KENTUCKY TRANSPORTATION CENTER

Transcription

1 Research Report KTC-05-27/SPR F KENTUCKY TRANSPORTATION CENTER RESILIENT MODULUS OF COMPACTED CRUSHED STONE AGGREGATE BASES

2 OUR MISSION We provie services to the transportation community through research, technology transfer an eucation. We create an participate in partnerships to promote safe an effective transportation systems. OUR VALUES Teamwork Listening an communicating along with courtesy an respect for others. Honesty an Ethical Behavior Delivering the highest quality proucts an services. Continuous Improvement In all that we o.

3 Research Report KTC-05-27/SPR F Resilient Moulus of Compacte Crushe Stone Aggregate Bases by Tommy C. Hopkins Tony L. Beckham Charlie Sun Program Manager an Research Geologist Senior Research Engineer Chief Research Engineer Kentucky Transportation Center College of Engineering University of Kentucky in cooperation with the Kentucky Transportation Cabinet The Commonwealth of Kentucky an Feeral Highway Aministration The contents of this report reflect the views of the authors, who are responsible for the facts an accuracy of the ata herein. The contents o not necessarily reflect the official views or policies of the University of Kentucky, Kentucky Transportation Cabinet, nor the Feeral Highway Aministration. This report oes not constitute a stanar, specification, or regulation. November 7, 2007

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5 Abstract iii 1. Report No. 2. Government Accession KTC-05-27/SPR F No. 4. Title an Subtitle Resilient Moulus of Compacte Crushe Stone Aggregate Bases 3. Recipients catalog no 5. Report Date November 7, Performing Organization Coe 7. Author(s) Tommy C. Hopkins, Tony L. Beckham, an Charlie Sun 9. Performing Organization Name an Aress University of Kentucky Transportation Center College of Engineering 176 Oliver Raymon Builing Lexington, Kentucky Sponsoring Agency Coe Kentucky Transportation Cabinet 200 Mero Street 8. Performing Organization Report No. KTC Work Unit No. (TRAIS) 11. Contracts or Grant No. KYSPR Type of Report an Perio Covere Frankfort, Ky Sponsoring Agency Coe 15. Supplementary Notes Prepare in cooperation with the Kentucky Transportation Cabinet an the Unite States Department of Transportation, Feeral Highway Aministration 16. Abstract In recent years, the American Association of State Highway Transportation Officials (AASHTO) has recommene the use of resilient moulus for characterizing highway materials for pavement esign. This recommenation evolve as result of a tren in pavement esign of using mechanistic moels. Although much progress has been mae in recent years in eveloping mathematical, mechanistic pavement esign moels, results obtaine from those moels are only as goo as the material parameters use in the moels. Resilient moulus of aggregate bases is an important parameter in the mechanistic moels. The main goal of this stuy was to establish a simple an efficient means of preicting the resilient moulus of ifferent types of Kentucky crushe stone aggregate bases. To accomplish this purpose, resilient moulus tests were performe on several ifferent types of aggregate bases commonly use in pavements in Kentucky. Specimens were remole to simulate compaction conitions typically encountere in the fiel. Tests were performe on wet an ry specimens. The compacte specimens were 6 inches in iameter an 12 inches in height Crushe limestone base materials inclue Dense Grae Aggregate (DGA), an Crushe Stone Base (CSB). Number 57s, crushe river gravel, recycle concrete, an asphalt rainage blanket samples were submitte for testing by engineers of the Kentucky Transportation Cabinet. A new mathematical resilient moulus moel, evelope in a previous stuy by researchers of the University of Kentucky Transportation Center (UKTC), was use to relate resilient moulus to any selecte, or calculate, principal stresses in the aggregate base. This moel improves the means of obtaining best ata fits between resilient moulus an stresses. Furthermore, the resilient moulus can be preicte, using the UKTC resilient moulus moel, when the stress conition an type of Kentucky base aggregate are known. Multiple regression analysis is use to obtain moel coefficients, k 1, k 2, an k 3, of the relationships between resilient moulus an confining an eviator stresses use in the testing proceure. Also, multiple regression analysis was performe using other moels evelope by the National Cooperative Highway Research Program (NCHRP Project 1-37A, 2001) an Uzan (1985) to obtain the moel coefficient, k 1, k 2, an k 3. The resilient moulus ata an the UKTC moel, as well as moels evelope by NCHRP an Uzan, are reaily available to esign personnel of the Kentucky Transportation Cabinet. Computer software was evelope in a client/server an Winows environment. This program is embee in the Kentucky Geotechnical Database, which resies on a Cabinet server in Frankfort, Kentucky. 17. Key Wors Highways, Resilient Moulus, Soils, Moel, Design, Subgrae 19. Security Classification (of this report)--- Unclassfie Form DOT (8-72) 20. Security Classification. (of this page)-- None 18. Distribution Statement Unlimite, with the approval of the Kentucky Transportation Cabinet 21. No. of Pages Price

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7 Table of Contents v TABLE OF CONTENTS LIST OF FIGURES...vii LIST OF TABLES...xi EXECUTIVE SUMMARY... xv INTRODUCTION... 1 OBJECTIVES... 3 SCOPE OF STUDY... 3 BACKGROUND... 4 SAMPLING AND GEOTECHNICAL PROPERTIES... 4 Bulk Samples... 4 Geotechnical Test Methos an Physical Properties... 5 Graation an Dry Unit Weights... 5 RESILIENT MODULUS TESTING Testing Equipment System Components Compaction of Aggregate Specimens Resilient Moulus Testing Protocol REVIEW OF MATHEMATICAL MODELS FOR RELATING RESILIENT MODULUS AND STRESSES TEST RESULTS AND ANALYSIS Multiple Correlation Analysis Resilient Moulus Test Data an Regression Coefficients of Moels 3, 4, 5, an Storage an Accessibility of Values of Resilient Moulus of Compacte Aggregates Variation of Resilient Moulus an Dry Density Repeatability of Resilient Moulus Testing Equipment Synthetic Specimen of PVC No. 57 Aggregate CONCLUSIONS RECOMMENDATIONS REFERENCES Appenix A. Determination of Coefficients for Resilient Moulus Moels Using Simple/Multiple Regression Analysis General Linear regression Determine the Coefficients for Resilient Moulus of Aggregate Materials...55

8 Table of Contents vi Example of calculating k 1, k 2, an k 3 from the Test Data for UKTC Moel (Moel 5) Appenix B. Values of Testing Stresses an Resilient Moulus Recore During Testing of Compacte Specimens of Dense Grae Aggregates As Receive From the Proucer Appenix C. Values of Testing Stresses an Resilient Moulus Recore During Testing of Compacte Specimens Representing the Upper, Center, an Lower Specification Limit Graations of Dense Grae Aggregate Appenix D. Values of Testing Stresses an Resilient Moulus Recore During Testing of Compacte Specimens Representing the Upper, Center, an Lower Specification Limit Graations of Crushe Stone Base Aggregates Appenix E. Values of Testing Stresses an Resilient Moulus Recore During Testing of Specimens of Number 57s Crushe Limestone As Receive From the Proucer an Compacte At Different Relative Densities...73 Appenix F. Values of Testing Stresses an Resilient Moulus Recore For Five Repeat Tests of Number 57s Crushe Limestone Compacte To the Same Relative Density Appenix G. Values of Testing Stresses an Resilient Moulus Recore During Testing of River Gravel Specimens Compacte to Different Relative Compaction Values...81 Appenix H. Values of Testing Stresses an Resilient Moulus Recore During Testing of Crushe Recycle Concrete Specimens Compacte to Different Relative Compaction Values... 85

9 List of Figures vii LIST OF FIGURES Figure 1. Definition of resilient moulus... 2 Figure 2. Relative subgrae stress levels for ifferent pavement thickness... 2 Figure 3. Stress-strain hysteresis loop an resilient moulus etermination... 3 Figure 4. Comparison of upper, center, an lower graation curves to the graation curve of DGA sample as receive... 5 Figure 5. Upper, center, an lower graation curves of Crushe Stone Base (CSB) specimens blene accoring to specifications... 6 Figure 6. Upper an lower specification graation curves compare to the graation curve of No. 57 crushe limestone sample as receive... 6 Figure 7. Graation curve of crushe river gravel (quartz)... 7 Figure 8. Graation curve of recycle concrete sample... 7 Figure 9. Moisture-ensity relationship of the DGA specimen as receive from quarry Figure 10. Moisture-ensity relationship of the DGA specimen representing the upper specification graation Figure 11. Moisture-ensity relationship of the DGA specimen representing the center specification graation Figure 12. Moisture-ensity relationship of the upper graation curve of the Crushe Stone Base Figure 13. Moisture-ensity relationship of the center graation curve of the Crushe Stone Base Figure 14. Vibratory equipment an shaker table...12 Figure 15. View of resilient moulus testing equipment Figure 16. View of aggregate specimen in the triaxial chamber Figure 17. View of loaing actuator Figure 18. LVDTs an loa cell are mounte insie triaxial cell Figure 19. Placing aggregate an compaction of a specimen in a split mol Figure 20. Haversine loaing form Figure 21. Resilient moulus test in progress Figure 22. Example illustrating the three-imensional plane of Moel 5 an selecte testing stress points Figure 23. Comparisons of R 2 -values obtaine from regression analysis using

10 List of Figures viii Moels 3, 4, 5, an Figure 24. Regression plane of Moel 4 an potential ivergence problems at small stresses Figure 25. Regression plane of Moel 6 an potential ivergence problems at small stresses Figure 26. Regression plane of Moel 5. As or approaches zero, M 3 r converges to the constant, k Figure 27. Results of Regression analyses from Moel 3 for DGA specimens blene an remole to graation specification limits Figure 28. Results of regression analyses from moel 3 for remole DGA specimens of as receive aggregate Figure 29. User log-on graphical user interface screen for gaining access to the Kentucky Geotechnical Database an resilient moulus ata Figure 30. Main menu of the Kentucky Geotechnical Database Figure 31. Gaining access to resilient moulus test results for compacte soils an aggregates in the Kentucky Geotechnical Database Figure 32. Graphical user interface showing resilient moulus as a function of eviator stress for a selecte type of aggregate Figure 33. Display of resilient moulus summary ata in the atabase Figure 34. View of resilient moulus test ata for a selecte aggregate specimen Figure 35. GUI screen for searching ata Figure 36. Gaining access to resilient moulus test recor for a selecte specimen in the Kentucky Geotechnical Database Figure 37. GUI screen for accessing the complete resilient moulus test ata Figure 38. GUI screen for obtaining etaile resilient moulus test ata Figure 39. Complete resilient moulus test recor for a selecte aggregate specimen Figure 40. Variation of resilient moulus, M r, as a function of ry ensity of Dense Grae Aggregate specimens Figure 41. Comparison of DGA graation as receive an teste from a proucer in Kentucky an the approximate upper an lower graation limits of crushe limestone reporte by Bouali an Robert (1998) Figure 42. Variation of resilient moulus, M r, as a function of ry ensity of No. 57 crushe stone specimens Figure 43. Variation of resilient moulus, M r, as a function of ry ensity of crushe

11 List of Figures ix river gravel Figure 44. Variation of resilient moulus, M r, as a function of ry ensity of recycle concrete aggregate... 45

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13 List of Tables xi LIST OF TABLES Table I. Summary table of typical values of resilient moulus obtaine at three selecte testing stress conitions... xvii Table 1. Listing of geotechnical test methos... 5 Table 2. Graations of Dense Grae Aggregate, Crushe Stone Base, an No. 57 Stone... 8 Table 3. Graations of River Gravel an Recycle Concrete samples... 9 Table 4. Characterizing the ensity of granular materials on the basis of relative ensity Table 5. Dry ensities an moisture contents of specimens of Dense Grae Aggregate an Crushe Stone Base Table 6. Dry ensities an moisture contents of specimens of No.57 Stone, River Gravel, an Recycle Concrete Table 7. Testing stresses Table 8. Summary of Propose Resilient Moulus Moels Table 9. Coefficients k i an R 2 of aggregate samples for four ifferent resilient moulus moels Table 10. Coefficients k i an R 2 of aggregate samples for four ifferent resilient moulus moels (Continue.) Table 11. Comparison of numerical values of M r obtaine from Moels 3, 4, 5, an 6 an calculate at stresses of 3 = 3 an = Table 12. Comparison of numerical values of M r obtaine from Moels 3, 4, 5, an 6 an calculate at stresses of 3 = 10 an = Table 13. Comparison of numerical values of M r obtaine from Moels 3, 4, 5, an 6 an calculate at stresses of 3 = 20 an = Table 14. Comparison of average values of resilient moulus an percent ifference relative to Moel 5 for granular materials inclue in the testing program Table 15. Minimum an maximum resilient values observe for ifferent specification graation limits of DGA Table 16. Minimum an maximum resilient values observe for ifferent specification graation limits of Crushe Stone Base Table 17. Ninety-five percent confience levels of resilient tests repeate on a PVC cyliner an No. 57 stone aggregate Table A-1. Original Test Data... 57

14 List of Tables xii Table A-2. Converte Data Table B-1. Dense Grae Aggregate (DGA ) Table B-2. Dense Grae Aggregate (DGA ) Table B-3. Dense Grae Aggregate (DGA ) Table B-4. Dense Grae Aggregate (DGA ) Table B-5. Dense Grae Aggregate (DGA ) Table B-6. Dense Grae Aggregate (DGA ) Table C-1. Dense Grae Aggregate (DGA : Upper Graation) Table C-2. Dense Grae Aggregate (DGA : Center Graation) Table C-3. Dense Grae Aggregate (DGA : Lower Graation) Table D-1. Crushe Stone Base Upper Graation Curve Table D-2. Crushe Stone Base Center Graation Curve Table D-3. Crushe Stone Base Lower Graation Curve Table E-1. Number 57s (NoVullex ) Table E-2. Number 57s (NoVullex ) Table E-3. Number 57s (NoVullex ) Table E-4. Number 57s (NoVullex ) Table E-5. Number 57s (NoVullex ) Table E-6. Number 57s (NoVullex ) Table F-1. Number 57s (NoVullex ) Table F-2. Number 57s (NoVullex ) Table F-3. Number 57s (NoVullex ) Table F-4. Number 57s (NoVullex ) Table F-5. Number 57s (NoVullex ) Table G-1. River Gravel, RGRAV Table G-2. River Gravel, RGRAV Table G-3. River Gravel, RGRAV Table G-4. River Gravel, RGRAV Table G-5. River Gravel, RGRAV Table G-6. River Gravel, RGRAV Table H-1. Recycle Concrete, RECON Table H-2. Recycle Concrete, RECON Table H-3. Recycle Concrete, RECON

15 List of Tables xiii Table H-4. Recycle Concrete, RECON Table H-5. Recycle Concrete, RECON Table H-6. Recycle Concrete, RECON Table H-7. Recycle Concrete, RECON

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17 Executive Summary xvi EXECUTIVE SUMMARY This stuy evelope as a result of a process review conucte in the early nineties by the Feeral Highway Aministration (FHWA) of the Kentucky Transportation Cabinet s proceure for selecting parameters for pavement esign. As a result of this stuy, FHWA recommene "that an in-epth assessment be mae of the most appropriate strength test to accommoate Kentucky's future nees an that resilient moulus testing be given consieration for informational esign values, evaluation of other research efforts, an keeping up with state-of-the-art practices. Moreover, mechanistic pavement esign moels, which are uner evelopment by the American Association of Highway Transportation Officials (AASHTO), will rely on the resilient moulus of aggregate bases an soils as important moel input parameters (ARA, Inc., 2004). In the esign of pavements, resilient moulus has been use for characterizing the non-linear stress-strain behavior of base aggregates an soil subgraes subjecte to traffic loaings. The AASHTO 1993 Guie for Design of Pavement Structures recommene that highway agencies use a resilient moulus (M r ), obtaine from repeate loa triaxial test, for the esign of subgraes an bases. In 2004, the National Cooperative Highway Research Program (NCHRP) release the New Mechanistic Empirical Design Guie for pavement structures. This final report was entitle, Guie for Mechanistic Empirical Design of New an Rehabilitate Pavement Structures, NCHRP 1-37A. In the M-E Design Guie, the resilient moulus of unboun materials is require as input to characterize layers for their structural esign. As recommene by the guie for esign inputs, the resilient moulus of unboun materials may be obtaine irectly from a resilient moulus test or available correlations. When the resilient moulus is obtaine from a resilient moulus test, the guie esignates the input as Level 1, or the highest input level. If the resilient moulus is obtaine from correlations, then the guie esignates the input as Level 2. This stuy was sponsore as a means of responing to the factors cite above an to put the Kentucky Transportation Cabinet in a position to take avantage of the latest highway esign technology. Numerous resilient moulus tests have been performe previously on compacte soils (Hopkins et al, 2001). Several months were require to purchase, evelop compaction an testing protocol, an make operational the necessary equipment for performing resilient moulus tests on Kentucky soils an aggregate bases. This current stuy focuse on performing resilient moulus tests on a variety of aggregates commonly use for aggregate base construction in Kentucky. Types of crushe limestone aggregates commonly use in Kentucky inclue Dense Grae Aggregate (DGA), an Crushe Stone Base (CBS). River gravel is a potential source of aggregate base in the western portion of the state an was inclue in the stuy. Other aggregate materials use on occasion inclue recycle concrete, Number 57 crushe stone, an asphalt rainage blankets, which were also inclue in the stuy. The M-E Design Guie requires the material coefficients k 1, k 2, an k 3. A review was conucte of ifferent mathematical moels that have been propose for relating resilient moulus to principal stresses. Four mathematical moels appear to be useful for this purpose, which inclue those propose by See (1967), Hopkins et al, 2001 an Ni et al, 2002 (UKTC Moel), Halin (2001- AASHTO Moel), an Uzan (1985). Coefficients, k 1, k 2, an k 3, for those moels are obtaine using multiple regression analysis of all stanar testing stresses an corresponing resilient moulus values. The moels provie best ata fits between resilient moulus an testing stresses. Coefficients for each test are liste in the report. In all tests reporte herein (except the asphalt rainage blanket) an for the latter three moels cite above, values of R 2 were equal to or greater than Resilient moulus equipment previously use to perform tests on compacte soils was use in the series of tests on aggregates. However, an aitional triaxial chamber an loa actuator that woul

18 Executive Summary xvii accommoate large aggregate specimens ha to be purchase. The large triaxial cell obtaine accommoates aggregate specimens measuring 6 inches in iameter an 12 inches in height. The esign of the triaxial chamber an loa actuator permits the placement of the LVDTs (Linear Variable Displacement Transucers) an loa cell insie the chamber. This eliminates system strain uring the measurement of the resilient moulus testing an loa ue to piston friction. The equipment is controlle by computer software uring all phases of testing. An overhea crane was installe to facilitate the lifting an placement of the heavy testing hea that contains the loa actuator for loaing large specimens. Particle size analyses were performe on the ifferent types of aggregates. When sufficient fine material was present moisture-ensity relationships were establishe. Moisture-ensity relationships establishe from test proceure, AASHTO T-99 (2000), were use to remol aggregate specimens for resilient moulus testing. All resilient moulus aggregate specimens measure 6 inches in iameter an 12 inches in height. If sufficient fines were not present in the aggregate to efine a moisture-ensity relationship, then the maximum an minimum values of ry ensity were etermine using a shaker table an large mols. Specimens were mole at ifferent values of relative compactions an teste. Typical values of resilient moulus obtaine from the UKTC resilient moulus moel at three, selecte stress states of the ifferent aggregates are illustrate an summarize in the table on page xvii. Base on results reporte herein, the following observations, conclusions, an recommenations are mae: Resilient moulus, by efinition, is not a constant value but varies with stress conitions in base aggregates. Values of resilient moulus increase as the ry ensity increases. However, increases of resilient moulus were more noticeable an larger for well-grae aggregates than resilient moulus values of uniformly-grae aggregates. Values of resilient moulus of ense grae aggregate (DGA) generally were larger than values of the resilient moulus of the number 57s, Crushe Stone Base (CSB), river gravel, an recycle concrete Resilient moulus tests coul not be performe on DGA specimens that represente the upper graation limit (Kentucky Transportation Cabinet Stanar Specifications, 2004) an remole to about 95 percent of maximum ry ensity an optimum moisture content (AASHTO T-99). The upper graation curve allows a maximum of 13 percent particles finer than the U.S. Stanar 200 sieve. The combination of a large percentage of fines an a moisture content near optimum create high pore water pressures uring cyclic loaing, although the test is performe in an unraine state. Consequently, cyclic loaing control was a problem. By testing the DGA specimen at moisture contents smaller than optimum moisture content, the test coul be performe. The buil up of excess pore pressures in the fiel has been observe inirectly in DGA bases (an subgrae fine-graine soils), as evience by the migration of fines to the surfaces of pavements. A number of tests were performe to efine the resilient moulus of aggregates commonly use in pavement bases in Kentucky. Data that were evelope will provie a goo means for efining Level 1, as well as Level 2, resilient moulus input to the mechanistic moel evelope by AASHTO (American Association of State Highway an Transportation Officials).

19 Executive Summary xviii Table II. Summary table of typical values of resilient moulus obtaine at three selecte testing stress conitions. Aggregate Base Type Specimen Number 3 = 3 = 3 (psi) As receive Dense Grae Aggregate (DGA) Crushe Stone Base (CSB) (As Receive) No. 57 Stone Blene to Ky Specifications As receive Repeat Tests Crushe River Gravel (As Receive) Recycle Concrete (As Receive) Resilient Moulus, M r (psi) Dry Density Moisture Content Percent of Maximum Dry Density Selecte Stresses 3 = 10 3 = 20 = 20 = 40 (psi) (psi) (lbs/ft 3 ) (%) DGA ,657 37,014 65, DGA ,179 36,167 61, DGAVULLEX ,293 40,022 73, DGAVULLEX ,193 34,342 58, DGAVULLEX ,506 53,434 86, DGAVULLEX ,388 41,031 62, DGAUPPER ,271 48,125 73, DGACENTER ,893 35,139 68, Relative Density DGALOWER ,601 39,502 74, >100 CSBUPPER ,621 46,892 77, CSBCENTER ,823 42,635 73, CSBLOWER ,043 34,732 58, No57VULLEX ,575 43,738 64, No57VULLEX ,281 47,307 59, No57VULLEX ,749 39,274 58, No57VULLEX ,577 43,882 64, No57VULLEX ,963 42,747 60, No57VULLEX ,041 44,620 65, No57VULLEX ,784 49,689 73, No57VULLEX ,189 47,889 69, No57VULLEX ,094 53,889 78, No57VULLEX ,196 47,070 68, No57VULLEX ,714 52,726 74, RGRAV ,790 36,839 63, RGRAV ,740 35,663 63, RGRAV ,351 38,163 68, RGRAV ,524 33,826 59, RGRAV ,546 32,353 56, RGRAV ,071 39,046 65, RECON ,584 43,388 73, RECON ,421 36,892 58, RECON ,372 34,982 60, RECON ,412 33,845 57, RECON ,306 36,969 61, RECON ,044 40,557 66, RECON ,950 37,380 60,

20 Executive Summary xviii Stuies are neee to examine the following areas of research, which may affect the value of resilient moulus of aggregate bases: The effect of ifferent graations (or particle sizes) of the base materials on the value of resilient moulus nees to be examine. The maximum, or the permissible, percentage of fines (the amount finer than the U. S. Stanar No. 200 sieve) for DGA an Crushe Stone Bases shoul be etermine which woul not allow excess pore water pressures to buil up uner cyclic loaing of the resilient moulus test. Limite magnitues of fines an moisture contents coul be etermine by performing resilient moulus on specimens compacte to ifferent moisture contents an percentages of fines. The effect of migratory subgrae fines (clay-size particles) on the resilient moulus of base materials nees to be examine. During issipation of excess pore pressures, fine clay-size particles from the subgrae are pushe into the lower portion of the base aggregate. Strengths (an resilient moulus) of the base materials ecrease when excess pore pressures occur in the soil subgrae. Seconly, as fines (uncontrolle) enter the bottom of base aggregates from an untreate, fine-graine subgrae, excess pore pressures may buil up in the base aggregates ue to the increase of fines. The effectiveness of geofabrics (use as grae separators) to prevent migration of fines into the bottom of the aggregate base nees to be stuie. Although the migration of fines may be prevente, the geofabric may clog an cease functioning with increasing time. If the material allows fine particles to pass into the base, then the resilient moulus of the base is altere. In either case, the resilient moulus of the base or/an subgrae will be altere. Extensive geotechnical research nees to be performe to examine filter requirements between base aggregates an clayey subgraes an how this relationship affects resilient moulus of bases. Finings of this type of research coul help reefine an improve the engineering functions of graations of typical base aggregates commonly use in Kentucky. To prevent migration of subgrae fines into base aggregates, filter criteria must be met between a given type of soil subgrae an a selecte type of base aggregate. Moreover, when filter fabric is use as a grae separator to prevent the migration of subgrae fines into the base aggregates, filter criteria must be satisfie between the subgrae soils an the fabric. This novel approach has goo potential for improving the function an performance of base aggregates. Tests nee to be performe to aequately efine the resilient moulus of chemically stabilize subgraes. This stuy i not aress this important etermination. In the pavement system, a chemically treate subgrae may function as a base in some cases or as a subbase in others. Chemical stabilization of subgraes in Kentucky is increasingly being use to improve the poor engineering properties of soils. Sufficient testing shoul be performe to provie Level 1, as well as Level 2, resilient moulus ata input to the mechanistic moel evelope by AASHTO. Chemical amixtures to be examine shoul inclue hyrate lime, Portlan cement, an lime kiln ust. Typical soils foun in Kentucky shoul be inclue in the stuy.

21 Executive Summary xix With completion of this stuy on the resilient moulus of aggregates, the Kentucky Transportation Cabinet is in a goo position to implement the use of mechanistic pavement esign moels. A secon stuy, sponsore by the Kentucky Transportation Cabinet, focuse on efining the resilient moulus of compacte soils commonly locate in Kentucky. Both soake an unsoake specimens were teste. Consequently, ata for efining the resilient moulus of aggregates an soils are available for use in the mechanistic pavement esign moel evelope for AASHTO. However, a thir stuy is neee to efine the resilient moulus of chemically treate subgraes.

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23 INTRODUCTION Resilient moulus has been propose as a means of characterizing the elastic properties of pavement materials. It is expresse as the ratio of eviator stress applie to the pavement layers (an the aggregate base layer) an the resilient axial eformation recovere after release of the eviator stress. Assumptions are mae tacitly that pavement materials are esigne for loaing in the elastic range an that the resilient moulus is the only parameter neee to esign the thickness of a pavement. Several types of aggregate bases are use in esigning an constructing flexible pavements in Kentucky. A structural layer coefficient of 0.14, or a California Bearing Ratio (CBR) of 100 percent, is usually assigne to the aggregate base for esign purposes (AASHTO, 1993). Although empirical relations have been use in the past to estimate the resilient moulus of aggregate bases, the tren in recent years is to measure the resilient moulus of aggregates an soils using laboratory tests. The value of resilient moulus is stress-strain epenent. That is, the value changes as stress an strain conitions change. AASHTO (American Association of State Highway an Transportation Officials, 1993, 2000) an SHRP (Strategic Highway Research Program, 1989) publishe a testing stanar an protocol, T-294, for performing resilient moulus of aggregates. Equipment for performing resilient moulus tests of aggregates an soils aggregates has steaily evolve an improve over the past few years. Several mathematical expressions are available for moeling the resilient moulus of aggregates an soils. These inclue such moels as propose by Moossazaeh an Witczak (1981), Dunlap (1963), See et al. (1967), May an Witczak (1981) an Uzan (1985), Hopkins et al (2001) an Ni et al, Effectiveness of those moels to preict resilient moulus is iscusse in this report. Comparisons are mae among the various moels. The tren in the esign of highway pavements consists of using mechanistic moels (ARA, Inc. 2004). Although much progress has been mae in recent years in eveloping mathematical, mechanistic pavement esign moels, results obtaine from those moels are only as goo as the material parameters entere into the moels. In 1986 an 1993, the American Association of State Highway Transportation Officials (AASHTO Guies) recommene the use of resilient moulus for characterizing highway materials for pavement esign (Mohamma et al., 1995). To promote this concept, the 1962 flexible pavement esign equation originally publishe by the Highway Research Boar (1962) was moifie in the 1993 AASHTO Guie to inclue the resilient moulus of soils. This approach attempts to make use of the mechanical properties of the asphalt, or concrete, base courses, an soil subgraes. Many state transportation agencies have use, or continue to use, empirical pavement esign methos involving soil support values, California Bearing Ratio (CBR), or R-values. Accoring to Mohamma et al., (1995), empirical values an esign approaches o not aequately represent the response of pavement to the ynamic loaing cause by moving vehicles. The resilient moulus concept arose as a result of efforts to better simulate the loaing of pavements by moving vehicles. The resilient moulus test for soils was originally evelope by See et al. (1967) an was later formulate for highway applications (Claros et al., 1990). The resilient moulus test provies a relationship between eformation (or strain) an stresses in pavement materials, incluing aggregate bases an subgrae soils, subjecte to moving vehicular wheels. Hence, it is not necessarily a fixe value but varies accoring to the applie stresses of moving vehicles an the resulting stress level in the pavement layers. The test measures the stiffness of a cylinrical specimen of aggregate or soil that is subjecte to a cyclic or repeate axial loa. It provies a means of analyzing ifferent materials an soil conitions, such as moisture an ensity,

24 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 2 an stress states that simulate the loaing of actual wheels. For a given eviator stress, the resilient moulus, M r, is efine as the slope of the eviator-axial strain curve, or simply the ratio of the amplitue of the repeate axial stress to the amplitue of the resultant recoverable axial strain, or (Figure 1): where Δ M= r Δε axial Δ = 1 3 = eviator stress, 1 an 3 = major an minor principal stresses, an Δε = recoverable axial strain. axial (1) The specimen is subjecte to repeate loaing at a particular stress level an the recoverable strain is measure. Ieally, the specimen exhibits only elastic strains at the time the resilient moulus is measure. The resilient moulus can, therefore, be thought of as the secant Young s Moulus of a certain material typically ifferent than the initial tangent value (Houston et al., 1993). Resilient moulus is use in many pavement an railroa track esigns. This moulus can be use for either the asphalt or subgrae level when the materials are subjecte to moving ynamic loas. As shown in Figure 2, the stress level in a subgrae varies with the thickness of the pavement. If the pavement is thin, then the cyclic eviator stresses are large. When the pavement is thick, the cyclic eviator stresses in the subgrae are small. Consequently, the magnitue of the applie cyclic loa is varie over a range of anticipate subgrae stress values, as shown in Figure 3, in resilient moulus testing to measure the variation of the resilient moulus, or stiffness. Values of resilient moulus of aggregate bases are neee to use in mechanistic pavement esign moels evelope by the American Association of State Highway Transportation Officials (AASHTO, Halin, 2001). Resilient Moulus, M r = Δ Δ ε ε axial axial Figure 1. Definition of resilient moulus. Subgrae 3 Thin Pavement Large Stresses 3 3 Asphalt Base Course = Elements Δ Δε axial Thick Pavement Small Stresses 3 Subgrae Figure 2. Relative subgrae stress levels for ifferent pavement thickness.

25 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 3 Deviator Stress Δε a Δ Δ M r = Δ ε a Resilient Moulus M r 1 2 ε axial (Strain) 3 Deviator Stress Figure 3. Stress-strain hysteresis loop an resilient moulus etermination. OBJECTIVES Highways in Kentucky are constructe with various types of aggregate bases. Furthermore the graation can vary greatly. The objective of this stuy was to etermine values of resilient moulus of ifferent aggregate bases commonly use in pavements in Kentucky. A major intent of this stuy was to follow through on a suggestion mae by FHWA in 1993 "that an in-epth assessment be mae of the most appropriate strength test to accommoate Kentucky's future nees an that resilient moulus testing be given consieration for informational esign values, evaluation of other research efforts, an keeping up with state-of-the-art practices." Another major intent of this stuy was to put the Kentucky Transportation Cabinet in a position (from a esign point of view) to use the new mechanistic moels evelope by AASHTO. Initially, consierable stuy time was require for purchasing the resilient moulus testing equipment, evaluating the equipment, an making the equipment operational. SCOPE OF STUDY Few states or agencies have performe a large number of resilient moulus tests mainly because the test requires expensive, specialize testing equipment an software, the testing proceure is complex, an it is time consuming. The scope of this stuy mainly inclue efining values of the resilient moulus of ifferent types of aggregates commonly use in highway pavement bases in Kentucky, examining mathematical expressions, or moels, for relating resilient moulus an stresses, an

26 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 4 evising an easy means for Cabinet engineers to access the resilient moulus ata an mathematical moels. Consierable efforts were evote to evising a compaction protocol for large specimens. This proceure require attention to many etails. A summary of the resilient moulus ata generate in this stuy is containe in this report an etaile information for each test appears in the Kentucky Geotechnical Database, which is house on a server of the Kentucky Transportation Cabinet. Resilient moulus equipment use to perform the tests is fully escribe. A limite number of tests were performe on aggregate specimens an a synthetic specimen to evaluate the reliability an repeatability of the testing equipment. BACKGROUND Values of resilient moulus, M r, of unboun aggregate, subbase an subgrae are main input parameters in the mechanistic-empirical pavement esign proceures evelope in the NCHRP (National Cooperative Highway Research Program) Project 1-37A (Halin, 2001). To evelop the necessary input ata, the Kentucky Transportation Cabinet has sponsore two research stuies to generate resilient moulus values. This stuy represents the secon research stuy sponsore by the Kentucky Transportation Cabinet an it focuses on efining the resilient moulus of aggregates commonly use in Kentucky to construct pavement bases. In the first stuy (Hopkins et al, 2001), sponsore by the Kentucky Transportation Cabinet, resilient moulus tests were performe on several ifferent types of typical soils use in Kentucky to construct subgraes. The tests were performe on specimens compacte to 95 percent of maximum ry ensity an optimum moisture (AASHTO T-99). Both unsoake an soake specimens were teste. Each soil sample was classifie accoring to the AASHTO an Unifie Classification Systems. Data are available for etermining the resilient moulus of a given soil type when the soil classification is known. Interpretation can be mae using the group inex of the soil type. In the first stuy, a new relationship, or mathematical moel, was evelope that relates the resilient moulus to testing stresses. Multiple regression analysis was use to etermine the k-coefficients (so calle k 1, k 2, an k 3 ) of the new moel. All testing stresses are use in the analysis to efine the coefficients. Resilient moulus ata of numerous soil types are store in the Kentucky Geotechnical Database (Hopkins, et al 2005). The atabase is locate on a server of the Kentucky Transportation Cabinet. Bulk Samples SAMPLING AND GEOTECHNICAL PROPERTIES Bulk samples of crushe limestone bases most commonly use in Kentucky were collecte from actual prouction runs at selecte quarries. These inclue: Dense Grae Aggregate (DGA) Crushe Stone Base (CSB). Other sample types submitte by engineers of the Kentucky Transportation Center for resilient moulus testing inclue: Number 57 crushe limestone Crushe river gravel (quartz)

27 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 5 Recycle crushe concrete Asphalt rainage blanket. Table 1. Listing of geotechnical test methos. Type of Test Test Metho Moisture Content AASHTO T (1996) Maximum Dry Density 1 (Shaker Table) Relative Density--Metho Devise Minimum Dry Density 1 Relative Density--Metho Devise Particle Size Analysis AASHTO T AASHTO T Moisture-Density Relations AASHTO T 99 Metho D Resilient Moulus of Aggregates AASHTO T (1996) 2 AASHTO T (2003) 3 1. A way of characterizing the in-place ensity of a granular material. 2. This stanar metho permitte internal or external placement of the LVDTs an loa cell. The LVDT sensors an loa cell were place internally in the chamber for all tests reporte herein. The number of conitioning cycles repeate loa applications-- use in the tests were 200 an not 1000, as specifie by AASHTO T , or ,as specifie by AASHTO Loa applications use in the tests were 100 for following sequence numbers, as specifie by AASHTO AASHTO T specifies mounting, externally, the LVDT sensors an loa cell. Percent Finer by weight) Upper Limit-Ky Spec Lower Limit-Ky Spec Center Limit-Ky Spec. As Receive Diameter (mm) Figure 4. Comparison of upper, center, an lower graation curves to the graation curve of DGA sample as receive. Geotechnical Test Methos an Physical Properties Test methos use to etermine classifications an engineering properties of the bulk samples are tabulate in Table 1. Stanar test methos of AASHTO were generally followe. Graation an Dry Unit Weights Two series of resilient moulus tests were performe on specimens of Dense Grae Aggregate (crushe limestone). In the first series, six resilient moulus tests were performe on the DGA sample as receive. Graation of the DGA sample as it was receive from the proucer is shown in Figure 4 an compare to the upper, center, an lower graation specification limits (as specifie by the Kentucky Specifications for Roa an Brige Construction (2004)). The Kentucky specifications allow the percentage finer than the U. S. Stanar No. 200 sieve to range from 4 to

28 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC The percent finer than the No. 200 sieve for the as receive sample was about 8. As shown in Figure 4, an at a particle size below 3 mm, the graation representing the center of the upper an lower specification graations containe slightly larger particle sizes than the particle sizes of the as receive sample. The secon series of resilient moulus tests were performe on blene DGA materials representing the upper an lower graation specifications limits, as well as a graation curve representing the center of the upper an lower curves (Figure 4). Three resilient moulus tests were performe on Crushe Stone Base (CSB). Different particle sizes of the crushe stone aggregate were blene to uplicate the upper an lower specification graation limits, as shown in Figure 5, an form two specimens for testing. The thir blene specimen represente the center graation curve. The Percent Finer by weight) Percent Finer By Weight Upper Limit-Ky Spec. Upper Limit (Ky Spec.) As Receive Center Gra Diameter (mm) Figure 5. Upper, center, an lower graation curves of Crushe Stone Base (CSB) specimens blene accoring to specifications Diameter (mm) Lower Limit-Ky Spec. Lower Limit (Ky Spec.) Figure 6. Upper an lower specification graation curves compare to the graation curve of No. 57 crushe limestone sample as receive. Kentucky specifications allow the percentage finer than the U. S. Stanar No. 200 sieve to range from 0 to 8 for CSB material. Graation of the Number 57 crushe limestone as receive is shown in Figure 6 an compare to the upper an lower graation limits of the Kentucky specifications. Six resilient moulus tests were performe on this material. Also, resilient moulus tests were performe on the same specimen of the No. 57 stone five times to examine repeatability of the testing equipment an operator. The Kentucky specifications allow the percentage finer than the U. S. Stanar No. 8 sieve to range from zero to 5 for this material.

29 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 7 The graation of the Crushe River Gravel as receive is shown in Figure 7. Percentage finer than the U. S. Stanar No. 200 sieve of this material was 4. Six resilient moulus tests were performe on this material. Since recycle concrete is use on occasion as base material, eight tests were performe to characterize the resilient moulus of this material. Graation of the sample as receive is shown in Figure 8. Only 1.7 percent of the particle sizes were finer than the U. S. Stanar No Values of graations for the aggregates inclue in the testing program for resilient moulus are liste in Tables 2 an 3. The approach use to form specimens for resilient moulus testing was epenent on whether a moisture-ensity relationship, as obtaine from AASHTO T-99, coul be establishe. When a relationship coul be establishe specimens were remole to a certain percentage of the maximum ry ensity an optimum moisture content, or selecte target values. A moisture-ensity relationship, as shown in Figure 9, was establishe for the DGA sample (Figure 4) as receive from the quarry. Relationships were also establishe for the upper an center DGA graation specification samples (see Figure 4). Those relationships are shown in Figures 10 an 11, respectively. Values of maximum ry ensity of the three ifferent DGA samples only range from to lbs/ft 3. Optimum moisture contents of the three samples were essentially the same an range from 6.7 to 6.9 percent. Moisture-ensity relationships for the Crushe Stone Base were establishe for the upper an center graation specifications limits. Moisture-ensity relationships for those samples Percent Finer by Weight Diameter (mm) Figure 7. Graation curve of crushe river gravel (quartz). Percent Finer by Weight Diameter (mm) Figure 8. Graation curve of recycle concrete sample. are shown in Figures 12 an 13, respectively.

30 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 8 Table 2. Graations of Dense Grae Aggregate, Crushe Stone Base, an No. 57 Stone. Sizes of Coarse aggregates Amounts Finer than Each Laboratory Sieve (Square Openings) Percentage by Weight U. S. Sieve Size 2 1/2 1 1/2 1 3/4 1/2 3/8 No. 4 No. 10 No. 30 No. 40 No. 60 No. 200 Sieve Opening (mm) Base Type Specimen Number DGA DGA Dense Grae Aggregate (DGA) As Receive DGAVULLEX DGAVULLEX DGAVULLEX DGAVULLEX Specification Limits Crushe Stone Base Specification Limits DGAUPPER DGACENTER DGALOWER CSBUPPER CSBCENTER CSBLOWER Size No. 57 Stone As Receive No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX As Receive (Repeat Tests) No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX

31 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 9 Table 3. Graations of River Gravel an Recycle Concrete samples. Sizes of Coarse aggregates Amounts Finer than Each Laboratory Sieve (Square Openings ) Percentage by Weight U. S. Sieve Size No. 1 1/2 1 3/4 1/2 3/8 No. 4 No No. 30 No. 50 No. 100 No. 200 Sieve Opening (mm) Base Type River Gravel As Receive Recycle Concrete As Receive Specimen Number RGRAV RGRAV RGRAV RGRAV RGRAV RGRAV RECON RECON RECON RECON RECON RECON RECON RECON

32 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 10 DGA AS Receive Dry Unit Weight (Lbs/Ft 2 ) γ ω Max opt = = 68. (%) Moisture Content (%) Figure 9. Moisture-ensity relationship of the DGA specimen as receive from quarry. If moisture-ensity relationships coul not be establishe from AASHTO T-99, then another approach was aopte to remol resilient moulus specimens. This conition usually occurs when there are insufficient fines (percent finer than the US Stanar sieve No. 200) in the aggregate. In those cases, the relative ensity concept was use. Relative ensity is use to characterize the ensity of granular materials (Lambe, 1969) an it is efine as follows: γ γ max - γ min D r = x x 100% γ γ - γ max min (4) where γ γ max min = ry unit weight of aggregate in ensest conition, = ry unit weight of aggregate in loosest coniton, an γ = in-place ry unit weight of aggregate specimen. When the maximum ry ensity coul not be etermine from AASHTO T-99, ry ensity of the aggregate in the ensest state was etermine using a shaker table an equipment shown in Figure 14. By weighing the material after shaking an noting the volume of container, the ry ensity of the aggregate in the ensest conition was etermine. The ry ensity of the

33 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 11 Dry Unit Weight (Lbs/Ft 2 ) γ ω Max opt = = 67. (%) DGA Upper Graation Moisture Content (%) Figure 10. Moisture-ensity relationship of the DGA specimen representing the upper specification graation. Dry Unit Weight (Lbs/Ft 2 ) Crushe Stone Base Upper Specification Limit Graation Curve γ ω Max opt = = 62. (%) Moisture Content (%) Figure 12. Moisture-ensity relationship of the upper graation curve of the Crushe Stone Base. Dry Unit Weight (Lbs/Ft 2 ) DGA Center Graation 143 γ Max = ωopt = 69. (%) Moisture Content (%) Figure 11. Moisture-ensity relationship of the DGA specimen representing the center specification graation. Dry Unit Weight (lbs/ft 2) Crushe Stone Aggregate Center Specification Limit Graation Curve γ ω Max Opt. = lbs/ Ft = 55. % Moisture Content (%) Figure 13. Moisture-ensity relationship of the center graation curve of the Crushe Stone Base.

34 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 12 aggregate in the loosest conition was etermine by loosely placing the aggregate by han in one of the containers shown in Figure 14. By weighing the material an Frequency Controller noting the volume of container, the ry ensity of the aggregate in the loosest conition was etermine. Descriptive terms that may be use to characterize conveniently the ensity of granular materials on the basis Vibrating Table of relative ensity are presente in Table 4. For example, when the relative ensity is some value between Figure 14. Vibratory equipment an shaker table zero an 15 percent, the ensity state is escribe as Very Loose. If the relative ensity ranges from 85 to 100, then the ensity state may be escribe as Very Dense. Resilient moulus specimens of the following aggregate samples were remole at selecte relative ensities: Blene DGA material representing the lower specification graation curve Blene Crushe Stone aggregate representing the lower specification graation curve Number 57 aggregate River Gravel Recycle Concrete. Values of maximum ry ensities an optimum moisture content from AASHTO T-99 for aggregates that containe sufficient fines, maximum an minimum values of ry ensities of aggregates that i not contain sufficient fines to perform AASHTO T-99, an target an actual remoling ry ensities an moisture contents are given in Tables 5 an 6. Resilient moulus specimens of DGA as receive from the proucer were compacte to percents of maximum ry ensity ranging from 72 to 100. Moisture contents of the specimens range from 5.2 to 6.3, which were slightly Table 4. Characterizing the ensity of granular materials on the basis of relative ensity. Relative Density (%) Descriptive Term 0-15 Very loose Loose Meium Dense Very Dense

35 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 13 Table 5. Dry ensities an moisture contents of specimens of Dense Grae Aggregate an Crushe Stone Base. Aggregate Base Type DGA Specimen Description an Type As Receive Moisture-Density Relationships 1 Maximum an Minimum Dry Density Target Values Actual Values Maximum Dry Optimum Moisture Max. Min. Dry Density 2 Optimum Moisture Dry Density Moisture Content Relative. Density, Percent of Max. Specimen Number Density 1 Content Content Dr Dry Density (%) (lbs/ft 3 ) (lbs/ft 3 ) (lbs/ft 3 ) (lbs/ft 3 ) (%) (lbs/ft 3 ) (%) (%) (%) DGA DGA DGAVULLEX DGAVULLEX loose DGAVULLEX DGAVULLEX Specification Limits Crushe Stone Base Specifications Limits DGAUPPER DGACENTER DGALOWER CSBUPPER CSBCENTER CSBLOWER Maximum ry ensity an optimum moisture content obtaine from AASHTO T-99, Metho D.

36 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 14 Table 6. Dry ensities an moisture contents of specimens of Number 57 stone, River Gravel, an Recycle Concrete. Specimen Description an Type Aggregate Base Specimen Number Type No. 57 Stone As Receive Repeats River Gravel 1 (Quartz) As Receive Recycle Concrete 2 As Receive Asphalt Drainage Blanket As Receive Maximum an Minimum Density Target Values Actual Values Max. Min. Moisture Dry Density Content Dry Density (lbs/ft 3 ) Moisture Content Relative. Density, Dr (%) (lbs/ft 3 ) (lbs/ft 3 ) (%) (lbs/ft 3 ) (%) No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX CS1-57s (VULLEX ) (VULLEX ) (VULLEX ) (VULLEX ) (VULLEX ) RGRAV RGRAV RGRAV RGRAV RGRAV RGRAV RECON RECON RECON RECON RECON RECON RECON ADB (teste at Room Temperature 70 0 F) 1. Hyroscopic moisture content of specimen = 2.5 percent. Moisture content of specimen as receive an teste = 6.6 percent. 2. Moisture content of specimen as receive =8.9 percent

37 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 15 smaller in value than the optimum moisture content of 6.8 percent. Blene DGA specimens representing the upper an center specification graation curves were compacte to 84 an 89 percent of maximum ry ensity, respectively. Blene Crushe Stone specimens representing the upper an center specification graation curves were compacte to 96 an 98 percent of maximum ry ensity, respectively. Blene resilient moulus specimens representing the lower specification curves of DGA an Crushe Stone Base were compacte to relative ensities of about 100 percent, or to a very ense state. Relative ensities of specimens of No. 57 aggregate range from about zero to 100 percent. Relative ensities of River Gravel specimens range from about 4 to 100 percent. The recycle concrete specimens were compacte to relative ensities ranging from zero to a value greater than 100 percent. That is, the ry ensity of one specimen (RECON ) exceee by about 10.4 lbs/ft 3 the maximum ry ensity obtaine from the shaker table test. For the other specimens of this material, the relative ensities range from zero to about 100 percent. Testing Equipment RESILIENT MODULUS TESTING The resilient moulus testing equipment, Figure 15, locate at the University of Kentucky Transportation Center, is a moel RMT-1000, obtaine from the Structural Behavior Engineering Laboratories, of Phoenix, Arizona. The system consists of a pressure control panel, plexiglass triaxial cell, a hyraulic power supply, an a computer an software for controlling the testing of a resilient moulus specimen. The system is a complete, close-loop, servo hyraulic triaxial testing system. The equipment esign shown in Figure 16 eliminates the nee for a large loaing (reaction) frame. The base an top of the triaxial cell is constructe of stainless steel. The chamber is plexiglass, or acrylic plastic, as shown in Figure 16. The cell is rate to withstan a confinement stress of 150 psi. The triaxial chamber accommoates aggregate specimens measuring 6 inches in iameter an 12 inches in height. A loa actuator, as shown in Figures 16 an 17, applies repeate loas. A close-up view of the loa actuator is shown in Figure 17. Various loa forms of ifferent shapes are available for applying loaing sequences. An overhea crane was installe to lift an place the loa actuator on the large, specially esigne, triaxial cell. The triaxial system has self-containe internal transucers. The triaxial testing cell rests on a massive concrete block. System Components The servo controller is a Moel with ual AC/DC feeback signal conitioning for loa an eformation transfer. The signal conitioning system is a series 5 moel 300, 4- channel for 2 internal LVDT s an 2 pressure transucers. A view of the LVDTs mounte internally, on the sies of a specimen, is illustrate in Figure 18. A loa cell is mounte at the base of the specimen in the triaxial chamber. The porous stone is mounte flush in the base, as shown in Figure 18. The LVDT Transucer calibrator is a Moel 139. It has a 1-inch travel range an a resolution of inches. The loa cell, pressure transucer, an pore pressure transucer are calibrate using shunt calibration with preset resistance.

38 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 16 RESILIENT MODULUS TESTING EQUIPMENT Computer Software Control Loa Actuator Plexiglass Chamber Aggregate Specimen: Diameter = 6 in. Height = 12 in. Loa Actuator Hyraulic Power Supply Pressure Control Panel Figure 15. View of resilient moulus testing equipment. Large Triaxial Chamber Overhea Crane Loa Actuator Figure 16. View of aggregate specimen in the triaxial chamber. Figure 17. View of loaing actuator.

39 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 17 Aggregate Specimen: 6 x 12 Internal LVDT Porous Stone (Mounte Flush-into peestal) Internal Loa Cell Compaction of Aggregate Specimens After measuring the exact amounts of aggregate an water to form an aggregate specimen of a pre-selecte ry ensity an moisture content (Hopkins an Beckham, 1993; Hopkins et al., 1995; Hopkins et al., 2002), the material was compacte in increments of about 2 to 3 inches in a split mol, as shown in Figure 19. A proctor hammer was use to compact the specimen in small increments. Material that sometimes remaine after the specimen mol ha been compacte was weighe. On some occasions, a small amount of material remaine in the pan. That is, not all of the material coul be place in the mol. However, this i not occur too frequently. The actual ry ensity an moisture content was base on measuring the weight an moisture content of the material after the test. Resilient Moulus Testing Protocol In the resilient moulus testing reporte herein, essential elements of AASHTO T (1996)- 20 th eition- an T (2003)-24 th Eition- were followe. However, there were two major exceptions. The loa cell an LVDTs were not locate externally, as shown by the latter stanar. Rather the loa cell an LVDTs were locate internally, as shown in Figure 18 an in the former stanar above. Consiering that extremely small strains are involve in testing Compaction of Specimen aggregate specimens, internal location of the LVDTs ais in eliminating system strains. By locating the loa cell internally, DGA Large Split Mol errors ue to friction of the piston Thick Membrane are eliminate. Both AASHTO T an T specify a conitioning cycle to be applie to the aggregate specimen. In the former stanar, the conitioning sequence consiste of 1000 loa applications. The eviator stress an the confining stress are hel at 15 psi an 20 psi, respectively, uring conitioning. In AASHTO T , loa Concrete Peestal Figure 18. LVDTs an loa cell are mounte insie triaxial cell. Vacuum Line Figure 19. Placing aggregate an compaction of a specimen in a split mol.

40 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 18 applications are specifie an the eviator an confining stress are hel at 15 psi. Specimen conitioning is intene to eliminate the effects of initial permanent eformation an specimen loaing imperfections an not cause permanent plastic eformation. The other exception in this stuy consiste of applying only 200 loa applications in the conitioning sequence instea of the 500 to 1000 loa applications specifie by AASHTO T The loaing sequence is illustrate in Table 7. Use of 200 loa applications was an effort to avoi estroying the integrity of the specimens before applying testing sequences. Using too many loa applications in the conitioning stage runs the risk of causing unrecoverable eterioration of the specimens before the actual testing begins because of high stress levels an the lengthy testing cycle of the proceure. Deviator an confining stresses were equal to 15 psi. After placing the remole specimen in a triaxial assembly, Figures 16 through 18, repeate loas were applie. In the proceure, 16 loa sequences are use. The first test sequence involve the conitioning phase. After the conitioning sequence, 100 loa applications were use for each subsequent loa sequence. The average recovere eformations for each LVDT are recore at the last five cycles. The computer ata acquisition system recors the mean eviator loa an the mean recovere eflection. The system then calculates the mean resilient moulus by iviing the mean resilient strain by the applie eviator stress. The specimen is loae using a haversine shape loa form. The loa pulse is in the form, (1- cos (x))/2, as shown in Figure 20. A Haversine stress pulse was chosen because it better represents the shape of a truck loaing on pavement an similar to the loa pulse applie by nonestructive testing evice, that is, the Falling Weight Deflectometer (FWD). The magnitue of the cyclic loa is varie to measure the behavior in aggregate stiffness, or moulus. Before instrumenting the sample, it was visually checke for uniformity an suspecte samples were rejecte. A view of a resilient moulus test in progress is shown in Figure 21. REVIEW OF MATHEMATICAL MODELS FOR RELATING RESILIENT MODULUS AND STRESSES Mathematically, resilient moulus, M r, has been efine as: where M r a =, (5) a ε = 1 3 = eviator stress, 1 = major principal stress, 3 = minor principal stress, an ε = axial strain recoverable after release of the eviator stress. Deformation properties of aggregates are not constant. They are etermine by both intrinsic properties of soils an the stresses applie to the soils. A number of mathematical moels have been propose for moeling the resilient moulus of soils an aggregates. Most mathematical expressions relate resilient moulus, the epenent variable, to one inepenent variable, either the eviator stress,, or confining stress, 3, or the sum of principle stresses, sum (= ), or the

41 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 19 Table 7. Testing stresses. Sum of Confining the Stress, or Major Principl Cell Deviator Principle e Pressure Stress, Stress, Stresses Number Test 3 1, θ of Sequence (psi) (psi) (psi) (psi) Cycles 1 Conitioning M r is calculate by averaging cycles The number conitioning cycles specifie by in AASHTO T ranges is In this stuy 200 conitioning loa cycles were use. Maximum applie Loa Factor (%) HAVERSINE PHASE SHIFT FROM SINE WAVE 1-COS(X) Performing Resilient Moulus Test 2 Loa Rest 0.1 s 0.9 s Figure 20. Haversine loaing form. Computer Controlle Aggregate Specimen Diameter = 6 inches Height = 12 inches Time (Sec.) Loa 0.1 s Rest Figure 21. Resilient moulus test in progress.

42 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 20 two inepenent variables, an 3. Some wiely publishe resilient moulus moels are examine below. As shown by this review an analysis of available moels, only the later four moels are use in the analyses of resilient moulus ata reporte herein. Moossazaeh an Witczak (1981) referre to hereafter as Moel 1--propose the following relationship for presenting resilient moulus ata: M r = k 1 p a k2, (6) where k 1 (y-intercept) an k 2 (slope of the line) are coefficients obtaine from a linear regression analysis an p a is a reference pressure. In this moel, the effect of the confining stress is not consiere. Dunlap (1963)--Moel 2-- suggests the following relationship: M r k 3 = k1 p a 2, (7) where k 1 an k 2 are regression coefficients an 3 is the confining stress. The influence of the eviator stress is ignore in this relationship. See et al. (1967)--(Moel 3)-- suggests that the resilient moulus is a function of the sum of the principle stresses, or M r = k1 p sum a k 2. (8) The term, sum, is the sum of principal stresses ( ), or for the triaxial compression case, the term is equal to ( ). This expression appears in the AASHTO Pavement Design Guie (1993) an in the testing stanar, AASHTO T (2000). Relationships given by Equations 6 an 7 o not consier the effect of shear stress on the resilient moulus of soils. May an Witczak (1981) an Uzan (1985) --Moel 4--propose another moel that consiers the effects of shear stress, confining stress, an eviator stress, or M r = k1 p sum a k 2 pa k 3. (9) The terms, k 1, k 2, an k 3, are correlation regression coefficients. Uner ientical loaing ( = = ), Uzan s moel will lea to a value of M r that either goes to zero when the 1 2 3

43 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 21 coefficient, k 3 >0, or, M r will become infinite in the case of k 3 <0. In all of the moels cite above, a regression fit can be mae for a selecte confining stress. However, when the confining stress changes, the coefficients change. Another resilient moulus moel propose in 2002 (Ni, B., Hopkins, T. C., an Sun) an 2001 (Hopkins, T. C., Beckham, T. L., Sun, L., an Ni, B.), an referre herein as Moel 5, is as follows: M r 3 = k1 pa + 1 k 2 pa 1 + k 3. (10) In this moel, the coefficients, k 1 an k 2, will always be positive. For most situations the coefficient, k 3, is negative for soils an aggregates. As shown by the relationship given by Equation 10, the resilient moulus increases as the confining stress increases. The moulus will increase or ecrease, as in most cases, with the increase of shear stress. When both 3 an approach zero, the value of resilient moulus, M r, approaches the value of k 1, which is the initial resilient moulus value an a property of the soil. How the resilient moulus of soils changes from its initial value epens on the stress path an the stress state applie to the soil mass. The coefficients, k 1, k 2, an k 3, are erive from test ata using multiple correlation regression analysis (See Appenix A). Another mathematical expression appears in a summary pamphlet prepare by the research team for stuy NCHRP (National Cooperative Highway Research Program) Project 1-28A (Halin, 2001) Moel 6. This relationship is, as follows: M r = k1 p sum a k 2 τ p oct a 1 + k 3, (11) where: sum = sum of all orthogonal normal stresses acting at a given point (or as liste in the summary, sum is efine using the symbol, θ, which is efine as the bulk stress). τ = Octaheral shear stress acting on the material, or oct τoct = ( ( 1 2 ) + ( 2 3) + ( 3 1). (12) 2 Equation 11 represents the more general case, that is, 2 is not equal to 3. If 2 equals 3, then Equation 12 becomes τ = ( ) = ( ) = = eviator stress oct

44 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 22 an Equation 11 becomes M r = k1 p sum a k 2 pa 1 + k 3. (13) Equations 9 an 10 (Moels 4 an 5) are base on the assumption that the normal stresses, 2 an 3, are equal an represent a specific case (triaxial case). If 2 is not equal to 3, then Equations 9 an 10 may be written for the more general case, or M r = k1 p sum a k 2 τ p oct a k 3, (14) an M r 3 = k1 p a + 1 k2 τ p oct a 1 + k3. (15) Consequently, Equations 9 an 10 become Equations 14 an 15. In the resilient moulus test, the intermeiate principal stress, 2 is equal to the minor principal stress, or confining stress, 3, an the sum of the principal stresses, θ, or = + + = + 2. (16) sum The eviator stress is efine as = 1 3 an solving for the major principal stress, = +. (17) 1 3 Inserting Equation 17 into Equation 16, the sum of the principle stresses may be efine (for the triaxial case)

45 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 23 θ = + 2 = ( + ) + 2 = + 3 (18) The sum of the principle stresses appears in the resilient moulus moel equations, Equations 9 an 11, propose by Uzan an NHCRP. Values of the sum of the major principal stresses an the major principal stresses, 1, corresponing to testing stresses, the confining stress, 3 an the eviator stress, are shown in Table 7. The various moels propose for characterizing the resilient moulus of granular materials are summarize tin Table 8. Table 8. Summary of Propose Resilient Moulus Moels. Moel Number 1 Reference Inepenent variable Equation Moossazaeh an Witczak (1981) (Deviator stress) 2 Dunlap (1963) 3 (Confining Stress) M M k2 r = k1 pa r k2 3 = k1 p a 3 See, H.B., Mitry, F. G., Monosmith, C. L, an Chan, C. K. (1967) sum (Sum of the Principle Stresses) M r = k1 p sum a k2 4 Uzan (1985) May, R.W. an Witczak, M. W.; (1981). sum, k2 k3 sum M r = k1 p a pa 5 UKTC (Ni, Hopkins, an Sun, 2002), 3 k2 k3 3 M r = k p + a p a 6 NCHRP (National Cooperative Highway Research Program) Project 1-28A Halin, 2001) sum, τ oct M r = k1 p sum a k2 τ p oct a 1 + k3 or, if 2 = 3, then, sum\ or M r = k1 p sum a k2 pa 1 + k3

46 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 24 Multiple Correlation Analysis TEST RESULTS AND ANALYSIS In the relationships expresse by Equations 6, 7 an 8 (Moels 1, 2, an 3), respectively, only two variables are involve, as shown in Table 8. The resilient moulus is a epenent variable while either, the eviator stress, confining stress, or the sum of the principle stresses is an inepenent variable. Consequently, only simple correlation analysis can be performe on those equations. The relation propose by Moel 3 was applie to the experimental ata obtaine from the ifferent materials because it is a simpler moel than the more complex relations expresse by Moels 4, 5, an 6 (Equations 9, 10, an 11). Moel 3, (Equation 8) is a linear moel between the logarithms of the resilient moulus an sum of the principle stresses. Although the DGA Specimen M r equation for Moel 3 contains only one inepenent Multiple variable, θ, the confining stress, Regression 3, an the eviator stress,, Analysis are inclue in the θ -term. It can be presente conveniently in a two-imensional graph, whereas the results of Moels 4, 5, an 6 must be presente in a three-imensional graph, as 3 iscusse below. Results of Moel 3 analysis were inclue herein an compare to results obtaine from Moels 4, 5, an 6 In the testing proceure, however, the value of resilient moulus is an inepenent variable an a function of two inepenent variables, the confining stress, 3, an the eviator stress,. Moels 4, 5, an 6, expresse by Equations 9, 10, an 11, respectively, involve two inepenent variables. The resilient moulus is the epenent variable an the sum of the principle stresses an eviator stress are inepenent variables in Moel 4. In Moel 5, the resilient moulus is the epenent variable while the eviator stress an confining stress are inepenent variables. In Moel 6, the resilient moulus is the epenent variable an the sum of the principle stresses an the eviator stresses are the inepenent variables. Hence, the regression equations of the three moels represent a regression plane in a three-imensional rectangular coorinate system, as illustrate in Figure 22. Resilient Moulus Test Data an Regression Coefficients of Moels 3, 4, 5, an 6 In the multiple regression correlation analysis of Moels 4, 5, an 6, all values of M r obtaine at the 15 selecte testing stresses (See Table 7) were use, collectively, to obtain the coefficients, k 1, k 2, an k 3 of the multiple regression plane, as illustrate in Figure 22. The coefficient of multiple Figure 22. Example illustrating the three-imensional plane of Moel 5 an selecte testing stress points.

47 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 25 correlation, R 2, was etermine for each of the tests an for each moel. This coefficient escribes how well the testing points fit the regression plane. Multiple regression coefficients, k 1, k 2, an k 3 were etermine for the compacte aggregates an all of the materials in this manner. The multiple regression equations use to obtain the coefficients, k 1, k 2, an k 3 are given in Appenix A. Multiple regression coefficients, k 1, k 2, an k 3 etermine from Moels 4, 5, an 6, for the compacte aggregates an other materials are summarize in Tables 9 an 10. Coefficients, k 1 an k 2, obtaine from linear regression analysis using Moel 3 are also inclue in the summary tables. Dry ensities an moisture contents of each specimen were liste in Tables 4 an 5. Values of R 2 of the four moels (3, 4, 5, an 6) are also liste. Percentile test values as a function of R 2 for Moels 3, 4, 5, an 6 are compare in Figure 23. Excluing R 2 -values of the asphalt rainage blanket an PVC tests, the average R 2 -values obtaine from Moels 4, 5, an 6 for the aggregate materials were ientical, or numerically equal to The average R 2 - value for Moel 3 was equal to Obtaining large values of R 2 inicates that the testing equipment was very stable, operator error was not pronounce, an the moel equations consistently provie a goo means of fitting the Percentile Test Value NCHRP-Moel 6 UKTC-Moel 5 UZAN-Moel 4 See et al.,(1967)-moel 3 See Uzan UKTC NCHRP Figure 23. Comparisons of R 2 -values obtaine from regression analysis using Moels 3, 4, 5, an 6. regression plane. Resilient moulus moels propose by Uzan, UKTC, an NCHRP are nonlinear material moels. Practically, when any nonlinear material moel is built into a numerical analyzing program an iteration proceure will be use as the metho of solution. Although the average R 2 -values of Moels 4, 5, an 6 were ientical, situations may arise where values of the resilient moulus compute from Moels 4 an 6 may iverge. This case may happen on the pavement surface area locate away from the loaing location. It coul represent a potential problem when the moels may be applie in nonlinear analyses. For example, whenever the coefficient k 2 or k 3 is negative in Uzan s moel (Moel 4), an sum or approaches zero, the resilient moulus may iverge, or become very large. This situation is illustrate epicte in Figure 24. In the case of a small value of, a normal situation for an area locate away from the loaing area, M r may become unstable. In the test ata shown in Tables 9 an 10 for the granular materials inclue in the testing program, all of the k 2 - coefficients from Uzan s moel were positive. However, all of the k 3 -coefficients were negative for that moel. R 2

48 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 26 Table 9. Coefficients k i an R 2 of aggregate samples for four ifferent resilient moulus moels Sample 1 See et al. Moel 3 Uzan's Moel 4 UKTC Moel 5 NCHRP Moel 6 k 1 k 2 R 2 k 1 k 2 k 3 R 2 k 1 k 2 k 3 R 2 k 1 k 2 k 3 R 2 DGA DGA DGAVULLEX DGAVULLEX DGAVULLEX DGAVULLEX DGAUPPER DGACENTER DGALOWER CSBUPPER CSBCENTER CSBLOWER No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX ; DGA Dense Grae Aggregate; No. 57 Number 57 crushe limestone

49 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 27 Table 10. Coefficients k i an R 2 of aggregate samples for four ifferent Resilient Moulus Moels (Continue). Sample 1 See et al. Moel 3 Uzan's Moel 4 UKTC Moel 5 NCHRP Moel 6 k 1 k 2 R 2 k 1 k 2 k 3 R 2 k 1 k 2 k 3 R 2 k 1 k 2 k 3 R 2 RGRAV RGRAV RGRAV RGRAV RGRAV RGRAV RECON RECON RECON RECON RECON RECON RECON ADB PVC PVC PVC PVC PVC CSB Crushe Stone Base; RGRAV River Gravel; RECON Recycle Concrete; ADB Asphalt Drainage Blanket; PVC Polyvinyl Chlorie

50 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 28 M(psi) Uzan (Moel 4) sum (psi) Specimen DGA r M k2 k3 sum r = k1 pa pa sum or 0 k 2 or k 3= -value M Diverges r (psi) Figure 24. Regression plane of Moel 4 an potential ivergence problems at small stresses. sum or 0 k 2 = -value M Diverges r M(psi) r M NCHRP (Moel 6) r = k1 p sum a k2 pa 1 + k3 When k 2 is negative in the NCHRP moel an sum becomes small, or approaches zero, M r may become large an iverge. This potential problem is illustrate in Figure 25. It shoul be note, however, that for granular materials inclue in the testing program all k 2 -coefficents 1 were positive, as shown in Tables 8 an 9. In the UKTC Moel, when the values, 3 an become small, or approach zero, the value of M r approaches the value of k 1. As illustrate in Figure 26, the value of Mr approaches a point in the three-imensional graph. If 3 is not equal to zero an approaches zero, then M r is a line in the M r - 3 plane. The value of M r approaches the term, k2 3 k pa sum (psi) (psi) Specimen DGA Figure 25. Regression plane of Moel 6 an potential ivergence problems at small stresses. If is not equal to zero an 3 approaches zero, then M r is a line in the M r - plane. The value of M r approaches the term, k pa k. In any of the three cases liste above, M r converges to a value an remains stable. 1 On rare occasions, negative values of k 2 obtaine from the NCHRP moel have been observe for resilient moulus tests performe on compacte specimens of soil. Negative k 2 -coefficients were obtaine for two cases of 68 unsoake (or as compacte ) specimens that were teste. Negative k 2 -coefficients were also obtaine for two cases of 60 soake compacte specimens that were teste. Multiple coefficients of correlations of those four specimens were 0.930, 0.958, 0.650, an 0.993, respectively.

51 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 29 Coefficients of correlation inicate that Moels 4, 5, an 6 best escribes variation of the resilient moulus. An average value of R 2 obtaine from each moel was equal to If a slightly lower error may be tolerate, then Moel 3 coul be use, provie ivergence of M r. given by the moel equation is not a problem. An average value of R 2 was only slightly less than Typical graphical relations from Moel 3 of M r as a function of for sum DGA specimens are shown in Figures 27 an 28. Similar results may be obtaine for the other aggregates. Some ata scatter is evient, as shown in the figures. Negative values of k 2 obtaine from Moel 3, which coul cause M r to iverge, were not observe for the granular materials inclue in this testing program.. Numerical values of resilient moulus preicte by Moels 3, 4, 5, an 6 are compare in Tables 11, 12, an 13. Average values of resilient moulus obtaine for the granular materials for the selecte stresses, 3 an are Resilient Moulus,M r (psi) DGA Graation Specification Limits R 2 = DGAUPPER (psi) DGACENTER 61-1 DGALOWER 62-1 an 0; M Sum of Principle Stresses, 3 r Converges to k1 sum (psi) Figure 27. Results of Regression analyses from Moel 3 for DGA specimens blene an remole to graation specification limits. M r k pa = k + M(psi) r shown in those tables. Values of M r were compute at three selecte stresses of 3 an, as shown in the three tables. The values of stresses selecte for comparative purposes represent low, about mirange, an high values of 3 an liste previously in Table 7. UKTC (Moel 5) Specimen DGA (psi) Values of sum which appear in Moels 4 an 6 were compute from stresses selecte for 3 an using Equations 16, 17, an 18. Percentage ifferences of average numerical values (shown in Tables 11, 12, an 13) of resilient moulus obtaine from Moels 3, 4, 5, an 6 are summarize in Table 14. k2 3 M r = k1 + 1 p a k3 1 1 pa Mr = k + k3 1 p + a Figure 26. Regression plane of Moel 5. As or 3 approaches zero, M r converges to the constant, k 1.

52 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 30 Resilient Moulus,M r (psi) DGA DGA DGA DGA DGA DGA DGA As Receive R 2 = sum Sum of Principle Stresses, (psi) Figure 28. Results of regression analyses from moel 3 for remole DGA specimens of as receive aggregate. Percentages ifferences of the average resilient moulus values (granular materials) obtaine from the ifferent moels are shown relative to the average value of resilient moulus obtaine from Moel 5 (UKTC). Average values of resilient moulus from Moel 3 range from 7.6 percent larger an 10.5 percent smaller than average values of resilient moulus from Moel 5. Average values of resilient moulus from moel 4 range from 0.3 to 3.7 percent smaller than values obtaine from Moel 5. Average values of resilient moulus from Moel 6 range from 0.3 to 5 percent smaller than values from Moel 6. Moels 4, 5, an 6 yiele very similar values of resilient moulus for the range of selecte stresses. Storage an Accessibility of Values of Resilient Moulus of Compacte Aggregates All resilient moulus test ata pertaining to the compacte aggregate specimens resies in the Kentucky Geotechnical Database (Hopkins et al., 2005). The program, using this atabase, is in a client/server Winows environment an the atabase resies on a prouction server of the Kentucky Transportation Cabinet. Values of resilient moulus in the atabase are reaily available to personnel of the Kentucky Transportation Cabinet statewie. All key istrict an central office personnel can access the ata through the client-server network. Users have two means of accessing ata on the client-server application in the Geotechnical Database. After the user logs on (Figure 29), the graphical user interface (GUI) shown in Figure 30 appears. By clicking on Engineering Application, another menu appears as shown in Figure 31. After clicking on Resilient Moulus, the GUI screen in Figure 32 appears. By clicking on an aggregate type uner Sample Information, shown in the left-han portion of Figure 32, twoimensional plots of resilient moulus as a function of a selecte stress component appears. In the current analytical version, values of resilient moulus for a selecte specimen may be plotte as a

53 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 31 Table 11. Comparison of numerical values of M r obtaine from Moels 3, 4, 5, an 6 an calculate at stresses of 3 = 3 an = 3. Moel 3 Moel 4 Moel 5 Moel 6 Sample Description Dense Grae Aggregate (DGA) As Receive Specification Limits Crushe Stone Base No. 57 Stone River Gravel As Receive Repeats Recycle Concrete Sample Number See s Moel sum = 12 psi Uzan s Moel sum = 12 psi = 3 psi UKTC 3 = 3 psi = 3 psi NCHRP sum = 12 psi = 3 psi Resilient Moulus, M r (psi) DGA DGA DGAVULLEX DGAVULLEX DGAVULLEX DGAVULLEX DGAUPPER DGACENTER DGALOWER CSBUPPER CSBCENTER CSBLOWER No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX RGRAV RGRAV RGRAV RGRAV RGRAV RGRAV RECON RECON RECON RECON RECON RECON RECON Average Mr-Values (Granular Materials) Asphalt Drainage Blanket ADB PVC PVC PVC Cyliner PVC PVC PVC

54 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 32 Table 12. Comparison of numerical values of M r obtaine from Moels 3, 4, 5, an 6 an calculate at stresses of 3 = 10 an = 20. Sample Description Dense Grae aggregate (DGA) As Receive Specification Limits Crushe Stone Base No. 57 Stone River Gravel As Receive Repeats Recycle Concrete Sample Number Moel 3 See s Moel sum = 50 psi Moel 4 Uzan s Moel sum = 50 psi = 3 psi Moel 5 UKTC 3 = 10 psi = 20 psi Resilient Moulus, M r (psi) Moel 6NCHRP Moel 6 sum = 50 psi = 3 psi DGA DGA DGAVULLEX DGAVULLEX DGAVULLEX DGAVULLEX DGAUPPER DGACENTER DGALOWER CSBUPPER CSBCENTER CSBLOWER No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX RGRAV RGRAV RGRAV RGRAV RGRAV RGRAV RECON RECON RECON RECON RECON RECON RECON Average Mr-Values (Granular Materials) Asphalt Drainage Blanket ADB PVC Cyliner PVC PVC PVC PVC PVC

55 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 33 Table 13. Comparison of numerical values of M r obtaine from Moels 3, 4, 5, an 6 calculate at stresses of 3 = 20 an = 40. Sample Description Dense Grae aggregate (DGA) As Receive Specificatio n Limits Crushe Stone Base No. 57 Stone River Gravel As Receive Repeats Recycle Concrete Sample Number Moel 3 Moel 4 See s Moel Uzan s Moel sum = 100 psi sum = 100 psi = 40 psi Moel 5 UKTC 3 = 20 psi = 40 psi Resilient Moulus, M r (psi) Moel 6NCHRP Moel 6 sum = 100 psi = 40 psi DGA DGA DGAVULLEX DGAVULLEX DGAVULLEX DGAVULLEX DGAUPPER DGACENTER DGALOWER CSBUPPER CSBCENTER CSBLOWER No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX No57VULLEX RGRAV RGRAV RGRAV RGRAV RGRAV RGRAV RECON RECON RECON RECON RECON RECON RECON Average Mr-Values (Granular Materials) Asphalt Drainage Blanket ADB PVC Cyliner PVC PVC PVC PVC PVC

56 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 34 function of either the confining stress, 3, the eviator stress,, or the sum of the principle stresses, sum. In Figure 32, the resilient moulus is shown as a function of the eviator stress. By clicking Check Moel, the user may select a moel type from a ropown menu an graph the ata. Coefficients (k 1, k 2, or k 3 ) of each moel equation are isplaye at the bottom of the GUI screen in Figure 32. Each time the user clicks on a specimen number in the left-han portion of Figure 32, multiple regression analysis is automatically performe using the three ifferent moels shown in the right-han portion of Figure 32. The coefficients of each moel are isplaye for each three-imensional plane. Multiple regression equations use in the atabase are presente in Appenix A. The user may also recall an isplay resilient moulus test ata by clicking Data uner the Show button on a ropown menu, as illustrate in Figure 33. In this case, the ata are isplaye as shown in that figure; an enlarge view of the summary ata is isplaye in Figure 34. The tabulations show the specimen number, sequence number, values of resilient moulus for each test sequence, the confining stresses, 3, the eviator stresses,, an the sum of the principle stresses,, for each test sequence. Although the Table 14. Comparison of average values of resilient moulus an percent ifference relative to Moel 5 for granular materials inclue in the testing program. Moel 3 = 3 psi Percent 3 = 10 psi Percent 3 = 10 psi Percent Difference Difference Difference = 3pi = 20 psi = 20 psi sum = 12 sum = 50 psi sum = 50 psi M r (psi) M r (psi) psi M r (psi) See (Moel 3) Uzan (Moel 4) UKTC (Moel 5) NCHRP (Moel 6) sum ata for each aggregate specimen shown in Figure 34 resies in the Kentucky Geotechnical Database, the summary ata for each specimen are also given in Appenices B through H. If the user chooses to view the entire test ata recor of resilient moulus of a selecte specimen in the atabase, then the following proceure is available: Figure 29. User log-on graphical user interface screen for gaining access to the Kentucky Geotechnical Database an resilient moulus ata.

57 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 35 Figure 30. Main menu of the Kentucky Geotechnical Database. Figure 31. Gaining access to resilient moulus test results for compacte soils an aggregates in the Kentucky Geotechnical Database.

58 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 36 Figure 32. Graphical user interface showing resilient moulus as a function of eviator stress for a selecte type of aggregate. Figure 33. Display of resilient moulus summary ata in the atabase.

59 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 37 Figure 34. View of resilient moulus test ata for a selecte aggregate specimen. In the atabase s main menu, Figure 30, the user clicks on Search Existing ata. When this event is execute, a GUI (Graphical User Interface) screen appears as shown in Figure 35. All resilient moulus ata of aggregates are store in a site labele Consequently, the number 4531 will appear in all aggregate specimen ientification numbers, as shown in Figure 32. Using the row number (or site number) shown in Figure 34 ( 4531 ), an inserting this number into the box labele Site Row Number in the GUI shown in Figure 35, an clicking the search button, a GUI screen appears, as shown in Figure 36. Clicking on Samples in the upper right-han corner of Figure 36, listings of specimen numbers appear in the lower right-han corner of this figure. By ouble-clicking on any esire specimen number in the lower right-han corner of Figure 36, the GUI screen shown in Figure 37 appears. By clicking the Properties tab in Figure 37, the GUI screen shown in Figure 38 appears. Clicking on the foler labele Resilient Moulus obtains etaile resilient moulus ata for a selecte specimen number, as illustrate in Figure 39.

60 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 38 (Insert Row Number) Figure 35. GUI screen for searching ata. (Open Foler) (Double Click) Figure 36. Gaining access to resilient moulus test recor for a selecte specimen in the Kentucky Geotechnical Database.

61 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 39 (Click) Figure 37. GUI screen for accessing the complete resilient moulus test ata. (Click) Figure 38. GUI screen for obtaining etaile resilient moulus test ata.

62 Resilient Moulus of Compacte Crushe Stone Aggregate Bases--Hopkins, Beckham, an Sun UKTC 40 (Open Foler) Figure 39. Complete resilient moulus test recor for a selecte aggregate specimen. Variation of Resilient Moulus an Dry Density Because ry ensities of ifferent types of aggregates vary in the fiel, numerous resilient moulus tests were performe on selecte aggregate types to etermine the effect of the variation of ry ensity on the values of resilient moulus. Aggregate types inclue Dense Grae Aggregate, Crushe Stone Base, No. 57 Stones, River Gravel, an Recycle Concrete. Resilient moulus test results obtaine for specimens of the ense grae aggregate (as receive from the proucer) compacte at ifferent ry ensities are shown in Figure 40. Values of resilient moulus shown in Figure 40 are those obtaine from Moel 5 (UKTC), which are liste Tables 11, 12, an 13. The maximum ry ensity an optimum moisture content (Figure 9) of this well grae material were lbs/ft 3 an 6.8 percent, respectively. In this plot, resilient moulus values of DGA specimens were calculate at three selecte stress conitions an graphe as a function of ry ensity. The percent of maximum ry ensity of this series of tests range from 72 to 100. For example, the highest an lowest values of M r observe for specimen DGA were 65,554 an 14,657 psi, respectively. Dry ensity an moisture content of this specimen were an 5.9 percent, respectively. The specimen ha been compacte at 93 percent of maximum ry ensity. As shown in Figure 40, the resilient moulus values change slightly as the percent of maximum ry ensity increase from 72 percent (103.6 lbs/ft 3 ) to about 96 percent (136.6 lbs/ft 3 ). However from about 96 percent of maximum ry ensity to 100 percent of maximum ry ensity (142.2 lbs/ft 3 ) a sharp increase occurre in the values of resilient moulus. For example, from 72 percent to about 96 percent, the resilient moulus of the lower curve in Figure 40 increases only approximately 4 percent. From about 96 percent to 100 percent of maximum ry ensity the M r -value increases about 37 percent. The M r -value of the upper curve increases about 7 percent when the percent of