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University M icrofilm s International 3 0 0 North Z ee b Road Ann Arbor, M ichigan 4 8 1 0 6 USA St. John's Road, Tyler's Green High W ycom be, Bucks, England H P 10 6HR 7615096 B O K E R * T H O M A S D Q M J N I C NM AH R E S I L I E N T C H A R A C T E R I S T I C S OF M I C H I G A N C 0 H E 8 I 0 N L E S S R O a O B E D S O I L S IN C O R R E L A T I O N TO THE 8 0 I L S U P P O R T VALUES* MICHIGAN STATE UNIVERSITY# PH.D.# University. Microfilms International 300 n « fe huau, ahn nnBon. mi aukk 1976 RESILIENT CHARACTERISTICS OF MICHIGAN COHESIONLESS ROADBED SOILS IN CORRELATION TO THE SOIL SUPPORT VALUES By Thomas Dominic Nmah Boker A DISSERTATION Submitted to Michigan S ta te U n iv e r s ity in p a r t i a l f u l f i l l m e n t o f the requirements f o r the degree o f DOCTOR OF PHILOSOPHY Department o f C i v i l and S a n ita ry Engineering 1978. ABSTRACT RESILIENT CHARACTERISTICS OF MICHIGAN COHESIONLESS ROADBED SOILS IN CORRELATION TO THE SOIL SUPPORT VALUES By Thomas Dominic Nmah Boker The design o f f l e x i b l e highway pavements, according to the AASHO In te rim Guide 1972, req uires re p re s e n ta tiv e s o il support values (SSV) o f the subgrade m a te r ia ls . Soil support values serve as an index which expresses the r e l a t i v e a b i l i t y o f a subgrade s o il to support the t r a f f i c loadings. Several bag and block (undisturbed) samples were c o lle c te d from under e x is tin g highway pavements which showed severe signs o f d is t r e s s . A sample p reparatio n procedure was e s ta b lis h e d to d u p lic a te f i e l d moisture content and d e n s ity . The r e s i l i e n t c h a ra c te r­ i s t i c s o f the Michigan cohesionless roadbed s o ils were obtained using repeated load t r i a x i a l te s ts on recompacted and undisturbed samples. These c h a r a c te r is t ic s include r e s i l i e n t modulus (MR) , r e s i l i e n t s t r a in (e R) and permanent s t r a in (e p) . The te s ts r e s u lts were c o r re la te d to the s o il support value scale o f the AASHO In te rim Guide f o r design o f f l e x i b l e pavement s tru c tu re s . This c o r r e la t io n was then checked again st f i e l d data t h a t were obtained by the Michigan Department o f S tate Highway and T ra n s p o rta tio n . A s im p lifie d procedure was developed to implement the r e s u lts o f t h is research study to the AA£H0 In te rim Guide f o r design o f f l e x i b l e high­ way pavements. To The M in is te r of Public Works of Lib eria Hon. Gabriel J. Tucker ACKNOWLEDGEMENTS The w r ite r wishes to express his sincere appreciation to his academic advisor, Dr. G ilb e rt Y. Baladi, fo r his encouragement, pa­ tience and aid throughout the w rite rs doctorial studies and fo r his guidance during the preparation o f th is thesis. Thanks are also due to the other members of the w rite rs guidance committee: Dr. O.B. Andersland, R.K. Wen, Dr. Bradley and Dr. M. Mortland. The w r ite r wishes to thank the Michigan Department of Highway and Transportation fo r t h e ir fin ancial assistance and also expresses his appreciation to Mr. E. Novak, Mr. J. Burge, Dr. Fred Hsia, Mr. K. Allemeier and Mr. G. Mainfort fo r t h e ir helpful suggestions during the course of this project. Appreciation is also extended to the Liberian Government, espe­ c i a l l y to the M in is try o f Public Works of Liberia fo r t h e ir financial support during the w rite rs doctorial studies. To Mr. Rodney Lentz, Mr. John Li and Mr. Anwar Khattak fo r th e ir helpful suggestions. The w r it e r extends his appreciation to Mr. Stanley Clark and Mr. Gordon Rouse, fo r in s t a llin g the required equipment fo r experimentation, Mr. Roel Mendoza fo r the d ra ftin g work and Mrs. Jan Swift fo r the typing work. The w r it e r pays special t r ib u t e to his w ife , Ruth and his daughter, Broh-Barnih fo r t h e ir wonderful patience during the period of the w rite rs doctorial studies. TABLE OF CONTENTS List of Figures-------------------------------- vi List of Tables--------------------------------- xi List of Symbols-------------------------------- xii Chapter One I chapter Introductions-------------------------------------1 Introductions----------------------------------- 1 REVIEW OF LITERATURE---------------------------3 Material Characterization UsingRepeated load Triaxial Test------------------------------------- 3 II Factors Affecting Resilient Modulus-----------------5 A. Cohesive Soil--------------------------------- 5 1. Number of Stress Applications--------------- 5 2. Stress Intensity--------------------------- 5 3. Density and Water Content----------------- 5 B. Cohesionless Soils-----------------------------8 1. Number of Stress-Applications--------------- 8 2. Stress Intensity--------------------------- 8 3. Confining Pressure-----------------8 4. Relative Density and Degree of Saturation 9 III Correlations of Soil Support Values to Material Characterizations--------------------------------- 9 A. Correlations Between California Bearing Ratio (CBR) and Soil Support Values (SSV)------------ 10 B. Correlations Between Modulus of Deformation (Triaxial Test) and SSV----------------------- 10 C. Correlation Between SSV and Resilient Modulus 10 IV Sample Preparation For RepeatedLoad Triaxial TViO I V Test Equipments and Procedure--------------------- 15 Chapter Three FIELD AND LABORATORY INVESTIGATIONS--------------- 17 I Field Investigations----------------------------- 17 A. Site Selection------------------------------- 17 B. Sampling Techniques-------------------------- 17 C. Traffic and Other Field and Design Data-------- 21 D. Converting Mixed Traffic To Equivalent 18 Kip Axle load------------------------------------ 21 XI Laboratory Investigations-------------------------A. Test Materials---------------------------------B. Method of Sample Preparation--------------------C. Test Procedures--------------------------------- 26 26 27 37 Chapter Pour TEST RESULTS---------------------------------------41 I Test Data------------------------------------------ 41 II Repeated Load Triaxial Test--------------------------41 A. AASHO Roadbed Soil------------------------------ 41 B. Michigan Cohesicnless Roadbed Soil--------------- 56 III Triaxial and Direct Shear Results------------------ 56 chapter Five DISCUSSION AND INTERPRETATIONS OF TEST RESULTS------- 87 I General-------------------------------------------- 87 II Triaxial and Direct Shear Test Results------------ 87 A. Angle of Internal Friction-----------------------87 B. Modulus of Deformation and Soil Support Value (SSV)------------------------------------------ 93 III Resilient Modulus of the AASHO Roadbed Soil-----------99 A. Effect of Sample and Test Variables On The Resilient Modulus------------------------------ 101 1. Degree of Saturation and Stress Level-------- 101 2. Number of Load Repetitions------------------ 103 B. Effect of Sample and Test Variables On The Comrculative Permanent Deformation--------------- 105 IV Resilient Modulus of Michigan Cohesionless Subgrade Soils------------------------------------------- 106 A. Introduction-----------------------------------106 B. Effect of Test Variables----------------------- 107 C. Effect of Sample Variables--------------------- 113 1. Water Content------------------------------ 114 2. Dry Density-------------------------------- 114 3. Caipactive Effort-------------------------- 114 V Correlation of Resilient Modulus of The Michigan Cohesionless Roadbed Soils To The Soil Support A. Choices of Variables--------------------------- 118 B. The Resilient Modulus Vs Soil Support Values 120 VI Implementation-------------------------------------123 Chapter Six CCNCLUSICN AND RECOMMENDATIONS------------------- — 135 I Conclusion---------------------------------------- 136 II Recarmendations------------------------------------ 136 BIBLIOGRAPHS-------------------------------------------------137 APPENDICES---------------------------------Appendix A Description of MTS System— Appendix B Test Results------------- v LIST OF FIGURES Figure 2.1 Page Effect of Stress Intensity on Resilient Charateristics for AASHO Road Test Subgrade Soil (15) ................ 2.2 Water Content - Dry Density - Resilient Modulus Relationship for Subgrade Soil (47) ................... 2.3 7 Correlation between Soil Support Value (SSV) and California Bearing Ratio (CBR), (2) ................... 2.4 6 11 Design Chart for Terminal Serviceability index of 2.5 (Based an AASHO Interim Guide Except for Addition of Modulus of Deformation Scale), (6) ................. 2.5 12 Correlation Chart for Estimating Soil Support Value (SSV), (16) ......................................... 14 3.1 Cross Sections of Test Sites 1-N and 1-S ............. 19 3.2 Dry Density Vs. Water Content for AASHO Roadbed Soil, (Using Mold and Hamner Designed for this Project) ............................................ 3.3 Grain Size Distribution Curve for AASHO Roadbed Soil (36) 3.4 29 Grain Size Distribution Curve for Recanpacted Sand from Test Sites ................................ 3.5 Test Site 1 - N .................. 31 Grain Size Distribution Curve for Undisturbed Sand Samples Fran 3.7 30 Grain Size Distribution Curve for "Undisturbed1' Sand Samples From 3.6 28 Test 1-S ....................... 32 Grain Size Distribution Curve for Undisturbed Sand Samples Fran Test Site 2-N .................. vi 33 Figure 3.8 Grain Size Distribution Curve for Undisturbed Sand Samples From Test Site 2 - S .............. 4.1 Resilient Modulus Vs. Number of Cycles for AASHO Roadbed Soil 4.2 Resilient Modulus Vs. Number of Cycles for AASHO Roadbed Soil 4.3 Resilient Modulus Vs. Number of Cycles for AASHO Roadbed Soil 4.4 Resilient Modulus Vs. Number of Cycles for AASHO Roadbed Soil 4.5 Relationship Between Stress, Water Content and Resilient Modulus of AASHO Roadbed Soil 4.6 Permanent Deformation Vs. Deviatoric Stress for AASHO Roadbed Soil 4.7 Permanent Deformation Vs. Deviatoric Stress for AASHO Roadbed Soil 4.8 Permanent Deformation Vs. Deviatoric Stress for AASHO Roadbed Soil 4.9 Resilient Modulus Vs. Confining Pressure for Recompacted Cohesionless Samples 4.10 Resilient Modulus Vs. Confining Pressure for Recompacted Cohesionless Samples 4.11 Resilient Modulus Vs. Confining Pressure for Undisturbed Samples 4.12 Resilient Modulus Vs. Confining Pressure for Undisturbed Samples 4.13 Resilient Modulus Vs. Sum of Principal Stress for Recompacted Cohesionless Samples vli Figure 4.14 Resilient Modulus Vs. Sum of Principal Stresses for Recompacted Cohesionless Samples 4.15 Resilient Modulus Vs. Sum of Principal Stresses for Recompacted Cohesionless Samples 4.16 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Cohesionless Samples 4.17 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Cohesionless Samples 4.18 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Cohesionless Samples 4.19 Stress Strain Curves for Recompacted Cohesion­ less Samples 4.20 Stress Strain Curves for Recompacted Cohesion­ less Samples 4.21 Stress Strain Curves for Recompacted Cohesion­ less Samples 4.22 Direct Shear Rest Results for Recompacted Dry Cohesionless Samples 5.1 Angle of Friction Vs. Internal Void Ratio for Recompacted Sand From Test Sites 5.2a Stress Paths for Direct Shear and Triaxial Tests 5.2b Mohr Circles for Unconsolidated Undrained Tests on Partially Saturated Soil 5.3 Deviator Stress for Determining the Modulus of Deformation as Required for Pavement Design 5.4 Stress - Strain for Recompacted Cohesionless Soils viii Figure 5.5 Stress - Strain for Recompacted Cohesionless Soils 5.6 Stress - Strain for Recompacted Cohesionless Soils 5.7 Correlation of Estimated Soil Support Value With the Modulus of Deformation of Subgrade Materials 5.8 Typical Load-Displacement Output 5.9 Resilient Strain Vs. Number of Stress Applications for AASHO Roadbed Soil 5.10 Typical Plot of Resilient Modulus Vs. Confining Pressure for Recompacted Cohesionless Sample 5.11 Resilient Modulus Vs. Sum of Principal Stresses for Recompacted Sand Samples 5.12 Effect of Dry Density on and for Recompacted Cohesionless Samples at Relatively the Same Water Contents 5.13 Effect of Dry Density on and for Recompacted Cohesionless Samples at Relatively the Same Water Content 5.14 Relationship Between Constants of Equations 2.3 and 2.4 for Undisturbed Sand Samples 5.15 Relationship Between Constants of Equations 2.3 and 2.4 for Recompacted Sand Samples 5.16 Correlation Between Soil Support Value and Dynamic CBR 5.17 Resilient Modulus Vs. SSV for Recompacted And Undistrubed Cohesionless Soils (© = 15 psi) ix Figures 5.18 Resilient Modulus Vs. SSV for Recompacted and Undisturbed Cohesionless Soils 5.19 Resilient Modulus Vs. (0 = 30 psi) SSV for Recompacted and Undisturbed Cohesionless Soils 5.20 Pavement Thickness Vs. (0 = 20 psi) Deviatoric Stresses or Vertical Stresses x LIST OF TABLES Table 3.1 General Information of Test Sites 3.2 Field Data 3.3 Testing Program 4.1 Repeated Load Triaxial Test Results for the AASHO Roadbed Soil 4.2 Summary of Permanent Deformation of the AASHO Roadbed Soil 4.3 Results of Repeated Load Triaxial Tests for Recompacted Sand Samples 4.4 Results of Repeated Load Triaxial Tests for Undisturbed Sand Samples 5.1 Modulus of Deformation of Recompacted Cohesionless Samples 5.2 Summary of Repeated Load Test Restults of Undisturbed M ichigan Cohesionless Material 5.3 Summary of Repeated Load Test Results of Recompacted Michigan Cohesionless Material 5.4 Resilient Modulus at Different First Stress Invariant For Undisturbed Sand Samples 5.5 Resilient Modulus at Different First Stress Invariant For Recompacted Sand Samples 5.6 Summary of Data for SSV and Resilient Modulus of Recompacted Cohesionless Soil Samples. 5.7 Summary of Data for SSV and Resilient Modulus of U ndisturbed Cohesionless Soil Samples 5.8 Comparisons of Field and Laboratory Soil Support Values 5.9 Functions Values for the One Layer Elastic Model 5.10 Vertical Stress at the Subgrade Level in a Pavanent Section xi LIST OF SYMBOLS SSV = Soil Support Value w = Water Content Dry Density S = Degree of Saturation = Total Vertical Stress a3 = Confining pressure = Deviatoric Stress 9 = Sum of Principal Stress or First Stress invariant Mj. = Resilient Modulus er = Resilient Strain °1^ct3 ~ Principal Stress Ratio £p - Permanent Strain e. - Total Strain t K^,K2 /K3,K4 = Constants C1,C2,C3,C4 = Constants CBR = California Beaming Ratio SN = Structional Number R = Regional Factor SN = Weighted Structural Number w 18 = Number °f 18 Kip Simple Axle Load applications DDT = Equivalent 18 kip Axle Load m Ccnmercial Trucks. Daily Traffic Or Number of DPC = Caily Passenger Cars And Light Truck Traffic PSI = Present Serviceability Index SV = Slope Variance RD = Rut Depth xii C + P = Cracking and Batching Gs = Specific Gravity Cu - Uniformity Coefficient Nc = Nuriber of Cycles For Conditioning Samples = Number of Cycles For Test Samples $ = Peak Angle of Internal Friction t = Thickness Of The Pavement Sections Dq = Initial Diameter of Sample Hq = Initial Height of Sample Aq = Initial Cross Sectional Area CF = Calibration Factor a]_ _ a 3 = Deviatoric Stress (a1 -o^)^ = Deviatoric Stress at Failure e£ = Strain at Failure xiii CHAPTER 1 Introduction The major problem confronting highway engineers today is that of properly estimating material strength factors for use in the existing empirical and quasi-rational design methods of flexible pavements. Engineers have recognized the impor­ tance of these factors for a long time; however, differences still exist among them as to when, where, and how to estimate such factors and what distress criteria to use. A great deal of these differences can be attributed to varying degree of empiricism associated with each of the design methods and to the lack of precise and quantitative descriptors as to what constitutes a flexible pavement failure. Further, the appli­ cation of stresses to pavement materials by moving wheel loads is a transient one, while these materials have been character­ ized in the past by their static behavior under static load­ ing. A more realistic test procedure to characterize pavement materials should be one in which the loads applied to the specimens are also transient. The repeated load triaxial test is one such test. The primary objectives of this study include: 1. Establishing a sample preparation method that will simulate the field densities and moisture contents. 2. Conducting cyclic triaxial tests to evaluate the resilient characteristics and measure the cumulative compressive strain of cohesionless subgrade materials for pulsating stresses simulating those generated by 18 kip single axle load. 3. Conducting conventional triaxial tests to evaluate the stress strain behavior and the strength param­ eters of the subgrade materials. 4. Correlating the resilient modulus of the subgrade materials obtained in (2) above to the soil support values as defined in the American Association of State Highway Officials 1 (AASHO) interim guide. These tests were conducted using the following mate rials: 1) AASHO roadbed (A-6) materials 2) Block cohesionless subgrade soil samples 3) Bag cohesionless soil samples The A-6 materials were received upon request from the Illinois Department of Highway, while the cohesionless samples were obtained in cooperation with Michigan Department of State Highway and Transportation (MDSH&T) from under existing high­ way pavements. 2 CHAPTER 2 Review of Literature Recognition, of the need for improving methods and de­ veloping theories to quantify, adequately, the complex mechanism of pavement subgrade interaction has generated considerable activities in the area of pavement evaluation and design in general, and material characterization in par­ ticular. tConsequently, there exists in the recently published literatures several excellent state of the art papers dealing specifically with pavement design and the role of material characterization techniques (1, 2, 10, 31, 40).* Hence, no attempt will be made here to reiterate these works, except to emphasize the significance of the repeated load triaxial test­ ing technique and its application to pavement design. Most design methods of flexible highway pavements are empirical and quasi-rational in that they evolve from an assessment of material strength through a logical rational to provide a pavement design for the intended loadings (10, 18, 23, 29, 38, 39). Consequently, it is quite common to obtain different design thicknesses from various design methods for identical or same input factors (18). Part of the differences is attributed to the material characterization techniques and the various ways of interpreting the test results. Hence, any material characterization technique should adequately simulate field conditions. I. Material Characterization Using Repeated Load Triaxial Test In recent years, the significance of the rules of a proper characterization technique of subgrade materials, the envi­ ronmental conditions, and the anticipated traffic loading in the spectrum of variables that control the life cycle of highway pavements has been most profound (18). Most researchers recommended and used the repeated load triaxial test as a mean for material characterization 39, 40, 45). (15, 24, 25, 31, 32, 38, In this test, cylindrical soil samples are *Figures indicate references in the Bibliography 3 carefully prepared and placed in a test chamber where it is subjected to an initial isotropic pressure. A periodic axial stress is then applied with constant or pulsating confining pressure to simulate the action of traffic loading. The test variables and the sample conditions should be specified to simulate field conditions. These variables include confining pressure, deviatoric stress, duration and frequency of load­ ing, number of cycles, water content and degree of compaction. A detailed review of the effects of these variables on the test results may be found in Reference 40 from which a sum­ mary is presented in the next section. Throughout this report, the resilient modulus, the re­ silient, the permanent and the total strains will be defined as follows: al mr = "" °3 ^ £ ---- 1 er = eT - ep (2.2) where M r = resilient modulus = total vertical stress = confining pressure e = recoverable strain (resilient strain) correr sponding to a particular number of stress repetition Ep = permanent strain eT = total strain (sum of resilient and permanent strain) 4 II. Factors Affecting the Resilient Modulus A. Cohesive Soils 1. Number of Load Applications Silt and/or clay subgrade materials generally exhibit a stiffening behavior and an increase in the total and resilient deformations with increase in the number of load applications (15, 16, 24, 25, 29, 30, 31, 32, 40). Dehlen (40) recommended the use of 200 load applications (sample conditioning) for minimizing the varia­ tions in axial deformations caused by end imperfections. He stated that, once the sample was conditioned, the resilient characteristics could be determined at low number of load applications. He also noted the possibility of testing at various stress levels for low number of load repetitions. Seed et. al. (15) recom­ mended that the resilient characteristics could be determined at 10,000 load applications. 2. Stress Intensity The resilient modulus of cohesive soils de­ creases as the deviatoric stress increases (12, 15, 20, 22, 24, 25, 30, 31, 38, 39, 40). This relationship was found to be the case for an increase of deviatoric stress from two to ten pound/square inch (psi). Further increases were found to have slight effects as shown in Figure 2.1. 3. Density and Water Content The higher the compaction water contents the higher is the resilient deformation and the lower is the resilient modulus 31, 38, 40). (15, 20, 25, 30, Figure 2.2 shows that for a given compaction effort, the resilient deformation is 5 •H CO o* a p 12,000 After 200 Stress Repetitions 8,000 4-1 Cu < • HH *H 0) 9 0 4,000 Pi 0 10 20 30 50 Deviatoric Stress (psi) 16,000 After 100,000 Stress Repetitions 09 Q(0 iPH 3 *3 O 12,000 8,000 c a) 4,000 to a; pi J L 1 J 10 20 I 30 L 40 50 Deviatoric Stress (psi) FIGURE 2.1 EFFECT OF STRESS INTENSITY ON RESILIENT CHARACTERISTICS FOR AASHO ROAD TEST SUBGRADE SOIL (15). 6 148 Deviatoric Stress = 2psi Confining Pressure= 2psi After 1000 load repetitions Frequency = 20cycles/min \ 136 Dry Density (lb/ft ) M r =50 132 128 30,000 20,000 10,000 124 _L 8 _L 6 J. 10 Water Content (Z) FIGURE 2.2 WATER CONTENT - DRY DENSITY - RESILIENT MODULUS RELATIONSHIP FOR SUBGRADE SOIL (47). 7 lower on the dry side than on the wet side of the optimum water content (15, 38). B. Cohesionless Soils 1. Number of Stress Applications The number of load applications has minimum effect on the resilient response of cohesionless soils (8, 9, 12, 24, 25, 26, 27, 29, 31, 32, 40). Thus, the resilient characteristics could be determined after 1050 to 1100 load repetitions. The first one thousand cycles were used for sample conditioning to minimize the effects of end imperfections (31, 32). 2. Stress Intensity While the stress level has considerable effects on the resilient response of cohesive soils, it was found to have a slight to no­ effects on the resilient characteristics of granular materials (8, 9, 24, 25, 29, 32). Thus, one cohesionless soil sample could be tested at various deviatoric stresses provided that the confining pressure is kept constant. 3. Confining Pressure Investigators have suggested an exponential type functions (Equations (2.3) and (2.4)) re­ lating the resilient modulus and the confining pressure for granular materials (8, 9, 12, 15, 24, 29, 40). K2 . .(2.3) or K4 8 . .(2.4) where Kl' K3' K2 an<^ K4 are constants deter­ mined by least square fitting method. = confining pressure and 0 4. = sum of principal stresses. Relative Density and Degree of Saturation Most investigators have also found that the resilient modulus of granular materials increases as the relative density increases (8, 9, 12, 15, 23, 24, 29, 38, 40). Hicks and Monismith (24) found that the resilient modulus of granular material increased by 50% from loose to dense samples (24). The nature of the effect of the degree of saturation upon the resilient response of test samples is a complex one and it appears to be related to many other parameters such as aggre­ gate type and drainage conditions during test (23, 26, 27, 29). In general, as the degree of saturation increases, the resilient modulus (based on effective stress analysis) decreases and the total deformation increases. Ill. Correlations of Soil Support Values (SSV) to Material Characterization The basic design equation, developed from the results of the AASHO road test, is valid for one soil support value (SSV) representing the roadbed soils at the test site under conditions existed at the time of testing. Thus, it was necessary to assume a soil support value scale to accommodate the variety of soils which could be encountered at other sites (2). This assumed soil support scale, however, has no defined relationship to any of the strength parameters of the roadbed soils. Consequently, several correlations re­ lating the SSV to different test results were developed by 9 local agencies and highway departments. These correlations include: A. Correlations between California bearing ratio and soil support values (CBR) (SSV). The Utah state Department of Highways determined the CBR of compacted samples of the AASHO Road Test roadbed soils, the crushed stone base materials, and other soil types. An imperical logarithmic scale, shown in Figure 2.3, was then assumed to relate the CBR and the estimated SSV of these materials. Also, Figure 2.3 shows the same correlation ploted to arithmetic scales. B. Correlation between modulus of deformation (triaxial test) and SSV Chou et. al. (6) presented a tentative procedure for subgrade evaluation to estimate the SSV. They conducted triaxial type tests on subgrade soil sam­ ples at field densities and moisture contents. Modulus of deformations were then calculated and correlated to an assumed SSV scale, as shown in Figure 2.4. C. Correlation between SSV and resilient modulus Van Til et. al. conducted an extensive evaluation of AASHO interim guides for design of pavement struc­ tures (16). They concluded that "vertical compressive strain on the subgrade was the most significant factor effecting the performance of the roads at the AASHO road test." As a result of their work, they established a relationship between the soil support value and the resilient modulus of the subgrade soil. They used 3000 psi as the modulus of the subgrade soil at the AASHO road test and 40,000 psi as the modulus of the crushed stone materials. These two values were the limiting resilient modulus values on 10 Soil Support Value (SSV) 1 .0 2 .0 3 .0 4 .0 |_____ ■_____ ]_____ . T 2 3 45 5 .0 I 10 6 .0 I 7.0 I 8 .0 > 20 30 40 50 9I.0 10.0 ---- 1--100 200 C a lifo r n ia Bearing Ratio (CBR) 10 Soil Support Value 8 6 4 2 0 0 40 60 80 100 120 S ta tic CBR Value Fig. 2 .3 C o rrelation between Soil Support Value (SSV) and C a lifo r n ia Bearing Ratio (CBR), ( 2 ) . 140 .6 S- ■5 ai £ 10 ,000 ' 10 i/i 8, 00 0 PSI 6,000- Modulus of Deformation 4 ,0 0 0 . 5,000 .8 7 3,000 6 2,000 . 5 1 , 5 0 0 -•** . 3 1 ,0 00 500 600 c 9 2 o < 3u ia ^ u -r00 i— ■ - gj s_ o Q. CL 3 to o to ( to tJaO> P3 € 1,000 500 o -M O 100 «3 «3 L SO O O 10 _> O) to C 0 ■1 2 5, f O s_ I CT> 0) n 3 S_ s_ to L) 3 tto 4 - -* -o ai +j cn •i— QJ IS I Z to -5 to to •1 20-Year T r a f f i c Analysis Figure 2 -4 . Design c h a rt f o r term inal s e r v i c e a b i l i t y index o f 2 .5 (based on AASHO In te rim Guide except f o r a d d itio n o f modulus o f deformation s c a le ), ( 6 ), 12 their scale, as shown in Figure 2.5. Van Til et. al. recommended that "effort should be made to strengthen the validity of the soil support scale as new ana­ lytical tools and methods of characterizing material properties become available." IV. Sample Preparation for Repeated Load Triaxial Testing Several methods of sample preparation technique have been developed by researchers 40). (8, 9, 23, 25, 26, 27, 29, 38, These include: 1. Static and dynamic techniques were used for the compaction of fine grained soils. Larew Ahmed and (22) conducted tests on silty clays using static compaction method which was previously employed by Leonards (20). Soil cakes were prepared and statically compacted in steel molds (3.5 inches in height and 20 inches in d iameter). Specimens were then obtained, sealed in an aluminum foil, and waxed before testing. Taninoto and Nishi (30) prepared silty clay soil samples using the CBR compaction apparatus. They compacted their specimens in five equal layers using 10 blows per layer. 2. Impact techniques were most often used for the compaction of granular soils Yoder (40). Haynes and (23) used a 5.5 pound hammer falling 12 inches, but they did not specify the number of layers and blows, and the sample size. Mitry (26) compacted his sand samples in 12 equal layers. His final sample size was 6.5 inches in height and 3.8 inches in diameter. The number of blows per layer was increased as each layer was added to minimize the variation of density throughout the sample. Allen and Thompson 13 (3) prepared their aggregate to cn ■ (SSV), n o Soil Support Value (SSV) M 00 (16). t-1 5 H o R-Value (California) U1 55 CJ R-Value (Washington) o ►*1 CBR (Kentucky) 0 JO w cn H H o Texas Triaxial Class 1 o H Group Index CJ Ul ui cn O Resilient Modulus M H f cn 02 T3 ►CJ O 3 c £ 3 o o o o o o o (psi) samples on a triaxial chamber base plate using impact techniques. They used a split mold h a v ­ ing 6 inches in diameter and 12 inches in height. The hammer had a striking face of 2 inches in diameter, weighed 10 pounds, inches. and dropped 18 The specimens were encased in two latex membranes to prevent leakage. 3. Hicks (25) used a vibration technique to compact dry, partially saturated, and saturated sand samples. The vibrations were induced by v i b r a ­ ting a rigid cap placed on the top of the soil layer. All layers were vibrated for a period of fifteen seconds. The compacted soil samples with the cap were then mounted in the triaxial cell. De-aired water was percolated up through the sample and back pressure technique was used to obtain saturated samples. Mitry used an air hammer which led to the crushing of some soil grains and puncturing of the membranes. Thus, he placed the soil in a steel mold and vibrated it on a shaking table. The soil samples were compacted in two equal layers, each was vibrated for a fifteen seconds period. A fifteen pound surcharge was placed on top of the sample during vibration. Regardless of the type of sample preparation technique, Seed et. al. (15) recommended that all laboratory samples should closely duplicate the field density and moisture contents. V. Test Equipments and Procedure Investigators recommended the repeated load triaxial test as a mean for material characterizations 26, 27, 29, 30, 40, 41). (8, 9, 22, 25, The test equipments include: 1. Loading piston. 2. Triaxial cell of suitable size. 15 3. Cyclic air supply. 4. Linear variable differential transducers {L V D T ) suitably mounted for measuring the deformation due to the applied load. 5. Controller to regulate speed of testing at frequencies up to 3 cycles per second. 6. Load cell. 7. Recording equipments. 8. Rubber membranes. 9. Compaction equipments. 10. O-rings of suitable size. The test procedure include the following s t e p s : 1. 2. Measure and record weight and height of sample. Place suitable membrane around the sample. 3. Secure membrane to the top and base caps with O-rings. 4. Place the sample in the triaxial cell. 5. Apply predesignated confining pressure. 6. Apply the desired cyclic stress. 7. Record the applied load and deflection at various number of cycles depending on the soil samples. Kalcheff and Hicks (9) suggested the following sequence of stresses for testing a single specimen of granular material. Confirming pressure ( ) (psi) Axial stress 2 6 5 15 10 30 20 60 2 6 (ct^) (psi) They also recommended a load duration time of 0.1 seconds and frequency of 30 cycles per minute. 16 CHAPTER 3 Field and Laboratory Investigations I. Field Investigations A. Site Selection The test sites of this study were selected on existing highway sections which showed severe p a v e ­ ment distress. General informations concerning topography, pavement conditions and locations of test sites are given in Table 3.1, while their cross sections are shown in Figure 3.1. B. Sampling Techniques Two sampling techniques were used to obtain dis­ turbed and undisturbed samples. In the first, section of the surface of an existing pavement the outer traffic wheel path) a (along approximately three feet square was cut and removed using a rotary con­ crete saw. The insitu densities and moisture c o n ­ tents of the base, subbase and subgrade materials were determined and bag samples were then collected. Problems were encountered in some areas due to the nature of the materials technique, (cobbles). In the second the undisturbed samples were obtained by digging a test pit along the ditch of the highway leaving a standing column of soil having sides eight by eight inches. This column of soil was carefully trimmed to a depth of about twelve inches. A plywood box without its top and bottom was then centered around the soil column and paraffin wax was poured into the space between the sample and the box until the wax level reached the top of the box. The wax was allowed to congeal and the soil column with the box was then severed from the ground by a spade and turned upside down. grass, etc.) All foreign materials (weeds, and soils were removed to a depth of 17 TABLE 3.1. TEST SITES 1-N 1-S GENERAL INFORMATIONS OF TEST SITES GENERAL DESCRIPTION Hilly to gently undulating glacial deposits of boulder, clay, sand and gravel formed at the border of an ice sheet. Surfaces are generally rough and broken. Some areas are mainly leveled or gently undulating sandy and gravelly soils. SAME 2-N SAME 2-S SAME PAVEMENT CONDITIONS GENERAL LOCATION Discrete longitudinal and Transverse cracks in passing lane. Some longitu­ dinal cracks in outer wheel path. North of Lansing, northbound on U.S. 27 and about 200300 yds from the inter­ section of U.S. 27 and 1-75 Highways. Predominantly transverse with some longitudinal cracks. Few alligator cracks in outer wheel path About 100 feet south of test site 1-N north bound Discrete longitudinal and transverse cracks in passing land. Longitudinal cracks along the outer wheel path. North of Lansing, southbound on U.S. 27 and located about 200-300 yds from the intersection of U.S. 27 and 1-75 highways. Patching and transverse cracks in passing lane. About 150-200 feet south of test site 2-N 33.6 33.5 21. 0 24.0 Elev.-0.00 Class AA Sioulder Elev.-0.04 E le v . - l.03 Back Slope Back Slope 11.5"Base Course Class AA Shoulder 32.5 32.2 20.9* 22.5 11.8 E le v . - l. 02 Elev-0.19 Elev. 0.00 12.5 4 .5 "B it Cone. Elev-0.17 Back Slope Elev.-0.49 Elev.-2.71 Class AA Shoulder 10" Base Course Class AA Shoulder Fig. 3.1 - Cross Sections o f Test Sites 1-N and 1-S Bau Slope 36.8 Elev.-0.23 Elev-0.08 4 .5 "B it Cone. Elev.-0.00 Elev-0.46 E le v . - l.41 Elev,-3,40 Back Slope Back Slope Class AA Shoulders Elev.-2.82' 12,2'* Base Course Class AA Shoulders ro o 34.7 34.5 20. 0 ' 1 2 .2 * Elev.+0.14 Back Slope Elev-2.93 4 .5 "B it Cone. Elev.0.00 Elev.-0.02 Elev-0.51 Elev.-1.27' Elevt -3.34 Class AA Shoulder 10.5" Base Course Class AA Shoulder Figure 3.1 Continued - Cross-Section of Test Site 2-N and 2-S. Back Slope about half an inch below the sides of the box to provide space for the wax which was poured on the top of the soil until itfilled the box.Finally, the bottom of the box wasattached. Three samples were obtained from each test pit. C. Traffic and Other Field and Design Data The data listed in Table 3.2 was provided by the Michigan Department of State Highway and Transpor­ tation (MDSH&T). D. These include: 1. thickness of pavement sections at the test site, 2. rut depths of the asphalt concrete surface, 3. field densities and moisture contents, 4. slope variances, 5. regional factor, 6. traffic data for a 15 year period, and 7. structural coefficients Converting Mixed Traffic to Equivalent 18 Kip Axle Load Pavement performance as measured by the present serviceability index (PSI) is related to the loga­ rithm of the number of load applications 43). (2, 16, 18, Consequently, several methods for converting mixed traffic data to equivalent 18 kip axle load exist throughout the literatures. Some of these methods use a constant multiplier to convert the daily passenger cars (DPC) to equivalent 18 kip axle load. Others use a certain percentage of the average daily traffic (ADT) to obtain the DPC. Highter and Harr (43) studied pavement deflection data gathered at the AASHO road test and several Air Force bases. They developed an equation re­ lating the present serviceability index (PSI) to the cumulative total peak deflection that is caused by several vehicles (trucks and airplanes). Thus, the effects of heavy and/or light vehicles on a 21 TABLE 3.2. Sites Layers SC Asphalt Concrete 0.42 4.5 1.89 Base 0.12 10.0 1.20 T (INS) S” (INS) cu ^(pcf) H {2) --- -- --- 4.3 106.5 3.8 100.0 7.5 --- -- 4.21 1-N to PSN FIELD DATA Top-Subbase 0.08 14.0 Subgrade --- --- Asphalt Concrete 0.42 5.5 2.31 Base 0.12 11.5 1.38 1.12 RD(INS) (in/mile) PSI W R 18 SSV 0.150 74.67 1.40 2560 x 103 4 5.23 0.325 74.67 1.30 2560 x 10* 4 4.47 0.375 66.91 1.34 2560 x 103 4 5.07 to 1-S 4.4 4.65 Top-Subbase 0.08 12.0 0.96 108.0 3.9 Subgrade --- --- -- 99.9 4.6 Asphalt Concrete 0.42 4.5 1.89 Base 0.12 12.2 1.46 2-N --- - — 3.0 4.30 Top-Subbase 0.08 12.6 0.96 107.2 2.7 Subgrade --- --- --- 103.9 3.1 TABLE 3.2. Continued 2-S Asphalt Concrete 0.42 ' 4.5 1.89 Base 0.12 10.5 1.26 --- 3.5 4.11 0.425 Top-Subbase 0.08 12.0 0.96 104.5 6.2 Subgrade -- -- -- 110.2 5.1 to U> T SN PSN SC Thickness of pavement components Structural number of pavement components Total structural number of pavement components Structural coefficients Y Dry density W Water content R0 Rut depth SV Slope variance R Regional factor PSI Present serviceability index wia Number of 18 kip loadings 77.66 1.16 2560 x 103 4 5.40 pavement section were additive and linear. It should be mentioned that in their study, they did not in­ clude the effects of traffic distribution of passes per coverage) and Yoder and Witczak over the pavement. (number Deacon (44) (18) developed an expression to predict the equivalent repetitions of a standard vehicle* producing a unit damage. Their expression depends o n : 1. the number of passes within time interval, 2. the frequency, 3. equivalent wheel load factor which is defined as the damage per pass caused to a specific pave­ ment system by the vehicle in question relative to the damage per pass of an arbitrarily selected standard vehicle moving on the same pavement, 4. total number of passes at a specific distance, and 5. the width of traffic area and tire prints Similar expression was developed by Baladi (34) for predicting pavement peak deflections accounts for the lateral position of the vehicle, placement.** i.e., lateral He also measured deflections due to trucks having 18 kip load on back axle and compact vehicles having 2 kip loads on back axle using a linear variable differential transducer (LVDT) beam. He found that the peak pavement deflection due to a compact vehicle was about one-ninth (1/9) the peak deflection due to a truck. *Any vehicle can be defined as a standard if the pavement d e ­ flection it produces is assigned unity. Pavement deflections due to any other vehicles can then be scaled relative to the standard. **The lateral placement is defined as the distance between the nearest edge of the pavement structure and the wheel path. 24 In this study, the conversion of mixed traffic to equivalent 18 kip load repetitions as outlined by the AASHO method was not adequate to calculate the SSV from Equations 3.1 and 3.2, since the results were negative. Therefore, a different approach was developed using concepts by Highter and Harr Deacon (44), Yoder and Witczak (43), (18) and Baladi (34). This approach assumes that an 18 kip axle load (standard axle) produce a unit damage per pass to the pavement section in question and the effects of different vehicles are additive. Thus, based on Baladi data, one pass of a passenger car will pro­ duce about l/9th the unit damage of the standard axle. Consequently, nine passes of this car is needed to induce a unit damage to the pavement.* The approach further assumes that one pass of a truck with a standard axle will produce one full coverage of the loaded strip of the highway pavement. The number of passes of a passenger car that pro­ duce a full coverage is simply related to the ratio of the radius of contact area of the truck tire pressure) to that of the passenger car (2 5 psi tire pressure). 4/3 or 1.3. (80 psi This ratio was approximately Thus, the equivalent 18 kip axle load per day is equal to the number of passes made by 18 kip axle load truck plus the number of passenger cars divided by 9(1.3) - 11.7 or Wtl8 = DDT + DPC/11.7 where DDT = equivalent 18 kip axle load in daily traffic or number of commercial trucks DPC — daily passenger cars and light truck traffic *Caution should be exercised in using this method since it neglects the effects of fatigue and its relation to the magnitude of peak pavement deflection. 25 (3.1) Using Equation 3.1, the equivalent 18 kip load repetitions on the test sites was calculated to be 2.56 x 10.6 repetitions. The present serviceability index (PSI) and the soil support values (SSV)(see Table 3.2) of the high­ way pavements at the test sites at the time of s a m p ­ ling were calculated using the following e q u a t i o n s : PSI = 5.03 - 1.91 log1Q (1+SV) - 1.38 (RD)2 - 0.Ol/C+P log Wtl8 - 9.36 log (SN+1) - 0.20 + log 0. 40 + (3.2) 4.2 - Pt 4.2 - 1.5 1094 (SN+1)5 *19 + log ^ + 0 . 3 7 2 (SSV - 3.0) (3.3) where PSI = present serviceability index SV = shape variance RD = rut depth SN = structural number of pavement section Pt = present serviceability at time t. Wtl8 = number of equivalents 18 kip single axle load repetitions II. C+P = cracking and patching R = regional factor SSV = soil support value Laboratory Investigations A. Test Materials Three different materials were tested in this study. 1. These include: AASHO roadbed soils materials (A-6) and the crushed stone (both materials were received upon 26 request from the Illinois Department of H i g h w a y ) . The compaction (see Appendix A for the compaction effort) and the grain size distribution curves of the A-6 materials are shown in Figures 3.2 and 3.3, respectively. Its plastic and liquid limits were reported as 16.4% and 29.4%, respectively (36). 2. Bag and box samples of the cohesionless Michigan roadbed soils that were obtained at the test sites (see Section 1 a b o v e ) . The grain size d i s ­ tribution curve of the bag sample is shown in Figure 3.4. While Figures 3.5, 3.6, 3.7, and 3.8 show the grain size distribution curves of the box "undisturbed" samples. The uniformity coefficient and the specific gravity are also shown in the figures. Methods of Sample Preparation The recompacted samples were prepared using a modified version of the procedure outlined in refer­ ence (31). For future investigations, the writer recommends the following p r o c e d u r e : 1. Determine the initial water content cent) of the soil (w^ in p e r ­ (if other than oven-dried material is to be u s e d ) . 2. Tighten the sample base into place on the tri­ axial cell base. It is essential that an air­ tight seal be obtained. 3. Place the porous stone and the sample cap on the sample base (two stones are required if drainage from both ends is desired for saturated sp e c i m e n s ) . Determine the height of the base, cap, and stone to the nearest 0.01 inch and record these values. 4. Remove the sample cap and place the rubber m e m ­ brane over the sample base and porous stone. Fix the membrane in place with an 0-ring. Dry Density, (pcf) 115 110 105 e? 103 10 11 12 13 14 15 16 17 18 19 20 Water Content % Fig. 3-2 Dry Density Vs. Water Content fo r AASHO Roadbed S o il, (Using Mold and Hammer Designed for this P r o je c t). 28 21 Percent Passing by Weight 100 4.76 2.0 0.42 0.074 0.02 0.005 0.002 Equivalent Grain Size Diameter (mm) Figure 3.3 Grain Size Distribution Curve for the AASHO Roadbed Soil (36). Specific Gravity, 2.69 100 r % Passing by Weight Uniformity C o e ffic ie n t, 2,0 TTToi Equivalent Grain Size (mm) Fig. 3.4 Grain Size D is trib u tio n Curve fo r Recompacted Sand from Test Sites S p e c ific G ra v ity = 2 . 6 9 U n ifo rm ity C o e f f ic ie n t = 2 . 0 100 90 80 % Passing by Weiqht 70 60 50 40 30 20 10 0 10 1 0.1 0.01 Equivalent Grain Size in (mm) Fig. 3.5 Grain Size D is t r ib u tio n Curve For “Undisturbed" Sand Samples From Test S ite 1-N 31 ioo r Specific Gravity =2. 69 Uniformity C oefficient = 2 . 0 ■M -C CD >1 -Q CD C 10 Equivalent Grain Size (mm) Fig. 3.6 Grain Size D istrib u tio n Curve fo r Undisturbed Sand Samples From Test Site 1-S 100 90 Specific Gravity =2. 69 Uniformity C oefficient = 2 . 0 80 70 % Passing by Weight 60 50 40 30 20 10 0 10 0.1 Equivalent Grain Size (mm) Fiq. 3.7 Grain Size D is trib u tio n Curve fo r Undisturbed Sand Samples from Test Site 2-N 90 80 Specific Gravity - 2.69 70 Uniformity Coefficient = 2 . 0 60 50 40 30 20 10 0 10 1 0.1 Equivalent Grain Size (mm) -ain Size D is trib u tio n Curve fo r Undisturbed Sand Samples from Test Site 2-S 5. Place the split mold around the sample base and draw the rubber membrane up through the mold. Tighten the split mold firmly into place. Ex­ treme care should be taken to avoid puncturing the membrane. 6. 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 perimeter of the mold. The vacuum is maintained throughout the compaction procedure. 7. Use calipers to determine to the nearest 0.01 inch the inside diameter of the membrane-lined mold. Determine to the nearest 0.01 inch the distance from the top of the porous stone to 8. the rim of the mold. Determine the volume of sample to be prepared. The diameter of the sample is the diameter de­ termined in step 7, and its height is a value less than that determined in step 7, but at least two times the diameter. 9. Place the required mass of soil into a mixing pan. Allow approximately 300 grams more than required for compaction. Add the required amount of water and mix thoroughly. 10. Determine the weight of wet soil and mixing pan and record it. 11. Place the wet soil in a plastic bag and secure with a rubber band around the opening. Place the plastic bag in a humid room or humid con­ tainer and allow the soil to sit for about 12. twelve hours. Determine the actual soil water content. 35 13. Place the amount of wet soil required for one layer* into the mold. spillage. Exercise care to avoid Use the spatula to draw the material away from the edge of the mold and form a small mound at the center of the mold. 14. Compact the soil until the distance from the surface of the compacted layer to the rim of the mold is equal to the distance measured in step 7 minus the thickness of the lift determined in step 13. 15. Repeat steps 13 and 14 for each new lift, but increase the number of blows for each new lift in order to minimize the variation of den­ sity within the sample (81, 90, 43, 31, 36). The measured distance from the surface of the compacted layer to the rim of the mold is suc­ cessively reduced by the thickness of each new lift from step 13. The final surface should be smooth and horizontal. 16. When compaction is completed, observe the weight of the mixing pan plus excess soil and record it. This weight minus the weight determined in step 10 is the weight of wet soil incorporated in the specimen. 17. Place the sample cap on the surface men. of the speci­ Roll the rubber membrane off the the mold and over the sample cap. rim of If the sample cap projects above the rim of the mold, the membrane should be sealed tightly against the cap with an o-ring seal. If it does not, the seal can be applied later. ♦ N o r m a l l y , the thickness ot one layer is about 1-1.5 inches (31, 40). Also, the total number of layers should be deter­ mined from previous compaction tests to duplicate field den­ sities and water contents. 36 18. Place the entire assembly on the loading machine in preparation for the repeated load testing. Disconnect the vacuum line from the mold and connect it to the sample. The undisturbed cohesionless soil samples were prepared in a freezing environment as f o l l o w s : 1. Place the block sample, trimming equipments, and base, rubber membranes O - r i n g ) , split mold, cap (rolled up onto an and a pair of gloves in a freezer for about forty-eight hours. 2. Pry the protective box off the paraffin enclosed sample, chip off the paraffin, cut the sample in half, and roughly trim each to a cylindrical shape having about four inches in diameter using large teeth wood saw. 3. Place the sample on the trimmer machine and trim it to a final diameter of about two and oneeighths of an inch using finer teeth wood saw. Remove sample and place it on the removable sample base. 4. Place the sample cap on the top of the sample and roll the rubber membrane over the cap. 5. Fix the membrane in place with rubber strips and an O-ring seal. 6. Attach the split mold around the sample and transfer the sample to the loading machine of the triaxial equipment. 7. Apply vacuum to the sample, remove the mold, and allow the sample to thaw for about twenty-four 8. hours. Measure and record the height and diameter of the sample. Test Procedure The following test procedure was applied after placing the recompacted or undisturbed cohesionless samples on the triaxial equipment: 1. Install a linear variable differential transducer (LVDT) on the removable sample base. 2. Put the plate of the triaxial cell in place and set the voltage reading of the load cell to a less than 0.06 volts by adjusting the Set Point dial {see Appendix A for detail description of MTS system). A voltage reading less than 0.06 volts insures an initial load due to the weight of the plate to be close to zero. Tighten the plate in place. 3. Adjust the LVDT to monitor voltage readings be­ tween plus and minus ten volts. 4. Disconnect the vacuum supply and open the interior of the sample to the atmosphere. 5. Apply the required confining pressure and detect any leakage using the line opened to the atmos­ phere . 6. Move the actuator of the MTS closed loop system (see Appendix A) until the required initial axial stress is applied to the sample (see Table 3.3). Apply the deviatoric stress using the Span dial. 7. Adjust the gain and rate dials whenever the move­ ment of the pointers observed on the strip chart recorder is observed to deviate from a sine wave. 8. Set the frequency dial to the desired frequency. A frequency of one cycle per second for a sinus­ oidal command wave form was selected in this study). Engage the Run control button to conduct the test. 9. Use 200 and 1000 cycles to condition the AASHO A-6 and the cohesionless samples, respectively. 10. Evaluate the resilient modulus of the cohesion­ less materials at 500 cycles and that of the A-6 materials at 100, 200, 500, 1000, 2000, 5000, and 10,000 cycles. 38 Hence, the resilient modulus TABLE 3.3. Materials A-6 AiionU SUBGRADE Materials Sand (Undisturbed and Remolded) TESTING PROGRAM a3 aH °d Nc 0 2.5 5.0 7.5 5 10 15 200 10,000 2 2.5 5.0 7.5 5 10 15 20 10,000 5 2.5 5.0 7.5 5 10 15 200 10,000 10 2.5 5.0 7.5 5 10 15 200 10,000 2 2.5 5.0 7.5 10.0 5 10 15 20 1000 500 5 2.5 5.0 7.5 10.0 5 10 15 20 1000 500 10 5.0 7.5 10.0 10 15 20 1000 500 15 7.5 10.0 15 20 1000 500 .. - number of cycles for conditioning samples. - total number of cycles for test samples. 39 nt could be calculated using either the strip chart recorder, the voltmeter output, or the mini com­ puter. 11. Remove the load from the sample at the completion of test. Reduce the confining pressure to zero, dismantle the cell and remove the LVDT clamps. Determine the moisture content and the weight of samples. Also, obtain the grain size distribu­ tion curve for the undisturbed cohesionless samples. 40 CHAPTER 4 Test Results I. Test D a t a : Appendix B provides complete lists and graphs of the test results of the repeated load and conventional tri­ axial tests of the AASHO roadbed soil and the Michigan cohensionless roadbed materials. II. Repeated Load Triaxial T e s t : A - AASHO Roadbed Soil In all tests, the samples were prepared at different water contents and densities using the same compactive effort, and tested at various deviatoric stresses. Also, the cell pressure was kept constant throughout each test. Table 4.1 provides a list of the sample and test variables, the resilient modulus and the resilient strain of the AASHO roadbed soil. It should be noted that the data were calculated^at 10,000 load applications. Figures 4.1 through 4.4 display plots of the resilient modulus as a function of the number of load repetitions (N). The sample variables (water content and dry deni sity) and the deviatoric stresses are listed in the figures. Figure 4.5 shows plots of the resilient modulus as a function of the deviatoric stress, the numbers next to the data points indicate the water content of the samples. Each of the four curves in the figure repre­ sents a specific water content that is indicated in a circle next to the curve. Also, all four curves were obtained by visual inspection. The cumulative permanent strains at 10,000 load appli­ cations along with the samples and test variables are listed in Table 4.2. Figures 4.6 through 4.8 provide plots of the cumulative permanent deformation versus the 41 TABLE 4.1. SAMPLE REPEATED LOAD TRIAXIAL TEST RESULTS FOR AASHO ROADBED MATERIAL e in % ^3 (psi) W (%) y (pcf ) °l/03 ^R(psi) 4.3 0 18.2 110.8 - 6005 0.072 14.4 4.4 10 17.5 112.0 1.44 7017 0.063 3 9.3 4.3 5 17.7 111.2 1.86 6227 0.070 4 8.7 8.7 0 17.5 107.2 3627 0.239 5 10.9 8.9 2 16.8 113.3 5.45 6202 0.143 6 13.9 8.9 5.0 17.3 108.0 2.78 4010 0.223 7 18.9 8.9 10.0 16.7 112.4 1.89 6050 0.146 8 13.2 13.2 0.0 17.8 108.0 4972 0.265 9 15.4 13.4 2.0 17.2 111.0 7.70 5485+ 0.244 10 17.6 12.6 5.0 17.0 112.5 3.52 3888 0.324 11 23.3 13.3 10.0 16.8 110.5 2.33 4859 0.274 12 4.3 4.3 0.0 15.2 109.7 22009 0.020 13 9.2 *" 4.2 5.0 16.2 110.2 12643 0.033 14 8.7 8.7 0.0 16.3 111.4 5722 0.152 15 10.8 8.8 2.0 16.8 111.4 5.40 5613 0.157 16 14.0 9.0 5.0 16.1 111.0 2.80 6398 0.141 17 19.6 9.6 10.0 15.7 111.6 1.96 9933 0.076 18 13.4 13.4 0.0 16.4 110.7 - 5770 0.232 CT1 (psi) (psi) 1 4.3 2 42 - - 1.84 - r "TABLE 4.1 C o n t d " SAMPLE No. (Psi> d (pSi) 0 3 (psi) W (%) Y (pcf) CTl/03 ^(Psi) e r in % 19 15.4 13.4 2.0 16.4 111.3 7.7 5282 0.254 20 18.4 13.4 5.0 16.3 111.4 3. 68 5078 0.264 21 23. 7 13.7 10.0 16.0 111.5 2.37 5645 0.243 22 4.0 4.0 0.0 14.1 106.5 - 21985 0.018 23 6.5 4.5 2.0 14.6 110.1 3.25 20600 0.022 24 4.5 4.5 0.0 14.8 106.4 - 18713 0.024 25 14.5 4.5 10.0 15.3 109.3 13641 0.033 26 9.4 9.4 0.0 14.9 109.8 8402 0.112 27 11.4 9.4 2.0 14.0 107.9 5.70 10874 0.086 28 14.4 9.4 5.0 14.8 107.5 2.88 9848 0.095 29 19.7 9. 7 10.0 15.7 110.8 1.97 7464 0.130 30 14.1 14.1 0.0 14.3 108.7 7474 0.188 31 16.1 14.1 2.0 14.3 105.7 8.05 7780 0.181 32 19.1 14.1 5.0 14.8 111.0 3.82 5929 0.237 33 24.4 14.4 10.0 14.7 107.5 2.44 6000 0.240 34 5.0 5.0 0.0 12.3 101.8 - 23286 0.021 35 6.4 4.4 2.0 10.6 94.0 3.2 25500 0.071 3'6 4.7 4.7 0.0 11.8 98.6 - 26491 0.018 43 1.45 - - "TABLE 4.1. Contd" SAMPLE No. ai (psi) (psi) °3 (psi) W (%) Y Cpcf ) 37 12.0 10.0 2.0 11.7 101.9 38 9.4 9.4 0.0 11.0 99.7 39 14.4 9.4 5.0 11.5 98.0 40 19.7 9.7 10.0 11.4 97.8 41 14.4 14.4 0.0 11.4 98.9 42 16.1 14.1 2.0 11.8 99.8 43 19.1 14.1 5.0 11.0 44 24.1 14.1 10.0 11.5 a l/03 ^(psi) 15046 0.066 16975 0.055 2.88 15561 0.060 1.97 15000 0.065 13035 0.111 8.05 12449 0.113 98.5 3.82 13700 0.103 97.8 2.41 13028 0.108 6.00 - - ai = Total Vertical Stress Y = ad = Deviatic Stress «R= Resilient Modulus °3 W = Confining Pressure er= Resilient Strain = Water Content 44 £ in % r x 103 (p s i) Modulus Resilient 10F od = 4.7 psi Y = 99.7 pcf od - 9.4 psi Y = 101.9 pcf 0(j = 9.4 psi Y 100 200 500 1000 2000 5000 NUMBER OF CYCLES Fig. 4.1 R e silien t Modulus Vs. Number o f Cycles fo r AASHO Roadbed S o il. = 98.9 pcf 10,000 od = 14,4 psi Modulus ^ w=16.4%, Y =110*?Pcf» o D— □ w=16.3%, Y =111.4pcf, o' = 8 . 3ps i O w=16.3%, y =111.4pcf, a — Resilient O- 100 200 500 1000 2000 5000 10,000 Number of O c l e s F i g u r e 4. 2 = 13. 3p.si a— — — R e s i l i e n t M o d u l u s Vs. N u m b e r of C v e l e s for A A S b O R o a d b e d Soils. = i3.4psi W= 17.5% y = 112.0 pcf W= 16.8% y= 113.0 pcf W= 18.2% y= 110.8 pcf VI = 17.5% y 107.7 pcf 9.2 psi 7 6 Resilient Modulus x 103, (psi) 8 4 3 2 100 200 500 1000 2000 5000 NUMBER OF CYCLES Fig. 4.3 R e silien t Modulus Vs. Number o f Cycles fo r AASHO Roadbed S o il. 10000 = 106.5 pcf 25 14.75% = 106.4 pcf 14.9% = 109.8 pcf = 111.0 pcf 20 15 10 5 100 200 500 1000 2000 5000 NUMBER OF CYCLES Fig. 4.4 R e silie n t Modulus Vs. Number o f Cycles fo r AASHO Roadbed S o il. 10,000 Numbers in Circles Indicate Water Content Curves. % Numbers by Data Points Indicate % Water Content. 16.2 .1 7 . 5 A14.3 n & 14.7 Deviatoric Stress, (psi) . 4.5 Relationship Between Deviatoric Stress, Water Content and Resilient Modulus of AASHO Roadbed Soil. TABLE 4.2. N cycles SUMMARY OF PERMANENT DEFORMATION OF THE AASHO ROADBED SOIL W(%) yh a3 J (psi) (pcf) £ a, (Psi) P 7o 10,000 94.0 10.6 2 4.7 0.0420 10,000 99.0 11.4 2 9.7 0.0400 10,000 99.8 11.8 2 14.7 0.084 10,000 99.0 11.2 5 4.7 0.058 10,000 98.0 11.0 5 9.7 0.078 10,000 98.5 11.0 5 14.7 0.081 10,000 97.5 11.1 10 4.7 0.065 10,000 97.9 11.4 10 9.7 0.067 10,000 97.8 11.4 10 14.7 0.074 10,000 108.7 14.1 0 4.4 0.098 10,000 108.8 14.1 0 9.7 0.140 10,000 108.7 14.3 0 14.7 0.700 10,000 110.1 14.6 2 4.4 0.063 10,000 107.9 14.5 2 9.7 0.0995 10,000 105.7 14.3 2 14.7 10,000 107.1 14.1 5 4.4 0.0141 10,000 107.5 14.9 5 9.7 0.1003 10,000 111.0 14.8 5 14.7 0.1495 50 0.203 "TABLE 4.2. Contd" N cycles w(%) Yj ^3 (pcf) (psi) °d (psi) f •'k e % P 10,000 107.2 15.1 10 4.7 0.159 10,000 111.8 15.7 10 9.7 0.4125 10,000 107.5 14.7 10 14.7 0.630 10,000 109.8 18.3 0 4.4 2.2151 10,000 110.7 16.4 0 14.7 1.620 10,000 112.1 16.1 2 4.7 0.3495 10,000 111.4 16.8 2 9.7 0.6687 10,000 111.3 16.4 2 14.7 10,000 110.2 16.2 5 4.4 0.2349 10,000 111.0 16.1 5 9.7 0.4384 10,000 111.4 16.3 5 14.7 2.3391 10,000 110.4 16.1 10 4.4 0.1508 10,000 111.6 15.7 10 9.7 10,000 111.5 16.0 10 14.7 2.3509 10,000 113.9 16.6 0 4.4 0.9339 10,000 107.7 17.5 0 9.7 0.7433 10,000 108.0 17.8 0 14.7 3.1500 51 1.005 I 0.4453 "TABLE 4.2. Co ntd " N cycles W(%) CT3 d (pcf ) (psi) (psi) £ % P 10,000 108.0 17.8 0 14.7 3.1500 10,000 109 ■: 17.0 2 4.4 0.4306 10,000 113.0 16.8 2 9.7 1.9122 10,000 111.0 16.1 5 4.4 0.2329 10,000 107. 7 17.5 5 9.7 1.5200 10,000 112.5 17.0 5 14.7 2.1833 N = Number of Cycles a3 = Confining Pressure = Dry Density a, = Deviatoric Stress W = Water Content £ - Permanent Strain P Y a 52 («) f ir - 0.25 psi psi Permanent Deformation, psi 0.25 Deviatoric Stress, (psi) Fig. 4.6 Permanent Deformation Vs. Deviatoric Stress for AASHO Roadbed Soil. N = 10,000 cycles. W = 16.3% W = 15.0% Permanent Deformation, (%) W = 11.0% 0.75 0.50 0.25 Deviatoric Stress,(psi) Fig. 4.7 Permanent Strain Vs. Deviatoric Stress fo r AASHO Roadbed S o il, N = 10,000 cycles. Deformation, { %) 16.6% 14.4% psi 0.75 Permanent 0.50 0.25 5 10 Deviatoric Stress (psi) Fig. 4.8 Permanent Deformation Vs. Deviatoric Stress for AASHO Roadbed Soil, N = 10,000 cycles. 15 deviatoric stress. The water contents of the samples and the cell pressures are listed in the figures. It should be noted that each data point in the figures represents one test of one sample. B - Michigan cohesionless roadbed soil The recompacted cohesionless soil samples were p r e ­ pared at field water contents and densities using d i f ­ ferent compactive efforts layer was v a r i e d ) . (the number of blows per These water contents and densities along with the test variables are listed in Table 4.3. Also, tabulated are the resilient modulus and resilient strains. Similar data of the undisturbed samples are listed in Table 4.4. Figures 4.9 and 4.10 display plots of the resilient modulus of the recompacted samples as functions of the confining pressure. The water contents and densities of the samples and the test sites are listed in the figures. Parallel plots of the undisturbed samples are shown in Figure 4.11 and 4.12. The effects of the vertical stress on the resilient response of cohensionless soils were analyzed using the sum of principal stresses (equation 2.4). Typical corresponding plots of the resilient modulus versus the sum of principal stresses (0) for the recompacted sam­ ples are shown in Figures 4.13 through 4.15. contents, dry densities, shown in the figures. The water and the test sites are also Equivalent plots for the u n ­ disturbed samples are shown in Figures 4.16, 4.17, and 4.18. III. Triaxial and Direct Shear Test R e s u l t s : The test data of the recompacted cohesionless soil samples are provided in Appendix B. Typical plots of the principal stress ratio versus percent strain are shown in Figures 4.19, 4.20 and 4.21. 56 The cell pres- * f TABLE 4.3. Sample w(z> RESULTS OF REPEATED LOAD TRIAXIAL TESTS FOR RECOMPACTED SAND SAMPLES Y (pcf) S (Z) 0l(pal) 9.667 . °d{psl) °3(psl) °l/03 0 (psi) ^R(psi) er x 10-6 4.667 5.00 1.933 19.667 13731 340 19.167 9.167 10.00 1.917 39.167 48112 191 32.330 17.330 15.00 2.516 62.333 64733 268 33.670 18.670 15.00 2.245 63.667 50348 371 21.500 14.000 7.500 2.867 36.500 30895 453 23.000 17.000 6.00 3.833 35.000 31744 536 15.330 11.330 4.00 3.833 23.333 23923 474 7.167 4.670 2.50 2.B67 12.167 13327 350 7.667 5.670 2.00 3.834 11.667 14480 391 43.000 28.000 15.00 2.867 73.00 59104 474 28.667 18.670 10.00 2.867 48.667 39403 474 10.000 5.000 5.00 2.000 20.000 34375 145 15.000 5.000 5.00 3.000 25.000 29000 303 20.000 15.000 5.00 4.000 30.000 32813 457 20.000 10.000 10.00 2.000 40.000 48003 208 1 j 1 2-N-l 3.33 103.12 14.35 "TABLE 4.3. Coned" Sample 2-S-4 Ul 00 l-S-2 W (2) 3.33 4.8 T(pcf) S(2) 103.95 105.6 22.04 Ej X 10 ^ °l/a3 Vsl) HR(P»1) 10.00 2.54 45.357 47681 322 20.000 10.00 3.00 50.00 48125 415 35.714 20.714 15.00 2.38 65.714 64315 322 6.700 4.700 2.00 3.35 10.700 10824 430 9.900 4.900 5.00 1.98 19.900 18540 260 14.700 9.700 5.00 2.94 24.700 17529 550 19.700 9.700 10.00 1.97 39.700 22420 430 24.700 14.700 10.00 2.47 44.700 24000 612 30.100 20.100 10.00 3.01 50.100 25737 ' 780 29.700 14.700 15.00 1.98 59.700 29001 506 35.100 20.100 15.00 2.34 65.100 30000 660 14.380 9. 380 5.00 2.876 24.380 22872 410 19.080 14.080 5.00 3.816 29.080 27446 512 9.690 4.690 5.00 1.938 19.690 25000 187 ° 1(pa1 ) °d(psl) 25.357 15.357 30.000 °3(psl) "TABLE 4.3. Cont" Sample U Y (pcf) S< « °3(psl) °l/o3 V s1) 9.380 *10.00 1.938 39.380 30496 307 28.767 18.767 10.00 2.877 48.767 35878 523 24.075 14.075 10.00 2.408 44.075 33471 280 29.410 14.410 15.00 1.961 59.410 41323 349 33.767 18.767 15.00 2.251 63.767 40661 461 9.524 4.524 5.00 1.900 19.524 12603 359 14.383 9.383 5.00 2.880 24.383 11089 861 19.048 9.048 10.00 1.905 39.048 13572 666 24.075 14.075 10.00 2.408 44.075 16890 833 29.075 14.075 15.00 1.940 59.075 21285 661 33.767 18.767 15.00 2.250 63.767 22872 820 6.700 4.700 2.00 3.350 10.700 15478 300 12.00 10.000 2.00 6.000 16.000 16000 625 9.70 4.700 5.00 1.940 19.700 31999 146 19.38 l-N-3 7.04 107.7 34.2 U1 V£> £—S—3 4.92 106.2 ( 22.95 £r x 10“6 °d(psi) al(psl) 1 "TABLE 4.3. Cone" Sample 1-S-l W(D 4.5 Y (pcf) 104.4 S(7.) 20.04 ■ Degree of Saturation o, ■ Total Vertical Stress 1 0 . * Devlatonic Stress a S(Z) 17.61 er x 10-6 °l(psi) °d(psl) °3(psi) °l/o3 ®(os 1) Vpsl) 28.667 18.667 10.00 2.867 48,67 23811 784 34.000 19.000 15.00 2.267 64,00 26B33 708 28.667 13.667 15.00 1.911 58,67 21792 627 43.667 28.667 15.00 2.911 73.67 31489 910 15.083 11.333 3.75 14.022 22.58 19317 587 7.083 5.333 1.75 4.047 10.58 12554 425 21.500 ’ 14.000 7.50 2.880 36.50 21930 638 22.670 16.670 6-00 3.778 34.67 21525 774 6.830 4.330 2.50 2.733 11.83 14586 297 ■ Confining Pressure n principal Stresses (0 . + 2o ) 1 3 “ Resilient Modulus R er • Resilient Strain TABLE 4.4. Sample 1-N-l l-N-2 RESULTS OF REPEATED LOAD TRIAXIAL TESTS FOR UNDISTURBED SAND SAMPLES u (%) 2.64 5.0 Y (pcf) 97.97 89.6 S<%) 9.99 15.47 al( psi) °d( psi) a3(psi) °l/03 6 (psi) Vpsi) e r x 10'6 6.464 4.464 2.0 3.232 10.464 21484 207.8 9.286 4.286 5.0 1.857 19.286 27500 155.8 19.286 14.286 5.0 3.857 29.286 25000 571.4 24.643 14.643 10.0 2.484 44.643 34300 426.9 28.57 18.57 10.0 2.857 48.57 34290 540.0 29.286 14.286 15.0 1.952 59.286 40441 353.0 34.286 19.286 15.0 2.286 64.286 39495 488.0 8.30 6.3 2.0 4.15 12.30 15386 410.0 10.10 5.1 5.0 2.02 20.10 20999 242.9 14.90 9.9 5.0 2.98 24.90 22000 450.0 19.70 14.7 5.0 3.94 29.70 22976 640.0 17.20 7.2 10.0 1.720 37.20 46890 150.0 25.30 15.3 10.0 2.53 45.30 41517 490.0 "TABLE 4.4. Cont" Sample l-N-3 2-N-l W (%) 3.97 3.2 Y(pcf) 98.88 98.9 S(%) 15.38 12.41 °l/03 8(psi) M Rfpsl) 10.0 3.03 50.30 40.000 382.5 15.6 15.0 2.04 60.60 58612 270.0 20.3 15.0 2.35 65.30 52443 390.0 °l(psi) °d(psi) 30.30 20.3 30.60 35.30 °3(psi) £ r X 10 ^ 6.430 4.430 2.0 3.205 10.430 20224 219.0 9.430 4.430 5.0 1.886 19.430 22151 200.0 19.215 9.215 10.0 1.922 39.215 25598 390.5 24.176 14.176 10.0 2.4176 44.176 25887 548.0 29.138 19.138 10.0 2.9138 49.138 26793 714.3 29.176 14.176 15.0 1.945 59.176 29187 455.7 34.138 19.138 15.0 2.276 64.138 30915 619.0 9.768 4.768 5.0 1.950 19.768 22352 213.30 24.305 14.305 10.0 2.431 44.305 25749 555.6 19.531 9.531 10.0 1.953 39.531 26000 359.6 10.0 1.907 49.07 27687 688.8 29.07 19.07 "TABLE 4.4. Cont" Sample 2-N-2 2-N-3 U (%) 3.16 3.52 Y (pcf ) 97.4 106.5 S (%) 11.96 16.45 °l(psi) °d(psl) °3(pei) °l/a3 6(psi) M_. R(psi) 29.305 14.305 15.0 1.954 59.305 31556 453.3 32.711 17.711 15.0 2.18 62.711 31880 555.6 6.476 4.476 2.0 3.238 10.476 6797 659.0 9.476 4.476 5.0 1.895 19.476 9176 487.8 12.46 7.46 5.0 2.492 22.46 10547 707.0 18.93 13.93 5.0 3.786 28.93 10868 1282.0 24.257 14.257 10.0 2.4257 44.257 17193 829.0 28.568 18.568 10.0 2.8568 48.568 18568 1000.0 29.257 14.257 15.0 1.950 59.257 20157 707.0 33.568 18.568 15.0 2.238 63.568 20575 902.0 6.310 4.310 2.00 3.155 10.310 10500 411.0 9.640 4.64 5.0 1.92 19.640 17000 270.0 13.621 8.621 5.00 2.724 23.621 16058 537.0 19.450 9.45 1.945 39.450 29924 315.8 10.0 e r x 10 6 "TABLE 4.4. Cont" Sample 2-N-4 W (%) 2.70 Y (pcf ) 101.0 S(%) 16.51 cr x 10 6 °l(pai) 0d(psi) 03(psi) °l/03 0(psi) MR(psi) 24.589 14.589 10.0 2.459 44.589 26399 553.0 29.231 19.231 10.0 2.923 49.231 28107 684.0 29.589 14.589 15.0 1.972 59.589 39598 368.4 33.568 18.568 15.0 2.238 63.568 36748 505.0 6.177 4.177 2.0 3.089 10.177 7325 568.0 9.535 4.535 5.0 1.907 19.535 17817 254.0 13.951 8.951 5.0 2.790 23.951 18002 497.22 19.322 14.322 5.0 3.864 24.322 18000 795.7 18.752 8.752 10.0 1.8752 38.752 30086 291.0 23.924 13.924 10.0 2.3924 43.924 29175 477.3 28.698 18.698 10.0 2.8698 48.698 30471 614.0 28.924 13.924 15.0 1.928 58.924 37358 373.0 34.096 19.096 15.0 2.273 64.096 38192 500.0 6.277 4.277 2.0 3.139 10.277 18712 228.6 "TABLE 4.4. Cont" Sample 1-S-l l-S-2 U (%) 6.98 12.05 y (pcf ) 92.88 95.07 S(%) 23.37 42.55 t x 10 ^ °l(psi) 0d(psi) °3(psi) °l/o3 0(psi) ^Rlpsi) 9.099 4.099 5.0 1.820 19.099 22416 182.9 14.267 9.267 5.0 2.853 24.267 21975 423.0 18.900 13.900 5.0 3.78 28.90 24326 571.4 19.267 9.267 10.0 1.9267 39.267 27961 331.4 23.900 13.900 10.0 2.390 43.90 30407 457.1 28.890 18.890 10.0 2.889 48.89 33058 571.4 28.90 13.90 15.0 1.927 58.90 38009 365.7 33.534 18.534 15.0 2.236 63.534 36857 502.9 5.949 3.949 2.0 2.975 9.949 12506 315.8 9.464 4.464 5.0 1.893 19.464 18578 240.3 14.272 9.272 5.0 2.854 24.272 17976 515.8 19.272 9.272 10.0 1.9272 39.272 25167 368.4 24.423 14.423 10.0 2.442 44.423 25853 557.9 29.231 19.231 10.0 2.923 49.231 25362 758.3 r "TABLE 4.4. Cont" Sample 2-S-l 2-S-2 U (%) 4.26 3.00 Y (pcf ) 106.27 102.6 S(%) 19.92 12.76 03(psi) °l/a3 6(psi) ^R(psi) e x 10 6 r 14.08 15.0 1.939 59.08 30399 463.2 33.544 18.544 15.0 2.236 63.544 30638 605.3 6.282 4.282 2.0 3.141 10.282 7980 536.6 9.282 4.282 5.0 1.856 19.282 19694 217.4 14.223 9.223 5.0 2.845 24.223 17188 536.6 19.223 9.223 10.0 1.9223 39.223 25818 357.2 24.163 14.163 10.0 2.4163 44.163 26395 536.6 29.104 19.104 10.0 2.9104 49.104 29010 658.5 29.493 14.493 15.0 1.966 59.493 33762 429.3 34.10 19.10 15.0 2.273 64.70 37651 507.29 9.70 4.70 5.0 1.94 19.70 16494 280.0 14.70 9.70 5.0 2.94 24.70 17785 550.0 °l(psi) ad(psi) 29.08 20.0 15.0 5.0 4.00 30.0 19793 760.0 24.4 19.4 5.0 4.88 34.4 20971 930.0 "TABLE 4.4. Cont" Sample W <%) Y (pcf) S(%) er x 10 ^ °3( psi) °l/a3 6 (psi) 10.0 10.0 2.00 40.0 26391 380.0 25.0 15.0 10.0 2.50 45.0 29877 500.0 30.1 20.1 10.0 3.01 50.0 30161 660.0 35.0 20.1 15.0 2.33 65.0 40602 490.0 °1( psi) °d(psi) 20.0 ^(psi) 1 W = Water Content = Dry Density S = Degree of Saturation = Total Vertical Stress 0 a. = Deviatonic Stress er = Resilient Strain u = Confining Pressure = Sum of Principal Stresses (o^ + 2o^) = Resilient Modulus w% 80 h 70 h o ------------- o • ------------- 3 o -© Ci------------- A A ---------- -A A " “ — —A Y PC f 4 .80 3.68 5.00 105.6 107.2 104.0 4.92 5.57 2.78 104.1 103.95 111 .50 Resilient Modulus x 10 (psi) 2-S = Test S i t e 2-S 1-S = Test S i t e 1-S 10 Confining Pressure, ( p s i) Fig. 4.9 Resilient Modulus Vs. Confining Pressure for Recompacted Cohesionless Samples. 72 15 2-N 4 70 - / Resilient Modulus x 10 (psi) 50 - '""O'' ** 30 “ w% o----------- O o— o— ------- o £>-----------A A --- ------- A A ---- — —A - 7.04 3.20 3.15 3.30 3.33 4.50 Ypcf 107.7 104.6 105.9 105.6 103.3 104.4 2-N = Test Si te 2-N 1-S = Test S i t e 1-S 1-N = Test S i t e 1-N 1___________ 0 5 _L 10 If Confining Pressure, o^* ( p s i ) Fig. 4.10 Resilient Modulus Vs. Confining Pressure for Recompacted Cohesionless Samples 73 1-S W% YPCf o ----- ------- O Q----- ------- • o -------------o A— ------- A Cl--- -----a A —— 2 .6 4 5 .0 0 4.00 3 .2 0 3.20 3 .5 0 98 .0 89.6 99.00 9 8.9 97.4 106.5 1-N 1-N == Test S i t e 1-N 2-N == Test S i t e 2-N 1-N 2-N Modulus x 10 (psi) 60r Resilient 2-N 1 -N * 2-N 5 Confining Pressure Fig. 4.11 10 15 (psi) Resilient Modulus Vs. Confining Pressure for Undisturbed Cohesionless Samples. 74 W% 6 0— o — -------- o • — -- —9 o— -------- © ------- * Ypcf 2 .7 0 6 .9 8 12.10 4.30 101 .0 93 .0 95 .0 106.0 Resilient Modulus x 10 (psi) 2-N = Test S i t e 2-N 2-S = Test S i t e 2-S - 1-S = TEst S i t e 1-S . 10 Confinind Pressure ( p s i ) Fig. 4.12 Resilient Modulus Vs. Confining Pressure for Undisturbed Cohesionless Samples. 75 15 70 60 Resilient Modulus x 10 (psi) 50 40 30 20 Test Site 2-S O- 10 -A W = 5.57% Y 0 10 30 50 70 90 Sum of Principal Stresses, e, (psi) Fig. 4.13 ResilientModulus Vs. Sum of Principal Stresses for Recompacted Cohesionless Samples. 76 = 103.95 pcf 100 80 (psi) Test Site W = 3.68% 40 Resilient Modulus x 10 60 = 104.4 pcf = 405.6 pcf = 107.2 pcf Test Site W = 7.04% = 107.7 pcf Sum of Principal Stresses, e, (psi) Fig. 4.14 Resilient Modulus Vs. Sum of Principal Stresses for Recompacted Cohesionless Samples 77 80 60 40 Test Site 2-N O — O □ D 3.1% 3.15% 3.3% 3.33% 20 = = = = 104.6 106.9 105.6 103.1 0 10 30 50 70 90 Sum o f Principal Stresses, (psi) Fig. 4.15 Resilient Modulus Vs. Sum of Principal Stresses for Recompacted Cohesion!ess Samples pcf pcf pcf pcf Resilient Modulus x 10 (psi) 50 40 30 Test Site 1-S = 93 pcf = 95 pcf 6.98% 20 O -- O Test Site 2-S o - -a £>--10 4.3% 3.0% Y = 102.6 pcf 0 10 30 50 70 90 Sum o f Principal Stresses, e, ( p s i) Fig. 4.16 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Cohesionless Samples. 79 50 - / - 30 - 20 - Resilient Modulus x 10 (psi) 40 Test Site 2N w= w= w= w= 10 30 50 TO 3/2% 3.2% 3.5% 2.7% Y Y Y Y = = = = ter Sum of Principal Stresses, (p s i) Fig. 4.17 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Cohesionless Samples. 80 98. pcf pcf 97. 106 5 pcf 101 pcf (psi) Modulus x 10 Test S ite 1-N Resilient □ □ = 98 pcf = 89 pcf = 99 pcf Sum o f Pr incip al Stresses, ( p s i) Fig. 4.18 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Cohesionless Samples. 81 CO D 6 / Stress Ratio % Principal o3(psi) •— Strain {%) Fig, 4,19 Stress-Strain Curve for Recompacted Cohesionless Samples. • "Y( pcf ) n 11.0 4.1 107.8 0 “ ** "O 20.5 2.9 102.0 6 ------- a 16.0 3.60 106.0 i i 8 10 i 12 8 7 6 Ratio 3 Principal 4 Stress 5 Ypcf o?(psi) O— -O 10.0 15.5 20.5 2 2 4 6 Strain {%) Fig. 4.20 Stress-Strain Curve fo r Recompacted Cohesionless Samples 8 3.24 3.12 3.22 10 107.8 111.6 100.3 ro o D O 00 d ai: in (/) 01 c/i (/) 01 L. +J to u 40 s+oj W(%) y(pcf) o3(psi) • ------------ 1 4.06 107.8 11.00 O — — -O 3.60 108.6 16.00 2.90 102.0 20.5 0" <0 •r- — *o > 0) o 20 I_________ I_________ I_________ i 4 6 8 10 S train, (%) Fig. 5.5 Stress Vs, Strain f o r Recompacted Cohesionless Soils. i 100 Deviatoric Stresses, (p s i) 80 60 40 O- 20 0 2 3 wm Y(pcf) 2.46 108.8 15.0 4.15 101.8 20.5 4.13 110.0 9.50 4 5 Strain, (») Fig. 5.6 Stress Vs. S train fo r Recompacted Cohesionless S o ils . 1o Support Value 9 The numbers shown are the s i t e numbers 8 7 6 #20 Estimated Soil 5 21 Assumed c o rre la tio n between modulus of deformation and soil support value 27 3 2 1 bOO 1000 6000 20000 Modulus o f Deformation, (p s i) Figure 5.7 C o rre la tio n o f estimated soil support value w ith the modulus o f deformation o f subgrade m ate ria ls . (6) 98 high relative to a SSV of 5.5 by Equation 3.1. (maximum value) determined The differences in the two values may be attributed to the limitations of the procedures. These include: 1. Variations of resilient modulus from 1100 psi for the AASHO roadbed soil to 10,000 psi for the crushed stone materials were assigned paralled variations of SSV from 3.0 to 10.0. 2. The correlation was developed for a confining pressure of 3. 1 0 psi. The triaxial test does not simulate the action of a vehicle over a pavement section. These limitations have suggested the use of repeated load triaxial tests to simulate the transient effect of the loading vehicle and consequently correlating these results to the soil support values. I l l . Resilient Modulus of the AASHO Roadbed Soil Figure 5.8 shows a typical load and deformation out­ put for the AASHO roadbed soils as a function of time or number of load applications. The amplitude AB being the total deformation of the sample during that particular cycle, while A* B 1 represents the recoverable deformation. (resilient) The algebraic difference between AB and A 1 B ' is related to the permanent deformation of the sam­ ple during the same loading cycle. The total, resilient and permanent strains of the test samples were calculated by dividing the corresponding deformations, AB, A 1 B 1, and (AB-A'B'), by the original sample height respectively. The amplitude CD in Figure 5.8 represents the deviatoric load applied to the sample at the designated cycle. This load divided by the product of the resilient strain and the cross-sectional area of the sample is equal to the resilient modulus of the material at the cycle in ques­ tion. It should be noted that throughout this study, 99 0030 0025 0020 a. ooio 0005 A' 95 96 37 100 Number of Cycle 15.0 12.5 10.0 5.0 2.5- 95 96 97 98 99 Number of cycle Figure 5.8 Typical Load and Deformation Output 100 100 the test data were reduced and the resilient moduli were calculated during the test (on-line data reduction) by interfacing with the cyclic triaxial system an Automation Alpha / LSI-2/10 minicomputer (8 k memory, BV/TTI/RTC/AL processor, 12-bit digital I/O module, 16 channel A/D - D/A convertor). These calculations were checked later using the strip chart recorder output. A. Effect of Sample and Test Variables on the Resilient Modulus The resilient modulus of the obtained in this study ranged from about 2800 to (see Table B.l.) depending on ables. the 2 0 , 0 0 0 psi sample and test vari­ These include: 1 . degree of saturation 2 . deviatoric stress 3. 1. AASHO roadbed soil (water content), (stress level), and the number of load applications Degree of saturation and The test samples of the stress level: AASHO roadbed materials were compacted at different water contents using the same compactive effort and they were tested at different deviatoric stresses. Figure 4.5 displays plots of the resilient modulus of these soil samples as a function of deviatoric stress. The numbers next to the data points in the figure indicate the sample water contents, while the incircled numbers designate the estimated water contents corresponding to those of the curves. The four curves in Figure 4.5 were drawn by visual inspection. Examination of the figure indicates that, at the same deviatoric stress, the resilient modulus increases as the water content decreases. This was expected because an increase in the sample moisture content will increase its plastic behavior and decrease its stiffness which leads to larger resilient strains 101 and hence lower resilient modulus. Recalling that the samples were subjected to deviatoric stresses simulating those of 18 kip single axle loads and that the resilient strain could be used as a measure of the work done to the sub­ grade, it follows that the higher the field water content the higher the work done to the pavement section. This concept will be explained some more in Section B below. Further examination of Figure 4.5 indicates that, for all four curves, the higher the devia­ toric stress the lower the resilient modulus. This is due to the non-linear behavior of the materials, that is the relationship between stress and strain is not linear. The importance of this may be stated as follows; the applied deviatoric stress on the sample produced a small total strain which is composed of two parts, re­ coverable strain (plastic). (elastic) and permanent strain Increasing the deviatoric stress will increase the resilient and the permanent strains of the subgrade which are related to fatigue and rutting of the pavement in question respectively. Also, the maximum deviatoric stress applied to the subgrade in a pavement section is a function of the loading vehicle, tire pressure, pavement thickness and pavement materials. Assuming that an 18 kip single axle load is the maximum load per axle will travel the pavement in question and that the subgrade soil samples do in the field. represent the subgrade materials It follows that the maximum devia­ toric stresses that need to be investigated in the laboratory are those applied to the subgrade in the pavement section as a consequence of the passage of a loading vehicle having 18 kip load 102 per axle. Further, when designing a pavement section, the thicknesses of the pavement com­ ponents should be those which minimize fatigue and rutting of the subgrade. Some additional aspects and uses of the effect of water content and deviatoric stress on pave­ ment behavior will be discussed in Section B below. 2. Number of Load Repetitions (N). Figures 4.1, 4.2, 4.3, and 4.4 show plots of the resilient modulus of the AASHO roadbed materials as a function of the number of load application. The water contents and densities of the test samples and the applied deviatoric stresses are listed in the figures. It can be noted that, for all tests, the resilient modulus (Mr ) increases as the number of load repetitions (N) increases. Also, the rate of change of with respect to (N) appears to be associated (M_) with the applied deviatoric stress and with the samples water content and density. A large num­ ber of repeated stress applications causes absorbed and/or free water in the vicinity of the contact area between clay particles in the sample to be extruded to the surrounding voids bringing the particles closer together. This process is known to cause stiffening of the samples and thus decreasing the resilient strain as shown in Figure 5.9. As a consequence, the resilient modulus will increase. It should be noted that no similar behavior was observed in equivalent tests on granular soils. Further examination of Figures 4.1, 4.2, 4.3, 4.4 and 5.9 indicates that, in the range of the test data, the effects of the sample variables 103 0.3 0.2 S 17.8% 108.0 pcf 13.2 psi 17.3% 108.0 pcf 8.9 psi Resilient Axial 18.2% 110.8 pcf 4.0 psi 0.1 100 1000 10.000 Number of Stress Applications Figure 5.9 Resilient Strain Vs Nunber of Stress Applications for AASHO Roadbed soil. 100.000 (water content and density) on the rate of change of the resilient modulus or resilient strain with respect to the number of load applications (the slope of the curves in the figures) are not clearly defined. This is due to the narrow range of water contents at which tests were conducted. The objective of the study at the time was to prepare the laboratory samples at a range of water contents simulating those that are likely to exist in the field. Tests at wider range of water contents are required before such effects can be analyzed. It seems, however, that the higher the water content the higher the slope of the curves in the figures. B. Effect of Sample and Test Variables on the Cumulative Permanent Deformation Plots of the cumulative permanent deformation of the AASHO test samples as a function of deviatoric stress are shown in Figures 4.6, 4.7 and 4.8. The water content of the samples and the confining pressures are listed in the figures. Each data point in the figures represent one independent test and one sample. a) It can be noted that: the higher the deviatoric stress the higher the permanent deformation, and b) for the same deviatoric stress, the higher the water content the higher the permanent defor­ mation and the higher the slope of the curve. Cumulative permanent deformation (ruts) in subgrade materials are recognized as the major cause of distress in flexible pavement (45). It causes rutting of the surface which follow the tire tracks or local depressions of the pavement surface. Thus, the question arises as to what could be done to minimize pavement rutting. Examination of Figures 4.6, 4.7, and 4.8 indicates 105 that for water content of about % the cumulative per­ manent deformations of the test samples are almost con­ 1 1 stant for a range of deviatoric stress of 5 to 15 psi and a corresponding range of cell pressure of This indicates that the permanent deformation 2 to 1 0 psi. (ruts) of the AASHO subgrade materials and consequently the work done to the pavement section in question could be m i n i ­ mized if the material is to be placed and compacted at a water content of about 1 1 % which is on the dry side of the compaction curve (Figure 3.2). The compaction of a clay like soil such as the AASHO roadbed materials at a water content dry of optimum will end up with extremely soft and compressible materials when soaked (saturated) under spring conditions unless it is subjected to a high confining (lateral) pressure. If, on the other hand, soaking is not possible then the compacted soils will behave a brittle like materials and it may suddenly collapse resulting in a catastrophic failure. A solution to the problem may be obtained by maximizing the compac­ tion energy so that the optimum moisture content tends toward 11%. The only limitation to this solution is an economical one. IV. Resilient Modulus of the Michigan Cohensionless Subgrade Soils A. Introduction The repeated load triaxial tests of the recompacted and undis­ turbed Michigan cohesionless roadbed soil samples were designed and conducted to study several variables that were thought to influence the resilient characteristics of the materials. These variables include water content, density, confining pressure and vertical stress. The undistrubed samples were tested under insitu conditions (density and water content) that existed at the time of sampling. The density and water content of the recompacted samples ware varied to simulate those that are likely to exist in the field throughout the life cycle of the pavement. The confining pressure 106 and vertical stress were varied to duplicate those applied to the subgrade in a pavement sections as a consequence of the passage of loading vehicles. These variations were applied to each of the reccmpacted and undistrubed samples as it was outlined in Chapter 3. Also, for both recompacted and undisturbed samples (as in the case of the conventional triaxial tests) the interior of the sample was opened to the atmosphere and hence the pore air and water pressure ware atmospheric and negative respectively. Consequently, all the test data are presented and discussed on the basis of total rather than effective stress analysis. Tables 4.3 and 4.4 provide lists of the test results for the recompacted and undisturbed samples respectively. The water content and density of the samples are also listed in the tables. Typical plots of the resilient modulus (to a logarithmic scale) as a function of the confining pressure (to a logarithmic scale) and of the sum of principal stresses (to a logarithmic scale) are shown in Figures 5.10 and 5.11 respectively. The rest of the data are shown in Figures B.l through B.43 in Appendix B. It should be noted that the values of the resilient modulus at confining pressure of less than 2 psi are in error. This is due bo the tendency of the pressure regulator to drift slightly at low stresses. Also, at these low stresses, the sample deformations were small and in the range of the accuracy of the linear varable differential transducer (LVDT). Further, as had been found to be the case in previous studies by several investigators, the number of load applications was found to have slight to no effects on the resilient modulus of cohesionless soils. B. Effect of Test Variables A study of Figures 5.10, 5.11 and B.l through B.43 and analyses of the data listed in Tables 4.3 and 4.4 have directed that the resilient modulus and the cell pressure may be related 107 functionally by equation (2.3), while the resilient modulus and the first stress invariant (the sum of principal stresses) could be related by equation (2.4) = *-1 ^3 * 2 (2.3) “ r = 1^0*4 (2.4) The constants of equations (2.3) and least (2.4) warecalculated squares analyses and they arelisted inTables using (5.2) and (5.3) along with the coefficient of correlation and the samples water content and density. Examination of the values of the coefficient of correlations have indicated that, for most tests, there exists a slightly better correlation betwaen the resilient modulus and the confining pressure (equation 2.3) than between the former and the first stress invariant (equation 2.4) . This last equation, however, account for the effect of the total vertical stress on the resilient modulus of the materials which is lacking in equation (2.3). Examination of Figures (5.10) and (5.11) and of the value of the constants of equations (2.3) and (2.4) indicates that: 1. The higher the confining pressure the higher the resilient modulus. This was expected because as the confining pressure increases, the side portions of the sample is held more firmly in place and thereby reducing the resilient axial stain which increases the resilient modulus. This can be stated differently as follow: increasing the confining pressure will decrease the elastic compression of the soil skeleton. This phenomenan was also reported by Morgan (27). 2. No consistent functional relationship was found between the resilient modulus and the total vertical, stresses. Most of the test data, however, show a decrease in the resilient modulus as the total vertical stress increases 108 Table 5.2 Load Test Results o f Undisturbed Michigan Cohesionless M aterial {%) Dry Density (pcf) Degree of Saturation (%) 1-N-l 2.64 98.0 10.00 16000 l-N-2 5.00 89.6 15.50 7900 l-N-3 4.00 99.00 15.40 2-N-l 3.20 98.9 2-N-2 3.20 2-N-3 V W mr 2 * K/ 4 RZ K3 K4 0.32 0.96 9400 0.34 0.88 0.71 0.94 1800 0.82 0.89 16900 0.22 0.93 11600 0.22 0.95 12.40 12900 0.32 0.92 8760 0.30 0.88 97.40 12.00 4200 0.59 0.98 1358 0.66 0.98 3.50 106.5 16.50 1600 0.66 0.98 1945 0.71 0.95 2-N-4 2.70 101.0 16.50 4700 0.79 0.98 1171 0.85 0.96 1-S-l 6.98 93.00 23.4 13400 0.36 0.92 6700 0.40 0.93 l-S-2 12.10 95.10 42.6 9000 0.45 0.997 4225 0.48 0.98 2-S-l 4.30 106.3 20.00 5400 0.71 0.97 1600 0.75 0.94 2-S-2 3.00 102.6 12.80 6300 0.67 0.93 1500 0.78 0.96 ____ 1 K1 ro PC Sample No. Water Content Summary of Repeated R2 Table 5.3 Summary o f Repeated Load Test Results o f Recompacted Michigan Cohesionless M ate rial. Sample No. Water Content (*) Dry Density (pcf) Degree of Saturation (%) mr = V a"2 K1 *2 Hr - K38K4 R2 K3 K4 R2 1-N-l 7.04 107.7 34.2 12255 0.44 0.91 5133 0.50 0.93 2-N-3 3.20 104.6 14.3 7749 0.73 0.99 2759 0.72 0.93 2-N-4 3.15 106.9 14.96 10058 0.51 0.86 3491 0.58 0.87 2-N-2 3.30 105.6 13.93 9457 0.85 1.00 2021 0.90 0.94 2-N-l 3.33 103.1 14.35 8000 0.73 0.96 1445 0.88 0.88 104.4 20.04 16935 0.54 0.98 2217 0.85 0.90 1-S-l 4.50 l-S -2 4.80 105.6 22.04 7998 0.48 0.98 3320 0.53 0.96 l-S -3 3.68 107.2 17.61 11447 0.32 0.85 .5962 0.36 0.87 2-S-l 5.00 104.1 22.10 11520 0.60 0.96 2595 0.75 0.90 2-S-2 4.92 106.2 22.95 4745 0.55 0.85 2017 0.57 0.84 2-S-3 5.57 103.95 24.52 11936 0.61 0.97 4201 0.64 0.86 l-S -4 2.78 111.50 14.91 8779 0.53 0.93 2952 0.60 0.95 50 (/) 40 CL Resilient Modulus xlO 30 Sample 2-S-l 20 Total Vertical Stresses 0 □ u & 6.282 9.282 14.223 19.22 psi psi psi psi A 24.16 29.10 psi psi O Q 29.49 ' psi 34.10 psi 10 3 4 5 10 20 Confining Pressure, ( psi ) Figure 5.10 Typical Plot o f R e silie n t Modulus Vs. Confining Pressure fo r Recompacted Cohesionless Sample. 30 100 10 Sample 2-S-2 fcl = 3.00% ad= 102.6 pcf Mn = 1 5 0 0 8 °'78 Resilient Modulus x 10 , (psi) 50 - 1 5 10 50 Sum o f P rin c ip a l Stresses, 0 (p s i) Figure 5.11 Resilient Modulus Vs Sum of Principal Stresses for Reccmpacted Sand Samples. 112 100 for the same confining pressure. This could be generalized as follow: the higher the deviatoric stress the higher the resilient strain and the lower the resilient modulus. 3. The resilient modulus of the materials varies with the first stress invariant (sum of principal stresses) . This variation, however, could not be generalized for the entire range of the test variables (confining pressure and vertical stress). Consequently, equation (2.4) is valid for certain variation of the first stress invariant. This does not include increasing the vertical stress at a constant confining pressure. Thus, as it may be seen, equation (2.4) have no important significant to laboratory test results in relating the resilient modulus to the first stress invariant. However, the expression was used successfully in predicting pavement deflection in the field (45) . The ratio of the vertical stress to the lateral stress in the subgrade under a pavsnent section is constant and it depends on the insitu physical properties of the materials. Consequently, equation (2.4) hold for such conditions. Further, the importance of this relation becomes apparent when relating laboratory test results to field investigations. C. Effect of Sample Variables 1. Water Content: Analyses of the data provided in Tables (4.3), (4.4), (5.2) and (5.3) have failed to show any relationship between the resilient modulus and the water content of the samples. This could be attributed to the small range of water content at which the samples ware tested. Also, the compaction effort of the recampacted samples was varied as to obtain field density and water content. This variation had its own effects on the resilient modulus which could not be separated from the effects of the water content. 113 2. Dry Density: Examination of equations (2.3) and (2.4) have indicated that the constants ( k^, , k^, and k^) may be related to the work done to the sample during the cyclic loading tests which is related to the sample dry density. The denser the sample, the higher the.energy used to overcane the friction between particles and the lower the work done to the sample. Figure (5.12) shows plots of the constants k^ and as a function of dry density for reccmpacted samples at relatively same water content, while Figure (5.13) shows plots for the constants k2 and k^ as a function of dry density for the same samples. It can be noticed that the denser the material the higher the value of the constants k^ and k^ and the lower the values of k^ and k4 . Recalling that the constants Jc, and k^ are the exponents in equations (2.3) and (2.4), it follows that the denser the materials the lower the values of k2 and k^ and the less is the rate of change of resilient modulus with respect to the confining pressure or the first stress invariant (Jo, and k4 represent the slopes of equations (2.3) and (2.4) respectively) . Thus, the sensitivity of the resilient characteristics of cohesionless materials to the lateral pressure or first stress invariant decreases as the materials becomes denser. 3. Compaction Effort: Figure (5.14) shows plots of the constants k^ and k^ (to an arithmetic scale) against the corresponding values of k^ and k^ (to a logarithmic scale), for the undisturbed cohesionless samples. Examination of the figure suggests that k^ and k^ or k^ and k^ may be related functionally as k2 = - C2 log k^ 114 (5.1) 10.0 ro o X tn 3.2% _L 100 103 106 108 3 Dry Density, lbs/ft Figure 5.12 Effect of Dry Density on k. and k~ for Feccmpacted Cohesionless Samples at Relatively Same Water Contents. 115 1.0 & ---- & k. O---- O k or k 0.9 0.8 0.6 0.5 100 103 106 Dry Density , lbs/ft Figure .13 108 3 Effect of Dry Density cn k„ and k . for Fecompacted Cohesionless Samples at Eelatively Same Water Contents 116 and k 1.0 pj 1000 Figure 2000 3000 5000 7000 10000 5.14 Relationship between Constants of Equations (2.3) and (2.4) for Undisturbed Sand Samples. or k4 = C3 ~ C4 log k 3 (5*2) where CL , C„/ G and are constants depending on the '3 characteristics of tha samples. Figure (5.15) shows similar plots for the reccmpacted samples. It can be seen that the constants k^, k^, and k4 are not related. Recalling that both the undisturbed and recanpacted samples were tested under similar ranges of confining pressures, vertical stresses, water contents, dry densities and number of cycles, and that the only difference between the two samples was the compaction, effort (various compaction efforts were used in the preparation of the recompacted samples). It follows that the constants of equations (5.1) and (5.2) may be used as indicators of the compaction effort. Further research in this area is needed before any definite conclusion can be made. V. Correlation of Resilient Modulus of the Michigan Cohesionless Roadbed Soils to the Soil Support Value A. Choice of Variables It was shown in section IV above that the resilient modulus of the cohesionless materials is a function of the confining pressure, stress level, compaction effort and density. These variables could be and they were controlled in the laboratory tests on recompacted samples. In the field, however, the values of these variables at the subgrade level depend on the pavement thickness, time of the year, axle load, tire pressure, relative location of the point in question with respect to the wheel paths and several other parameters. Thus, any laboratory investigations of subgrade materials should be conducted under a range of conditions that are likely to exist during the life cycle of the pavement. Also, when designing a pavement section, consideration should be given to the most unfavorable conditions under which the pavement is expected to exist. 118 1.0 0.6 * •o 8 0.4 0.2 1000 Figure 5.15 2000 3000 5000 and 7000 10000 20000 Relationship between Constants of Equations (2.3) and (2.4) for Recompacted Sand Samples. Data from the AASHO road test showed that the vertical stress applied to the subgrade, as a consequence of the passage of an 18 kip single axle load, was about 10 psi (36) . Results of theoretical analyses of a three layers pavement system, using the " CHEVRON" computer program, showed that, for any loading vehicle, the induced lateral stress at the subgrade level is less than 5 psi (25, 36). Preliminary calculations using three layer stress factors that were developed by Jones ( 51 ) showed that, for the pavement section shown in Figure (3.1), the induced lateral stress at the subgrade level due to the passage of an 18 kip single axle load was about 2.5 psi. Thus, it was decided that confining pressures of 2.5 and 5 psi and first stress invariants of 15, 20 and 30 psi could be taken as representative values of the induced stresses at the subgrade level for different pavement thickness. These stresses in conjunction with the values of the constants k^ and k^ (see Tables 5.2 and 5.3) were used in equation (2.4) to calculate the resilient modulus which will be correlated later to the soil support value*.Tables (5.4) and (5.5) provide lists of these calculated resilient modulus for the first stress invariant shown. The values of the constants k^, k^, k^ and , the samples location, density and water content and the field soil support values from Table (3.2) are also listed in the tables**. B. The Resilient Modulus Vs. Soil Support Values A preliminary correlation of resilient modiolus to soil support value was conducted using equation (5.3) (8 ) . E = 1500 CBR (5.3) where E - Dynamic modulus (resilient modulus) CBR = Dynamic California bearing ratio * As stated in section IV above, Equation (2.4) is used to relate laboratory test results to field data ** These values were calculated using equation (3) . 120 Table 5.4 Sample No. Water Content (*) Resilient Modulus at Different First Stress Invariant For Undisturbed Sand Samples. Dry Density LBS/FT3 Resilient t'odulus at Sun of Principal Stress Regression Constants K1 Kz h *4 9=15ps i 0=20psi 8=30psi 1-N-l 2.64 98.0 16000 0.32 9400 0.34 23600 26000 29900 l-N-2 5.00 89.6 7900 0.71 1800 0.82 16600 21000 29300 l-N-3 4.00 99.0 16900 0.22 11600 0.22 21000 22400 24500 2-N-l 3.20 98.9 12900 0.32 8760 0.30 19700 21500 24300 2-N-2 3.20 97.4 4200 0.59 1358 0.66 8100 9800 12800 2-N-3 3.50 106.5 6100 0.66 1945 0.71 13300 16300 21800 2-N-4 2.70 101.0 4700 0.79 1171 0.85 11700 14900 21100 1-S-l 6.98 93.00 13400 0.36 6700 0.40 19800 22200 26100 l-S-2 12.10 95.10 9000 0.45 4225 0.48 15500 17800 21600 2-S-l 4.30 106.3 5400 0.71 1600 0.75 12200 15100 20500 2-S-2 3.00 102.6 6300 0.67 1500 0.78 12400 15500 21300 Table 5.5 Resilient Modulus at Different First Stress Invariant For Recompacted Sand Samples. Water Content (*) Dry Density LBS/FT3 Z-S-l 5.00 104.1 2-S-2 4.92 2-S-3 Sample No. Resilient Modulus at Sum or ' Principal Stress Regression Constants K2 *3 K4 0=15psi e=20psi e=30psi 11520 0.60 2595 0.75 19800 24500 33300 106.2 4745 0.55 2017 0.57 9400 11000 14000 5.57 103.95 11936 0.61 4201 0.64 23800 28600 37000 2-N-l 3.33 103.1 8000 0.73 1445 0.88 15700 20200 28800 2-N-2 3.30 105.6 9456 0.85 2021 0.90 23100 30000 43100 2-N-3 3.20 104.6 7746 0.73 2759 0.72 19400 23900 31900 2-N-4 3.15 106.9 10058 0.51 3491 0.58 16800 19800 25100 1-S-l 4.50 104.4 16935 0.54 2217 0.85 22200 28300 39900 1-5-2 4.BO 105.6 7998 0.48 3320 0.53 13900 16200 20100 l-S-3 3.68 107.2 11447 0.32 5962 0.36 15800 17500 20300 1-5-4 2.78 111.5 8779 0.53 2952 0.60 15000 17800 22700 1-N-l 7.04 107.7 12255 0.44 5133 0.50 19900 23000 28100 K1 Field SSV 5.40 5.1 4.5 5.2 The CBR values of the cohesionless Michigan roadbed materials were calculated using values of the resilient modulus corresponding to first stress invariants of 15, 20 and 30 psi {See Tables 5.4 and 5.5). The soil sipport values corresponding to these CBR were then estimated losing Figure (5.16). Tables (5.6) and (5.7) provide lists of these calculations for reocmpacted and undisturbed samples respectively. Figures (5.17), (5.18) and (5.19) show plots of the soil support value as a function of the resilient modulus for first stress invariants of 15, 20 and 30 psi respectively. Table (5.8) provide lists of calculated and field soil supported values. It can be noticed that the field values compare very well with those calculated for first stress invariant of 15 psi which is corresponding to a total vertical stress of 1 0 psi and a confining pressure of 2.5 psi. These stresses are likely to be induced at the subgrade level for the pavement thickness in question as a consequence of the passage of 18 kip single axle load (36, 25) . Examination of Figure (5.17) have indicated that the resilient modulus of Michigan cohesionless soil and the SSV could be related by a logarithmic type function. This function (when a control point having M^ = 3000 psi and SSV = 3.0 corresponding to the AASHO roadbed materials was introduced) was found to be SSV = 1.96 log Mr + % 19^5Q -3.98 (5.4) The successful correlation of resilient modulus to the soil support value for a range of water content, dry density and campaction effort should not be interpreted as unlimited license to use equation (5.4). This equation is valid for the range of the test data and the particular pavement thickness that was shown in Figure (3.1) . V. Implementations The use of the correlation of the SSV to the resilient modulus as developed in this study will require estimating the stresses likely to exist in subgrade materials as a consequence of the passage of a loading vehicle. In this study, the vertical stresses likely to 123 79.5 r 2 3 .5 20 -20 . 69 -6.75 - 30 a> o c co C_) +J oc co c_> OJ a. co s_ o Cu CL 3 a as *p— o to -1 .25 - 0.50 . 0.25 0 Figure 5.16 C o rre la tio n Between Soil Support Value and Dynamic CBR ( 2 ) . 124 R-Value - .9.75 { 300 PSI) -140 -80 Table 5.6 Summary of Data For SSV and Resilient Modulus of Becanpacted Cohesionless Soil Sanples Sample No. Water Content % Dry Density (pcf) Resilient Modulus,(Mp).California Bearing Ratio,(CBR), and Soil Support Value, (SSV) for Sum of Principal Stresses Shown. 0=20 0=15 0=30 H.(psi) CBRX SSV Mr(psO CBR% SSV M r(psi) CBR* SSV 6.00 33300 22.2 6.3 124 2-S-l 5.00 104.1 19800 13.2 5.5 24500 16.3 2-S-2 4.92 106.2 9400 6.3 4.5 11000 7.3 4.6 14000 9.3 5.2 2-S-3 5.57 103.95 23800 15.9 5.8 28600 19.1 6.2 37000 24.7 6.4 2-N-l 3.33 103.1 15700 10.5 5.25 20200 13.5 5.6 28800 19.2 6.1 2-N-2 3.30 105.6 23100 15.4 5.8 30000 20.0 6.3 43100 28.7 6.7 2-N-3 3.20 104.6 19400 12.9 5.5 23900 15.9 5.8 31900 21.3 6.2 2-N-4 3.15 106.9 16800 11.2 5.3 19800 13.2 5.6 25100 16.7 5.9 1-S-l 4.50 104.4 22200 14.8 5.70 28300 10.9 6.1 39900 26.6 6.5 l-S-2 4.BO 105.6 13900 9.3 5.2 16200 10.8 5.3 20100 13.4 5.6 l-S-3 3.68 107.2 15800 10.5 5.25 17500 11.7 5.4 20300 13.5 5.6 l-S-4 2.78 111.5 15000 10.0 5.2 17800 11.9 5.5 22700 15.1 5.75 1-N-l 7.04 107.7 19900 13.3 5.6 23000 15.3 5.8 28100 18.7 6.1 Table 5 . 7 Summary of Data For SSV and Resilient Modulus of Undisturbed Cohesionless Soil Samples. Sample No. Water Content X Dry Density {pcf) Resilient Modulus,(Mp).California Gearing Ratio,(COR] , and Soil Support Value, (SSV) 6=15 for Sum of Principal Stresses Shown. 0=20 Mr(ps1) CBRX SSV Kr(ps1) CBRX SSV Mf(ps1) CBRX SSV 6=30 1-N-l 2.64 98.0 23600 15.7 5.8 26000 17.3 6.0 29900 20.0 6.3 l-tl-2 5.00 89.6 16600 11.' 5.3 21000 14.0 5.60 29300 19.5 6.1 l-N-3 4.00 99.0 21000 5.7 22400 14.9 5.75 24500 16.3 5.9 2-N-l 3.20 98.9 19700 13.1 5.6 21500 14.3 5.7 24300 16.2 5.9 2-N-2 3.20 97.4 8100 5.4 4.2 9800 6.5 4.5 12800 8.5 4.9 2-N-3 3.50 106.5 13300 8.9 5.0 16300 10.9 5.3 21800 14.5 5.4 2-N-4 2.70 101.0 11700 7.8 4.6 14900 9.9 5.2 21100 14.1 5.4 1-S-l 6.96 93.00 19800 13.2 5.6 22200 14.8 5.75 26100 17.4 6.0 l-S-2 12.10 95.10 15500 10.3 5.2 17800 11.9 5.5 21600 14.4 5.7 2-S-l 4.30 106.3 12200 8.1 4.8 15100 10.1 5.2 20500 13.7 5.65 2-S-2 3.00 102.6 12400 8.3 4.8 15500 10.3 5.2 21300 14.2 5.7 14.0 ' Table 5 . 8 Comparisons of Field and Laboratory Soil Support Values Field And Laboratory Soil Support Values For First Stress Invariant Shown 0=15 0=20 e=30 Test Sites ssvF Z-S 5 .4 19800 5.5 0 .9 8 24500 6 .0 0 .9 0 33300 6 .3 0 .8 6 1-S 4 .5 13900 5 .2 0 .8 7 16200 5 .3 0 .8 5 20100 5.6 0 .8 0 1-N 5 .2 19900 5.6 0 .9 3 23000 5 .8 0 .9 0 28100 6 .1 0 .8 5 2-N 5.1 15700 5.3 0 .9 6 20200 5 .6 0 .9 1 28800 6.1 0 .8 4 ssvF Mr(psi) ssvL SS?[ SSVp Mr(psi) SSVp = Field Soil Support Value. SSV^ = Laboratory Soil Support Value. Mr = Resilient Modulus. SSVL ssvL SSVp Mr(psi) ssvL SSVL 10 Soil Support Values 8 6 4 Reconpacted Samples Undisturbed Samples 2 15 psi 0 10 20 25 Resilient Modulus x 10J, (psi) Figure 5.17 Resilient Modulus Vs SSV for Recompacted and Undisturbed Cohesionless Soils. 7 Soil Support Values 6 4 Undisturbed Samples Reccnpacted Samples 30 psi 2 0 20 40 3 Resilient Modulus x 10 , (psi) Figure 5.18 50 Resilient Modulus Vs SSV for Reconpacted and Undisturbed Cohesionless Soils. 7 Soil Support Values 6 4 Undisturbed Samples Feoampacted Samples 20 psi 2 0 10 20 25 Resilient Modulus x 10^(psi) Figure 5.19 Resilient Modulus Vs SSV for Recompacted and Undisturbed Cohesionless Soils. exist in the subgrade of flexible pavements was calculated using one layer elastic model (for poisson ratio If 0.5) that was developed by Ahlvin and Ulery (10). The equation takes the form of az = p (A + B) (5.5) where ctz = Vertical stresses below pavement surface p = Tire pressure (80 psi was assumed) A, B = Functions which depend on the depth below a pavement section and on the offset distances, a = Radius of a loaded area (a = 6.0 inches) for 18 kip single axle and 80 psi tire pressure) z = Depth below pavement surface divided by the radius of the contact area (a) in radii, r = Offset distance frcm the center of the loaded area divided by the radius of the contact area (a) in radii. The functions A and B are tabulated in Table (5.9). The vertical stress calculated on the basis of equation (5.5) are provided in Table (5.10). Figure (5.20) shows plots of pavement thickness as functions of the deviatoric and vertical stresses. The curve labelled in contact area of 6.0 inches which is corresponding to an 18 kip single axle load having 80 psi tire pressure), while the one designated was duplicated fran Figure (5.8). Thus, the SSV of cohesionless roadbed materials could be estimated as follow. a. Determine the vertical and lateral stresses that are likely to exist at the subgrade level in the pavement section under consideration using Figure (5.20). b. Conduct a repeated load triaxial test under the stresses calculated in (a) above using samples with water content and density that are likely to exist in the field. c. Use equations(5.4) or Figure (5.17) to calculate the SSV. d. Implement the AASHO Interim Guide for the design of flexible highway pavements. 130 Table 5.9 Function Values For The One Layer Elastic Model (10). Function A Depth (i) in Radii 0 ill 0.2 0.3 0.4 0.3 O.ti , 07 i 0.8 1 0.9 1 > ! 1.2 I 1.3 2.5 3 4 5 <> 7 8 *J 10 Offset (r) in Radii 0 1.0 .90050 .80388 .71265 .62861 .55279 .48550 .42654 .37531 .33104 .29289 .23178 .16795 .10557 .07152 .05132 .02986 .01942 .01361 .01005 .00772 .00612 0.2 0.4 0.6 0.8 1 1.2 2 1.5 1.0 1.0 .5 1.0 1.0 0 0 .89748 .B8679 .86126 .78797 .43015 .09645 .027B7 .79824 .77884 .73483 .63014 .38269 .15433 .05251 .70518 .68316 .62690 .52081 .34375 .17964 .07199 .53767 .44329 .31048 .18709 .08593 .62015 .59241 .54403 .51622 .46448 .38390 .20156 .18556 .09499 .47691 .45078 .40427 .33676 .25588 .17952 .10010 .41874 .39491 .35428 .29833 .21727 .17124 .10228 .36832 .34729 .31243 .26581 .21297 .16206 .10236 .32492 .30669 .27707 .23832 .19488 .15253 .10094 .2B763 .27005 .24697 .21468 .17868 .14329 .09849 .12570 .09192 .22795 .21662 .19890 .17626 .15101 .16552 .15877 .14804 .13436 .11892 .10296 .0804 B .10453 .10140 .09647 .09011 .08269 .07471 .06275 .07098 .06947 .06698 .06373 .05974 .05555 .01880 .05101 .05022 .04886 .04707 .0-1487 .04241 .03839 .02976 .02907 .02802 .02832 ,02749 .02651 .02490 .01835 .01938 .01307 .00976 .00755 .00600 .00477 0 3 0 .00856 .01680 .02440 .03118 .03701 4 0 5 0 6 0 10 8 0* 0 12 14 0 0 .00211 .00419 .00622 .00084 .00167 .00250 .00042 .00083 .00048 .00020 .01013 .00407 .00209 .00118 .00053 .00025 .00014 .00009 .01742 .01935 .02142 .02221 .02143 .01980 .01592 .01249 .00983 .00784 .00635 .00520 .00438 .00761 .00871 .01013 .01160 .01221 .01220 .01109 .00949 .00795 .00661 .00554 .00466 .00397 .00393 .00459 .00548 .00659 .00732 .00770 .00768 .00708 .00628 .00548 .00472 .00409 .00352 .00226 .00269 .00325 .00399 .00463 .00505 .00536 .00527 .00492 .00445 .00398 .00353 .00326 .00097 .00115 .00141 .00180 .00214 .00242 .00282 .00298 .00299 .00291 .00276 .00256 .00241 .00050 .00029 .00018 .00073 .00094 .00115 .00132 .00160 .00179 .00188 .00193 .00189 .00184 .00043 .00056 .0006B .00079 .00099 .00113 .00124 .00130 .00134 .00133 .00027 .00036 .00043 .00051 .00065 .00075 .00084 .00091 .00094 .00096 .04558 .05185 .05260 .05116 .04496 .03787 .03150 .02193 .01573 .01168 .00894 .00703 .00566 .00465 Table 5.10 Continued. Function B 3cp(h Offset (r) in Radii (0 in Radii 0 0.1 0.2 j 0.3 0.4 1 05 t 0.6 1 07 0.8 0.9 1 1.2 1.5 ■_> 2.5 3 4 5 6. 7 8 9 10 0.2 0 0 .09852 .18857 .28362 .32016 .35777 .37831 .38487 .3BQ91 .36962 .35355 .31485 .25602 .17889 .12807 .09487 .05707 .03772 .02666 .01980 .01526 .01212 .10140 .19306 .26787 .32259 .35752 .37531 .37962 .37408 .36275 .34553 .30730 .25025 .18144 .12633 .09394 .05666 .03760 0.6 0.4 0 0 .11138 .20772 .28018 .32748 .35323 .36308 .36072 .35133 .33734 .32075 .28481 .23338 .16644 .12126 .09099 .05562 .13424 .23524 .29483 .32273 .33106 .32822 .31929 .30699 .29299 .27B19 .24836 .20694 .15198 .11327 .08635 .05383 I 0.8 0 .18796 .25983 .27257 .26925 .26236 .25411 .24638 .23779 .22891 .21978 .20113 .17368 .13375 .10298 .08033 .05145 0 .05388 .08513 .10757 .12404 .13591 .14440 .14986 .15292 .15404 .15355 .14915 .13732 .11331 .09130 .07325 .04773 .03384 .02468 .01868 .01459 .01170 1.2 1.5 2 3 0 -.07899. -.07759 -.04316 -.00766 .02165 .04457 .06209 .07530 .08507 .09210 .10002 .10193 .09254 .07869 .06551 .04532 0 -.02672 -.04448 -.04999 -.04535 -.03455 -.02101 -.00702 .00614 .01795 .02814 .04378 .05745 .06371 .06022 .05354 .03995 0 -.00845 -.01593 -.02166 -.02522 -.02651 0 -.00210 -.00412 -.00599 4 5 6 8 0 0 0 0 0 -.00084 -.00042 -.00166 -.00083 -.00024 -.00010 -.00245 10 12 0 14 0 -.00991 -.00388 -.00199 -.00116 -.00049 -.00025 -.00014 -.00009 -.02329 -.01005 -.01115 -.00608 -.00344 -.00210 -.00092 -.00048 -.00028 -.00018 .00023 -.00995 -.00632 -.00378 -.00236 -.00107 .01385 -.00669 -.00600 -.00401 -.00265 -.00126 -.00068 -.00040 -.00026 .02836 .00028 -.00410 -.00371 -.00278 -.00148 -.00084 -.00050 -.00033 .03429 .00661 -.00130 -.00271 -.00250 -.00156 -.00094 -.00059 -.00039 .03511 .01112 .00157 -.00134 -.00192 -.00151 -.00099 -.00065 -.00046 .03066 .01515 .00595 .00155 -.00029 -.00109 -.00094 -.00068 -.00050 .02474 .01522 .00810 .00371 .00132 -.00043 -.00070 -.00068 -.00049 .01968 .01380 .00867 .00496 .00254 .00028 -.00037 -.00047 -.00045 .01577 .01204 .00842 .00547 .00332 .00093 -.00002 -.00029 .00037 .01279 .01034 .00779 .00554 .00372 .00141 .00035 -.00008 -.00025 .01054 .00888 .00705 .00533 .00386 .00178 .00066 .00012 -.00012 .00924 .00879 .00764 .00631 .00501 .00382 .00199 Table z r a p t A,B oz 5.10 Vertical Stress at the Suixjrade Level in a Pavement Section Radius of Loaded Area Pavement Thickness r/a z/a A B 6.0 6.0 6.0 6.0 6.0 6.0 12.0 18.0 30.0 42.0 48.0 54.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0 3.0 5.0 7.0 8.0 9.0 .10557 .05132 .01942 .01005 .00772 .00612 .17889 .09487 .03772 .01980 .01526 .01212 = = = = = = = Depth below Pavement Surface (inch), Offset Distance (inch), Radius of Contact Area (inch), Tire Pressure (psi), Pavement Thickness (inch), Functions Provided in Table 5.14, and Vertical Stress (psi). o z 22.8 11.7 4.6 2.4 1.8 1.5 60.0 Pavement Thickness, (inches) 50.0 Vertical Stress (from Equation 5.1) ^ 40.0 Deviatoric Stress (after Chou et al Estimated Portion 30.0 20.0 10.0 0 5.0 10.0 15.0 20.0 Deviatoric Stresses or Vertical Stresses, (psi) Figure 5.20 Pavement Thickness Vs. Deviatoric Stresses or Vertical Stresses. 25.0 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS I. Conclusions On the basis of the results of this study, the following conclusions are made for Michigan cohesionless roadbed soils. A. The resilient modulus and the cumulative permanent deformation of the AASHO roadbed soils is a function of the deviatoric stress, water content, dry density and the number of load applications. B. The cumulative permanent deformation of the AASHO roadbed soil is independent of the deviatoric stress at a water content of about 11%. C. . The resilient modulus of the Michigan cohesionless roadbed soil is independent of the number of load applications. It is a function, however, to the stress level, water content and dry density. D. Equations (2.3) and (2.4) do represent the variations of the resilient modulus of the Michigan cohesionless roadbed soil with respect to the lateral and vertical stresses respectively. Also, equation (2.3) relates laboratory test results while equation (2.4) relates laboratory observations to field performance. E. The constants of equations (2.3) and (2.4) could be used as indicators of the: a . Work done to the pavement, b . Compaction effort, and c . Dry density* F. The resilient modulus of the Michigan cohesionless roadbed soil is related to the soil support value through equation (5.3) . G. Results were simplified and a procedure was developed to implement the AASHO Interim Guide to the design of flexible highway pavements. 135 H. The sample preparation technique outlined in Chapter 3 duplicates as closely as possible the field density and water content. II. Recommendations The results of this investigation have demonstrated the applicability of the repeated load triaxial testing method as a basis of material characterizations. The resilient modulus of the Michigan cohesionless subgrade soil was successfully obtained and correlated to the soil support value and hence the AASHO Interim Guide for flexible pavement design could be implemented. To maximize the benefits of this study at the lowest possible cost, it is advisable that a study be undertaken to examine the following: a. The resilient characteristics of cohesive readbed soils and their relation to the soil support value. b. The relationship between the laboratory investigations and a field material characterization technique that will use a rapid nondestructive method. It is also recommended that efforts be expended to employ equation (5.4) to cohesive and cohesionless materials using results of repeated load triaxial tests on cohesive roadbed soils. 136 BIBLIOGRAPHY BIBLIOGRAPHIE 1. Carey, W. N. , and Irick, P. E . , "The Pavement Concept," HRB Bulletin 250, 1960, pp. 40-58. Serviceability 2. AASHO Committee on Design, AASHO INTERIM GUIDE FOR DESIGN OF PAVEMENT STRUCTURES, 19 72 American Association of State Highway Officials, Washington, D.C. 1972. 3. Allen, J. J . , and M. R. Thompson, "Resilient Response of Granular Materials Subjected to Time-Dependent Lateral Stresses," Transportation Research Record 510, Soil Mechanics, 1974. 4. Bishop, A. W . , and D. J. Henkel, THE MEASUREMENT OF SOIL PROPERTIES IN THE TRIAXIAL TEST, 2nd Ed. Edward Arnold (Publishers) Ltd., London, 1962. 5. Burmister, D. M . , "The Theory of Stresses and Displacements in Layered Systems and Applications to the Design of Airport Runways," Highway Research Board Proceedings, Vol. 23, 1943. 6. Chu, T. Y. , W. K. Humphries, and 0. S. Fletcher, "Application of AASHO Road Test Findings to the Design of Flexible Pave­ ment Structures in South Carolina," Highway Research Record No. 131. 7. Drake, W. B . , and J. H. Havens, "Re-Evaluation of Kentucky Flexible Pavement Design Criterion," Highway Research Board, Bulletin 233, 1959. 8. Hicks, R. G . , and C. L. Monismith, "Factors Influencing the Resilient Response of Granular Materials," Highway Research Record, No. 345, 1970. 9. Kalcheff, I. V., and Hicks, R. G . , "A Test Procedure for Determining the Resilient Properties of Granular Materials," 76th Annual Meeting of the ASTM, Philadelphia, June 1973. 10. Liddle, W. J . , "Application of AASHO Road Test Results to the Design of Flexible Pavement Structures," Proc. Inter­ national Conference on Structural Design of Asphalt Pavements, pp. 42-51. April 1963. 11. McClean, D. B., and C. L. Monismith, "Estimation of Permanent Deformation in Asphalt Concrete Layers Due to Repeated Traffic Loading," Transportation Research Record, No. 510, 1974. 12. Monismith, C. L . , H. B. Seed, F. G. Mitry, and C. K. Chan, "Prediction of Pavement Deflections from Laboratory Tests," Proceedings of the Second International Conference on Structural Design of Asphalt Pavements, University of Michigan, 1967. 137 13. Peattie, K. R . , "A Fundamental Approach to the Design of Flexible Pavements," Proceedings of the International Con­ ference on Structural Design of Asphalt Pavements, University of Michigan 1962a. 14. Ramasamooj, D. V. K. Majidyadeh and E. M. Kauffman, ''The Design and Analysis of Flexibilibty of Pavements," Proc. of the Third International Conference on Structural Design of Asphalt Pavements', University of Michigan, 1972, pp. 692-704. 15. Seed, H. B . , C. K. Chan, and C. E. Lee, "Resilience Charac­ teristics of Subgrade Soils and Their Relation to Fatigue Failures in Asphalt Pavements," Design of Asphalt Pavements, pp. 611-636 April 1962. 16. Van Til, C. J . , B. F. McCullough, B. A. Vallerga, and R. G. Hicks, "Evaluation of AASHO Interim Guides for Design of Pavement Structures," National Co-operative Highway Research Program Report 138, Highway Research Board, Washington, D.C. 1972. 17. Yoder, E. J . , PRINCIPLES OF PAVEMENT DESIGN, John Wiley and Sons, Inc., New York, 1959. 18. Yoder, E . J . , and Witczark, P R I N C I P L E S OF 2nd Edition, John Wiley and Sons, 1972. 19. THE AASHO ROAD TEST, Highway Research Board, Special Report 61E, pp. 291-320. 20. Lawrence, H. G . , and Leonards, G. A., "A Strength Criterion for Repeated Loads," Proceedings of the Highway Research Board, Vol. 41, 1962. 21. Burmister, D. M . , "Evaluation of Pavement Systems of the Washo Road Test by Layered System Methods," Highway Research Board, Bulletin 177, 1958. 22. Ahmed, S. B . , Load Strength Conference on University of 23. Haynes, J. H . , and Yoder, E. J . , "Effects of Repeated Loading on Gravel and Crushed Stone Base Course Materials used in the AASHO Road Test," Highway Research Board 39, Washington, D.C., 1963. 24. Hicks, R. G., and Monismith, C. L . , "Prediction of the Resilient Response of Pavements Containing Granular Layers Using Non-Linear Elastic Theory," Proceedings, Third Inter­ national Conference on the Structural Design of Asphalt Pavements, London, England, 1972. PAVEMENT D E S IG N , and Larew, H. G . , "A Study of the Repeated Moduli of Soils," Proceedings International the Structural Design of Asphalt Pavements, Michigan, 1962. 138 25. Hicks, R. G., "Factors Influencing the Resilient Properties of Granular Materials," Ph.D. Thesis, University of California, Berkeley, 1970. 26. Mitry, F. G . , "Determination of the Modulus of Resilient Deformation of Untreated Base Course Materials," Ph.D. Thesis, University of California, Berkeley, 1964. 27. Morgan, J. R . , "The Response of Granular Materials to Re­ peated Loadings," Proceedings, Third Conference Australian Road Research Board, Part 2, 1966. 28. Pell, P. S., and Brown, S. F., "The Characteristics of Materials for the Design of Flexible Pavement Structures," Proceedings, Third International Conference on the Structural Design of Asphalt Pavements, London, England, 1972. 29. Seed, H. B., Mitry, F. G., Monismith, C. L . , and Chan, C. K . , "Factors Influencing the Resilient Deformations of Untreated Aggregate Base in Two-Layer Pavements Subjected to Repeated Loading," Highway Research Board 190, Washington, D.C., 1967. 30. Tanimoto, K . , and Nishi, M . , "On Resilience Characteristics of Some Soils Under Repeated Loading," Soils and Foundations, Vol. 10, No. 1, 1970. 31. __________ i "Test Procedures for Characterizing Dynamic Stress-Strain Properties of Pavement Materials," Transportation Research Board, Special Report 162, Washington, D.C. 1975. 32. Allen, J. J., "The Effects of Non-Constant Lateral Pressures on the Resilient Response of Granular Materials," Ph.D. Thesis, University of Illinois at Urbana-Champaign, May 197 3. 33. Bayer, R. E., "Predicting Pavement Performance Using Time Dependent Transfer Functions," Joint Highway Research Project, Purdue University and Indiana State Highway Commission, September 1972, No. 32. 34. Baladi, G. Y. , "Invariant Properties of Flexible Highway Pavements," Ph.D. Thesis, Purdue University, December 1976. 35. Brabston, W. N . , W. R. Barker, and Harvey, G. G., "Develop­ ment of a Structural Design Procedure for All-Bituminous Concrete Pavements for Military Roads," Soils and Pavements Laboratory, U.S. Army Engineer Waterways Experiment Station, July 1975. 139 36. Vesic, A. S., and L. Donaschuk, "Theoretical Analysis of Structural Behavior of Road Test Flexible Pavements," National Co-operative Highway Research Program Report 10, Highway Research Board, Washington, D.C., 1964. 37. Scott, R. F., "Principles of Soil Mechanics," Addison Wesley Publishing Company, Inc. 1962. 38. Barker, W. R . , "Elasto Plastic Analysis of A Typical Flexible Airfield Pavement," Soils and Pavements Laboratory, U.S. Army Engineer Waterways Experiment Station, Unpublished report. 39. Seed, H. B . , McNeil, R. L . , and J. De Guenin, "Increased Resistance to Deformation of Clay Caused by Repeated Loading," ASCE Journal of Soil Mechanics and Foundation Division, May 1958. 40. Young, M. A., and Baladi, G. Y . , "Repeated Load Triaxial Testing— State of the Art," Division of Engineering Research, Michigan State University, 1977. 41. Chaichanavong, T., "Dynamic Properties of Ice and Frozen Clay Under Cyclic Triaxial Loading Conditions," Dissertation for the Degree of Ph.D., Michigan State University, 1976. 42. Higher, W. H . , and Harr, M. E . , "Cumulative Deflection and Pavement Performance," Transportation Engineering Journal of ASCE, Vol. 101, Aug. 197 5. 43. Harr, M. E . , "Influence of Vehicle Speed on Pavement De­ flection," Proceedings Highway Research Board, Vol. 41, 1962. 44. Deacon, J. A., "Equivalent Passages of Aircraft With Respect to Fatigue Distress of Flexible Airfield Pavements, "Pro­ ceedings AAPT, Vol. 40, 1971. 45. Kirwau, R. W . , and Glynn, T. E . , "Theoretical and Experi­ mental Investigation into Basic Properties of Boulder Clay," Final Technical Report, European Research Office, U.S. Army, Sept. 1967. 46. Dehler, G. L . , "The Effect of Non Linear Material Response on the Behavior of Pavements Subjected to Traffic Load," Ph.D. Thesis, University of California, 1969. 47. Monismith, C. L . , and Finn, F. N . , "Flexible Pavement Design: A State of the Art 1975." Proceedings, Pavement Design For Practicing Engineers, Specialty Conference, Georgia Institute of Technology, June 1975. 140 48. Barksdale, R. D . , "Compressive Stress Pulse Times in Flexible Pavements for Use in Dynamic Testing," Highway Research Board 345, 1971. 49. Seed, H. B . , and Chan, C. K . , "Effect of Stress History and Frequency of Stress Application on Deformation of Clay Subgrade Under Repeated Loading," Proceedings HRB, Vol. 37, (1958) pp. 555-575. 50. Brown, S. F., and Pell, P. S., "A Fundamental Structural Design Procedure for Flexible Pavements," Proceedings of the Third International Conference on Structural Design of Asphalt Pavements, University of Michigan, 1972 pp. 369-381. 51. Jones, A., "Tables of Stresses in Three-Layer Elastic Systems, Highway Research Board Bulletin 114, 1945. 52. Girwan, R. W . , Colynn, T. E . , and Bonner, C. A., "The Significance of Materials Properties in Flexible Pavement Analysis," Final Technical Report. University of Dublin Engineering School, June, 1973. 53. Whitman, R. V., and Lambe , W. T . , SOIL MECHANICS, M.I.T., John Wiley and Sons, Inc. 1969. 54. Johnson, H. C., "Application of Electro-Hydraulic Servo Control to Physical Testing," Proceedings of the National Conference on Fluid Power, XVIII, Chicago, October, 1964. 55. Newland, P. L . , and Allely, B. H . , "Volume Changes in Drained Triaxial Tests on Granular Materials,” Geotechnique Vol. 7, 1957. /t 141 APPENDICES Appendix A Description of the MTS System I. The MTS System. A detailed description of the MTS system may be found in r e fe r ­ ence (41). Figure A.l shows the cyclic t r ia x ia l te st equipments that were used for this research program. equipments is provided in Figure A.2. A schematic diagram of the The te st set up consisted of these basic components which include: 1. An MTS electrohydraulic closed loop te st system which consisted of the actuator, servovalve, hydraulic power supply, servo and hydraulic controllers and a control box. 2. A t r ia x ia l c e l l , which contained the samples, a compac­ tion hammer and a s p lit mold. 3. Output recording devices which monitored the load (stress) and displacement (strain) during the tests. II. The MTS Electro-Hydraulic Closed-Loop Test System. A schematic representation of the MTS electro-hydraulic closed loop te st system is shown in Figure A.3. 1. The system was composed of: An MTS hydraulic power supply Model 506.02, 6.0 gpm (0.02/4m3/min/3000 p s i) , 2. A hydraulic control unit Model 436.11 with a function generator, 3. A Model 406.11 controller (servovalve con troller with AC and DC feedback signal conditioning), 142 Figure A..1 Cyclic Triaxial Test Equipments 143 Strip Chart Recorder Transient Store Digital Multimeter Oscilloscope Function Generator Servovalve Hydraulic Power Supply Servo Controller Actuator ■Load Frame Switching Panel .Triaxial Cell Load Cell 9 □ Figure A.2 Schematic of Cyclic Triaxial Test Equipment Blank Page 145 Double Sided Pi ston 500.10 Hydraulic Power Supply Serve valve Actuator Amp!i fied Differenc between Signals 435.11 Hydraulic Control 1er Function Generator Basic Closed Loop 406.11 Controller Command Signal Sample Signal Junction Load Cell //////////// Figure A.3 Schematic of MTS Electrohydraulic Closed Loop Test System 146 4. An actuator Model 204.52, 5.5 Kip with a 540.54 gpm servo­ valve and 5. A Linear Variable D iffe re n tia l Transformer (LVDT). The system operates as follows: 1. A command signal (voltage) from the function generator in the 435.11 (see Figure A.3) or other external source is input to the 406.11 where i t 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. 2. The difference (error) between the two signals is ampli­ fied and applied to the torque motor in the servovalve coupled to the actuator. 3. The torque motor drives a p ilo t stage which in turn drives a power stage of the servovalve which directs hydraulic flu id under pressure to one side or the other of the double sided actuator piston to cause the actuator to move. 4. 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, fo r a ll practical purposes, to be subjected to a loading equal to the command signal. A more complete treatment of closed loop testing theory is given by Johnson (54). 147 A. MTS 406.11 Controller The front panel of the 406.11 c o n tro lle r is shown in Figure A.4. The controls indicated by the c irc le d numbers are discussed in order below. 1. The panel voltmeter has two functions. F ir s t , i t can be used to indicate the error between the command signal and the feedback transducer. Second, i t can be used to in d i­ cate the voltage output of feedback transducer "XDCR1," XDCR2, or the servovalve drive. (The servovalve regulates the flow of hydraulic pressure between the hydraulic power supply and the actu a to r.) For the cyclic t r ia x i a l tests a negative error means compression and positive error means tension to the specimen. The panel voltmeter was most often used to monitor the e rro r between the com­ mand 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. 2. The Set Point control provides a s ta tic command signal (voltage). d ia l. There are 1000 divisions on the Set Point Each division is equivalent to 20 mv. A positive command signal (Set Point between 500 and 1000) produces actuator piston compression; a negative command signal (Set Point between 500 and 000) produces actuator piston extension. When the feedback signal is from the LVDT in the actuator, Set Point is used to move the actuator up 149 ron UlUT itcir «<•!, I Ml Mf ^ U l I»V 1^ 'IMJflS niif a iiUii in n i t i i ' Figure A.4 i' i ' / ii iH li'i Controls and Indicators on 406.11 Front Panel or down even with no specimen in the loop. When the feedback is from any other transducer the Set Point con­ trol establishes a static level of response of the speci­ men. When feedback was from the LVDT mounted across the sample, Set Point could be used to obtain zero loading on the sample. 3. The Span control establishes theamplitude of a command signal waveform during cyclic loading. about the Set Point level. the Span control d ia l. amplitude of 10 mv. 4. The amplitude is There are 1000 divisions on Each division is equivalent to an The Span was used to vary the strain amplitude during cyclic t r ia x ia l 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 system at optimum Gain, the sample was subject­ ed to a low frequency, low aimplitude square wave loading. The feedback signal was monitored with an oscilloscope. The Gain control was turned clockwise until small o s c il­ lations were observed at the peak of the square wave, as shown in Figure A.5b. At this point the Gain was reduced until the oscillations stopped, as shown in Figure A.5c. The Rate (described below) was adjusted to eliminate "overshoot" at the corner of the peak of the square wave as shown in Figure A.5c. 150 / s V J a) Overdamped, Gain too low rvu n b) Underdamped, Gain to high c) Optimum Gain Figure A. 5 Gain and Stability Adjustment 151 5. The Rate control helps prevent "overshoot" at high Gain setting s. The Rate was adjusted a f t e r the Gain has been set as described above. 6. The Feedback Select position determines which feedback signal w ill be used in the closed loop te s t c i r c u i t . This may be the signal from Transducer Conditioner 1 (XDCR1), Transducer Conditioner 2(XCDR2), or from an ex­ ternal transducer conditioner (EXT). 7. The Cal f a c to r , Zero, and Find/Coarse controls provide ad­ justment of the signal fo r transducer XDCR1. In general, the transducer used with XDCR1 was an LVDT. Cal Factor was used to adjust the voltage output from LVDT. The Cal Factor was adjusted to obtain + 10 volts when the core of the LVDT moved 0.100 inch. The Zero control introduces an e le c tr ic a l o ffs e t to the signal from the LVDT. d ia l. I t has 1000 divisions on the A Zero control s etting o f 500 corresponds to zero voltage o f f s e t. The Zero control provides negative e le c ­ t r i c a l o ffs e t when i t is between (000) and (500) and p o sitive o ffs e t when i t is between (500) and (1000). The Fine/Coarse switch determines the operating range fo r the Zero control. When i t is selected to Find, the e le c tr ic a l o ffs e t from the Zero control per division is lower than when i t is selected to Coarse. In this experiment, high e le c tr ic a l o ffs e t is necessary therefore the switch was selected to Coarse. 152 8. The Excitation, Zero, and (xl/xlO ) switch provide adjust­ ment of the signal for transducer (XDCR2). In general, the transducer used with XDCR2 was a load c e ll. The Excitation was used to adjust the voltage output from the load c e ll. I t has 1000 divions on the d ia l. The Excitation was adjusted to obtain 25 mv per 10 lbs of loading using a 5 Kip load ce-1 with a s e n s itiv ity of 2 mv/volt. The Zero control introduces an e le c tric al offset to the signal from the load c e ll. on the d ia l. I t had (1000) divisions A Zero control setting of (500) corresponds to zero voltage offs e t. I t provides positive electrical offset when i t is between 500 and 1000. The xl/xlO switch determines the operating range for the signal from the load c e ll. When in the (xlO) position the signal from the load cell is amplified 10 times that of the xl position. The xl position was used in the lab­ oratory investigations phase of this research program. 9. The Limit Detector determines which transducer conditioner (XDCR1 or XDCR2) signal w ill be monitored in the "failsafe" c irc u it. I f the switch is set on INTLK the fa ils a fe in te r ­ lock c irc u it w ill turn o ff the hydraulic power supply when the signal voltage is greater or lower than a selected range of voltage. I f the switch is set on IND the Limit Detector w ill indicate, by the Upper or Lower red lig h t on 153 the panel, when the signal voltage is greater or lower than a selected range of voltage. The Reset is used to extinguish the indicator lig h t when the signal voltage level is within the selected v o lt­ age range. I f the lig h t for the Limit Detector is s t i l l l i t with the f a ils a fe interlock c ir c u it in operation, the hydraulic power supply cannot be engaged. Therefore, before applying the hydraulic power supply the lig h t has to be extinguished with the Reset button. I f the switch is in the o f f position the fa ils a fe c ir c u it is inoperative. 10. The Upper and Lower lim it controls are used to select the range of acceptable voltage. The Upper lim it is set at the most positive or least negative li m i t . The Lower lim it is set at the most negative or least positive lim it . Each l im it dial has 1000 divisions corresponding to 10 volts. 11. Program is used to input an external source of command signal. B. MTS 436.11 Controller The front panel of the 436.11 is shown in Figure A.6. The controls indicated by the circled numbers are discussed in order below. 1. The Power control applied AC operating voltage to the control unit. 2. The Hyd Pressure Low or High or Hydraulic Off control is used to turn the hydraulic power supply on and o f f . 154 (The lAidiMt I FUNCTION GENERATOR RCL UN fllQUINCT HTD Pfivj 11raTHnr.m y 155 E MERG ENCY STOP Pm in«»i COUNT INPUT 0*1 NOOlia • * • lilllMl Figure A.6 Controls and Indicators on 436.11 Front Panel 500.10 hydraulic power supply has no low pressure option.) 3. The Program Stop or Run control' is used to s ta r t or stop generation of a command signal waveform. 4. 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 e ffe c t. 5. The Wave Form control of the Function Generator module is used to select the type of command waveform to be gener­ ated. Square, tria n g u la r and harmonic waveforms are availab le. 6. The frequency vernier and range selector are used to obtain the desired frequency characteristics of the com­ mand waveform. Frequencies between 0.01 and 1100 cycle/ sec. are a v a ilab le . C. Control Box. The control box fo r this research program was b u ilt at Michi­ gan State U niversity. Figure A .7 through A .10 jrovide the sche­ matic representation of the control box. were used to build the control box. MODULUS BOARD 12) 6) 56K resistors 1/4 watt 100K resistors 8) 47K resistors 2) 33K resistors 4) 27K resistors 2) 12K resistors 2) 1OK resistors 156 The parts lis te d below 0 c -1 Oil L O A ^ C ELL 'tb C s .2 . HO 5EG.VO V K L V E J r r i 0 (N T SUfcl 0 0 1 0 EXT 1 0 MODULUS LOAD LVUT o o CP 1 OF 2. o o l 1M e Lt'BT L oad 0 THE 0 lOhk 0 Z \ N T 2. 0 “ ‘ 0 0 0 Figure A-7 Cabinet-Rear View - V 2 °f Full Scale. INT 2 0 T V lE R . 2. 0 LVDT 0 E)CT3 117VAC LOM> LV/bT SERV.O V A L V E M ULT. E*T \ INT ! o EKT3 UN L V b T X \HTZ 0»l -i " V v 0^ r£. ,, L LW\ r✓t f |IC>*v / ^ \ iw y OFFSET 0 0 iOM» OTl Of wOJ'i- WvT ^ \ tB’'1 f Vo** f VX ____ /Jo° c" l v / ^ v V 0Mt f y PLV1>T V V- St>i< LVDT oo;e K i. 10V O GAJN o PWR OM V iy Btt-oui ov O O FFSET o FLIP Afccwe 10V 6 L M LOAb CH 2. dEi.o'v MULT 6 u /b T 6 LOM> CHI 4 C.H2. O V 0 Figure A-8 Cabinet-Front View -l/2 of Full Scale. o o o o o \i k e.K^) r^A/'--- DKMPIN6 (tjlue.) life fc2(l3) INPUT P IN L_ 20 (. 3) ft ^ X 8 H i 2* Hi PIN 22(0 L V D T (L FLIP 0AT>) Jttc ; e.5(lt) "P C2.(fc) SPPT < 28 ( 21) SfcK R 4< » lL 5 fcK O . O S \ mT C W ( 8) \A/— *- ~ ^ h - 7) J_ 5 & K .^ T O-W • X tv ts) R7 (2f) Si.KR.K><>) O.lAfrtt C H 7) PIN IIU) PIN l8(s) 02(4) If-m^O OOK piNn(u) LVDT G A ’M OUt v u t PIN i:T(8) Q , 2.70A. R.18 (31) - 5V < KU(n) + \5 V IOOK, M7 K n V --- R.2l0«) P M 13 00 ) v* 2 \ 3 ( 3H) H IG H L IM IT ( * ?.?v) £vo) PnMt'j) L.VOT — + (lOAb) v. 2 7 0 A C c - CZT f MH33) PI (T) I U W O I00K vV" - I Tv 2 .2 0 A _ R.20(^|) JOOKfLIHOs) > H7< J^tlL(37) _L F ig u re A -9 S chem atic D iagram o f th e C o n tro l Box (D am ping). PIN H(1) r Jf LO W LIMIT ( ^ 0 , 2 . v) (fflu' M o d u lu s (g reen) R-SftJ)i 5'.K. CJ(?0 StK. HH(?0 SZK. atuH o. z^ f PIN 2.2(1) OAL •'!_VDT) C.3(7) 47K. R-I8t3t) vV lOOft 160 47 F. IOOK 100(28) C3M> v V

PDT \ook LOAD Cuv7>T) O U T P U T t o COMPUTED iook. ^ ..AJ\^— 27 K Rl4(3i) 27 N. »5V (UZfo) OFFSET -»5V 6 47 K. fcll(Zl} PIN U (7 ) 0.575- 6 AIM , OFF$ET ~ 5 ,0 V IO K 103(31). PiM 18(5) O U T P U T C H A R T Figure A-10 T O R EC O R D E R Schematic Diagram of the Control Box (Modulus). r-o„0 .66 Resilient Modulus x 10 , (psi) 100 1 10 100 Sum of Principal Stresses, 9, (psi) Fig. B-l R e s ilie n t Modulus Vs. Sum of Principal Stresses fo r Undisturbed Sand Samples. 177 100 Sample l-S -2 10 W = 1 2 .1 0 % Yd = 95.00 pcf Mn = 42259°•48 5 Resilient Modulus x 10 ,(p si) 50 5 10 50 100 Sum of Principal Stresses, 9 , (p s i) Fig. B-2 R e s ilie n t Modulus Vs. Sum of Principal Stresses fo r Undisturbed Sand Sample. 178 Modulus x 10 (psi) 100 r Sample 1-N-l W = 2.64% y^= 98.0 pcf Resilient Md = 9400e°•' Sum of Principal Stresses, e, (psi) Fig. B-3 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Sand Sample. 179 Resilient Modulus x 10‘J (psi) 100 Sample 2-N-l 0.31 Mn = 88OO0 10 *4I 1 10 100 Sum of Principal Stresses, e, (psi) Fig. B-5 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Sand Samples. 180 Modulus x 10 , (psi) 100 Sample l-N -3 99.00 pcf Resilient 117009° *22 10 loo Sum o f Principal Stresses, e, (psi) Fig. B-6 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Sand Samples. 181 {psi) 100 Modulus x 10 Sample l-N -2 W = 5.00% Y d = 89.6 pcf Resilient Mn = 18000°*82 100 Sum of Principal Stresses, 9, ( ps1) Fiq. B-7 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Sand Samples. 182 100 Resilient Modulus x 10 (PS1) 50 Sample 2-N-4 W = 2.70% Yj = 100.0 pcf 10 5 TI 5 10 Sum of Principal Stresses, 9, (psi) 50 Fig. B-8 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Sand Sample. 183 100 Modulus x 10 , {p s i) 100 Sample 2-N-3 W = 3.50% y h = 106.50 pcf Resilient Mn = 194500,71 100 Sum of Principal Stresses, e, (psi) Fig. B-9 Resilient Modulus Vs. Sum of Principal Stresses for Undisturbed Sand Sample. 184 3(~ Sample l-S -4 Mn = 29526 Resilient Modulus x 10 , (psi) 100k 0.60 Sum of Princioal Stress, 0, (psi) Fig. B-10 R esilient Modulus Vs. Sum of Principal Stresses for Recompacted Sand Sample. 185 100 Modulus x 10 , (psi) 80 Sample 2-N-l 0.88 Resilient 14450 Sum of Principal Stresses, 0, (p s i) Fig. 8-11 R esilient Modulus Vs. Sum of Principal Stresses for Recompacted Sand Sample. 186 Sample 2-N-2 W =3. 3% Y , = 105.64pcf o » _ onoi.0.90 -M C Q a: 6.464 9.286 19.286 24.643 28.57 29.286 34.286 psi psi psi psi psi psi psi 10 40 10 Figure B.31 Resilient Modulus Vs. Confining Pressure Recompacted Sand Samples. for Sample l-S-2 Total Vertical Stresses 10 o 5.949 14.272 9.464 D 24.423 A S7 19.272 A 29.231 O 29.080 Q 33.544 □ psi psi psi psi psi psi psi psi □ 10 10 Figure B.32 Resilient Modulus Vs. Confining Pressure for Recompacted Sand Samples. Sample 2-S-l Total Vertical • 6.282 psi 0 14.223 psi o 19.223' psi & 24.163 psi 29.104 psi □ 29.493 psi ■ 34.10 psi 100 50 10 10 20 Confining Pressure, (psi) Figure B.33 Resilient Modulus Vs. Confining Pressure for Undisturbed Sand Samples. Sample 2-S-2 Total Vertical Stresses o # 9.7 14.7 psi psi o 20.0 psi • 24.4 psi S7 20.0 psi £ 25.0 psi A 30.1 psi P 35.0 psi 100 50 10 5 10 20 Confining Pressure, (psi) Figure B.34 Resilient Modulus Vs. Confining Pressure for Undisturbed Sand Samples. Sample 1-N-l Total Vertical Stresses o 6.464 9.206 psi psi o 19.286 psi A 24.643 psi A 28.57 psi ■ 29.286 psi □ 34.286 psi • 100 to Q. mo - 50 (/) 3 3 -o O 4-1 C 20 0) at □£ id 2 5 10 20 Confining Pressure, (psi) Figure B.35 .Resilient Modulus Vs. Confining Pressure for Undisturbed Sand Samples. 210 Sample l-N-2 Total Vertical Stresses 00 CL ro O loo r • 8.30 psi o 10.10 psi o 14.90 psi €> 19.70 psi A 17.20 psi A 25.30 psi A 30.30 psi □ 30.60 psi ■ 35.30 psi X 00 X3J O C oac 10 2 5 10 20 Confining Pressure, (psi) Figure B.37 R e s ilie n t Modulus Vs. Confining Pressure fo r Undisturbed Sand Samples. 212 Sample 2-N-l Total Vertical Stresses 100 l/l CL 50 on o • 9.768 psi A 24.305 psi A 19.531 psi A 29.07 psi □ 29.305 psi ■ 32.711 psi CO 3 "O o -cw OJ 10 CO U 0<2 10 20 Confining Pressure, (psi) Figure B.38 Resilient Modulus Vs. Confining Pressure for Undisturbed Sand Samples. 213 Sample 2-N-2 Total Vertical Stresses 5CT U 1 a. n • 6.476 psi o 9.476 psi 3 12.46 psi © £ 18.93 psi 24.257 psi A 28.568 psi a 29.257 psi □ 33.568 psi o x in 3 O T3 10 L) aC: 1 2 5 10 20 Confining Pressure, (psi) Figure B.39 Resilient Modulus Vs. Confining Pressure for Undisturbed Sand Samples. 214 Sample 2-N-3 Total Vertical Stresses Cl. sor O X • 6.310 psi o 9.640 psi O 13.621 psi A 19.450 psi A 24.589 psi A 29.231 psi □ 29.589 a 33.568 psi psi “O o c 10 to OJ t Tfr Confining Pressure, (psi) Figure B.40 R esilient Modulus Vs. Confining Pressure for Undisturbed Sand Samples. 215 Sample 1-S-l Total Vertical Stresses { /) a. 100 ro o 50 < /} 3 • 6.277 psi o 9.099 psi o 14.267 psi o A 18.900 19.267 psi psi A 23.900 psi A 28.890 ps:i □ 28.90 psi ■ 33.534 psi a> i/> DcCu 10 1 2 5 10 15 Confining Pressure, (p s i) Figure B.41 R e s ilie n t Modulus Vs. Confining Pressure for Undisturbed Sand Samples. 216 Sample 2-N-4 Total Vert ical Stresses 6.177 9.535 13.951 19.322 100r i/j CL CO o 8.752 23.924 28.698 28.924 34.096 X in 3 O ■M Cu < T3 (/> Qa£> Confining Pressure, (p s i) Figure B.42 R e s ilie n t Modulus Vs. Confining Pressure fo r Undisturbed Sand Samples. 217 Sample l-S-2 Total Vertical Stresses 100 t /l CL 50 oo o • 5.949 psi o 9.464 psi 9 14.272 psi A 19.272 psi A 24.423 psi A 19.231 psi □ 29.08 psi ■ 33.544 psi l/l 3 "O Eo ■M C a> £ i/i u o<; 10 1 10 20 Confining Pressure, (psi) Figure 8.43 Resilient Modulus Vs. Confining Pressure for Undisturbed Sand Samples. 218 TABLE B. 2, Sample No. 1 TEST RESULTS OF CONVENTIONAL TRIAXIAL TEST OF THE COHESIONLESS MICHIGAN! ROADBED SOIL Load D ia l cm P lb s. AL (in s ) 1.60 32.63 0.01 0 .16 m P A c (p s i) al (p s i) 7 .14 4.57 A c sq. in . V °3 (p si) ° l /0 3 19.57 4.57 1.30 6.15 125.4 0.02 0.32 7.15 17.54 32.54 17.54 2.2 13.80 281.4 0.03 0.48 7.16 39-30 54.30 39-30 3-6 18.00 367.1 0.04 0.64 7 .17 51-18 66.18 51.18 4.4 21.00 428.2 0.05 0.80 7-18 59-61 74.61 59.61 5.0 25.00 509-2 0.06 0.96 7 .20 70.85 88.85 70.85 5.7 26.00 530.2 0.07 1.10 7 .2 1 73.57 68.57 73.57 5.9 26.00 530.2 0.08 1.28 7.22 73.45 88.45 73.45 5.9 26.50 540.4 0.10 1.60 7-24 74.62 89.62 74.62 6.0 27-00 550.6 0.11 1.76 7-25 75.90 90.90 75.90 6.1 27.5 560.8 0.16 2.56 7.31 76.68 91-68 76.68 6.1 27.5 560.78 0.21 3.36 7.37 76.05 91-05 76.05 6.1 25.5 540.39 0.26 4.16 7.44 72-68 87.68 72.68 5.9 25.0 509.8 0.31 4.96 7.50 68.00 83-00 68.00 5.5 24.5 499.6 0.36 5-76 7.56 66.07 81.07 66.07 5.4 24.0 489.4 0.41 6.56 7.63 64.17 79.17 64.17 • 5.3 D - 3. 02 Inches o Hq - 6.25 inches CF - 20 39216 lb s / f t 3 - 15.00 psi Aq - 7.126 sq. in s . ^ °l~ °3 ^ f " 78,00 Ps l W - 2.52 Cf - 2.42 Yd - 108.8 l b s / f t 3 219 Table B.2 Sample No. 2 Continued P A c ( p s i) al ( p s i) ar ° 3 (p s i) 7.21 53-76 69.26 53-76 4 .5 0 .4 3 7 .2 2 66.38 81.88 66.38 5 -3 0.036 0.59 7.23 73-33 88.83 73.3 3 5 .7 560.78 0.046 0.76 7.24 77.42 92.92 77-42 6.0 30.00 611.76 0.056 0.9 2 7.26 84.32 99-82 84.3 2 6 .1 31.00 632.16 0.0 66 1.09 7 .27 86.99 102.49 86.9 9 6 .6 32.50 662.75 0.076 1.25 7.28 91-05 106.55 91.0 5 6 .1 32.50 662.75 0.086 1 .4 2 7.29 9 0.90 106.40 9 0 .9 0 6.9 32.50 662.75 0.096 1-58 7-30 90.75 106.25 90.7 5 6 .0 35.00 713.73 0.1 06 1.75 7.32 97.56 113.06 97.5 6 7 .3 35.00 713.73 0.116 1.91 7.33 97.40 112.90 9 7 .4 7-3 35.00 713-73 0.166 2.74 7.39 97.56 112.07 9 6 .5 7 7.2 36.00 734.12 0.216 3-56 7.45 98.50 114.00 9 8 .5 0 7 .4 37.00 754.51 0.266 4.39 7 .52 100.36 115-86 100.36 7 -5 37.50 764.71 0.366 6.04 7.65 99-96 115.46 99.9 6 7 .5 37.00 754.51 0.456 7 .69 7.79 96.90 112.40 9 6 .9 0 7 -3 36.00 734.12 0.5 66 9.34 7.93 92.59 108.09 92.59 7 .0 35.5 723.92 0.6 66 10.98 8 .07 89.66 105.16 89.6 6 6 .8 load chare (ca) P (l b s ) AL (In s ) «c> 19.00 387.45 0.016 0.26 23-50 479.22 0.026 26.00 530.20 27.50 A c sq. Ins D 0 * 3.025 inches H 0 SB. 6.065 Inches * 7.188 sq. inches (o1- o 3) f « 102.0 psi a 3.122 Ef - 5.02 a 111.6 l b s / f t 3 Ao w Yd CF - 20.39216 lbs/cm ■ 1 5.5 psi 220 V °3 Table B.2 Continued Sample No 3 A Reading (cm) P (lbs) AL (ins) (%)- 0.50 10.20 0.008 0.13 7.20 0.55 11.22 0.018 0.29 2.50 50.98 0.028 5.40 110.12 12.20 P A °1 (psi) °l“°3 (psi) V ° 3 (psi) 1.417 21.417 1.417 1.1 7.21 1.556 27.556 1.556 1.1 0.46 7.22 7.06 29-06 7.06 1.4 0.048 0.78 7.24 15.27 36.23 15.23 1.8 248.78 0.058 0.94 7.26 34.29 55.29 34.285 2.7 17.80 362.98 0.068 1.11 7.27 49*94 70.94 49*94 3.5 19.00 387.45 0.088 1.14 7.29 53-13 74.13 53.13 3.6 20.50 418.04 0.098 1.59 7.30 57.23 78.23 47.23 3.8 20.50 418.04 0.108 1.76 7.32 57.14 78.14 57.14 3-8 23.00 469.02 0.118 1.92 7.33 64.00 85.00 64.00 4.1 25.50 520.00 0.168 2.73 7.39 70.37 91.37 70.37 4.5 c sq. ins c (psi) Table B.2 Continued Sample No A 222 P (lbs) AL (ins) e (%)• 25-5 520.00 0.218 3.54 7.45 27.00 550.59 0.268 4.36 28.00 570.98 0.318 29.00 591.37 27.50 27.00 Reading (cm) 25.5 D 0 W o ffr ° 3 (psi) al/03 (psi) 68.78 89.78 68.78 4.4 7.52 73.26 94.26 73-26 4.6 5.17 7.58 75.33 96.33 75.33 4.7 0.368 6.00 7.65 77.34 98.34 77 .34 4.8 560.78 0.418 6.80 7.71 72.71 93-71 72.71 4.6 550.59 0.518 8.43 7.85 70.14 91.14 70.14 4.4 0.618 10.05 8.00 65.07 86.07 65.07 4.2 520.00 = 3.025 inches sq. ins 5 psi °3 - 20‘ * 3.22% 101.2 lbs/ft c CF = 20.32916 lbs/cm - 7.188 sq. inches Yd = c (psi) °1 (psi) H ■= 6.15 inches o A P A (0r ° 3 )£ = 76.00 psi G f = 5.00% 3 Table B.2 Continued 4 Load chare (cm) P (lb s ) AL (Ins) (2) 0.25 5.098 0.025 0.40 7.22 0.71 10.71 0.71 1.10 1.60 A c (sq. Ins) P A (p s i) «<*4 t rt Q. Sample Ho V °3 (p s i) ° l /o 3 2 .00 40.73 0.045 0.72 7-24 5-63 15.63 5.63 10.00 203.92 0.065 1.05 7.26 28.07 38.0? 28.07 3.8 12.50 254.90 0.085 1.37 7-29 34.98 44.98 34.98 4.5 13.50 275.29 0.105 1.69 7.31 37-65 47.65 37.65 4.8 14.50 295.69 0.125 2.01 7-34 40.31 50.64 40-31 5 .0 15.00 305.88 0.175 72.81 7.40 4.36 51.36 41.36 5.1 15-00 305-88 0.225 3.62 7.46 41.02 51.02 41.02 5.1 15-00 305.88 0.325 5.23 7.58 40.33 50.33 40.33 5.0 13-50 275-29 0.425 6.83 7.71 35.683 45.68 35.68 4.6 13.50 275.29 0.525 8.44 7.85 35.07 45.07 35.07 4.5 13.00 265.10 0.625 10.05 7.99 33-18 43.18 33.18 4.3 D 0 CF - 20.39216 lb s /c n 3.025 Inches Oj ■ 10.00 psi H - 6.220 Inches 0 A 0 V Yd • ( A c (sq. ins) 0.90 18.35 0.011 0.18 2.90 59.14 0.021 232.5 18.00 11.40 5 D ■■ 3.004 inches o - CF - 20 39216 lb s/cm Ho • 6 .1 0 Inches " 20.50 p s i Aq - 7.083 sq. inches M " 7 4 - 00 - 4-13Z eE - 3.00Z Yd - 101.8 l b s / f t 3 224 °r°3 ° l /0 3 (p s i) Table B.2 Continued Load Sample chart No (cm) 6 1 (p s i) 13.68 V°3 ° l /o 3 7 -3 2 P_ A c (p s i) 9.18 (p s i) 9 .1 8 1.9 A 1-50 30.59 AL (in ) 0.0 11 2 .9 59.19 0.0 2 1 0.3 3 7.3 3 8.07 17.57 8 .0 7 1 .8 7-5 159.98 0.031 0 .9 9 7 .3 9 21.11 30.61 21.11 3 .2 1 1 .0 229.31 0.091 0 .6 5 7-35 30.52 90.02 30.5 2 9 .2 13.20 269.18 0.051 0.81 7 .3 7 36.52 96.02 36.5 2 9 .8 20.50 918.09 0.0 6 1 0 .9 7 7 .3 8 56.65 66.15 56.6 5 7 .0 20.50 918.09 0.0 81 1.29 7 .9 0 56.99 65.99 56.99 6 .9 20.0 0 907.89 0.0 91 1 .99 7 -91 55.09 69.59 55.09 .6.8 20.0 0 907-89 0 .1 0 1 1 .60 7 .9 3 59.89 69.39 59.89 6 .8 19.50 397.65 0.151 2 .9 0 7 .9 9 53-09 62.59 53-09 6 .6 18.5 377.25 0.2 0 1 3-19 7 .5 5 99-97 59.97 99.97 6 .3 1 7 .0 396.67 0.251 3-98 7 .6 1 95-55 55.05 95.55 5 .8 ' P (lb s ) G a) 0.1 7 c (sq. in s) i D “ 3.008 0 CF - 20.392X6 lbs/fe3 H ■ 6.181 o Oj - 9.5 psi Ao w M 7.307 - 55.0 psi ef - 2.OZ - 4.13Z 110.0 *d - 225 Table B.2 Continued Sample No 7 c «> A c (sq. i n s ) P A c ( p s i) °1 (p s i) V °3 (p s i) V 0.016 0 .2 6 7.1 30 2.502 13-502 2.5 02 1.2 30.588 0.0 2 6 0 .4 2 7-140 4.284 15.284 4.284 1.4 3 .00 61.176 0 .0 3 6 0 .5 8 7 .1 5 0 B.556 19.556 8.556 1 .8 9 .0 0 183.529 0 .0 4 6 0 .7 4 7 .1 6 0 25.633 36.663 25.633 3-3 16.25 331.73 0 .0 5 6 0 .9 1 7 .170 46.217 57.217 46.217 5 .2 20.00 407.84 0 .0 6 6 1 .0 7 7.184 56.771 67.771 56.771 6 .2 22.50 458.624 0 .0 7 6 1 .2 3 7.198 63.743 74.743 63.743 6 .8 25-00 509.80 0 .1 2 6 2 .0 3 7.255 70 .2 69 81.269 70.269 7 .4 2 5 .0 0 509.80 0 .1 7 5 2 .8 5 7.316 69.6 8 3 80.633 69.683 7 -3 2 5 .0 0 50 9 .8 0 0.2 76 4 .4 7 7.439 68.531 79.531 68.531 7 .2 2 5 .0 0 509.80 0.3 7 6 6 .0 8 7.568 67.363 78.363 67.363 7 .1 2 5 .0 0 509-80 0.4 76 7 .7 0 7.700 66.208 77.208 66.208 7 -0 25.0 0 509.80 0.5 76 9 .3 2 7.830 65.034 76.034 65.034 6 .9 23.75 484.314 0.6 7 6 1 0.9 4 7-980 60.691 71.691 60.691 6 .5 23.75 404.314 0.7 76 1 2 .5 6 8.128 59.586 70.000 59-536 6 .4 chare reading (cms) P (lb s ) AL (in s ) 0 .8 7 5 17.843 1 .500 D 3.0 0 8 inches CF ■ 20.39216 lbs/cm H 6.181 inches a^j «■ 1 1.0 0 p s i A 7.1073 sq. in s ( a 1- a 3) f ■ 52.00 psi o- oo- * 4.4% M - 4.06% a - 107.8 lbs/ft3 226 a3 Table B.2 Continued Sample No 8 ch a rt reading (cms) F p’ (lb s ) AL (in s ) w A c (sq. in s ) Ac (p s i) ‘l (p s i) V °3 ( p s i) V °3 2 .50 50 .9 8 0 .0 1 3 0 .2 2 7 .5 7 6 .7 3 8 27-238 6.7 38 1 .3 6 .0 0 12 2 .3 5 0 .0 2 3 0 .4 0 7 .5 8 16 .1 4 3 36.643 16.143 1.8 12.50 2 5 4 .9 0 0 .0 3 3 0 .5 7 7 .5 9 33-575 5 4 .0 7 5 33.575 2 .6 21.0 0 428.24 0 .0 5 3 0 .9 2 7 .6 2 5 6 .2 1 4 76.714 56.214 3 .7 23-00 469.02 0 .0 6 3 1 .0 9 7.6 9 6 0.9 6 7 81 .4 17 60.967 4 .0 27.5 0 5 6 0 .7 8 0 .0 9 3 1 .6 1 7-6 7 7 3 .0 9 4 93-594 73-094 4.6 28.75 5 8 6 .2 7 0.1 1 3 1 .9 5 7 .7 0 7 6 .1 4 9 96.649 76.149 4 .7 28.7 5 586 .2 7 0.1 3 3 2 .3 0 7 .7 3 7 5 .8 8 96.3 8 0 75.880 4 .7 28.75 586.27 0.1 6 3 2 .8 2 7 .7 7 7 5 .4 8 2 95.982 75.482 4 .7 28.75 587.27 0 .2 1 3 3 -6 3 7.8 4 74 .8 0 8 ,95.308 74.808 4 .6 26.5 0 540.39' 0.2 63 4 .5 4 7 .9 1 7 4 .1 3 6 94.636 74.136 4 .6 2 5.50 520.00 0 .3 1 3 5 .4 1 7 .9 8 7 3 .4 6 7 93-967 73*467 4 .6 25.00 520.00 0 .3 6 3 6 .2 7 8 .05 7 2 .7 9 2 93.292 72.992 4.6 25.00 52 0 .00 0 .3 8 3 6 .6 1 8 .0 8 72.531 93-031 72.5 31 4 .5 24.50 499.61 0 .4 1 3 7 .1 3 3 8 .1 3 72.1 2 2 92.622 72.122 4 .5 - D - 3.10 0 inches 0 CF - 2 0 .3 92 1 6 lbs/cm H - 5 .7 9 Inches o °3 ■ A - 7.549 sq. 0 (wr inches W - 2.907. Ef yd « 102.00 l b s / f t 3 227 ■ 2 0 .5 p s i °3>f * 3.007. 79 00 psi Table B.2 Continued -Sample No 9 Chart Reading (an) P (lb s ) AL (ins) (Z) 0.375 7.647 0.004 0.07 7.11 1.625 33.131 0.009 0.15 2.25 45.881 0.014 2.50 50.98 3.75 It. 25 A P A C (p s i) °1 (p s i) °r°3 (p s i) ° l /0 3 1.075 17.075 1.075 1.1 7.12 4.655 20.655 4.655 1.3 0.23 7 .1 3 6.437 22.437 6.437 1.4 0.024 0 .39 7.14 7-145 23.145 7.145 1.4 76.471 0.034 0.56 7.15 10.70 26.700 10.70 1.7 86.667 0.044 0 .7 2 7.16 12.106 28.106 12.106 1.8 c (sq. in s) 5.25 107.06 0.054 0 .8 8 7 .17 14,932 30.932 14.932 1.9 10.25 209-02 0.064 1.04 7 .1 8 ' 29.103 45.103 29.103 2.8 23.75 484.31 0.114 1.86 7.24 66.875 82.875 66.875 5.2 27.50 560.78 0.164 2 .68 7 .30 76.788 92.788 76.788 5.8 28.75 536.27 0.214 3-49 7 .37 79.602 95.602 79-602 6.0 30.00 611.76 0.264 4.31 7 .4 3 82.370 98.37 82.370 6.1 30.00 611.76 0.314 5.13 7.49 81.667 97.666 81.667 6.1 30.00 611.76 0-364 5.94 7-56 80.964 96.964 80.964 6.1 28.75 586.27 0.464 7.58 7 .69 76.238 92.238 76.238 5.8 28.75 586.27 0.564 9.21 7 .8 3 74.834 90.832 74.834 5.7 27.50 560.78 0.664 10.84 7.97 70.353 86.353 70.353 5-4 Dq - 3.008 inches CF - 20.39216 lbs/cm Hq - 6.125 inches ■ 16.00 psi Ao » 7.10725 sq. inches (Oj^O-j) ■ 82 .0 0 psi W ef - 5.4 2 - 3.602 T . “ 108.6 l b s / f t ^ a 228 . Table 6-3. Results of Direct Shear Tests on Dry Coheslonless Soil Samples. Sample Number 1 2 Weight of Dry Soil, (LBS) 0.201 0.185 Cross Sectional Area, (sq. ft.) 0.0346 Height of Sample, (cms) 9.80 3 4 5 6 7 8 9 0.184 0.215 0.215 0.185 0.199 0.185 0.194 0.0346 0.0345 0.0346 0.0346 0.0346 0.0346 0.0346 0.0346 1.60 1.60 2.10 1.80 1.80 1.80 1.60 1.20 Initial Dial Reading 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 Final 126.6v 143.00 161.40 123.00 138.00 150.00 150.00 141.00 158.00 3868.8 6254.5 8930.0 3345.5 5527.3 7272.0 7272.0 5903.0 8436.00 246.3 397.6 568.3 212.0 351.0 462.9 462.9 370.0 537.0 6448.0 10464 14510 6448 10464 14510 14510 10464 14510 410.5 666.1 923.7 410.5 661.1 923.7 923.7 666.8 923.7 35 35 15 15 15 15 25 25 101.0 101 89.3 89.3 89.3 89.3 99.5 99.5 Dial Reading Load at Failure, (Kgs) Shear Stress at Failure (psi) Normal Load, (Kgs) Normal Stress (psi) No. of Slows Dry Density, (LBS/FT^) 35 101.0 Dq - I n i t i a l Diameter of Sample Hq = I n i t i a l Height of Sample A = I n i t i a l Cross sectional area, o W = Water Content Yj = Dry Density CF = Calibration Factor (oi - = Deviatoric Stress at Failure = Strain at fa ilu re 230