l to C.10 and C.21 to C.34. Plots of ep versus degree of saturation for 10000 load applications are shown in Figure 4.22. Study of this figure showed that permanent deformation did tend to increase with increasing degree of saturation. However, the effect was not significant. 121 4. Normalizing Effect of Static Stress-Strain One of the objectives of this research project was to develop a simple procedure capable of characterizing cumulative permanent strain without the necessity of conducting dynamic tests. This led to study of the factors affecting the static and dynamic behavior of granular soil. For static loading these factors include confining pressure, moisture content, dry density, and overconsolidation (stress history). These same factors were found to influence the cumulative permanent strain under cyclic loading. This finding suggested that the sample behavior under static loading could be used as an indicator of that under cyclic loading. Static triaxial tests were conducted on sand samples which had been prepared identically to those tested under cyclic loading condi- tions. This required one static test sample for each combination of density, moisture content, and confining pressure used during the cyclic testing program. The stress-strain curves for these tests are shown in Figures 4.1 through 4.4. It was shown previously that, for all sand samples, the cumulative permanent strain for a given principal stress difference is dependent upon the confining pressure and density as shown in Figures 5.8 and 5.12. These same parameters were found to be the major controlling factors in the static stress-strain behavior of the sand samples. In order to minimize the effect of confining pressure as well as sample density on permanent strain, it seemed reasonable to express cyclic stress difference in terms of the ratio of its absolute value to the peak static strength, (Sd), of an identical sample. Hence, each value 122 of 0d used in the test program was normalized by dividing it by the peak strength, Sd, of an identical sample tested at the same confining pressure in a static triaxial test. These normalized values of cyclic principal stress, (od/Sd), versus cumulative permanent strain at ten thousand cycles were plotted in Figure 5.13. Comparison of Figure 5.13 with plots of cyclic principal stress difference versus perma- nent strain shown in Figure 5.8 showed that expressing °d as a ratio of 5d reduces the effect of confining pressure on permanent strain. This was expected since strength depends on confining pressure. Further examination of Figure 5.13 indicated that for completion of the normalization process, the dynamic permanent strain should be expressed as a ratio of a static strain value. This value should have the following characteristics: 1) It should contain the plastic deformation characteristics of the sand under the particular static test conditions, i.e., the strain correSponding to a stress near the sample strength. 2) It should be a well defined value that is reproducible by different operators. Based on these characteristics the static strain at 95 percent of peak strength was selected as the normalizing value. At this stress level a large amount of the total static strain is permanent, thus representing the plastic characteristics of the material. Also, at this stress level the strain value is well defined. To illustrate, a static stress-strain curve is shown in Figure 5.14. The dashed line in the figure indicates the 95% strength and the corresponding strain. 123 .zaezem Hzmz NuzmmmaaHo mmmmem NN QNNHN<3Io~I mo; z~ muzmmuummo mmmmhm 4u omN~4c=u uw_oncmaxz n. Av n. AV 0006 ~.o «.0 o.o w.o o.p uifiuadis DLlPlS HPad r de DILDKJ OLDU BDUBJB;JLG 553415 [e 127 5. Development of Constitutive Relationship The principal objective of this research project was to obtain a constitutive relationship that will predict the amount of perma- nent strain that will occur under any number of load applications at any specified stress level. This relationship should account for sample variables (density, moisture content, etc.) and confining pressure as well as cyclic principal stress difference and number of load applications. Equation 5.1 expresses the cumulative permanent strain as a function of the number of load repetitions. The parameters a and b of the equation were thought to represent characteristics of the sample behavior under the particular testing conditions. Thus, it was found convenient to develop the constitutive relationship starting from equation 5.1. Recall that the value of parameter a represents the permanent strain caused by the first load appli- cation. The value of parameter b indicates the rate at which perma- nent strain accumulates with increasing number of load repetitions. Therefore, expressing parameters a and b as functions of the sample variables and the testing conditions may provide the desired consti- tutive relationship. It was discussed in section 4 of this chapter that the static stress-strain results of a sand sample can be used to predict the cumulative permanent strain of an identical samp1e tested under cyclic loading conditions. Changes in material and/or testing conditions are reflected by changes in static stress-strain behavior and in parameters a and b. Thus.normalizing the cyclic stress and 128 strain with respect to static stress and strain will eliminate or reduce the effect of these variables. The cyclic principal stress difference was normalized by dividing it by the peak static strength, (Sd). The cumulative permanent strain at 10,000 load applications was normalized by dividing it by a static strain corresponding to a stress equal to 95% of strength. It should be noted at this time that the static stress-strain data should be obtained from a sample identical in every respect to the dynamically tested specimens. This required one static test for each combination of density, water content and confining pressure used in the dynamic testing program. Figure 5.2 shows a plot of cyclic principal stress difference versus parameter a of equation 5.1 for three different confining pressures. After applying the above normalizing procedure, the data were replotted in Figure 5.16. Examination of this figure indicated that the data from all tests collapsed together to form a single curve. By inspection it was found that this curve could be repre- sented by the following function: -O.15 a/EO-955d = ln (1 - od/Sd) (5.3) where a = regression parameter from equation 5.1 c.955d= static strain at 95% of static strength 0d = cyclic principal stress difference Sd = static strength This can be rewritten to give _ _ -o.15 a - so ’55d 1n (1 od/Sd) (5.4) Similar plots of normalized principal stress difference versus para- meter b of equation 5.1 is shown in Figure 5.17. Study of the Cyclic Principal Stress Difference Peak Static Strength 129 .9 . .8 —- .7 - .6 - .5)- y = 99% AASHTO T-180 a d c) o - 5.0 psi / _ 0 -o 15 3 - - 6.953“ — ln(l- d/S) ' B 03 - 25.0 pSl .3 d o 03 = 50.0 p51 v = 99% AASHTO T-99 d A! 03 = 5.0 psi I I A J O 0.1 0.2 0.3 0.4 Parameter a Static Strain at 0.95 Peak Static Strength FIGURE 5.16 NORMALIZED CYCLIC PRINCIPAL STRESS DIFFERENCE VERSUS NORMALIZED PARAMETER a. 130 .n awhmz muzmmmmmHo mmmmhm 4u QUNH4 .u I .3 OO u S. \W OO0.0 u NO 8.8.. n O. NOOOOO n O .OO.-. O52... NOO ... O. n \ .O .3 mm n ma JO OOOO u N.. O . . 8-. 8:2,. OOO n O. 4 H E H C 8.8 O O..NO O OO.-. BIOS. OOO n O. 0 \V o .. .mg m u mo IOO O .. as + c I m IIOI - \Oo JOO a T II II | I 'U‘a L 0.. unbuauls 3L391S Head aouauajjta ssauqs ledgoulud otloxj 131 figure showed that the effect of sample density vanishes but each value of confining pressure yielded a distinctly separate curve. Note that the shape of these curves is similar to static stress- strain curves. Konder (29), Konder and Zelasko (30,31) and Duncan and Chan (17) have suggested that static stress-strain curves can be approximated by hyperbolic functions. Barksdale (5) demonstrated the applicability of a hyperbolic function to describe the relationship between cumu- lative permanent strain and cyclic stress at a specific number of load applications for unstabilized base material. Monismith, et a1 (36) also applied a hyperbolic relationship to permanent strain and cyclic principal stress difference at a specific number of stress applications for fine grained subgrade soil. His relationship was of the following form. = cp/(n + me ) , (5.5) Cd p where n and m are regression constants. c cumulative permanent strain p 0d cyclic principal stress difference Rewriting equation 5.5 in a linear form yields ep/od = n + map (5.6) As can be seen from equation 5.6, a plot of ep/od versus Ep should yield a straight line. Least squares techniques can then be applied to obtain the best fit line and the regression constants n and m. For static stress-strain data, the value of n represents the recipro- cal of the initial tangent modulus and m is the reciprocal of an 132 asymtotic stress difference, (0 Recall that the 1 ' 03)ultimate' data presented in Figure 5.17 appear to be similar in shape to the static stress-strain curves. Thus, it seems reasonable to extend the previous hyperbolic relationships concept (equation 5.5) to the curves in Figure 5.17. After rearrangement,equation 5.6 becomes od/Sd = b/(n + mb) (5.7) where the symbols are as previously defined. Rewriting this in linear form gives b/(od/Sd) = n + mb (5.8) Least squares technique was used to obtain the best fit straight lines for the data at each confining pressure. The values of n and m which were determined are shown in Figure 5.17 along with plots of the resulting hyperbolic curves and the coefficients of correlation. Inspection of the figure indicated that equation 5.8 described the data rather well. Rearranging equation 5.8 and solving forb yields (od/Sd)n b = 1 - m(od/Sd) (5.9) Note that the coefficients n and m in the last equation have differ- ent values for each confining pressure. Thus, to complete the constitutive equation n and m should be expressed as functions of confining pressure. The values of n and m were plotted against the confining pressure in Figure 5.18. Inspection of the figure indicated that n can be related to confining pressure by a linear function. The relationship for m was found to be logarithmic. Equations 5.10 and 5.11 were obtained, using least square fitting technique, to Confining Pressure, (psi) 50 4O 30 20 10 133 l I I J 0.80 0.85 0.90 0.95 1.00 Regression Constants n and m FIGURE 5.18 RELATIONSHIP BETWEEN CONFINING PRESSURE AND REGRESSION CONSTANTS n AND m. .05 134 represent these functional relationships. n (0.809399 + 0.003769 03) x 10-“ (5.10) m 0.856355 + 0.049650 1n 0, (5.11) Substituting these relationships into equation 5.9 yields (Gd/5d)(0.809399 + 0.003769 03) x 10‘“ b = l - (0.856355 + 0.049650 ln 03)(od/Sd) (5°12) The completed constitutive equation can be obtained by sub- stituting the expressions for parameters a (equation 5.4) and b (equa- tion 5.12) into equation 5.1. Making these substitutions yields ‘0.15 + (Gd/5d)" c = e 1an (5.13) p 0.953d 1n (1 - od/Sd) where n and m are given by equations 5.10 and 5.11, respectively. The first part of the right hand side of the equation represents the permanent strain caused by the first load cycle. The second part, on the other hand, represents the change in cumulative permanent strain between cycle one and cycle N. It should be noted that the cumulative permanent strain in equation 5.13 is dependent upon the static strength and strain, the cyclic principal stress difference and the confining pressure. To check the reliability of equation 5.13, values of permanent strains after the first loading cycle, the change in cumulative permanent strain through 10,000 load applications, and the total cumulative permanent strains were calculated using equation 5.13. These calculated values along with the corresponding measured ones are listed in Table 5.2. The measured and calculated permanent strains due to the first load cycle are presented in columns 4 and 135 mmm.m. mwe.o. Nom.o. Nwm.m .wm.w mow.o Om.mO o.mm mu Omm.o nem.o Om..m Oom.e ome.m mem.~ mw.ON o.mN ma www.mm .OO.NO Omm.oe oON.mm .om... Fen... .~.m. o.m mo mam.mm mum.m~ mom.m~ mmn..m Nm~.m Oms.n .~.u. o.m mu mNO.- noo.mm mm..m. m.m.m. mom.m NmO.m om.O. o.m um< was..~ Omm.- nmm.m. NmO.m. mo..o NNO.~ mn.O. o.m mm< nmm..~ m-.mm Onn.m. mom.u. O.N.m ow~.~ mn.¢. o.m m< Nom.m ~m..~. .mm.m mwo.w Npm.m OOo.O mo.o. o.m mm 0mm.m nu..o. mOm.o mwm.n mmm.m ww~.~ mm.m o.m <2zo.: KOO mm4u>u o<04 no mmmzaz mzmzm> z.u .o Lassa: coco. ooom 80m com. com ooe com 00. om mm o. m N . Eda- 1 1 fl dq-qfiqd d d JluJIW- A) I ddfiqu4 q 1 d o mwm.o mmm.o .-O. x OO.O.O " O .-O. x OOOO.N I O .IOm .-O. x OOO.O n O .-O. x..O.m. I O .OO O.Om n OO .OO O.OO I OO I .OO O.mN n .O .OO O.ON...O OOO.. n 3 OOO.. u O ..OO .OO O.OO. n O. .OO N.OO. n O. Nx m.aEOm Au .x m.aamm Av I , as queuewuad ‘UIPJ %z-Ol x) ( 150 CHAPTER VI CONCLUSIONS AND RECOMMENDATIONS 1. Conclusions Based on the results of this research project and in the range of the material tested, sample parameters and test variables the following conclusions were drawn: 1. The relationship between accumulated permanent strain and number of load repetitions can be represented by a logarithmic equation of the form 8p = a + b 1n N (5.1) At any confining pressure and number of load repetitions the relationship between the cyclic principal stress difference and the cumulative permanent strain can be represented by a hyperbolic function. Stress history has a significant effect on permanent strain. Cycling at low stress levels improves the sand's resistance to permanent strain at moderately higher levels of cyclic principal stress difference. The significance of this is that limiting axle loads during early life of a pavement may reduce rutting under heavier axle loads applied later. Moisture content had only a slight effect on permanent strain. 151 The effect of sample variables and testing variables can be eliminated from the relationship between cycle stress and permanent strain by normalizing the cyclic principal stress difference and permanent strain with respect to parameters obtained in static triaxial tests. This means that permanent strain under cyclic loading can be predicted from the results of static tests. Cumulative permanent strain after any number of cyclic load applications can be predicted using equation 5.13. The constitutive equation for cumulative permanent strain (equation 5.13) has the potential to be a useful design tool in rational pavement design procedures. 2. Recommendations The results of this research study is a significant advance in simplified methods of material characterization. However, much research remains to be done to fully develop its useful potential. It is recom- mended that further research be directed towards the following: 1. The applicability of equation 5.13 to a wider range of cohesionless soils should be studied. The applicability of equation 5.13 to cohesive soils should be studied. The effect of loading frequency may have some effect on permanent strain for some types of materials. This effect needs investigation. The effect of moisture content on cumulative permanentstrain may be important for some materials and should be investigated. 152 Field verification should be carried out to compare results predicted by equation 5.13 with actual subgrade rutting. The concept of normalizing dynamic behavior with respect to static test results should be investigated for appli- cation to the asphalt pavement layers with the objective of developing a constitutive relationship to predict permanent strain. LIST OF REFERENCES 10. 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E., "Resilience Characteris- tics of Subgrade Soils and Their Relation to Fatigue Failures in Asphalt Pavements," Proceedings of International Conference on Structural Design of Asphalt Pavements, University of Michigan, 1962. Pp 611-636. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 157 Shackel, B., "Factors to be Considered in the Drafting of Com- paction Specifications for Soils," Proceedings, Australian Road Research Board, Vol. 8, Part 3, Session 8, 1976, pp 23-34. Shackel, B., Makiuchi, K. and Derbyshire, J. R., "The Response of a Foamed Bitumen Stabilised Soil to Repeated Triaxial Loading." Proceeding, Australian Road Research Board, Vol. 7, Part 7, 1974, pp 74-89. Silver, Marshall L., "Comparison Between the Strengths of Undis— turbed and Reconstituted Sands from Niigata, Japan," Technical Report S-78-9, U. S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., August, 1978, 53 pages. STANDARD SPECIFICATIONS FOR HIGHWAY MATERIALS AND METHODS OF SAMPLING AND TESTING, 11th Edition, The American Association of State Highway and Transportation Officials, Washington, D. C., 1974. Taylor, D. W., FUNDAMENTALS OF SOIL MECHANICS, John Wiley and Sons, New York, 1948. TEST PROCEDURES FOR CHARACTERIZING DYNAMIC STRESS-STRAIN PROPER- TIES OF PAVEMENT MATERIALS, Special Report 162, Transportation Research Board, Washington, D. C., 1975. Trollope, D. H., Lee, I. K., and Morris, J., "Stresses and De- formation in Two-Layer Pavement Structures Under Slow Repeated Loading," Proceedings, Australian Road Research Board, Vol. 1, Part 2, 1962. Vinson, T. S., and Chaichanavong, T., “Dynamic Properties of Ice and Frozen Clay Under Cyclic Triaxial Loading Conditions," Report No. MSU-CE-76-4, Division of Engineering Research, Michigan State University, October, 1976. Vallerga, B. A., Seed, H. B., Monismith, C. L., and Cooper, R. S., ”Effect of Shape, Size, and Surface Roughness of Aggregate Particles on the Strength of Granular Materials," ASTM Special Technical Publication, No. 212, 1957, pp 63-74. Van Til, C. J., McCullough, B. F., Vallerga, B. A., and Hicks, R. G., "Evaluation of AASHO Interim Guides for Design of Pave- ment Structures," NCHRP 128, Washington, D. C., 1972. Yoder, E. J., and Witczak, M. W., "PRINCIPLES OF PAVEMENT DESIGN," 2nd Edition, John Wiley and Sons, Inc., New York, 1975. Young, M. A., and Baladi, G. Y., "Repeated Load Triaxial Testing- State of the Art," Division of Engineering Research, Michigan State University, March, 1977. 158 58. Johnson, H. C., "Application of Electro-hydraulic Servo Control to Physical Testing," Proceedings of the National Conference on Fluid Power, XVIII, Chicago, October, 1964. APPENDICES APPENDIX A DESCRIPTION OF EQUIPMENT A. The Cyclic Triaxial Test System A schematic diagram of the cyclic triaxial test equipment is shown in Figure A.1. The test set up consisted of the following components: 1. An MTS electrohydraulic closed loop test system which consisted of the actuator, servovalve. hydraulic power supply, servo and hydraulic controllers (This applies a cyclic principal stress difference to the sample). A triaxial cell, which contained the sample, load cell and LVDT. A control box for interfacing the MTS closed loop to the output recording equipment. Output recording equipment which monitored the load (stress) and displacement (strain) during the tests. B. The MTS Electrohydraulic Closed Loop Test System. A schematic representation of the MTS electrohydraulic closed loop test system is shown in Figure A.2. The system consists of: 1. An MTS hydraulic power supply, Model 506.02, 6.0 gal per min at 3000 psi. An MTS hydraulic control unit, Model 436.11 with a function generator. 159 160 .5553 .3. 2:5... as: O 8.35m 3O OOOO: E f / / / OO0.0.. is H \ :8 OOS. \ \ ..mu .O.xm... IO. a:.:uu.3w mucumo...umo .m..o..:ou 2O... OOO._III[ / .2: 3.3%.... .3833: .338 Oouuauu< so..ocucou o>gmm x.aa=m .mzoa u..=O.uaz .mu.oum¢ .Lmzu O.L.m r. m> .O>o>..mm 161 .1 gumming Function unc ion ...... .3 .. Command Generator LVDT ¥~ Signal Weave“ 406. n 436. n °qP8\ Controller Hydraulic Load + 5‘ Controller Cell “F— Amplified Difference Clgged Between p Signals I 506.02 " T1 Hydraulic Double- ‘ 7‘7 Power Sided + " Servo-l Supply Piston valve j 5 7 Actuator FIGURE A.2 SCHEMATIC OF MTS ELECTROHYDRAULIC CLOSED LOOP TEST SYSTEM. 162 An MTS Model 406.11 controller (servovalve controller with AC and DC feedback signal conditioning). An MTS actuator, Model 204.52, capacity of 5.5 kips with a Model 252.23A-Ol servovalve. A Strainsert load cell Model FL5U-2SGKT. Maximum capacity 5,000 pounds. The system operates as follows: 1. A command signal (voltage) from the function generator in the 435.11 (see Figure A.2) or other external source is input to the 406.11 where it is compared to the feedback signal (voltage) from a transducer (e.g., a load cell or LVDT) monitoring the response of the specimen in the closed loop. The difference (error) between the two signals is ampli- fied and applied to the torque motor in the servovalve coupled to the actuator. The torque motor drives a pilot stage which in turn drives a power stage of the servovalve which directs hydraulic fluid under pressure to one side or the other of the double sided actuator piston to cause the actuator to move. The movement of the actuator causes the specimen to res- pond in such a way that the transducer monitoring the specimen "feeds back" a signal which is equal to the command signal. The speed at which these steps are executed causes the sample, for all practical purposes, to be subjected to a loading equal to 163 the command signal. A more complete treatment of closed loop testing theory is given by Johnson (58). C. MTS 406.11 Controller The front panel of the 406.11 controller is shown in Figure A.3. The controls indicated by the circled numbers are discussed in order below. 1. The panel voltmeter has two functions. First, it can be used to indicate the error between the command signal and the feedback transducer. Second, it can be used to indi- cate the voltage output of feedback transducer "XDCRl," XDCRZ, or the servovalve drive. (The servovalve regulates the flow of hydraulic pressure between the hydraulic power supply and the actuator.) For the cyclic triaxial tests a negative error means compression and positive error means tension to the specimen. The panel voltmeter was most often used to monitor the error between the command signal and the feedback transducer before applying the hydraulic pressure. To insure that the actuator does not move when hydraulic pressure was applied, the error signal must be zero. The Set Point control provides a static command signal (voltage). There are 1000 divisions on the Set Point dial. Each division is equivalent to 20 mv. A positive command signal (Set Point between 500 and 000) produces actuator piston compression; a negative command signal (Set Point between 500 and 1000) produces actuator piston extension. 164 rnquoL_ . 5 0‘ v 0 VII. 13.0....[5047 Winn...» f... ......v .../01.. Am. Amy ZO=¢=vxu .6, 0.: lo.- D‘ IOOF. J .4 . 2 ... / :2: :2.- ..O. o 0.30- a...- p32» 8.0. muggomhzou ...mo¢ m.z m.< mmsc.m 2:“ a L- 0‘ / .3. . ‘ A..|Ilu-uo- O O a): 165 When the feedback signal is from the LVDT in the actuator, Set Point is used to move the actuator up or down even with no specimen in the loop. When the feedback is from any other transducer the Set Point control establishes a static level of response of the specimen. With feedback from theload cell, Set Point was used to apply static compressive loads for the static triaxial tests. Set Point was also used to apply static load of one-half Gd for the cyclic triaxial tests. The Span control established the amplitude of a command sig- nal waveform during cyclic loading. The amplitude is about the Set Point level. There are lOOO divisions on the Span control dial. Each division is equivalent to an amplitude of lo mv. The Span was used to set the load amplitude during cyclic triaxial testing. The Gain control establishes the rate and accuracy of response of the actuator ram to the command signal. The Gain control is therefore used to improve the response of the closed loop test system which includes the specimen. To set the systemat optimum Gain, the sample was subjected to a low frequency, low amplitude square wave loading. The feedback signal was moni- tored with an oscilloscope . The Gain control was turned clock- wise until small oscillations were observed at the peak of the square wave, as shown in Figure A.4b. At this point the Gain was reduced until the oscillations stopped, as shown in Figure A.4c. The Rate (described below) was adjusted to eliminate "overshoot" at the corner of the peak of the square wave as shown in Figure A.4c. 166 a) Overdamped, Gain too low w J U‘ b) Underdamped, Gain to high r—i c) Optimum Gain FIGURE A.4 GAIN AND STABILITY ADJUSTMENT 167 The Rate control helps prevent "overshoot" at high Gain settings. The Rate was adjusted after the Gain has been set as described above. The Feedback Select position determines which feedback signal will be used in the closed loop test circuit. This may be the signal from Transducer Conditioner l (XDCRl), Transducer Conditioner 2 (XCDRZ), or from an external trans— ducer conditioner (EXT). For the current research it was desired to control the load amplitude. Therefore Feedback Select was placed in position XDCRZ to feedback the signal from the load cell to use in the closed loop circuit. The Cal factor, Zero, and Fine/Coarse controls provide ad- justment of the signal for transducer XDCRl. In general, the transducer used with XDCRl was an LVDT. Cal Factor was used to adjust the voltage output from the LVDT. The Cal Factor was adjusted to obtain 1 l0 volts when the core of the LVDT moved 0.l00 inch. The Zero control introduces an electrical offset to the signal from the LVDT. It has l000 divisions on the dial. A Zero control setting of 500 corresponds to zero voltage offset. The Zero control provides negative elec- trical offset when it is between (000) and (500) and positive offset when it is between (500) and (lOOO). The Fine/Coarse switch determines the operating range for the Zero control. When it is selected to Fine, the electrical offset from the Zero control per division is I68 lower than when it is selected to Coarse. In this experi- ment, high electrical offset is necessary therefore the switch was selected to Coarse. The Excitation, Zero, and (xl/xlO) switch provide adjust- ment of the signal for transducer (XDCRZ). In general, the transducer used with XDCRZ was a load cell. The Excitation was used to adjust the voltage output from the load cell. It has lOOO divisions on the dial. The Excitation was adjusted to obtain 20 mv per pound of loading using a 5 Kip load cell. The Zero control introduces an electrical offset to the signal from the load cell. It has (lOOO) divisions on the dial. A Zero control setting of (500) corresponds to zero voltage offset. It provides positive electrical off- set when it is between 500 and 1000. The xl/xlO switch determines the operating range for the signal from the load cell. When in the (xlO) position the signal from the load cell is amplified 10 times that of the xl position. The xlO position was used in the labora- tory investigations phase of this research program. By selecting the xl0 position the 5,000 pound load cell functioned effectively as a 500 pound load cell. This was desireable because of the relatively small loads used in the testing program. High output signals could thus be obtained without the danger of the load cell being over- stressed. 10. ll. 12. 169 The Limit Detector determines which transducer conditioner (XDCRl or XDCRZ) signal will be monitored in the "failsafe" circuit. If the switch is set on INTLK the failsafe inter- lock circuit will turn off the hydraulic power supply when the signal voltage is greater or lower than a selected range of voltage. If the switch is set on IND the Limit Detector will indicate, by the Upper or Lower red light on the panel, when the signal voltage is greater or lower than a selected range of voltage. The Reset is used to extinguish the indicator light when the signal voltage level is within the selected voltage range. If the light for the Limit Detector is still lit with the failsafe interlock circuit in operation, the hydraulic power supply cannot be engaged. Therefore, before applying the hydraulic power supply the light has to be extinguished with the Reset button. If the switch is in the off position the failsafe circuit is inoperative. The Upper and Lower limit controls are used to select the range of acceptable voltage. The Upper limit is set at the most positive or least negative limit. The Lower limit is set at the most negative or least positive limit. Each limit dial has 1000 divisions corresponding to 10 volts. Program is used to input an external source of command signal. 170 D. MTS 436.11 Controller The front panel of the 436.ll is shown in Figure A.5. The controls indicated by the circled numbers are discussed in order below. 1. The Power control applied AC operating voltage to the control unit. The Hyg_Pressure Low or High or Hydraulic Off control is used to turn the hydraulic power supply on and off. The Program Stop or Run control is used to start or stop generation of a command signal waveform. Emergency Stop is used to stop the hydraulic power supply and generation of the command signal waveform. Emergency Stop and Hyd Off have the same effect. The Wave Form control of the Function Generator module is used to select the type of command waveform to be genera- ted. Square, triangular and harmonic waveforms are avail- able. The frequency vernier and range selector are used to obtain the desired frequency characteristics of the command waveform. Frequencies between 0.0l and llOO cycle/sec. are available. The counter indicates the number of elapsed cycles in increments of ten. The Count Input control is used to select the method of controlling the number of cycles during a test. If Program is selected the duration of the test must be preset. ‘17] " ”“me Mr'vvwx'. .qopr FUNCTION GENERAIOR moumcv r-— —~ -_I I Pun" n. . III --» o POWER RMENGENCY 510' (GUN! INPU‘ WAVEFORM . ow ,__. [—- on 4. a? I "06“. o ’ o lung“ K. I 0 .v‘ <.--.rr'. nut-.- "at: , 14 a}. FIGURE A.5 MTS 436.11 CONTROL UNIT. 172 After the required number of cycles the program will auto- matically stop and the End Count will light up. If the Off position is selected the program will run until the operator pushes Stop or the Failsafe system is triggered. E. Control Box The control box was built at Michigan State University. The front panel of the box is shown in Figure A.6. The control box allows for switching between two complete MTS electrohydraulic closed loop systems so that output recording equipment can be shared. Also, elec- tronic circuits are incorporated which can be used to offset and amplify output signals so they are compatible with the input require- ments of a mini-computer. Provision is also made for recording the unadultrated output signals. Voltage offsets are also provided to offset large constant voltages so that amplitudes of cyclic signals can be recorded with better resolution. F. Output Recording Equipment The following equipment was used to monitor the load cell and LVDT during the testing program. 1. A Sanborn Model 150 strip chart recorder with two DC Coupling Preamplifiers, Model lSO-lBOO. Both load and deformation were recorded directly on the strip chart recorder. 2. A Simpson Model 460 digital voltmeter. The voltmeter was used to monitor both load cell output and LVDT output during the experimental set up. The voltmeter was also 173 FIGURE A.6 CONTROL BOX. FIGURE A.7 SPLIT SAMPLE MOLD AND COMPACTION HAMMER. l74 used to monitor both load and deformation during the static triaxial tests and to monitor load as static load of one- half “d was being applied. 3. A Tektronic Model 013 dual beam storage oscilloscope with two SAlBN dual trace amplifiers. G. MSU Mold and Compaction Hammer The MSU mold and compaction hammer are shown in Figure A.7. The mold was made in two pieces from aluminum. The inside of the mold was lined with porous plastic so that vacuum applied would be evenly distributed and would suck the rubber membrane smoothly to the sides. When assembled, the two halves of the mold were held together by adjustable hose clamps. The inside diameter of the mold was 2.l8l inches and the maximum length of sample which could be formed was 5.5 inches. The compaction hammer had a contact face of two inches in diameter and a two pound weight with a drop of six inches. APPENDIX B CALIBRATION INFORMATION Linear Variable Differential Transformer (LVDT) Sample deformation was measured with an LVDT which was calibrated to produce t ten volts output for a full range deflection of t one-tenth of an inch. Calibration was performed using a micrometer which read to nearest .OOOl inch. The LVDT was mounted in a bracket holding the micrometer. Movement of the LVDT core was measured with the micro- meter and the calibration factor of the MTS signal conditioner was adjusted to produce the desired voltage output. Load Cell The load cell used had a maximum capacity of five kips. Because the expected loads were much smaller than this the xl/xlO switch (see Appendix A) on the MTS controller was set to xlO. This amplified the output signal so that the full output signal of ten volts could be obtained at a load of five hundred pounds. Calibration of the load cell was done by applying known loads to the cell and adjusting the excitation setting to produce the desired voltage output. The load was applied using lead bricks which had been previously weighed to the nearest one-hundreth of a pound. The excitation setting was adjusted to produce the desired calibration of twenty millivolts per pound. 175 l76 Strip Chart Recorder The calibration of the strip chart recorder was checked before each test using the built-in Cal button which applies a one hundred millivolt signal. The static response was also checked by comparing the strip chart reading with the voltage reading on the Simpson 460 voltmeter for the same output signal. The dynamic response of the strip chart was determined by others (53) to be unaffected up to fifty hertz. This was done using a function generator and a power supply to simultaneously apply and compare a signal to the strip chart recorder and an oscilloscope. Some effect on output was noted for slow paper speeds and low stylus temperature. Proper paper speeds and stylus temperatures to use at each loading frequency so that accurate readings would be obtained were marked on the recorder. APPENDIX C DATA This Appendix contains the data obtained from the cyclic tri- axial tests on highway subgrade sand plotted as permanent strain versus number of load cycles. 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