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2009

Fundamental characterization of unbound basecourse materials under cyclic loadingAaron Matthew AustinLouisiana State University and Agricultural and Mechanical College, aausti3@lsu.edu

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Recommended CitationAustin, Aaron Matthew, "Fundamental characterization of unbound base course materials under cyclic loading" (2009). LSU Master'sTheses. 2263.https://digitalcommons.lsu.edu/gradschool_theses/2263

FUNDAMENTAL CHARACTERIZATION OF UNBOUND BASE

COURSE MATERIALS UNDER CYCLIC LOADING

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 Aaron Austin

B.S., Louisiana Tech University, 2002 May, 2009

ii

ACKNOWLEDGEMENTS

I consider the completion of this research as dedication and support of a group of

people rather than my individual effort. I wish to express gratitude from the deep in my

heart to everyone assisted me to fulfill this work.

First of all, I would like to express my sincere thanks and appreciation to my

advisor Professor Louay N. Mohammad for his support, thoughtful guidance,

encouragement, and help throughout the course of this work. I am also grateful to him

for accepting me as his graduate research assistant and providing me with uninterrupted

financial support for my Master’s studies which gave me an opportunity to expand my

knowledge in Geotechnical Engineering.

I would like to thank Dr. Munir Nazzal, Dr. Mostafa Elseifi, and Dr. Radhey

Sharma for being on my advisory committee. Their cooperation, guidance, and patience

have been invaluable. I wish to acknowledge Louisiana Transportation Research Center

(LTRC) for providing me wonderful research facilities. I would like to give my thanks to

Amar Raghavendra and Keith Beard for training and technical advice.

Last but certainly not least, I would like to express my gratitude to my parents and

supporting family for their encouragement. The goal of obtaining a Masters degree is a

long term commitment, and their patience and moral support have seen me through to the

end. Thank you.

iii

TABLE OF CONTENTS

ACKNOWLEDGEMENTS .............................................................................................ii

LIST OF TABLES .......................................................................................................... v

LIST OF FIGURES ........................................................................................................ vi

ABSTRACT .................................................................................................................viii

CHAPTER 1 INTRODUCTION ..................................................................................... 1

1.1 Background ....................................................................................................... 1

1.2 Problem Statement ............................................................................................ 2

1.3 Objectives .............................................................................................................. 3

1.4 Scope of This Study ............................................................................................... 3

1.5 Outline................................................................................................................... 4

CHAPTER 2 LITERATURE ........................................................................................... 5

2.1 Introduction ........................................................................................................... 5

2.2 Deformation Behavior of Unbound Granular Materials .......................................... 5

2.2.1 Stresses in Unbound Granular Layers .......................................................................... 5

2.2.2 Deformation Characteristics of Unbound Materials ..................................................... 7

2.3 Factors affecting Resilient and Permanent Deformation Properties ........................ 9

2.3.1 Stress State ............................................................................................................... 10

2.3.2 Number of Load Cycles ............................................................................................ 12

2.3.3 Effects of Moisture Content\Suction.......................................................................... 13

2.3.4 Stress History ........................................................................................................... 15

2.3.5 Density ..................................................................................................................... 17

2.3.6 Load Duration and Frequency ................................................................................... 18

2.4 Shakedown Theory .............................................................................................. 18

2.5 Modeling of Permanent Strain Behavior .............................................................. 22

2.5.1 Resilient Modeling Behavior ..................................................................................... 22

2.5.2 Permanent Deformation Modeling Behavior ............................................................. 25

CHAPTER 3 METHODOLGY ..................................................................................... 28

iv

3.1 Experimental Testing Program ............................................................................. 28

3.2 Testing Setup of Triaxial Tests ............................................................................ 28

3.3 Sample Preparation .............................................................................................. 30

3.3.1 Static Triaxial Compression Test ............................................................................... 30

3.3.2 Sample Size .............................................................................................................. 32

3.4 Repeated Load Triaxial (RLT) Tests .................................................................... 32

3.4.1 Resilient Modulus Test ............................................................................................. 33

3.4.2 Single-Stage RLT Test .............................................................................................. 34

3.4.3 Multi-Stage RLT Test ............................................................................................... 37

CHAPTER 4 ANALYSIS OF RESULTS ...................................................................... 41

4.1 Physical Properties Test Results ........................................................................... 41

4.2 Static Triaxial Tests Results ................................................................................. 44

4.3 Repeated Load Tri-axial Testing .......................................................................... 46

4.3.1 Single-Stage RLT Test Results-Resilient Strain ......................................................... 50

4.3.2 Single-Stage RLT Test Result-Permanent Strain ....................................................... 52

4.4 Multi-Stage Test Results ...................................................................................... 53

4.5 Shakedown Limits ............................................................................................... 61

CHAPTER 5 CONCLUSION AND RECOMMENDATIONS ...................................... 71

5.1 Conclusions ......................................................................................................... 71

5.2 Recommendations ............................................................................................... 72

REFERENCES.............................................................................................................. 74

APPENDIX A: RESILIENT MODULUS ..................................................................... 82

APPENDIX B: MOISTURE DENSITY CURVES ........................................................ 85

APPENDIX C: PERMANENT DEFORMATION CURVES......................................... 86

APPENDIX D: CALCULATIONS ............................................................................... 93

VITA............................................................................................................................. 95

v

LIST OF TABLES

Table 2.1 Models proposed to Predict Permanent Strain after Lekarp et. al. 2000 .......... 26

Table 3.1 Load Pulse Used in the Resilient Modulus Procedure ..................................... 36

Table 3.2 Stress Sequence: Limestone ........................................................................... 38

Table 3.3 Stress Sequence: Sandstone ........................................................................... 39

Table 3.4 Molding Moisture Regime for Mult-Stage ..................................................... 40

Table 4.1 Physical Properties Results ............................................................................ 43

Table 4.2 Summary Limits ............................................................................................ 70

vi

LIST OF FIGURES Figure 2.1 Stress components acting on an element (Lekarp 97) ...................................... 5

Figure 2.2 Stress beneath a rolling wheel load (Lekarp, Dawson) .................................... 6

Figure 2. 3 Stress-Strain Behavior of UGMSs (Werkmeister 2003)................................. 7

Figure 2. 4 Hysteresis Loop for One Cycle of Loading (Lekarp 1997) ............................. 8

Figure 2. 5 Typical RLT for Unbound Slate Waste (Dawson and Nunes) ......................... 9

Figure 2. 6 Stress Influence on Permanent Strain in a Granite Gneiss-Material (Bar 72) 11

Figure 2. 7 Influence of Drainage of Permanent deformation (Dawson 90) .................... 14

Figure 2. 8 Effect of Stress History on Permanent Strain (Brown and Hyde 1975) ......... 16

Figure 2. 9 Effect of Density on Permanent Strain ......................................................... 18

Figure 2. 10 Permanent Deformation Behavior at Low Stress Level (Werk 2003) ......... 19

Figure 2. 11 Permanent Deformation Behavior at High Stress Levels (Werk 2003) ....... 20

Figure 2. 12 Shakedown Range Behavior (Arnold 2004) ............................................... 20

Figure 2. 13 Elastic/Permanent Behavior Under RLT Loading (Johnson 1996) .............. 22

Figure 3. 1 MTS Tri-axial Testing Machine ................................................................... 29

Figure 3. 2 Preparation of Testing Limestone Samples .................................................. 31

Figure 3.3 Applied Load and Response of Samples in RLT Test.................................... 35

Figure 4. 1 Particle Size Distribution of Tested Aggregates ........................................... 42

Figure 4. 2 Stress-Strain Curves for Granite Static Compression Test ............................ 44

Figure 4. 3 Stress-Strain Curves for Limestone Static Compression Test ....................... 45

Figure 4. 4 Stress-Strain Curves for Sandstone Static Compression Test ........................ 45

Figure 4. 5 Ultimate Shear Strength in p-q space ........................................................... 46

Figure 4. 6 Residual Shear Strength in p-q space ........................................................... 47

vii

Figure 4. 7 Resilient Modulus vs. Bulk Stress ................................................................ 49

Figure 4. 8 Resilient Modulus Coefficients of Tested Materials: a) k1 b) k2 c) k3 ........... 49

Figure 4. 9 Results of Single-Stage RLT Test a) Resilient Strain Variation of Load Cycles b) Measured and Predicted Resilient Modulus Values ........................................ 51 Figure 4. 10 Vertical Permanent Strain Variations with Number of Cycles .................... 54

Figure 4. 11 Vertical Permanent Strain Rate vs. Vertical Permanent Strain .................... 54

Figure 4. 12 Multi-Stage Cumulative Permanent Strain ................................................. 55

Figure 4.13 Multi-Stage Test Results Permanent Strain Rate for a) Limestone b) Sandstone c) Granite ..................................................................................................... 58 Figure 4.14 Resilient Strain Multi-Stage Test ................................................................ 62

Figure 4. 15 Shakedown Limits for Limestone at Optimum Moisture Content ............... 64

Figure 4. 16 Shakedown Limits for Sandstone at Optimum Moisture Content ............... 64

Figure 4. 17 Shakedown Limits for Sandstone at Dty of Optimum Moisture Content..... 65

Figure 4. 18 Shakedown Limits for Sandstone at Wet of Optimum Moisture Content .... 65

Figure 4. 19 Shakedown Limits for Limestone at Dry of Optimum Moisture Content .... 66

Figure 4. 20 Shakedown Limits for Limestone at Wet of Optimum Moistures Content .. 66

Figure 4. 21 Effect of Saturation on m a) Elastic Limit b) Plastic Limit ......................... 67

Figure 4. 22 Effect of Saturation on d a) Elastic Limit b) Plastic Limit .......................... 68

Figure 4. 23 Intercept vs. Degree of Saturation for Limestone ....................................... 69

Figure 4. 24 Intercept vs. Degree of Saturation for Sandstone ........................................ 69

viii

ABSTRACT

Pavements are a layered system each layer distinguished by different materials as

required by traffic and subgrade conditions. A base course is an intermediate layer

constructed of high quality stone aggregates: quality based on physical properties such as

gradation, hardness, and texture. Although indicative of performance, physical properties

do not directly measure performance. This thesis presents the results of a comprehensive

experimental testing program that was conducted to examine the behavior of unbound

granular base materials under cyclic loading and to evaluate the effect of the stress level

and moisture content on strain behavior. Three base materials, namely granite, limestone

and sandstone, were selected. Different physical properties tests were conducted on the

materials considered. In addition, static and repeated load triaxial (RLT) tests were

performed in this study. Three different types of RLT tests were used including: resilient

modulus, single-stage, and multi-stage RLT test. The single-stage and multi-stage RLT

tests results were analyzed within the framework of the shakedown theory. The results of

this study showed that for resilient modulus the materials preformed the following, with

the materials listed highest to lowest: limestone, granite and sandstone; while for

permanent deformation, the materials were listed highest to lowest: sandstone, limestone

and granite. In addition, the results demonstrated that the change in slope (m) of

shakedown limits with the degree of saturation was more pronounced at lower stress

levels (elastic limit) than that at higher stress levels (plastic limit). Finally, the results

showed a significant effect of degree of saturation on the intercept of the shakedown

limits at both low and high stress levels. The change in intercept was greater for

limestone than sandstone for changes in degree of saturation.

1

CHAPTER 1 INTRODUCTION 1.1 Background

Pavement structures are built to support loads induced by traffic vehicle loading and

to distribute them safely to the subgrade soil. A conventional flexible pavement structure

consists of a surface layer of asphalt (AC) and a base course layer of granular materials

built on top of a subgrade layer. Pavement design procedures are intended to find the

most economical combination of AC and base layers’ thickness and material type, taking

into account the properties of the subgrade and the traffic to be carried during the service

life of the roadway. Pavement materials are required to: (1) spread wheel loads to reduce

the load on the soft underlying subgrade (soil) and/or other weaker pavement materials;

(2) not fail in shear (i.e. shoving or rutting) with the applications of wheel loads;(3) have

a minimal deformation, where most of the deformation occurs in the subgrade.

The two main structural failure mechanisms considered in the design of a flexible

pavement structure are permanent deformation (rutting) and fatigue cracking. Rutting is

the result of an accumulation of irrecoverable strains in the various pavement layers. For

thin to moderately thick pavements, subgrade and granular base layers contribute most to

rutting of a pavement. Fatigue cracking has been defined as the phenomenon of fracture

under repeated or fluctuating stress having a maximum value generally less than the

tensile strength of the material (Ashby and Jones, 1980).

Although base course layer is an intermediary element of the pavement structure, its

correct functioning in the road pavement layers is vitally important. The major structural

function of a base layer is to distribute the stresses generated by wheel loads acting on the

wearing surface so that the stresses transmitted to the subgrade will not be sufficiently

2

great to result in excessive deformation or displacement of that foundation layer. Also,

while transferring these stresses, the base layer must not undergo excessive permanent

deformation and withstand shoving.

Material Characteristics is a principal factor entered into flexible pavement design

methods to determine layer thickness and type. Unbound base course materials (UGMs)

are considered for pavement design primarily on their physical properties with exception

of resilient modulus, which is a performance parameter expressing stiffness that replaced

the structural support value in 1986. Although an improvement, the resilient modulus

alone does not duly characterize the functionality of the unbound granular material layer.

As stated earlier, in addition to transfer of loading to the subgrade, the material must be

capable of safely handling stresses without excessive deformation. Leading to further

improve on the characterization of the UGM, the permanent deformation component

must be accounted for and included with the resilient modulus to fully evaluate the

engineering behavior of the UGM to ensure proper functionality of the base course layer.

1.2 Problem Statement

A principal component included in the design of flexural pavements is the

characterization of those materials that make up the pavement layers. Aiding in the

development of the M-E design guide, areas identified by Strategic Highway Research

Program (SHRP) and other M-E implementation projects such as Federal Highway

Admistration (FHWA) and National Cooperative Highway Research Program (NCHRP)

require further material characterization research include:

Resilient Modulus for granular materials

Permanent Deformation properties for granular materials

3

Overall performance of a pavement structure depends highly on the proper

characterization of material properties.

Currently, Unbound Granular Materials (UGMs) are characterized on the basis of

physical properties such as gradation, plasticity, hardness, durability, and on the basis

static shear strength tests. These properties are determined either empirically

(correlations) or from testing procedures that do not properly consider the relevance to

the cyclic loading behavior of the material. These physical properties or strength

characteristics from static load testing are insufficient to characterize the dynamic

response of materials within a pavement layer. For this reason, to simulate accurate field

conditions, the UGMs must undergo cyclic loading to characterize the dynamic response

behavior. The observed distresses in the field (rutting, flexural cracking) are a direct

result of the dynamic traffic loading, thus characterizing materials behavior with cyclic

loading will aid as a predictor for field performance.

1.3 Objectives

The primary objective of the research study is to characterize the deformational

behavior of unbound granular base materials under cyclic loading and examine the effects

of the state of stress and moisture content on this behavior.

1.4 Scope of This Study

To achieve the aforementioned objectives an experimental testing program was

conducted on three base course materials: Granite, Limestone and Sandstone. The

experimental testing program included conducting physical properties tests, as well as

static and repeated loading triaxial tests. Physical properties tests consisted of gradation,

standard proctor, specific gravity, absorption, coarse aggregate angularity, and Micro-

4

Deval tests. Three types of repeated load tri-axial test were conducted: resilient modulus,

single stage permanent deformation, and multi-stage permanent deformation. The results

multi-stage RLT tests were analyzed within the framework of the shakedown theory. To

examine the effects of moisture content, single samples were tested at wet and dry

moisture regimes to evaluate the effect of moisture on shakedown behavior.

1.5 Outline

Including this introductory chapter this thesis is divided into five chapters. A brief

summary of the contents of the other four chapters are as follows:

Chapter 2 presents an extensive literature review on the behavior of UGMs, outlining

important factors that affect the engineering behavior of UGMs.

Chapter 3 describes the materials used and the methodologies of the experimental testing

program implemented in this study to evaluate the laboratory performance of the UGMs

considered.

Chapter 4 contains full details of test results and analytical discussions.

Finally, Chapter 5 summarizes and concludes this research work and provides

recommendations for future research.

5

CHAPTER 2 LITERATURE

2.1 Introduction A review of the literature providing information on the cyclic loading behavior of

UGMs was surveyed. The literature investigation focused on the various factors that

affect the deformation behavior (permanent and resilient) of UGMs and modeling

techniques. The beginning of the chapter introduces and explains the various factors and

how they relate to deformation behavior. Later in the chapter is an introduction to the

application of shakedown theory. Finally, an overview of models developed to predict

the deformation behavior of UGMs is presented.

2.2 Deformation Behavior of Unbound Granular Materials

2.2.1 Stresses in Unbound Granular Layers

The stresses acting on an elemental cube can be defined by its normal and shear

stresses on opposing faces of the cube, as shown in Figure 2-1. By a rotation of the

element, the state of stress will assume a position of no shear stress acting on mutually

perpendicular opposing faces. The resulting stresses are represented as normal stresses,

defined as principal stresses σ1, σ2 and σ3 (Figure 2-1)

Figure 2.1 Stress components acting on an element (Lekarp 97)

6

The principal stresses are physical invariants that are independent of the coordinate

system chosen (e.g., Cartesian, Polar). In the absence of traffic loading, a confining

pressure from overburden and previous stress history is the applied stress condition.

The pavement structure in the field is subjected to loads induced by wheel loadings

provided by traffic. An element in a pavement is subjected to a stress pulse, each

consisting of vertical, horizontal and shear component. These stresses are mutable and

change as the wheel load passes. From Figure 2.2, the principal stresses (stresses without

a shear stress) are horizontal and vertical when the shear component is zero, that is,

directly beneath the center of the wheel. As the wheel moves away, a reversal of the shear

stress occurs. The stress reversal is commonly referred to as principal stress rotation.

Figure 2.2 Stress beneath a rolling wheel load (Lekarp, Dawson)

7

2.2.2 Deformation Characteristics of Unbound Materials

The strain behavior both resilient and permanent of UGMs under traffic loading

has been one the main research topics in pavement engineering for many years.

Researchers characterized the deformation response by a recoverable (resilient)

deformation and a residual (permanent) deformation (Lekarp 1997). Both permanent and

resilient deformations are a function of the applied stress. Henceforth, the dynamic

deformation response is controlled by the stress-strain behavior of the material. A typical

relationship is shown in Figure 2-3, as the stress increase the material’s resistance to

further deformation decreases.

Figure 2. 3 Stress-Strain Behavior of UGMSs (Werkmeister 2003)

At low levels of stress, the stiffness of the material increases as stress increases

(strain hardening). The strain hardening causes particle rearrangement and the particles

move closer together. Eventually from further increases in stress the UGM strain

behavior softens (strain softening), additional increases in stress will cause collapse.

UGMs are quite different from soils in their response to cyclic loading. UGMs are an

8

assemblage of, often inhomogeneous and non-isotropic, macroscopic particles in contact

with each other. The horizontal and vertical stresses are positive in UGMs since they do

not carry any significant amount of tensile stresses.

The strain behavior of UGMs under compressive stresses is highly complex

because of the existence of resilient and permanent strains even at small levels of stress.

UGMs in a pavement structure are subjected to large number of loadings during the

service life of the pavement. The resilient deformation recovers after each load cycle,

whereas the permanent deformation accumulates (sometime digressively) with each load

cycle. The rate of accumulation depends on material properties, the stress level, and

loading conditions (Arnold 2004). The complex stress-strain behavior for UGMs is given

by non-linear curve. The behavior is further characterized by a hysteric loop that occurs

during the application of stress for each cycle. The resilient and permanent strain can be

evaluated at the hysteresis loop for the each load cycle. Figure 2-4 gives the general idea

for a single hysteresis loop.

Figure 2. 4 Hysteresis Loop for One Cycle of Loading (Lekarp 1997)

The results of a RLT are shown below in Figure 2-5. The plot expresses typical

cyclic loading behavior for UGMs. Some researchers suggest that the permanent

9

deformation rate or permanent deformation per cycle diminishes with loading cycles

(Arnold 2004). By a comparison of the hysteresis loops from the graph, the hysteresis

loops become more narrow at increasing cycles, showing a markedly decrease in

permanent deformation. Of course, this is often the case for lower stress levels,

depending upon stress levels, permanent deformation may increase, decrease, remain

constant or increase and quickly fail with increasing load cycles.

Figure 2. 5 Typical RLT for Unbound Slate Waste (Dawson and Nunes)

2.3 Factors affecting Resilient and Permanent Deformation Properties

For the purpose of design, it is important to consider how deformation behavior of

UGMs varies with changes in different influencing factors. From studies found in

literature, the resilient and permanent strains of UGMs are affected by several factors

described below.

10

2.3.1 Stress State

The available literature from studies show that “stress level” is one of the most

important factors affecting the resilient response of UGMs. Many studies have shown a

very high degree of dependence on confining pressure and the bulk stress for the resilient

modulus for UGMs (Mitry ,1964; Monosmith et al.,1967; Hicks, 1970; Smith and Nair,

1973; and Sweere, 1990). Monosmith et al. (1967) reported an increase as great as 500%

in resilient modulus for a change in confining pressure from 2.9 psi (20 kPa) to 29

psi(200 kPa). Smith and Nair (1973) noticed a 50% increase in resilient modulus when

bulk stress increased from 10 psi (70 kPa) to 20.3 psi (140 kPa) .

Suggested from researchers, deviator stress is said to be much less influential on

material stiffness than confining pressure. A study by Morgan (1966) showed the

resilient modulus to decrease slightly with increasing repeated deviator stress under

constant confinement. While a study by Hicks (1970) describes the resilient modulus as

being unaffected by the magnitude of deviatoric stress, as long as there is not excessive

plastic deformation. On the other hand, Hicks and Monismith reported a slight softening

of the material at low deviator stress levels and slight stiffening at higher stress levels.

The accumulation of permanent strain is directly related to deviator stress and

inversely related to confining pressure (Morgan 1966). Conversely, for a constant

deviator stress, the accumulation of permanent strain increased with a reduction in

confining stress. Clearly, confining pressure and deviator stress play a primary role in the

accumulation of permanent strain.

Barksdale (Barksdale 1972) conducted a number of RLT test on UGMs at

confining pressures and up to 100,000 cycles. Barksdale concluded that permanent

11

strains were highly dependent on the applied load and increased when confining pressure

decreased and deviator stress increased (Figure 2-6)

Figure 2. 6 Stress Influence on Permanent Strain in a Granite Gneiss-Material (Bar 72)

Researchers suggest that the magnitude of permanent strain settles down to a

constant value related to the ratio of deviator stress to confining pressure (Barksdale,

1972,; Lashine et al, 1971; Pappin, 1979;Paute et al., 1996; Lekarp and Dawson, 1998).

Lekarp and Dawson (1998) also showed that an increase in stress path length in p-q space

increased the magnitude of permanent strain. Other researchers have used the relationship

of permanent strain in terms of proximity to the static shear failure line (Raymond and

Williams 1978; Pappin 1979; Thom 1988; Paute et al. 1996). This has been refuted by

Lekarp and Dawson who suggest that the mechanism for failure under cyclic loading is

different than of that for static loading.

12

2.3.2 Number of Load Cycles

Researchers investigated the effect of number of load cycles on the resilient

deformation of granular materials, and they concluded the resilient deformation increased

slightly due to loss of moisture during testing ( Moore et al 1970). In contrast, other

researchers suggested the resilient deformation stabilizes after 50-100 load cycles as after

25,000 cycles (Hicks, 1970; Allen and Thompson, 1974).

The growth of permanent deformation in granular materials under repeated a

gradual process during which each load cycle contributes a small increment to the

accumulation of strain. For increasing loads cycles the accumulative strain will always

increase (Arnold 2004). Paute et. al (1996) argued that the rate of increase of permanent

strain is digressive in behavior to such an extent to define a limit value for the

accumulation of permanent strain. While other researchers ( Morgan, 1996; Barksdale,

1972; Sweere, 1990) have reported continuously increasing permanent under repeated

loading. Moreover, Theyse (2002) also reported that for high stress, the permanent strain

increased at a constant rate but between 5,000 and 10,000 load cycles an exponential

increase in permanent strain occurred resulting in collapse shortly after.

According to Lekarp and Dawson (1998), settling down of the permanent stain

rate is achievable only at low applied stresses. In recent work by Kolisoja (1998), tests

were conducted that involved very a large number of cycles. The work revealed that

permanent strain became stable and then suddenly unstable suggesting the behavior may

not be expressed as simple function.

13

2.3.3 Effects of Moisture Content\Suction

Monosmith and Finn (1977) reported that the presence of moisture in a pavement

system is one of the most important environmental considerations. Water is needed as

lubricant to achieve high levels of compaction during construction. The moisture content

will vary from the “as-built” moisture content by the ingress of moisture from changes in

seasonal changes or capillary action. More importantly, the performance of the pavement

structure is dependent upon the permeability of the UGM and drainage conditions of the

structure. If there is a build-up of moisture, the pavement may develop excess pore water

pressure decreasing effective stress leading to reduced strength transpiring in localized

failures and rutting. The effect of high water pressure in UGMs in pavement layers in the

laboratory and in the the field from a combination of a high degree of saturation and low

permeability, due to poor drainage, leads to low effective stress , and consequently, low

stiffness and deformation resistance (Hynes and Yoder, 1963; Barksdale, 1972; Maree et

al., 1982; Thom and Brown, 1987; Dawson et al 1996).

The moisture content of UGMs has been found to affect the resilient modulus

characteristics in the laboratory and field. Several researchers reported a marked

dependency of resilient modulus on the moistures content, with the modulus decreasing

with growing moisture content (Haynes and Yoder, 1963; Hicks and Monosmith, 1971;

Barksdale and Itani, 1989; Dawson et al, 1996; Heydinger et al, 1996). For instance,

Hicks and Monosmith (1971) showed that the resilient modulus deceased as the moisture

increased beyond the optimum moisture content.

Researchers suggest the effect of moisture is also dependant on stress analysis,

total or effective. On one hand, a decrease in resilient modulus is achieved only if the

14

analysis is based on total stress (Mitry, 1964; Seed et al., 1967; Hicks, 1970). On the

other hand, the resilient modulus remains unchanged if the results are analyzed on basis

of effective stress (Pappin, 1979). However, Thom and Brown (1987) argued that the

moisture acts as a lubricant and would cause deformation of the granular assembly and

reduce resilient modulus, without the presence of excess pore pressure. They proved the

hypothesis with a series of test on crushed stone.

As mentioned earlier, high water content within an UGM causes a reduction in

stiffness and deformation resistance of the material. Figure 2-7 shows RLT test results

demonstrating the behavior of both samples started at the same moisture content; one of

which was allowed to drain like a proper functioning pavement; the other was not

allowed to drain and experienced greater growth in permanent deformation.

Figure 2. 7 Influence of Drainage of Permanent deformation (Dawson 90)

Haynes and Yoder (1963) conducted a study and found the total permanent strain

rose by more than 100% as the degree of saturation increased from 60 to 80%. Thom and

Brown (1987) suggested that a large increase in permanent strain could occur even

without the generation of excess pore water pressure, and stated further that a relatively

15

small increase in water can trigger a dramatic increase in permanent deformation.

Furthermore, the result of wetting as increased rutting has been observed in in-situ

vehicle simulator test trials (Maree et. al, 1982).

In summary, it seems that moisture content has a profound influence on the

permanent and resilient response for UGMs. This is mainly due to the apparent cohesion

caused by soil suction of the unsaturated assembly. If suction is increased, the pore water

pressure reduces and thus the effective stress is increased. Suction (eq. 2.1) is present in

all UGMs and has a significant effect on the effective stress.

푠 = 푢 − 푢 Equation 2.1

where:

푠 = matric suction

푢 =pore air pressure;

푢 = pore water pressure

Effective mean stress (푝 ) is the total mean normal stress minus the pore water

pressure(푢 ). As suction controls effective stress, effective stress governs the effective

level of confining stress, which if increased, has the effect of increasing a material

strength. However, most RLT tests do not control or measure suction so total stresses are

used for testing purposes.

2.3.4 Stress History

Stress history does have an effect on the resilient response of UGMs. The stress

history seems to appear as a consequence of progressive densification and particle

rearrangement under repeated loading (Dehlen, 1969). Therefore, researchers suggest a

prescribed number of cycles ranging from 100 to 1000 load repetitions to eliminate stress

16

history effects (Boyce el. Al, 1976; Hicks, 1970; Allen, 1973). Researchers suggest

stress history effect can be avoided by using low stresses to avoid excessive permanent

deformations, allowing large numbers of resilient modulus test to be carried out

sequentially on the same sample to determine resilient behavior of the material (Brown

and Hyde, 1975; Mayhew, 1983).

The permanent deformation behavior of UGMs is directly related to the stress

history. From repetitive loading, like traffic, the stiffness of the material gradually

increases, causing a reduction in permanent deformation for subsequent loadings. Brown

and Hyde (1975) studied the impact of stress history on the permanent strain of UGM

assemblies. The results of the study are illustrated in Figure 2-8. Given the test results

below, the stress dependency on the permanent strain of the material is evident. For

instance, the permanent strain resulting from a successive increase in the stress level is

considerably smaller than the strain that occurs when the highest stress is applied

immediately.

Figure 2. 8 Effect of Stress History on Permanent Strain (Brown and Hyde 1975)

17

Even though the effects of stress history are obvious in laboratory testing, further

testing to fully evaluate the observance of stress history’s impact on permanent strain has

been ignored. Still, researchers suggest the effects of stress history can be eliminated by

using a new specimen each time for testing.

2.3.5 Density

The general trend is that resilient modulus increases with increases in dry density.

Researchers who studied the impact of density on uniform sand reported resilient

modulus increased up to 50% for loose to dense specimens (Robinson, 1974; Trollope,

1962). Theoretically, additional compaction results in a greater number of particle

contact improving the resilient response of the material. However, others reported that

an increase in dry density is relatively insignificant on the resilient response (Thom and

Brown, 1989; Selig, 1991).

For the compaction of the granular assembly of UGMs is quite significant for

resistance to permanent deformation and long term stability. From the results presented,

the resistance to permanent deformation in UGMs under repetitive loading apparently

improves with greater dry density. For example, Barksdale (1972) studied the behavior

of several granular materials and reported an average of 185% more permanent strain

when the material was compacted at 95% instead of 100% of maximum dry density

(Standard Proctor Density), refer to Figure 2-9.

Increasing the dry density, as reported by Holubec (1969), promotes a reduction

in permanent strains for crushed aggregates in particular. This behavior is not noticeable

for rounded aggregates, as these aggregates are initially at a higher compacted density

than angular aggregates for the same level of compaction.

18

Figure 2. 9 Effect of Density on Permanent Strain

2.3.6 Load Duration and Frequency

The resilient behavior of UGMs is unaffected by load duration and frequency.

This aforementioned statement has been validated by several studies amongst different

researchers. For example, Seed et al. (1965) reported the resilient modulus increased

only slightly when the frequency was increased from 20 min to 0.3 s. Meanwhile, an

increase in stress duration incrementally of 0.1, 0.15 and 0.25 s had no effect on resilient

modulus or Poisson’s ratio (Hicks, 1970).

2.4 Shakedown Theory

A key objective of pavement design is keep permanent deformations of structural

layers within tolerable limits. As mentioned earlier, the mechanism responsible for

deformations are from cyclic traffic loadings. For many years, cyclic loading models

have been used to explain the plastic limit or “Shakedown” behavior of structures

(Melan, 1936). Researchers argued that this type of analysis could be used as an approach

to model pavement deformations (Sharp 1983; Sharp and Booker, 1984). During the

19

fledgling days of the AASTO road test, researcher noticed that the measured

serviceability index stabilized after a finite number of load applications, providing early

justification for a shakedown approach behavior analysis.

Limit analysis has long been used to determine failure criteria for UGMs under

static loading. To evaluate a traffic loading condition, the shakedown theory has been

extended to pavement analysis to determine the failure behavior for UGMs under cyclic

loadings. The shakedown theory uses the number of cycles and stress ratio , σd\σ3, as the

parameters to explain the permanent deformation behavior. For if the stress ratio is small

enough, then the permanent strain will tend to a limit demonstrating an asymptotic or

shakedown behavior, refer to Figure 2-10.

Figure 2. 10 Permanent Deformation Behavior at Low Stress Level (Werk 2003)

If the stress ratio is increase, permanent strains are likely to increase, to capture

the total behavior a logarithmic model is needed (Figure 2-11). If the ratios are increased

further, strain may upsurge rapidly leading to collapse. These ranges of behaviors can be

determined using the shakedown concept and are displayed below (Figure 2-12).

20

Figure 2. 11 Permanent Deformation Behavior at High Stress Levels (Werk 2003)

Figure 2. 12 Shakedown Range Behavior (Arnold 2004)

In recent years several researchers have applied the shakedown concept to

describe the observed permanent strain behavior in RLT test. The results of their

findings are reported as a shakedown ranges: A,B and C. The associative stress

conditions are linked to their corresponding boundary for each shakedown range. Ranges

for shakedown can be defined as (Arnold et al., 2004):

21

Range A is the plastic shakedown range, and for this to occur the response must

show high strain rates per load cycle for a finite number of load applications

during the initial compaction period. After the compaction period the permanent

strain per load cycle decreases until the response becomes entirely resilient and no

further permanent strain occurs. This range occurs at low stress levels.

Range B is the plastic creep shakedown range, initially the behavior is similar to

Range A during the initial compaction period. After this time the permanent

strain either decreases or remains constant. For the duration of the RLT the

permanent strain is acceptable, and the response does not settle down to resilient

entirely. But in this range, if the cycles were continued excessively perhaps 2

million, the material is prone to collapse.

Range C is the incremental collapse shakedown range where initially compaction

period may be observed, which after permanent strain increase with increasing

load cycles.

These three shakedown behavior ranges were derived based simply on the fact that it is

possible to classify all permanent strain/rutting plots with number of cycles. Johnson

(1986) identified four possible shakedown ranges: elastic; elastic shakedown; plastic

shakedown. Figure 2-13 show the behavior of a UGM through increasing stress and

deformation. The elastic response is highly unlikely for granular materials, so for UGMs

the elastic response can be ignored leaving the elastic shakedown, or range A, as the first

observed behavior previously defined.

22

Figure 2. 13 Elastic/Permanent Behavior Under RLT Loading (Johnson 1996)

Now that the understanding of the components material behaviors is defined, and

the shakedown concept can adopt upper and lower bound limit theorems. For the key of

pavement design relies on the ability to prevent excessive permanent strain leading to

early failure. Thus, the shakedown concept can be used as a handy performance tool to

assess the permanent strain potential of the material: such as, the material will experience

progressive accumulation of permanent strain leading to collapse; or conversely, the

material undergoes digressive accumulation of permanent strain leading to a settling

down effect or “shakedown state.”

2.5 Modeling of Permanent Strain Behavior

2.5.1 Resilient Modeling Behavior

For the most part, the resilient behavior of UGMs has been modeled by means of

curve fitting, some models will be discussed. Another approach for characterizing the

stress strain relationship is to decompose both stresses and strains into volumetric shear

component; such models will not be discussed for they are beyond the scope of this

23

paper. Researchers use a constitutive relationship to link state of stress to resilient

modulus.

Dunlap (1963) and Monosmith (1967) suggested this relationship between modulus and

confining pressure:

푀 = 푘 휎 or 푀 = 푘 Equation 2.2

Where:

휎 = 푐표푛푓푖푛푖푛푔 푝푟푒푠푠푢푟푒

Hicks in (1970) suggested the following relationship commonly known as the

K-휃 model:

푀 = 푘 휃 Equation 2.3

where:

휃 = 푠푢푚 표푓 푝푟푖푛푐푖푝푎푙 푠푡푟푒푠푠푒푠

푘 푘 = 푟푒푔푟푒푠푠푖표푛 푐표푒푓푓푖푐푖푒푛푡푠

The simplicity of the model has made it very useful, but has mainly two drawbacks. First,

the model assumes a constant poison’s ratio. Second, the effect of stress on the resilient

modulus is accounted for solely by the sum of principal stresses. However, the model is

widely accepted and several versions can be found in literature.

Uzan (1985) included deviator stress into the K-휃 model and expressed the

relationship as:

푀 = 푘 푝 Equation 2.4

or

푀 = 푘 푝 Equation 2.5

24

where:

휃 = 푏푢푙푘 푠푡푟푒푠푠

푝 = 푎푡푚표푠푝ℎ푒푟푖푐 푝푟푒푠푠푢푟푒

푞 = 푑푒푣푖푎푡표푟푖푐 푠푡푟푒푠푠

푘 , 푘 ,푘 , = 푟푒푔푟푒푠푠푖표푛 푐표푒푓푓푖푐푖푒푛푡푠

휏 = 표푐푡푎ℎ푒푑푟푎푙 푠ℎ푒푎푟 푠푡푟푒푠푠 , replaces q for 3-dimensional state

The Uzan model has been shown to be superior to the K-휃 model and will most

likely replace it for routine analysis. For the three dimensional state, the model has been

further modified by adding a +1 term to avoid the modulus from tending to zero as 휏

tends to zero:

푀 = 푘 푝 + 1 Equation 2.6

This model was suggested for use in the determination of the resilient modulus by the

NCHRP project 1-37 “Development of the 2002 Guide for the design of New and

Rehabilitated Pavement Structures.”

Kolisoja(1997) in included the effect of material density in both the K-휃 and the

Uzan models. These are the modified models:

푀 = 퐴(푛 − 푛)푝 .

Equation 2.7

푀 = 퐵(푛 − 푛)푝 . .

Equation 2.8

where:

퐴 푎푛푑 퐵 = 푚푎푡푒푟푖푎푙 푐표푛푠푡푎푛푡푠

푛 = 푝표푟표푠푖푡푦 표푓 푡ℎ푒 푎푔푔푟푒푎푔푡푒

25

The NCHRP 1-37 project concluded with a proposed model based on overall

goodness of fit statistics:

log = 푘 + 푘 + 푘 + 푘 Equation 2.9

푥, 푦 = 푝푎푖푟 표푓 푠푡푟푒푠푠 푝푎푟푎푚푒푡푒푟푠 푒푞푢푎푙 푡표 푒푖푡ℎ푒푟 휎 ,휎 표푟 (휃, 휏 )

휎 = 푐표푛푓푖푛푖푛푔 푠푡푟푒푠푠 and 휎 = 푐푦푙푖푐 푙표푎푑푖푛푔 푠푡푟푒푠푠

푘 = 푝표푝푒푟푡푦 푟푒푙푎푡푒푑 푡표 푡ℎ푒 푐푎푝푖푙푙푎푟푦 푠푢푐푡푖표푛 푖푛 푝푎푟푖푡푖푎푙푙푦 푠푎푡푢푟푎푡푒푑 푈퐺푀푠

푘 = 푎푑푑푖푡푖표푛푎푙 푚푎푡푒푟푖푎푙 푝푎푟푎푚푒푡푒푟

2.5.2 Permanent Deformation Modeling Behavior

A primary goal of research into long term behavior of UGMs has been to develop

models to predict permanent strain/rutting for design purposes. In the past, several

researchers have attempted to outline procedures to predict permanent deformation. For

its simplicity many relationships were developed from permanent strain RLT test, some

researcher say too simple, as principal stress rotation effects are ignored. The aim of the

model is to predict the magnitude of permanent strain at a certain number of loads and

stress conditions; both variables are easily controlled in RLT test and probably

contributed to the development of many models.

Because of the complex strain behavior, it reasonable to suggest that more than

one model is needed to fully describe the permanent strain behavior of UGMs. To

simplify the failure criteria, several researchers have attempted to relate failure at cyclic

loading to the monotonic shear failure line. As a common approach, it has received

mixed reviews. Refer to table 2.1 on next page for a listing of models; and for further

discussion on models below, visit: State of the Art. II: Permanent Strain Response of

Unbound Aggregates by Fredrick Lekarp et al.

26

Table 2.1 Models proposed to Predict Permanent Strain after Lekarp et. al. 2000

Expression Eqn. Reference Parameters

휀 , = 푎휀 푁

2.30 Ververka (1979) 휀 ,

휀∗ ,

휀∗ , 푁

휀 ,

휀 ,

휀

휀

휀

퐾

퐺

푞

푝

푞

푝

푝∗

푝

퐿

= accumulated permanent strain after 푁 load cycles = additional permanent axial strain after first 100 cycles = accumalated permanent axial strain after a given number of load cycles 푁 ,푁 > 100 = permanent volumetric strain for 푁 > 100 = permanent shear strain for 푁 > 100 = permanent strain for load cycle 푁 = permanent strain for first load = resilient strain = bulk modulus with respect to permanent deformation = shear modulus with respect to permanent deformation = deviator stress = mean normal stress = modified deviator stress = 2/3 q = modified mean normal stress = √3 p = stress parameter defined by intersection of the static failure line = reference stress = stress path Length

퐾 (푁) = 푃

휀 , ( ) ,퐺 (푁) =

푞3휀 , (푁)

2.31

퐺 = 퐴 √푁

√푁 + 퐷 ,퐺퐾 =

퐴 √푁√푁 + 퐷

2.32

Jouve et al. (1987)

휀 ,

푁 = 퐴푁

2.33 Khedr (1985)

휀 , = 푎 + 푏 log푁

2.34 Barksdale (1972)

휀 , = 푎푁

2.35 Sweere (1990)

휀 , = (푐푁 + 푎)(1 − 푒 )

2.36 Wolff&Visser(1984)

휀∗ , = 퐴 √푁

√푁 + 퐷

2.37 Paute et al. (1998)

휀∗ , = 퐴 1−푁

100

2.38 Paute et al. (1996)

휀∗ , = 휀 =1푁 휀 2.39 Bonaquist &Witczak

(1987)

27

table continued Expression Eqn. Reference Parameters

휀 , =푞/푎휎3

푏

1−푅푓푞 /2(퐶cos휑+ 휎3 sin휑)

(1− sin휑)

2.40 Barksdale(1972)

휎

푁

푆

휀 .

퐶

휑

fnN

푅

ℎ 퐴

퐴2−퐴4 퐷2−퐷4

푚

푎, 푏, 푐,푑 퐴,퐵

= confining pressure = number of load applications = static strength = static strain at 95 percent of static strength = apparent cohesion =angle of internal friction = shape factor = ratio of measured strength to ultimate hyperbolic strength ratio = repeated load hardening parameter, a function of stress to strength ratio = a material and stress-strain parameter given (function of stress ratio and resilient modulus) = parameters which are function of stress ration q/p =slope of the static failure line =Regression parameters (A is also the limit value for the maximum permanent axial strain)

휀 , = 휀 . ln 1−푞푆

.+

푎(푞/푆)1− 푏(푞/푆) ln(푁)

2.41

Lentz and Baladi(1981)

휀 , = 0.9푞휎

2.42

Lashine et al. (1971)

휀 , = (푓푛)퐿푞푝

.

2.43

Pappin (1979)

퐴 =

푞푝+ 푝∗

푏 푚− 푞푝 + 푝∗

2.44 Paute et al.

휀 , 푁(퐿/푝 )

= 푎푞푝

2.45 Lekarp and Dawson (1998)

휀 (푁) = 퐴 1−푁

100 ×1푝 ×

푞푝

2.46 Akou et al. (1999)

28

CHAPTER 3 METHODOLGY

This chapter includes a description of the research methodology used in this

study. The chapter outlines detailed information about the physical properties and

experimental testing.

3.1 Experimental Testing Program

An experimental testing program was performed on three types of unbound

granular materials used in construction of base course layers. The tested materials

included: limestone, sandstone, and granite materials. All materials were selected from

1.5 inch sieve crushed run materials provided by the appropriate quarries. Different

laboratory tests were first conducted to screen the physical properties that are typically

used in the selection and evaluation of base course material. The performed test included

sieve analysis (ASTM C136-06), Standard Proctor (ASTM D 792), specific gravity and

absorption, and coarse aggregate angularity (ASTM D 5821). Materials were sampled in

accordance with ASTM C702 .In addition, Micro-Deval (ASTM D 6928) test were

conducted to examine particle degradation of the considered material.

Tri-axial tests were conducted used in this study to characterize the shear strength

properties of base course granular materials in their field construction conditions and

examine their response under cyclic loading. To do this, two types of tri-axial test were

employed: static tri-axial test compression test (SCT) and repeated load tri-axial testing

(RLT). The triaxial tests conducted in this study are described below.

3.2 Testing Setup of Triaxial Tests All triaxial tests were performed using the Material Testing System (MTS) 810 machine

(Figure 3.1) with a closed loop and a servo hydraulic loading system. The

29

applied load was measured using a load cell installed inside the triaxial cell. This type of

set up reduces the equipment compliance errs as well as the alignment errors. The

capacity of the load cell used was ± 22.25 kN. The axial displacement measurements

were made using two Linearly Variable Differential Transducers (LVDT) placed between

the top platen and base of the cell to reduce the amount of extraneous axial deformation

measured compared to external LVDTs. Air was used as the confining fluid to the

specimens. Figure 3.1 illustrates the testing setup.

Figure 3. 1 MTS Tri-axial Testing Machine

30

3.3 Sample Preparation

AASHTO-T307 recommends that a split mold be used for compaction of granular

materials. Therefore, all samples were prepared using a split mold with an inner diameter

of 150 mm and a height of 350 mm. The material was first oven dried at a pre-specified

temperature and then mixed with water at the specified moisture content. The achieved

water contents were within ±0.5 percent of the target value. For single-stage RLT test and

static shear strength test, the material was placed within the split mold and compacted

using a vibratory compaction device to achieve the prescribed dry density determined

from the standard Proctor test. For the multi-stage samples utilized for shakedown the

target moisture content was varied on the wet and dry side of optimum moisture content

and then vibratory compacted to maximum to max dry density as determined from

standard proctor test. To achieve a uniform compaction throughout the thickness, samples

were compacted in six-50 mm layers. Each layer was compacted until the required

density was obtained; this was done by measuring the distance from the top of the mold

to the top of the compacted layer. The smooth surface on top of the layer was lightly

scratched to achieve good bonding with the next layer. The achieved dry densities of the

prepared samples were within ±1 percent of the target value. Samples were enclosed in

two latex membranes with a thickness of 0.3 mm. Figure 3.2 illustrates the preparation

procedure of limestone samples.

3.3.1 Static Triaxial Compression Test

As many pavement structures do not fail by shear, the RLT triaxial tests are considered

more representative of actual performance in the road. Nevertheless, the monotonic

triaxial compression tests provide valuable parameters that can be used to

31

evaluate strength and stiffness of pavement materials. Furthermore, it is commonly

thought that safe stress states for a pavement material are related to their ultimate shear

strength.

Drained triaxial compression tests were first performed to obtain the shear strength

properties of the different materials considered. The triaxial compression tests were

performed at three different confining pressures: 2, 7 and 10 psi (14, 48, and 69 kPa

Figure 3. 2 Preparation of Testing Limestone Samples

32

respectively). The strain rate used in those tests was less than ten percent strain per hour

to ensure that no excess pore water pressure developed during testing. Two response

parameters were recorded for each static triaxial test: ultimate shear strength (USS) and

residual shear strength (RSS).

3.3.2 Sample Size

Dimensions of the sample tested in the triaxial experiment are based on the

maximum particle size of its material. AASHTO recommends that for untreated granular

base material, the tested sample should have a diameter greater than five times the

maximum particle size of that material. In addition, other studies recommend the use of

samples with 6 in (150 mm) and diameter 12 in (300 mm ) height for a base material with

a maximum particle size greater than .75 in (19 mm) (NCHRP, 2004). Since the base

course material used in this study had a maximum particle size of .75 in, all samples were

prepared with 6 in diameter and 12 in height.

3.4 Repeated Load Triaxial (RLT) Tests

RLT tests were conducted to determine the properties of granular materials under

repeated loading that significantly influence the structural response and performance of

base course layers under traffic loading. In these tests, a repeated axial cyclic stress with

a haversine-shaped load-pulse and fixed magnitude was applied to 6 in diameter

cylindrical samples. The load pulse used in this study has 0.1 sec load duration and 0.9

sec rest period as shown in Figure 3.3. The resilient and permanent deformations (Figure

3.3) of the samples were measured during this test to calculate the resilient and plastic

strains, respectively. During a RLT test, cyclic deviator and confining stresses along with

vertical deformations were recorded. The difference between the maximum and

33

minimum deformation divided by the length over which this occurs gives the strain. Two

types of strains are determined: resilient (elastic); and permanent (plastic). The resilient

and permanent strains are defined in Equations 3.1 and 3.2 , respectively.

휀 (푁) = ( )

( ) Equation 3.1

휀 (푁) = ( )

( ) Equation 3.2

Where 퐿 is the original sample length,

휀 (푁) is the total resilient change in sample length at cycle N (mm),

휀 (푁) is the resilient change in specimen length at cycle N (mm/mm),

휀 (푁) is the resilient strain at cycle N (mm/mm), and

휀 (푁) is the permanent strain at cycle N (mm/mm).

Three different types of RLT tests were used in this study. The proceeding

sections describe the procedures followed in these tests.

3.4.1 Resilient Modulus Test

Resilient modulus tests were performed in accordance with AASHTO-T307

standard method for determining the resilient modulus of base course material

(AASHTO, 2003). In this test method the samples are first conditioned by applying 1,000

load cycles with a deviator stress 14 psi (93.0 kPa) and a confining stress of 15 psi (103.4

kPa). The conditioning step removes most irregularities on the top and bottom surfaces of

the test sample and also suppresses most of the initial stage of permanent deformation.

This step is followed by a sequence of loading with varying confining and deviator

stresses. The confining pressure is set constant, and the deviator stress is increased.

34

Subsequently, the confining pressure is increased, and the deviator stress varied. The

resilient modulus values are calculated at specified deviator stress and confining pressure

values as the ratio of the cyclic stress to the measured resilient strain (Equation 3.3). The

stress sequences followed in this method are shown in Table 3.1.

푀 = Equation 3.3

Where,

휎 is the maximum cyclic stress

휀 is the recoverable elastic strain

In order to determine the resilient modulus parameters of tested samples, the

average value of the resilient modulus for each stress sequence was first calculated. A

regression analysis was then carried out to fit each test data to the generalized constitutive

model given in Equation 2.6, which was adopted by the new Mechanistic-Empirical

Design Guide (NCHRP 1-37A).

3.4.2 Single-Stage RLT Test Single-Stage RLT tests were performed to determine the permanent and resilient

deformations of the considered materials at different number of load cycles. The test

consisted of applying 10,000 load cycles at a constant confining pressure 3 psi (21 kPa)

and peak cyclic stress 30 psi (230 kPa). The value of the confinement pressure was

chosen to match the field measurement of the lateral confining pressure within the base

course layer that was reported in different studies (Barksdale and Alba 1993). The peak

35

Figure 3.3 Applied Load and Response of Samples in RLT Test

36

Table 3.1 Load Pulse Used in the Resilient Modulus Procedure

cyclic stress was selected based on a previous finite element study (Nazzal 2006). Tests

were stopped after 10,000 load cycles or when the sample reached a permanent vertical

strain of seven percent. All samples were conditioned before the tests in a way similar to

that used in the resilient modulus tests. It is noted that the Single-Stage RLT procedure is

Sequence No. Confining Pressure Deviator Stress

Number of Load

Applications

kPa Psi kPa Psi 0

103 15 93 15 1000

1 21 3 21 3 100

2 21 3 41 6 100

3 21 3 62 9 100

4 34 5 34 5 100

5 34 5 69 10 100

6 34 5 103 15 100

7 69 10 69 10 100

8 69 10 138 20 100

9 69 10 207 30 100

10 103 15 69 10 100

11 103 15 103 15 100

12 103 15 207 30 100

13 138 20 103 15 100

14 138 20 138 20 100

15 138 20 276 40 100

37

similar to those followed in previous studies (Mohammad et. al. 2006; Nazzal et. al

2007).

3.4.3 Multi-Stage RLT Test

Multi-stage RLT tests were used in this study to determine the cyclic behavior of

the considered materials at different stress levels. The multi-stage testing was conducted

by increasing the vertical cyclic stress at each stage, while maintaining the cell pressure

constant. Maintaining cell pressure constant is common in many RLT standards such as

US AASHTO T 307-99 and Australia’s AG: PT/T053. Multi-stage RLT test included six

stages, with a gradually increasing of q/p ratio [q- deviatoric stress equal to 1-3; and p-

mean confining pressure equal to (1+2*3)/3] applied to the sample such that the stress

level moves closer (or above) the static failure line. During each stage 10,000 load cycles

of the same stress level were applied. Each cycle consisted of the same load pulse used in

single-stage RLT tests. Samples were compacted at optimum moisture content, and tested

at the confining stress of 3 psi (21 kPa) which was used in the single-stage RLT test. To

determine shakedown limits, additional multi-stage test were conducted at 6.5 psi (45

kPa) and 10 psi (70 kPa) for limestone and sandstone. Carrying further the application of

shakedown limits to UGMs, multi-stage testing was conducted on limestone and

sandstone at dry and wet of optimum moisture content. Using the void ratio at optimum

moisture content, the saturation ratio was calculated using equation 3.4. Next, the

moisture contents for wet and dry were obtained by shifting the degree of saturation by

an amount that would be encountered in Louisiana to reflect typical seasonal conditions,

allowing calculation of moisture contents at those moisture regime conditions, again by

using eq. 3.4. Results are listed in table 3.4. Following this table are the p and q loading

38

Table 3.2 Stress Sequence: Limestone Stress Levels For Multi-Stage RLT Test Limestone-Opt

Stage Test 1 Test 2 Test 3

p(psi) q(psi) p(psi) q(psi) p(psi) q(psi) I 4.3 3.8 7.4 8.5 12.6 18.0 II 6.1 9.1 10.4 17.5 18.0 34.3 III 9.0 18.0 12.8 24.9 21.3 44.0 IV 14.5 34.5 19.3 44.4 24.9 55.0 V 20.1 51.3 27.8 70.0 33.6 80.1 VI 21.3 54.8 31.4 81.4 34.0 82.6

Stress Levels For Multi-Stage RLT Test Limestone-Wet of Opt

Stage Test 1 Test 2 Test 3 p(psi) q(psi) p(psi) q(psi) p(psi) q(psi)

I 4.3 3.9 9.4 8.8 15.9 17.9 II 6.1 9.4 12.3 17.4 21.4 34.3 III 7.8 14.4 14.9 25.1 26.8 50.4 IV 12.5 28.3 21.3 44.4 37.2 81.7 V 14.6 35.0 24.7 54.5 38.8 86.4 VI 15.7 38.0 27.3 62.5 39.7 89.4

Stress Levels For Multi-Stage RLT Test Limestone-Dry of Opt

Stage Test 1 Test 2 Test 3 p(psi) q(psi) p(psi) q(psi) p(psi) q(psi)

I 5.8 8.1 15.8 27.5 20.4 31.0 II 8.4 16.2 20.1 40.3 26.0 47.8 III 10.7 23.0 222.2 46.8 38.1 84.0 IV 21.6 55.2 26.3 59.3 40.1 89.8 V 22.8 58.7 28.3 65.4 42.4 96.9 VI 23.3 61.0 32.6 77.8 42.8 98.5

39

Table 3.3 Stress Sequence: Sandstone Stress Levels For Multi-Stage RLT Test Sandstone-Opt

Stage Test 1 Test 2 Test 3

p(psi) q(psi) p(psi) q(psi) p(psi) q(psi) I 3.2 3.7 12.5 18.0 15.9 17.6 II 6.1 8.9 15.5 27.0 21.4 33.9 III 7.7 14.1 17.9 34.0 24.7 43.8 IV 14.5 34.3 23.3 50.2 29.5 58.2 V 16.6 40.7 27.3 62.4 30.9 62.6 VI 20.2 51.3 28.3 65.4 31.8 65.2

Stress Levels For Multi-Stage RLT Test Sandstone-Wet of Opt

Stage Test 1 Test 2 Test 3 p(psi) q(psi) p(psi) q(psi) p(psi) q(psi)

I 4.9 5.8 8.4 5.8 15.4 16.3 II 5.7 8.1 9.2 8.1 17.5 22.6 III 7.2 12.7 11.9 16.3 20.3 30.8 IV 9.4 19.1 14.0 22.6 25.8 47.4 V 10.5 22.6 16.8 30.8 28.3 54.8 VI 11.1 24.4 22.3 47.4 31.8 65.4

Stress Levels For Multi-Stage RLT Test Sandstone-Dry of Opt

Stage Test 1 Test 2 Test 3 p(psi) q(psi) p(psi) q(psi) p(psi) q(psi)

I 5.8 8.1 12.5 18.0 20.3 30.8 II 7.3 12.7 15.5 27.0 23.6 40.7 III 8.5 16.3 17.9 34.0 25.9 47.4 IV 13.3 30.8 23.3 50.2 34.2 72.5 V 16.6 40.7 27.3 62.4 36.0 77.8 VI 18.7 46.9 28.3 65.4 37.8 83.1

40

schemes in table 3.2 and 3.3, which were selected to delimit the different behavioral

trends for each range, and material, as described earlier.

Table 3.4 Molding Moisture Regime for Mult-Stage Material Wet Optimum Dry Limestone 5.3 % 6.5 % 7.7 % Sandstone 5.9 % 7.1 % 7.9 %

퐺 푤 = 푆 푒 Equation 3.4

Where, 퐺 = 푆푝푒푐푖푓푖푐 퐺푟푎푣푖푡푦

푤 = 푚표푖푠푡푢푟푒 푐표푛푡푒푛푡

푆 = 푆푎푡푢푟푎푡푖표푛 푅푎푡푖표

푒 = 푣표푖푑 푟푎푡푖표

41

CHAPTER 4 ANALYSIS OF RESULTS

This chapter presents the results of the experimental testing program that was

conducted to evaluate physical properties and to characterize the behavior of the course

materials under static as well as cyclic loading.

4.1 Physical Properties Test Results

Figure 4.1 shows the gradation obtained from the sieve analysis and hydrometer

tests for the considered materials, while Table 4.1 present a summary of the physical

properties test conducted on those materials. It is noted that all materials had the same

maximum nominal aggregate size of 25 mm. Furthermore, they were classified as A-1-b

and GW/sand according to the American Association of State Highway and

Transportation (AASHTO) classification system, and the Unified Soil Classification

System (USCS), respectively. However, there were some differences between the

materials in the percent of fines passing sieve size 0.075 mm, such that the granite had

lowest percentage of about 5, while the crushed lime stone had the highest percentage of

13.5. The gradation of the three materials considered was further evaluated using the

power-law method suggested by Ruth et al. (2002) . The power-law shown in Equation

4.1 characterizes the slope and the intercept constants of the coarse and fine aggregate

portions of the aggregate gradations. The divider sieve between the coarse and fine

aggregate used in the power law analysis was chosen to be 4.75 mm (No.4) sieve. Table

4.1 presents the power law gradation parameters for all the aggregate structures in this

study. It is noted that the granite had the highest nCa coefficient, followed by the

sandstone, then the crushed limestone. This indicates that the granite had the coarsest

gradation followed by the sandstone. However, the nfa value of the all materials was

42

similar. It is noted that a higher nfa value indicates that the fine portion of an aggregate

gradation is finer.

P = a (d) and P = a (d) Equation 4.1

Where,

PCA and PFA = percent by weight passing a given sieve that has an opening of width d

aCA = intercept constant for the coarse aggregate

nCA = slope (exponent) constant for the coarse

d = sieve opening width, mm

aFA = intercept constant for the fine aggregate

nFA = slope (exponent) for the fine aggregates

Figure 4. 1 Particle Size Distribution of Tested Aggregates

Table 4.1 shows that the considered aggregate had absorption values ranging from

0.9 to 2.1 percent. Furthermore, the table shows that the considered aggregates had a low

percentage of loss in the Micro-Deval test; however the granite had the lowest value of

0102030405060708090

100

0.01 0.1 1 10 100

Particle size (mm)

Perc

ent F

iner

LimestoneSandstoneGranite

43

5%. Many studies suggested the low percentage of loss indicates the ability of the

material to resist degradation during construction and under traffic loading (Hossain et al.

2008) Therefore, all materials are considered to be durable and resist degradation.

Table 4.1 also shows the maximum dry unit weight and optimum moisture

content obtained in the Standard Proctor test. It is noted that there are some differences in

the values obtained from the Standard Proctor test between the three aggregate materials;

however, the current specification does not have any limitations on those values, but uses

them as reference to which materials in the field are to be compacted. Table 4.1 shows

that the degree of saturation for sandstone aggregate at the optimum conditions

determined in the Standard Proctor test was at least ten percent higher than those of the

other materials.

Table 4.1 Physical Properties Results Property Limestone Sandstone Granite Gs 2.708 2.642 2.671 Absorption,% 1.7 2.1 0.9 Micro-Deval, Loss% 13.0 11.5 5.5 Max dry in Standard Proctor (lb/ft3) 142.0 136.2 132.0 Optimum Moisture Content,% 6.5 7.1 6 Degree of saturation,% 80.7 88 76.3 AASHTO classification A-1-b A-1-b A-1-b USCS classification GW/sand GW/sand GW/sand Coarse aggregate angularity, (%) 100 100 100

Power Law Analysis of Gradation aCa 36.0 27.1 15.313 nCa 0.28 0.37 0.55 aFa 29.9 28.0 14.792 nFa 0.32 0.36 0.38

Shear Strength Properties Peak friction angle 52.2 51.2 57.7 Cohesion- ultimate shear strength (psi) 3.65 3 0 Residual strength friction angle 47.5 46.5 49 Cohesion- residual shear strength (psi) 2 2 0

44

4.2 Static Triaxial Tests Results

Drained triaxial compression tests were on granite, limestone and sandstone

samples. The achieved dry unit weight and moisture content of the tested samples were

close to those specified in the field for construction of UGM base course layers in

Louisiana, which specifies that the materials should be mixed at the optimum moisture

content and compacted to 95% of the maximum dry unit weight as determined in

standard Proctor test. Figure 4.1 through Figure 4.3 present the average stress-strain

curves obtained from the drained triaxial compression tests conducted on three samples

for each material. The figures show that at the tested confining pressures and dry unit

weight the samples behaves as a loose granular material, such that they exhibit an

increase in shear strength with increasing strain, which is referred to as strain hardening,

and eventually reached peaked strain level ranging from 2- 4%.

Figure 4. 2 Stress-Strain Curves for Granite Static Compression Test

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12

Axial Strain %

Axial Stress psi

10 psi

7 psi

2 psi

45

Figure 4. 3 Stress-Strain Curves for Limestone Static Compression Test

Figure 4. 4 Stress-Strain Curves for Sandstone Static Compression Test

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12

Axial Strain %

Axial Stress psi

10 psi

7 psi

2 psi

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7 8 9

Axial Strain %

Axial Stress psi

10 psi

7 psi

2 psi

46

The results of the triaxial compression tests conducted on the different considered

materials were used to obtain the ultimate and residual (critical state) shear strength at

each of the three confining stresses used in this study. To determine the friction angle, the

slope of the line (M) that best fits each set of data in q-p space was found for each

material. The ultimate and residual strength in p-q space are represented below in Figures

4.5 and 4.6. Equations 4.1 and 4.2 were then employed to determine the corresponding

friction angle. The computed friction angles are shown Table 1. It is noted that granite

had the highest peak and residual shear strength friction angle followed by the crushed

limestone. Furthermore, the granite material did not have any cohesion, which may be

explained by the low percentage of fines that this material has.

Figure 4. 5 Ultimate Shear Strength in p-q space

4.3 Repeated Load Tri-axial Testing

The average value of the resilient modulus for the last ten cycles of each stress sequence

was first calculated from each of the resilient modulus test results; a regression analysis

Ultimate Shear Strength q-p space

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

p, psi

q, psi

Granite

Limestone

Sandstone

M =q/p

47

Figure 4. 6 Residual Shear Strength in p-q space

M = ( ) ( )

Equation 4.1

M = ( ) ( )

Equation 4.2

Where,

M = is slope of line connecting peak shear strength

M = is slope of line connecting residual or critical state shear strength φ = is peak friction angle φ s = is residual strength friction angle

Residual Shear Strength q-p space

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

0.00 5.00 10.00 15.00 20.00 25.00 30.00

p, psi

q,psi

Granite

Limestone

Sandstone

M =q/p

48

was then carried out to fit the data of each test to the generalized constitutive model given

in Equation 2.13, and determine the k1-3 coefficients for the different tested samples.

Figures 3a–c presents the k1-3 coefficients for the different granular material considered,

respectively. It is noted that for all tested soil samples, the k1coefficient had positive

values, which is expected, since the k1coefficient is proportional to the stiffness of a

material. Furthermore, the limestone had the highest k1 coefficient values followed by the

granite material. The relationship for Mr vs. Bulk stress should follow a linear

relationship with bulk stress being represented as the sum of the principal stresses.

Results from the fitted generalized model from triplicate samples for each material were

imputes to compute expected values and coefficient of variances. The graph and variance

in figure 4.7 show good agreement among tested samples for the individual materials

Figure 4.8b shows that granite had a higher k2 coefficients compared to the

crushed limestone and sandstone materials which had similar values. The k2 coefficient

describes the stiffening or hardening (higher modulus) of the material with increase in the

bulk stress. Therefore, the result in Figure 4.8b indicates that the effect of the confining

stress is more pronounced for granite compared to other materials considered in this

study. This result may be explained by the coarser gradation and the lower percentage of

fine materials that the considered granite had. Figure 4.8c shows that the average k3

coefficients had negative value for all tested materials. This expected since the k3

coefficients describes the softening of the material (lower modulus) with the increase in

the shear stress. It is noted that the sandstone material had very low k3 values compared

to the other materials tested in this study. This suggests that the sandstone material

exhibited less softening with the increase in the applied shear stress.

49

Figure 4. 7 Resilient Modulus vs. Bulk Stress

Figure 4. 8 Resilient Modulus Coefficients of Tested Materials: a) k1 b) k2 c) k3

0

10000

20000

30000

40000

50000

60000

70000

80000

0.0 20.0 40.0 60.0 80.0 100.0 120.0Bulk Stess , psi

Mr,

psi

SandStoneKenGranite

%CV k1 k2 k3 Sandstone 15.2 4.6 15.2 Limestone 2.8 2.3 11.5 Granite 9.4 11.7 8.7

a.

0

400

800

1200

1600

2000

Limestone Sandstone Granite

k1 (p

si)

50

Figure continued 4.3.1 Single-Stage RLT Test Results-Resilient Strain

Figure 4.9a presents the average vertical resilient strain curves obtained from the

results of the single stage RLT test that were conducted on the three types of base course

materials investigated in this study. The resilient strain had a similar trend in all

materials, such that it initially increased, then decreased as the number of load cycles

increased until reaching an asymptote at about 6,000 load cycles, and hence reaching a

steady resilient response. The reason for this behavior is that during the primary post

compaction stage, the sample accumulates more deviatoric strain in the horizontal

b.

00.10.20.30.40.50.60.70.80.9

Limestone Sandstone Granite

k2 (p

si)

c.-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

k3 (p

si)

Limestone Sandstone Granite

51

direction (perpendicular to the direction on which the cyclic load is applied), causing the

Poisson’s ratio to decrease slightly; this results in an increase in the sample stiffness and

hence a decrease in the resilient strain. It should be noted that the number of cycles

needed for the sample to reach a steady resilient response increases as the imposed

deviatoric stress is increased.

Figure 4.9a shows that the sandstone material had a much higher resilient strain

than the other two materials, and hence a much smaller resilient modulus. Furthermore,

the crushed limestone had lower resilient strain than the granite. These results are also

illustrated in Figure 4.9b, which presents the resilient modulus value measured after

10,000 cycles in the single-stage RLT tests and those predicted using the universal

resilient modulus model (Equation 2.13) based on k1-3 coefficient obtained from the Mr

RLT test. This figure shows that the predicted values were very similar to those

measured, indicating the reliability of this model prediction.

Figure 4. 9 Results of Single-Stage RLT Test a) Resilient Strain Variation of Load Cycles

b) Measured and Predicted Resilient Modulus Values

0

0.0003

0.0006

0.0009

0.0012

0.0015

0.0018

0.0021

0 2000 4000 6000 8000 10000

Res

ilien

t Str

ain

Load Cyles

Crushed limestone

Sandstone

Granite

a.

52

Figured continued 4.3.2 Single-Stage RLT Test Result-Permanent Strain

Figures 4.10 presents the average vertical permanent strain curves obtained from

the results of the single-stage RLT test for the three materials considered in this study.

Averages were calculated from triplicate samples; coefficients of variation are equal to or

less than 15%. For the three materials, the primary and secondary stages were only

experienced during this type of RLT test. The sandstone experienced by far the largest

permanent strain. Furthermore, the crushed limestone had accumulated a greater

permanent strain than the granite. It is noted that the three materials had similar behavior

during the initial load cycles, hence, during the primary post-compaction stage; however,

the differences between the materials in the permanent strain behavior were detected

during the secondary stage. This indicates that differences in permanent strain for the

considered materials did not mainly result from discrepancies in the materials’ initial

0

50

100

150

200

250

300M

r (M

Pa)

Limestone Sandstone Granite

Measured Predicted

b.

53

voids and density conditions, but rather from the properties that affect aggregate the

rotation and sliding mechanisms of the aggregate particle which results in the permanent

deformation in the secondary stage. Those properties include particle surface friction and

shape.

Since the single-stage RLT test included applying 10,000 cycles, it is of interest to

examine the permanent strain evolution at a higher number of load cycles. For this

purpose the single relation of the accumulative vertical permanent strain with the vertical

permanent strain rate was examined, Figure 4.11. In general, all materials had a high

permanent strain rate during the first load cycles, yet the permanent strain rate decreased

with each load cycle. However, the permanent strain rate of granite had decreased more

rapidly than the crushed limestone materials and reached smaller values at the end of the

RLT test. The permanent strain rate of sandstone also decreased but at much slower rate

than the other materials. According to the strain rate criterion proposed by Werkmeister

(2005) previously discussed in this paper, the response of granite is within Range A,

while the response of crushed limestone and sandstone is within Range B. However, it is

noted that the sandstone behavior is at the upper end of Range B close to Range C. This

suggests that if such stresses were experienced in the pavement structure, then the granite

material would be the only material to have a stable behavior, thus, it will have the best

performance among the other two materials. Furthermore, the sandstone is expected to

collapse causing the development of excessive rutting of the pavement structure.

4.4 Multi-Stage Test Results

Multi-stage RLT tests were conducted on the three unbound granular materials at

their optimum compaction condition to characterize their permanent and resilient

54

Figure 4. 10 Vertical Permanent Strain Variations with Number of Cycles

Figure 4. 11 Vertical Permanent Strain Rate vs. Vertical Permanent Strain

0

1

2

3

4

5

6

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Load cycle s

Perm

anen

t Str

ain

(%)

LimestoneSansdstoneGranite

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+000 1 2 3 4 5 6

Pe rmane nt Strain

Perm

anen

t Str

ain

Rat

e

LimestoneSandstoneGranite

A

B

C

55

deformation behavior at different stress levels. Figure 4.12 shows the results of the total

permanent strain during each loading stage for all tested materials. It is clear that the

permanent strain is stress dependent, such that it increased as the deviatoric stress

increased. However, this increase differed from one material to another. The sandstone

had accumulated the highest permanent strain at all stages. Furthermore, the highest

difference in the total accumulated permanent strain was observed at the fourth and fifth

stages, where the tertiary stage was reached.

Figure 4. 12 Multi-Stage Cumulative Permanent Strain

Figures 4.13b-d show the permanent vertical strain rate versus the permanent

vertical cumulative strain obtained from the results of the multi-stage RLT tests. It is

noted that the three different responses (Range A, Range B, Range C) were observed at

the different stages of cyclic loading. However, the stages at which those responses were

observed were different for each of the three materials considered in this study. The

Range A response was observed during stages I-III for sandstone and during stages I-II

for other two materials. It is noted that in Range A behavior plots as a convex-downwards

0

1

2

3

4

5

6

7

8

9

0 10000 20000 30000 40000 50000 60000 70000

Load Cycles

Perm

anen

t Str

ain

LimestoneSandstoneGranite

56

line because the permanent strain rate progressively decreases, effectively halting any

further accumulation of strain and leading to an asymptotic final (vertical) permanent

strain value. For this range, Figures 4.13b-d show that the level of accumulated strain

depends on the load level (deviator stress). Detailed inspection of the individual test

results shows that the number of cycles required, before plastic strain ceases, increases

with an increase in the load level.

Figures 4.13b-d show that the Range B response occurred during stage III for the

sandstone and during stage IV for the crushed limestone and granite materials. It is noted

that the behavior of the materials during the primary stage in Range B, the plastic creep

shakedown range, is similar to that in Range A. However, in the secondary stage the

behavior is different, such that the permanent strain accumulation decreases at relatively

smaller rate. The deformation in the secondary stage is due to the relative inter-particle

movement and the deformation of the particles themselves (Rodriguez et al. 1988). The

deformation at the inter-particle contact may be quite large, and consists initially of

distortion and eventually local fracture and crumbling, in addition to particle re-

orientation. The re-orientation mechanism is characterized by rotation and sliding of the

particles. The resistance to particle sliding and rotation depends on the inter-particle

friction of the material. One main difference between secondary stage in Range A and B,

is that in Range B the particle rearrangement, inter-particle slip, and the continued

frictional energy loss is associated with ongoing damage. This damage can result in

reaching constant level of permanent strain rate, where permanent strain increases

linearly, leading to material incremental collapse, and thus to reach the tertiary stage. The

number of cycles to reach incremental collapse depends on the stress level; the higher the

57

applied stress are, the fewer the number of load cycles required to reach to the tertiary

stage. The results in Figures 4.13b-d show that at the third stage, the sandstone material

reached Range B behavior, suggesting that lower stress than the other materials was

needed to overcome particle resistance to sliding and rotation for this material and cause

higher damage.

Figures 4.13b-d show that the Range C response was initially observed during

Stage IV, V and VI for the sandstone, crushed limestone, and granite, respectively

Furthermore, it is noted that in Range C, the incremental collapse shakedown range, the

material exhibits continuing incremental permanent strain with each additional stress

cycle. Thus, the response is always plastic, and each stress application results in a

progressive increment in the magnitude of permanent strain. The initial behavior

observed in other ranges (A, B) is probably the same as that shown in Range C, but

compressed into a fewer number of stress applications as a consequence of the much

higher cyclic stress level applied. In addition the tertiary stage occurs at a much lower

number of load cycles. This suggests that the Range C stresses are high enough to cause

significant energy loss per cycle. Hence, a great degree of damage occurs almost from the

beginning of cyclic load application.

The non-stable material behavior and large permanent strain rates at high stress

levels in Range B and C result from the relatively large-scale particle re-orientation. One

of the causes of the large-scale particle re-orientation is the grain abrasion and particle

crushing. This is governed by the magnitude of applied stresses, and the mineralogy and

strength of the individual particles themselves. Recalling the result of Micro-Deval test,

granite had a much lower percentage loss than the other considered materials, which

58

Figure 4.13 Multi-Stage Test Results Permanent Strain Rate for a) Limestone b) Sandstone c) Granite

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+000 1 2 3 4 5 6 7

Permenant Strain

Perm

enan

t St

rain

Rat

eStage IStage IIStage IIIStage IVStage VStage VI

B

C

A

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+000 1 2 3 4 5 6 7 8 9

Permenant Strain

Perm

enan

t Str

ain

Rat

e

Stage IStage IIStage IIIStage IVStage V

B

C

A

a.

b.

59

Figure continued

suggests that it has the better ability to resist attrition under severe loading. This may be

one of the reasons for the lower permanent strain accumulation that granite exhibited

during the unstable behavior at higher stress level compared to the other two materials.

The shear strength properties obtained in the SCT test, which showed higher friction

angle for the granite, provides another reason to explain this phenomenon.

Figure 4.14 shows the resilient strain at different stages for each material. As for

the permanent strain, the resilient strain was stress dependent. However, the limestone

and granite materials had the lowest and highest resilient strain at all stages, respectively.

The resilient strain behavior was different than that in the permanent strain. The granite

and limestone had similar trends in the first four stages, such that the resilient strain

increased initially then decreased until reaching a steady constant value. However, the

initial increase in the resilient strain was magnified with the increase in the stress level.

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+000 1 2 3 4 5

Permanent Strain

Perm

anen

t St

rain

Rat

eStage IStage IIStage IIIStage IVStage VStage VI

B

C

A

c.

60

Furthermore, this increase was greater for granite material than for the crushed limestone

material. Some differences were observed in the resilient strain behavior between the

granite and the crushed limestone in stage VI, such that the crushed limestone had the

same behavior observed in the previous stages, while for the granite, the resilient strain

initially increased at high rate. This increase continued but at lower rate; then the resilient

strain decreased at very low rate till the end of the stage. In the sixth stage a minor initial

increase in the resilient strain was detected for the granite, while the limestone continued

with the same resilient strain magnitude observed at the end of fifth stage. The sandstone

resilient strain behavior was similar in the first four stages, such that it initially increased

at high rate, then increased but at very low rate until the end of each stage. While in fifth

stage, the resilient strain increased linearly until the samples collapsed.

The previous results are clearly demonstrating that the resilient strain behavior is

distinct from that of the permanent strain. Furthermore, the relation between the resilient

and permanent strain is not constant but varies with the stress level and base course

material under consideration. Therefore the resilient modulus, which is computed based

on the resilient strain, cannot be used to predict or evaluate the permanent strain

resistance. Hence, it cannot solely be used to comprehensively evaluate the performance

of base course materials under traffic loading.

The results of RLT tests is also indicating that the current specification for base

course materials is not capable of predicting their response under cyclic loading, and

hence their field performance. For example, the gradation of the crushed limestone does

not comply with the Louisiana specification for base course materials of having

maximum 12% passing sieve size 0.075 mm. In addition the granite material has about

61

5% of its particles finer than 0.075 mm which is the minimum value required by the same

specification. However, both of those materials showed good performance under low and

high levels of cyclic stress. It is clear that the physical properties currently used to

evaluate and select base course materials do not represent the performance of these

materials. Therefore, there is a need for changing the current specification such that it

includes properties that affect the response of the materials under cyclic loads. The

selected properties may have to be at the micro-scale or even nano-scale. However, with

the lack of knowledge of those properties, the material permanent and resilient strain

behavior under loading and environmental conditions similar to those encountered in the

field is recommended to be examined during the selection and evaluation procedure of

base course materials using Mr, single stage, and multi-stage RLT tests. These tests can

also facilitate the use of non-conventional base course materials such as recycled or

marginal materials.

4.5 Shakedown Limits

Following the initial characterization of the three UGMs, additional multi-stage

RLT testing was conducted on crushed limestone and sandstone samples compacted at

optimum moisture content to determine shakedown limits. To determine how shakedown

limits are affected by moisture content, UGMs samples were tested at wet and dry of

optimum moisture content while maintaining maximum dry density as determined by

standard proctor. Long term performance of UGMs is dependent upon change in

moisture content. During construction materials are compacted at optimum moisture

content and maximum dry density, yet problems arise in performance and are attributed

to fluctuations in moisture content from seasonal variations. The three shakedown ranges

62

Figure 4.14 Resilient Strain Multi-Stage Test

were derived based simply on the fact that is possible to classify all permanent strain with

number of load cycles in one of three types. Long term permanent strain rate is either

decreasing with number of load cycles-Range A; remaining constant with increasing load

cycles-Range B; or increasing with increasing load cycles with likely premature failure-

Range C. As proposed by Werkmeister et al. (2005), cumulative strain versus permanent

strain rate plots were used to aid in determining the shakedown ranges.

After determining the shakedown ranges for each testing stress from the results of

multi-stage RLT tests, the boundary between these ranges is interpolated assuming a

linear function and plotted in p-q space. The stress invariants p and q provide an efficient

means of characterizing a stress state of both axial and radial stresses. The boundary

between shakedown range A and B was taken as the best fit straight line through the

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0 10000 20000 30000 40000 50000 60000 70000

Load Cycles

Res

ilien

t Str

ain

LimestoneSandstoneGranite

63

highest vertical testing stress possible for shakedown range A for the three tests at

maximum mean stresses. For B/C boundary, a best fit line was fitted to the lowest

vertical stresses where shakedown range C occurred. Figures 4.15 and 4.16 show the

shakedown range boundaries for crushed limestone and sandstone compacted at optimum

moisture content plotted along with the static failure line in p-q space.

Not surprisingly for Limestone, the boundary for B/C region is close in proximity

to the static failure line. The plastic limit for sandstone was below the static shear

strength line. The failure mechanism is different for cyclic loading, suggesting failure of

the material cannot be predicted by static shear strength.

To quantify the effect of moisture on shakedown, sandstone and limestone were

tested at wet and dry of optimum moisture content. The proceeding figures 4-17 through

4-20 show the effect of the change in moisture regime on shakedown limits for Sandstone

and Limestone materials.

The results for the limits are tabulated below at each corresponding degree of saturation

in table 4.2, where m and d are the corresponding slope and intercept in p-q space.

Noticeably, the slope of the elastic and plastic limits are relatively stable with respect to

degree of saturation for both limestone and sandstone UGM’s; m increase. digressively

for both the elastic and plastic limits, but at higher stresses (plastic limits) change in m is

smaller than for smaller stresses (elastic limit) for both materials. Refer to figure 4.21

The results clearly show an increase in intercept for a decrease in degree of

saturation for both materials and limits, Figure 4.22. By lowering the degree of

saturation, the increase in d is most likely to be a direct result of an increase in suction

from decreased moisture in the sample.

64

Figure 4. 15 Shakedown Limits for Limestone at Optimum Moisture Content

Figure 4. 16 Shakedown Limits for Sandstone at Optimum Moisture Content

0

15

30

45

60

75

90

105

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00p (psi)

q (psi)

Ultimate Shear StrengthPlastic Shakedown LimitElastic shakedown Limit

Range A

Range C

Range B

0

15

30

45

60

75

90

0 5 10 15 20 25 30 35p (psi)

Ultimate Shear StrengthElastic Shakedown LimitPlastic Shakedown Limit

Range A

Range BRange C

65

Figure 4. 17 Shakedown Limits for Sandstone at Dty of Optimum Moisture Content

Figure 4. 18 Shakedown Limits for Sandstone at Wet of Optimum Moisture Content

0

15

30

45

60

75

90

0 5 10 15 20 25 30 35

q (psi)

p (psi)

Ultimate Shear StrengthPlastic Shakedown LimitElastic Shakedown Limit

Range C Range B

Range A

0

15

30

45

60

75

90

0 5 10 15 20 25 30 35

q (psi)

p (psi)

Ultimate Shear StrengthPlastic Shakedown LimitElastic Shakedown Limit

Range C

Range B

Range A

66

Figure 4. 19 Shakedown Limits for Limestone at Dry of Optimum Moisture Content

Figure 4. 20 Shakedown Limits for Limestone at Wet of Optimum Moistures Content

0

15

30

45

60

75

90

105

0 5 10 15 20 25 30 35 40

q (psi)

p (psi)

Ultimate Shear StrengthElastic Shakedown LimitPlastic Shakedown Limit

Range C

Range A

Range B

0

15

30

45

60

75

90

105

0 5 10 15 20 25 30 35 40

q (psi)

p (psi)

Ultimate Shear StrengthElastic shakedown LimitPlastic Shakedown Limit

Range C

Range B

Range A

67

Figure 4. 21 Effect of Saturation on m a) Elastic Limit b) Plastic Limit

0

0.5

1

1.5

2

2.5

m

Limestone Sandstone

WetOptDry

0

0.5

1

1.5

2

2.5

m

Limestone Sandstone

WetOptDry

a

b

68

Figure 4. 22 Effect of Saturation on d a) Elastic Limit b) Plastic Limit

0

0.5

1

1.5

2

2.5

3

3.5

4

d, psi

Limestone Sandstone

WetOptDry

0

1

2

3

4

5

6

7

8

d, psi

Limestone Sandstone

WetOptDry

b

a

69

Figures 4.23 and 4.24 quantify the linear association for change in d with change in

degree of saturation represented by the slope of the line. Thus overall, the drier the

material will allow shakedown behavior beyond the static failure line at optimum due

Figure 4. 23 Intercept vs. Degree of Saturation for Limestone

Figure 4. 24 Intercept vs. Degree of Saturation for Sandstone

y = -0.21Sr + 21.438R2 = 0.993

y = -0.11Sr + 10.907R2 = 0.997

0

1

2

3

4

5

6

7

8

60 65 70 75 80 85 90 95 100Sr %

d, psi

Plastic Limit

Elastic Limit

y = -0.1535x + 15.623, R2 = 0.8757

y = -0.1003x + 10.307R2 = 0.9272

0

1

2

3

4

5

60 65 70 75 80 85 90 95 100

d, psi

Sr %

Plastic LimitElastic Limit

70

to the increase in d from increased suction. Limestone displayed and higher increase in d

with respect to change in degree of saturation than sandstone, 21% for Limestone vs.

15% for Sandstone. This can be partly explained by the limestone’s finer gradation, for a

finer gradation will allow greater suction due to the meniscus water being retained in the

many voids created by fines. Moreover, limestone was a better performer in both resilient

and permanent deformation properties than sandstone, which was characterized as less

stiff and less resistant to permanent deformation than both limestone and granite.

Table 4.2 Summary Limits Material Elastic Limits Plastic Limits Limestone %Sr ,%w m d m d 95, 7.7 1.2613 0.3604 1.92 1.0168 80, 6.5 1.9443 2.1573 2.2646 3.8124 65, 5.3 2.1285 3.6762 2.2597 7.5133 Elastic Limits Plastic Limits Sandstone %Sr ,%w m d m d 95, 7.9 1.3667 0.537 1.8201 0.5371 88, 7.1 1.600 1.839 1.9806 2.8475 73, 5.9 1.704 2.8727 1.9838 4.1818

71

CHAPTER 5 CONCLUSION AND RECOMMENDATIONS

5.1 Conclusions

This paper documented the results of a laboratory testing program that was conducted

to characterize the behavior of unbound granular base materials under different loading

conditions, and examine the effect of different physical properties on this behavior. Three

different types of granular base materials were investigated in this study, namely

limestone, sandstone, and granite. Physical properties and static and repeated load triaxial

tests were performed on the considered materials. Three different types of RLT tests were

used in this study including resilient modulus, single-stage, and multi-stage RLT tests.

The results of the single-stage and multi-stage were analyzed within the framework of the

shakedown theory. Based on the results of this paper, the following conclusions can be

drawn:

The sandstone experienced by far the largest permanent and resilient strain in both

single-stage and multi-stage RLT test. In addition, the granite had the lowest

permanent strain but experienced higher resilient strain than the limestone.

The three materials investigated in this study had similar behavior during the

primary post-compaction stage; however, the differences between the materials in

the permanent strain behavior were detected during the secondary stages.

The limestone and granite had similar permanent strain behavior at low and

intermediate stress levels; however, limestone experienced the unstable Range C

72

shakedown behavior at higher stress levels than granite did. This was attributed to

the granite’s lower percentage loss in the Micro-Deval test and its higher friction

angle.

The resilient and permanent strains are stress dependent. However, the resilient

strain behavior is distinct from that of the permanent strain.

The resilient modulus cannot be used to evaluate the permanent strain resistance

of a base course material. Hence, it cannot solely be used to characterize the

response of base course materials under traffic loading.

There is a need for changing the current specification such that it includes

properties that affect the response of the materials under cyclic loads. The

selected properties may have to be at the micro-scale or even nano-scale.

From the results of shakedown limits, it is evident that degree of saturation affects

the shakedown behavior of UGM’s. The degree of saturation is inversely related

to the intercept of the shakedown limits allowing shakedown beyond the static

failure line.

5.2 Recommendations

The multi-stage RLT test provides a promising tool to characterize the structural response

and stability of different types of base course materials at loading condition similar to

those encountered in a pavement structure. To fully understand the full spectrum of

shakedown behavior, the UGM’s, given the elastic and plastic ranges in table 4.2, should

73

be tested at 1 million cycles to confirm stable and unstable behavior. Once behavior is

confirmed, ranges can be used in finite element packages to calculate strain in a given

base course layer for moisture regime and stress conditions.

74

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82

APPENDIX A: RESILIENT MODULUS

Sandstone

Level Mr1 (psi)

Mr2 (psi)

Mr3 (psi)

Mr Avg (psi) Stdev Cv %

1 10266.3 9579.2 8892.0 9579.2 687.1 13.9 2 11735.2 10900.6 10155.0 10930.3 790.5 13.8 3 12123.1 11500.0 12931.6 12184.9 717.7 16.9 4 13703.0 12312.9 14936.5 13650.8 1312.5 10.4 5 15279.4 14271.4 16561.0 15370.6 1147.5 13.3 6 18575.1 16284.8 16420.3 17093.4 1284.9 13.3 7 21086.1 18771.8 22783.4 20880.4 2013.7 10.3 8 23577.7 22241.3 26225.1 24014.7 2027.5 11.8 9 22446.8 23046.9 33684.4 26392.7 6321.9 4.1

10 23627.08 24995.2 30855.3 26492.5 3839.7 6.8 11 27958.5 25123.1 27119.7 26733.7 1456.5 18.3 12 28434.5 31320.8 30666.8 30140.7 1513.3 19.9 13 30128.4 31584.7 33723.4 31812.2 1808.2 17.5 14 35419.0 34378.3 26917.3 32238.2 4637.3 6.9 15 38121.2 35212.7 40035.1 37789.7 2428.2 15.5

Limestone

Level

Mr1 (psi)

Mr2 (psi)

Mr3 (psi)

Mr Avg (psi) Stdev Cv %

1 26036.9 21210.5 23623.7 23623.7 2413.2 9.7 2 19885.0 23118.3 21501.7 21501.7 1616.6 13.3 3 20274.3 24900.0 22587.1 22587.1 2312.8 9.7 4 28828.9 25685.2 30580.9 28365.0 2480.6 11.1 5 29710.8 27378.2 32793.8 29960.9 2716.4 11.0 6 31354.9 30068.7 33376.5 31600.0 1667.4 18.9 7 42659.8 35012.6 46700.3 41457.6 5935.8 6.9 8 45088.5 41205.8 47753.4 44682.6 3292.6 13.5 9 47435.5 43017.8 50952.4 47135.2 3975.8 11.8

10 51646.3 47313.8 54842.3 51267.5 3778.5 13.5 11 51588.3 48876.5 55160.8 51875.2 3151.9 16.4 12 57084.3 53221.5 62075.3 57460.4 4438.8 12.9 13 60728.3 58303.1 66351.1 61794.2 4128.5 14.9 14 63548.7 62025.2 68913.7 64829.2 3618.3 17.9 15 70292.3 68089.2 75430.7 71270.7 3767.3 18.9

83

Granite

Level Mr1 (psi)

Mr2 (psi)

Mr3 (psi)

Mr Avg (psi) Stdev Cv %

1 18617.1 17179.2 19453.7 18416.7 1150.4 16.0 2 19674.4 18023.1 20724.4 19474.0 1361.7 14.3 3 23848.2 21023.9 26071.2 23647.7 2529.6 9.3 4 24956.0 22018.7 27292.0 24755.6 2642.3 9.3 5 26828.5 24030.1 29025.5 26628.0 2503.7 10.6 6 37285.4 33132.5 40836.9 37084.9 3856.1 9.6 7 37576.5 34102.8 40448.8 37376.0 3177.7 11.7 8 40106.1 37045.2 42565.6 39905.6 2765.6 14.4 9 45323.3 41156.5 48888.8 45122.9 3870.0 11.6

10 47220.1 43028.5 50810.4 47019.7 3894.8 12.0 11 52850.5 48301.5 56798.2 52650.1 4251.8 12.3 12 59809.9 52089.6 66928.8 59609.4 7421.6 8.0 13 63053.7 58109.8 67396.2 62853.2 4646.4 13.5 14 62780.3 58523.5 66435.8 62579.9 3959.9 15.8 15 63401.6 59444.2 66757.7 63201.2 3660.8 17.2

84

Level Cf(psi) Dev(psi) Mr(psi) CV% Bulk Stress N-Bulk Stress OCT stress Pre Mr SSR SST Error1 3.1 5.7 10266.4 5.8 15.0 1.0 1.2 10037.5 120451656.5 1.15E+08 0.000502 3.1 8.8 11735.3 8.7 18.1 1.2 1.3 11337.7 93602745.1 8.61E+07 0.001153 5.0 4.8 11937.8 4.8 19.8 1.3 1.2 11947.2 82180544.0 8.24E+07 0.000004 5.0 9.9 13703.0 9.7 24.9 1.7 1.3 13863.8 51104204.0 5.34E+07 0.000145 5.0 14.9 15279.4 14.5 29.9 2.0 1.5 15633.7 28931427.4 3.29E+07 0.000546 10.0 9.9 18575.1 9.8 39.8 2.7 1.3 18644.2 5608859.9 5.94E+06 0.000017 10.0 20.1 21086.1 19.8 50.0 3.4 1.6 21667.6 429088.4 5.42E+03 0.000768 10.0 29.9 23577.7 29.9 59.8 4.1 2.0 24395.8 11446801.8 6.58E+06 0.001209 15.0 9.8 22446.9 9.9 54.8 3.7 1.3 22794.4 3175257.8 2.06E+06 0.00024

10 15.0 14.7 23627.1 14.8 59.8 4.1 1.5 24172.9 9988272.4 6.84E+06 0.0005311 15.0 30.1 27958.5 30.1 75.1 5.1 2.0 28155.4 51021152.8 4.82E+07 0.0000512 19.8 14.9 28434.5 14.9 74.4 5.1 1.5 27721.0 45003500.9 5.51E+07 0.0006313 20.0 20.0 30128.5 20.0 80.1 5.4 1.6 29134.1 65959350.3 8.31E+07 0.0010914 20.0 40.2 35419.0 40.2 100.3 6.8 2.3 33944.0 167223265.6 2.08E+08 0.00173

a.

The table is an example of the utilizing solver to solve for regression coefficients.

Constitutive Generalized Model fit using Excel Solver

k1(psi) k2(psi) k3 R2 671.6144 0.628759 0.033566 0.937

85

APPENDIX B: MOISTURE DENSITY CURVES

Standard Proctor a)Limestone b) Sandstone c)Granite

MOISTURE - DENSITY PLOT

125.0

130.0

135.0

140.0

145.0

0.0% 2.0% 4.0% 6.0% 8.0% 10.0%

MOISTURE CONTENT, %

DR

Y D

EN

SIT

Y

pcf

MOISTURE - DENSITY PLOT

130.0

132.0

134.0

136.0

138.0

0.0% 5.0% 10.0%MOISTURE CONTENT, %

DR

Y D

EN

SITY

pcf

MOISTURE - DENSITY PLOT

125.0126.0127.0128.0129.0130.0131.0132.0133.0

0.0% 2.0% 4.0% 6.0% 8.0%

MOISTURE CONTENT, %

DR

Y D

EN

SIT

Ypc

fa

b

c

86

APPENDIX C: PERMANENT DEFORMATION CURVES

Multi-Stage Limestone-w% = 5.3 a) 3.0 psi cp b) 6.5 psi cp c)10 psi cp

Permenant Strain Curve

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

0 10000 20000 30000 40000 50000 60000

Cycles

Perm

anen

t Str

ain

Permenant Strain Curve

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

Cycles

Perm

anen

t Str

ain

Permenant Strain Curve

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

0 10000 20000 30000 40000 50000 60000 70000

Cycles

Perm

anen

t Str

ain

a.

b.

c.

87

Multi-Stage Limestone-w% = 6.5 a) 3.0 psi cp b) 6.5 psi cp c)10 psi cp

Permenant Strain Curve

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

0 10000 20000 30000 40000 50000 60000

Cycles

Perm

anen

t Str

ain

Permenant Strain Curve

0.0%1.0%2.0%3.0%4.0%5.0%6.0%7.0%8.0%9.0%

0 10000 20000 30000 40000 50000

Cycles

Perm

anen

t Str

ain

Permenant Strain Curve

0.0%0.5%1.0%1.5%2.0%2.5%3.0%3.5%4.0%4.5%5.0%

0 10000 20000 30000 40000 50000 60000

Cycles

Perm

anen

t Str

ain

a.

c.

b.

88

Multi-Stage Limestone-w% = 7.9 a) 3.0 psi cp b) 6.5 psi cp c)10 psi cp

Permanent Strain Curve

0.0%1.0%2.0%3.0%4.0%5.0%6.0%7.0%8.0%9.0%

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

Cycles

Perm

anen

t Str

ain

Permanent Strain Curve

00.010.020.030.040.050.060.07

0 10000 20000 30000 40000 50000 60000 70000

Cycles

Perm

anet

n St

rain

Permanent Strain Curve

0.0%0.5%1.0%1.5%2.0%2.5%3.0%3.5%4.0%

0 10000 20000 30000 40000 50000 60000 70000

Cycle

Perm

anen

t Str

ain

a.

b.

c.

89

Multi-Stage Sandstone-w% = 5.9 a) 3.0 psi cp b) 6.5 psi cp c)10 psi cp

Permenant Strain Curve

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

0 10000 20000 30000 40000 50000 60000 70000

Cycles

Perm

anen

t Def

orm

atio

n

Permenant Strain Curve

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

0 10000 20000 30000 40000 50000 60000

Cycles

Perm

anen

t Str

ain

Permanent Strain Curve

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

0 10000 20000 30000 40000 50000 60000

Cycles

Perm

anen

t Str

ain

a.

b.

c.

90

Multi-Stage Sandstone-w% = 7.1 a) 3.0 psi cp b) 6.5 psi cp c)10 psi cp

Permenant Strain Curve

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

0 10000 20000 30000 40000

Cycles

Perm

anen

t Str

ain

Permenant Strain Curve

0.0%1.0%2.0%3.0%4.0%5.0%6.0%7.0%8.0%9.0%

0 10000 20000 30000 40000 50000

Cycles

Perm

anen

t Str

ain

Permenant Strain Curve

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

0 10000 20000 30000 40000 50000 60000

Cycles

Perm

anen

t Str

ain

a.

b.

c.

91

Multi-Stage Sandstone-w% = 7.9 a) 3.0 psi cp b) 6.5 psi cp c)10 psi cp

Permenant Strain Curve

0.0%0.2%0.4%0.6%0.8%1.0%1.2%1.4%1.6%1.8%

0 10000 20000 30000 40000 50000 60000 70000

Cycles

Perm

anen

t Str

ain

Permenant Strain Curve

0.0%0.5%1.0%1.5%2.0%2.5%3.0%3.5%4.0%

0 10000 20000 30000 40000 50000 60000 70000

Cycles

Perm

anen

t Str

ain

Permanent Strain Curve

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

0 10000 20000 30000 40000 50000 60000 70000

Cycles

Perm

anen

t Str

ain

a.

b.

c.

92

Single-Stage-3.0 psi cp a) Limestone b) Sandstone c) Granite

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

0 2000 4000 6000 8000 10000 12000

Load cycles

Perm

anen

t Str

ain

Sample 1

Sample 2

Sample 3

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

0 2000 4000 6000 8000 10000 12000

Load cycles

Perm

anen

t Strai

n

Sample 1

Sample 2

Sample 3

0.0%

0.2%

0.4%0.6%

0.8%

1.0%

1.2%

1.4%1.6%

1.8%

2.0%

0 2000 4000 6000 8000 10000 12000

Load cycles

Perm

anen

t Str

ain

Sample 1

Sample 2

Sample 3

a.

b.

c.

93

APPENDIX D: CALCULATIONS

Calculate the average axial deformation for each specimen by averaging the readings from the two axial LVDTs. Convert the average deformation values to total axial strain (Ta), in/in, by dividing by the gauge length, L.

Perform the calculations to obtain the resilient and permanent strain values using the following equations:

res(N)r(N)

0 p(N 1)L (1 )

per(N)p(N)

0 p(N 1)L (1 )

Where

L0: initial sample length (mm or in.) ; res(N) : resilient (recoverable) change in sample length at cycle N, see

Figure 2 (mm or in.); per(N) : permanent (irrecoverable) change in specimen length at cycle N,

see Figure 2 (mm or in.); r(N 1) : resilient strain at cycle N-1 (mm/mm or in/in); and

p(N 1) : permanent strain at cycle N (mm/mm or in/in).

Compute the resilient modulus (Mr) using the following equation:

devr

rM

Where

Mr: resilient modulus (MPa or psi)

dev : deviatoric stress (Mpa or psi)

r : resilient strain (mm/mm or in/in)

Compute the permanent strain rate (.p ) using the following equation

( j) (i)p

. p p

j i

94

Where .p : permanent strain rate (strain /cycle)

( j)p : permanent strain at cycle j

(i)p : permanent strain at cycle i

i and j: ith and jth cycle numbers

Compute the and mean effective pressure (p) for each stage in each sequence using the following equation

1 2 31 ( )3 3

d

cp

Where d is the devitoric stress c is the confining stress Note: The above calculations are referenced in “Test Method for Multi-Stage Repeated Loading Triaxial Test.”

95

VITA

Aaron Austin was born in November, 1978, to Howard C. Austin and Aurelia W. Austin.

Being the ninth of eleven children, Aaron was the first in his family to graduate high

school and go on to college. Aaron enrolled at Louisiana Tech University in the Fall of

1996 and graduated in Spring 2002. At that time of graduation, America was still healing

from the terrorist attacks on September 11, 2001, and the economy had stalled from the

trauma. Despite the economy, Aaron joined the Louisiana Department of Transportation

and began work as Geotechnical Research Engineer. In the fall of 2006 Aaron resigned

from Louisiana Department of Transportation and entered the civil engineering graduate

program at Louisiana State University. Aaron Austin will graduate on May 12th, 2009 and

will receive a master’s degree in civil engineering with an emphasis in geotechnical

engineering.