Sep 30, 2004 - requirements for the degree of. Master of Science in Civil Engineering in ... important role throughout the course of my graduate study at LSU.
DEVELOPMENT OF RESILIENT MODULUS PREDICTION MODELS FOR BASE AND SUBGRADE PAVEMENT LAYERS FROM IN SITU DEVICES TEST RESULTS
A Thesis
Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering in The Department of Civil and Environmental Engineering
by Ravindra Gudishala B.S., Sri Krishna Devaraya University, Andhra Pradesh, India 2000 December 2004
ACKNOWLEDGMENTS
I wish to express my deepest and sincere appreciation to my advisor Dr. Louay N. Mohammad for his guidance and encouragement throughout the course of this study. His constant support and enthusiastic participation in this research are very much appreciated. I would also like to thank Dr. Mohammad for providing me with uninterrupted financial support throughout my graduate studies. I would like to thank Dr. John B. Metcalf and Dr. Murad Abu-Farsakh for being on my committee. Thanks are due to Dr. Ananda Herath, post doctoral researcher at the Louisiana Transportation Research Center, who has provided valuable help throughout the course of this study. In addition, I would like to thank Research Associates Amar Raghavendra, Keith Beard and Dr. Zhong Wu at Louisiana Transportation Research Center for their help in my experimental study. I would also like to thank my friends Shiva kalyan, Sandeep, Khaleed and Zhang for their help and encouragement during course of my research. Finally, I wish to express my gratitude for the love of my family, especially my mother Bhagyalakshmi, whose constant inspiration and support has played an important role throughout the course of my graduate study at LSU.
ii
TABLE OF CONTENTS
Acknowledgments............................................................................................................... ii List of Tables………………………………………………………………….vi List of figures ....................................................................................................................viii Abstract................................................................................................................................ xi Chapter 1............................................................................................................................... 1 INTRODUCTION.................................................................................................. 1 1.1 PROBLEM STATEMENT................................................................................ 1 1.2 OBJECTIVES ....................................................................................................... 3 1.3 SCOPE .................................................................................................................... 3 Chapter 2............................................................................................................................... 7 LITERATURE REVIEW...................................................................................... 7 2.1 INTRODUCTION .............................................................................................. 7 2.2 SIGNIFICANCE AND BACKGROUND OF RESILIENT MODULUS TEST ...................................................................................................... 7 2.2.1 FACTORS AFFECTING RESILIENT RESPONSE OF COHESIVE SOILS…………………………………………………..11 2.2.2 FACTORS AFFECTING RESILIENT RESPONSE OF UNBOUND GRANULAR MATERIALS…………………………...12 2.3 DYNAMIC CONE PENETROMETER (DCP)........................................12 2.3.1 APPLICATIONS OF DCP……………………………………..15 2.3.2 FACTORS AFFECTING DCP TEST RESULTS……………...16 2.3.3 CORRELATIONS BETWEEN DCP AND MODULUS……...17 2.4 LIGHT FALLING WEIGHT DEFLECTOMETER (LFWD) ..............20 2.4.1 APPLICATIONS OF LFWD…………………………………..22 2.4.2 FACTORS AFFECTING LFWD MODULI…………………...23 2.4.3 CORRELATIONS BETWEEN LFWD MODULUS AND RESILIENT MODULUS……………………………………………23 2.5 GEOGAUGE .....................................................................................................23 2.5.1 APPLICATIONS OF GEOGAUGE…………………………..26 2.5.2 FACTORS AFFECTING GEOGAUGE MODULUS………...27 2.5.3 CORRELATIONS BETWEEN GEOGAUGE AND RESILIENT MODULUS……………………………………………27 iii
Chapter3..............................................................................................................................28 METHODOLOGY................................................................................................28 3.1 INTRODUCTION ............................................................................................28 3.2 EXPERIMENTAL WORK AND DATA COLLECTED.......................28 3.2.1 COLLECTION OF TESTING MATERIALS…………………28 3.2.2 COLLECTION OF IN SITU TEST DEVICE RESULTS……..33 3.2.3 LABORATORY TESTING PROGRAM………………………33 3.2.4 FIELD TESTING PROGRAM………………………………...35 3.3 REPEATED LOAD TRIAXIAL TESTING ..............................................35 3.3.1 FABRICATION OF COHESIVE SOIL SPECIMENS………...35 3.3.2 FABRICATION OF GRANULAR MATERIAL SPECIMENS..38 3.3.3 TEST PROCEDURE…………………………………………..41 3.3.4 LOAD FORM APPLIED IN RLT TESTING…………………44 3.3.5 MEASUREMENT OF LOAD, CONFINING PRESSURE AND AXIAL DISPLACEMENT…………………………………………..44 3.3.6 CALCULATION OF MR FROM DATA COLLECTED IN RLT TESTING……………………………………………………………45 Chapter 4.............................................................................................................................47 RESULTS AND RESILIENT PREDICTION MODELS DEVELOPMENT .................................................................................................47 4.1 INTRODUCTION ............................................................................................47 4.2 REPEATED LOAD TRIAXIAL TEST RESULTS ..................................47 4.2.1 RLT TEST RESULTS FOR COHESIVE SOILS………………47 4.2.2 DEVELOPMENT OF GENERALIZED MR MODEL FOR RLT RESULTS OF COHESIVE SOIL……………………………...49 4.2.3 RLT TEST RESULTS FOR GRANULAR MATERIALS……...52 4.2.4 DEVELOPMENT OF GENERALIZED MR MODEL FOR RLT RESULTS OF GRANULAR MATERIALS…………………………56 4.3 DEVELOPMENT OF RESILIENT MODULUS PREDICTION MODELS....................................................................................................................57 4.3.1 DETERMINATION OF REPRESENTATIVE RESILIENT MODULUS FOR MODEL DEVELOPMENT……………………..57 4.3.1.1 RESILIENT MODULUS VALUES OF COHESIVE AND GRANULAR MATERIALS AT SELECTED STRESS STATE…59 4.3.2 STATISTICAL ANALYSIS…………………………………….61 4.3.2.1 PREDICTION OF MR FOR COHESIVE SOILS………..61 4.3.2.2 PREDICTION OF MR FOR GRANULAR MATERIALS…………………………………………………...77
iv
Chapter 5.............................................................................................................................89 SUMMARY AND CONCLUSIONS .....................................................89 5.1 SUMMARY OF DEVELOPED MODELS ................................................89 5.2 CONCLUSIONS................................................................................................90 5.3 RECOMMENDATIONS.................................................................................91 REFERENCES..........................................................................................................92 APPENDIX .............................................................................................................101 VITA ..........................................................................................................................122
v
LIST OF TABLES
Table 1.1 Test factorial-cohesive materials.............................................................................................5 Table 1.2 Test factorial continued-granular materials ..........................................................................6 Table 2.1 Input levels for 2002 design guide .........................................................................................9 Table 3.1 Physical properties of cohesive materials [3]......................................................................29 Table 3.2 Gradation analysis of granular materials [3] .......................................................................30 Table 3.3 Test results collected for cohesive soils from AITT study [3]........................................36 Table 3.4 Test results collected for granular materials from AITT study [3].................................37 Table 3.5 RLT testing sequence for cohesive materials.....................................................................41 Table 3.6 RLT testing sequence for granular materials......................................................................42 Table 4.1 Results of model fitting for cohesive materials..................................................................51 Table 4.2 Results of model fitting for granular materials ..................................................................56 Table 4.3 Resilient Modulus values of cohesive materials at selected stress state.........................60 Table 4.4 Resilient Modulus values of granular materials at selected stress state .........................61 Table 4.5 Ranges of dependent and independent variables for cohesive materials(Geogauge) ...................................................................................................................62 Table 4.6 Correlation matrix of dependent and independent variables for cohesive materials(Geogauge) ..................................................................................................62 Table 4.7 Results from regression analysis between laboratory MR and Geogauge modulus for cohesive materials................................................................................................66 Table 4.8 Ranges of independent and dependent variable for cohesive materials(LFWD modulus) .......................................................................................................71 Table 4.9 Results from regression analysis between laboratory MR and LFWD for cohesive materials .......................................................................................................................72 vi
Table 4.10 Ranges of independent and dependent variables for cohesive materials(DCP) ............................................................................................................................74 Table 4.11 Results from regression analysis between laboratory MR and DCPI cohesive materials .......................................................................................................................74 Table 4.12 Ranges of independent and dependent variables for granular materials(Geogauge) ...................................................................................................................77 Table 4.13 Correlation matrix of independent and dependent variables for granular materials (Geogauge) ..................................................................................................78 Table 4.14 Results from regression analysis between laboratory MR and Geogauge modulus for granular materials.................................................................................................82 Table 4.15 Ranges of independent and dependent variables for granular materials(LFWD) ........................................................................................................................84 Table 4.16 Results from regression analysis between laboratory MR and LFWD modulus for granular materials.................................................................................................85 Table 4.17 Ranges of independent and dependent variables for granular materials(DCP) ............................................................................................................................87 Table 4.18 Results from regression analysis between laboratory MR and DCPI modulus for granular materials.................................................................................................87 Table 4.19 Summary of developed models for cohesive materials..................................................89 Table 4.20 Summary of developed models for granular materials...................................................90
vii
LIST OF FIGURES
Figure 2.1 Dynamic Cone Penetrometer..............................................................................................13 Figure 2.2 Average strength profile of an existing flexible pavement(Source [48])....................14 Figure 2.3 Typical test profiles of DCP ................................................................................................15 Figure 2.4 Light Falling Weight Deflectometer...................................................................................20 Figure 2.5 Geophone [3]..........................................................................................................................21 Figure 2.6 Screen of the Prima software [3].........................................................................................22 Figure 2.7 Geogauge.................................................................................................................................24 Figure 2.8 Schematic of Geogauge [51] ................................................................................................25 Figure 3.1 Gradation of crushed limestone-1 ......................................................................................31 Figure 3.2 Gradation of crushed limestone-2 ......................................................................................32 Figure 3.3 Gradation of RAP..................................................................................................................32 Figure 3.4 Gradation of sand ..................................................................................................................33 Figure 3.5 Test plan ..................................................................................................................................34 Figure 3.6 Photograph illustrating the preparation of cohesive specimen .....................................38 Figure 3.7 Vibratory compaction device and split mold assembly ..................................................39 Figure 3.8 Mixing the granular material with water ............................................................................40 Figure 3.9 Compaction of granular materials.......................................................................................40 Figure 3.10 Large triaxial cell used for testing granular materials ....................................................43 Figure 3.11 Small triaxial cell used for testing cohesive materials....................................................43 Figure 3.12 Load form used in RLT testing.........................................................................................44
viii
Figure 3.13 Load Cell installed inside Triaxial cell ..............................................................................45 Figure 3.14 Schematic of RLT test ........................................................................................................46 Figure 4.1 Typical RLT result for cohesive material ..........................................................................48 Figure 4.2 Typical RLT result for cohesive material ..........................................................................48 Figure 4.3 Variation of Resilient modulus with dry density and moisture content for cohesive material ..................................................................................................................49 Figure 4.4 Resilient Modulus of granular materials ............................................................................52 Figure 4.5 Resilient Modulus versus bulk stress for RAP .................................................................53 Figure 4.6 Resilient Modulus versus bulk Stress for crushed limestone-1 .....................................53 Figure 4.7 Effect of dry density on Resilient Modulus of sand........................................................55 Figure 4.8 Effect of dry density on Resilient Modulus of RAP .......................................................55 Figure 4.9 Typical pavement section .....................................................................................................59 Figure 4.10 Scatter plot between laboratory MR and Geogauge modulus......................................64 Figure 4.11 Scatter plot between laboratory MR and dry density .....................................................64 Figure 4.12 Scatter plot between laboratory MR and water content ................................................65 Figure 4.13 Scatter plot between laboratory MR and plasticity index ..............................................65 Figure 4.14 Residuals versus predicted values .....................................................................................68 Figure 4.15 Residuals versus dry density...............................................................................................68 Figure 4.16 Residuals versus ratio ..........................................................................................................69 Figure 4.17 Predicted Resilient Modulus from Geogauge versus measured Resilient Modulus (for Cohesive materials) ...........................................................................69 Figure 4.18 Comparison between developed model and models available in literature ........................................................................................................................................70
ix
Figure 4.19 Predicted Resilient Modulus from LFWD versus Measured Resilient Modulus (for Cohesive materials)............................................................................................73 Figure 4.20 Predicted Resilient Modulus from DCP versus Measured Resilient Modulus (Cohesive Materials) ..................................................................................................75 Figure 4.21 Comparison between developed model and models available in literature ........................................................................................................................................76 Figure 4.22 Scatter plot of laboratory MR and water content for granular materials....................78 Figure 4.23 Scatter plot of laboratory MR and dry density for ganular materials .........................79 Figure 4.24 Scatter plot of laboratory MR and percent passing 0.075 mm sieve...........................79 Figure 4.25 Scatter plot of laboratory MR and percent passing 4.75 mm sieve.............................80 Figure 4.26 Scatter plot of laboratory MR and Geogauge modulus.................................................80 Figure 4.27 Residuals versus Geogauge modulus raised to 0.54......................................................83 Figure4.28 Predicted Resilient Modulus from Geogauge versus Measured Resilient Modulus (Granular Materials)..................................................................................83 Figure 4.29 Predicted Resilient Modulus from LFWD modulus versus measured Resilient modulus (Granular Materials) ..................................................................................86 Figure 4.30 Predicted Resilient Modulus from DCP versus measured Resilient Modulus (for granular materials)..............................................................................................88
x
ABSTRACT
Currently, the design of flexible pavements is generally conducted based on static properties such as California Bearing Ratio and soil support value. These properties do not represent the actual response of the pavement layers under traffic loadings. Recognizing this deficiency, the current and the 2002 mechanistic –empirical guide for design of pavement structures recommended the use of resilient modulus for characterizing the base and subgrade soil and for the design of flexible pavements. The objective of this study was to develop models to estimate the resilient modulus of base and subgrade soils from in situ test devices. Two types of cohesive soils and three types of granular soils commonly used in Louisiana were considered. Three types of in situ devices Geogauge, Light Falling Weight Deflectometer, Dynamic Cone Penetrometer and a laboratory repeated triaxial test were conducted on the soil types evaluated at various moisture content and dry density combinations. Statistical models for predicting the resilient modulus were developed based on the field and laboratory test results. These models correlate the resilient modulus to the in-situ test devices test results and basic soil properties. Good agreement was observed between predicted and measured values of the resilient modulus from the laboratory triaxial test.
xi
Chapter 1
INTRODUCTION This thesis documents the research methodology and findings of a laboratory measurement of resilient modulus of granular and cohesive materials and statistical analysis performed to correlate the laboratory resilient modulus to the modulus estimated from test device results. Chapter 1 presents problem statement, objective and scope of the research work. Chapter 2 presents the background and significance of the Repeated Load Triaxial tests, and an overview of the different in situ devices. Chapter 3 describes the methodology used for collecting the in situ test results and conducting the laboratory resilient modulus testing. Chapter 4 discusses the laboratory results from Repeated Load Triaxial testing and statistical analysis performed to correlate the in situ devices results to laboratory resilient modulus. Chapter 5 presents the summary, conclusions and recommendations of the research. 1.1 PROBLEM STATEMENT The current criteria concerning quality control/quality assurance (QA/QC) for the construction of pavement base courses and subgrade is mainly based on performing in-place moisture and in-place density tests according to the Louisiana Standard Specifications for Roads and Bridges (2000 Edition) [1]. These criteria assume that base courses and subgrade will perform satisfactorily in the field throughout their expected design life as long as an adequate field density is achieved. In general, the field density is measured relative to a maximum dry density under an optimum moisture content determined in laboratory proctor tests. However, the design parameters of base course and subgrade materials in a pavement design are not based on density values or moisture contents but rather 1
on the material’s dynamic engineering strength and/or stiffness values such as the resilient modulus. The resilient modulus is defined as the ratio of deviator stress to recoverable elastic strain under repeated loading test. It is generally referred to as an appropriate measure of stiffness for unbound pavement materials (i.e., soil) in a pavement structure. In a mechanistic-empirical (M-E) pavement design procedure such as the 2002 pavement design guide, resilient modulus is used as the primary design parameter of paving materials [2]. Since laboratory maximum dry density tests may not provide equivalent or similar strength/stiffness criteria (resilient modulus) as required in the pavement design, there exists a missing link between the design process and criteria used to evaluate construction process. This missing link makes it difficult to estimate a stiffness value achieved in the field during the construction process. Therefore, to be able to produce a durable base course and subgrade layer in the field, the criterion used to evaluate construction should have a tool that helps in comparing resilient modulus values achieved during construction process to the values used in the M-E pavement design. With the advent of the new devices like Geogauge and Light Falling Weight Deflectometer that assess the QA/QC construction process it is becoming easier to estimate stiffness of the pavement layers during the construction process [3]. Although, the devices can estimate reliable stiffness values of the pavement layers, they are not representative of design stiffness values used in the M-E pavement. This happens mainly due to 1) the stresses applied by the in situ devices are not representative of traffic and 2) the in situ devices are not designed for estimating the pavement layers stiffness (resilient modulus). The problem occurring due to the first reason can be solved to some extent by correlating the stiffness estimates from in situ devices to the design resilient modulus determined 2
in the laboratory. Thus, the correlations developed will serve the purpose of a tool to estimate the resilient modulus of pavements layers during the construction process. The goal of this study was to develop resilient modulus prediction models for the base and subgrade pavement layers from in situ test devices such as Dynamic Cone Penetrometer, Geogauge and Light Falling Weight Deflectometer. The results of this research are anticipated to provide a relatively simple, cost-effective and repeatable approach to estimate the resilient modulus of base course and subgrade soils for use in field verification of the construction resilient modulus compared to the one used in the design and or a M-E pavement design procedure. 1.2 OBJECTIVES The primary objective of this study is to develop models to estimate the resilient modulus of base and subgrade pavement layers from in situ test devices such as Geogauge, Dynamic Cone Penetrometer (DCP), and Light Falling Weight Deflectometer (LFWD). The secondary objective is to examine the effects of soil type, stress level, moisture content, and dry density on the resilient characteristics of investigated base and subgrade materials. 1.3 SCOPE The scope of this study includes conducting repeated load triaxial (RLT) tests to determine the resilient modulus of materials similar to the ones used in the recently completed Louisiana Transportation Research Center (LTRC) study titled “Assessment of In situ Test Technology (AITT) for Construction Control of Base Courses and Embankment” [3]. The AITT study included conducting tests in both laboratory and field on wide range of materials using three in situ devices Geogauge, DCP and LFWD. The combination of material types, material classification, proctor test results, and test location (field or lab) in the AITT 3
study, which also forms the test factorial in this study, is summarized in Table 1.1 and Table 1.2. In addition, moisture content and dry density combination used for conducting tests in AITT study is also shown in Tables 1.1 and 1.2. Three sample replicates were tested in RLT test for each combination of moisture content and dry density listed in Table 1.1. The test results from three in situ test devices (DCP, Geogauge and LFWD), and soil properties considered were obtained from the AITT study. Statistical analyses are performed to develop models, which predict the resilient modulus from the in situ devices measurements along with the physical properties of the soils, such as moisture content, dry density, etc.
4
Table 1.1 Test factorial-cohesive materials Type of Soil ID Material
*
Location
Optimum Maximum Moisture moisture Dry Density Content content (%) KN/m3 (%)
Clay
Clay-1 Lab 13.1 18.5 11 Clay-2 Lab 12.5 Clay-3 Lab 14.6 Clay-4 Lab 13.9 Clay-5 Lab 8.4 Clay-6 Lab 9.4 Clay-7 Lab 13.3 Clayey Clayey Lab 18.6 16.3 19.0 Silt Silt-1 Clayey Lab 15.4 Silt-2 Clayey Lab 20.1 Silt-3 Clayey Field 18.5 Silt(ALF) Clay LA-182 Field 17.1 17.5 21.2 US-61 Field 16.4 16.5 15.6 * Location gives the information about test location in AITT study
5
Dry Density KN/m3
AASHTO Classification
Plasticity Index
17.6 18.7 16.6 18.6 15.2 16.9 17.4 16.1
A-6
15
A-4
6
A-4 A-6
4 13
15.9 16.0 16.5 15.9 16
Table 1.2 Test factorial continued-granular materials Type of Soil ID Material
*
Location
Optimum Maximum Moisture moisture Dry Density Content content (%) KN/m3 (%)
Dry Density KN/m3
AASHTO Classification
Crushed CL1-1 Limestone CL1-2 CL1-3 CL1-4 CL2 Sand Sand-1 Sand-2 Sand-3 Sand-4 Sand-5 Sand-6 Recycled Rap-1 Asphalt Rap-2 Pavement Rap-3 Rap-4
Field Field Field Lab Lab Lab Lab Lab Field Field Field Field Field Field Lab
5.9
22
A-1-a
3.2 4.2
19.8 17.1
18.7 19.1 21.1 19.3 19.6 17.7 16.3 16.1 16.1 17.2 17.3 15.8 16.9 18.0 17.1
8.6
4.8 5.2 5.6 6.1 3.2 2.0 2.5 2.2 3.3 2.9 2.7 11.9 11.4 11.6 13.3
18.5
6
Plasticity Index
A-3 Non Plastic
A-1-a
Chapter 2
LITERATURE REVIEW 2.1 INTRODUCTION This chapter presents an overview of the different types of tests used in the study, which include the repeated load triaxial test, Geogauge test, Dynamic cone penetrometer test and Light falling weight deflectometer test. In addition, this chapter also provides information on the existing correlations between the in situ devices (used in this study) and resilient modulus. 2.2 SIGNIFICANCE AND BACKGROUND OF RESILIENT MODULUS TEST The concept of a resilient modulus of a material was originally introduced by Seed et al. [4] in 1962. Seed et al. defined “resilient modulus” as the ratio of applied dynamic deviatoric stress to the resilient or recovered strain under a transient dynamic pulse load [5]. The concept of resilient modulus soon gained popularity in the pavement community because a large amount of evidence was being gathered that the resilient pavement deflection, obtained from devices such as the Benkelman beam and California deflectometers, possessed a better correlation to field performance than the total pavement deflection [4]. In the last several decades, the resilient modulus has become a well recognized mode of material characterization for all pavement material layers (subgrade, subbase, and base). The resilient modulus for most unbound pavement materials is stress dependent [6]. Many nonlinear models have been proposed over the years for incorporating the effects of stress level on the resilient modulus, such as the bulk stress model 7
for granular soils, the deviatoric stress model for cohesive soil [7,8], and the Octahedral stress model [8,9]. A general form for these models can be expressed as [10]: k
2 θ − 3k6 τ oct + k7 M R = k1 pa p a pa
k3
(2.1)
in which MR is the resilient modulus, θ = σ1 + σ2 + σ3 is the bulk stress, τoct = (1/3)[(σ1 - σ2)2 + (σ1 - σ2)2 + (σ1 - σ2)2 ]1/2 is the octahedral shear stress, σ1, σ2, σ3 are the principal stresses, pa is the atmospheric pressure, and k1, k2 , k3, k6, and k7 are material parameters, subject to the constraints k1>0, k2≥0, k3≤0, k6≤0, and k7≥1. The Louisiana Department of Transportation and Development (LDOTD) design’s its pavement structures in accordance with the 1993 American Association of State Highway and Transportation Officials (AASHTO) Guide for the Design of Pavement Structures. These procedures include an evaluation of the support characteristics of base, subbase and subgrade (i.e., soils) in terms of the resilient modulus. Currently, LDOTD estimates the resilient modulus of subgrade soil based on the following correlation [11]: 53 53 M R = 1500 + 450 (SSV − 2) − 2.5 (SSV − 2 ) 5 5
2
(2.2)
where MR = resilient modulus SSV = soil support value The soil support value used to determine the resilient modulus is obtained from a database based on the parish system.
8
The new 2002 pavement design guide is based on the Mechanistic-Empirical (ME) design procedures. The M-E procedures for pavement design require comprehensive material characterization incorporating changes in material properties as a function of the state of stress (stress dependency), environmental conditions (temperature and moisture), aging, and continual deterioration under traffic loading [2]. The determination of the resilient modulus of paving materials is essential for the design and analysis of pavement structure in the implementation of the 2002 M-E guide for the design of the pavement structure. The general approach for selecting design inputs for materials in 2002 Design Guide is a hierarchical system. In its simplest and most practical form, the hierarchical approach is based on the philosophy that the level of engineering effort exerted in the pavement design process should be consistent with the relative importance, size and cost of the design project [12]. In keeping with the hierarchical approach, material characterization is comprised of three input levels. Level 1 represents a design approach philosophy of the highest practically achievable reliability, Levels 2 and 3 have successively lower reliability. A general tabulation of resilient modulus characterization methods is given in the Table 2.1 Table 2.1 Input levels for 2002 design guide Material
Input Level 1
Input Level 2
Granular Materials
Measured resilient modulus in laboratory Measured resilient modulus in laboratory
Estimated resilient modulus from correlations Estimated resilient modulus from correlations
Cohesive Materials
9
Input Level 3 Default resilient modulus Default resilient modulus
The resilient modulus of soils can be determined from repeated load triaxial (RLT) tests in the laboratory or back calculated from nondestructive deflection tests (NDT) in the field using methods such as falling weight deflectometer (FWD), Road Rater or Dynaflect. Generally, the RLT test requires well-trained personnel and expensive laboratory equipment and it is also considered relatively time-consuming. The resilient modulus backcalculated from the field NDT deflection data can produce inconsistent backcalculated modulus results when different backcalculation programs are chosen. Many factors contribute to this variation, such as the elastic-layered theory used in backcalculation programs, the static loading assumption, variable and unknown depths of stiff layers at the bottom of subgrade in a pavement structure, and the relative stiffness between layers and environmental conditions [13]. For these reasons, it is desirable to develop models to estimate the resilient modulus (MR) of base course and subgrade soils based on simple to use and cost-effective testing devices. Various empirical correlations have been used to determine the resilient modulus in the last three decades. Van Til et al [10] related resilient Modulus of subgrade soils to the soil support value employed in the earlier AASHTO design equation. He also made a correlation chart in which the values of MR can be determined by the internal friction of R-value, CBR, and Texas triaxial classification value. Many other correlations between MR, CBR, R-value and soil support values were also developed [14]. LDOTD currently estimates the resilient modulus of soils using correlations developed based on soil properties (e.g. grain size and Atterberg index) and R-value [14,15]. The major limitations on those relationships lie in that either they fail to reflect the dynamic nature of traffic loads, or they are only based on those existing conditions, thus, they are applicable for conditions developed [8].
10
More recent studies use different laboratory or in situ methods to determine the resilient characteristics of subgrade and base soils. Baig and Nazarian [16] used thin-shears of piezo-ceramic material, called bending elements to measure MR of subgrade soils in the laboratory. Mohammad et al. [17] reported results of the applicability of friction cone penetration tests in estimation of the resilient modulus of subgrade soil. Several researchers [18,19,20,21] used the seismic pavement analyzer (SPA) to determine the resilient modulus of pavement layers or monitor the variation in moduli as a function of the deterioration of pavement. There are many other new technologies used in estimation of pavement’s resilient modulus, such as the Impulse-echo test [22], Ground-penetrating radar [23], Free resonant column [24], Surface waves [25], and Artificial neural networks [26]. 2.2.1 FACTORS AFFECTING RESILIENT RESPONSE OF COHESIVE SOILS Over the past several years many researchers have studied the factors affecting the resilient response of cohesive soils. Mohammad et al. [8,9] observed an increase in resilient modulus with the increase in confining pressure. Several studies [8,9,10] showed that the resilient modulus of cohesive soils is affected by deviator stress. These observations confirm the stress-dependent nature of the resilient modulus of subgrade soil. Many studies [8,16,27,28] showed that the resilient modulus of the soil decreases as the moisture content increases. Several other investigators [29,30,31,32] reported that dry unit weight, size of the specimen and stress pulse shape used in repeated load triaxial testing are other factors influencing the resilient modulus of the cohesive soils. Mohammad et al. [33,34] reported that frequency of the stress pulse used in repeated load triaxial test along with other factors like sequence of stress levels and conditioning methods are other factors, which affect the resilient response of cohesive soils.
11
2.2.2 FACTORS AFFECTING RESILIENT RESPONSE OF UNBOUND GRANULAR MATERIALS The effect of various factors on the resilient response of the granular materials is well understood from the previous research studies. Mohammad et al. [33,34] and several researchers [34,35,36,37,38,39] reported that stress level is the significant factor that affects the resilient modulus of granular material. The studies of other investigators [40,41,42,43] on the effect of dry density showed that the resilient modulus increased with the increase in the dry density. Previous research investigations of the effect of aggregate gradation have indicated no general trend regarding the influence of fines (percentage that passes no.200) on the MR response [42,43]. Other studies [44,45,46] showed that the resilient modulus decreased with the increase in moisture content. Mohammad et al. [34] and other researchers [36,37] have reported the shape of stress pulse and duration of stress pulse used in repeated load triaxial testing as the other important factors influencing the resilient modulus of granular materials. In this research, the test results from three in situ test devices are used to develop models to predict resilient modulus of base and subgrade soils. As stated in the scope, the results from the AITT study [3] were used in this study to develop the resilient modulus prediction models from laboratory measured resilient modulus. A brief description of each device is presented in the following sections: 2.3 DYNAMIC CONE PENETROMETER (DCP) The Dynamic Cone Penetrometer (DCP) was developed in South Africa as an in situ pavement evaluation device to evaluate the strength of pavement systems [47]. The device consists of two rods, with an upper rod containing a handle, a 17.6 lbs (8 kg) drop hammer with 575 mm drop distance, and a connection to the lower rod. The lower rod contains an anvil and a replaceable 60o cone apex as shown in Figure 2.1.
12
Handle Limit of Height Hedge
575 mm
Drop Weight Hammer (mass = 8 kg)
Slide rod
1792 mm
Anvil Upper Scaled Rod
Lower Scaled Rod
Tempered Cone tip 20 mm
Figure 2.1 Dynamic Cone Penetrometer To operate the DCP requires two persons, one to drop the hammer and the other to record the penetration depth. The DCP test is conducted by dropping the hammer either one or more times depending upon the strength of the soil at the test location. For each sequence of hammer drop, a penetration reading is recorded. The process continues until the desired depth of testing is reached, or the full length of the lower rod is buried. The data recorded is then processed to calculate the penetration index, which is simply the ratio of the penetration depth to the number of blows. The penetration index (PI) is expressed in terms of inches per blow or millimeters per blow. The results from a DCP test are plotted on the graph with Y axis showing penetration depth and X axis showing the 13
number of blows. A typical plot of DCP test results is presented in Figure 2.2. The slope of the graph at any point is expressed in terms of millimeters/blow, known as the dynamic cone penetration index (DCPI) that represents the resistance offered by the material. The DCPI is also referred in the literature as penetration rate (PR). The lower values of DCPI indicate a stiff material whereas higher values indicate a soft material.
Figure 2.2 Average strength profile of an existing flexible pavement(Source [48])
14
The DCP test is different from the other cone penetrometer tests, such as friction cone penetration test (CPT) [18], by its dynamic loading system, in which the cone is driven into the soil instead of being pushed at a constant rate. Because of its dynamic loading characteristic and simplicity in use in situ, DCP has become one of the popular tools to evaluate strength of pavement base, subbase, and subgrade materials. 2.3.1 APPLICATIONS OF DCP Because of its simple and economical design DCP is being applied in the field to characterize the subgrade and base materials in several ways. One of the greatest advantages of the DCP device lies in its ability to provide a continuous record of relative soil strength with the depth. By plotting a graph of penetration index versus depth, one can observe the profile showing layer depths and strength conditions as shown in Figure 2.3.
0
0
Blows/100 mm 10
20
1
Peat
2 3 4 5
Soft Clay
Depth(m)
6 7 8
.
9 10
Medium dense Sand
11 12 13
Stiff Clay
14 15
Figure 2.3 Typical test profiles of DCP
15
Pavement engineers very often require a preliminary assessment of the in situ soils in a relatively short time. Time and other practical constraints like space requirements prevent pavement engineers from conducting a detailed in situ characterization using heavier equipment like FWD. In such situations DCP would be an effective device due to its relatively small and lightweight design [49]. Kleyn et al [50] used DCP to locate the potentially collapsible soils. Minnesota Department Of Transportation is using DCP successfully for locating high strength layers in pavement structures, identifying weak spots in constructed embankments, measuring the uniformity of in situ base material and for supplementing foundation testing for design purposes [49]. Because of the DCP’s proven capability as an effective tool in the assessment of the in situ strength of sub base/base materials and subgrade it can be used for QC/QA in highway construction [51]. Many states in the United States and several other countries across the world are using DCP as an effective tool in site characterization of pavement layers and subgrades [51].Currently there are more than dozen DOT’s and federal agencies using the DCP to assess the strength and uniformity of pavement structures [52]. 2.3.2 FACTORS AFFECTING DCP TEST RESULTS Over the past years many researchers have studied the affects of several factors like density, gradation, soil type, moisture content and maximum aggregate size that affect the DCP test results. Hasan[53] reported that DCPI is considerably affected by moisture content, AASHTO soil classification and dry density for fine grained soils. Kleyn[50] reported that plasticity, density, moisture content and gradation were the
16
important factors influencing the DCP values for the fine grained soil. George et al. [13] reported that maximum aggregate size and coefficient of uniformity were important factors affecting the DCPI of granular materials. Liveneh, et al.[54], reported that there was no effect of vertical confinement on the DCPI values of the cohesive subgrade from the upper layers. At the same time he observed a noticeable effect of vertical confinement on the granular subgrade from upper layers. 2.3.3 CORRELATIONS BETWEEN DCP AND MODULUS The literature review showed that there have been very few studies that attempted to correlate the DCP from the field to the laboratory resilient modulus. The following are the few studies that have correlated DCPI to the modulus. Chen et al [47] conducted a regression analysis between the back calculated moduli from FWD and the penetration ratio (PR). His results indicated that the PR values have a good relationship with the resilient modulus of soils in a range of 10 to 60 mm/blow of PR values. Based on the results Chen et al proposed the following relationship: Μ FWD = 338(PR )
−0.39
for 10 < PR < 60
(2.3)
where MFWD is in MPa PR = penetration rate, ratio of penetration depth to the number of blows required to reach the depth expressed in mm/blow Hasan[53] developed a simple regression model correlating DCPI with MR for fine grained soils at optimum moisture content: M R = 7013.065 − 2040.783 ln( DCPI )
(2.4)
where DCPI is expressed in inches/blow and MR in psi 17
Based on the DCP tests and CBR-DCP relationships developed in Malaysia during the 1987 National Axle Load study Chai, et al [55] proposed the following model to determine the subgrade elastic modulus:
E = 17.6(269 / DCP )
0.64
(2.5)
E is in MN/m2 and DCP = blows/300 mm penetration Chai, et al.[55] also correlated the backcalculated elastic modulus to DCP value with the following relationship:
E = 2224(DCP )
−0.996
(2.6)
E = backcalculated subgrade elastic modulus in MN/m2 Jianzhou, et al.[56] used FWD deflection data and DCP results to develop a relationship between the DCPI and backcalculated subgrade moduli:
E = 338(DCPI )
−0.39
(2.7)
E = backcalculated elastic modulus in MPa DCPI is expressed in mm/blow De Beer[57] proposed a simple correlation between elastic modulus and DCP-PR that has the following the form:
Log (E s ) = 3.05 − 1.07 Log (PR )
(2.8)
where PR is penetration ratio and Es is elastic modulus.
18
George et al.[13] conducted a comprehensive study to correlate the DCPI values to the laboratory resilient modulus. They proposed two different models based on their investigation, one for the coarse grained soils and another for the fine grained soils. The following are the proposed models. For fine grained soils
(
M R = a o (DCPI ) γ dr a1
a2
+ (LL / wc )
a3
)
(2.9)
MR = Resilient modulus in MPa, DCPI = penetration Index, mm/blow, Wc= Actual moisture content, % LL = liquid limit in % γdr= Density ratio, filed density/maximum dry density ao,a1,a2 and a3 are regression coefficients. For Coarse grained soils M R = a o ( DCPI / log cu ) a1 ( wcr
a2
+ γ dr ) a3
(2.10)
where MR = resilient modulus in MPa DCPI = dynamic cone penetration index in mm/blow cu = coefficient of uniformity wcr = moisture ratio, field moisture/optimum moisture γdr = density ratio, field density/maximum dry density ao,a1,a2 and a3 are regression coefficients. Pandey et. al. [58] conducted a comprehensive study to correlate DCPI to the back calculated modulus from falling weight deflectometer and proposed the following model MR = 357.87 x (DCPI)-0.6445
(2.11)
19
Where MR is in MPa and DCPI is in mm/blow 2.4 LIGHT FALLING WEIGHT DEFLECTOMETER (LFWD) LFWD, also known as Light Drop Weight Tester, was originally developed in Germany as an alternative in situ testing to the plate bearing test. LFWD consists of a loading device that produces a defined load pulse, a loading plate, and one center geophone sensor (Figure 2.5) [59]. Three loading plates of varying diameter of 100mm, 200mm and 300 mm, are used depending on the strength of investigated soils.
Figure 2.4 Light Falling Weight Deflectometer
20
Figure 2.5 Geophone [3] There are different types of LFWD’s available in the market. The LFWD used in the study is the PRIMA-100 developed by Carl Bro Pavement Consultants1. It weighs about 26 kg and has a 10 kg falling weight, which can produce a load pulse of about 15- 20 milliseconds. It has a load range of 1- 15 KN and can measure a maximum deflection of upto 22 mm [60]. The diameter of the loading plate used in this study is 200 mm.1 The LFWD test is conducted by freely dropping a weight of 10 kg from a certain height (normally about 85 cm) onto a loading plate (usually 200 mm in diameter), which generates an impulse load on the ground. The center sensor attached to LFWD plate measures and reports a center deflection of the plate to the test control system. The control system used in this case is the prima software supplied by the manufacturer of the LFWD. The software uses the center deflection to compute the modulus based on the solution given by Boussineq for an applied load over a single circular loaded area on an elastic half space [3]. The equation used to calculate the modulus can be expressed as follows.
1
Carl Bro Pavement Consultants is a division of Carl Bro group providing pavement consultancy services and falling weight deflectometers.
21
Figure 2.6 Screen of the Prima software [3]
E LFWD =
2 * (1 − υ 2 )σR
2
(2.12)
δc
where R = radius of the plate
δ c = deflection measured under the plate υ = Poisson’s ratio σ = applied stress 2.4.1 APPLICATIONS OF LFWD Since LFWD can measure in situ pavement response (deflection) under an impulse load, LFWD provides a valuable tool for highway engineers in simulation of pavement response to dynamic loads. In addition, the LFWD test has many advantages, such as easy-to-handle (operated by one person), time-saving and cost-saving. Therefore, it is suitable for application in earthworks and road 22
construction for determining the soil bearing capacity and compaction or consolidation of soils and non-cohesive subbases, as well as for soil improvement applications. 2.4.2 FACTORS AFFECTING LFWD MODULI According to the manufacturer of the Prima 100 LFWD [61], water content, dry density and the subsurface conditions of the tested surface are important factors influencing the LFWD moduli. The study conducted by Fleming et al [60] showed that the type of transducer used and stress dependency of materials both affect the measured modulus with the Light Falling Weight Deflectometer. 2.4.3 CORRELATIONS BETWEEN LFWD MODULUS AND RESILIENT MODULUS The literature review conducted showed that there are very few studies, which attempted to correlate the LFWD moduli to the laboratory measured resilient modulus. However, there are studies that correlated LFWD moduli to the Falling Weight Deflectometer moduli (FWD). Fleming et. al. [60] correlated the moduli from the FWD to the LFWD moduli and reported the equation 2.13. Nazzal [51] also reported similar relationship as given by equation 2.13. MFWD = 1.031 ELFWD
(2.13)
2.5 GEOGAUGE In response to the need for a faster, cheaper, safer, and more accurate compaction testing device, the Federal Highway Administration (FHWA) joined with the U.S. Department of Defense’s Advanced Research Programs Administration (ARPA) to co-sponsor a study to investigate the possible use of military technology. The result product is called Soil Stiffness Gauge or
23
Geogauge, manufactured by Humboldt Manufacturing Co. of Chicago, Figure 2.7 [62].
Figure 2.7 Geogauge Geogauge instrument is 28 cm in diameter, 25.4 cm in height, portable cylinder with 88 mm inner diameter and 114 mm outer diameter and it weighs about 10 kg. Geogauge uses technology borrowed from the defense industry, which is capable of measuring very small deflections under very small loads [62]. The Geogauge is equipped with a vibration shaker, which generates a very small dynamic force at 25 steady state frequencies ranging from 100 to 196 Hz. Sawangsuriya et al. [63] measured the force generated by Geogauge and reported it as approximately 9 N. The force is transmitted to ground by an annular ring attached to the foot of the Geogauge. The resulting displacement is measured by velocity sensors (v1, v2) attached to the flexible plate (shown in figure 2.8)
24
1. Rigid Foot with annular ring 2. Rigid Cylindrical Sleeve 3 Clamped Flexible Plate 4. Electro mechanical shaker 5. Upper Velocity Sensor 6. Lower Velocity Sensor 7. External Case 8. Vibration Isolation mounts 9. Electronics 10. Control & Supply 11. Power Supply
Figure 2.8 Schematic of Geogauge [51] The resulting displacement, which is less than 1.27x10-6 m, is used to calculate the stiffness. The value of the stiffness at each frequency is calculated to compute an average stiffness value of 25 steady state frequencies. The measured soil stiffness from Geogauge is then used to calculate the elastic modulus based on the equation given by Egorov [64]. The equation relates static stiffness K to the linear elastic, homogeneous and isotropic half space of elastic modulus E. The equation has the following functional form [51]
K=
ER (1 − υ 2 )ω (n )
(2.14)
where E = modulus of elasticity 25
υ = Poisson’s ratio of the elastic medium R= outer radius of the annular ring ω(n) = a function of the ratio of the inner diameter and outer diameter of the annular ring. For the ring geometry of the Geogauge parameter ω(n) is equal to 0.565 hence equation reduces to
K=
1.77 ER 1−υ 2
(
(2.15)
)
Based on equation the Geogauge stiffness can be converted to an elastic modulus by the equation proposed by CA consulting engineers that has the following form
E geo = H SG
(1 − υ ) 2
(2.16)
1.77 R
where Egeo = elastic stiffness modulus in MPa R = radius of Geogauge foot and HSG = Geogauge stiffness reading in MN/m 2.5.1 APPLICATIONS OF GEOGAUGE Since the Geogauge device only weighs about 10 kg and it can measures the inplace stiffness of compacted soil at a rate of about one test per minute, Geogauge possesses a great potential as an in situ tool for estimating the field resilient modulus in highway project. A good example to date of using Geogauge is the Minnesota Department of Transportation (MnDOT) trunk highway 610 project in Brooklyn Park, Minn. At one site of this project, more than 1,300 soil stiffness values have been reported to be successfully measured by using Geogauge [62].
26
Most of the research organizations and the state transportation departments are using Geogauge for controlling the compaction process of subgrade, subbase and subgrade [65]. Another potential application that has been explored by other researchers [52,66] was to correlate the stiffness modulus to the resilient modulus. 2.5.2 FACTORS AFFECTING GEOGAUGE MODULUS Research studies [67,68], conducted on the evaluation of Geogauge concluded that density, moisture content, boundary conditions and stiffness of underlying layers all affect the measured Geogauge modulus. 2.5.3 CORRELATIONS BETWEEN GEOGAUGE AND RESILIENT MODULUS The studies conducted previously did not attempt to correlate the Geogauge modulus to laboratory measured resilient modulus. However, few studies [49,67] conducted a comparison study between laboratory determined resilient modulus and Geogauge modulus from the field. Chen et. al.[66] correlated the back calculated resilient modulus from FWD to Geogauge stiffness and proposed following equation M R = 37.654(k ) − 261.96
(2.17)
where MR = resilient modulus determined from the FWD (MPa) K = stiffness determined from the Geogauge (MN/m) Wu et. al.[70] correlated the back calculated resilient modulus from FWD to Geogauge modulus and proposed the following equation
M R = 22.69e 0.12 K SSG
(2.18)
where MR = resilient modulus determined from FWD(MPa) KSSG = stiffness determined from the Geogauge (MN/m) 27
Chapter3
METHODOLOGY 3.1 INTRODUCTION This chapter presents the methodology used to collect the materials for use in RLT testing and results of the in situ devices tests conducted on the materials used in the AITT study [3]. In addition this chapter also presents the procedure used for conducting repeated load triaxial tests on the collected materials from the AITT study. 3.2 EXPERIMENTAL WORK AND DATA COLLECTED 3.2.1 COLLECTION OF TESTING MATERIALS This task of the study involved collection of the materials and their physical properties used in the AITT study [3] for use in RLT testing program. Tables 3.1 and 3.2 present the physical properties of the cohesive and granular soils, respectively. The cohesive soils included two material types for each of the laboratory and field location as shown in Table 3.1 The granular soils included three material types as shown in Table 3.2. The materials selected in the study are commonly used for the construction of subgrade and embankments in Louisiana [68]. The cohesive material Clayey Silt tested in the study had an optimum moisture content of 18.6 percent, maximum dry density of 17.5 KN/m3 and is classified as A-4 and CL-ML according to the AASHTO and Unified Soil Classification System (USCS) respectively. Similar classifications were made for other cohesive materials types and are shown in Table 3.1. The results from the proctor tests for the cohesive materials are also shown in Table 3.1. 28
Table 3.1 Physical properties of cohesive materials [3] Type of Soil Location Soil ID LL PL PI Sand(%) Silt(%) Clay(%) Maximum dry density(KN/m3) γd Optimum moisture content (%) wopt AASHTO Classification USCS Classification
Clayey Silt Lab Clayey Silt 27 21 6 9 72 19 17.5
Clay Lab Clay 31 16 15 35 37 28 18.5
Clay Field US-61 31 18 13 31 41 28 16.5
Clay Field LA-182 22 18 4 59 28 14 17.5
18.6
13.1
16.4
17.1
A-4
A-6
A-6
A-4
CL-ML
CL
CL-ML
CL-LM
Three granular materials crushed-limestone, sand and Recycled Asphalt Pavement (RAP) were used in this study. Table 3.2 shows the results from sieve analysis, proctor tests and soil classification of the granular materials. The crushed lime stone labeled as “crushed limestone-1” obtained from field is modified by adding 10 % clay material. The material was modified due to the practical difficulties [3] in conducting the Geogauge test. The crushed limestone-1 had an optimum water content of 5.2 percent, maximum dry density of 22 KN/m3 and is classified as A1-a and GC according to AASHTO and USCS respectively. The gradation of crushed limestone-1 is shown in Figure 3.1. The crushed lime stone labeled as “crushed limestone-2” is another limestone obtained from field. The crushed limestone-2 had an optimum water content of 3.2 percent, maximum dry density of 19.8 KN/m3 and is classified as A-1-a and GW according to AASHTO and 29
Table 3.2 Gradation analysis of granular materials [3] Sieve Size # mm inch 62.50 2 1/2 50.00 2 37.50 1 1/2 25.00 1 1/4 19.00 1 19.05 3/4 15.88 5/8 12.70 1/2 9.53 3/8 4.75 No.4 2.36 No.8 1.18 No.16 0.85 No.20 0.60 No.30 0.42 No.40 0.30 No.50 0.18 No.80 0.15 No.100 0.075 No.200 Cu Cc AASHTO(Classification) USCS(Classification) Optimum water content(%) Maximum dry density (KN/m3)
Crushed Limestone-1
Crushed Limestone-2
Recycled Asphalt Sand Pavement
100 100 100 98.4 94.3 83.8 78.4 72.2 65.6 52.7 33.7 30.6 24.5 20.3 18.5 17.1 16.4 15.3 12.9 25.7 2.3 A-1-a GC
100 100 100 98.8 96.6 87.9 82.2 75.9 67.5 50.4 36.3 33.4 26.3 19.6 17.1 15.03 13.4 12.5 10.6 150.0 2.9 A-1-a GW
100 100 100 100 100 100 100 100 100 99.0 95.8 89.4 68.5 10.5 0.6 0.2 1.7 1.0 A-3 SP
100 96.5 95.9 94.3 92.7 89.1 85.8 80.8 71.4 51.8 36.5 33.9 27.1 19.3 13.9 9.7 4.9 3.1 0.45 21.0 0.4 A-1-a GP
5.9
3.2
4.2
8.6
22.0
19.8
17.1
18.6
USCS classification respectively. The gradation of crushed limestone-2 is shown in Figure 3.2. RAP had an optimum water content of 8.6 percent, maximum dry density of 18.6 KN/m3 and was classified as A-1-a and GP according to
30
AASHTO and USCS classification respectively. The gradation of RAP is shown in Figure 3.3. Sand had an optimum water content of 4.2 percent, maximum dry density of 17.1 KN/m3 and was classified as A-3 and SP according to AASHTO and USCS classification respectively. The gradation of sand is shown is shown in Figure 3.4.
Percent Passing
Gradation of Crushed Limestone-1 100 90 80 70 60 50 40 30 20 10 0 0.01
0.10
1.00
10.00
Sieve Size in mm
Figure 3.1 Gradation of crushed limestone-1
31
100.00
Percent Passing
Gradation of Crushed Limestone-2 100 90 80 70 60 50 40 30 20 10 0 0.01
0.10
1.00
10.00
100.00
Sieve Size in mm
Figure 3.2 Gradation of crushed limestone-2
Percent Passing
Gradation of RAP 100 90 80 70 60 50 40 30 20 10 0 0.01
0.10
1.00 Sieve Size in mm
Figure 3.3 Gradation of RAP
32
10.00
100.00
Percent Passing
Gradation of Sand 100 90 80 70 60 50 40 30 20 10 0 0.01
0.1
1
10
Sieve Size in mm
Figure 3.4 Gradation of sand 3.2.2 COLLECTION OF IN SITU TEST DEVICE RESULTS In this task the results from all three in situ test devices, namely Geogauge, DCP and LFWD were collected from the AITT report [3]. The results collected are categorized by the type of the materials (granular or cohesive) and are summarized in Tables 3.3 and 3.4. The following is a brief description of the method of preparation of test layers and testing procedures, used in both Laboratory and Field to conduct the in situ tests. However, for detailed description of test procedures readers are advised to refer to the original AITT [3] report. Figure 3.5 shows the test plan used for this task. 3.2.3 LABORATORY TESTING PROGRAM The samples in the lab were prepared in two test boxes of dimensions 5 feet length x 3 feet width x 3 feet depth [68]. All samples were prepared on 12 inch compacted clay layer, which served as subgrade layer throughout the testing
33
program. The samples were compacted using a vibratory compactor in two lifts of 8 inches each.
AITT STUDY
LAB TESTING
Cohesive materials
FIELD TESTING
Cohesive materials
Granular materials
Granular materials
Geogauge DCP LFWD
Geogauge DCP LFWD
Materials Collected For Repeated Load Triaxial Testing Figure 3.5 Test plan The moisture content and dry density of the prepared layers was measured using nuclear density gauge at 4 inches, 8 inches and 12 inches from the surface of the prepared layers. All the results collected from the lab are labeled as lab in the column of location in Table 3.3 and Table 3.4. All the tests Geogauge, LFWD and DCP were conducted on the surface of the top layer. The DCP test result was averaged over a depth of 8 inches from the surface to obtain DCPI. 34
3.2.4 FIELD TESTING PROGRAM The field tests were conducted on highway sections selected from different projects in Louisiana, six test sections and three trench sections constructed at the Louisiana Transportation Research Center’s Pavement Research Facility (PRF) Site. Trench sections constructed at the PRF site had dimensions of 4 feet x 15 feet x 3 feet. Each trench consisted of three layers, each of which had a thickness of 12 inch. Vibratory compactor was used for compaction process to achieve target dry density at given moisture content. The moisture content and dry density was measured using nuclear density gauge. All the results collected from the field are labeled as field in the column of the location. 3.3 REPEATED LOAD TRIAXIAL TESTING The RLT tests were performed according to the AASHTO T-294 “Standard Method of test for Resilient Modulus of Unbound Granular Base/Subbase Materials and Subgrade Soils – SHRP Protocol P46” [71] using the closed loop servo hydraulic system. 3.3.1 FABRICATION OF COHESIVE SOIL SPECIMENS In this task, cohesive specimens of required dimensions (2.8 in x 5.6 in) were prepared by using the materials collected according to AASHTO T-294. First, the material collected was oven dried at the pre-specified temperature. After oven drying the material, it was then pulverized to obtain a homogeneous material. The pulverized material was then thoroughly mixed with water and compacted in four layers with a rammer dropped from a height of 12 inch in steel mold of specified dimensions. The target water content and dry density used was similar to the one used in the AITT study [3].
35
Table 3.3 Test results collected for cohesive soils from AITT study [3] Type of Material Clay
Soil ID
Location
Moisture Content (%)
Dry density KN/m3
Geogauge Modulus (MPa) * N Mean STD 7 173.3 15.5 7 179.4 19.8 7 136.7 13.2 7 154.1 13.5 7 80 4.6 7 240.8 20.6 7 162.3 34.1 5 56.4 8.7
Clay-1 Lab 11 17.6 Clay-2 Lab 12.5 18.7 Clay-3 Lab 14.6 16.6 Clay-4 Lab 13.9 18.6 Clay-5 Lab 8.4 15.2 Clay-6 Lab 9.4 16.9 Clay-7 Lab 13.3 17.4 Clayey Clayey 19.0 16.1 Lab Silt Silt-1 Clayey 15.4 15.9 5 67 2.9 Lab Silt-2 Clayey 20.1 16 5 16.3 1.9 Lab Silt-3 Clayey 18.5 16.5 5 77.8 3.3 Silt(ALF Field ) Clay LA-182 Field 21.2 15.9 5 54.5 1.3 US-61 Field 15.6 16 5 80 3.3 STD- Standard Deviation, C.V.- Coeffecient of Variation, *N – number of tests
36
C.V.(%) 8.9 11.1 9.7 8.7 5.7 8.6 21 15.5
LFWD Modulus (MPa) * N Mean STD 3 182.3 19.0 3 4 52.5 10.3 4 134.9 63 4 48.6 9.4 5 314.9 39.5 7 228.6 72.3 4 31.4 4.4
C.V.(%) 10.4 19.7 46 19.4 12.5 33.5 13.9
4.3
5
49.8
8.5
17.1
18.8
11.4
5
28.5
13.2
46.3
27
4.3
5
35.5
4.3
12.1
29
2.4 4.2
5 5
37.1 69.3
7.6 10.9
20.6 15.8
53.8 10.2
DCPI (mm/ blow) 12 16.7 23 13 18.4 15 22.5 26.1
Table 3.4 Test results collected for granular materials from AITT study [3] Type of Material
Soil ID Location
Crushed CL1-1 Limestone CL1-2 CL1-3 CL1-4 CL2 Sand Sand-1 Sand-2 Sand-3 Sand-4 Sand-5 Sand-6 Recycled Rap-1 Asphalt Rap-2 Pavement Rap-3 Rap-4
Field Field Field Lab Lab Lab Lab Lab Field Field Field Field Field Field Lab
Moisture Content (%) 4.8 5.2 5.6 6.1 3.2 2 2.5 2.2 3.3 2.9 2.7 11.9 11.4 11.6 13.3
Dry density KN/m3 18.7 19.1 21.1 19.3 19.6 17.7 16.3 16.1 16.1 17.2 17.3 15.8 16.9 18 17.1
Geogauge Modulus (MPa) *
N 5 5 5 5 5 7 9 5 5 5 5 5 5 5 5
Mean 57.4 73.1 95.6 155.3 124.7 56.4 49.7 49.7 40.8 54.2 58.3 57 77 126.2 98.3
STD 1.6 2.9 3.6 4.9 9.5 4.8 2.7 1.1 2.2 1.5 4.3 2.4 1.7 6.4 3.7
STD- Standard Deviation, C.V.- Coeffecient of Variation, *N – number of tests
37
LFWD Modulus (MPa) C.V.(%) 2.8 4 3.8 3.1 7.6 8.5 5.4 2.3 5.4 2.9 7.5 4.2 2.3 5.1 3.8
*
N 5 5 5 4 3 4 6 5 5 5 5 5 5 5 4
Mean 34.5 57.3 82.7 74.4 131.2 18 40.7 20.6 12.5 25.5 41.8 29 52 116.2 138.3
STD 4.6 5.3 3.1 12.7 3.9 5.7 3.8 5.3 2.2 4 1 4.6 6.8 5.1 33.8
DCPI (mm/ blow) C.V.(%) 13.5 9.3 3.8 17.2 3 55.8 13.9 27.6 18 15.8 2.3 15.9 13.1 4.4 24.5
43.8 23.1 9.8 13.7 8.8 25.5 27.4 61 66.7 23.4 18.8 30.3 16.1 10 9
The water content of the prepared samples was within ± 0.3 percent of the target water content. The dry density of the prepared samples was within ± 1 percent of the target dry density. Three sample replicates were prepared for each investigated variable listed in Table 1.1. Figure 3.6 demonstrates the process of cohesive specimen preparation.
Figure 3.6 Photograph illustrating the preparation of cohesive specimen 3.3.2 FABRICATION OF GRANULAR MATERIAL SPECIMENS The procedure followed to fabricate the granular material specimens was different as compared to the cohesive soil specimens. The granular material lack cohesion, which makes the task of transferring the specimen to the triaxial cell most challenging. AASHTO T-294 procedure recommends special procedures for compaction and transferring of the granular specimens. AASHTO T-294 requires usage of split molds for compaction of granular materials. The 38
dimensions of the granular material sample to be tested for repeated load triaxial testing is based on the nominal maximum particle size of the aggregate. The two split molds of dimensions 4.0 (diameter) x 8.0 (height) inches and 6.0 x 12.0 inches were used in this study. All the granular materials with nominal maximum size of less than 19.0 mm were compacted in 4.0 x 8.0 inch. The granular materials with nominal particle size greater than 19.0 mm were compacted in 6.0 x 12.0 inches. The vibratory compaction device was used for compaction of the granular material specimens. Figure 3.7 shows the vibratory compactor and split mold used for preparation of granular material specimen. To achieve the uniform compaction throughout the specimen, samples were compacted in 2 inch lift thickness. Each layer was compacted until the required density was obtained as indicated by measuring the distance from the top of the mold to the top of the compacted layer. The smooth surface on top of the lift was lightly scratched to achieve good bonding with the next lift. The dry density achieved was within ± 1 percent of target value. The water content achieved was within ± 0.5 percent of the target value as specified by AASHTO-294. Figure 3.8 shows the mixing process of granular material with water. Figure 3.9 shows the procedure used for compaction for granular materials.
Figure 3.7 Vibratory compaction device and split mold assembly 39
Figure 3.8 Mixing the granular material with water
Figure 3.9 Compaction of granular materials
40
3.3.3 TEST PROCEDURE The repeated load triaxial tests were performed at the confining and deviator stress levels recommended in the AASHTO T-294 procedure.
The load
sequence used for testing cohesive materials is shown in Table 3.5 and for granular materials in Table 3.6. Table 3.5 RLT testing sequence for cohesive materials Sequence No. *
Confining Pressure
Deviator Stress
KPa
Psi
KPa
Psi
Number of Load Applications
6 6 6 6 6 6 3 3 3 3 3 0 0 0 0 0
28 14 28 41 55 69 14 28 41 55 69 14 28 41 55 69
4 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10
1000 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
0 41 1 41 2 41 3 41 4 41 5 41 6 21 7 21 8 21 9 21 10 21 11 0 12 0 13 0 14 0 15 0 * (conditioning)
41
Table 3.6 RLT testing sequence for granular materials Sequence No.
Confining Pressure
Deviator Stress
KPa
Psi
KPa
Psi
Number of Load Applications
15 3 3 3 5 5 5 10 10 10 15 15 15 20 20 20
103 21 41 62 34 69 103 69 138 207 69 103 207 103 138 276
15 3 6 9 5 10 15 10 20 30 10 15 30 15 20 40
1000 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
0* 103 1 21 2 21 3 21 4 34 5 34 6 34 7 69 8 69 9 69 10 103 11 103 12 103 13 138 14 138 15 138 *(conditioning)
The samples were conditioned by applying 1,000 repetitions of a specified deviator stress at the specified confining pressure. Conditioning eliminates the effects of specimen disturbances from sampling, compaction, and specimen preparation procedures and minimizes the imperfect contacts between platens and the specimen. The specimen is then subjected to different stress sequences. The stress sequence is selected to cover the expected in service range that a granular subbase/base and subgrade material experiences because of traffic loading [71]. The large and small triaxial cells used for testing in this study are shown in Figure 3.10 and Figure 3.11 respectively.
42
Figure 3.10 Large triaxial cell used for testing granular materials
Figure 3.11 Small triaxial cell used for testing cohesive materials 43
3.3.4 LOAD FORM APPLIED IN RLT TESTING The test specimens in the RLT testing are subjected to haversine load form as shown in Figure 3.12. Each cycle of the load form has a 0.1 second loading time and 0.9 seconds of rest period. Load Duration 0.1 sec
Rest Period 0.9 sec
Load
Haversine Load Pulse
Time 1 Cycle
Figure 3.12 Load form used in RLT testing 3.3.5 MEASUREMENT OF LOAD, CONFINING PRESSURE AND AXIAL DISPLACEMENT The load applied to the specimen in RLT test is measured by load cell installed inside the triaxial cell as shown in Figure 3.13. This type of the set up reduces the equipment compliance errors and also alignment errors, which significantly affect the measured values of resilient modulus [30,31]. The capacity of the load cell used to measure the load applied on cohesive specimens is ± 600 lbf. The capacity of the load cell used to measure the load applied on granular specimen is ± 5000 lbf. The resulting deformation from the applied load is measured by Linearly Variable Differential Transducer’s (LVDT) placed between the top 44
platen and base of the cell to reduce the amount of extraneous axial deformation measured compared to external LDVTs. The confining pressure applied to the specimen was measured by a pressure transducer.
LVDTs Clamp
Load Cell
Figure 3.13 Load Cell installed inside Triaxial cell
3.3.6 CALCULATION OF MR FROM DATA COLLECTED IN RLT TESTING During testing, the specimen is subjected to a dynamic deviator stress and a static confining stress provided by means of a triaxial pressure chamber. The load applied to the specimen is measured by the load cell located inside the triaxial cell. The deformation resulting from the applied load is measured by two spring loaded LVDT’s attached on diametrically opposite ends of the specimen. The resilient modulus of the specimen is then calculated as the ratio of the deviatoric stress to the resilient axial strain at a given stress level. Schematic of RLT testing is shown in Figure 3.14
45
MR =
σd εr
(2.19)
where σd = deviator stress and εr = resilient strain
σ1-σ3 = Repeated Deviator Stress
σ3 Confining Pressure
σ2 = σ3
Stresses Applied to a Triaxial Specimen
Load
σd = Deviator Stress
Vertical Deformation
0.1 s
0.9 s Time εr = Resilient Deformation
Time Figure 3.14 Schematic of RLT test 46
Chapter 4
RESULTS AND RESILIENT PREDICTION MODELS DEVELOPMENT 4.1 INTRODUCTION This chapter discusses the results from the repeated load triaxial tests performed in the lab for both granular and cohesive materials. In addition, this chapter also presents the methodology adopted in development of prediction models to estimate the resilient modulus of cohesive and granular materials from the in situ test device test results considered. 4.2 REPEATED LOAD TRIAXIAL TEST RESULTS 4.2.1 RLT TEST RESULTS FOR COHESIVE SOILS Typical results from the repeated load test for cohesive soils are shown in Figure 4.1 and Figure 4.2. As expected the results exhibited the stress dependent nature of the cohesive soils. Two types of cohesive soils were used in this study as listed in Table 3.1. The two types of soils were tested at different combinations of moisture content and dry density similar to the ones selected in the AITT study [3]. The combinations of moisture content and dry density were selected such that they fall on either side of the of the optimum moisture content on the proctor density curve for a given soil type. A typical variation of resilient modulus with the moisture content and dry density is shown in Figure 4.3 for material clay. From the Figure it can be seen the resilient modulus followed a trend similar to the dry density. The behavior of the resilient modulus property is as expected and can be attributed to the improved soil properties due to compaction. 47
1000
Resilient Modulus, MPa
Resilient Modulus of Clay gd=18.7 KN/m3 w.c.. = 13.9%
Confining pressure = 41.3 KPa Confining pressure = 20.7 KPa Confining Pressure = 0 KPa
100
10 10
Deviator Stress, KPa
100
Figure 4.1 Typical RLT result for cohesive material 1000
Resilient Modulus, MPa
Resilient Modulus of Clayey Silt gd =16.7 KN/m3 w.c. = 18.5%
Confining pressure = 41.3 KPa Confining pressure = 20.7 KPa Confining Pressure = 0 KPa
100
10 10
Deviator Stress, KPa
Figure 4.2 Typical RLT result for cohesive material 48
100
Laboratory MR,MPa
80
optimum w.c & Max. DD from proctor test
20 18 16
70
14
60
12
50
10
40
8
30
6
20
4
10
2
0
0 8.5
9.4
11.0
12.5
13.3
14.6
Water Content, (%)
Dry Density, KN/m3
90
σc = 14 KPa σd = 41 KPa
MR Sample Dry density
Figure 4.3 Variation of Resilient modulus with dry density and moisture content for cohesive material
4.2.2 DEVELOPMENT OF GENERALIZED MR MODEL FOR RLT RESULTS OF COHESIVE SOIL For 2002 M-E Design Guide software, resilient modulus is a required input to the structural response computation models. The resilient modulus has a significant effect on computed pavement responses by 2002 M-E Design Guide software [12]. The resilient modulus input required by 2002 Design Guide software can be estimated based on the input level required (level 1,2 or 3 as shown in Table 2.1). For input level 1, resilient modulus is estimated from laboratory tests using a generalized constitutive model expressed as follows (12)
θ M R = k1 Pa Pa
k2
τ oct + 1 Pa
k3
(3.1)
where M R = resilient modulus, psi 49
θ = bulk stress = σ1+σ2+σ3 psi σ 1 = major principal stress psi σ 2 = intermediate principal stress= σ3 psi σ 2 = minor principal stress/ confining pressure psi
τ oct =
1 (σ 1 − σ 2 ) 2 + (σ 1 − σ 3 ) 2 + (σ 2 − σ 3 ) 3 3
psi
Pa = normalizing stress (atmospheric pressure) = 14.7 psi k1, k2, k3 = regression constants obtained by fitting resilient modulus test data to equation
Coefficient k1 is proportional to Young’s modulus. Thus, the values for k1 are expected to be positive since MR can never be negative. Increasing the volumetric stress θ should produce stiffening or hardening of the materials, which results in higher MR. Therefore, exponent k2, of the bulk stress term for the above constitutive equation should be positive. Coefficient k3 is the exponent of octahedral shear stress term. The values for k3 should be negative since increasing the shearing stress will produce a softening of the material [12] It is important to note here that the input parameters required for 2002 Design Guide software (input level 1) are parameters k1, k2 and k3 but not the actual test results. Therefore, coefficients k1, k2 and k3 were determined for cohesive materials tested in this study. The coefficients and statistics obtained by fitting the RLT test results to the model are presented in Table 4.1. To fit the non linear model given by equation 3.1 non linear optimization technique available in Solver software within MS-EXCEL was used. In performing the non linear optimization technique initial values of the unknown parameters k1, k2, and k3 are fed into the software. Therefore, to obtain those initial values for the parameters k1, k2, and k3, RLT test results were fitted to the model by performing a linear regression in the log-log scale on the model given by equation 3.1. The k1, k2 and k3 parameters obtained by linear regression were 50
then used as seed values for a nonlinear optimization performed using Solver in MS-EXCEL for fitting RLT test results to the model in arithmetic scale. Thus, the values were obtained for k1, k2 and k3. Se/SY ratio shown in Table 4.1 represents the ratio of the standard deviation of the errors to the standard deviation of the original results from RLT test. This ratio is a measure of the improvement in prediction achieved by using the model instead of the mean [10]. A ratio of Se/SY of less than 0.5 is desired for an improved prediction model. Table 4.1 Results of model fitting for cohesive materials Type of Material Clay
Clayey Silt
Clay
Soil ID
k1
k2
k3
R2
Se/SY
Clay-1 Clay-2 Clay-3 Clay-4 Clay-5 Clay-6 Clay-7 Mean Range ClayeySilt-1 Clayey Silt-2 Clayey Silt-3 Clayey Silt(ALF) Mean
1157 1386 986 1347 1031 1138 1237 1183 400 997 1261 831 924
0.38 0.40 0.22 0.40 0.36 0.45 0.46 0.38 0.24 0.30 0.25 0.34 0.33
-2.27 -2.35 -2.74 -2.02 -2.17 -2.36 -2.61 -2.36 0.72 -3.25 -2.89 -3.40 -3.47
0.96 0.90 0.97 0.90 0.97 0.83 0.90 0.91 0.92 0.90 0.91
0.16 0.30 0.13 0.33 0.14 0.37 0.30 0.27 0.24 0.25 0.26
1003
0.30
-3.25
-
-
Range LA-182 US-61
430 810 1180
0.09 0.23 0.22
0.64 -3.39 -3.01
0.91 0.94
0.26 0.21
51
4.2.3 RLT TEST RESULTS FOR GRANULAR MATERIALS Typical result from RLT test for the granular materials is shown in Figure 4.4. As expected granular materials resilient modulus increased with the increase in the bulk stress. Bulk stress (represented by θ) is the sum of the three principal stresses σ1,σ2, and σ3 applied to a granular specimen in RLT testing. The behavior of material RAP as shown in Figure 4.5 was different as compared to other granular material tested in this study. For granular material at constant confining stress, the resilient modulus increases with the increase in bulk stress
Resilient Modulus, MPa
1000
Resilient Modulus Of Granular Materials Sand gd= 17.7 KN/m3 w.c.= 2.2% R2=0.93 Crushed Limestone-1 gd= 21.1 KN/m3 w.c.= 5.4% R2=0.93 RAP gd= 18 KN/m3 w.c.= 11.5% R2 = 0.80
100 100
1000 Bulk Stress, KPa
Figure 4.4 Resilient Modulus of granular materials 52
550
σc = 138 KPa
Resilient Modulus, MPa
500
σc = 103 KPa
450 400
350
σc = 69 KPa σc = 34 KPa
300
σc = 21 KPa
Resilient Modulus of RAPgd = 18 KN/m3 w.c. = 11.5%
250 200
400 600 Bulk Stress, KPa
800
Figure 4.5 Resilient Modulus versus bulk stress for RAP
500
Resilient Modulus, MPa
σc = 138 KPa
400 σc = 103 KPa
300
σc = 69 KPa
σc = 34 KPa
200 σc = 21 KPa
Resilient Modulus of Crushed Limestone-1 gd = 21.1 KN/m3 w.c. = 5.4%
100 200
400 600 Bulk Stress, KPa
800
Figure 4.6 Resilient Modulus versus bulk Stress for crushed limestone-1
53
as shown in Figure 4.6. The increase in resilient modulus is due to the increase in the frictional resistance among the granular particles. But for the RAP, the presence of asphalt coating around the granular particles resulted in lower frictional resistance among the granular particles and thus resulting in lower resilient modulus with the increase of bulk stress. Figures 4.7 and 4.8 show the effect of dry density on the resilient modulus of the granular materials used in the study. At similar water content, with the increase in dry density, resilient modulus of the investigated materials increased. AASHTO T-294 recommends using the bulk stress model also known as K-θ model to express the results of a resilient modulus. The K-θ model in its general form can be expressed as:
M R = K 1θ k 2 (3.2) where θ = sum of principal stresses σ1, σ2 and σ3 in Kpa In RLT test σ2 = σ3 confining pressure in Kpa K1 and k2 are the parameters obtained by fitting the test results to the model.
The parameter K1 represents the intercept on the Y-axis when the model shown above by equation 3.2 is drawn on log-log scale. The parameter k2 represents the slope of the line represented by equation 3.2 on log-log scale. The resilient modulus results from RLT tests were fitted with K-θ model and the effect of increase in dry density is clear from the parameters K1 and k2 in the Figures 4.7 and 4.8. With the increase in dry density for RAP K1 increased from 38 to 73 whereas, k2 decreased from 0.4 to 0.3. The change in parameters K1 and k2 is due to improved stress train characteristics of the material, which in turn is due to increase in dry density.
54
500
Resilient Modulus, MPa
400
Effect of Dry Density on Resilient Modulus of Sand gd= 17.7 KN/m3 W.C.= 2.2% R2=0.94 gd= 16.3 KN/m3 W.C. = 2.2% R2=0.90
300
MR= 31.4θ0.36 200
MR= 17.1θ0.44
100 100 Bulk Stress, KPa
1000
Figure 4.7 Effect of dry density on Resilient Modulus of sand
800 700
Resilient Modulus, MPa
600
Effect of Dry Density on Resilient Modulus of RAP gd= 18 KN/m3 w.c.= 11.5% R2=0.80 gd= 16.9 KN/m3 W.C. = 11.5% R2= 0.82
500 400
MR= 73θ0.3
300
MR= 38θ0.4 200
100 100
1000 Bulk Stress, KPa
Figure 4.8 Effect of dry density on Resilient Modulus of RAP 55
4.2.4 DEVELOPMENT OF GENERALIZED MR MODEL FOR RLT RESULTS OF GRANULAR MATERIALS The model (equation 3.1) used for fitting the RLT results for cohesive materials is also used to fit the results of RLT for granular materials. The model parameters and test statistics obtained by fitting the data into the model is presented in Table 4.2. Table 4.2 Results of model fitting for granular materials Type of Material
Soil ID
k1
k2
k3
R2
Se/SY
Crushed Limestone
CL1-1 CL1-2 CL1-3 CL1-4 CL2 Mean Range Sand-1 Sand-2 Sand-3 Sand-4 Sand-5 Sand-6 Mean Range Rap-1 Rap-2 Rap-3 Rap-4 Mean Range
1859 1724 1711 1546 2013 1771 467 1802 1430 1430 1301 1652 1652 1727 501 2041 2400 3036 2772 2406 995
0.48 0.56 0.52 0.54 0.50 0.52 0.08 0.47 0.61 0.61 0.65 0.49 0.49 0.48 0.18 0.55 0.57 0.45 0.55 0.55 0.10
-0.41 -032 -0.32 -0.28 -0.30 -6.66 6.38 -0.43 -0.65 -0.65 -0.67 -0.51 -0.51 -0.47 0.24 -0.92 -0.78 -0.66 -0.91 -0.92 0.26
0.92 0.97 0.97 0.97 0.98 0.98 0.96 0.96 0.97 0.97 0.97 0.85 0.93 0.92 0.91 -
0.26 0.14 0.18 0.16 0.12 0.14 0.16 0.16 0.15 0.15 0.15 0.33 0.23 0.26 0.28 -
Sand
Recycled Asphalt Pavement
56
4.3 DEVELOPMENT OF RESILIENT MODULUS PREDICTION MODELS 4.3.1 DETERMINATION OF REPRESENTATIVE RESILIENT MODULUS FOR MODEL DEVELOPMENT The main objective of this study is to develop resilient modulus prediction modulus for subgrade and base layers from in situ device test results (Geogauge, LFWD, DCP). It is anticipated that the developed prediction models will be adapted as a tool for comparison of resilient modulus achieved in the field to the one used in pavement design during the construction of pavement. Because, prediction models will be acting as a tool, it becomes important to choose a single resilient modulus value from the RLT test that will be used in the pavement design. Samples used for RLT testing are subjected to fifteen stress combinations as specified by AASHTO T-294. The result from the RLT test is a set of resilient moduli for a given sample computed at different stress states. It is well known that the resilient modulus of both granular and cohesive materials is a function of both confining pressure and deviatoric stress. Since, for model development only one laboratory resilient modulus value for each sample is required, a value representative of the field should be calculated. AASHTO T-294 does not recommend any single combination of confining and deviator stress for use in design purposes. Most pavement design methods, including the AASHTO methods, presently use in the thickness selection process a single value of the resilient modulus of each layer [72]. Therefore, to select design resilient moduli the representative stress state acting upon each layer must be either known or assumed [72]. The results from the new research [73] recommend using a deviator stress of 41 KPa and a confining pressure of 14 KPa for calculating the design resilient modulus for the subgrade soils from RLT test. For Subbase/base it recommends 57
using a deviatoric stress of 103.35 KPa and a confining pressure of 34.45 KPa from RLT test. Although, the recommended values are used for developing prediction models from all three devices used in this study, an example demonstrating the process of calculating stress states occurring in flexible pavement is shown. For this purpose, the confining and deviatoric stresses occurring in the field under a standard axle of 18 kip on typical flexible pavement section were calculated employing the KENLAYER software [6]. Since, this study involved both granular and cohesive materials it is assumed that granular materials will be used as base layer and cohesive material as subgrade. The configuration of the pavement used and the modulus for each layer are shown in Figure 4.9. The stress points considered for granular base material was at the mid height of the layer. The results from the program yielded a confining pressure of approximately 21 KPa and a deviatoric stress of 103.5 KPa for the base layer. It is believed that the residual lateral stresses are developed in the granular layers during the construction process that can become locked into the layer [74,75,76]. Uzan [74] has pointed out that the residual stress of 14 KPa has been observed for cohesionless soils. In addition, Selig [77] concluded that the residual lateral stress plays an important role limiting permanent deformation in the bottom of a granular base. Therefore, it can be seen that the total confining pressure developed in a granular base amounts to 34.5 KPa after accounting for the residual stresses developed during construction. To calculate the stresses developed in the subgrade layer a point at a depth of 8 inches into the subgrade layer from the surface was chosen. The results from the KENLAYER yielded a deviator stress of approximately 41 KPa and confining pressure of 14 KPa after adding the overburden stress.
58
Load = 9000 lb Contact pressure = 68.9 Mpa
Asphalt Concrete layer of E = 34.45 MPa
6 in.
σ1 = 103 KPa 12 in.
σ3 = 34 KPa
Base Layer of E = 275.6 MPa
σ1 = 41 KPa σ3 = 14 KPa
Subgrade Modulus E = 34.45 MPa
Figure 4.9 Typical pavement section
4.3.1.1 RESILIENT MODULUS VALUES OF COHESIVE AND GRANULAR MATERIALS AT SELECTED STRESS STATE After selecting a combination of deviator and confining stress for cohesive materials the next step is to compute the resilient modulus values at the given stress state. The AASHTO-T-294 does not include the stress combination of 14 KPa confining and 41 KPa deviator stress for cohesive materials in the test sequence. Therefore, resilient modulus was interpolated for the stress state in
59
question. The interpolated values are shown in Table 4.3. The values shown in the Table 4.3 are average of three samples. Table 4.3 Resilient Modulus values of cohesive materials at selected stress state Type of Material Clay
Soil ID
Clay-1 Clay-2 Clay-3 Clay-4 Clay-5 Clay-6 Clay-7 Clayey Silt Clayey Silt-1 Clayey Silt-2 Clayey Silt-3 Clayey Silt(ALF) Clay LA-182 US-61 STD- Standard Deviation C.V.-Coefficient of Variation
Mean MR MPa 72 82.4 57.2 83.4 66.6 69.6 70.5 48.4 67.1 49.5
STD MPa 8.2 5.5 5.1 7.9 2.2 6.7 1.2 0.3 0.4 3.1
12 7 9 10 4 11 2 1 1 8
42.6
3.5
8
38.8 62.2
4.1 9.7
11 16
C.V.(%)
For the granular base materials, the stress state selected for computing resilient modulus was confining pressure of 34.5 KPa and deviator stress of 103.5 KPa. The AASHTO-T-294 stress sequence used for testing granular materials includes the stress state selected for model development. Therefore, the measured resilient moduli from the test as listed in Table 4.4 are used in the model development. The values shown in Table 4.4 are average of three samples.
60
Table 4.4 Resilient Modulus values of granular materials at selected stress state Type of Material Crushed Limestone
Sand
Recycled Pavement Material
Soil ID CL1-1 CL1-2 CL1-3 CL1-4 CL2 Sand-1 Sand-2 Sand-3 Sand-4 Sand-5 Sand-6 Rap-1 Rap-2 Rap-3 Rap-4
Mean MR MPa 197 213 201 190 246 203 153* 153* 143 180** 180** 180 238 298 247
STD MPa 6 8.52 2.01 7.6 41.8 14.2 24.5 24.5 4.3 18.8 18.8 5.4 7.1 8.9 34.6
C.V.(%) 3 4 1 4 17 7 16 16 3 10 10 3 3 3 14
* , ** similar results were used for two samples because target moisture content and target dry density were within limits specified by test protocol T-294
4.3.2 STATISTICAL ANALYSIS In statistical terms regression analysis is a method for analyzing a relationship between two or more variables in such a manner that one variable can be predicted by using information on others [78]. In the context of a regression analysis the predicted variable is called dependent variable and other variable is called independent variable. From this point onwards the laboratory resilient modulus (MR) will be referred to as the dependent variable and other variables as independent. 4.3.2.1 PREDICTION OF MR FOR COHESIVE SOILS 4.3.2.1.1 PREDICTION OF MR FROM GEOGAUGE MODULUS Since Geogauge device was developed to asses the in situ properties of the material, it will not be realistic to expect a one to one relation between laboratory determined resilient modulus and Geogauge modulus. Therefore, other physical 61
properties of the cohesive soils, namely liquid limit (LL), plasticity index (PI), moisture content and dry density were included in correlation analysis. Table 4.5 lists all dependent and independent variables and their ranges considered initially for the development of regression models. Table 4.5 Ranges of dependent and independent variables for cohesive materials(Geogauge) Type of Variable
Symbol used for the variable
Dependent
MR
Range
LL
Measured laboratory resilient Modulus in MPa Measured Geogauge modulus in MPa Liquid Limit, %
PI
Plasticity Index, %
4-15
γd
Dry density(KN/m3)
15.3-18.9
w%
Water content (%)
8.5-20.9
EGEO Independent or Explanatory
Description
38.7-83.4 16.3179.4 22-31
The first step in developing the multiple regression models will be to select the appropriate independent variables to be included in the prediction models. This involves computing the pair wise correlation coefficient between all the variables expected to be used in the model. Correlation coefficient provides a convenient Table 4.6 Correlation matrix of dependent and independent variables for cohesive materials(Geogauge) Variables
MR
EGEO
LL
PI
γd
w%
MR EGEO
1 0.76
0.70 1
0.78 0.67
0.79 0.78
0.68 0.71
-0.76 -0.73
LL PI γd w%
0.78 0.79 0.68 -0.76
0.67 0.78 0.71 -0.73
1 0.92 0.47 -0.80
0.92 1 0.52 -0.85
0.47 0.52 1 -0.33
-0.80 -0.85 -0.33 1
62
index of strength of the linear relationship between two variables [78]. Table 4.6 lists all the variables initially considered and the correlations between them. The maximum value of correlation coefficient varies from -1 to +1. A value of ±1 indicates a very strong relationship between two variables. The sign of correlation coefficient indicates a positive or negative relationship. Normally a correlation coefficient of greater than 0.60 is considered as significant value. This indicates that all the independent variables have a significant relationship with dependent variable MR. Although, all the independent variables have significant relationship with MR they are highly correlated between them. For example, if one considers two independent variables LL and PI they have a correlation coefficient of 0.92 between them. This shows that, out of the two correlated independent variables one would be sufficient for prediction model development.
Therefore, dry
density, water content and PI along with the measured Geogauge modulus were selected to be considered for the model development analysis. 4.3.2.1.2 MODEL DEVELOPMENT For developing the prediction model, some basic principles are followed. Initially scatter plots of the dependent variable versus each of the potential explanatory variables were plotted. The scatter plots help in determining likely relationship between dependent and independent variables. In addition, scatter plots also help in checking the cause and effect relationship between dependent variable and independent variable. Normally under ideal conditions it is anticipated that the value of MR at a given stress state would increase with the increase in dry density and decrease with increase in moisture content. From the scatter plots shown in Figures 4.10 through 4.13 it can be seen that the trend between MR and explanatory variables 63
90 Laboratory Mr, MPa
80 70 60 50 40 30 20 10 0 0
50
100
150
200
250
300
Geogauge Modulus,MPa
Figure 4.10 Scatter plot between laboratory MR and Geogauge modulus
90 Laboratory Mr, MPa
80 70 60 50 40 30 20 10 0 13
14
15
16
17
18 3
Dry Density KN/m
Figure 4.11 Scatter plot between laboratory MR and dry density
64
19
20
90 Laboratory Mr, MPa
80 70 60 50 40 30 20 10 0 13
15
17
19
21
23
Water Content, (%)
Figure 4.12 Scatter plot between laboratory MR and water content
90 Laboratory Mr, MPa
80 70 60 50 40 30 20 10 0 0
2
4
6
8
10
12
14
16
Plasticity Index, (%)
Figure 4.13 Scatter plot between laboratory MR and plasticity index
like dry density, water content and Geogauge modulus is consistent with the anticipated relationship. After determining the trend between MR and other variables the next step is to perform the linear regression on the selected
65
variables. For this purpose statistical analysis software (SAS)2 was employed. The ordinary least squares regression analysis in SAS was used to select an appropriate model based on highest R2 , lowest root mean square error (RMSE) value and a variable inflation factor of less than 10. The model parameters for the regression analysis were selected based on the cause and effect relationship between MR and explanatory variables. Different transformations were applied to explanatory variables based on the trial and error process to meet the statistical requirements as described above. Lowest RMSE value results in narrowest confidence intervals. Variable inflation factor of less than 10 indicates absence of any multicollinearity [78]. Multicollinearity arises when two or more independent variables are highly correlated between them [79]. Multicollinearity, when present, is always associated with unstable estimated regression coefficients [79]. The results of the analysis performed by including the appropriate variables in the model are shown in the Table 4.7. Table 4.7 Results from regression analysis between laboratory MR and Geogauge modulus for cohesive materials Model Parameters 0.3 MR, (EGEO) ,( γd/w %)
R2
RMSE 9.15
0.64
MR,(EGEO)
10.28
0.51
MR, (EGEO)0.3 ,(γd/w%),PI
9.59
0.65
MR,(EGEO)
21.61
0.57
MR, (EGEO) ,(γd/w%),PI
12.23
0.43
MR, ((EGEO)0.3/(w%)), γd
8.81
0.67
MR, ((EGEO)0.3/(w%))
15.4
0.57
MR, (EGEO), (γd/w%)
11.60
0.43
0.3
2
SAS is the Statistical Analysis Software developed by SAS Institute Inc.
66
Based on the results from regression analysis the following model was chosen because the RMSE value of 8.81 was the lowest and the R2 value of 0.67 was the highest among various models considered.
(EGEO) 0.3 M R = 86.7 + 2.2γ d w% where
(3.3)
EGEO = measured Geogauge modulus in MPa w% = measured water content in percent γ d = measured dry density in Kn/m3
To check for possible multicollinearity for the specified model, residuals were plotted against the predicted MR values from the model. Residuals here are defined as the difference between original MR values and the MR values predicted from the model. From the Figure 4.14 it is evident there is no distinct pattern among the residuals, ruling out the multicollinearity. Therefore, the model is well specified. After selecting the model a series of statistical tests were performed on the model to check for any violations, of the assumptions made by ordinary least squares regression theory in estimating the regression coefficients. The important assumption made by the least square theory is the constancy of error variance. The violation of this assumption is referred to as the heteroscedasticity of the error terms [78]. To test for any possible heteroscedasticty, residuals are plotted against each of the explanatory variables as shown in Figures 4.15 and Figure 4.16. The plotted points in each graph form a satisfactory band, suggesting a very little evidence of heteroscedasticity in the model. Apart from the graphical method to check for possible heteroscedasticity, non graphical method [80] can also be used to check for the possible heteroscedasticity. The common test used to check for the possible heteroscedasticity is called White test, which tests the null hypothesis that the variance of the residuals is homogenous. Therefore, if the probability value is very small, we would have to reject the null hypothesis and 67
accept the alternative hypothesis that the variance is not homogenous. The probability value from the test was 0.3276. Thus, null hypothesis is accepted.
15
Residuals, MPa
10 5 0 30
40
50
60
70
80
-5 -10 -15 Predicted Values of MR, MPa
Figure 4.14 Residuals versus predicted values
15
Residuals,MPa
10 5 0 12
13
14
15
16
17
-5 -10 -15 Dry Density, KN/m3
Figure 4.15 Residuals versus dry density
68
18
19
20
15
Residuals, MPa
10 5 0 0
0.1
0.2
0.3
0.4
0.5
80
100
-5 -10 -15 (EGEO)0.3/w%
Predicted Resilient Modulus, MPa
Figure 4.16 Residuals versus ratio
100 90 80 70
Line of Equality
60 50 40 30 20 10 0 0
20
40
60
Measured Resilient Modulus, MPa
Figure 4.17 Predicted Resilient Modulus from Geogauge versus measured Resilient Modulus (for Cohesive materials)
69
The F test for the multiple regression is conducted to validate the significance of the relationship between resilient modulus and other independent variables included in the model. The associated probability is designated as Pr > F or pvalue. A small p-value implies that the model is significant in explaining the variation in the dependent variable. The p-value for the F-test was less than 0.0001. The results from the SAS analysis are provided in Appendix.These results indicate that the developed model is effective in predicting the MR of cohesive soils from Geogauge modulus and other physical properties of soil. The plot showing the measured resilient modulus versus predicted resilient modulus is shown in Figure 4.17. Figure 4.18 presents a comparison of the currently developed resilient modulus prediction model from Geogauge test results to the other models reported by Chen et al. [66] and Wu[70].
Predicted Resilient Modulus, MPa
400
200
0 Upper 95% C.I. Line of Equality Chen et.al Current Research Wu Lower 95% C.I.
-200 30
40 50 60 70 80 Measured Resilient Modulus, MPa
90
Figure 4.18 Comparison between developed model and models available in literature 70
4.3.2.1.3 PREDICTION OF MR FROM LFWD MODULUS For developing the model to predict the resilient modulus of cohesive materials from LFWD modulus statistical analysis similar to the one explained in section 4.3.2.1.1 was performed and the results from the analysis are summarized in this section. Table 4.8 lists all dependent and independent variables and their ranges considered initially for regression model development. Table 4.8 Ranges of independent and dependent variable for cohesive materials(LFWD modulus) Type of Variable
Symbol used for the variable
Description
Range
Dependent
MR
Measured laboratory resilient Modulus in MPa
38.7-83.4
ELFWD
Measured LFWD modulus in MPa
28.5-314.5
LL
Liquid Limit, %
22-31
PI
Plasticity Index, %
4-15
γd
Dry density(KN/m3)
15.3-18.9
w%
Water content (%)
8.5-20.9
Independent or Explanatory
The model parameters used for the regression analysis and the results from the regression analysis are presented in Table 4.9. The appropriate model was selected based on highest R2, lowest RMSE and variable inflation factor of less than 10.
71
Table 4.9 Results from regression analysis between laboratory MR and LFWD for cohesive materials R2
Model Parameters MR, (ELFWD) , w%
RMSE 18.10
0.64
MR, (ELFWD) 0.21
9.27
0.52
MR, (ELFWD) 0.21 ,(γd/w%),PI
9.6
0.62
MR,(ELFWD)
37.4
0.37
MR, (ELFWD) ,(γd/w%),PI
13.6
0.16
MR, ((ELFWD) 0.21/w %)
18.6
0.50
MR, ((ELFWD)0.21/w%) , (γd)
8.9
0.60
Based on the results from the regression analysis R2 and RMSE values for the following model were 0.60 and 8.9 respectively.
(ELFWD) 0.21 + 2.53γ d M R = 101 w%
(3.4)
where ELFWD = Measured LFWD modulus in MPa w% = measured water content in percent γd = measured dry density in KN/m3 The F test for the multiple regression is conducted to validate the significance of the relationship between resilient modulus and other independent variables included in the model. The associated probability is designated as Pr > F or pvalue. A small p-value implies that the model is significant in explaining the variation in the dependent variable. The p-value for the F-test was less than 0.0001. The results from the SAS analysis for checking the assumptions made in estimating regression coefficients are provided in Appendix.
72
Predicted Resilient Modulus, MPa
90 80 70
Line of Equality
60 50 40 30 20 10 0 0
20
40
60
80
Measured Resilient Modulus, MPa
Figure 4.19 Predicted Resilient Modulus from LFWD versus Measured Resilient Modulus (for Cohesive materials)
These results indicate that the developed model is effective in predicting the MR of cohesive soils from LFWD modulus and other physical properties of soil. The plot showing the measured resilient modulus versus predicted resilient modulus is shown in Figure 4.19. It is noted that there were no models reported in the literature that predict the laboratory MR from the LFWD modulus. 4.3.2.1.4 PREDICTION OF MR FROM DCP For developing the model to predict the resilient modulus of cohesive materials from DCPI statistical analysis similar to the one explained in section 4.3.2.1.1 was performed and the results from the analysis are summarized in this section. Table 4.10 lists all dependent and independent variables and their ranges considered initially for regression model development. The model parameters used for the regression analysis and the results from the regression analysis are presented in Table 4.11. The appropriate model was selected based on highest R2, lowest RMSE and variable inflation factor of less than 10. 73
Table 4.10 Ranges of independent and dependent variables for cohesive materials(DCP) Type of Variable
Symbol used for the variable
Description
Range
Dependent
MR
Measured laboratory resilient Modulus in MPa
38.7-83.4
DCPI
Measured DCP index in mm/blow
10.25-53.8
LL
Liquid Limit, %
22-31
PI
Plasticity Index, %
4-15
γd
Dry density(KN/m3)
15.3-18.9
w%
Water content (%)
8.5-20.9
Independent or Explanatory
Table 4.11 Results from regression analysis between laboratory MR and DCPI cohesive materials R2
Model Parameters -0.44 MR, ((DCPI) /w%) , γd
8.3
0.68
MR, ((DCPI) -0.44/w%)
16.6
0.53
MR,(DCPI)-0.44
9.53
0.55
8.5
0.71
MR,(DCPI)
39.51
0.59
MR, (DCPI) ,(γd/w%),PI
12.1
0.38
MR, (DCPI),(γd/w%)
12.80
0.25
-0.44
MR, (DCPI)
RMSE
,(γd/w%),PI
Based on the results from regression analysis the R2 and RMSE for the following chosen model were 0.68 and 8.3 respectively.
74
M R = 1100 where
( DCPI ) −0.44 + 2.39γ d w%
(3.5)
DCPI = measured dynamic cone penetration index in mm/blow w% = measured water content in percent γd = measured dry density in kN/m3
The F test for the multiple regression is conducted to validate the significance of the relationship between resilient modulus and other independent variables included in the model. The associated probability is designated as Pr > F or pvalue. A small p-value implies that the model is significant in explaining the variation in the dependent variable. The p-value for the F-test was less than 0.0001. The results from the SAS analysis for checking the assumptions made in
Predicted Resilient Modulus, MPa
estimating regression coefficients are provided in Appendix.
90 80 70 60
Line of Equality
50 40 30 20 10 0 0
20
40
60
80
Measured Resilient Modulus, MPa
Figure 4.20 Predicted Resilient Modulus from DCP versus Measured Resilient Modulus (Cohesive Materials)
75
These results indicate that the developed model is effective in predicting the MR of cohesive soils from DCPI and other physical properties of soil. The plot showing the measured resilient modulus versus predicted resilient modulus is shown in Figure 4.20. Figure 4.21 presents a comparison of the currently developed resilient modulus prediction model from DCP test results to the other models reported by Hasan [53], Pandey et al. [58] and George et al.[13].
Predicted Resilient Modulus, MPa
250 Upper 95% C.I. Line of Equality Current Research Hasan Pandey et. al George et. al. Lower 95% C.I.
200
150
100
50
0 30
40 50 60 70 80 Measured Resilient Modulus, MPa
90
Figure 4.21 Comparison between developed model and models available in literature
76
4.3.2.2 PREDICTION OF MR FOR GRANULAR MATERIALS 4.3.2.2.1 PREDICTION OF MR FROM GEOGAUGE Granular base materials have different physical properties as compared to the cohesive subgrade soils. Therefore, for developing prediction models for granular materials physical properties like percent passing 0.075 mm sieve, percent passing 4.75 mm sieve were considered for statistical analysis. Table 4.12 lists all dependent and independent variables and their ranges considered initially for regression model development. Table 4.12 Ranges of independent and dependent variables for granular materials(Geogauge) Description
Type of Variable
Symbol used for the variable
Dependent
MR
Measured laboratory resilient Modulus in MPa
143-298
EGEO
Measured geo gauge modulus in MPa
40.8-126.2
P0.075
Percent passing 0.075 mm sieve
0.2-13
P4.75
Percent passing 4.75 mm sieve
50-99
γd
Dry density(KN/m3)
15.8-21.1
w%
Water content (%)
2-13.3
Independent or Explanatory
Range
For selecting the appropriate independent variables to be included in the regression analysis correlation coefficient between all the variables expected to be used in the model were calculated and are shown in Table 4.12. A correlation coefficient of greater than 0.60 is considered as significant value. From the Table 4.13 it can be seen that except the variable percent passing 0.075 mm sieve and
77
dry density all the independent variables have a significant relationship with dependent variable MR. Table 4.13 Correlation matrix of independent and dependent variables for granular materials (Geogauge) Variables
MR
EGEO
P0.075
P4.75
γd
w%
MR EGEO
1 0.90
0.90 1
0.13 0.32
-0.67 -0.69
0.41 0.59
0.62 0.46
P0.075
0.13
0.32
1
-0.58
0.85
-0.13
P4.75 γd w%
-0.67 0.41 0.62
-0.69 0.59 -0.73
-0.58 0.85 -0.13
1 -0.52 -0.69
-0.52 1 -0.10
-0.69 -0.10 1
For developing the prediction model, some basic principles are followed. Initially scatter plots of the dependent variable versus each of the potential explanatory variables were plotted. The scatter plots help in both determining likely relationship between dependent and independent variables. In addition, scatter plots also help in checking the cause and effect relationship between dependent variable and independent variable.
Laboratory MR , MPa
350 300 250 200 150 100 50 0 0
2
4
6
8
10
12
14
Water Content, (%)
Figure 4.22 Scatter plot of laboratory MR and water content for granular materials 78
Laboratory MR , MPa
350 300 250 200 150 100 50 0 15
16
17
18
19
20
21
22
3
Dry density, KN/m
Figure 4.23 Scatter plot of laboratory MR and dry density for ganular materials
Laboratory MR , MPa
350 300 250 200 150 100 50 0 0
2
4
6
8
10
12
Percent Passing 0.075 mm sieve
Figure 4.24 Scatter plot of laboratory MR and percent passing 0.075 mm sieve
79
14
Laboratory MR , MPa
350 300 250 200 150 100 50 0 0
20
40
60
80
100
120
Percent Passing 4.75 mm sieve
Figure 4.25 Scatter plot of laboratory MR and percent passing 4.75 mm sieve
Laboaratory M R , MPa
350 300 250 200 150 100 50 0 0
20
40
60
80
100
120
Geogauge, MPa
Figure 4.26 Scatter plot of laboratory MR and Geogauge modulus
80
140
Normally under ideal conditions it is anticipated that the value of MR at a given stress state would increase with the increase in dry density and decrease with increase in moisture content. From the scatter plot in Figure 4.22 it can be seen that, with the increase in water content, MR value increases. This behavior is due to the fact that that at given stress state material RAP recorded highest resilient modulus value for the granular materials tested in this study. The material RAP was tested at moisture content, which is wet of optimum. The water content was also very high as compared to water content of other granular materials tested in this study. Therefore the resilient modulus value showed an increase with the increase in the water content values. From Figure 4.23 it can be seen that trend between MR and dry density is consisted with the anticipated one. From Figures 4.24 and 4.25 it can be seen that the trend between MR and other explanatory variables is not well defined. This is due to the reason that the granular materials tested in this study did not have much variation in terms of explanatory variables, percent passing 4.75 mm sieve and percent passing 0.075 mm sieve. After determining the trend between MR and other variables the next step is to perform the linear regression on the selected variables. For this purpose statistical analysis software (SAS) was employed. The ordinary least squares regression analysis in SAS was used to select an appropriate model based on highest R2 , lowest root mean square error (RMSE) value and a variable inflation factor of less than 10. The results of the analysis performed by including the appropriate variables in the model are shown in the Table 4.14. Based on the regression analysis performed following model was chosen, which has the R2 of 0.83 and RMSE of 17.50. M R = 20.3(E GEO )
0.54
(3.6)
81
Table 4.14 Results from regression analysis between laboratory MR and Geogauge modulus for granular materials R2
RMSE 16.38
0.90
MR,(EGEO)0.54,w%, γd
16.38
0.87
MR, (EGEO) 0.54 ,(γd/w %),
17.7
0.84
MR,(EGEO)
17.49
0.83
MR, (EGEO) ,(γd/w%),P4.75
24.09
0.73
MR, (EGEO),(γd/w%)
34.6
0.40
MR, (EGEO) 0.54,
Model Parameters γd ,w %,P0.075,P4.75
0.54
where EGEO = measured Geogauge modulus in MPa MR = measured resilient modulus in MPa The selected model has only one explanatory variable. Therefore, the problem of multicollinearity does not exist. After selecting the model a series of statistical tests were performed on the model to check for any violations, of the assumptions made by ordinary least squares regression theory in estimating the regression coefficients. The important assumption made by the least square theory is the constancy of error variance. The violation of this assumption is referred to as the heteroscedasticity of the error terms [79]. To test for any possible heteroscedasticty, residuals are plotted against the explanatory variable as shown in Figure 4.27. The plotted points in each graph form a satisfactory band, suggesting a very little evidence of heteroscedasticity in the model. The non graphical test referred as white test [80] is performed to check for the constancy of error variance, which tests the null hypothesis that error term has constant variance. The probability value for the test was 0.072. Thus, null hypothesis is accepted.
82
30
Residuals, Mpa
20 10 0 5
7
9
11
13
15
-10 -20 -30 (EGEO)0.54
Predicted Resilient Modulus, MPa
Figure 4.27 Residuals versus Geogauge modulus raised to 0.54 350 300
Line of Equality
250 200 150 100 50 0 0
50
100
150
200
250
300
350
Measured Resilient Modulus, MPa
Figure4.28 Predicted Resilient Modulus from Geogauge versus Measured Resilient Modulus (Granular Materials)
The F test for the multiple regression is conducted to validate the significance of the relationship between resilient modulus and independent variable included in the model. The associated probability is designated as Pr > F or p-value. A small 83
p-value implies that the model is significant in explaining the variation in the dependent variable. The p-value for the F-test was less than 0.0001. The results from the SAS analysis are provided in Appendix. These results indicate that the developed model is effective in predicting the MR of granular materials from Geogauge modulus. The plot showing the measured resilient modulus versus predicted resilient modulus is shown in Figure 4.28. 4.3.2.2.2 PREDICTION OF MR FROM LFWD For developing the model to predict the resilient modulus from LFWD modulus, statistical analysis similar to the one explained in section 4.3.2.2.1 is performed. The explanatory variables considered for model development are similar to the ones described in previous section except the LFWD modulus. Table 4.15 lists all dependent and independent variables and their ranges considered initially for regression model development. Table 4.15 Ranges of independent and dependent variables for granular materials(LFWD) Type of Variable
Symbol used for the variable
Description
Range
Dependent
MR
Measured laboratory resilient Modulus in MPa
143-298
P0.075
Measured LFWD modulus in MPa Percent passing 0.075 mm sieve
P4.75
Percent passing 4.75 mm sieve
50-99
γd
Dry density(KN/m3)
15.8-21.1
w%
Water content (%)
2-13.3
ELFWD Independent or Explanatory
84
12.5138.3 0.2-13
The model parameters used for the regression analysis and the results from the regression analysis are presented in Table 4.16. The appropriate model was selected based on highest R2, lowest RMSE and variable inflation factor of less than 10. Table 4.16 Results from regression analysis between laboratory MR and LFWD modulus for granular materials R2
Model Parameters 0.25, MR, (ELFWD) γd ,w %,P0.075,P4.75
RMSE 17.1
0.90
MR,(ELFWD)0.25,w%, γd
16.38
0.80
MR, (ELFWD) 0.25, (γd/w %)
22
0.76
MR,(ELFWD)
18.8
0.70
MR, (ELFWD) ,(γd/w%),P4.75
42.82
0.17
MR, (ELFWD), (γd/w %)
63.3
0.40
0.25
Based on the regression analysis performed following model was chosen, which has the RMSE of 18.8 and R2 of 0.70
M R = 73.3(E LFWD )
0.25
(3.7)
where ELFWD = measured LFWD modulus in MPa MR = measure resilient modulus in MPa
The F test for the multiple regression is conducted to validate the significance of the relationship between resilient modulus and independent variable included in the model. The associated probability is designated as Pr > F or p-value. A small p-value implies that the model is significant in explaining the variation in the dependent variable. The p-value for the F-test was less than 0.0001. The statistical 85
analysis performed to check the assumptions made in estimating the regression coeffecients from the SAS analysis are provided in Appendix. These results indicate that the developed model is effective in predicting the MR of granular materials from LFWD modulus. The plot showing the measured resilient
Predicted Resilient Modulus, MPa
modulus versus predicted resilient modulus is shown in Figure 4.29.
300 250
Line of Equality
200 150 100 50 0 0
50
100
150
200
250
300
Measured Resilient Modulus, MPa
Figure 4.29 Predicted Resilient Modulus from LFWD modulus versus measured Resilient modulus (Granular Materials)
4.3.2.2.3 PREDICTION OF MR FROM DCP For developing the model to predict the resilient modulus from DCP, statistical analysis similar to the one explained in section 4.3.2.2.1 is performed. The explanatory variables considered for model development are similar to the ones described in previous section except the DCPI. Table 4.17 lists all dependent and independent variables and their ranges considered initially for regression model development.
86
Table 4.17 Ranges of independent and dependent variables for granular materials(DCP) Type of Variable
Symbol used for the variable
Description
Range
Dependent
MR
Measured laboratory resilient Modulus in MPa
143-298
DCPI
Measured DCP index in mm/blow
8.8-66.67
P0.075
Percent passing 0.075 mm sieve
0.2-13
P4.75
Percent passing 4.75 mm sieve
50-99
γd
Dry density(KN/m3)
15.8-21.1
w%
Water content (%)
2-13.3
Independent or Explanatory
The model parameters used for the regression analysis and the results from the regression analysis are presented in Table 4.18. The appropriate model was selected based on highest R2, lowest RMSE and variable inflation factor of less than 10. Table 4.18 Results from regression analysis between laboratory MR and DCPI modulus for granular materials Model Parameters -0.25 MR, (DCPI) , γd ,w %,P0.075,P4.75
R2
RMSE 18.05
0.86
23.3
0.73
MR, (DCPI) -0.25 , (γd/w %),
24.6
0.67
MR,(DCPI)-0.25
19.94
0.64
MR, (DCPI) ,(γd/w%),P4.75
95.24
0.19
MR, (DCPI), (γd/w %)
124.1
0.36
-0.25
MR,(DCPI)
,w%, γd
87
Based on the regression analysis performed following model was chosen which has R2 of 0.64 and RMSE of 19.94
M R = 415.4(DCPI )
−0.25
(3.8)
where DCPI = measured dynamic cone penetration index in mm/blow MR = measured resilient modulus in MPa The F test for the multiple regression is conducted to validate the significance of the relationship between resilient modulus and independent variable included in the model. The associated probability is designated as Pr > F or p-value. A small p-value implies that the model is significant in explaining the variation in the dependent variable. The p-value for the F-test was less than 0.0001. The results from the SAS analysis to check the assumptions made in estimating regression coefficients are provided in Appendix. These results indicate that the developed model is effective in predicting the MR of granular materials from DCP. The plot showing the measured resilient modulus versus predicted resilient modulus is
Predicted Resilient Modulus, MPa
shown in Figure 4.30. 300 250
Line of Equality
200 150 100 50 0 0
50
100
150
200
250
300
Measured Resilient Modulus, MPa
Figure 4.30 Predicted Resilient Modulus from DCP versus measured Resilient Modulus (for granular materials) 88
Chapter 5
SUMMARY AND CONCLUSIONS 5.1 SUMMARY OF DEVELOPED MODELS The main objective of this study was to develop resilient modulus prediction models for subgrade and base layers from the results of in situ test devices such as Geogauge, LFWD and DCP. To achieve this objective a series of repeated load triaxial tests were conducted on three type of granular and two types of cohesive materials in the laboratory at moisture and dry density levels similar to those presented in recent completed AITT [3] study at LTRC. The results from the RLT tests were correlated to the in situ testing devices results collected from the AITT study. Prediction models were developed for estimating resilient modulus of cohesive and granular materials from in situ test device results. Tables 4.19 and 4.20 present a summary of the developed resilient modulus models for the various in situ test devices considered for cohesive and granular materials, respectively. Table 4.19 Summary of developed models for cohesive materials Test Device Geogauge
LFWD
DCP
Model To Predict Resilient Modulus M R = 86.7
(EGEO)0.3 + 2.2γ d w%
(E ) 0.21 + 2.53γ d M R = 101 LFWD w%
M R = 1100
( DCPI ) −0.44 + 2.39γ d w%
89
RMSE
R2
8.8
0.67
8.9
0.60
8.3
0.68
Table 4.20 Summary of developed models for granular materials Test Device
Model To Predict Resilient Modulus
RMSE
R2
Geogauge
MR = 20.3(EGEO)
17.7
0.83
LFWD
M R = 73.3(E LFWD )
18.8
0.70
DCP
M R = 415.4(DCPI )
19.9
0.64
0.54
0.25
−0.25
5.2 CONCLUSIONS Based on the results presented, the following conclusions are drawn The resilient modulus of both cohesive and granular materials is stress dependent and is affected by physical properties of the material. The stress strain behavior of granular material RAP was different as compared to the other granular materials tested in this study. Good agreement was observed between developed models and lab measured resilient modulus values. Models developed provided best prediction of resilient modulus when compared to the one available in literature. Models developed for predicting the resilient modulus of granular materials are independent of soil properties.
90
The RMSE and R2 values for the model that predicts resilient modulus from DCP device results are better compared to other devices for cohesive materials. The RMSE and R2 values for the model that predicts resilient modulus from Geogauge device results are better compared to other devices for granular materials. k1, k2, and k3 parameters were obtained by fitting the RLT test results to the generalized model.
5.3 RECOMMENDATIONS It is recommended that the further tests be conducted to validate the models developed in this study by conducting more field testing and including large variety of materials in the test factorial.
91
REFERENCES 1. “Louisiana Standard Specifications for Roads and Bridges, “ State of Louisiana, Department of Transportation and Development, Baton Rouge, 1992 Edition 2. Ali, H.A. and Tayabji, S.D., “Evaluation of Mechanistic-Empirical Performance of Prediction Models for Flexible Pavements”, Transportation Research Record, 1629, TRB 1999 3. Nazzal M. and Seyman E., “Assessment of In situ Test Technology (AITT) for Construction Control of Base Courses and Embankment”, LTRC Report No 389, Louisiana Transportation Research Center, Baton Rouge, 2004. 4. Seed, H.B., Chan, C.K., and Lee, C.E.(1962). “Resilience characteristics of subgrade soils and their relation to fatigue failures in asphalt pavements.” Proc. 1st Int. Conf. On the Struct. Design of Asphalt Pavements, Ann Arbor, Mich. 5. Matthew W. Witczak., Xicheng Qi and Muhmmad W. Mirza “Use of Non-Linear Subgrade Modulus in AASHTO Design Procedure”, Journal of Transportation Engineering May/June 1995. 6. Huang, Y. Pavement Analysis and Design, Prentice-Hall, Inc., 1993 7. American Association of State Highway and Transportation Officials (AASHTO. Guide for Design of Pavement Structures. Washington, D.C., 1986/1993. 8. Mohammad, L.N., and Puppala, A., "Resilient Properties of Laboratory Compacted Subgrade Soils," National Academy of Science, Transportation Research Record No. 1504, 1995, pp 87-102 9. Mohammad, L.N., Huang, B., Puppala, A, and Allen A., “A Regression Model for Resilient Modulus of Subgrade Soils.” National Research 92
Council Journal of the Transportation Research Board, No. 1687, 1999, pp. 47-54. 10. Andrei, D., Development of a harmonized Test Protocol for the Resilient Modulus of Unbound materials Used in Pavement Design, Thesis of Master of Science, University of Maryland, College Park, MD, 1999. 11. Mohammad, L.N., Titi,H. and Herath,A., “Effect Of Moisture Content and Dry Unit Weight On The Resilient Modulus Of Subgrade Soils Predicted By Cone Penetration Test.” Report No: FHWA/LA.00/355. 12. “Guide for Mechanistic-Empirical Design Of New and Rehabilitated Pavement Structures.”- Part2. Design Inputs- NCHRP Final ReportMarch 2004 . 13. George, K.P., Waheed Uddin., “Subgrade Characterization For Highway Pavement Design”, Final Report Mississippi Departrment of Transportation, December 2000 14. Van Til, McCullough, B., Vallerga, B. and Hicks, R., Evaluation of AASHTO Interim Guides for Design of Pavement Structures, NCHRP 128, Highway Research Board, 1972. 15. Mohammad, L.N., Puppala, A. J., and Alavilli, P., “Investigation of the Use of Resilient Modulus for Louisiana Soils in the Design of Pavements”, Project No. 92-2GT, FHWA/LA-94/283, Louisiana Transportation Research Center, Baton Rouge, 1994 16. Temple, W.H. and Shah, S.C. “Louisiana Experimental Base Project”, Research Project No.74-1G, FHWA/LA-87/192, Louisiana Transportation Research Center, Baton Rouge, 1987. 17. Baig, S and Nazarian, S., “Determination of Resilient Modulus of Subgrades using Bender Elements”, Transportation Research Record, 1504, pp 79-86, TRB 1995. 18. Mohammad, L.N., Titi, H and Herath, A., “Investigatation of the Applicability of Intrusion Technology to Estimate the Resilient Modulus 93
of Subgrade Soil”, Project No. DTFH71-97-PTP-LA-14, FHWA/LA00/332, Louisiana Transportation Research Center, Baton Rouge, 2000 19. Nazarian, S., Baker, M. and Crain, K., “Use of seismic Pavement analyzer in Pavement Evaluation”, Transportation Research Record, 1505, pp 1-8, TRB 1995 20. Tawfig, K., Sobanjo, J., Armaghani, J. “Curvilinear Behavior of Base Layer Modulus from Deflection and Seismic Methods”, Transportation Research Record, 1716, pp55-63, TRB 2000 21. Yuan, D., Nazarian, S., Chen, D-H, and Hugo, F., “Use of seismic Pavement Analyzer to Monitor Degradation of Flexible Pavements Under Texas Mobile Load Simulator”, Transportation Research Record, 1615, pp 3-10, TRB 1998 22. Nazarian, S., Rojas, J., Yuan, D., Abdallah, I., Scullion, T., “Relating Laboratory and Field Moduli of Texas Base Materials”, Transportation Research Record, 1639, pp 1-11, TRB 1998 23. Dos Reis, H., Habboub, A. and Carpenter, S., “ Nondestructive Evaluation of Complex Moduli in Asphalt Concrete with an Energy Approach”, Transportation Research Record, 1681, pp 170-178, TRB 1999 24. Kim, D., Kweon,G. and Lee, K., “Alternative Method of Determining Resilient Modulus of Compacted Subgrade Soils using Free-Free Resonant Column Test”, Transportation Research Record, 1577, pp 6269, TRB 1997 25. Loulizi, A., Al-Qadi, I., Bhutta, S. and Flintsch, G., “Evaluation of Geosynthetics Used as Spearators”, Transportation Research Record, 1687, pp 104-111, TRB 1999 26. Kim, Y., and Kim Y.R., “prediction of layer Moduli from Falling Deflectometer and Surface Wave Measurements using Artificial Neural Nerwork”, Transportation Research Record, 1639, pp 53-61, TRB 1998
94
27. Romero,S. and Pamukcu, S., “Characterization of granular Systems by Digital Signal Processing of Low Strain Wave Response”, Transportation Research Record, 1548, pp 38-45, TRB 1996 28. Fredlund, D.G., Bergan, A.T., and Wong, P.K., “Relation Between Resilient Modulus and Stress Conditions for Cohesive Subgrade Soils” Transportation Research Record, 642, pp 77-81. 29. Allen, A.J. “Development of a correlation between physical and fundamental properties of Louisiana soils.” Master’s Thesis, Dept. of Civil Engineering, Louisiana State University, Baton Rouge, 1996. 30. Monismith, C.L. “MR testing-Interpretation of Laboratory Results for Design Purposes”. Workshop on Resilient Modulus Testing, Oregon State University, Corvallis, 1989. 31. Drumm, E.C., Reeves, J.S., Madgett, M.R., and Trolinger, W.D. “Subgrade Resilient Modulus Correction for Saturation Effects”. Journal of Geotechnical and Geoenvironmental Engineering, Vol 123, No.7, July 1997, pp 663-670. 32. Nataatmadja, A., and Parkin, A., “Characterization of Granular Materials for Pavements”, Canadian Geotechnical Journal, Vol.26, No. 4, 1989 33. Mohammad, L.N., Puppala, A.J., and Alavalli, P., Influence of Testing Procedure and LVDT Location on Resilient Modulus of Soils”, Transportation Research Record, No. 1462, 1994, pp. 91-101. 34. Mohammad, L.N., Puppala, A., and Alavalli, P., Effect of Strain Measurements on Resilient Modulus of Granular Soils”, Dynamic Geotechnical Testing, Second Volume, ASTM STP 1213, ASTM,1994,pp.202-221 35. Gonzalo Rada and Matthew W. Witczak. “Comprehensive Evaluation of Laboratory Resilient Moduli Results for Granular Material”, Transportation Research Record, No 810, pp 23-33 36. Monismith, C.L., Seed, H.B., Mitry, F.G., and Chan, C.K., Prediction of Pavement Deflections from Laboratory Tests. Proc., 2nd International 95
Conference on the Structural Design of Asphalt Pavements, Ann Arbor, MI, Aug. 1967 37. Monismith, C.L., Hicks, R.G., and Salam, Y.M., Basic Properties of Pavement Components. Federal Highway Administration, Berkeley, CA, Final Rept. FHWA-RD-72-19, Sept. 1971 38. Kalcheff, I.V., Rational Characterization of Granular Bases. Proc., 1st Federally Coordinated Program on Research Progress Review, San Francisco, CA, Sept. 1973 39. Chou, Y.T., Engineering Behavior of Pavement Materials-State of the Art. Federal Aviation Administration; U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS, Final Rept. FAA-RD-77-37, Feb.1977 40. Smith,W.S., and Nair, K., Development of Procedures for Characterization of Untreated Granular Base Course and Aphalt-Treated Base Course Materials. Federal Highway Administration, Oakland, CA, Final Rept. FHWA-RD-74-61, Oct. 1973 41. Barenberg, E.J., Response of Subgrade Soils to Repeated Dynamic Loads-State of the Art. Proc., Allerton Park Conference on Systems Approach to Airfield Pavements, Champaign, IL March 1970. 42. Chou, Y.T., Evaluation of Nonlinear Resilient Modulus of Unbound Granular Materials from Accelarated Traffic Test Data. U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS, Final Tech. Rept. S-76-12, Aug. 1976 43. Kalcheff, I.V., Characteristics of Graded Aggregates As Related to Their Behavior Under Varying Loads and Environments. Proc., Conference on Utilization of Graded Aggregate Base Materials in Flexible Pavements, Oak Brook, IL, March 1974 44. Kalcheff, I.V., and Hicks, R.G., A Test Procedure for Determining the Resilient Properties of Granular Materials. Journal of Testing and Evaluation, ASTM, Vol. 1 No.6, Nov 1973.
96
45. Yoder, E.J., and M.W. Witczak. Principles of Pavement Design, 2nd ed. Wiley, New York, 1975. 46. Johnson, T.C., “Is Graded Aggregate Base the solution in Frost Areas? “Proc., Conference on Utilization of Graded Aggregate Base Materials in Flexible Pavements, Oak Brook, IL, March 1974. 47. Chen, J., Hossain M. and Latorella T.M., “Use of Falling Weight Deflectometer and Dynamic Cone Penetrometer in Pavement Evaluation”, Transportation Research Record, 1655, pp 145-151, TRB 1999 48. Newcomb-D.E., Chabourn-BA., Van-Deusen-DA, and Burnham-TR, Initial Characterization of Subgrade Soils and Granular Base Materials at the Minnesota Road Research Project”, Report No. MN/RC-96/19, Minnesota Department of Transportation, St. Paul, Minn, December 1995 49. Burnham, Tom., Johnson, Dave., “In Situ Foundation Characterization Using the Dynamic Cone Penetrometer”, Minnesota Department of Transportation, 1993 50. Kleyn, E., Maree, J., and Savage, P., “The Application of a Portable Pavement Dynamic Cone Penetrometer to Determine In Situ Bearing Properties of Road Pavement Layers and Subgrades in South Africa,” Proceedings of the Second European Symposium on Penetration Testing, Amsterdam, May, 1982 51. Nazzal, M., “Field Evaluation of In situ Test Technology for QC/QA During Construction of Pavement Layers and Embankments”, Master Thesis, Louisiana State University, December-2003 52. Siekmeier, J.A., Young, Duane, and Beberg, D.(2000) “Comparison of the Dynamic Cone Penetrometer With Other Tests During Subgrade and Granular Base Characterization in Minnesota, Nondestructive Testing of Pavements and Backcalculation of Moduli: Third Volume, ASTM STP 1375, p175-188. S.D. Tayabji and E.O. Lukanen, Eds., American Society for Testing and Materials.
97
53. Hassan, A., “The Effect of Material Parameters on Dynamic Cone Penetrometer Results for Fine-grained Soils and Granular Materials”, Ph.D Dissertation, Oklahama State University, Stillwater, 1996 54. Liveneh, M., Ishai, and Liveneh, N.A., “Effect of Vertical Confinement on Dynamic Cone Penetrometer Strength Values in Pavement and Subgrade Evaluation,” Transportation Research Record 1473. 55. Chai, G., and Roslie, N., “The Structural Response and Behavior Prediction of Subgrade Soils using Falling Weight Deflectometer in Pavement Construction”, 3rd International Conference on Road and Airfield Paavement Technology, April 1998. 56. Jianzhou, C., Mustaque, H., and Latorella, T.M., “Use of Falling Weight Deflectometer and Dynamic Cone Penetrometer in Pavement Evaluation”, Paper Presented in Transportation Research Board, Washington, D.C., January 1999. 57. De Beer, M., “Use of Dynamic Cone Penetrometer in the Design of Road Structures”, Geo-techniques in African Environment, Balkema Rotterdam pp 167-176 58. Pandey B.B., Srinivasa Kumar R., and Sudhakar Reddy K., “Regression Models for Estimation of In Situ Subgrade Moduli from DCP Tests”, Indian Highways, July 2003 pp 5-19 59. Zorn Company, “Test Device and Road Construction”, http://www.zorn-online.de/en/products/td-rc, Germany, 2001 60. Fleming, P.R., Frost, M.W., Rogers, C.D.F.(2000) “A Comparison of Devices for Measuring Stiffness In Situ,” Proceedings of the Fifth International Conference on Unbound Aggregate In Roads, Nottingham, United Kingdom,2000. 61. Prima 100 User Manual- Carl Bro Pavement Consultants 62. Fiedler, S., Nelson, C., Berkman, F., and DiMillio, A., “Soil Stiffness Gauge for Soil Compaction Control”, Public Road, FHWA, Vol. 61, No.4, 1998 98
63. Sawangsuriya, A., Edil, T., Bosscher, P., “Laboratory Evaluation of The Soil Stiffness Gauge”, 81st Annual Meeting of the Transportation Research Board, January 2002, Washington, D.C. 64. Egorov, K.E., “Calculation of Bed for Foundation with Foot Ring,” proceeding of 6th International Conference on Soil Mechanics Foundation Engineering, Volume-2, pp 41-45. 65. Ali, Maher., Thomas, Bennert., Nenad, Gucunski., “Evaluation of the Humboldt Stiffness Gauge” Final Report-January 2002, NJDOT 66. Chen, Dar-Hao., Wu, Wei., He, Rong., Bilyeu, John., Arrelano, Mike., “Evaluation of In-Situ Resilient Modulus Testing Techniques,” Transportation Research Board Annual Meeting-1999. 67. Saawangsuriya, A., “Evaluation of the Soil Stiffness Gauge,” M.S. Thesis, University of Wisconsin-Madison-WI,2001. 68. Seyman, Ekrem., “Laboratory Evaluation of In-situ Tests as Potential Quality Control/Quality Assurance Tools,” Master Thesis, Louisiana State University-Baton Rouge,2003. 69. Sawangsuriya, A., “Comparison of Moduli Obtained From The Soil Stiffness Gauge With Moduli From Other Tests,” Transportation Research Board 81st Annual Meeting-2002. 70. Wu, W., Arellano, M., Chen, D-H., Bilyeu, J., He, R., “Using a Stiffness gauge as an Alternative Quality Control Device in Pavement Construction,” Texas Department of Transportation, Austin, TX. 71. AASHTO, “Standard Method of Test for Resilient Modulus of Unbound Granular Base/subbase Materials and Subgrade Soil-SHRP Protocol P46”, AASHTO Designation: T-294-92. Washington, D.C.,1992 72. NCHRP Web Doc 14 “Laboratory Determination of Resilient Modulus for Flexible Pavement Design” Final Report1998. http://www.nap.edu/openbook/nch014/html/1.html
99
73. NCHRP Project 1-28 A “Harmonized Test Methods for Laboratory Determination of Resilient Modulus For Flexible Pavement Design.” 74. Uzan, J., “Characterization of Granular Materials”, Tranportation Research Record Number -1022, Symposium on Mechanics of Granular Materials. 75. Duncan, J.M., and Seed, R.B, “Compaction-Induced Earth Pressures Under Ko Conditions”, ASCE, Vol. 112, No. 1, January, pp1-23. 76. Allen, J.J. and Thompson, M.R.,(1974), “Resilient Response of Granular Materials Subjected to Time-Dependent Lateral Stresses”, Transportation Research Board, TRR No.510, pp. 1-13. 77. Selig, E.T., “Tensile Zone Effects on Performance of Layered Systems”, Geotechnique, Vol. 37, No. 3, pp. 247-254. 78. Freund, R.J., and Wilson W.J., “Statistical Methods”, Second Edition, Elsevier Science 2003. 79. “Volumes I and II Scientific Approaches for Transportation Research” NCHRP Project 20-45 Final Report: February 19, 2001. 80. Regression with SAS Chapter 2- Regression Diagnostics http://www.ats.ucla.edu/stat/sas/webbooks/reg/chapter2/sasreg2.htm
100
APPENDIX
101
The REG Procedure Model: MODEL1 Dependent Variable: Mr Independent variables: Geogauge modulus, Water content, drydensity (Cohesive Material) NOTE: No intercept in model. R-Square is redefined. Analysis of Variance Source
DF
Sum of Squares
Mean Square
Model Error Uncorrected Total
2 10 12
47306 777.18878 48083
23653 77.71888
Root MSE Dependent Mean Coeff Var
8.81583 61.71917 14.28378
R-Square Adj R-Sq
F Value
Pr > F
304.34
|t|
1
86.77643
26.38941
3.29
0.0082
1
2.25076
0.46304
4.86
0.0007
Parameter Estimates Variable Confidence Limits geopowbywc 27.97715 145.57570 Dry_Density_Kn_m3_ 1.21905 3.28247
Label
DF
Type II SS
Standardized Estimate
Variance Inflation
1
840.37010
0.40561
9.41303
1
1836.34016
0.59958
9.41303
Dry Density(Kn/m3)
95%
Correlation of Estimates Variable
Label
geopowbywc Dry_Density_Kn_m3_
Dry Density(Kn/m3)
geopowbywc
Dry_Density_ Kn_m3_
1.0000 -0.9454
-0.9454 1.0000
Collinearity Diagnostics
Number
Eigenvalue
Condition Index
1 2
1.94539 0.05461
1.00000 5.96859
--Proportion of Variation-Dry_Density_ geopowbywc Kn_m3_ 0.02730 0.97270
Test of First and Second Moment Specification DF
Chi-Square
Pr > ChiSq
3
3.45
0.3276
103
0.02730 0.97270
Correlation Matrix Materials(LFWD)
of
Dependent
and
Independent
Variables
for
Variables
MR
ELFWD
LL
PI
γd
w%
MR ELFWD
1 0.61
0.61 1
0.78 0.53
0.79 0.63
0.68 0.60
-0.76 -0.64
LL PI γd w%
0.78 0.79 0.68 -0.76
0.53 0.63 0.60 -0.64
1 0.92 0.47 -0.80
0.92 1 0.52 -0.85
0.47 0.52 1 -0.33
-0.80 -0.85 -0.33 1
Cohesive
90 Laboratory Mr, MPa
80 70 60 50 40 30 20 10 0 0
50
100
150
200
LFWD Modulus,MPa
Scatter Plot between Laboratory MR and LFWD modulus
104
250
300
350
2.5 2 Residuals, Mpa
1.5 1 0.5 0 -0.5 35
45
55
65
75
85
-1 -1.5 -2 Predicted values of MR, Mpa
Residuals versus Predicted values (Model from LFWD modulus for cohesive materials)
15
Residuals, Mpa
10 5 0 0
0.05
0.1
0.15
0.2
0.25
-5 -10 -15 (ELFWD )0.21/w%
Residuals versus ratio (Cohesive materials)
105
0.3
0.35
0.4
23:01 Thursday, September 30, 2004
1
The REG Procedure Model: MODEL1 Dependent Variable: Mr Independent variables: LFWD modulus, Water content, drydensity (Cohesive Material) NOTE: No intercept in model. R-Square is redefined. Analysis of Variance Source
DF
Sum of Squares
Mean Square
Model Error Uncorrected Total
2 10 12
45326 805.51535 46132
22663 80.55154
Root MSE Dependent Mean Coeff Var
8.97505 60.64917 14.79831
R-Square Adj R-Sq
F Value
Pr > F
281.35
|t|
1
2.53357
0.41270
6.14
0.0001
1
100.98907
34.53936
2.92
0.0152
Parameter Estimates Variable Confidence Limits
Label
Dry_Density_Kn_m3_ 1.61402 3.45312 lfpowbywc 24.03057 177.94757
Dry Density(Kn/m3)
DF
Type II SS
Standardized Estimate
Variance Inflation
1
3035.82743
0.68247
7.07758
1
688.64258
0.32504
7.07758
95%
Correlation of Estimates Variable
Label
Dry_Density_Kn_m3_ lfpowbywc
Dry Density(Kn/m3)
Dry_Density_ Kn_m3_
lfpowbywc
1.0000 -0.9267
-0.9267 1.0000
Collinearity Diagnostics
Number
Eigenvalue
Condition Index
1 2
1.92667 0.07333
1.00000 5.12565
--Proportion of Variation-Dry_Density_ Kn_m3_ lfpowbywc 0.03667 0.96333
Test of First and Second Moment Specification
1
DF
Chi-Square
Pr > ChiSq
3
2.58
0.4610
107
0.03667 0.96333
Correlation Matrix of Dependent and Independent Variables for Cohesive Materials(DCP) Variables
MR
DCPI
LL
PI
γd
w%
MR DCPI
1 -0.77
-0.77 1
0.78 -0.88
0.79 -0.7
0.68 -0.38
-0.76 0.67
LL PI γd w%
0.78 0.79 0.68 -0.76
-0.88 -0.7 -0.38 0.67
1 0.92 0.47 -0.80
0.92 1 0.52 -0.85
0.47 0.52 1 -0.33
-0.80 -0.85 -0.33 1
2
Residuals, Mpa
1.5 1 0.5 0 -0.5
40
45
50
55
60
65
-1 -1.5 -2 Predicted Values of MR , Mpa
Residuals versus Predicted Values (DCP)
108
70
75
80
15
Residuals, Mpa
10 5 0 15
16
17
18
19
20
-5 -10 -15 Dry Density, Kn/m3
Residuals versus Dry density (DCP)
15
Residuals, Mpa
10 5 0 0
0.005
0.01
0.015
0.02
-5 -10 -15 (DCPI)-0.44/w%
Residuals versus ratio
109
0.025
0.03
0.035
23:01 Thursday, September 30, 2004
(Cohesive Material)
1
The REG Procedure Model: MODEL1 Dependent Variable: Mr Independent variables: DCPI, Water content, drydensity
NOTE: No intercept in model. R-Square is redefined. Analysis of Variance Source
DF
Sum of Squares
Mean Square
Model Error Uncorrected Total
2 11 13
52163 758.90217 52921
26081 68.99111
Root MSE Dependent Mean Coeff Var
8.30609 62.32231 13.32763
R-Square Adj R-Sq
F Value
Pr > F
378.04
|t|
1
2.39469
0.39206
6.11
ChiSq
3
3.72
0.2933
111
0.03127 0.96873
Dependent Variable: Mr Independent Variable: Geogauge Modulus (Granular Materials) NOTE: No intercept in model. R-Square is redefined. Analysis of Variance Source
DF
Sum of Squares
Mean Square
Model Error Uncorrected Total
1 13 14
593557 3980.23700 597537
593557 306.17208
Root MSE Dependent Mean Coeff Var
17.49777 202.34692 8.64741
R-Square Adj R-Sq
F Value
Pr > F
1938.64
ChiSq
1
3.23
0.0723
113
1.00000
Correlation Matrix of Dependent and Independent Variables for Granular Materials(LFWD) Variables
MR
ELFWD
P0.075
P4.75
γd
w%
MR ELFWD
1 0.80
0.80 1
0.13 0.3
-0.67 -0.65
0.41 0.48
0.62 0.49
P0.075 P4.75 γd w%
0.13 -0.67 0.41 0.62
0.3 -0.65 0.48 0.49
1 -0.58 0.85 -0.13
-0.58 1 -0.52 -0.69
0.85 -0.52 1 -0.10
-0.13 -0.69 -0.10 1
350
Laboratory Mr, Mpa
300 250 200 150 100 50 0 10
30
50
70
90
110
130
150
LFWD Modulus, Mpa
Scatter Plot between Laboratory MR and LFWD modulus (Granular materials)
114
50 40 Residuals,Mpa
30 20 10 0 -10 1.5
2
2.5
-20 -30 -40 (ELFWD )0.25
Residual versus LFWD modulus raised to 0.25
115
3
3.5
1 September 30, 2004
23:01 Thursday,
1
The REG Procedure Model: MODEL1 Dependent Variable: Mr Independent Variable: LFWD Modulus(Granular Materials) NOTE: No intercept in model. R-Square is redefined. Analysis of Variance Source
DF
Sum of Squares
Mean Square
Model Error Uncorrected Total
1 12 13
499625 3998.61866 503624
499625 333.21822
Root MSE Dependent Mean Coeff Var
18.25427 193.98899 9.40995
R-Square Adj R-Sq
F Value
Pr > F
1499.39
ChiSq
1
0.04
0.8465
117
1.00000
Correlation Matrix of Dependent and Independent Variables for Granular Materials(DCP) Variables
MR
DCPI
P0.075
P4.75
γd
w%
MR DCPI
1 -0.71
-0.71 1
0.13 -0.23
-0.67 0.53
0.41 -0.52
0.62 -0.40
P0.075 P4.75 γd w%
0.13 -0.67 0.41 0.62
-0.23 0.53 -0.52 -0.40
1 -0.58 0.85 -0.13
-0.58 1 -0.52 -0.69
0.85 -0.52 1 -0.10
-0.13 -0.69 -0.10 1
350
Laboratory Mr, Mpa
300 250 200 150 100 50 0 0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
DCPI, mm/blow
Scatter plot between laboratory MR and DCPI (Granular materials)
118
40
Residuals, Mpa
30 20 10 0 -10
0.2
0.25
0.3
0.35
0.4
0.45
-20 -30 (DCPI)-0.25,mm/blow
Residuals versus DCPI raised to negative 0.25
119
0.5
0.55
0.6
Dependent Variable: Mr Independent Variable: DCPI NOTE: No intercept in model. R-Square is redefined. Analysis of Variance Source
DF
Sum of Squares
Mean Square
Model Error Uncorrected Total
1 13 14
539660 5172.39147 544833
539660 397.87627
Root MSE Dependent Mean Coeff Var
19.94684 194.63263 10.24845
R-Square Adj R-Sq
F Value
Pr > F
1356.35
ChiSq
1
0.04
0.8482
121
1.00000 23:01 Thursday,
VITA
Ravindra Gudishala was born in India on July 29th 1978. He received his bachelor’s degree in civil engineering from Sri Krishna Devaraya University, Ananatapur, India in August 2000. He came to United States to pursue master’s degree in civil engineering in August 2001 at Louisiana State University, Baton Rouge, Louisiana. He is anticipated to fulfill requirements for master’s degree in civil engineering in December 2004.
122
