Estimation of Resilient Modulus Model Parameters for Different Soil Types, Study notes of Design

Download Estimation of Resilient Modulus Model Parameters for Different Soil Types and more Study notes Design in PDF only on Docsity! W is co n si n H ig h w ay R es ea rc h P ro g ra m Determination of Typical Resilent Modulus Values for Selected Soils in Wisconsin SPR# 0092-03-11 Hani H. Titi, Mohammed B. Elias, and Sam Helwany Department of Civil Engineering and Mechanics UW-Milwaukee May 2006 WHRP 06-06 Wisconsin Highway Research Program Project ID 0092-03-11 Determination of Typical Resilient Modulus Values for Selected Soils in Wisconsin Final Report Hani H. Titi, Ph.D., P.E. Associate Professor Mohammed B. Elias, M.S. Graduate Research Fellow and Sam Helwany, Ph.D., P.E. Associate Professor Department of Civil Engineering and Mechanics University of Wisconsin – Milwaukee 3200 N. Cramer St. Milwaukee, WI 53211 Submitted to The Wisconsin Department of Transportation May 2006 Abstract The objective of this research is to develop correlations for estimating the resilient modulus of various Wisconsin subgrade soils from basic soil properties. Laboratory testing program was conducted on common subgrade soils to evaluate their physical and compaction properties. The resilient modulus of the investigated soils was determined from the repeated load triaxial test following the AASHTO T 307 procedure. The laboratory testing program produced a high quality and consistent test results database. The high quality test results were assured through a repeatability study and also by performing two tests on each soil specimen at the specified physical conditions. The resilient modulus constitutive equation adopted by NCHRP Project 1-37A was selected for this study. Comprehensive statistical analysis was performed to develop correlations between basic soil properties and the resilient modulus model parameters ki. The analysis did not yield good results when the whole test database was used. However, good results were obtained when fine-grained and coarse-grained soils were analyzed separately. The correlations developed in this study were able to estimate the resilient modulus of the compacted subgrade soils with reasonable accuracy. In order to inspect the performance of the models developed in this study, comparison with the models developed based on LTPP database was made. The LTPP models did not yield good results compared to the models proposed by this study. This is due to differences in the test procedures, test equipment, sample preparation, and other conditions involved with development of both LTPP and the models of this study. iv Acknowledgement This research project is financially supported by the Wisconsin Department of Transportation (WisDOT) through the Wisconsin Highway Research Program (WHRP). The authors would like to acknowledge the WisDOT Project Research Committee: Bruce Pfister, Steven Krebs, and Tom Brokaw, for their guidance and valuable input in this research project. The authors also would like to thank Robert Arndorfer, WHRP Geotechnical TOC Chair for his support and Dennis Althaus for his effort and help in collecting soil samples. The research team would like to thank many people at UW-Milwaukee who helped in the accomplishment of the research project, namely: Joe Holbus who manufactured the special compaction molds, Jaskaran Singh who helped in performing experimental testing on different soils, Dan Mielke, who helped in soil properties testing, and Rahim Reshadi, who helped in various stages during the assembly of the dynamic materials test system. The effort and help of Adam Titi during the preparation of the report is appreciated. The authors would like to thank Dr. Marjorie Piechowski for the valuable comments on the final report. v Table of Contents Abstract…………………………………………………………………………………...... iv Acknowledgement………………………………………………………………………... v List of Tables……………………………………………………………………………….. viii List of Figures………………………………………………………………………............ x Executive Summary ………………………………………………………………………. xii Chapter 1: Introduction…………………………………………………………............... 1 1.1 Problem Statement………………………………………………………….. 1 1.2 Research Objectives……………………………………………………….... 2 1.3 Scope……………………………………………………………………….. 2 1.4 Research Report……………………………………………………………. 3 Chapter 2: Background…………………………………………………………………... 4 2.1 Determination of Resilient Modulus of Soils….………………………........ 4 2.2 Factors Affecting Resilient Modulus of Subgrade Soils……………………. 8 2.2.1 Soil Physical Conditions….…….………………………………….... 8 2.2.2 Effect of Loading Conditions ……………………………………….. 8 2.2.3 Other Factors Affecting Resilient Modulus of Subgrade Soils……… 9 2.3 Resilient Modulus Models ………………………………… ………………. 10 2.4 Mechanistic – Empirical Pavement Design ……………………………….. . 13 2.5 Soil Distributions in Wisconsin .……………………………………………. 14 Chapter 3: Research Methodology ………………………………………………………. 18 vi Table 4.19: Summary of t-statistics for regression coefficients used in resilient modulus model parameters for non-plastic coarse-grained soils……………………...….. 72 Table 4.20: Correlations between the resilient modulus model parameter k1 and basic soil properties for plastic coarse-grained soils….……………...................................... 74 Table 4.21: Correlations between the resilient modulus model parameter k2 and basic soil properties for plastic coarse-grained soils………………………………………... 74 Table 4.22: Correlations between the resilient modulus model parameter k3 and basic soil properties for plastic coarse-grained soils……………... ………………………... 75 Table 4.23: Correlation matrix of model parameters and soil properties for plastic coarse- grained soils …………………………………...……………................................ 79 Table 4.24: Summary of t-statistics for regression coefficients used in resilient modulus model parameters for plastic coarse-grained soils ……………...……………..… 79 ix List of Figures Figure 2.1: Repeated load triaxial test setup ( Instron 8802 dynamic materials test system)…………………………………………………………………………… 5 Figure 2.2: Definition of the resilient modulus in a repeated load triaxial test …………… 6 Figure 2.3: Schematic of soil specimen in a triaxial chamber according to AASHTO T 307 ………………………………………………………………………………………… 7 Figure 2.4: Wisconsin pedological soil groups (Hole, 1980) …………………………….. 15 Figure 2.5: Wisconsin Soil Regions, Madison and Gundlach (1993) …………………….. 17 Figure 3.1: Locations of the investigated Wisconsin soils………………………………… 19 Figure 3.2: Pictures of some of the investigated Wisconsin soils ....……………………… 20 Figure 3.3: The UWM servo-hydraulic closed-loop dynamic material test system used in this study ………………………………………………………………………… 22 Figure 3.4: Special mold designed to compact soil specimens according to AASHTO T 307 requirements ……………………………………………………………….. 24 Figure 3.5: Conditions of unit weight and moisture content under which soil specimens were subjected to repeated load triaxial test……………………...…………….. 25 Figure 3.6: Preparation of soil specimen for repeated load triaxial test……...…………... 26 Figure 3.7: Computer program used to control and run the repeated load triaxial test for determination of resilient modulus……………………………....……………… 27 Figure 4.1: Particle size distribution curve of Dodgeville soil……....……………………. 32 Figure 4.2: Results of Standard Proctor test for Dodgeville soil ....……………...………. 32 Figure 4.3: Particle size distribution curve of Antigo soil…….. ....………………………. 33 Figure 4.4: Results of Standard Proctor test for Antigo soil…... ....…………..…………... 33 Figure 4.5: Particle size distribution curve of Plano soil....……………………….………. 35 Figure 4.6: Results of Standard Proctor test for Plano soil ….....………………….……… 35 Figure 4.7: Particle size distribution curve of Kewaunee soil-1…………………......……. 36 Figure 4.8: Results of Standard Proctor test for Kewaunee soil-1………………..……….. 36 x Figure 4.9: Results of repeated load triaxial test on Antigo soil compacted at 95% of maximum dry unit weight (Jdmax) and moisture content more than wopt. (wet side)……………………………………………………………………………... 39 Figure 4.10: Results of repeated load triaxial test on Dodgeville soil compacted at maximum dry unit weight (Jdmax) and optimum moisture content (wopt.)…….. ... 41 Figure 4.11: Results of repeated load triaxial test on Dodgeville soil compacted at 95% of maximum dry unit weight (Jdmax) and moisture content less than wopt. (dry side)……............................................................................................................... 43 Figure 4.12: Results of repeated load triaxial test on Dodgeville soil compacted at 95% of maximum dry unit weight (Jdmax) and moisture content more than wopt. (wet side)....................................................................................................................... 45 Figure 4.13: The effect of unit weight and moisture content on the resilient modulus of the investigated soils……………………………………………………………. 49 Figure 4.14: The effect of the moisture content on the resilient modulus of the investigated soils ……………………………………………………………….. 50 Figure 4.15: Histograms of resilient modulus model parameters ki obtained from statistical analysis on the results of the investigated Wisconsin soils................... 45 Figure 4.16: Comparison of resilient modulus model parameters (ki) estimated from soil properties and ki determined from results of repeated load triaxial test on investigated fine-grained soils ………………………………………………….. 61 Figure 4.17: Predicted versus measured resilient modulus of compacted fine-grained soils……………………………………………………………………………... 65 Figure 4.18: Comparison of resilient modulus model parameters (ki) estimated from soil properties and ki determined from results of repeated load triaxial test on investigated non-plastic coarse-grained soils….................................................... 69 Figure 4.19: Predicted versus measured resilient modulus of compacted non-plastic coarse-grained soils …………………………………………………………….. 73 Figure 4.20: Comparison of resilient modulus model parameters (ki) estimated from soil properties and ki determined from results of repeated load triaxial test on investigated plastic coarse-grained soils ……………………………………….. 76 Figure 4.21: Predicted versus measured resilient modulus of compacted plastic coarse- grained soils.......................................................................................................... 80 Figure 4.22: Predicted versus measured resilient modulus of Wisconsin fine-grained soils using the mode developed in this study and the LTPP database developed models….………………………………………………………………………… 83 Figure 4.23: Predicted versus measured resilient modulus of Wisconsin non-plastic coarse-grained soils using the mode developed in this study and the LTPP database developed models……………………………………………………..... 84 Figure 4.24: : Predicted versus measured resilient modulus of Wisconsin plastic coarse- grained soils using the mode developed in this study and the LTPP database developed models ………………………………………………………………... 85 xi Chapter 1 Introduction 1.1 Problem Statement The design and evaluation of pavement structures on base and subgrade soils requires a significant amount of supporting data such as traffic loading characteristics, base, subbase and subgrade material properties, environmental conditions and construction procedures. Currently, empirical correlations developed between field and laboratory material properties are used to obtain highway performance characteristics (Barksdale et al., 1990). These correlations do not satisfy the design and analysis requirements since they neglect all possible failure mechanisms in the field. Also, most of these methods, which use California Bearing Ratio (CBR) and Soil Support Value (SSV), do not represent the conditions of a pavement subjected to repeated traffic loading. Recognizing this deficiency, the 1986 and the subsequent 1993 American Association of State Highway and Transportation Officials (AASHTO) design guides recommended the use of resilient modulus (Mr) for characterizing base and subgrade soils and for designing flexible pavements. The resilient modulus accounts for soil deformation under repeated traffic loading with consideration of seasonal variations of moisture conditions. A major effort was recently undertaken by the National Cooperative Highway Research Program (NCHRP) to develop Mechanistic-Empirical pavement design procedures based on the existing technology in which state of the art models and databases are utilized. The NCHRP project 1-37A: “Development of the 2002 Guide for Design of New and Rehabilitated Pavement Structures” was recently completed and the final report and software was published on July 2004. The outcome of the NCHRP project 1-37A is the “Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures,” which is currently undergoing extensive evaluation and review by state highway agencies across the country. Currently, the Wisconsin Department of Transportation (WisDOT) uses the AASHTO 1972 Design Guide for flexible pavement design in which the SSV is used to characterize subgrade soils. There is a need to adopt the mechanistic-empirical methodology for pavement design and rehabilitation in Wisconsin, which uses the resilient modulus to characterize subgrade soils. The mechanistic-empirical approach takes into account several important variables such as repeated loading, environmental conditions, pavement materials, and subgrade materials. The mechanistic-empirical pavement design should significantly reduce variations in pavement performance as related to design life and produce significant savings from reductions in premature failures and lower maintenance over the life cycle of the pavements (NCHRP Project 1-37A Summary, 2000 and 2001). Therefore, WisDOT is currently reviewing and evaluating the new guide for adoption and implementation in the design of pavement structures. The new mechanistic-empirical pavement design guide requires design input parameters that were not previously 1 evaluated by WisDOT for pavement design such as the resilient modulus of Wisconsin subgrade soils. However, conducting resilient modulus tests requires specialized and expensive equipment. In addition, the resilient modulus test is laborious and time consuming. These limitations signify the need for developing methodologies to reliably estimate the resilient modulus of Wisconsin subgrade soils based on correlations with fundamental soil properties. 1.2 Research Objectives The primary objective of this research project is to develop a methodology for estimating the resilient modulus of various Wisconsin subgrade soils from basic soil properties. The following specific objectives are identified for successful accomplishment of this research: 1. To conduct repeated load triaxial tests to determine resilient modulus of representative Wisconsin subgrade soils. WisDOT engineers and the research team will select these “typical” subgrade soils. The focus is on investigating the effect of soil type, soil physical properties, stress level, and environmental conditions on the resilient modulus of the selected soils. This work establishes a test result database that is used to develop correlations between various soil properties and the resilient modulus model parameters. 2. To develop and validate correlations (models) between soil properties and the resilient modulus model parameters. Applicability of theoretical and statistical methods for developing these correlations is investigated. 1.3 Scope The laboratory-testing program is conducted on selected soils that are considered representative of the soil distributions in Wisconsin. The repeated load triaxial test is conducted to determine the resilient modulus of the selected soils according to the standard procedure: AASHTO T 307. Other laboratory tests are conducted following standard test procedures that are used by WisDOT. The resilient modulus correlations with soil properties, that are developed and validated, are based on the results of the experimental testing program. 1.4 Research Report This report summarizes the research effort conducted at the University of Wisconsin- Milwaukee (UWM) to evaluate resilient modulus of common Wisconsin subgrade soils. A laboratory testing program was conducted on soils representative of the soil distributions of Wisconsin. Laboratory testing was conducted to evaluate basic properties and to determine the resilient modulus of the investigated soils. Comprehensive statistical analysis was performed to develop correlations between basic soil properties and the resilient modulus model input parameters. The resilient modulus model is the constitutive equation developed by NCHRP project 1-28A and adopted by the NCHRP project 1-37A 2 for the “Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures.” This report is organized in five chapters. Chapter One presents the problem statement, objectives and scope of the study. Background information on resilient modulus of subgrade soils is summarized in Chapter Two. Chapter Three describes the research methodology and laboratory-testing program conducted on Wisconsin subgrade soils. Chapter Four presents the test results, statistical analysis, and the models developed to estimate the resilient modulus of Wisconsin subgrade soils from basic soil properties. Finally, Chapter Five presents the conclusions and recommendations of the study. 3 S tr es s (V o r S tr ai n ( H D ev ia to r L o ad ( k N ) 0.1 0.9 Time (s) (a) Shape and duration of repeated load Resilient strain, H r Strain D ev ia to r st re ss , V d Plastic strain, H p Time (t) Stress (b) Stresses and strains of one load cycle Figure 2.2: Definition of the resilient modulus in a repeated load triaxial test 6 AASHTO T 307 requires a haversine-shaped loading waveform as shown in Figure 2.2a. The load cycle duration, when using a hydraulic loading device, is 1 second that includes a 0.1 second load duration and a 0.9 second rest period. The repeated axial load is applied on top of a cylindrical specimen under confining pressure. The total recoverable axial deformation response of the specimen is measured and used to calculate the resilient modulus. AASHTO T 307 requires the use of a load cell and deformation devices mounted outside the triaxial chamber. Air is specified as the confining fluid, and the specimen size is required to have a minimum diameter to length ratio of 1:2. Figure 2.3 shows a schematic of soil specimen in a triaxial chamber according to AASHTO T 307 requirements. Figure 2.3: Schematic of soil specimen in a triaxial chamber according to AASHTO T 307 7 2.2 Factors Affecting Resilient Modulus of Subgrade Soils Factors that influence the resilient modulus of subgrade soils include physical condition of the soil (moisture content and unit weight), stress level and soil type. Many studies have been conducted to investigate these effects on the resilient modulus. For example, Zaman (1994) reported that the results of the repeated load triaxial test depend on soil gradation, compaction method, specimen size and testing procedure. The effect of some of these factors on the resilient modulus of subgrade soils is significant. Li and Selig (1994) reported that a resilient modulus range between 14 and 140 MPa can be obtained for the same fine-grained subgrade soil by changing parameters such as stress state or moisture content. Therefore, it is essential to understand the factors affecting the resilient modulus of subgrade soils. 2.2.1 Soil Physical Conditions Research studies showed that the moisture content and unit weight (or density) have a significant effect on the resilient modulus of subgrade soils. The resilient modulus of subgrade soil decreases with the increase of the moisture content or the degree of saturation (Barksdale 1972, Fredlund 1977, Drumm et al. 1997, Huang 2001, Butalia 2003, and Heydinger 2003). Butalia et al. (2003) investigated the effects of moisture content and pore pressures buildup on the resilient modulus of Ohio soils. Tests on unsaturated cohesive soils showed that the resilient modulus decreases with the increase in moisture content. Drumm et al. (1997) studied the variation of resilient modulus with a post-compaction increase in moisture content. Soil samples were compacted at maximum dry unit weight and optimum moisture content; then the moisture content was increased. Investigated soils exhibited a decrease in resilient modulus with the increase in saturation. Heydinger (2003) stated that moisture content is the primary variable for predicting seasonal variation of resilient modulus of subgrade soils. The effect of unit weight on the resilient modulus of subgrade soils also has been largely investigated (e.g., Smith and Nair 1973, Chou 1976, Allen 1996, Drumm 1997). Test results indicated that the resilient modulus increases with the increase of the dry unit weight (density) of the soil. However, this effect is small compared to the effect of moisture content and stress level on resilient modulus (Rada and Witczak 1981). At any dry unit weight (density) level, the resilient modulus has two values: one when the soil is tested under dry of optimum moisture content and another value when the soil is tested under wet of optimum moisture content. The resilient modulus of the soil compacted on the dry side of optimum is larger than that when the soil is compacted at the wet of optimum. 2.2.2 Effect of Loading Conditions The resilient modulus is a stress-dependent soil property as it is a measure of soil stiffness. According to Rada and Witczak (1981), the most significant loading condition 8 where Mr is the resilient modulus, T is the bulk stress =V1 V 2 V 3 , and k1 and k2 are material constants. Although this model was used to characterize the resilient modulus of granular soils, it does not account for shear stress/strain and volumetric strain. Uzan (1985) demonstrated that the bulk stress model does not sufficiently describe the behavior of granular materials. May and Witczak (1981) modified the bulk stress model by adding a new factor as follows: 2M K k T k (2.3)r 1 1 where K1 is a function of pavement structure, test load and developed shear strain. Deviatoric Stress “Semi- log” Model The deviator stress is the cyclic stress in excess of confining pressure. The resilient modulus of cohesive soils is a function of the deviatoric stress, as it decreases with increasing the deviatoric stress. The deviatoric stress model was recommended by AASHTO to estimate resilient modulus of cohesive soils. In the deviatoric stress model, the resilient modulus is expressed by the following equation: 4M r k3V d k (2.4) where Vd is the deviator stress and k3 and k4 are material constants. The disadvantage of the deviatoric stress model is that it does not account for the effect of confining pressure. Li and Selig (1994) reported that for fine-grained soils the effect of confining pressure is much less significant than the effect of deviatoric stress. However, cohesive soils that are subjected to traffic loading are affected by confining stresses. Uzan Model Uzan (1985) studied and discussed different existing models for estimating resilient modulus. He developed a model to overcome the bulk stress model limitations by including the deviatoric stress to account for the actual field stress state. The model defined the resilient modulus as follows: 2 3M k T k V k (2.5)r 1 d where k1, k2, and k3 are material constants and T and Vd are the bulk and deviatoric stresses, respectively. 11 By normalizing the resilient modulus and stresses in the above model, it can be written as follows: ª T º k2 ªV d º k3 M r k1 Pa (2.6)« » « » P P¬ a ¼ ¬ a ¼ where Pa is the atmospheric pressure, expressed in the same unit as Mr, Vd and T. Uzan also suggested that the above model can be used for all types of soils. By setting k3 to zero the bulk model is obtained, and the semi-log model can be obtained by setting k2 to zero. Octahedral Shear Stress Model The Uzan model was modified by Witzak and Uzan (1988) by replacing the deviatoric stress with octahedral shear stress as follows: ª º k2 ªW º k3T octM k P (2.7)r 1 a « » « » P P¬ a ¼ ¬ a ¼ where Woct is the octahedral shear stress, Pa is the atmospheric pressure, and k1, k2, and k3 are material constants. AASHTO Mechanistic-Empirical Pavement Design Models The general constitutive equation (resilient modulus model) that was developed through NCHRP project 1-28A was selected for implementation in the upcoming mechanistic- empirical AASHTO Guide for the Design of New and Rehabilitated Pavement Structures. The resilient modulus model can be used for all types of subgrade materials. The resilient modulus model is defined by (NCHRP 1-28A): §V · k2 §W · k3 b octM r k1Pa ̈ ¸ ¨ 1¸ (2.8)¨ ¸ ¨ ¸P P© a ¹ © a ¹ where: Mr = resilient modulus Pa = atmospheric pressure (101.325 kPa) Vb = bulk stress = V1 + V2+ V3 V1 = major principal stress V2 = intermediate principal stress = V3 for axisymmetric condition (triaxial test) V3 = minor principal stress or confining pressure in the repeated load triaxial test Woct = octahedral shear stress k1, k2 and k3 = model parameters (material constatnts) 12 2.4 Mechanistic-Empirical Pavement Design The NCHRP project 1-37A: “Development of the 2002 Guide for Design of New and Rehabilitated Pavement Structures” was recently completed and the final report and software was published on July 2004. The outcome of the NCHRP 1-37A is the “Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures,” which is currently undergoing extensive evaluation and review by state highway agencies across the country. The Wisconsin Department of Transportation is currently reviewing and evaluating the new guide for adoption and implementation in design of pavement structures. The new Mechanistic-Empirical guide requires numerous design input parameters that were not previously evaluated by WisDOT for pavement design. For flexible pavements, this includes the determination of the resilient modulus of subgrade soils as input parameter. This parameter can be determined by carrying out a laboratory testing program following the AASHTO T 307 procedure. Design procedures for the new Mechanistic-Empirical guide are based on the existing technology in which state of the art models and databases are utilized. Design input parameters are required generally in three major categories: (1) traffic; (2) material properties; and (3) environmental conditions. The new Mechanistic-Empirical design guide also identifies three levels of design input parameters in a hierarchical way. This provides the pavement designer with flexibility in achieving pavement design with available resources based on the significance of the project. The three levels of input parameters apply to traffic characterization, material properties, and environmental conditions. The following is a description of these input levels: 1. Level 1: These design input parameters are the most accurate, with highest reliability and lowest level of uncertainty. They require the designer to conduct laboratory/field testing program for the project considered in the design. This requires extensive effort and would increase cost. 2. Level 2: When resources are not available to obtain the high accuracy level 1 input parameters, then level 2 inputs provide an intermediate level of accuracy for pavement design. Level 2 inputs can be obtained by developing correlations among different variables such as estimating the resilient modulus of subgrade soils from the results of basic soil tests. 3. Level 3: Input parameters that provide the highest level of uncertainty and the lowest level of accuracy. They are usually typical average values for the region. Level 3 inputs might be used in projects associated with minimal consequences of early failure such as low volume roads. 13 (1) Soils of northern and eastern Wisconsin Region E: forested, sandy loamy soils with uplands covered by loamy soils underlain by calcareous silt. Region Er: forested, loamy or clayey soils underlain by dolomite bedrock with calcareous materials in some parts. Region F: forested, silty soils. Uplands covered by silt over very dense acid loam till, also Antigo and Brill soils occur. Region G: forested, loamy soils. Uplands covered by silty materials over acid. Antigo silt loam is found in some areas in which silt overlay sand and gravel. Region H: forested, sandy soils. There are also some places where loamy materials over acid sand and gravel exist. Region I: forested, clayey or loamy soils. There are thin silty materials that overlie calcareous red clay till exist near Lake Michigan and some other places. (2) Soils of central Wisconsin Region C: forested, sandy soils. Also sandy materials overlie limy till in uplands. Region Cm: prairie, sandy soils. The region is dominated by dark sandy soils. Region Fr: forested, silty soils over igneous and metamorphic rock (3) Soils of Southwestern and Western Wisconsin Region A: forested, silty soils or deep silty and clayey soils that sometimes overlie limestone bedrock. Region Am: prairie, silty soils. Silty soils overlying limestone on broad ridge tops. Region Dr: forested soils over sandstone bedrock. (4) Soils of Southeastern Wisconsin Region B: forested, silty soils. Organic soils have formed where plant materials accumulated. Region Bm: prairie, silty soils. Uplands are covered by silty loamy soils overlaying limy till. Clayey soils over limy till occur near Milwaukee and Racine-Kenosha. (5) Statewide Soils Region J: wetland soils, occurs in depression and drainage ways across the state. Soils are varied between silty clayey loamy sandy as well as organic soils. 16 Figure 2.5: Wisconsin Soil Regions, Madison and Gundlach (1993) 17 Chapter 3 Research Methodology A laboratory testing program was conducted on nineteen soils, which comprise common subgrade soils in Wisconsin. The testing program was conducted at the Geotechnical and Pavement Research Laboratory at the University of Wisconsin-Milwaukee. Soil samples were subjected to different tests to determine their physical properties, compaction characteristics, and resilient modulus. In this chapter, a description of the soils collected and laboratory tests and equipment used is presented. 3.1 Investigated Soils The investigated soils were selected by the WisDOT project oversight committee to represent common soil distributions in Wisconsin. Disturbed soil samples were collected by Wisconsin DOT personnel and then delivered to UWM. The locations of these soils are shown on a map of Wisconsin in Figure 3.1. The investigated soils were selected so that test results can be utilized to establish and validate correlations to estimate resilient modulus of Wisconsin soils from basic soil properties. The soils cover a wide range of types and were obtained from various places across Wisconsin as shown in Figure 3.1. Pictures of some soil samples are presented in Figure 3.2. 3.2 Laboratory Testing Program 3.2.1 Physical Properties and Compaction Characteristics Collected soils were subjected to standard laboratory tests to determine their physical properties and compaction characteristics. Soil testing consisted of the following: grain size distribution (sieve and hydrometer analyses), Atterberg limits (liquid limit, LL and plastic limit, PL), and specific gravity (Gs). Soils were also subjected to Standard Proctor test to determine the optimum moisture content (wopt.) and maximum dry unit weight (Jdmax). Laboratory tests were conducted following the standard test procedures used by WisDOT. Therefore, most laboratory tests were conducted according to the standard procedures of the American Society for Testing and Materials (ASTM). Only the Standard Procter test was conducted following the AASHTO T 99: Standard Method of Test for Moisture – Density Relations of Soils Using a 2.5-kg (5.5 lb) Rammer and a 305­ mm (12-in) Drop. Table 3.1 presents a summary of the standard tests used in this study. In order to obtain quality test results, most tests were conducted twice. The results of the two tests were compared. A third test was performed when the results of the two conducted tests were not consistent. 18 Table 3.1: Standard tests used in this investigation Soil Property Standard Test Designation Particle Size Analysis ASTM D 422: Standard Test Method for Particle –Size Analysis of Soils Atterberg Limits ASTM D 4318: Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils Specific Gravity ASTM D 854: Standard Test Method for Specific Gravity of Soils Standard Proctor Test AASHTO T 99: Standard Method of Test for Moisture – Density Relations of Soils Using a 2.5-kg (5.5 lb) Rammer and a 305­ mm (12-in) Drop ASTM Soil Classification ASTM D 2487: Standard Classification of Soils for Engineering Purposes (Unified Soil Classification System) AASHTO Soil Classification AASHTO M 145: Classification of Soils and Soil-Aggregate Mixtures for Highway Construction Purposes 3.2.2 Repeated Load Triaxial Test A repeated loading triaxial test was conducted, to determine the resilient modulus of the investigated soils, following AASHTO T 307: Standard Method of Test for Determining the Resilient Modulus of Soils and Aggregate Materials. The test was conducted on compacted soil specimens that were prepared in accordance with the procedure described by AASHTO T 307. Dynamic Test System for Materials The repeated load triaxial test was conducted using a state of the art Instron FastTrack 8802 closed loop servo-hydraulic dynamic materials test system at UWM. The system utilizes 8800 Controller with four control channels of 19-bit resolution and data acquisition. A computer with FastTrack Console is the main user interface. This is a fully digital controlled system with adaptive control that allows continuous update of PID terms at 1 kHz, which automatically compensates for the specimen stiffness during repeated load testing. The loading frame capacity of the system is 250 kN (56 kip) with a series 3690 actuator that has a stroke of 150 mm (6 in.) and with a load capacity of 250 kN (56 kip). The system has two dynamic load cells 5 and 1 kN (1.1 and 0.22 kip) for measurement of the repeated applied load. The load cells include integral accelerometer to remove the effect of dynamic loading on the moving load cell. Figure 3.3 shows pictures of the dynamic materials test system used in this study. 21 (a) Loading frame (b) Triaxial cell (c) Control software Figure 3.3: The UWM servo-hydraulic closed-loop dynamic materials test system used in this study 22 Specimen Preparation Compacted soil specimens were prepared according to the procedure described by AASHTO T 307, which requires five-lift static compaction. Therefore, special molds were designed and used to prepare soil specimens by static compaction of five equal layers. This compaction method provided uniform compacted lifts while using the same weight of soil for each lift. Figure 3.4 depicts pictures of the molds used to prepare soil specimens and pictures of specimen preparation procedure. The molds were made in three different diameters: 101.6, 71.1, and 35.6 mm (4.0, 2.8, and 1.4 in.). For each soil type, compacted soil specimens were prepared at three different unit weight-moisture content combinations, namely: maximum dry unit weight and optimum moisture content, 95% of the maximum dry unit weight and the corresponding moisture content on the dry side, and 95% of the maximum dry unit weight and the corresponding moisture content on the wet side, as depicted in Figure 3.5. In order to ensure the repeatability of test results, a special study was conducted on soil specimens prepared under identical conditions of moisture content and unit weight. Statistical analysis was performed on the test results to evaluate the test repeatability. Thereafter, a repeated load triaxial test was performed on two specimens of each soil at the specified unit weight and moisture content. After a soil specimen was prepared under a specified unit weight and moisture content, it was placed in a membrane and mounted on the base of the triaxial cell. Porous stones were placed at the top and bottom of the specimen. The triaxial cell was sealed and mounted on the base of the dynamic materials test system frame. All connections were tightened and checked. Cell pressure, LVTD’s, load cell, and all other required setup were connected and checked. Figure 3.6 shows pictures of specimen preparation for the repeated load triaxial test. Specimen Testing The software that controls the materials dynamic test system was programmed to apply repeated loads according to the test sequences specified by AASHTO T 307 based on the material type. Once the triaxial cell is mounted on the system, the air pressure panel is connected to the cell. The required confining pressure (Vc) is then applied. Figure 3.7 shows pictures of the software used to control and run the repeated load triaxial test. The soil specimen was conditioned by applying 1,000 repetitions of a specified deviator stress (Vd) at a certain confining pressure. Conditioning eliminates the effects of specimen disturbance from compaction and specimen preparation procedures and minimizes the imperfect contacts between end platens and the specimen. The specimen is then subjected to different deviator stress sequences according to AASHTO T 307. The 23 (a) Compacted specimen (b) Housing a specimen in the membrane (c) Seating a specimen on the cell base (d) Placing the top cap (e) Assembling the triaxial cell (f) Mounting the cell on the loading frame Figure 3.6: Preparation of soil specimen for repeated load triaxial test 26 Figure 3.7: Computer program used to control and run the repeated load triaxial test for determination of resilient modulus 27 Chapter 4 Test Results and Analysis This chapter presents the results of the laboratory testing program, analyses and evaluation of test results, and statistical analysis to develop resilient modulus prediction models. Physical and compaction properties of the investigated soils are presented and evaluated. In addition, the results of the repeated load triaxial test to evaluate the resilient modulus of the investigated soils are discussed. Statistical analyses are conducted to develop correlations for predicting the resilient modulus model parameters from basic soil properties. A critical evaluation and validation of the proposed correlations and discussion of the results are also presented. 4.1 Properties of the Investigated Soils Evaluation of soil properties and identification and classification of the investigated soils are important steps to accomplish the research objective since the resilient modulus is highly influenced by soil properties. The investigated soils comprise common types that occur in Wisconsin. The results of laboratory tests conducted to evaluate soil properties are presented in Table 4.1. Soil names in Table 1 are described according to the Soil Conservation Services (SCS). The soil horizon designation is for the depth at which the soil sample was obtained. The data on soil properties consists of particle size analysis (sieve and hydrometer); consistency limits (LL, PL, and PI); specific gravity; maximum dry unit weight and optimum moisture content; soil classification using the Unified Soil Classification System (USCS); and soil classification using the AASHTO method including group index (GI). The following is a brief description of selected soils. Dodgeville Soil (B) Test results indicated that the soil consists of 97% of fine materials (passing sieve #200) with a plasticity index PI = 12, which was classified as lean clay (CL) according to the USCS and clayey soil (A-6) according to the AASHTO soil classification with a group index GI = 13. Figure 4.1 shows the particle size distribution curve of Dodgeville soil. The results of the Standard Proctor test on Dodgeville soil are depicted in Figure 4.2. Results of test #1 showed that the maximum dry unit weight Jdmax =15.9 kN/m 3 and the optimum moisture content wopt. = 19.6%, while results of test #2 indicated that Jdmax = 16.25 kN/m 3 and wopt. = 18.0 %. The results of the compaction tests are considered consistent. Antigo Soil (B) Figure 4.3 depicts the particle size distribution curve of Antigo soil. This soil consists of 91% passing sieve #200 with plasticity index PI = 11, which was classified as lean clay (CL) according to USCS and clayey soil (A-6) according to the AASHTO soil classification with GI=9. Standard Proctor test results showed that the average maximum dry unit weight Jdmax = 17.5 kN/m 3 and the corresponding average optimum moisture content wopt. = 14.5%, as shown in Figure 4.4. 28 Table 4.1 (cont.): Properties of the investigated soils Soil name, horizon and location Passing Sieve #200 (%) Liquid Limit LL (%) Plastic Limit PL (%) Plasticity Index PI (%) Specific Gravity Gs Optimum Moisture Content wopt. (%) Maximum Dry Unit Weight Unified Soil Classification System (USCS) Group Index (GI) AASHTO Soil Classification Jdmax (kN/m 3 ) Jdmax (pcf) Dubuque, C, Iowa County 72 35 23 12 2.55 18.0 16.6 105.7 CL (Lean clay) 8 A-6 (Clayey soil) Eleva, B, Trempealeau County 20 NP NP NP 2.64 7.3 20.4 129.9 SM (Silty sand) 0 A-2-4 (Silty or clayey gravel and sand) Sayner-Rubicon, C, Vilas County 1 NP NP NP 2.65 - - - SP (Poorly graded sand with gravel) 0 A-1 (Stone fragments, gravel and sand) NP: Non plastic Soil name, horizon and emax e min location Plainfield, C, 0.73 0.45 Wood County 0.68 0.44 Sayner-Rubicon, C, Vilas County 0.71 0.45 3 1 Particle size (inch) 0.1 0.01 0.001 0.0001 P er ce nt fi ne r (% ) 100 80 60 40 20 0 Dodgeville soil (B) 10 1 0.1 0.01 0.001 Particle size (mm) Figure 4.1: Particle size distribution curve of Dodgeville soil (B) 13 14 15 16 17 18 D ry u ni t w ei gh t, J d (k N /m 3 ) 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 D ry u ni t w ei gh t, J d (lb /ft 3 ) Dodgeville soil (B) Test 1 Test 2 0 4 8 12 16 20 24 28 32 36 40 Moisture content, w(%) Figure 4.2: Results of Standard Proctor test for Dodgeville soil (B) 32 P er ce nt fi ne r (% ) Particle size (inch) 1 0.1 0.01 0.001 0.0001 100 80 60 40 20 0 Antigo soil 100 10 1 0.1 0.01 0.001 Particle size (mm) Figure 4.3: Particle size distribution curve of Antigo soil 16 17 18 19 D ry u ni t w ei g h t, J d (k N /m 3 ) 102 104 106 108 110 112 114 116 118 120 D ry u ni t w ei gh t, J d (p cf ) Antigo soil Test 1 Test 2 0 5 10 15 20 25 Moisture content, w (%) Figure 4.4: Results of Standard Proctor test for Antigo soil 33 Particle size (inch) 1 0.1 0.01 0.001 0.0001 0 20 40 60 80 100 P er ce nt fi ne r (% ) Kewaunee soil - 1 100 10 1 0.1 0.01 0.001 Particle size (mm) Figure 4.7: Particle size distribution curve of Kewaunee soil - 1 15 16 17 18 19 20 D ry u ni t w ei gh t, J d (k N /m 3 ) 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 D ry u ni t w ei gh t, J d (p cf ) Kewaunee soil - 1 Test 1 Test 2 0 5 10 15 20 25 Moisture content, w(%) Figure 4.8: Results of Standard Proctor test for Kewaunee soil - 1 36 Table 4.2: Results of the standard compaction test on the investigated soils Soil Test 1 Test 2 Average Jdmax (kN/m 3 ) wopt. (%) Jdmax (kN/m 3 ) wopt. (%) Jdmax (kN/m 3 ) wopt. (%) Antigo 17.5 14.5 17.5 14.5 17.5 14.5 Beecher 18.3 14.1 18.3 13.7 18.3 13.9 Goodman 19.1 10.5 NA NA 19.1 10.5 Plano 20.7 8.0 20.3 7.5 20.5 7.8 Dodgeville 15.9 19.6 16.2 18.0 16.1 18.8 Dubuque 16.5 18.0 16.7 18.0 16.6 18.0 Chetek 20.1 8.4 20.1 8.5 20.1 8.5 Eleva 20.2 7.5 20.7 7.1 20.4 7.3 Pence 19.1 8.5 NA NA 19.1 8.5 Gogebic 16.0 17.5 15.0 20.5 15.5 19.0 Miami 16.5 18.4 16.7 17.8 16.6 18.1 Ontonagon -1 17.5 17.5 NA NA 17.5 17.5 Ontonagon -2 16.0 22.0 NA NA 16.0 22.0 Kewaunee - 1 18.2 12.8 18.2 12.5 18.2 12.7 Kewaunee - 2 19.0 13.0 18.9 14.0 19.0 13.5 Shiocton 16.0 11.0 15.7 11.3 15.9 11.2 Withee 17.6 15.5 17.2 15.8 17.4 15.7 37 Table 4.3: Typical results of the repeated load triaxial test conducted according to AASHTO T 307 Test Sequence No. Confining Stress Vc (kPa) Deviator Stress Vd (kPa) Antigo wet #1 Mr (MPa) Deviator Stress Vd (kPa) Antigo wet #2 Mr (MPa) Mean SD CV (%) Mean SD CV (%) 1 41.4 12.45 49.65 0.30 0.60 12.35 57.96 0.24 0.41 2 41.4 24.91 43.30 0.45 1.04 24.92 51.74 0.14 0.28 3 41.4 36.71 36.72 0.08 0.21 36.94 44.83 0.16 0.36 4 41.4 47.90 30.55 0.08 0.25 48.11 37.13 0.07 0.19 5 41.4 59.36 28.33 0.07 0.24 59.67 34.18 0.05 0.15 6 27.6 12.29 40.79 0.17 0.43 12.24 48.69 0.19 0.39 7 27.6 23.98 30.23 0.09 0.28 24.15 38.65 0.18 0.46 8 27.6 35.51 26.00 0.09 0.34 35.82 32.97 0.11 0.33 9 27.6 48.44 24.22 0.07 0.29 47.79 29.92 0.03 0.11 10 27.6 60.25 23.31 0.03 0.14 59.80 28.28 0.04 0.15 11 13.8 12.08 30.67 0.16 0.53 12.02 37.60 0.19 0.51 12 13.8 23.37 21.42 0.05 0.24 23.83 27.92 0.13 0.46 13 13.8 35.81 18.80 0.06 0.31 35.41 23.88 0.11 0.47 14 13.8 48.43 18.57 0.04 0.20 47.53 22.44 0.05 0.22 15 13.8 60.18 18.68 0.05 0.29 59.22 21.91 0.05 0.24 SD: Standard Deviation CV: Coefficient of Variation 38 Deviator Stress, Vd (psi) 2 4 6 8 10 10 100 20 40 60 80 200 R es ili en t M od ul us , M r ( M P a) 10,000 20,000 8,000 6,000 4,000 2,000 R e si lie nt M od ul us , M r ( ps i) Vc=41.4 kPa Vc=27.6 kPa Vc=13.8 kPa Dodgeville - Test 3 at Jdmax and wopt. 10 20 40 60 80 100 Deviator Stress, Vd (kPa) (a) Test on soil specimen #3 Deviator Stress, Vd (psi) 2 4 6 8 10 10 100 20 40 60 80 Deviator Stress, Vd (kPa) 10 100 20 40 60 80 200 R e si lie nt M od u lu s, M r ( M P a ) 10,000 20,000 8,000 6,000 4,000 2,000 R e si lie nt M od ul us , M r ( ps i) Vc=41.4 kPa Vc=27.6 kPa Vc=13.8 kPa Dodgeville - Test 5 at Jdmax and wopt. (b) Test on soil specimen #5 Figure 4.10: Results of repeated load triaxial test on Dodgeville soil compacted at maximum dry unit weight (Jdmax) and optimum moisture content (wopt.) 41 Deviator Stress, Vd (psi) 2 4 6 8 10 10 100 20 40 60 80 200 R es ili en t M od ul us , M r ( M P a) 10,000 20,000 8,000 6,000 4,000 2,000 R e si lie nt M od ul us , M r ( ps i) Vc=41.4 kPa Vc=27.6 kPa Vc=13.8 kPa Dodgeville - Test 6 at Jdmax and wopt. 10 20 40 60 80 100 Deviator Stress, Vd (kPa) (c) Test on soil specimen #6 Deviator Stress, Vd (psi) 2 4 6 8 10 10 100 20 40 60 80 Deviator Stress, Vd (kPa) 10 100 20 40 60 80 200 R es ili en t M od ul us , M r ( M P a) 10,000 20,000 8,000 6,000 4,000 2,000 R e si lie nt M od ul us , M r ( ps i) Vc=41.4 kPa Vc=27.6 kPa Vc=13.8 kPa Dodgeville - Test 7 at Jdmax and wopt. (d) Test on soil specimen #7 Figure 4.10 (cont.): Results of repeated load triaxial test on Dodgeville soil compacted at maximum dry unit weight (Jdmax) and optimum moisture content (wopt.) 42 Deviator Stress, Vd (psi) 2 4 6 8 10 10 100 20 40 60 80 200 R es ili en t M od ul us , M r ( M P a ) 10,000 20,000 8,000 6,000 4,000 2,000 R es ili en t M od ul us , M r ( ps i) Vc=41.4 kPa Vc=27.6 kPa Vc=13.8 kPa Dodgeville - Test 1 at 95% Jdmax (dry side) 10 20 40 60 80 100 Deviator Stress, Vd (kPa) (a) Test on soil specimen #1 Deviator Stress, Vd (psi) 2 4 6 8 10 10 100 20 40 60 80 Deviator Stress, Vd (kPa) 10 100 20 40 60 80 200 R es ili en t M od ul us , M r ( M P a ) 10,000 20,000 8,000 6,000 4,000 2,000 R e si lie nt M od ul us , M r ( ps i) Vc=41.4 kPa Vc=27.6 kPa Vc=13.8 kPa Dodgeville - Test 2 at 95% Jdmax (dry side) (b) Test on soil specimen #2 Figure 4.11: Results of repeated load triaxial test on Dodgeville soil compacted at 95% of maximum dry unit weight (Jdmax) and moisture content less than wopt. (dry side) 43 Table 4.4: Analysis of repeatability tests on Dodgeville soil tested at maximum dry unit weight and optimum moisture content Test Sequence Vc (kPa) Test #5 Test #6 Test #7 Mean Vd (kPa) Mean Mr (MPa) CV(Vd) CV(Mr)Vd (kPa) Mr (MPa) Vd (kPa) Mr (MPa) Vd (kPa) Mr (MPa) 1 12.4 75.0 12.8 76.0 12.5 76.9 12.6 76.0 1.6 1.2 2 24.7 73.1 25.1 73.1 24.9 72.7 24.9 73.0 0.8 0.3 3 41.4 37.3 71.1 37.7 68.7 37.2 68.3 37.4 69.4 0.8 2.2 4 49.2 65.3 49.7 61.8 49.0 62.7 49.3 63.3 0.7 2.9 5 60.6 58.8 61.4 55.5 60.4 56.9 60.8 57.1 0.8 2.9 6 12.4 69.7 12.7 70.6 12.4 70.7 12.5 70.3 1.5 0.8 7 24.5 65.1 24.9 63.1 24.5 63.7 24.6 64.0 0.9 1.6 8 27.6 36.6 60.5 37.2 58.1 36.6 58.8 36.8 59.1 0.9 2.1 9 48.5 56.8 49.2 53.9 48.3 54.9 48.7 55.2 1.0 2.6 10 60.1 53.3 60.9 50.3 60.0 51.8 60.3 51.8 0.8 2.9 11 12.2 62.1 12.6 62.4 12.3 62.3 12.4 62.3 1.6 0.2 12 24.3 55.5 24.6 54.2 24.2 54.5 24.3 54.7 0.8 1.3 13 13.8 36.1 51.6 36.5 49.7 35.9 50.1 36.2 50.5 0.9 1.9 14 47.6 48.5 48.5 46.4 47.4 47.1 47.8 47.3 1.2 2.2 15 59.2 46.0 60.2 43.7 58.9 45.3 59.5 45.0 1.1 2.7 4 6 Table 4.5: Analysis of repeatability tests on Dodgeville soil tested at 95% of maximum dry unit weight and moisture content less than the optimum moisture content (dry side) Test Sequence Vc (kPa) Test #1 Test #2 Test #4 Mean Vd (kPa) Mean Mr (MPa) CV(Vd) CV(Mr)Vd (kPa) Mr (MPa) Vd (kPa) Mr (MPa) Vd (kPa) Mr (MPa) 1 12.8 109.2 11.9 130.3 12.8 142.3 12.5 127.3 4.4 13.2 2 25.2 126.8 25.4 133.5 25.5 146.4 25.4 135.6 0.5 7.3 3 41.4 37.7 133.6 37.6 133.3 38.0 146.5 37.8 137.8 0.6 5.5 4 50.5 133.5 49.7 133.7 50.5 145.7 50.2 137.6 0.9 5.1 5 62.7 131.6 62.2 131.0 63.1 145.3 62.7 136.0 0.7 6.0 6 12.8 105.0 11.7 125.1 12.2 134.9 12.2 121.7 4.4 12.5 7 25.3 118.7 25.0 126.1 25.3 138.9 25.2 127.9 0.7 8.0 8 27.6 37.8 125.1 37.4 125.7 37.7 138.5 37.6 129.8 0.5 5.8 9 50.2 127.1 49.6 124.2 50.3 138.4 50.0 129.9 0.7 5.8 10 62.6 126.8 62.1 123.2 63.3 138.8 62.7 129.6 1.0 6.3 11 12.4 99.5 11.8 110.8 12.0 123.8 12.1 111.4 2.8 10.9 12 25.0 104.6 24.7 112.4 25.2 126.7 25.0 114.6 1.0 9.8 13 13.8 37.3 109.8 37.1 112.2 37.5 127.3 37.3 116.4 0.6 8.2 14 50.0 113.0 49.4 111.7 50.2 127.7 49.9 117.5 0.8 7.5 15 62.4 114.5 61.9 111.5 63.1 128.8 62.5 118.3 1.0 7.8 4 7 Table 4.6: Analysis of repeatability tests on Dodgeville soil tested at 95% of maximum dry unit weight and moisture content greater than the optimum moisture content (wet side) Test Sequence Vc (kPa) Test #1 Test #2 Mean Vd (kPa) Mean Mr (MPa) CV(Vd) CV(Mr)Vd (kPa) Mr (MPa) Vd (kPa) Mr (MPa) 1 12.6 33.7 12.3 25.3 12.5 29.5 1.4 20.2 2 24.5 24.3 24.5 19.5 24.5 21.9 0.2 15.5 3 41.4 36.6 20.4 35.9 15.5 36.2 17.9 1.2 19.1 4 48.2 17.1 47.3 13.2 47.8 15.2 1.2 18.1 5 59.7 14.9 59.2 13.0 59.5 13.9 0.5 9.5 6 12.0 19.1 12.1 16.7 12.0 17.9 0.2 9.4 7 23.4 13.1 23.6 12.3 23.5 12.7 0.8 4.4 8 27.6 35.5 12.3 36.0 12.0 35.8 12.2 1.0 1.8 9 48.0 12.8 48.3 12.2 48.1 12.5 0.4 3.5 10 59.9 13.2 60.0 12.3 59.9 12.7 0.1 4.9 11 11.9 15.0 11.9 12.8 11.9 13.9 0.0 11.1 12 22.7 10.1 23.5 9.4 23.1 9.7 2.4 5.0 13 13.8 35.1 10.1 36.0 9.4 35.6 9.7 1.9 4.7 14 47.8 11.0 48.5 10.2 48.2 10.6 1.1 5.3 15 59.8 11.9 60.7 11.0 60.3 11.4 1.0 5.6 4 8 at confining pressure Vc = 41.4 kPa, the resilient modulus decreased from Mr = 119 MPa at Vd = 12.5 kPa to Mr = 114 MPa at Vd = 60.7 kPa. The Beecher specimen tested at 95% Jdmax and w > wopt showed a decrease in the resilient modulus from Mr = 72 MPa at Vd = 13.6 kPa to Mr = 42 MPa at Vd = 60.3 kPa. Both specimens have similar unit weight values (Jd = 17.3 kN/m 3 ) and different moisture content. The Beecher specimen with lower moisture content exhibited higher resilient modulus values compared to the other specimen with higher moisture content under the same unit weight. The effect of increased moisture content of the soil on reducing the resilient modulus is significant. The soil specimen tested at Jdmax and wopt exhibited resilient modulus values less than the specimen compacted at 95% Jdmax and w < wopt (dry side). This is mainly attributed to the moisture content since the specimen compacted at optimum moisture content has 4% more moisture. Even though the specimen compacted at Jdmax has higher unit weight, the influence of moisture content surpassed the effect of unit weight. For many of the investigated soils, the resilient modulus values of the soil compacted at 95%Jdmax on the dry side are higher than Mr values of the same soil compacted at Jdmax and optimum moisture content. The soil compacted at moisture content less than the optimum and 95%Jdmax exhibited hardening and showed higher values of resilient modulus with the increase of the deviator stress. The soil compacted at unit weight of 95% Jdmax on the wet side exhibited low resilient modulus values compared to the same soil compacted at optimum moisture content. The results of repeated load triaxial test on the investigated soils are presented in Appendix B. 4.3 Statistical Analysis Results obtained from basic soil testing and repeated load triaxial test were used to develop correlations for predicting the resilient modulus model parameters using the resilient modulus constitutive equation selected by NCHRP Project 1-37A for the mechanistic-empirical pavement design. Repeated load triaxial tests were conducted, on average, six times on each soil type at three different moisture content levels and two dry unit weight levels (i.e. 95% Jdmax and Jdmax). It should be noted that Kewaunee soil was subjected to testing only once under each moisture content level due to unavailability of soil samples. 4.3.1 Evaluation of the Resilient Modulus Model Parameters The resilient modulus model is a general constitutive equation that was developed through NCHRP project 1-28A and was selected for implementation in the upcoming AASHTO Guide for the Design of New and Rehabilitated Pavement Structures. The resilient modulus model can be used for all types of subgrade materials. The resilient modulus model is defined by (NCHRP 1-28A): 51 §V · k2 §W · k3 b octM r k1Pa ̈̈ ¸̧ ¨̈ 1¸ (4.1) ¸P P© a ¹ © a ¹ where: Mr = resilient modulus Pa = atmospheric pressure (101.325 kPa) Vb = bulk stress = V1 + V2+ V3 V1 = major principal stress V2 = intermediate principal stress = V3 in axisymmetric condition (triaxial test) V3 = minor principal stress or confining pressure in the repeated load triaxial test Woct = octahedral shear stress k1, k2 and k3 = material model parameters The octahedral shear stress is defined in general as: 1 2 2 2W (V V )  (V V )  (V V ) (4.2)oct 1 2 1 3 2 3 3 For axisymmetric stress condition (triaxial), V2 = V3 and V1 - V3 = Vd (deviator stress), therefore the octahedral shear stress is reduced to: W 2 V (4.3)oct d 3 The resilient modulus, the bulk stress and the octahedral shear stress are normalized in this model by the atmospheric pressure. This will result in non-dimensional model parameters. Statistical analysis based on multiple linear regression was utilized to determine the resilient modulus model parameters k1, k2 and k3. The statistical analysis software STATISTICA was used to perform the analysis. In order to determine k1, k2, and k3 using the experimental test results, the resilient modulus model Equation 4.1 was transformed to: § M · §V · §W · r b octlog¨ ¸ log k1  k2 log¨ ¸  k3 log¨ 1¸ (4.4)¨ ¸ ¨ ¸ ¨ ¸P P P© a ¹ © a ¹ © a ¹ The resilient modulus is treated as the dependent variable, while bulk and octahedral shear stresses are used as the independent variables. The analysis was carried out for each soil type to evaluate the model parameters (k1, k2 and k3) from the results of the 15 stress combinations applied during repeated load triaxial test (15 load sequences according to AASHTO T 307). A total of 136 repeated load tests were used in the analysis. Results of this analysis are summarized in Table 4.7. 52 Table 4.7: Basic statistical data of the resilient modulus model parameters ki obtained from the test results of the investigated soils Parameter Mean Median Minimum Maximum Std. Dev. Standard Error k1 826.8 832.0 201.2 1318.7 250.4 21.47 k2 0.517 0.456 0.176 1.083 0.243 0.021 k3 -2.142 -1.919 -6.013 -0.105 1.373 0.118 The analysis showed that k1 ranges from 201.2 to 1318.7 with a mean value of 826.8. The magnitude of k1 was always > 0 since the resilient modulus should always be greater than zero. The parameter k2 which, is related to the bulk stress, varies between 0.176 and 1.083 with mean value of 0.517. The values of k2 were also greater than zero since the resilient modulus increases with the increase in the bulk stress (confinement). Since the resilient modulus decreases with the increase in the deviator stress, the parameter k3 ranges from -6.013 to -0.105 with a mean value of -2.142. The model parameters ki obtained from the statistical analysis on the repeated load test results are presented in histograms in Figure 4.15. 4.3.2 Correlations of Model Parameters with Soil Properties The resilient modulus model parameters k1, k2 and k3 were determined for all soil types. These parameters are then correlated to fundamental soil properties using regression analysis. The values of resilient modulus model parameters (k1, k2 and k3) were alternatively used as dependent variables while various fundamental soil properties were treated as independent variables. Various combinations of soil properties (independent variables) were used in the regression analysis. The general multiple linear regression model is expressed as: k E  E x  E x  ˜ ˜ ˜  E x  (4.5)i 0 1 1 2 2 k k where: ki = the dependent variable for the regression, (model parameters k1, k2 or k3) E0 = intercept of the regression plane Ei = regression coefficient xi = the independent or regressor variable, (in this study, soil property or a combination of soil properties)  = random error It should be noted that general nonlinear models that include factorial and polynomial regression were attempted in this study. The resulted correlations were not successful due to the existence of a large intercorrelation between the independent variables. In addition, some of the correlation coefficients conflict with the natural behavior of soils. As an example, the increase in the dry unit weight leads to a decrease in the resilient modulus. 53 The goal of the regression analysis is to identify the best subset of independent variables that results in accurate correlation between resilient modulus model parameters ki and basic soil properties. Several combinations of regression equations were attempted and evaluated based on the criteria of the coefficient of multiple determination (R 2 ), the significance of the model and the significance of the individual regression coefficients. In this study, a correlation matrix was used as a preliminary method for selecting material properties used in the regression analysis models. The magnitude of each element in the correlation matrix indicates how strongly two variables (whether independent or dependent) are correlated. The degree of correlation is expressed by a number that has a maximum value of one for highly correlated variables, and zero if no correlation exists. This was used to evaluate the importance of each independent variable (soil property) among other independent variables to the dependent variable (model parameters ki). Measure of Model Adequacy The coefficient of multiple determination was used as a primary measure to select the best correlation. However, a high R 2 does not necessarily imply that the regression model is a good one. Adding a variable to the model may increase R 2 (at least slightly) whether the variable is statistically significant or not. This may result in poor predictions of new observations. The significance of the model and individual regression coefficients were tested for each proposed model. In addition, the independent variables were checked for multicollinearity to insure the adequacy of the proposed models. Test for Significance of the Model The significance of the model is tested using the F-test to insure a linear relationship between ki and the estimated regression coefficients (independent variables). For testing hypotheses on the model: H0: E1 =E2= --- = Ek= 0 Ha: Ei  0 for at least one i where H0 is the null hypothesis, and Ha is the alternative hypothesis. The test statistic is: SSR / p F0 (4.6) SSE / n  p 1 where: SSR is the sum of squares due to regression, SSE is the sum of squares due to errors, n is the number of observations and p is the number of independent variables. H0 is rejected if F0>FD,p,n-p-1 where, D is the significance level (used as 0.05 for all purposes in this study). 56 Test for Significance of Individual Regression Coefficients The hypotheses for testing the significance of individual regression coefficient Ei is based on the t-test and is given by: H0: Ei = 0 Ha: Ei  0 The test statistic is: š E 0 i (4.7)t š 2V Cii š š where Cii is the diagonal element of (X / X) -1 corresponding to E i (estimator of Ei) and V is estimator for the standard deviation of errors, X (n,p) is matrix of all levels of the independent variables, X / is the diagonal X matrix, n is the number of observations, and p is the number of independent variables. H0 is rejected if _t0_ > tD/2,n-p-1 Multicollinearity Treatment Multicollinearity is a common problem in multiple regression analysis. It is recognized when a large intercorrelation between the independent variables exists. This can result in an incorrect estimate of regression coefficients. In this study, the inspection of individual elements of correlation matrix was used as a primary check for multicollinearity. A value of 0.8 indicates strong collinearity between two variables and will inflate the standard errors of the regression coefficients. The variance inflation factor (VIF) was also used to detect multicollinearity for each proposed model. The VIF is the set elements in the diagonal of the inverse of the correlation matrix. A conservative suggestion is to consider the maximum magnitude of an element in the VIF>4 as a multicollinearity problem. Some researchers consider the maximum magnitude of an element in the VIF>8 as a multicollinearity problem (Hines and Montgomery 1980). For this study, all proposed models were checked for multicollinearity. 4.3.3 Statistical Analysis Results In the first attempt of analysis, all data points were used to develop correlations between the resilient modulus model parameters (k1, k2 and k3) and selected soil properties. This analysis produced poor correlations as R 2 values were too low and models were insignificant for predicting the resilient modulus constitutive model parameters. Another 57 attempt of analysis was made in which fine-grained and coarse-grained soils were separated and analyzed independently. Table 4.8 presents a summary of the soil constituents based on particle size analysis. Table 4.8: Constituents of the investigated soils Soil Type/location Passing Sieve #200 (%) Sand (%) Silt (%) Clay (%) Antigo 91 - 76 15 Beecher 48 42 33 15 Goodman 15 53 14 1 Plano 27 66 23 4 Dodgeville 97 - 80 17 Dubuque 72 - 57 15 Chetek 29 69 25 4 Eleva 20 80 15 5 Pence 22 64 21 1 Gogebic 32 63 28 4 Miami 96 - 74 22 Ontonagon - 1 31 60 22 9 Ontonagon - 2 27 63 18 9 Kewaunee-1 30 67 25 5 Kewaunee-2 48 41 32 16 Plainfield 2 98 - - Sayner-Rubicon 1 82 - - Shiocton 41 58 41 0.1 Withee 35 62 24 11 Fine-Grained Soils Regression analysis was conducted on the results of the fine-grained soils. Different basic soil properties were included to obtain correlations with the resilient modulus model parameters k1, k2, and k3. Each correlation was examined from both physical and statistical points of view. If the model was not consistent with the observed behavior of soils, it was rejected. Many attempts were made in which basic soil properties were included. Tables 4.9-4.11 present summaries of the regression analysis results in which models to estimate k1, k2, and k3 from basic soil properties were obtained. Figure 4.16 depicts comparisons between ki values obtained from analysis of the results of the repeated load triaxial test (considered herein as measured values) and ki values estimated from basic soil properties using the proposed correlations (Tables 4.9-4.11). Examination of Tables 4.9-4.11 shows that these models are consistent with the natural behavior of the soils. These models are statistically validated later in this report. The magnitudes of R 2 for k1 correlations range between 0.83 and 0.88, which is considered acceptable. Lower R 2 values were obtained for k2 and k3 as shown in Tables 4.10 and 4.11. Figure 4.16 also 58 0 200 400 600 800 1000 1200 1400 1600 1800 k 1 e st im at ed f ro m b as ic s o il p ro p er ti es Model-1 Model-2 Model-3 Model-4 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 k1 estimated from repeated load triaxial test results (a) k1 0 0.2 0.4 0.6 0.8 1 k2 estimated from repeated load triaxial test results 0 0.2 0.4 0.6 0.8 1 k 2 e st im at ed f ro m b as ic s o il p ro p er ti es Model-1 Model-2 Model-3 (b) k2 Figure 4.16: Comparison of resilient modulus model parameters (ki) estimated from soil properties and ki determined from results of repeated load triaxial test on investigated fine-grained soils 61 k 3 e st im at ed f ro m b as ic s o il p ro p er ti es -6 -5 -4 -3 -2 -1 0 k3 estimated from repeated load triaxial test results Model-1 Model-2 Model-3 0 -1 -2 -3 -4 -5 -6 (c) k3 Figure 4.16 (cont.): Comparison of resilient modulus model parameters (ki) estimated from soil properties and ki determined from results of repeated load triaxial test on investigated fine-grained soils 62 Based on the statistical analysis on the results of the investigated fine-grained soils, the resilient modulus model parameters (ki) can be estimated from basic soil properties using the following equations: § · w k1 404.166  42.933PI  52.260J d  987.353 ̈ ¸ (4.8)¨ ¸w© opt ¹ § w · § J · k2 0.25113  0.0292PI  0.5573 ̈ ¸u¨ d ¸ (4.9)¨ ¸ ¨ ¸w© opt ¹ © J d max ¹ § · w k3 0.20772  0.23088PI  0.00367J d  5.4238 ̈ ¸ (4.10)¨ ¸w© opt ¹ where PI is the plasticity index, w is the moisture content of the soil, wopt. is the optimum moisture content, Jd is the dry unit weight, and Jdmax is the maximum dry unit weight. Table 4.12 presents the correlation matrix of soil properties used in the regression and model parameters for fine-grained soils. A summary of regression coefficients obtained for the fine-grained correlations with t-statistics at 95% confidence level is presented in Tables 4.13. The overall significance of ki correlations was verified based on the F-test. This means that ki and the estimated regression coefficients of independent variables for all correlations constitute a linear relationship. The results of the t-statistics showed that, (ignoring the significance of the intercept E0), the dry unit weight in both k1 and k3 models was insignificant in the case of fine-grained soils. The t-statistics were determined as 1.23 and 0.01 for the k1 and k3 models, respectively. The t-statistics are not significant if the absolute value of t0 (from table of parameter estimator) is less than tD/2,n­ p-1 (from statistics tables). The minimum value of t0 for a parameter to be significant at 95% confidence level is 1.96 if a large population was considered. Although Jd in k1 and k3 models for the fine-grained soils were found to be statistically insignificant, their presence is physically sound based on engineering judgment. Equations 4.8-4.10 were used in the resilient modulus constitutive Equation (4.1) to estimate the resilient modulus of the investigated fine-grained soils. The results are presented in Figure 4.17, which depicts the predicted versus the measured resilient modulus values. Inspection of Figure 4.17 indicates that the resilient modulus of compacted fine-grained soils can be estimated from Equation 4.1 and the correlations proposed by Equations 4.8-4.10 with reasonable accuracy. It should be emphasized that these correlations are developed based on analysis of test results on soils compacted at high unit weight values (between 95 and 100% of Jdmax) with a moisture content range around the optimum value. 63 Coarse-Grained Soils Regression analysis conducted on the test results of the coarse-grained soils (less than 50% passing sieve #200) resulted in poor correlations between ki values and basic soil properties. This is due to the fact that some of the investigated coarse-grained soils do not have plasticity characteristics (non-plastic soils). Therefore, coarse-grained soils were separated into two groups for the purpose of statistical analysis: plastic coarse-grained soils and non-plastic coarse-grained soils. This treatment significantly improved the proposed correlations between soil properties and ki. In addition, parameters related to the grain size characteristics of coarse-grained soils such as coefficient of curvature (Cc), coefficient of uniformity (Cu) and effective size (D10) were included in the analysis (Table 4.14). These parameters did not improve the results of the statistical analysis and therefore were excluded. Table 4.14: Characteristics of particle size distribution curves of investigated coarse-grained soils Soil Type Cu Cc D10 (mm) D30(mm) D50(mm) D60(mm) Beecher 102 1.29 9.04E-05 0.001 0.0038 0.0092 Goodman 82.91 1.15 0.0011 0.011 0.0422 0.0938 Plano 27.99 6.09 3.34E-04 0.0044 0.008 0.0094 Chetek 47.54 3.27 2.77E-04 0.0035 0.0106 0.0132 Eleva 29.6 6.2 8.00E-04 0.0109 0.0167 0.0232 Pence 38.35 3.93 5.12E-04 0.0063 0.014 0.0196 Gogebic 48.08 2.75 2.23E-04 0.0026 0.0079 0.0107 Ontonagon-C-1 32.19 4.1 2.39E-04 0.0027 0.0069 0.0077 Ontonagon-C-2 23.74 6.53 3.69E-04 0.0046 0.0076 0.0088 Kewaunee-1 28.8 4.58 2.57E-04 0.003 0.0061 0.0074 Kewaunee-2 110.2 1.2 8.88E-05 0.001 0.0038 0.0098 Plainfield 2.38 0.92 0.0066 0.0098 0.0132 0.0158 Sayner-Rubicon 3.03 0.83 0.0093 0.0143 0.0228 0.0281 Shiocton 30.54 4.32 1.25E-04 0.0014 0.0033 0.0038 Withee 47.6 2.77 1.82E-04 0.0021 0.0061 0.0087 Cc = coefficient of curvature, Cu = coefficient of uniformity, D10 = effective size, D30 = particle size corresponding to 30% finer, D50 = median size, D60 = particle size corresponding to 60% finer. A summary of the regression analysis on non-plastic coarse-grained soils is presented in Tables 4.15-4.17. The resilient modulus model parameters ki can be estimated from basic soil properties using the models presented in Tables 4.15-4.17. Figure 4.18 depicts comparisons between ki values obtained from analysis of the results of the repeated load triaxial test and ki values estimated from basic soil properties using the correlations presented in Tables 4.15-4.17. An examination of Figure 4.18 shows that ki prediction models are acceptable with R 2 values range from 0.59 to 0.79. These correlations were 66 obtained based on statistical analysis on test data that are limited to non-plastic coarse- grained soils compacted at relatively high unit weight. Extrapolation of these models at soil physical condition levels beyond this is not validated in this study. Table 4.15: Correlations between the resilient modulus model parameter k1 and basic soil properties for non-plastic coarse-grained soils Variable k1 correlations Model 1 Model 2 Model 3 Intercept 809.547 417.187 698.0361 PNo. 4 10.568 - - PNo. 40 -6.112 - -0.2280 %Sand - 8.203 - Jd - - 5.7180 w-wopt - - -55.0174 max. d d optw w J J u -578.337 -591.151 - PNo. 200/ PNo. 40 - 1092.588 - R 2 0.72 0.71 0.69 Table 4.16: Correlations between the resilient modulus model parameter k2 and basic soil properties for non-plastic coarse-grained soils Variable k2 correlations Model 1 Model 2 Model 3 Intercept 0.5661 0.36295 0.2435 PNo. 40 0.00671 -0.00364 0.00372 PNo. 200 -0.02423 - -0.01567 %Sand - 0.00828 - w-wopt 0.05849 0.05641 - woptuJdmax 0.001242 - - max. d d optw w J J u - - 0.5671 R 2 0.79 0.74 0.67 67 Table 4.17: Correlations between the resilient modulus model parameter k3 and basic soil properties for non-plastic coarse-grained soils Variable k3 correlations Model 1 Model 2 Model 3 Intercept -0.50792 2.4747 -1.7529 PNo. 4 - - 0.8472 PNo. 40 -0.041411 0.02541 0.0403 PNo. 200 0.14820 - -0.8765 %Sand - -0.06859 -0.8849 w-wopt -0.1726 -0.17352 -0.17176 woptuJdmax -0.01214 -0.00873 - R 2 0.67 0.65 0.59 68 Based on statistical analysis on the investigated non-plastic coarse-grained soils, the resilient modulus model parameters (ki) can be estimated from basic soil properties using the following equations: § w · § J · k1 809.547 10.568PNo.4  6.112PNo.40  578.337 ̈ ¸u ¨̈ ¸̧ (4.11)¨ ¸ d w J© opt ¹ © d max ¹ k 0.5661 0.006711P  0.02423P  0.05849(w  w )2 No.40 No.200 opt (4.12)  0.001242(w ) u (J )opt d max k 0.5079  0.041411P  0.14820P  0.1726(w  w )3 No.40 No.200 opt (4.13)  0.01214(w )u (J )opt d max where PNo.4 is percent passing sieve #4, PNo.40 is percent passing sieve #40, PNo.200 is percent passing sieve #200, w is the moisture content of the soil, wopt. is the optimum moisture content, Jd is the dry unit weight, and Jdmax is the maximum dry unit weight. The correlation matrix for basic soil properties and ki of non-plastic coarse-grained soils is presented in Table 4.18. A summary of regression coefficients obtained for non-plastic coarse-grained soils correlations with t-statistics at 95% confidence level is presented in Table 4.19. For non-plastic coarse-grained soils, ki models were significant based on the F-test. With the exception of the intercept in k3 model, all independent variables used in ki models were significant based on t0 (from table of parameters estimates). The absolute value of t0 for the intercept in k3 is 1. Equations 4.11-4.13 were used to estimate the resilient modulus of the investigated non- plastic coarse-grained soils. Figure 4.19 depicts comparison of the predicted versus measured resilient modulus values using these equations. Examination of Figure 4.19 demonstrates that the estimated resilient modulus values of compacted non-plastic coarse-grained soils are consistent with values obtained from repeated load triaxial test results. It should be emphasized that these correlations are developed on analysis of test results on soils compacted at high unit weight values (between 95 and 100% of Jdmax) with moisture content range around the optimum value. 71 Table 4.18: Correlation matrix of model parameters and soil properties for non- plastic coarse-grained soils Variable PNo.4 PNo.40 PNo.200 w-wopt woptuJdmax d max d optw w J J u k1 k2 k3 PNo.4 1.00 0.88 0.68 0.03 -0.04 0.03 0.05 -0.05 0.07 PNo.40 1.00 0.84 0.09 -0.00 0.09 -0.10 -0.10 0.19 PNo.200 1.00 0.11 0.32 0.12 -0.1 -0.19 0.29 w-wopt 1.00 -0.14 0.96 -0.83 0.81 -0.51 woptuJdmax 1.00 -0.11 0.02 -0.11 -0.18 d max d optw w J J u 1.00 -0.82 0.75 -0.45 k1 1.00 -0.84 0.55 k2 1.00 -0.81 k3 1.00 Table 4.19: Summary of t-statistics for regression coefficients used in resilient modulus model parameters for non-plastic coarse-grained soils Model Parameter k1 k2 k3 Parameter estimator t-statistic (95% CL) Parameter estimator t-statistic (95% CL) Parameter estimator t-statistic (95% CL) E0 809.547 3.48 0.5661 5.38 -0.5079 -1.00 E1 10.568 2.75 -0.02423 -4.76 0.1482 6.03 E2 -6.112 -2.61 0.00671 3.22 -0.041411 -4.12 E3 -578.337 -9.65 0.05849 11.98 -0.1726 -7.33 E4 - - 0.001242 2.95 -0.01214 -5.98 R 2 0.72 0.79 0.67 SEE 119.9 0.104 0.503 CL: confidence level, SEE: standard error of estimate 72 180 Non-plastic coarse-grained soils 160 140 120 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160 180 Measured resilient modulus (MPa) Figure 4.19: Predicted versus measured resilient modulus of compacted non-plastic coarse-grained soils P re di ct ed r es ili en t m od ul us ( M P a) 73 0 200 400 600 800 1000 1200 1400 k 1 e st im at ed f ro m b as ic s o il p ro p er ti es Model-1 Model-2 Model-3 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 k1 estimated from repeated load triaxial test results (a) k1 k 2 e st im at ed f ro m b as ic s o il p ro p er ti es 0.2 0.4 0.6 0.8 Model-1 0 0 0.2 0.4 0.6 0.8 k2 estimated from repeated load triaxial test results (b) k2 Figure 4.20: Comparison of resilient modulus model parameters (ki) estimated from soil properties and ki determined from results of repeated load triaxial test on investigated plastic coarse-grained soils 76 k 3 e st im at ed f ro m b as ic s o il p ro p er ti es -7 -6 -5 -4 -3 -2 -1 0 k3 estimated from repeated load triaxial test results Model-1 Model-2 Model-3 0 -1 -2 -3 -4 -5 -6 -7 (c) k3 Figure 4.20 (cont.): Comparison of resilient modulus model parameters (ki) estimated from soil properties and ki determined from results of repeated load triaxial test on investigated plastic coarse-grained soils 77 Based on statistical analysis on the investigated plastic coarse-grained soils, the resilient modulus model parameters (ki) can be estimated from basic soil properties using the following equations: k 8642.873 132.643P  428.067(%Silt)  254.685PI 197.230J1 No.200 d § w · (4.14)  381.400 ̈ ¸ ¨ ¸w© opt ¹ § J d · k 2.3250  0.00853P  0.02579LL  0.06224PI 1.73380¨ ¸ 2 No.200 ¨ ¸J© d max ¹ (4.15) § · w¨ ¸ 0.20911¨ ¸w© opt ¹ § J d · k3 32.5449  0.7691PNo.200  1.1370(%Silt)  31.5542¨̈ ¸̧  0.4128 w  wopt (4.16) J© d max ¹ where PNo.200 is percent passing sieve #200, %Silt is the amount of silt in the soil, LL is the liquid limit, PI is the plasticity index, w is the moisture content of the soil, wopt. is the optimum moisture content, Jd is the dry unit weight, and Jdmax is the maximum dry unit weight. The correlation matrix for basic soil properties and ki of plastic coarse-grained soils is presented in Table 4.23. A summary of regression coefficients obtained for plastic coarse-grained soils correlations with t-statistics at 95% confidence level is presented in Tables 4.24. The proposed ki models obtained for plastic coarse-grained soils were significant based on the F-test. For testing the individual variables included in ki models (ignoring the insignificance of the intercept E0) the percent passing sieve #200 (PNo. 200) in k2 model was not significant. The absolute value of t-statistics for this variable was 0.59. Although the percent of fines (PNo. 200) was found statistically insignificant, the presence of this variable in the model is more explanatory than other possible variables and with the overall model still providing closer fit to the measured data. Equations 4.14-4.16 were used to estimate the resilient modulus of the investigated plastic coarse-grained soils. Figure 4.21 shows a comparison of the predicted versus measured resilient modulus values using these equations. An inspection of Figure 4.21 demonstrates that the estimated resilient modulus values of compacted plastic coarse- grained soils are consistent with values obtained from repeated load triaxial test results. It should be emphasized that these correlations are developed on the analysis of test results on soils compacted at high unit weight values (between 95 and 100% of Jdmax) with moisture content range around the optimum value. 78 4.4 Predictions Using LTPP Models In order to inspect the performance of the models developed in this study, comparison with the models developed by Yau and Von Quintus (2004) based on the Long Term Pavement Performance database was made. It should be noted that the data used to develop LTPP models and the database of this study are not similar. One difference is that the AASHTO T 307 was used herein to perform the repeated load triaxial test. Other sources that may affect the outcome include sample preparation and nature of soils samples (undisturbed versus compacted). LTPP models (Yau and Von Quintus, 2004) are used to predict the resilient modulus of Wisconsin subgrade soils from the test results of this study. The resilient modulus values of Wisconsin subgrade soils predicted by LTPP models are then compared to the values obtained from test results and to the values predicted by the models developed herein. The LTPP prediction models (Yau and Von Quintus, 2004) used are presented in the following equations: LTPP equations for clay soils k1 1.3577  0.0106 %Clay  0.0437w (4.17) k 0.5193  0.0073PNo.4  0.0095PNo.40  0.0027PNo  0.0030LL2 .200 (4.18)  0.0049wopt k 1.4258  0.0288P  0.0303P  0.0521P  0.0251(%Silt)3 No.4 No.40 No.200 § w · (4.19)  0.0535LL  0.0672wopt  0.0026J d max  0.0025J d  0.6055 ̈ ¸ ¨ ¸w© opt ¹ LTPP equations for silt soils k1 1.0480  0.0177(%Clay)  0.0279PI  0.0370w (4.20) k2 0.5097  0.0286PI (4.21) k3 0.2218  0.0047(%Silt)  0.0849PI  0.1399w (4.22) 81 LTPP equations for sand soils k1 3.2868  0.0412P  0.0267PNo.4  0.0137(%Clay)  0.0083LL  0.0379wopt3 / 8 (4.23)  0.0004J d k 0.5670  0.0045P  2.98u105 P  0.0043(%Silt)  0.0102(%Clay)2 3 / 8 No.4 § J · § · (4.24)w5 0.0041LL  0.0014wopt  3.41u10 J d  0.4582¨ d ¸  0.1779 ̈ ¸¨ ¸ ¨ ¸J w© d max ¹ © opt ¹ k3 3.5677  0.1142P3/8  0.0839PNo.4  0.1249P200  0.1030(%Silt)  0.1191(%Clay) (4.25)§ J d · § w ·  0.0069LL  0.0103wopt  0.0017J d  4.3177¨ ¸ 1.1095 ̈ ¸¨ ¸ ¨ ¸J w© d max ¹ © opt ¹ LTPP equations for all soils: k 0.9848  0.0050P  0.0011P  0.0085(%Clay)  0.0089LL1 3/8 No.40 § · (4.26)w  0.0094PI  0.0235w  0.3290 ̈ ¸ ¨ ¸w© opt ¹ k2 0.4808  0.0037P3/8  0.0062PNo.4  0.0016PNo.40  0.0008PNo.200  0.0018(%Clay) (4.27)§ J d · § w ·  0.0078LL  0.0019PI  0.0111w  0.1232¨ ¸  0.0009 ̈ ¸¨ ¸ ¨ ¸J w© d max ¹ © opt ¹ k 9.6691 0.0302P  0.0065P  0.0192P  0.0115P  0.0040(%Clay)3 3/8 No.4 No.40 200 § J d · (4.28)  0.0075LL  0.0401PI  0.0020wopt  0.0039J d max  0.2750w  0.7177¨ ¸ ¨ ¸J© d max ¹ 2§ w · § J max · 1.0262 ̈ ¸  5.28x106 ¨ d ¸ ¨ ¸ ¨ ¸ © wopt ¹ © PNo.40 ¹ Figures 4.22-4.24 present comparisons of predicted and measured resilient modulus of fine-grained, non-plastic coarse-grained, and plastic coarse-grained Wisconsin soils using the LTPP models (Yau and Von Quintus, 2004). Inspection of Figures 4.22- 4.24 demonstrates that the models developed herein were able to estimate the resilient modulus of Wisconsin compacted soils better than the models of the LTPP study. The difference in the test procedures and other conditions involved with development of both LTPP and the models of this study contributed to this outcome. 82 20 40 60 80 100 120 140 160 180 180 Fine grained soils Fine grained soils 160 LTPP model for silt soils 140 P re d ic te d r es il ie n t m o d u lu s (M P a) P re d ic te d r es il ie n t m o d u lu s (M P a) P re d ic te d r es il ie n t m o d u lu s (M P a) 120 100 80 60 40 20 0 0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Measured resilient modulus (MPa) Measured resilient modulus (MPa) (a) Using proposed model (b) Using LTPP silt model 180 160 Fine grained soils LTPP model for all soils 140 120 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160 180 Measured resilient modulus (MPa) (c) Using LTPP model for combined (all) subgrade soils Figure 22: Predicted versus measured resilient modulus of Wisconsin fine-grained soils using the mode developed in this study and the LTPP database developed models 83