Ching-Jen Cheng, Dean, College of Engineering ..... study the resilient modulus characteristics of Florida pavement soils [Ping et al., 2000;. Ping et al., 2001; ...
THE FLORIDA STATE UNIVERSITY FAMU-FSU COLLEGE OF ENGINEERING
EVALUATION OF GRANULAR SUBGRADE MODULUS FROM FIELD AND LABORATORY TESTS
By BIQING SHENG
A Thesis submitted to the Department of Civil & Environmental Engineering in partial fulfillment of the requirements for the degree of Master of Science
Degree Awarded: Summer Semester, 2010
The members of the committee approve the thesis of Biqing Sheng defended on June 30, 2010.
__________________________________ Wei-Chou Virgil Ping Professor Directing Thesis
__________________________________ Tarek Abichou Committee Member
__________________________________ Ren Moses Committee Member
Approved: ____________________________________________________________ Kamal Tawfiq, Chair, Department of Civil & Environmental Engineering ____________________________________________________________ Ching-Jen Cheng, Dean, College of Engineering
The Graduate School has verified and approved the above-named committee members.
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ACKNOWLEDGEMENTS
I would like to express my sincere appreciation to my advisor, Dr. Wei-Chou Virgil Ping, for his instruction in my research work. Without him, this thesis would not have been possible. I would like to thank Dr. Tarek Abichou and Dr. Ren Moses, my thesis Committee member, for reading this thesis and offering constructive comments. Finally, I thank my family and friends for encouraging me move along.
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TABLE OF CONTENTS
List of Tables ................................................................................................................vii List of Figures .............................................................................................................. viii Abstract ......................................................................................................................... x
CHAPTER 1. INTRODUCTION ..................................................................................... 1 1.1 Background ...................................................................................................... 1 1.2 Scope of Study ................................................................................................. 3 1.3 Report Organization ......................................................................................... 3
CHAPTER 2. LITERATURE REVIEW ........................................................................... 4 2.1 General ............................................................................................................ 4 2.2 Basic Concepts ................................................................................................ 4 2.2.1 Soil Resilient Modulus .............................................................................. 4 2.2.2 Modulus of Subgrade Reaction ................................................................ 5 2.3 Resilient Modulus Tests ................................................................................... 6 2.4 Factors Affecting Resilient Modulus ................................................................. 9 2.5 Empirical Resilient Modulus Models ............................................................... 11 2.6 Modulus of Subgrade Reaction ...................................................................... 12
CHAPTER 3. EXPERIMENTAL PROGRAMS ............................................................. 18 3.1 General .......................................................................................................... 18
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3.2 Field Experimental Program ........................................................................... 18 3.3 Test-pit Experimental Program ....................................................................... 21 3.3.1 Test Materials ........................................................................................ 21 3.3.2 Test-pit Setup......................................................................................... 22 3.3.3 Test Sequence ....................................................................................... 22 3.4 Laboratory Experimental Program .................................................................. 24 3.4.1 Test Materials ........................................................................................ 24 3.4.2 Resilient Modulus Testing Program ....................................................... 24 3.4.3 Test Procedure ...................................................................................... 25 3.4.4 Determination of Resilient Modulus ....................................................... 26
CHAPTER 4. SUMMARY OF EXPERIMENTAL RESULTS ........................................ 37 4.1 Field Experimental Results ............................................................................. 37 4.1.1 Load-Deformation Curve Regression Model .......................................... 37 4.1.2 Plate Bearing Load Test Results............................................................ 40 4.2 Test-pit Test Results ....................................................................................... 40 4.2.1 Equivalent Resilient Modulus ................................................................. 40 4.2.2 Equivalent Resilient Modulus Results .................................................... 41 4.3 Laboratory Test Results .................................................................................. 42 4.3.1 Regression Analysis .............................................................................. 42 4.1.3 Moisture Effect on Resilient Modulus ..................................................... 43
CHAPTER 5. ANALYSIS OF EXPERIMENTAL RESULTS......................................... 52
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5.1 Comparison of Laboratory and Test-pit Test Results ...................................... 52 5.1.1 Layered System Simulation for Test-pit Study ....................................... 52 5.1.2 Comparison of Resilient Modulus from Laboratory Test and Test-pit Test ............................................................................ 53 5.1.3 Effect of Groundwater Level on Resilient Modulus ................................ 56 5.2 Comparison of Laboratory and Field Test Results .......................................... 57 5.2.1 Comparison of Secant Modulus and Laboratory Resilient Modulus ................................................................................... 57 5.2.2 Comparison of Resilient Modulus and Modulus of Subgrade Reaction ................................................................................. 58
CHAPTER 6. SUMMARY AND CONCLUSIONS ........................................................ 73 6.1 Summary ........................................................................................................ 73 6.2 Conclusions .................................................................................................... 74
REFERENCES .......................................................................................................... 76 BIOGRAPHICAL SKETCH ........................................................................................... 82
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LIST OF TABLES
Table 2.1 Summary of Resilient Modulus Prediction Models ....................................... 14 Table 3.1 Summary of Test Sites for Field Plate Load Test ......................................... 27 Table 3.2 Engineering Properties of Subgrade Material for Test-pit Test ..................... 28 Table 3.3 Summary of Material Properties for Laboratory Test .................................... 29 Table 3.4 Comparison of Test Procedures for Granular Soils ...................................... 30 Table 4.1 Secant Modulus and k Value from Plate Bearing Load Tests....................... 44 Table 4.2 Plate Load Equivalent Modulus Test Results ............................................... 45 Table 4.3 Laboratory Resilient Modulus Test Results of Subgrade (Field Plate Bearing Load Test Project) ....................................................... 46 Table 4.4 Laboratory Average Resilient Modulus at Different Moisture Conditions (Test-pit Plate Load Test Project)............................................... 47 Table 5.1 Comparison of Layer Modulus from Test-pit Plate Load Test and Laboratory Resilient Modulus ................................................................ 62 Table 5.2 Comparison of Modulus from Field Load Test and Laboratory Resilient Modulus ......................................................................................... 63
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LIST OF FIGURES
Figure 2.1 Illustration of Soils Behavior under Repeated Loads ................................... 16 Figure 2.2 Field Plate Bearing Load Test Schematic ................................................... 17 Figure 3.1 Field Falling Weight Deflectometer Test Setup ........................................... 31 Figure 3.2 Field Plate Bearing Load Test ..................................................................... 32 Figure 3.3 Test-pit System: (a) Overview of Test Pit; (b) Schematic Diagram of Loading System & Cross Sectional View .................................. 33 Figure 3.4 Test-pit Test Sequence for Different Water Level Adjustment..................... 34 Figure 3.5 Schematic of Laboratory Resilient Modulus Test Program ......................... 35 Figure 3.6 Schematic of Triaxial Test for Resilient Modulus Measurement .................. 36 Figure 4.1 Rectangular Hyperbolic Representation of Load-Deformation Curve ........................................................................................................... 48 Figure 4.2 Load-Deformation Curves of the Tested Soils............................................. 49 Figure 4.3 Laboratory Resilient Modulus vs. Moisture Content for Phase I and II Soils................................................................................................. 51 Figure 5.1 Comparison of Resilient Modulus from Laboratory Triaxial Test with Equivalent Layer Modulus from Test-pit Test ...................................... 64 Figure 5.2 Comparison of Resilient Modulus from Laboratory Test using Middle-Half LVDT with Resilient Modulus from Test-pit Test....................... 65 Figure 5.3 Comparison of Resilient Modulus from Laboratory Tests using Middle-Half LVDT and Full-Length LVDT .................................................... 66 Figure 5.4 Comparison of Resilient Modulus from Laboratory Test using Full-Length LVDT with Resilient Modulus from Test-pit Test ...................... 67 Figure 5.5 Equivalent Resilient Modulus at Different Groundwater Levels ................... 68 Figure 5.6 Percent Reductions of Resilient Modulus at Different Groundwater levels . 69
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Figure 5.7 Comparison of Laboratory Resilient Modulus with Secant Modulus at Deflection of 1.27 mm ............................................................... 70 Figure 5.8 Comparison of Laboratory Resilient Modulus with Average Secant Modulus at ½ P ult ............................................................................ 71 Figure 5.9 Comparison of Laboratory Resilient Modulus at ½ P ult with Modulus of Subgrade Reaction .................................................................. 72
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ABSTRACT
The Resilient Modulus of pavement subgrade materials is an essential parameter to determine the stress-stain characteristics of pavement structures subjected to traffic loadings for mechanistically based flexible pavement design procedure. The modulus of subgrade reaction is a required parameter for design of rigid pavements. The loaddeformation characteristics of the granular subgrade soils were investigated using the laboratory triaxial test, test-pit plate load test, and field rigid plate load bearing test. Several typical subgrade soils used for pavement construction in Florida were obtained for evaluation. The resilient modulus of subgrade materials were evaluated by laboratory triaxial testing program. The resilient properties of subgrade materials were found to be strongly influenced by the moisture content and test procedure. Then, a full scale laboratory evaluation of the subgrade performance was conducted in a test-pit facility to simulate the actual field conditions. The subgrade materials were tested under various moisture conditions that simulated different field groundwater level. It was shown that the resilient modulus of subgrade materials increases with the decrease of groundwater level. In addition, the field plate load testing program was carried out to evaluate the bearing characteristics of pavement base, subgrade, and embankment soils. A hyperbolic model was used to represent the relationship of the load-deformation curve obtained from the field plate load bearing test. Correlation relationships were established between the laboratory resilient modulus and the resilient modulus measured using test-pit facility. It was shown that the resilient modulus measured from laboratory test could be used to predict the resilient deformation of the pavement subgrade layers if an appropriate calculation method was used. Correlation relationship between the subgrade soil resilient modulus and the modulus of subgrade reaction was also established, which was found to be close to the theoretical relationship from the AASHTO design guide. These correlation relationships could be utilized in the Florida pavement design guide to better predict the resilient deformation of pavement subgrades.
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CHAPTER 1
INTRODUCTION
1.1 Background When design pavements, the characteristic of the subgrade upon which the pavement is placed is an essential design parameter need to be considered. Subgrade materials are typically characterized by their resistance to deformation under load, which can be either a measure of their strength or stiffness. In general, the more resistant to deformation a subgrade is the more loads it can support before reaching a critical deformation value. A basic subgrade stiffness/strength characterization is resilient modulus (MR). Both the AASHTO 1993 Design Guide [AASHTO, 1993] and the mechanistic based design methods [ARA, 2004] use the resilient modulus of each layer in design process. The modulus of subgrade reaction (k) is a required parameter for the design of rigid pavements [AASHTO, 1986 & 1993]. It estimates the support the layers below a rigid pavement surface course. The modulus of subgrade reaction is determined from the field plate bearing load test [Huang, 1993]. However, the field plate bearing load test is elaborate and time consuming. Recently, resilient modulus is commonly applied for both flexible and rigid pavement in the design guide [AASHTO, 1993]. Therefore, it was necessary to develop a relationship between the modulus of subgrade reaction (k) and the roadbed soil resilient modulus. For instance, a theoretical relationship was developed in the AASHTO Guide for Design of Pavement Structures [AASHTO, 1993, Vol. II]. Some other relationships based on the Long Term Pavement Performance (LTPP) database were established in the Mechanistic-Empirical Pavement Design Guide (MEPDG) [ARA, 2004] and elsewhere [Setiadji and Fwa, 2009, ASCE]. However, there has been no research on using field measured k values from actual pavement sites to evaluate and calibrate the established theoretical relationship between the modulus of subgrade reaction (k) and the soil resilient modulus obtained from laboratory resilient modulus test. 1
In Florida, several research projects in the past years have been conducted to study the resilient modulus characteristics of Florida pavement soils [Ping et al., 2000; Ping et al., 2001; Ping and Ling, 2007; Ping and Ling 2008]. Typical subgrade soils used for pavement construction in Florida were excavated and obtained from actual field sites for evaluation. A laboratory triaxial testing program was carried out to evaluate the resilient modulus of subgrade materials. The effects of moisture and soil properties on the resilient properties of subgrade materials were evaluated. In conjunction with the laboratory triaxial testing program, a full scale laboratory evaluation of the subgrade performance was conducted in a test-pit facility, which simulates the actual field conditions. The subgrade and base layer profile of a full-scale flexible pavement system was simulated in the test-pit facility. The subgrade materials were tested in the test-pit under various moisture conditions simulating different field pavement moisture conditions. In addition, and extensive field static plate bearing load testing program was also conducted to evaluate the bearing characteristics of pavement base, subbase, and subgrade soils [Ping, Yang, and Gao, 2002, ASCE]. Comparative studies were conducted to evaluate the resilient modulus from laboratory cyclic triaxial test and field experimental studies such as field plate bearing load test, falling weight deflectometer (FWD) test, and test-pit cyclic plate load test. Conducting the soil resilient modulus test in laboratory and selecting an appropriate resilient modulus value for pavement design are very complex processes. The processes are even much more time consuming, labor intensive, and costly on conducting in-situ field plate bearing load test and obtaining field measured k values. The field plate bearing load test cannot be conducted at various moisture contents and densities to simulate the different service conditions or the worst possible condition during the design life. Thus, it was necessary to develop a correlation between the modulus of subgrade reaction (k) and the soil resilient modulus [AASHTO, 1993]. In view of the past experimental studies conducted in Florida relating the laboratory resilient modulus with the field plate bearing load test results, there seems to be a need in re-examining the field experimental studies to evaluate and calibrate the established theoretical relationship between the modulus of subgrade reaction and soil resilient modulus.
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1.2 Scope of Study The objectives of this research study were to evaluate the load-deformation and resilient modulus characteristics of the granular subgrade soils based on the past field and laboratory experimental studies and to further correlate the field test results with the laboratory resilient modulus measurements. The targeted goal is two-fold: a) to establish the correlation relationships between the measured soil resilient modulus using laboratory triaxial test and the resilient modulus measured using plate load test in test-pit facility; b) to re-evaluate the correlation relationships between the subgrade soil resilient modulus and the modulus of subgrade reaction (k) using field measured experimental results. The theoretical relationship from AASHTO [AASHTO, 1993] will be evaluated based on the experimental studies. The calibrated correlation relationships could be utilized in the Florida pavement design guide for obtaining the realistic resilient modulus values from laboratory resilient modulus measurements.
1.3 Report Organization This report summarizes the experimental programs, test results, and analyses of the research study to evaluate the subgrade soil modulus. As an introduction, the background and objectives of this research study are presented in this chapter. A literature review of the research related to the study of subgrade soil modulus is summarized in Chapter 2. The past experimental programs, including a description of test equipment, test setup, and test procedure for the laboratory and field tests, are presented in Chapter 3. Chapter 4 summarizes and analyzes the experimental results of laboratory and field tests. After that, Chapter 5 presents the correlation relationships between laboratory test results and field test results. Finally, conclusions and recommendations of this research study are presented in Chapter 6.
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CHAPTER 2
LITERATURE REVIEW
2.1 General The 1993 AASHTO Guide for the Design of Pavement Structures has incorporated the resilient modulus of component materials into the design process [AASHTO, 1993]. Considerable attention has also been given to the development of mechanistic-empirical approaches for the design and evaluation of pavements [ARA, 2004]. The literature survey will proceed in five sections. In the first section, the basic concepts of resilient modulus and modulus of subgrade reaction will be reviewed. Then, the experimental evaluation of resilient modulus using laboratory and field tests will be discussed. This is followed by a review of evaluation of factors affecting the resilient modulus of subgrade soils. After that, empirical resilient modulus models used to predict the resilient modulus values are reviewed. Finally, the research studies on the modulus of subgrade reaction will be discussed.
2.2 Basic Concepts 2.2.1 Soil Resilient Modulus The resilient modulus is the elastic modulus to be used with the elastic theory. Most pavement materials, especially soils, are not pure elastic material, but exhibit elastic-plastic behavior. That means they act partly elastic under a static load but experience some permanent deformation. However, under repeated loads, they express other important properties. At the beginning, they perform just like they would under a static load. But after certain repetitions, the permanent deformation under each load repetition is almost completely recoverable. By this point, it can almost be considered elastic, if the repeat load is small enough compared to its strength, otherwise the soil structure would be damaged. Figure 2.1 illustrates the behavior of unbounded material under a sequence of repeating loads. Resilient modulus is a measurement of the elastic property of soil recognizing certain nonlinear characteristics, which is defined as the 4
ratio of the axial deviator stress to the recoverable axial strain, and is presented in the following equation:
MR =
σd εr
(2.1)
Where σd = axial deviator stress εr = axial recoverable strain This concept is derived from the fact that the major component of deformation induced into a pavement structure under the traffic loading is not associated with plastic deformation or permanent deformation, but with elastic or resilient deformation. Thus, the resilient modulus is considered to be a required variable for determining the stressstrain characteristics of pavement structures subjected to a traffic loading. Many factors influence the resilient modulus of soils. Moisture is one of the factors affecting the modulus of soils. The factors that influence the resilient modulus of soils also include the following: soil type, soil properties, dry unit weight, strain level, and test procedures. Thus, the resilient modulus test procedure and the selection of an appropriate design resilient modulus value for pavement subgrades have been significantly complicated. The lack of meaningful correlations between the field and laboratory resilient modulus values further complicates the issue.
2.2.2 Modulus of Subgrade Reaction The modulus of subgrade reaction (k) is a required parameter for the design of rigid pavements. It estimates the support the layer below a rigid pavement surface course. The modulus of subgrade reaction is determined from a field plate bearing load test with a circular plate (Figure 2.2). The load is applied at a predetermined rate until a pressure of 10 psi (69 kPa) is reached. The pressure is held constant until the deflection increase not more than 0.001 in. (0.025 mm) per minute for three consecutive minutes. The average of the three dial readings is used to determine the deflection. The modulus of subgrade reaction (k) is given by
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k measured =
p ∆
(2.2)
Where p = pressure on the plate, or 10 psi ∆ = deflection of plate in inch The k-value is determined from the field tests. Since the plate loading test is timeconsuming and expensive, it cannot be conducted at various moisture contents and densities to simulate the different service conditions or the worst possible condition during the design life. It is necessary to develop a relationship between the modulus of subgrade reaction (k) and the subgrade soil resilient modulus (MR). This allows the designer to treat the seasonal variation of the subgrade soil k-value by simply converting the same seasonal resilient modulus that would be used for flexible pavement design.
2.3 Resilient Modulus Tests It is well known that subgrade soils are nonlinear with an elastic modulus varying with the level of stress. The elastic modulus to be used with the layered systems is the resilient modulus obtained from repeated unconfined or triaxial compression tests [3]. The resilient modulus of unstabilized subgrade soils is highly dependent upon the stress state to which the material is subjected within the pavement in addition to other variables. As a result, constitutive models including the effect of stress state must be used to present laboratory resilient modulus test results, in a form suitable for use in pavement design. The resilient modulus depends on deviator stress and confining stress. Two popular and simple regression models are presented as follows: 1. when modulus is dependent on bulk stress: M R = k1θ k2
(2.3)
2. when modulus is dependent on confining pressure: M R = k 3σ 3
k4
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(2.4)
Where θ = bulk stress, sum of the principal stresses, (σ1+ σ2+ σ3) σ3 = confining pressure or minor principal stress k1, k2, k3, k4 = regression constants The U.S. Army Cold Regions Research and Engineering Laboratory (CRREL) conducted resilient modulus tests on materials from the MN/ROAD test site for the Minnesota Department of Transportation [Berg et al., 1996]. Laboratory resilient modulus tests were conducted on pavement materials to characterize their behavior under seasonal frost conditions, and to provide input necessary for modeling the materials with the Mechanistic Pavement Design and Evaluation Procedure. It was found that the modulus of all of the materials was stress dependent and increased as the degree of saturation decreased. Maher et al. [Maher et al., 2000] developed a laboratory testing program to determine the resilient modulus of typical New Jersey subgrade soils. A total of eight soils were tested at different levels of molded water content to determine their sensitivity to moisture content and cyclic stress ratio. Laboratory results were used to calibrate a statistical model for effectively predicting the resilient modulus of subgrade soils at various moisture content and stress ratios. Kim and Kim [Kim and Kim, 2007] developed a simplified repeated triaxial test procedure to investigate the typical sandy-silty-clay and silty-clay subgrade soils encountered in Indiana. It was shown that the simplified procedure was feasible and effective for design purpose. Recently, several field tests were involved to study the resilient behavior of subgrade soils. These field tests include, among others, falling weight deflectometer (FWD), dynamic cone penetrometer (DCP), plate load test, and so on. The field tests results were found to be comparable with the laboratory measured modulus. Newcomb et al. [Newcomb et al., 1995] conducted tests at MN/ROAD in 1994 including both FWD and DCP examinations to compare with Long Term Pavement Performance (LTPP) laboratory resilient modulus values. FWD results showed high variability due to varying surface conditions, soil moisture content, modulus values. DCP results compared well with laboratory values, but no correlations were identified. George and Uddin [George and Uddin, 2000] studied the resilient modulus of subgrade using dynamic cone
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penetrometer (DCP) and falling weight deflectometer (FWD) tests. Twelve as-built test sections reflecting typical subgrade soil materials of Mississippi were selected and tested with DCP and FWD before and after pavement construction. Undisturbed samples were tested in repeated triaxial machine for resilient modulus. It was found that the laboratory as well as backcalculated subgrade modulus calculations were usable in the field. Andrew et al. [Andrew et al., 1998] used falling weight deflectometer test to determine the seasonal variation in subgrade resilient modulus, and to develop a rational approach for the selection of a unique design season resilient modulus. The seasonal variation in FWD response was also compared to the measured variation in subgrade moisture, and the resilient modulus was predicted from existing correlations between index properties and soil moisture content. Bandara and Rowe [Bandara and Rowe, 2002] carried out a study to determine the relationships between laboratory determined subgrade resilient modulus and the results of Limerock Bearing Ratio (LBR) and FWD tests for certain Florida subgrade soils. FWD tests were conducted along the selected roadways and LBR tests were conducted on bulk subgrade soil samples. Preliminary relationships from FWD and LBR tests were developed for considered typical pavement sections. Flintsch et al. [Flintsch et al., 2003] found strong correlations between laboratory resilient modulus tests and backcalculated resilient modulus values from in-situ FWD measurements for unbound granular materials from 12 sites in Virginia. George et al. [George et al., 2004] explored a method for correlating FWD moduli with triaxial test laboratory moduli in a selected pattern on subgrade sections to ensure accuracy even in conditions of nonhomogenous subgrades. Mohammad et al. [Mohammad et al. 1999] evaluated the resilient modulus of subgrade soils by cone penetration test. Field and laboratory testing programs were carried out on two types of cohesive soils in Louisiana. A model was proposed to estimate the resilient modulus from the CPT data and basic soil properties. Predicted values of the resilient modulus were consistent with laboratory measurements. Tests on soil samples and at 12 field sites in Mississippi found that DCP index could be correlated in different ways for fine grained and coarse-grained soils, and that regression models could be improved by testing for other physical properties [Rahim and George, 2002].
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2.4 Factors Affecting Resilient Modulus As mentioned earlier, many factors influence the resilient modulus of soils. Tremendous amount of research work was developed to investigate the effects of those factors. Hicks and Monismith [Hicks and Monismith, 1971] analyzed the factors that may affect the resilient modulus of granular material. They found that the following factors may have a significant influence on the stress-deformation characteristics under shortduration repeated loads: 1) stress level (confining pressure), 2) degree of saturation, 3) dry density, 4) fine content, and 5) load frequency and duration. Burczyk et al. [Burczyk et al., 1994] conducted laboratory testing on subgrade cores obtained from 9 test sites in Wyoming. Several fundamental soil properties of these cores were determined and deflection data were used to determine resilient modulus values with backcalculation programs. The data analysis resulted in several important conclusions about factors that influencing the selection of a design subgrade resilient modulus value. The effect of moisture content is considered a major factor which may change the value of resilient modulus, which has been noticed a long time ago. Seed et al. [Seed et al., 1962] noted a rapid increase in resilient deformations for specimens of the AASHO road test subgrade soils compacted with water content above the optimum level. For specimens compacted below optimum water content, resilient deformations were characteristically low. Thompson and Robnett [Thompson and Robnett, 1976] summarized the effect of an AASHO road test on subgrade soil. It was found that the resilient modulus decreases as moisture increases. Barksdale et al. [Barksdale et al., 1989] prepared a report about the laboratory determination of resilient modulus for flexible pavement design due to the moisture sensitivity of resilient modulus. Drumm et al. [Drumm et al., 1997] summarized their tests of the effect of saturation on resilient modulus. All soils exhibited a decrease in resilient modulus with an increase in saturation, but the magnitude of the decrease in resilient modulus was found to depend on the soil type. More experimental studies have been carried out in recent years to evaluate the effect of moisture content on the resilient modulus of subgrade soils [Mohammad et al., 2002; Li and Qubain, 2003; Khoury and Zaman, 2004; Stolle et al., 2006; and Cortez, 2007]. The effects of subgrade soil moisture content on subsurface
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strain and stress distributions were explored. It was found that the resilient modulus decreases as moisture increases. The resilient modulus of fine-grained soil is dependent on moisture content and the degree of saturation has a significant influence on the stress-deformation characteristics of subgrade materials. The resilient modulus is also significantly influenced by the type of pavement soils. Chen et al. [Chen et al., 1994] investigated the variability of resilient moduli due to aggregate type. It was shown that for a given gradation, the difference in MR values due to aggregate sources were between 20 to 50%. Thompson and Robnett [Thompson and Robnett, 1976] concluded that soil properties that tend to contribute to low resilient modulus values are low plasticity, high silt content, low clay content and low specific gravity. From their study, regression equations were developed for predicting MR based on soil properties. The effect of dry density on the resilient response of subgrade soils was investigated by Trollope et al. [Trollope et al., 1962]. They reported that the resilient modulus of dense sand might be 50% higher than that of loose sand. The strain level also had an important effect on the resilient modulus. As the strain amplitude increased, the modulus of the soil decreased [Kim, 1991]. AASHTO T292-91I and T294-92 were two of the most extensively used test procedures. A new standard specification AASHTO T307-99 based on the SHRP Protocol P46 was adopted in 2000. The major improvement includes higher accuracy of the measurement devices, different measurement position, different confining and loading stress, and the specimen preparation method. Zaman et al. [Zaman et al., 1994] found that the T294-92 test procedure gave higher resilient modulus values than those obtained by using the T292-91I test procedure. Ping and Hoang [Ping and Hoang, 1996] had similar results. This phenomenon was attributed to the stress sequence, which had a stiffening and strengthening effect on the specimen structure as the stress level increased. Ping and Xiong [Ping and Xiong, 2003] investigated the influence of the LVDT positions on the resilient modulus test results. The investigation showed that the internal LVDT position leads to a better test result than that with an external position, and the internal full-length LVDT position has the most reliable test data.
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2.5 Empirical Resilient Modulus Models A very promising approach for obtaining resilient modulus for use in design, for at least most agencies, is to determine values of resilient modulus using generalized empirical relationships with statistically relevant, easy to measure physical properties of the material. Considering the large variation in resilient modulus along the route and important design changes in moisture with time, the use in design of empirical resilient modulus relationships is considered to be justified. A number of states have already developed generalized resilient modulus relationships for use in design, particularly for cohesive subgrade soils. Statistically based equations, graphs or chars would then be developed for each class of materials for the range of properties routinely used in design within the region of interest. Seed et al. [Seed et al., 1962] evaluated the influence on the undisturbed samples of the fine grained materials and found a relationship between the resilient modulus and the volumetric water content. The results from this model did not work well since the resilient modulus is based on only one parameter in this model, which contributes to inaccurate results. Carmichael and Stuart [Carmichael and Stuart, 1978] produced more than 3300 test data on 250 different types of fine-grained and granular materials to build the resilient modulus models. Two models were developed, one for fine-grained soils and the other for coarse-grained soils. Using the power model to express resilient modulus is a practical alternative to the slightly more accurate bilinear model. The bilinear resilient modulus model for fine-grained soils has a distinct breakpoint. The resilient modulus at the breakpoint was estimated by Thompson [Thompson, 1992]. Yau and Von Quintus [Yau and Von Quintus, 2002] studied the methods of choosing the right data for building the resilient modulus prediction models. They found that one equation did not fit all situations for all the soils. For greater accuracy, they tried to establish the model according to different material types. The prediction models for the subgrade soils were developed based on the constitutive equation with the regression constants k1, k2, and k3, which are material-specific. Zhang [Zhang, 2004] proposed a resilient modulus prediction model based on five types of granular subgrade soil commonly available in Florida. Several other prediction models, which correlate the laboratory resilient modulus data with the field data, were developed
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in the different states in the recent days [Herath et al., 2005; Malla and Joshi, 2008; Rahim and George, 2005; Rahim, 2005; and Han et al., 2006]. These methods allow designers and engineers to reduce their reliance on the expensive, time-consuming and difficult process of testing resilient modulus. A summary of these resilient modulus prediction models are listed in Table 2.1; wherein, MR = Resilient Modulus, MC = moisture content (%), θ = bulk stress (σ1+ σ2+ σ3), σ3 = confining pressure, σd = deviator stress, PI = plastic index (%), LL = liquid index (%), P200 = percentage passing #200 sieve (%), %clay = % particles finer than 2 micron size, Pa = normalizing stress, τoct = octahedral shear stress, Cu = uniformity coefficient, Cc = coefficient of curvature, k1, k2, and k3 = regression parameters. 2.6 Modulus of Subgrade Reaction The term subgrade reaction indicates the pressure between a loaded beam or slab and the subgrade on which it rests and on to which it transfers loads. The factors which determine the value of the coefficient of subgrade reaction was evaluated by Terzaghi [Terzaghi, 1955]. The concept of modulus of subgrade reaction was introduced to account for the stress-dependent behavior of typical subgrade soil by Fischer et al. [Fischer et al., 1984]. It is usually impractical to conduct plate bearing load tests in the field on representative subgrade soils for design projects. Thus, a theoretical relationship between the k value and resilient modulus was developed in the Appendix HH of the AASHTO design guide [AASHTO, 1993], which is as follows:
k measured (pci) =
M R (psi) 19.4
(2.5)
It should be noted that this theoretical relationship was developed based on the assumption that the roadbed material is linear elastic. Elastic layer theory and equations provide the basis for establishing the relationship. Recently, Kim et al. [Kim et al., 2007] adopted the portable falling weight deflectrometer to evaluate material characteristics of well-compacted subgrades. In addition, the static plate-bearing load test was used to evaluate the modulus of
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subgrade reaction. The test results show that there is a reasonable linear correlation between the dynamic deflection modulus and the modulus of subgrade reaction of wellcompacted subgrades. A comparative study of methods of determination of modulus of subgrade reaction was discussed by Sadrekarimi and Akbarzad [Sadrekarimi and Akbarzad, 2009]. Khazanovich et al. [Khazanovich et al., 2001] performed backcalculation analysis on the deflection data for the rigid pavements from LTPP database. A theoretical pavement system of an infinite pavement slab supported on a dense-liquid foundation was used to estimate the k-values. The following relationship was obtained k (MPa/m) = 0.296 E (MPa)
(2.6)
The k-E relationships generated by the MEPDG software can be closely represented by Equation (2.6). It should be noted that the k-value in Equation (2.6) is for full scale pavement slab but not the measured k value with 30 in. diameter plate. Setiadji and Fwa [Setiadji and Fwa, 2009] proposed a procedure to estimate modulus of subgrade reaction (k) from elastic modulus (E) by establishing an equivalency between two theoretical pavement models, a model of pavement slab supported by an elastic solid foundation and a model of pavement slab supported by a dense liquid foundation. Using the deflection test data of the LTPP database, it was found that there exists a relationship between the radii of relative stiffness of the two theoretical systems, which can be used to estimate k from given E value. This model was also compared to the k-E relationships derived previously by other researchers.
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Table 2.1 Summary of Resilient Modulus Prediction Models Reference
Prediction Model
Seed
M R = 27.06 − 0.006 MC forγ d > 100 pcf
[Seed et al., 1962]
M R = 18.18 − 0.004 MC forγ d < 100 pcf
Carmichael and Stuart [Carmichael and Stuart, 1978]
Coarse-Grained Soil:
log M R = 0.523 − 0.025MC + 0.544 log θ + 0.173SM + 0.197GR Fine-Grained Soil:
M R = 37.341 − 0.4566 PI − 0.6179 MC − 0.1424 P200 + 0.179σ 3 − 0.3248σ d + 36.722CH + 17.097 MH Thompson
M R = 4.46 + 0.098%clay + 0.119 PI
[Thompson, 1992] Yau and Von Quintus
θ M R = k1 Pa Pa
[Yau and Von Quintus, 2002]
k
2 τ oct Pa
k3
Malla and Joshi [Malla and Joshi, 2008] Zhang [Zhang, 2004] Rahim and George [Rahim and George, 2005]
ln M R = 2.01 − 0.041MC + 0.0108γ d ,max + 0.0243Cu − 0.119Cc θ Coarse-Grained Soil: M R = k1 Pa 1 + 1+ σ d σd Fine-Grained Soil: M R = k1 Pa 1 + 1+σc
Rahim [Rahim, 2005]
k2
k2
Coarse-Grained Soil:
γd M R = 324.14 MC + 1
0.8998
P200 log C u
−0.4652
Fine-Grained Soil: −0.609 2.18 LL P200 M R = 17.29 × γ d ,max + 100 MC + 1
14
Table 2.1 Summary of Resilient Modulus Prediction Models - Continued where,
MR = Resilient Modulus, MC = moisture content (%), θ = bulk stress (σ1+ σ2+ σ3), σ3 = confining pressure, σd = deviator stress, PI = plastic index (%), LL = liquid index (%), P200 = percentage passing #200 sieve (%), %clay = % particles finer than 2 micron size, Pa = normalizing stress, toct = octahedral shear stress, Cu = uniformity coefficient, Cc = coefficient of curvature, k1, k2, and k3 = regression parameters.
15
Figure 2.1 Illustration of Soil Behavior under Repeated Loads.
16
Figure 2.2 Field Plate Bearing Load Test Schematic
17
CHAPTER 3
EXPERIMENTAL PROGRAMS
3.1 General Several field and laboratory experimental studies were conducted in Florida to evaluate the resilient modulus characteristics of Florida pavement soils [Ping et al., 2000; Ping et al., 2001; Ping and Ling, 2007; Ping and Ling, 2008]. An extensive field static plate bearing load testing program was carried out to evaluate the in-situ bearing characteristics of pavement base, subbase, and subgrade soils [Ping, Yang, and Gao, 2002]. Typical subgrade soils were excavated from the field test sites and obtained for laboratory resilient modulus evaluation. A full scale laboratory evaluation of the subgrade performance was also conducted in a test-pit facility, which simulates the actual field conditions. The subgrade and base layer profile of a full-scale flexible pavement system was simulated in the test-pit facility. The subgrade materials were tested in the test-pit using cyclic plate bearing load test under various moisture conditions simulating different field pavement moisture conditions [Ping and Ling, 2008]. In conjunction with the field and full-scale laboratory experimental programs, a laboratory triaxial testing program was performed to evaluate the resilient modulus characteristics of the subgrade materials [Ping et al., 2002; Ping and Ling, 2008]. Subsequently, comparative studies were conducted to evaluate the resilient modulus from laboratory cyclic triaxial tests and field experimental studies. The field and laboratory experimental programs are presented as follows.
3.2 Field Experimental Program The primary objective of the field experimental program was to characterize the in-situ bearing behavior of pavement layers on selected types of pavement soils in Florida. To achieve this objective, a series of tests were conducted on several flexible pavement sites around Florida. The sites were evenly scattered within the state to better
18
represent different soil conditions in Florida (Table 3.1). The selection of sites took into account the following considerations: a) soil type and history, b) pavement layer homogeneity, c) layer thickness, d) field operational considerations. Granular materials (A-3 and A-2-4 soils) were most commonly encountered as roadbed in Florida. Thus, only the granular soils were analyzed in the field study [Ping et al., 2000]. Many different types of tests have been devised for measuring the characteristics of pavement structures in place. In Florida, plate bearing and Falling Weight Deflectometer (FWD) tests are commonly used for evaluating pavement structures at the FDOT. While the field plate bearing test is a destructive test, FWD is a nondestructive test. For this field study, these tests were used to determine the modulus of elasticity of pavement layers at the tested site under its natural moisture content and density. A Dynatest 8000 FWD system was used for the field testing program. The system consists of a Dynatest 8002E FWD trailer, a table top computer with a printer, and a Dynatest 8600 system processor interfaced with the FWD trailer as well as with the computer. A certain weight is mounted on a vertical shaft and housed in the trailer. The weight is hydraulically lifted to a predeterminated height and then dropped onto a rubber buffer system resulting in a load pulse of 25 to 30 msec. The load is applied to the surface of pavement through a load cell and a circular plate. The standard load plate has a 300 mm (11.8 in.) diameter. By use of different drop weights and heights, it can vary the impulse load to the pavement structure from about 6.7 to 120 kN (1,500 to 27,000 lb.) For flexible pavement, drops result in loads of approximately 27 kN (6,000 lb.), 40 kN (9,000 lb.), 53 kN (12,000 lb.), and 71 kN (16,000 lb.). The Dynatest 8000 has seven geophones spaced at radial distances of 0, 8, 12, 18, 24, and 36 inches apart from the center of the loading plate. The first sensor is always mounted at the center of the foot plate. Peak values of surface deflections are collected by the sensors and stored in or printed by the computer system. The FWD test setup is shown in Figure 3.1. After completion of the FWD test at each site, the in-service pavements were trenched. The asphalt concrete structural layer was cut, approximately 1.678×3.355 m (5.5×11 ft.), and removed. For each layer of the pavement beneath the asphalt concrete,
19
including the base and stabilized subgrade (subbase), the in situ moisture content and density were measured using a nuclear gauge device. The speedy moisture content test was also conducted to check the nuclear moisture content data. In Florida, the speedy moisture content test is designated as FM 5-507 in the Manual of Florida sampling and testing methods [FDOT, 2001]. The layer thickness was measured to determine the vertical pavement profile, which was used later in the FWD backcalculation program. Representative bag samples of each layer were taken for future testing of the resilient modulus in the laboratory. The plate bearing load test was conducted on the subgrade (embankment) layer (Figure 3.2). The test procedures employed may vary somewhat, depending on the adoptive agencies, but the method is generally in close agreement with ASTM D 1196 [ASTM, 2004]. In Florida, the plate load test is designated as FM 5-527 in the Manual of Florida sampling and testing methods [FDOT, 2000]. The test apparatus consisted of a water tanker with a total capacity of 27,240 kg (60,000 lb.) and a hydraulic jack with a spherical bearing attachment that was capable of applying and releasing the load increments. The hydraulic jack had sufficient capacity for applying the maximum load required and was equipped with an accurately calibrated gauge, which indicates the magnitude of the applied load. A 305 mm (12 in.) diameter circular steel plate was used for applying the load [ACI, 2006]. A schematic illustration of the test setup is shown in Figure 3.2. An aluminum alloy deflection beam was used to mount two graduated (in units of 0.001 inch) dial gauges for measuring deflections. Prior to applying the incremental testing loads, three seating loads were applied to seat the loading system and bearing plate. Each seating load was to produce a total deflection of about 0.762 m (0.03 in.). Each of the three seating loads was applied in four or five equal increments. After each increment of test load had been applied, the deflection was allowed to continue until a rate of no more than 0.0254 mm/min (0.001 in./min). The load and deflections were then recorded. This procedure continued until the average total deflection of 1.27 mm (0.05 in.) plus the average rebound deflection from the third seating load had been reached. The moisture and density of the subgrade layer were measured before the test and the soil samples were taken after the plate bearing load test. After completion of the plate
20
bearing load test program, the subgrade soil layer was excavated up to more than 1 m below the tested stratum to check the layer homogeneity. After completion of the field tests, representative samples of the subgrade materials were then obtained and transported to the laboratory. The basic properties of each soil were evaluated in the laboratory prior to the resilient modulus test. All soil materials were reconstituted in the laboratory to the in situ moisture and density conditions, and the optimum conditions for the resilient modulus test. Two replicate resilient modulus tests were conducted on each type of soil. This was done to investigate the repeatability of the test and to ensure the validity of the resilient modulus test results.
3.3 Test-pit Experimental Program The purpose of test-pit experimental program was to evaluate the resilient modulus of the subgrade materials with changing groundwater levels. The test-pit evaluation of subgrade soils served the following advantages: (1) The test-pit can be used to simulate the different material components of a pavement system on a full-scale basis. (2) The test-pit can facilitate the change of water level so as to simulate the different moisture conditions in a practical situation. (3) Together with a loading system, the test can be used to investigate the deformation characteristics of subgrade materials under the influence of static and dynamic loads.
3.3.1 Test Materials The subgrade materials under evaluation in the test-pit test were the typical A-3 (fine sand with %fines < 10% ) and A-2-4 (silty or clayey sand with %fines < 35%) commonly in use in Florida. A total of ten types of subgrade soil representing the percent of fines passing No. 200 sieve, which range from 4% to 30%, were evaluated in three stages of testing (Phase I, Phase II, and Phase III). The pertinent characteristics of the subgrade soils are presented in Table 3.2. The test materials were tested using
21
both the test-pit facility and the laboratory triaxial test under the same density and moisture conditions for the future comparison.
3.3.2 Test-pit Setup The complete setup of test-pit experiment is mainly comprised of two parts: fullscale test-pit and loading system. The schematic is shown in Figure 3.3. The FDOT test-pit is shaped like a rectangular reinforced concrete vessel that is 7.31 m (24 ft.) long, 2.44 m (8 ft.) wide, and 2.13 m (7 ft.) deep. Below the subgrade material was the standard embankment that was composed of three layers of different materials. The bottom layer was composed of a bed of 305 mm (12 in.) river gravel that facilitated the upward percolation of ground water. A builder’s sand layer that was 305 mm (12 in.) thick rested upon the river gravel and was kept separated with gravel by a permeable filter fabric. The third layer was a 305 mm (12 in.) depth of standard A-3 soil that was used as the top layer of simulated embankment. The test-pit was surrounded by a sump with an interconnecting channel system for controlling the water table. A hydraulic loading device was attached to an over-hanging 24 WF Beam which facilitated the transverse movement of the loading device, while the 24 WF beam itself traveled longitudinally above the test-pit, thus providing a two-dimensional selection of loading location. A standard 305 mm (12 in.) diameter rigid plate was used to simulate the single wheel load upon the tested soil. Vertical deformations of the soil were measured through linear variable displacement transducer (LVDT). To best simulate the dynamic impact of moving vehicles on the subgrade, the plate loads were conducted in a cyclic manner, on second per cycle with loading periods of 0.1 and 0.9 seconds for the rebound of tested materials. This was consistent with the loading frequency used in laboratory triaxial resilient modulus test. In order to achieve a certain deformation curve with respect to the number of load cycles, 30,000 load cycles were conducted.
3.3.3 Test Sequence The subgrade layer was prepared by achieving the maximum dry unit weight with a vibratory compactor for each layer. The water content and unit weight of each layer was recorded upon compaction. After the water level was set to the desired height, a
22
TDR probe was deployed for measuring the moisture content within each layer of subgrade material in the test pit. Sufficient time was allowed to ensure that the moisture equilibrium was completed through capillary action at each water level. The base clearance, which is defined as the clearance or separation between the groundwater level and pavement base layer within a pavement system, is also introduced to evaluate the water level. The groundwater level simulation was arranged as follows and is illustrated in Figure 3.4: 1. Drained condition – water level was at 610 mm (24 in.) below the top of the embankment (i.e., 1.5 m/5.0 ft. base clearance) 2. Optimum condition – water level was at the top of the embankment (i.e., 0.9 m/3.0 ft. base clearance) 3. Wet condition 1 – water level was at 305 mm (12 in.) above the embankment (i.e., 0.6 m/2.0 ft. base clearance) 4. Wet condition 2 – water level was at 610 mm (24 in.) above the embankment (i.e., 0.3 m/1.0 ft. base clearance) 5. Soaked condition – water level was at the top of the subgrade test material (i.e., 0.0 m/0.0 ft. base clearance) A standard 305 mm (12 in.) diameter rigid plate was used to simulate the single wheel load upon the tested soil. Two load types were applied: 137.8 kPa (20 psi) without a base layer and 344.5 kPa (50 psi) with a 127 mm (5 in.) limerock base layer in place. The soils were tested under 137.8 kPa (20 psi) loading first; then the base layer was added and the 344.5 kPa (50 psi) loading was applied. The test sequence was arranged as follows and is illustrated in Figure 3.4: •
Phase I soils (A-3): at water levels A, B, C, F, and H
•
Phase I soils (A-3 and A-2-4): at water levels B, C, F, and H
•
Phase II soils: at water levels A, B, C, F, and H
•
Phase III soils: at water levels B, C, D, E, F, G, H, I, and J
23
3.4 Laboratory Experimental Program The primary objective of the laboratory experimental program was to evaluate the resilient modulus characteristics of the Florida subgrade soils. To achieve the objective, samples of soil material were collected from the field test sites and from the test-pit test program. The subgrade soils were transported to the laboratory in Tallahassee for evaluation. The laboratory experimental program includes the test materials, the resilient modulus testing program, and the engineering property analysis [Ping et al., 2000; Ping and Ling, 2008].
3.4.1 Test Materials The soil materials consisted of A-3 soils, A-2-4 soils, and A-2-6 soils. The basic properties of each soil were evaluated in the laboratory prior to the resilient modulus test. A summary of the soil materials that were tested for basic properties characterization and classification is presented in Table 3.2 and Table 3.3 for information.
3.4.2 Resilient Modulus Testing Program For the resilient modulus test, all of the test protocols require the use of a triaxial chamber, in which confining pressure and deviator stress can be controlled. The test method for determining the resilient response of pavement materials is basically a triaxial compression test, in which a cyclic axial load is applied to a cylindrical test specimen. The load is measured by a load cell, while the resilient strain is measured. The test is usually conducted by applying a number of stress repetitions over a range of deviator stress levels and confining pressure levels representing variations in depth or location from the applied load. An MTS model 810 closed-loop servo-hydraulic testing system and a resilient modulus triaxial testing system were used in this study. The schematic of configuration of the test system is shown in Figure 3.5. The major components of this system include the loading system, digital controller, workstation computer, triaxial cell, and linear variable differential transducer (LVDT) deformation measurements system.
24
The schematic of triaxial cell setup is shown in Figure 3.6. In addition to two vertical LVDTs measuring the vertical displacements, a fixture attached with four horizontal LVDTs was designed to measure the horizontal displacements for the determination of Poisson’s ratio. This device was positioned in the middle half length of the specimen with four horizontal LVDTs attached at 90-degree intervals. The horizontal displacement can be obtained by averaging the measurements from the four horizontal LVDTs. The tests were performed using the AASHTO T292-91I [AASHTO, 1991] test standard for the Phase I and II soils, with both middle-half and full-length LVDT position measurements. The AASHTO T307-99 [AASHTO, 2003] test standard was used for the Phase III soils with full-length LVDT position measurement. The AASHTO T307-99 method was considered an improvement to the AASHTO T292-91I method. The T30799 method covers procedures for preparing and testing untreated subgrade and untreated base/subbase materials for determination of resilient modulus under conditions representing a simulation of the physical conditions and stress states of materials beneath the flexible pavements subjected to moving wheel loads. The original setup of LVDTs in Designation T307-99 was at an external position outside of the triaxial cell, but the location was changed to an internal position inside the cell for a better test results. As for the compaction effort, the 100% Modified Proctor was used for the Phase I and Phase II soils in accordance with AASHTO Designation T 180, while the 100% Standard Proctor was used for the Phase III soils in accordance with AASHTO Designation T 99. An updated controller with its advanced software was used to control the test processes and acquire the test data. The raw data was acquired using the mode of the Peak/Valley, which recorded the test data at its peak and valley levels of each cycle. The output of the data acquisition system includes a graphic display of sampled dynamic load and displacement waveforms and a data file. The data in data file format was selected for further data deduction and analyses.
3.4.3 Test Procedure The resilient modulus test procedures were basically followed from AASHTO T292-91I and AASHTO T307-99. The comparison of resilient modulus test procedures
25
for granular soils is shown in Table 3.4. Since the laboratory resilient modulus simulates the conditions in the pavement subgrade, the stress-state should be selected to cover the expected in-service range. Resilient properties of granular specimens should be tested over the range of confining pressures expected within the subgrade layer. A template was created to monitor the test sequences. In the test sequences, the confining pressures decrease while the deviator stresses increase during each confining pressure stage. The procedures are described as follows: •
Open a template and apply 50 repetitions (T292-91I) or 100 repetitions (T397-99) of the smallest deviator stress at the highest confining pressure. The average recoverable deformation of each repetition is recorded automatically.
•
Apply the same repetitions of each of the remaining deviator stresses to be used at the present confining pressure.
•
Decrease the confining pressure to the next desired level and adjust the deviator stress to the smallest value to be applied at this confining pressure.
•
Increase the deviator stress to the next desired level and continue the process until testing has been completed for all desired stress states.
•
Disassemble the triaxial chamber and remove all apparatus from the specimen.
3.4.4 Determination of Resilient Modulus During the resilient modulus test, after finishing the specimen conditioning stage, a series of tests with different deviator stresses at different confining pressure were performed and the data were recorded for every cycle of each test. However, only the last five cycles of each test were used for analyses following the AASHTO procedures. The resilient modulus was calculated from the load and deformation using the following equation:
MR =
Where σd = axial deviator stress εr = axial recoverable strain
26
σd εr
(3.1)
Table 3.1 Summary of Test Sites for Field Plate Load Test Embankment Location Lee County, Site A Lee County, Site B Polk County, Site A Polk County, Site B Clay County, Site A Clay County, Site B Martin County, Site A Martin County, Site B Osceola County, Site A Osceola County, Site B Seminole County, Site B Gadsden County, Site A Seminole County, Site A Jefferson County, Site B
27
Soil Type A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-2-4 A-2-4 A-2-4
Table 3.2 Engineering Properties of Subgrade Material for Test-Pit Test Soil Classification AASHTO USCS
Soil
Phase
A3-1 A3-2 A24-1 A24-2 A24-3
I I II I III
A-3 A-3 A-2-4 A-2-4 A-2-4
SW-SP SW-SP SC-SM SC-SM SC-SM
Passing No. 200 Sieve (%) 4 8 12 14 15
A24-4 A24-5 A24-6 A24-7 A24-8
II III II II III
A-2-4 A-2-4 A-2-4 A-2-4 A-2-4
SC-SM SC-SM SC-SM SC-SM SC-SM
20 23 24 30 30
Clay Content (%)* 6 3 10 4
Optimum Moisture Content (%) 10.0 11.5 12.1 10.5 9.2
8 6 5 16
10.0 8.8 10.7 12.0 10.3
Maximum Dry Unit Weight† pcf kN/m3
LBR ‡
Permeabil ity (cm/sec)§
106.5 112.0 110.6 122.0 118.2
16.7 17.6 17.4 19.2 18.6
22 45 30 124 83
5.5E-03 2.1E-03 3.1E-04 2.5E-04 2.8E-04
124.4 128.4 116.3 116.0 123.3
19.5 20.2 18.3 18.2 19.4
146 132 69 72 127
1.0E-04 7.4E-07 6.5E-05 2.0E-05 5.6E-07
* Particles finer than 0.002 mm † AASHTO T 180 and T 90 ‡ LBR: Limerock Bearing Ratio, LBR = 1.25*CBR (California Bearing Ratio) § AASHTO D5084-90
28
Table 3.3 Summary of Material Properties for Laboratory Test Embankment Location
Soil Type
Lee County, Site A Lee County, Site B Polk County, Site A Polk County, Site B Clay County, Site A Clay County, Site B Martin County, Site A Martin County, Site B Osceola County, Site A Osceola County, Site B Seminole County, Site B Gadsden County, Site A Seminole County, Site A Jefferson County, Site B
A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-2-4 A-2-4 A-2-4
29
Dry Density (pcf) 107.9 105.0 108.7 110.2 104.7 101.7 106.3 113.4 107.3 103.4 107.3 116.6 108.5 131.1
Moisture Content (%) 10.8 13.3 12.4 10.8 12.8 12.4 9.6 9.5 12.7 12.8 12.7 15.1 8.4 8.3
Table 3.4 Comparison of Test Procedures for Granular Soils Test method Procedure Unit Conditioning 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
AASHTO T292-91I Confining Deviator Load Pressure Stress Number psi psi 15 12 1000 15 7 50 15 10 50 15 15 50 10 5 50 10 7 50 10 10 50 10 15 50 5 3 50 5 5 50 5 7 50 5 10 50 2 3 50 2 5 50 2 7 50
30
AASHTO T307-99 Confining Deviator Load Pressure Stress Number psi psi 6 4 500 6 2 100 6 4 100 6 6 100 6 8 100 6 10 100 4 2 100 4 4 100 4 6 100 4 8 100 4 10 100 2 2 100 2 4 100 2 6 100 2 8 100 2 10 100
Figure 3.1 Field Falling Weight Deflectometer Test Setup
31
Figure 3.2 Field Plate Bearing Load Test
32
Nuclear Gauge
TDR
(a)
(b) Figure 3.3 Test-pit System: (a) Overview of Test Pit; (b) Schematic Diagram of Loading System & Cross Sectional View
33
344.5 kPa (50 psi) Load
TDR Probe
Subgrade Test Material
H
WT@36 in. WT@24 in.
D
G
I
WT@12 in.
C
F
J
WT@0 in.
B
E
Embankment Soil
River Gravel
Subgrade Test Material
Embankment Soil WT@-24 in.
Builder's Sand
Limerock Base Layer
A 137.8 kPa (20 psi) Load w/o Base Layer
344.5 kPa (50 psi) Load w/ Limerock Base Layer
Builder's Sand River Gravel
Figure 3.4 Test–Pit Test Sequence for Different Water Level Adjustments
34
Base Clearance
137.8 kPa (20 psi ) Load
Figure 3.5 Schematic of Laboratory Resilient Modulus Test Program
35
Figure 3.6 Schematic of Triaxial Test for Resilient Modulus Measurement
36
CHAPTER 4
SUMMARY OF EXPERIMENTAL RESULTS
4.1 Field Experimental Results The field experimental Program was conducted to evaluate the supporting characteristics of in situ pavement layers [Ping et al., 2000]. The experimental results from the field bearing plate load tests are presented in this section. The plate bearing load test results were calibrated by using secant modulus concept [Ping et al., 2000].
4.1.1 Load-Deformation Curve Regression Model In the field testing program the number of load applications, the angle of internal friction, and the geometry of the bearing plate are constant. Base on this information, after analyzing the data obtained from the field plate load test, a two-constant hyperbolic model was proposed to represent the relation of the load-deformation as follows:
P=
∆ a + b∆
(4.1)
where P = load ∆ = deflection a, b = constants. The representation of the load-deflection curve is illustrated in Figure 4.1. In order to determine the modulus of materials in situ by means of plate load tests, some assumptions concerning material behavior must be made. With the assumption that the soil layer is homogeneous, isotropic, elastic, and infinite in depth, the modulus of the material can be determined from the Equation (4.2) and (4.3).
E =
π pr 2∆
(1 − υ 2 )
37
(4.2)
Where, E = the modulus of elasticity of the material ∆ = deflection of plate associated with the pressure p = pressure applied to the surface of the plate r = radius of the circular plate υ = Poisson’s ratio 0.35 was chosen for the Poisson’s ratio of granular subgrade materials [Ping et al. 2003]. Equation (4.2) can be further derived from the following equation:
E=
1.38 pr ∆
(4.3)
Then, Equation (4.3) can be rewritten as follows:
E = 288.23
P ∆
(4.4)
While
p=
P πr 2
(4.5)
where E = modulus of elasticity of the material (MPa) P = load (kN) ∆ = deformation of the plate associated with the load P (×10-5 m) Replacing Equation (4.1) into Equation (4.4) yields the following two equations: 1 − bP E = 288.23 = f ( P) a
E=
288.23 = f (∆) a + b∆
38
(4.6)
(4.7)
In the two-constant hyperbolic model, the strength parameter was assumed to be related to the shape of the load-deformation parameter curve. From Equation (4.6), the modulus was dependent on the load P so that various modulus values were obtained due to the different applied load. Therefore, the use of a secant modulus seemed to be a logical approach to the analysis. The modulus in Equation (4.4) can be considered as a secant modulus. But it is necessary to select a value for the load (P) or deformation (∆). In the Florida method FM5-527, the modulus of the tested soil layer is calculated using the deflection of 1.27 mm (0.05 in.). It may not be able to perfectly reflect the characteristics of the soils to determine the moduli for soils of various strengths at the same deflection value. The average secant modulus, which depends only on the parameters of the load-deflection curve, was defined as follows:
∫ E=
Pult
0
Esec ant (@ P =
EdP
Pult
=
144.12 a
1 144.12 Pult ) = E = 2 a
(4.8)
(4.9)
It was found that the average secant modulus will be equal to the secant modulus when the applied load is equal to half of the ultimate load of the soil [Ping et al. 2002]. Modulus of subgrade reaction k is an essential parameter for the rigid pavement design. Combining Equations (2.2) and (4.1), it can be determined by the following equation:
k=
1 P P 1 − bP 1370.5 = 1370.5 = 1370.5 = 2 ∆ a a + b∆ πr ∆
where k = modulus of subgrade reaction (MPa/m) P = load (kN) ∆ = displacement (×10-5 m)
39
(4.10)
In the AASHTO design guide, ∆ is the displacement of a 30 in. (762 mm) diameter rigid plate under a given static pressure, p = 10 psi (68.9 kPa).
4.1.2 Plate Bearing Load Test Results The two-constant hyperbolic model (Equation (4.1)) was proposed to represent the load-deformation relationship. The load-deformation curve and hyperbolic function of each test soil are shown in Figure 4.2. The R-squared values are above 0.99. The model fits the data very well. The load-deformation relationship parameters a and b can be considered as representative of the soil strength, and were used to calculate the modulus of elasticity. The secant modulus at the deflection of 1.27 mm and average secant modulus values calculated from Equation (4.6) and (4.7) are presented in Table 4.1. The modulus of subgrade reaction k, which were calculated using Equation (4.10) with 12 in. diameter plate, and are also listed in Table 4.1.
4.2 Test-Pit Test Results Ten types of soil representing typical Florida subgrade materials were tested in the test-pit program [Ping and Ling, 2008]. For each soil, static and cyclic (up to 30,000 cycles for simulation of the dynamic effect) plate load tests were conducted under different levels of groundwater table. Since the resilient behavior of subgrade soil under the dynamic loading was influenced by the soil properties as well as the moisture profile for various groundwater levels. The test-pit experimental results are presented in reference to the various level of groundwater table.
4.2.1 Equivalent Resilient Modulus The resilient modulus obtained from the plate load tests on subgrade is based on Boussinesq’s theory of deflections at the center of a circular plate. Burmister has extended this theory to a two-layer elastic system [Burmister, 1943]. The layers are assumed to be homogeneous, isotropic, and elastic solid with a continuous interface, and with the bottom layer being infinite in depth. In the test pit, more than two layers of different materials are under the rigid test plate. An equivalent resilient modulus is used to indicate that the calculated composite resilient is not exactly the modulus of the
40
tested subgrade material, but an equivalent value under test pit situation. In the plate load test, a major portion of the stress inference occurs, according the theory, within a depth of two times of diameter. Because the tested subgrade layer thickness is three times of rigid test plate diameter, this equivalent modulus is very close to the resilient modulus of the subgrade. Under these circumstances, the equivalent single-layer resilient modulus under the cyclic loading on a two-layer system (base and subgrade layers) can be derived from the theory of elasticity:
E eR =
π pa ∆
(1 − υ 2 )
(4.11)
R
Where, EeR = Equivalent resilient modulus of a two-layer system ∆R = Resilient deflection of the two-layer system at N (number of cyclic load) p = Surcharge pressure from the circular plate a = Radius of the circular plate υ = Poisson’s ratio 0.35 was chosen for the Poisson’s ratio of granular subgrade materials [Ping et al. 2003]. The equivalent resilient modulus can be further derived from the following equation:
E eR =
1.38 pa ∆R
(4.12)
The static load test was cycled three times for a total of three static loads and followed with repeated rigid plate tests. The number of load cycles up to 30,000 was recorded. The equivalent resilient modulus was determined from the resilient deflections using Equation (4.12).
4.2.2 Equivalent Resilient Modulus Results The resilient modulus obtained from the plate load tests on subgrade is based on Boussinesq’s theory of deflections at the center of a circular plate. The equivalent
41
resilient modulus values were calculated using Equation (4.12). The plate load test results for the ten soils are summarized in Table 4.2, which records the average water content and plate load equivalent resilient modulus under different water level conditions.
4.3 Laboratory Experimental Results Both the AASHTO T292-91I and T307-99 test method were used to measure the resilient modulus of subgrade soils. During the resilient modulus test, specimen conditioning was conducted first. Then, a series of tests at different deviator stresses and confining pressures were performed, and the data were recorded for every cycle of the test. However, only the last five cycles were used for computation of resilient modulus. Of each condition, two replicate resilient modulus tests were conducted on each type of soil. The resilient modulus was calculated from the deviator stress and resilient strain using Equation (3.1).
4.3.1 Regression Analysis The resilient modulus test results were reported in a tabular form including the deviator stress, axial strain, confining pressure, and bulk stress. A regression model was used to get the regression equation of MR from the confining pressure and bulk stress as follows: when modulus is dependent on bulk stress: M R = k1θ k2
(4.13)
when modulus is dependent on confining pressure:
M R = k 3σ 3
k4
Where θ = bulk stress, sum of the principal stresses, (σ1+ σ2+ σ3) σ3 = confining pressure or minor principal stress k1, k2, k3, k4 = regression constants 42
(4.14)
In actual field conditions, the confining pressure at subgrade layers was found to be approximately 13.8 kPa (2.0 psi). Because the laboratory resilient modulus is stress dependent, a constant stress level has to be determined in selecting the resilient modulus of roadbed soils for pavement design.
The Asphalt Institute [AI, 1982]
recommended using a confining pressure of 13.8 kPa (2.0 psi) and a deviator stress of 41.4 kPa (6.0 psi) for subgrade layers in determining the resilient modulus [Ping and Ge, 1997]. Daleiden et al. [Daleiden et al., 1994] believed that using a deviator stress of 13.8 kPa (2 psi) and a confining pressure of 13.8 kPa (2 psi) could represent the average stress and pressure values that occurred in the subgrade under traffic loading and surcharge. Chen [Chen, 1999] found that the deviatoric stresses and confining pressures for the pavement structure under a 40 kN load were approximately 20 to 35 kPa (3-5 psi) and 7 to 14 kPa (1-2 psi), respectively. In a laboratory resilient modulus test, the resilient modulus value obtained at a deviator stress of 34.5 kPa (5.0 psi) under the confining pressure 13.8 kPa (2.0 psi) was considered representative of the in-situ subgrade modulus. Therefore, the average resilient modulus values at 2 psi confining pressure as well as at 11 psi bulk stress were obtained for each soil material. To compare the laboratory resilient modulus with the resilient modulus from test-pit test and field test, the laboratory resilient modulus results from those two projects are listed in Table 4.3 and 4.4 for the further comparison.
4.3.2 Moisture Effect on Resilient Modulus The representative resilient modulus data obtained from the bulk stress of 75.8 kPa (11.0 psi) at different moisture conditions are presented in Table 4.4. In general, the resilient modulus decreases with an increase in moisture content. Two exceptions were the slightly increase of soil A3-1 and A24-7 from optimum condition to soaked condition. This situation may be caused by the soil cohesion due to the added moisture. The effect of moisture content on the resilient modulus of Phase I and II soils is shown in Figure 4.3. It is clearly shown that the resilient modulus of subgrade materials usually decreases with an increase in moisture content. Specifically, moisture content has a significant effect on the resilient modulus of A24-2 soil and A24-7 soil whereas its effect is not significant on the resilient modulus of other types of soils [Ping et al. 2010].
43
Table 4.1 Secant Modulus and k Value from Plate Bearing Load Tests Embankment Location Soil Average Secant Modulus of Type Secant Modulus at Subgrade Modulus ∆=1.27 mm Reaction k (MPa) (MPa) (MPa/m) Lee County, Site A A-3 53.8 58.8 466.7 Lee County, Site B A-3 114.0 145.9 1054.7 Polk County, Site A A-3 71.5 114.8 667.3 Polk County, Site B A-3 156.0 244.8 1469.7 Clay County, Site A A-3 120.4 148.1 1214.9 Clay County, Site B A-3 121.7 166.6 1132.7 Martin County, Site A A-3 81.3 86.5 594.4 Martin County, Site B A-3 89.6 81.9 870.4 Osceola County, Site A A-3 114.8 117.7 1040.3 Osceola County, Site B A-3 78.1 92.8 581.1 Seminole County, Site B A-3 120.2 136.4 1102.4 Gadsden County, Site A A-2-4 123.1 152.1 1185.3 Seminole County, Site A A-2-4 121.5 158.2 1126.4 Jefferson County, Site B A-2-4 127.2 114.5 1144.2
44
Table 4.2 Plate Load Equivalent Modulus Test Results Water Level (in)
Test Sequence
-24 0 0 12 12 12 24 24 24 36
A B E C F J D G I H
A3-1
A3-2
A241
A242
A243
A244
A245
A246
A247
A248
209 186 183 260 99
178 591 195 542 378 119 335 220 112
Equivalent Resilient Modulus (MPa) 178 145 132 264 196
204 174 300 225
174 125 125 241 174
183 154 227 106
45
114 247 109 196 182 82 144 135 108
196 183 175 250 208
344 671 336 607 414 205 413 192 157
171 187 135 214 169
Table 4.3 Laboratory Resilient Modulus Test Results of Subgrade (Field Plate Bearing Load Test Project) Subgrade Soil Soil LAB MR at the state of stress of plate Type bearing load test (MPa) P(∆=1.27 mm) ½ P ult Lee County, Site A Lee County, Site B Polk County, Site A Polk County, Site B Clay County, Site A Clay County, Site B Martin County, Site A Martin County, Site B Osceola County, Site A Osceola County, Site B Seminole County, Site B Gadsden County, Site A Seminole County, Site A Jefferson County, Site B
A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-3 A-2-4 A-2-4 A-2-4
105.48 131.34 177.08 205.19 113.11 129.46 132.62 163.02 138.89 123.88 154.66 102.84 173.28 82.09
46
107.67 146.91 282.92 267.52 123.17 150.97 135.03 159.45 140.00 131.87 161.71 113.32 194.59 79.62
Table 4.4 Laboratory Average Resilient Modulus at Different Moisture Conditions (Test-pit Plate Load Test Project) Soil
Number of Specimen
A3-1 A3-2 A24-1 A24-2 A24-3 A24-4 A24-5 A24-6 A24-7 A24-8
2 2 2 2 2 2 2 2 2 2
Dry Condition Moisture Content (%) 6.2 5.4 7.1 8.4 7.8 7.7 6.7 -
Mr (MPa) Middle Full Half Length 167 116.9 208.2 120.2 140.6 96.5 540.6 305.7 212.0 142.5 125.7 109.4 775.3 285.2 -
Optimum Condition Moisture Content (%) 9.6 11.4 12.1 10.6 9.3 10.0 8.8 10.7 12.2 10.4
47
Mr (MPa) Middle Full Half Length 145.5 108.1 157.7 118.8 117.9 95.6 246.6 166.6 67.0 123.2 109.4 186.3 116.5 92.1 133.0 71.8 63.8
Soaked Condition Moisture Content (%) 15.2 13.6 14.1 11.5 12.0 11.7 13.3 -
Mr (MPa) Middle Full Half Length 149.5 81.8 137.7 91.9 107.6 90.8 182.6 97.2 121.6 100.0 94.8 68.9 136.3 71.7 -
asymptote
Load, P
Pult
Ei
Esec(at P = Pult/2)
P = ∆/(a+b∆) 1/b
Pult/2
tanθ = 1/a
Deformation, ∆ Figure 4.1 Rectangular Hyperbolic Representation of Load-Deformation Curve
48
Lee County, Site A
30
70 Load, P (x10 N)
20 P = ∆/(2.679+0.018∆)
15
2
R = 0.994 10 5
50 100 -5 Deformation, ∆ (x10 m)
P = ∆/(1.264+0.006∆)
30
2
R = 0.998
20
0
150
Polk County, Site A
60
50 100 -5 Deformation, ∆ (x10 m)
150
Polk County, Site B
120 100 Load, P (x10 N)
50 40
80
3
3
40
0
0
Load, P (x10 N)
50
10
0
30
P = ∆/(2.015+0.004∆) 2
R = 0.996
20
60
P = ∆/(0.924+0.002∆) 2
R = 0.998
40
10
20
0
0 0
50 100 -5 Deformation, ∆ (x10 m)
150
0
Clay County, Site A
80
50 100 -5 Deformation, ∆ (x10 m)
150
Clay County, Site B
80 70 Load, P (x10 N)
70
60
3
60
3
Load, P (x10 N)
60
3
3
Load, P (x10 N)
25
50 40
P = ∆/(1.197+0.006∆)
30
2
R = 0.994
20 10
40
P = ∆/(1.184+0.004∆)
30
2
R = 0.995
20 0
0
50 100 150 -5 Deformation, ∆ (x10 m)
200
0
Martin County, Site A
50 45 40 35 30 25 20 15 10 5 0
50 100 -5 Deformation, ∆ (x10 m)
150
Martin County, Site B
40 35 30
3
Load, P (x10 N)
Load, P (x10 N)
50
10
0
3
Lee County, Site B
80
P = ∆/(2.203+0.009∆) 2
R = 0.999
25 20
P = ∆/(1.44+0.017∆)
15
2
R = 0.993
10 5 0
0
50 100 150 -5 Deformation, ∆ (x10 m)
200
0
50 100 -5 Deformation, ∆ (x10 m)
Figure 4.2 Load-Deformation Curves of the Tested Soils
49
150
Osceola County, Site A
60
Load, P (x10 N)
40
3
3
Load, P (x10 N)
50
30
P = ∆/(1.255+0.009∆) 2
R = 0.999
20 10 0 0
50 100 -5 Deformation, ∆ (x10 m)
150
50 100 -5 Deformation, ∆ (x10 m)
150
Gadsden County, Site A
70 Load, P (x10 N)
50
60
3
3
Load, P (x10 N)
2
R = 0.999
80
60
40 P = ∆/(1.199+0.007∆)
30
2
R = 0.997
20 10
50 40
P = ∆/(1.171+0.006∆)
30
2
R = 0.996
20 10
0
0 0
50 100 -5 Deformation, ∆ (x10 m)
150
0
Seminole County, Site A
80
50 100 -5 Deformation, ∆ (x10 m)
150
Jefferson County, Site B
60
70 Load, P (x10 N)
50 3
60
3
Load, P (x10 N)
P = ∆/(2.291+0.006∆)
0
Seminole County, Site B
70
Osceola County, Site B
50 45 40 35 30 25 20 15 10 5 0
50 40
P = ∆/(1.187+0.005∆)
30
2
R = 0.995
20
40 30
P = ∆/(1.132+0.011∆) 2
R = 0.996
20 10
10 0
0 0
50 100 -5 Deformation, ∆ (x10 m)
150
0
50 100 150 -5 Deformation, ∆ (x10 m)
200
Figure 4.2 Load-Deformation Curves of the Tested Soils – continued
50
Resilient Modulus vs. Moisture Content (Confining Pressure 13.8 kPa, Deviator Stress 34.5 kPa)
800
A3-1 700
A3-2
A24-2 -3.4375
A24-1
y = 815392x
A24-2
Resilient Modulus (MPa)
600
A24-4
A24-7 -2.6846
y = 125793x
500
A24-6 A24-7
400 A24-4 -1.3427
y = 3141.5x 300 A3-2 -0.4252
y = 429.2x
A3-1 -0.1219
200
y = 202.71x A24-1
100
-0.3744
y = 294.13x
A24-6 -0.5543
y = 397.07x 0 4
6
8
10
12
14
16
Moisture Content (%)
Figure 4.3 Laboratory Resilient Modulus vs. Moisture Content for Phase I and II soils
51
CHAPTER 5
ANALYSIS OF EXPERIMENTAL RESULTS
5.1 Comparison of Laboratory and Test-pit Test Results The comparison of resilient modulus from laboratory triaxial test and test-pit plate load test is presented in this section. To compare with the laboratory triaxial test results, a layered system was employed to calculate the resilient modulus of each subgrade layer instead of the equivalent modulus for all of the layers. The comparison of the resilient modulus from laboratory triaxial test using middle-half LVDT measurement and full-length LVDT measurement is also presented. A correlation relationship between the laboratory test results and the test-pit test results will be developed.
5.1.1 Layered System Simulation for Test-pit Study In reality, the pavement has several layers. For a general pavement profile, from top to bottom the layers are asphalt concrete, base, subbase or stabilized subgrade, and embankment or roadbed subgrade layers. In test-pit tests, there were at least two layers: embankment and (stabilized) subgrade layers. For some tests, the third layer, a 127 mm (5 in.) limerock layer, was added on the top. Because the water table had different levels in different periods, the subgrade layer should be divided into several layers. To simplify the problem, all six subgrade layers were considered as one single layer. The purpose for setting up a layered system analysis for a test-pit test is to estimate the modulus for each subgrade layer instead of the equivalent modulus for all of the layers. Then the layer modulus for each subgrade can be compared with the results obtained from the laboratory resilient modulus tests. A layered system was established and the KENLAYER computer program [Huang, 1993] was utilized to estimate layered modulus and to find the state of stress at specific points within the subgrade layer. A trial and error procedure was utilized for estimating resilient modulus of the specific subgrade layer. In the procedure, an assumed layer modulus value was first input into the KENLAYER analysis to calculate 52
the deformation of the subgrade layer. If the calculated deformation was equal to the measured deformation, the assumed modulus value was the correct layer modulus. If the calculated deformation was not equal to the measured deformation, the assumed modulus value was readjusted until the calculated deformation matched the measured deformation. Providing 77.2 MPa (11,207 psi) for a soaked embankment, the layer modulus of a subgrade without a limerock base layer on top could be calculated based on the twolayer system. To obtain the subgrade layer moduli for those subgrades with limerock built on top, the limerock layer moduli should be obtained first. This can be done by treating the layers below the limerock layer as one layer based on the two-layer system. The subgrade layer moduli can be computed by providing the limerock moduli on top and the saturated embankment moduli below based on a three-layer system. Since the moisture conditions varied from layer to layer in the test pit, the moisture content was obtained by averaging the moisture content of the top four layers of subgrade (609.6 mm/24 in. in depth from the top of subgrade layer) from TDR measurements. The subgrade layer moduli are presented in Table 5.1.
5.1.2 Comparison of Resilient Modulus from Laboratory Test and Test-Pit Test The laboratory and test-pit tests were performed under various moisture conditions. In the laboratory tests, laboratory compacted specimens were subjected to soaking and drying to reach desired moisture conditions for testing, whereas in the test pit, the groundwater level was raised or lowered to a stabilized condition within the test pit. The laboratory resilient modulus and equivalent layer modulus generally represented the same kind of engineering property of the subgrade performance. The laboratory resilient modulus results calculated using both Equations (4.13) and (4.14) are listed with the subgrade layer modulus in Table 5.1. The layer modulus obtained from the plate load test in the test pit was compared with the laboratory measured resilient modulus from the triaxial tests. Resilient moduli measured from laboratory triaxial tests with both middle-half and full-length LVDT positions were compared with those from plate load tests at the following conditions:
53
•
Lab triaxial tests under dry conditions vs. plate load tests at 609.6 mm (24 in.) water level below embankment
•
Lab triaxial tests at optimum condition vs. plate load tests at 0 mm (0 in.) water level above embankment
•
Lab triaxial tests under wet conditions vs. plate load tests at 914.4 mm (36 in.) water level above embankment
The comparison is shown in Figure 5.1. For most cases, the resilient moduli from the laboratory triaxial test with middle-half LVDTs were close to the corresponding resilient moduli from the test-pit plate load test. The differences between the resilient modulus from the laboratory test and the plate load test were typically about 20 percent of the resilient modulus from plate load test, which is acceptable when moisture content effect were only considered. The 20 percent different was induced primarily because of the different methods used to obtain the moisture content in laboratory test and test-pit test, which was mentioned earlier. For both the test-pit test and the laboratory triaxial test, the optimum moisture conditions were obtained by directly compact the testing material at optimum moisture content. However, for the test-pit test, the soaked and dry conditions were obtained by soaking and draining the testing material that was compacted at optimum moisture, whereas for the laboratory triaxial test, the soaked and dry conditions were obtained by soaking the specimen in water or drying in the air with the mold after the specimen was compacted. Therefore, the moisture content between the laboratory test and test-pit test was not identical. Furthermore, the difference became larger when the resilient modulus from test-pit plate load test was above 200 MPa. This inconsistency of the resilient modulus is due to the fact that the rigid plate is used in the test-pit test; the pressure under the rigid plate is not uniform. It was also shown that the resilient moduli from the laboratory triaxial test with full-length LVDT are lower than the resilient moduli from the test-pit plate load test. The resilient modulus obtained from laboratory triaxial test with middle-half LVDT measurements had a better agreement with the resilient modulus from the test-pit plate load test than with the full-length LVDT measurements. A linear regression analysis was conducted to develop to correlation relationship between the laboratory resilient
54
modulus using middle-half LVDT and the test-pit layer modulus, which is shown in Figure 5.2. The relationship is shown as follow:
M R (Test - Pit) = 0.96 × M R (Middle - Half LVDT) (MPa)
(5.1)
It appeared that the resilient modulus resulting from the laboratory triaxial test with middle-half LVDT measurements were close to the subgrade layer modulus obtained from test-pit plate load test, which simulated the field conditions. The relationship between the resilient modulus measured from middle-half LVDT and the resilient modulus measured from full-length LVDT is shown in Figure 5.3:
M R (Middle − Half LVDT) = 1.53 × M R (Full - Length LVDT) (MPa)
(5.2)
The resilient moduli measured from full-length LVDT are generally lower than the resilient moduli measured from middle-half LVDT. The resilient modulus measured using middle-half LVDT were about 1.5 times larger than the resilient modulus measured using full-length LVDT. In some cases, the middle-half LVDT measurements cannot be performed due to difficulties with the experimental setup. In that situation, the resilient modulus measured from full-length LVDT could be used to estimate the resilient modulus measured from middle-half LVDT. The newest AASHTO laboratory resilient modulus test method T307-99 uses full-length LVDT instead of middle-half LVDT. Therefore, it is necessary to establish a relationship between the resilient modulus measured from full-length LVDT and the resilient modulus measured from testpit test, which is shown in Figure 5.4 as follow:
M R (Test - Pit) = 1.64 × M R (Full - Length LVDT) (MPa)
(5.3)
Since the field resilient modulus test procedure is complicate and timeconsuming, it is necessary to correlation the field resilient modulus value with the laboratory resilient modulus. Based on our correlation relationships shown in Equation (5.1) and (5.3), it was found that the laboratory resilient modulus could be utilized to 55
predict the subgrade resilient modulus in the pavement if an appropriate method was used. 5.1.3 Effect of Groundwater Level on Resilient Modulus As described previously, the resilient modulus is significantly influenced by moisture content, which is affected by the groundwater level. The effect of groundwater level on the resilient modulus of subgrade materials from the test-pit plate load test is shown in Figure 5.5. The groundwater level at the interface of subgrade and embankment soils (0.9 m (3.0 ft.) below base layer) was selected as the reference level. For all of the soils, a higher level of groundwater leads to a decrease in the resilient modulus of subgrade materials. The equivalent resilient modulus values for different types of soil were affected to a different extent under various levels of groundwater. For a change of groundwater from -0.6 m (-2.0 ft.) to 0.0 m (0.0 ft.) under 137.8 kPa (20 psi) plate loading without the base layer, the decrease in resilient modulus was significant for A3-1 and A24-1 soils. When the groundwater level was further increased to 0.3 m (1.0 ft.), there was not much change of resilient modulus values for most soils except for A24-6 soil. For the Phase III soils (A24-3, A24-5, and A24-8), the reduction in resilient modulus became much higher when the groundwater level was increased to 0.6 m (2.0 ft.). When 344.5 kPa (50 psi) plate loading was applied with a limerock base layer, the decrease in resilient modulus values was significant for all of the soils with increasing groundwater level from 0.3 m (1.0 ft.) to 0.9 m (3.0 ft.). For the Phase III soils, there was considerable reduction in resilient modulus with increasing groundwater level especially for the change of groundwater level from 0.3 m (1.0 ft.) to 0.6 m (2.0 ft.) and from 0.6 m (2.0 ft.) to 0.9 m (3.0 ft.). The percent reductions of the resilient modulus at different groundwater are shown in Figure 5.6. The resilient modulus at 0.3 m (1.0 ft.) groundwater level was considered as the reference value. A trend line was drawn to show the decrease of percent reduction with an decrease in the groundwater level. It was shown that the reduction in resilient modulus was significant when the groundwater level was increased from 0.0 m (0.0 ft.) to 0.9 m (3.0 ft.). The percent reduction could reach to 75% when the groundwater level was changed from 0.3 m (1.0 ft.) to 0.9 m (3.0 ft.). The change of
56
percent reduction was almost linear in relationship to the change of the groundwater level from 0.9 m (3.0 ft.) to 0.3 m (1.0 ft.). The decrease of percent reduction then became slower when the groundwater level was decreased to 0.0 m (0.0 ft.). However, there was very little difference in the resilient modulus when the groundwater level was decreased from 0.0 m (0.0 ft.) to -0.6 m (-2.0 ft.). Thus, a 0.0 m (0.0 ft.) groundwater level could be considered the optimum level in terms of the resilient modulus of subgrade materials.
5.2 Comparison of Laboratory and Field Test Results The comparison between the modulus from field plate bearing load test and resilient modulus from laboratory triaxial test at in situ conditions is presented in this section. Modulus of subgrade from field plate load test was calculated using hyperbolic model. Correlation relationships between the laboratory resilient modulus and the field secant modulus will be developed. Then, the resilient modulus will be compared to the modulus of subgrade reaction. A calibrated relationship will be developed to correlate the resilient modulus and the modulus of subgrade reaction.
5.2.1 Comparison of Secant Modulus and Laboratory Resilient Modulus To compare the plate bearing modulus with the laboratory resilient modulus, the state of stresses of the soil under the plate during the plate bearing test must be determined. According to the Burmister’s theory, the major portion of the total deformation occurs within a depth of two times the plate diameter (610 mm). A point, which is 305 mm (12 in.) below the plate and along a vertical line at an offset of 107 mm (4.2 in.) from the center of the plate, a distance equal to 0.7 times the radius of the plate, was selected to calculate the stress state. The lateral stresses at the point, resulting from the applied load, were determined using Boussinesq’s theory of stress distribution and the ELSYM5 computer program. The value of Poisson’s ratio was assumed to be 0.35. The lateral confining pressure caused by the weight of the material at the selected point can be determined by assuming it to be equal to the earth pressure at rest. In the case of granular materials, the coefficient of earth pressure at rest, k0, was assumed to be 0.5. This stress, when added to the lateral stress induced by the applied load, is
57
considered to be the controlling stress in defining the resilient modulus of the granular material at this point. The plate layer modulus and the laboratory resilient modulus are listed in Table 5.2. The comparisons between the secant modulus from field plate bearing load test and laboratory resilient modulus are shown in Figure 5.7 and 5.8. It can be found that the trend of an increasing laboratory resilient modulus with an increasing secant modulus was apparent. The laboratory resilient modulus at the state of stress of field test was close to the secant modulus at small deformation (1.27 mm), while the average secant modulus was lower than the laboratory resilient modulus at the half of ultimate load. From the load-deformation curve, it can be found that the curve is close to a straight line when the deformation is small. Then, the increase of load becomes slower than the increase of deformation. Therefore, due to the large deformation at the half of ultimate load, the secant modulus becomes smaller.
5.2.2 Comparison of Resilient Modulus and Modulus of Subgrade Reaction As mentioned earlier, it is usually impractical to conduct plate bearing load tests in the field on representative subgrade soils for design projects. Thus, it is necessary to develop a relationship between the modulus of subgrade reaction (k) and the roadbed soil resilient modulus (MR). This allows the designer to obtain the k value by simply converting the soil resilient modulus. The AASHTO theoretical relationship between the k value and resilient modulus, based on the assumption that the material is linear elastic, is as follows:
k measured =
MR 19.4
(5.4)
where MR in psi is determined under stress conditions simulating those expected in the field; and k is in pci. By changing the units of MR and k to MPa and MPa/m, the foregoing equation becomes the following: k measured = 2.028M R
58
(5.5)
Equation (5.4) was based on the definition of k using a 30 in. (762 mm) diameter plate. The deflection ∆ of a plate on a solid foundation can be determined by the following equation:
∆=
π (1 − v 2 )qa 2M R
(5.6)
where q = applied pressure, 10 psi v = Poisson’s ratio a = radius of the plate MR = resilient modulus The modulus of subgrade reaction, which is defined as the ratio between an applied pressure q and the deflection ∆, can be expressed as
k=
2M R q = ∆ π (1 − v 2 )a
(5.7)
It can be found that the modulus of subgrade reaction k is inversely proportional to the diameter of the plate [Huang, 1993]. If v = 0.45 and a = 15 in. (381 mm), then Equation (5.7) becomes
k (pci) =
M R (psi) 18.8
(5.8)
Due to the rigid plate restriction of the computer programs, AASHTO re-defined the equation of modulus of subgrade reaction, which is as follows:
k=
P V
59
(5.9)
where P is the magnitude of the load (in pounds) applied to the 30 in. plate and V is the volume (in cubic inches) of soil (directly beneath the plate) that is displaced by the load. This is considered a valid re-definition and allows the rigid loading plate constraint to be relaxed. Without the rigid plate restriction, an elastic layer computer program was used to predict the deflected shapes, displaced volumes and k-values under a 30 in. plate for a range of roadbed soil resilient moduli. Then, Equation (5.8) becomes Equation (5.4). However, it is well known that granular materials and subgrade soils are nonlinear with an elastic modulus varying with the level of stresses. Therefore, this theoretical relationship needs to be evaluated to be accommodated in the pavement design. The modulus of subgrade reaction k from the field plate load tests are listed in Table 5.2. It should be noted that our experiments were conducted using a plate with diameter of 305 mm (12 in.) in the plate bearing load test. Since the modulus of subgrade reaction k is inversely proportional to the diameter of the plate, the k-values has been converted to the values when the plate diameter in the plate bearing load test was 762 mm (30 in.). The comparisons between laboratory resilient modulus and modulus of subgrade reaction are presented in Figure 5.9. The relationship between laboratory resilient modulus and modulus of subgrade reaction for subgrade soils is shown as follows:
or
k (MPa/m) = 2.25 × M R (MPa )
(5.10)
k (pci) = M R (psi) / 17.5
(5.11)
The theoretical relationship was evaluated through the experimental results. It can be found that the relationship from experimental results is close to the theoretical relationship. As mentioned earlier, another relationship, which was developed from LTPP database in the MEPDG, is shown as follows: k (MPa/m) = 0.296 E (MPa)
60
(5.12)
It can be found that the k-value calculated using Equation (5.12) is lower than the kvalue calculated using Equation (5.5). Because Equation (5.12) was developed to estimate the k-values based on a theoretical pavement system of an infinite pavement slab supported on a dense-liquid foundation. The modulus of subgrade reaction is inversely proportional to the diameter of the plate. Thus, the k-value obtained from the full scale pavement slab in the MEPDG is lower than k-value measured using 30 in. diameter circular plate.
61
Table 5.1 Comparison of Layer Modulus from Test-Pit Plate Load Test and Laboratory Resilient Modulus Moisture Layer Laboratory Resilient Modulus (MPa) Soil Content Modulus Mr = k1θk2 Mr = k3σ3k4† (%)* from TestMiddle Full Middle Full pit Test Half Length Half Length (MPa) 8.1 242 171 128 166 123 A3-1 9.6 198 148 98 142 94 15.3 115 166 79 158 45 5.3 705 175 129 168 122 A3-2 11.4 295 159 123 153 118 13.7 239 115 84 123 91 7.1 194 140 97 135 95 A24-1 12.1 112 116 98 111 84 14.6 92 102 90 98 86 8.4 312 540 306 530 291 A24-2 10.4 204 216 154 206 146 11.7 161 205 85 190 80 A24-3 9.2 135 74 74 8.3 189 205 136 198 129 A24-4 10.0 113 117 111 125 105 12.3 63 114 99 109 94 A24-5 8.9 433 192 179 7.7 239 119 103 114 99 A24-6 10.7 144 117 93 112 89 11.4 131 115 78 106 76 7.0 443 761 286 725 267 A24-7 12.3 310 122 70 108 64 13.2 296 139 70 130 65.4 A24-8 10.4 241 65 69 * Moisture Content of the Lab Specimen † k values were obtained from Regression Analysis
62
Table 5.2 Comparison of Modulus from Field Plate Load Test and Laboratory Resilient Modulus Soil Lab MR at the state of Secant Average Modulus of Type stress of plate bearing load Modulus at Secant Subgrade test (MPa) ∆=1.27 mm Modulus Reaction k (MPa) (MPa) (MPa/m) P(∆=1.27 ½ P ult mm) A-3 105.48 107.67 58.8 53.8 186.7 A-3 131.34 146.91 145.9 114.0 421.9 A-3 177.08 282.92 114.8 71.5 266.9 A-3 205.19 267.52 244.8 156.0 587.9 A-3 113.11 123.17 148.1 120.4 486.0 A-3 129.46 150.97 166.6 121.7 453.1 A-3 132.62 135.03 86.5 81.3 237.8 A-3 163.02 159.45 81.9 89.6 348.2 A-3 138.89 140.00 117.7 114.8 416.1 A-3 123.88 131.87 92.8 78.1 232.4 A-3 154.66 161.71 136.4 120.2 441.0 A-2-4 102.84 113.32 152.1 123.1 474.1 A-2-4 173.28 194.59 158.2 121.5 450.6 A-2-4 82.09 79.62 114.5 127.2 457.7
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Laboratory Resilient Modulus (MPa)
400
MR(Middle-Half LVDT) MR(Full-Length LVDT) Linear (MR(Middle-Half LVDT)) Linear (MR(Full-Length LVDT))
300
Line of Equality
y = 0.81x
200 y = 0.51x
100
0 0
100
200
300
400
Equivalent Layer Modulus from Test-Pit Test (MPa)
Figure 5.1 Comparison of Resilient Modulus from Laboratory Triaxial Test with Equivalent Layer Modulus from Test-pit Test
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Layer Modulus from Test-Pit Test (MPa)
600
500
Line of Equality
400
y = 0.96x
300
200
100
0 0
100 200 300 400 500 Laboratory MR Using Middle-Half LVDT (MPa)
600
Figure 5.2 Comparison of Resilient Modulus from Laboratory Test using MiddleHalf LVDT with Resilient Modulus from Test-Pit Test
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Lab MR Using Middle-Half LVDT (MPa)
600
500
y = 1.53x
400
300
Line of Equality
200
100
0 0
100 200 300 400 500 Lab MR Using Full-Length LVDT (MPa)
600
Figure 5.3 Comparison of Resilient Modulus from Laboratory Tests using MiddleHalf LVDT and Full-Length LVDT
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Layer Modulus from Test-Pit Test (MPa)
600
500
y = 1.64x 400
300
Line of Equality 200
100
0 0
100 200 300 400 500 Lab MR Using Full-Length LVDT (MPa)
600
Figure 5.4 Comparison of Resilient Modulus from Laboratory Test using FullLength LVDT with Resilient Modulus from Test-Pit Test
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Resilient Modulus at 137.8 kPa (20 psi) Load without Base Layer Equivalent Resilient Modulus (MPa)
400 Groundwater level: -0.6 m (-2 ft.) 350
Groundwater level: 0 m (0 ft.) Groundwater level: 1 m (1 ft.)
300
Groundwater level: 2 m (2 ft.) 250 200 150 100 50 0 A3-1
A3-2 A24-1 A24-2 A24-3 A24-4 A24-5 A24-6 A24-7 A24-8 Soil Type
(a) Resilient Modulus at 344.5 kPa (50 psi) Load with Base Layer Equivalent Resilient Modulus (MPa)
700 600
Groundwater level: 0 m (0 ft.) Groundwater level: 0.3 m (1 ft.)
500
Groundwater level: 0.6 m (2 ft.) Groundwater level: 0.9 m (3 ft.)
400 300 200 100 0 A3-1
A3-2 A24-1 A24-2 A24-3 A24-4 A24-5 A24-6 A24-7 A24-8 Soil Type
(b) Figure 5.5 Equivalent Resilient Modulus at Different Groundwater Levels
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100
Percent Reduction
75 50 Trendline 25 0 -25 -50 0.9
0.6
0.3 0 -0.3 Groundwater Level (m)
-0.6
-0.9
Figure 5.6 Percent Reductions of Resilient Modulus at Different Groundwater Levels
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Secant Modulus at ∆=1.27 mm (MPa)
300
250
Line of Equality 200
150
y = 0.93x 100
50
0 0
50 100 150 200 250 Laboratory Resilient Modulus at the State of Stress of Plate Bearing Load Test (MPa)
300
Figure 5.7 Comparison of Laboratory Resilient Modulus with Secant Modulus at Deflection of 1.27 mm
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Average Secant Modulus at 1/2 Pult (MPa)
300
250
Line of Equality 200
150
100
y = 0.61x 50
0 0
50 100 150 200 250 Laboratory Resilient Modulus at the State of Stress of Plate Bearing Load Test (MPa)
300
Figure 5.8 Comparison of Laboratory Resilient Modulus with Average Secant Modulus at ½ P ult
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Modulus of Subgrade Reaction (MPa/m)
600
500
400
y = 2.25x 300
AASHTO Relationship y=2.03x
200
100
0 0
50 100 150 200 250 Laboratory Resilient Modulus (MPa)
300
Figure 5.9 Comparison of Laboratory Resilient Modulus at ½ P ult with Modulus of Subgrade Reaction
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CHAPTER 6
CONCLUSIONS
6.1 Summary Several field and laboratory experimental studies were conducted in Florida to evaluate the resilient modulus characteristics of Florida pavement soils [Ping et al., 2000; Ping et al., 2001; Ping and Ling, 2007; Ping and Ling, 2008]. An extensive field static plate bearing load testing program was carried out to evaluate the in-situ bearing characteristics of pavement base, subbase, and subgrade soils [Ping, Yang, and Gao, 2002]. Typical subgrade soils were excavated from the field test sites and obtained for laboratory resilient modulus evaluation. A full scale laboratory evaluation of the subgrade performance was also conducted in a test-pit facility, which simulates the actual field conditions. The subgrade and base layer profile of a full-scale flexible pavement system was simulated in the test-pit facility. The subgrade materials were tested in the test-pit using cyclic plate bearing load test under various moisture conditions simulating different field pavement moisture conditions [Ping and Ling, 2008]. In conjunction with the field and full-scale laboratory experimental programs, a laboratory triaxial testing program was performed to evaluate the resilient modulus characteristics of the subgrade materials [Ping et al., 2000; Ping and Ling, 2008]. Subsequently, comparative studies were conducted to evaluate the resilient modulus from laboratory cyclic triaxial tests and field experimental studies. The load-deformation characteristics of the granular subgrade soils were evaluated using the field static plate bearing load test. A two-constant hyperbolic model was used to represent the relationship of load-deformation curve. It was found that the hyperbolic model has a very good agreement with the load-deformation curve. Then the modulus of subgrade reaction (k) was calculated using the parameters of the regression analysis through this model. Full-scale dynamic pavement tests were conducted in test-pits to simulate vehicle dynamic impact on the pavement. It was found that the resilient modulus of 73
subgrade soils decreased with the increase of groundwater level. The decrease in resilient modulus was significant when the water level was increased from 0.6 m (2.0 ft.) below base layer to 0.0 m (0.0 ft.) below base layer for all types of soil, which could reach up to 75%. The increase of resilient modulus leveled off when the water level was decreased from 0.6 m (2.0 ft.) to 0.9 m (3.0 ft.) below base layer. The difference in equivalent resilient modulus at 0.6 m (2.0 ft.) below base layer and 0.9 m (3.0 ft.) below base layer was about 20%. When the groundwater level was raised from 0.6 m (2.0 ft.) below the top of embankment to the interface of the subgrade and embankment layers (base clearance from 1.5 m/5.0 ft. to 0.9 m/3.0 ft.), the equivalent resilient modulus was only changed slightly. Thus, 0.9 m (3.0 ft.) could be considered as an optimum base clearance for highway pavement. The laboratory triaxial testing program was conducted to evaluate the resilient modulus of subgrade materials from test-pit and field. It was shown that moisture content and test procedure have strong influences on the laboratory resilient modulus measurements. The laboratory resilient modulus of subgrade materials was found to decreases with an increase in moisture content.
6.2 Conclusions The conclusions based on the analyses and comparisons of the experimental results are summarized herein. The laboratory resilient modulus was compared to the resilient modulus from test-pit test. A layered system was employed to calculate the resilient modulus of each subgrade layer instead of the equivalent modulus of all the layers in test-pit plate load test. It was found that the resilient modulus from the laboratory triaxial test with middle-half LVDT were close to the corresponding layer modulus from the test-pit plate load test for most cases. The differences between the resilient modulus from the laboratory test and the plate load test were typically about 20 percent of the resilient modulus from plate load test, which is acceptable when moisture content effect were only considered. It was also shown that the resilient modulus from the laboratory triaxial test with full-length LVDT was lower than the layer modulus from test-pit test. Linear relationships were established to correlate the laboratory measured resilient modulus and the resilient modulus from test-pit test. The resilient modulus
74
measured from the triaxial test could be used to predict the subgrade resilient modulus of the highway pavement if an appropriate calculation method was used. Comparison between the laboratory resilient modulus and the modulus from static plate bearing load test was also conducted. It was found that the resilient modulus measured in laboratory at the state of stress of field test was close to the secant modulus at small deformation, while the average secant modulus at the half of ultimate load was lower than the laboratory resilient modulus. The resilient modulus measured in laboratory was compared to the modulus of subgrade reaction (k) measured from field test to re-evaluate the AASHTO theoretical relationship. A calibrated linear relationship was developed to correlate resilient modulus and modulus of subgrade reaction (k). It was found that the calibrated relationship based on the experimental results was close to the AASHTO theoretical relationship. The calibrated relationship could be utilized in the Florida pavement design guide for obtaining realistic resilient modulus values from laboratory measured resilient modulus values. Conducting the soil resilient modulus test in laboratory and selecting an appropriate resilient modulus value for pavement design are very complex processes. The soil resilient modulus is strongly affected by soil moisture content and test procedure. The relationships developed in this thesis work could be used to predict the realistic resilient modulus of the Florida highway pavement in the future design by simply converting it from the modulus of subgrade reaction (k).
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BIOGRAPHICAL SKETCH
Biqing Sheng was born on October 9, 1983 in Anhui, People’s Republic of China. He was admitted to the Department of Thermal Science and Energy Engineering at University of Science and Technology of China in September 1999. After graduating with a B.S. in July 2004, he was admitted to the Department of Mechanical Engineering at University of Nebraska-Lincoln. Then, he received his Master’s degree in Mechanical Engineering in 2007. He joined the graduate program at Department of Civil Engineering at FAMU/FSU College of Engineering, Florida State University in August 2008. He is expected to earn the Degree of Master of Science in Civil Engineering in summer 2010.
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