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SUBGRADE RESILIENT MODULUS PREDICTION FROM LIGHT

WEIGHT DEFLECTOMETER

Journal: Canadian Geotechnical Journal

Manuscript ID cgj-2016-0062.R1

Manuscript Type: Article

Date Submitted by the Author: 12-Jul-2016

Complete List of Authors: Mousavi, S. Hamed; North Carolina State University, Civil, Construction, and Environmental Engineering Gabr, Mohammed; North Carolina State University Borden, Roy; North Carolina State University

Keyword: resilient modulus, light weight deflectometer, subgrade,, MEPDG

https://mc06.manuscriptcentral.com/cgj-pubs

Canadian Geotechnical Journal

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Mousavi, Gabr, Borden

2

SUBGRADE RESILIENT MODULUS PREDICTION FROM LIGHT WEIGHT 1

DEFLECTOMETER 2

3

S. Hamed Mousavi, Corresponding Author 4

North Carolina State University 5

Graduate Research Assistant, Department of Civil, Construction, and Environmental 6

Engineering, North Carolina State University, Raleigh, NC 27695-7908; 7

Tel: 919-995-8792; Email: [email protected] 8

9

Mohammed A. Gabr 10


Professor, Department of Civil, Construction, and Environmental Engineering, North 12

Carolina State University, Raleigh, NC 27695-7908; 13

Tel: 919-515-7904 FAX: 919-515-7908; Email: [email protected] 14

15

Roy H. Borden 16


Professor, Department of Civil, Construction, and Environmental Engineering, North 18

Carolina State University, Raleigh, NC 27695-7908; 19

Tel: 919-515-7630 FAX: 919-515-7908; Email: [email protected] 20

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ABSTRACT 29

Resilient modulus has been used for decades as an important parameter in pavement structure 30

design. Resilient modulus, like other elasticity moduli, increases with increasing confining stress 31

and softens with increasing deviatoric stress. Several constitutive models have been proposed in 32

the literature to calculate resilient modulus as a function of stress state. The most recent model, 33

recommended by MEPDG and used in this paper, calculates resilient modulus as a function of 34

bulk stress, octahedral shear stress and three fitting coefficients, k1, k2, and k3. Work in this paper 35

presents a novel approach for predicting resilient modulus of subgrade soils at various stress 36

level based on light weight deflectometer (LWD) data. The proposed model predicts the MEPDG 37

resilient modulus model coefficients (k1, k2, and k3) directly from the ratio of applied stress to 38

surface deflection measured during LWD testing. The proposed model eliminates uncertainties 39

associated with needed input parameters for ELWD calculation, such as the selection of an 40

appropriate value of Poisson’s ratio for the soil layer and shape factor. The proposed model was 41

validated with independent data from other studies reported in the literature. 42

43

Keywords: resilient modulus, light weight deflectometer, subgrade, MEPDG 44

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INTRODUCTION 48

The use of resilient modulus ( rM ) has been substituted for the California Bearing Ratio (CBR) 49

in pavement design in order to consider the deformation behavior of base and subgrade layers 50

under cyclic loading condition. The magnitude of Mr depends on, soil types, its structure, 51

physical properties such as density and water content, as well as the applied stress state (Li 1994; 52

Rahim and George 2004, Liang et al. 2008). Studies have shown that same as other soil modulus, 53

resilient modulus of subgrade soils, increase by an increase of confining pressure and reduces 54

with an increase in deviatoric stress. The value of Mr is defined as the ratio of the cyclic axial 55

stress to the recoverable or resilient axial strain (NCHRP project 1-28A, 2004), as shown 56

schematically in Fig. 1 and expressed in Equation 1: 57

cyclic

r

r

Mσ

ε= (1) 58

Where: 59

cyclicσ : cyclic axial stress 60

:rε resilient axial strain 61

62

Figure. 1. Definition of resilient modulus 63

64

The Mr of a subgrade layer can be determined from laboratory testing following the AASHTO T-65

307 test protocol, which uses fifteen stress combinations: five deviatoric stress levels 13.8, 27.6, 66

41.4, 55.2 and 69 kPa (2, 4, 6, 8 and 10 psi) applied at three confining pressures 41.4, 57.6 and 67

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13.8 kPa (6, 4 and 2 psi). Different forms of constitutive models can be found in the literature 68

that allow for computing the Mr value as a function of one, two or three stress parameters such as 69

confining pressure, deviatoric stress, bulk stress and octahedral shear stress (e.g. Dunlap 1963; 70

Seed et al. 1967; Witczak and Uzan 1988; Pezo 1993; NCHRP project 1-28A 2004). The recent 71

universal constitutive model proposed in NCHRP 1-28A (MEPDG) is presented in Equation 2: 72

32

1. .( ) .( 1)kk oct

rM k PaPa Pa

τθ= + (2) 73

Where: 74

:rM resilient modulus 75

:aP atmospheric pressure 76

1 2 3, , :σ σ σ principal stresses 77

1 32 :θ σ σ= + bulk stress 78

1 3

2( ) :

3octτ σ σ= − octahedral shear stress 79

:ik regression constants; i:1, 2, and 3 80

81

Despite the good accuracy of the use of laboratory testing to determine Mr. values, the 82

requirement of using an expensive and sophisticated device to perform the Mr test is considered 83

as a disadvantage. Several studies have been undertaken to overcome this issue by estimating Mr 84

through the development of empirical correlations with the physical properties of soil (e.g. 85

Carmichael et al. 1985; Elliott et al. 1988; Drumm et al. 1990; Farrar and Turner 1991; Hudson 86

et al. 1994). These empirical correlations eliminate the expense of resilient modulus laboratory 87

testing, but they are generally not capable of capturing the stress dependency of the Mr, or 88

simulate various stress conditions encountered in the field. Many studies have been performed 89

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over the past two decades to model the stress dependency of the resilient modulus by predicting 90

the coefficients of constitutive model, NCHRP Project 1-28A 2004, using basic soil properties. 91

For example, Yau and Von Quintus (2002), Rahim and George (2004), and Nazzal and 92

Mohammad (2010) each proposed different models to estimate the constitutive model 93

coefficients (k1, k2, and k3) based on the physical properties of soils. Another approach is the use 94

of expedient in-situ approaches such as light weight deflectometer, LWD, and dynamic cone 95

penetrometer, DCP, testing to estimate Mr. For example, White et al. (2007) and Mohammad at 96

el. (2008) have proposed correlations to estimate the Mr of subgrade soil by LWD at one specific 97

confining pressure and deviatoric stress (confining pressure = 41.4 and 13.8 kPa and deviatoric 98

stress = 69 and 41.4 kPa, respectively). Since the Mr depends on the confining pressure and 99

applied deviatoric stress, these models become inapplicable for cases with different stress states. 100

Work in this paper presents a model to compute Mr. values of A-4 (ML, SM, and CL) and A-7-5 101

(MH) soils from LWD data at any stress state by estimating the MEPDG recommended 102

constitutive model parameters (k1, k2 and k3). The proposed model is based on the use of LWD 103

measured data, the ratio of applied stress to the measured surface deflection, rather than on the 104

use of LWD-estimated Mr, in order to minimize uncertainties involved with the selection of 105

Poisson’s ratio and shape factor input parameters. The validity of the proposed model for A-1-b 106

(SP) and A-6 (CL-ML) soils, is examined by using data presented in the literature. 107

BACKGROUND 108

The LWD is a portable falling weight deflectometer for measuring in-situ modulus of soil 109

(Fleming 2007). Compared to the falling weight deflectometer (FWD), the LWD is cheaper and 110

more convenient to perform. The device used in this study was a Prima 100, as shown in Fig. 2, 111

and consisted of 10 kg falling weight, which can induce 15-20 ms pulse load up to 450 kPa, with 112

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its 20-cm diameter plate (radius = 10 cm). A geophone is used to measure surface deflection, 113

right at the center of the plate load. Surface deflection and applied load are monitored and 114

recorded through Prima 100 software. Fig. 3 shows an example of applied load and surface 115

deflection for one drop. 116

117

Figure 2. Prima 100 sketch (after Vennapusa, 2008) 118

119

The in-situ modulus is calculated based on Boussineq’s static elastic half space theory by 120

assuming a homogeneous isotropic soil layer (Fleming 2007). Therefore Poisson’s ratio and 121

shape factor are assigned as input parameters to the software to calculate the modulus per 122

Equation 3 (Fleming 2007). 123

2.(1 ). .rLWD

fE

ν σ

δ

−= ( 3 ) 124

Where: 125

:LWDE surface Modulus (MPa) 126

:σ applied stress (kPa) 127

:δ surface Deflection (µm) 128

:f shape factor 129

:ν Poisson’s ratio 130

:r radius of plate (mm) 131

132

Figure 3. Example of recorded applied stress and surface deflection during LWD 133

testing 134

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As previously mentioned, there are few empirical correlations to approximate the Mr of subgrade 135

soil from LWD measurements. Although the main advantage of these models is that they can 136

capture actual moisture and density conditions of the soil layer, they are mostly limited to one 137

specific stress state. White et al. (2007) proposed the model presented in Equation 4 to predict Mr 138

of subgrade soil from ELWD with an assumed Poisson’s ratio of 0.35 and shape factor of 2

π and 2 139

for cohesive and cohesionless soils, respectively, at a confining pressure = 41.4 kPa (6 psi) and 140

deviatoric stress = 69 kPa (10 psi). 141

( 45.3)

1.24

LWDr

EM

+= 142

(4) 143

With ,r LWDM E in MPa 144

Mohammad et al (2008) presented the model in Equation 5 in order to estimate Mr from LWD 145

data by assuming a Poisson’s ratio of 0.4 and a shape factor of 2

π for cohesive soil and 2 for 146

cohesionless soils, at a confining pressure 13.8 kPa (2 psi) and deviatoric stress 41.4 kPa (6 psi). 147

These stress values were chosen to represent the stress state at the top of the subgrade layer 148

under standard single axle loading of 80 kN (18 kips) and tire pressure of 689 kPa (100 psi) with 149

a 50-mm asphalt wearing course, 100-mm asphalt binder course and 200-mm aggregate base 150

course (Mohammad et al. 2008; Rahim and George 2004; Asphalt Institute 1989). 151

0.1827.75r LWDM E= × 152

(5) 153

With ,r LWDM E in MPa 154

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EXPERIMENTAL PROGRAM 155

A series of laboratory and in-situ LWD tests were performed to evaluate subgrade soil modulus 156

properties of four 4.88-m (16-ft) wide by 15.2-m (50-ft) long test sections located in the 157

Piedmont area, North of Greensboro, North Carolina. In this case, LWD testing was conducted in 158

the field to monitor the variation of subgrade modulus across the test sections. As shown in Fig. 159

4, the LWD tests were carried out at four locations within each test section; those locations were 160

offset 1-m (3.3-ft) away from boreholes, from which Shelby tubes were obtained. In parallel, a 161

laboratory testing program including resilient modulus testing and physical properties 162

characterization was performed on undisturbed samples retrieved from within the LWD 163

influence zone, (a depth = 1.5~ 2 diameter of the LWD loading plate, as was specified by 164

Mooney and Miller 2007; Khosravifar et al. 2013; Senseney et al. 2016), as presented in Table 165

1, and indicated in Fig. 1. 166

167

Figure 4. Location of resilient modulus specimens and LWD tests (dimensions in cm). 168

169

MATERIALS 170

Basic index property tests, including grain size distribution, Atterberg limits, and specific gravity 171

were conducted on the specimens after the Mr tests were completed. As shown in Table 1 and 172

Fig. 5, the site soils were classified as A-7-5 (MH), A4 and A4-a (SM, ML and CL, 173

respectively). The high plasticity specimens, A-7-5, were taken from the deeper depths, and 174

correspond to natural soil, while the low plasticity soils (A4 and A4-a) were located at shallower 175

depths and corresponded to compacted fill. 176

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177

Table 1. Summary of Sample Properties 178

179

Figure 5. Grain size distributions of resilient modulus samples 180

181

LWD MEASUREMENTS 182

Subgrade modulus values were measured at the test site by LWD (with 20 cm plate) following 183

the ASTM E2583-07. To do so, the plate is located horizontally on the surface, and first three 184

seating drops were considered to provide full contact between the plate load and the subgrade; 185

which followed by another three drops to obtain data for estimation of the surface modulus, 186

LWDE . The LWD

E values were calculated using Equation 3 and assuming a Poisson’s ratio of 187

0.35. A shape factor of 2

π was selected for the MH soil, and 2 for the ML, SM, and CL soil, 188

(Mooney and Miller 2007; White et al. 2007). Two LWD test stations were located about 1 m 189

apart on each side of the boreholes, from which samples for resilient modulus testing were 190

collected, as shown in Fig. 4. At each station, 3 ELWD were measured. The Standard deviation 191

and coefficient of variation of the six LWD measurements corresponding to the resilient modulus 192

laboratory specimen are presented in Table 2. The COVs are less than 5%. Hence for comparison 193

sake, the average of six field measured LWDE values was used to estimate the Mr from LWD. The 194

calculated Mr values were compared to the laboratory-measured Mr values for specimens 195

retrieved from the corresponding borehole within the LWD effective zone, as summarized in 196

Table 2. 197

As previously mentioned, the assumption of Poisson’s ratio and shape factor can lead to various 198

estimates of ELWD. In order to overcome the ambiguities with which values to use, the ratio of 199

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applied stress to surface deflection,σ

δ, from LWD direct measurements; which is representative 200

of soil layer elasticity, is directly used herein in the proposed model development, instead of 201

computing the ELWD by Equation 3. 202

The applied stress to surface deformation ratios from the LWD measurements are summarized in 203

Table 2 and are shown associated with the Specimen Number upon which the subsequent Mr 204

tests were performed. 205

LABORATORY TESTING: RESILIENT MODULUS 206

Resilient modulus tests were performed on undisturbed soil specimens following AASHTO T-207

307. Resilient modulus at each load combination was computed as the ratio of the cyclic axial 208

stress to average resilient axial strain for the last 5 of the 100 applied load cycles. Laboratory 209

results from each specimen were imported into MATLAB in order to evaluate fitting coefficients 210

for the MEPDG universal constitutive model, as presented in Equation 2. The calculated k1, k2, 211

and k3 values are provided in Table 2 along with the respective coefficient of determination (R2). 212

213

Table 2. Summary of LWD Measurements and Mr Model Parameters 214

215

EFFECT OF LWD INPUT PARAMETERS 216

Although input parameters such as Poisson’s ratio and shape factor can be approximated for 217

particular cases from values presented in literature, it is difficult to select appropriate values for 218

these input parameters for site specific conditions. Poisson ratio values between 0.2 to 0.5 are 219

recommended in the literature (Bishop 1977). Various shape factors are recommended for 220

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different scenarios. The shape factor can be varied between 2

π for a rigid loading plate, 1.33 and 221

2.67 for parabolic contact stress distribution in cohesive soils and granular soils, respectively, 222

and 2 for a uniform contact stress distribution (Terzaghi and Peck 1967; Mooney and Miller 223

2007; Vennapusa and White 2007; Prima 100 software). The uncertainties associated with 224

selecting these parameters can induce significant variation in the value of calculated modulus, as 225

illustrated in Fig. 6. For the case shown, the computed LWDE for sample H1-1 can change from 226

110 up to 220 MPa by changing the shape factor from 1.33 to 2.67 at a given Poisson’s ratio of 227

0.2. In addition, it can be observed that the effect of Poisson’s ratio becomes more pronounced 228

with increasing shape factor, and can produce up to a 30% change in the computed elastic 229

modulus value. 230

231

Figure 6. Effect of Poisson ratio and shape factor on ELWD (specimen H1-1). 232

233

EXISTING MODELS 234

As previously mentioned, White et al. (2007) Mohammad et al (2008) proposed empirical 235

correlations to approximate the Mr of subgrade soil from LWD measurements at one specific 236

confining pressure and deviatoric stress. 237

The performance of these correlations in estimating the laboratory-measured Mr values from the 238

current study are both shown in Fig. 7. It can be seen that both correlations have generally 239

overpredicted the measured values; however the Mohammad et al. correlation underestimates the 240

Mr of the more highly plastic soils. 241

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242

Figure 7. Laboratory-measured Mr vs. that predicted from existing models 243

244

DEVELOPMENT OF LWD CORRELATION 245

As previously noted, the existing models for subgrade Mr determination from LWD data are 246

limited to a specific stress level. A change in pavement structure layer thickness, axial load, and 247

tire pressure can lead to changes in stresses within the layers. In order to overcome this 248

restriction and eliminate uncertainties associated with selecting appropriate Poison’s ratio and 249

shape factor values, the ratio of applied stress to surface deflection as measured during LWD 250

testing was used. The coefficients of the MEPDG model are functionally related to the elastic 251

modulus (k1), stiffness hardening (k2) and strain softening (k3) behavior of the soil (Yau and 252

Quintus, 2002). Accordingly, the proposed model was developed to correlate k1, k2, and k3 to the 253

ratio of σ

δ obtained from LWD measurements, with the advantage of having the ability to 254

estimate Mr. at other stress levels once these parameters are defined. The new model was 255

developed from regression analyses on the laboratory and field measurement data from the 256

cohesive (A-7-5) and cohesionless (A-4a) soils. 257

MEPDG COEFFICIENTS FROM LWD 258

Multilinear regression analyses was performed on three quarters of the data set to develop a 259

model to calculate resilient modulus indirectly at any stress level from LWD data through 260

estimating the MEPDG formula coefficients. The proposed correlation is presented in Equation 261

6, with the definition of constants presented in Table 3. Figs. 8(a-c) shows the calculated 262

coefficients, k1, k2, and k3, from curve fitting of the laboratory results versus the ratio of the 263

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measured applied stress to the surface deformation in the field. The proposed model predicts the 264

k1, k2 and k3 coefficients with a coefficient of determination ( R2) of 0.71, 0.82, and 0.55. 265

1 2 ( )ik C Cσ

δ= + 266

(6) 267

i :1,2,3 268

Table 3. Constant Coefficients of Developed Model 269

270

Figure 8. (a) Computed k1 vs. σ/δ, (b) Computed k2 vs. σ/ δ, and (c) Computed k3 vs. σ/δ. 271

Following AASHTO T-307, laboratory resilient modulus test is performed at 15 different stress 272

level, 5 deviatoric stress, 13.8, 27.6, 41.4, 55.2 and 69 kPa (2, 4, 6, 8 and 10 psi), at 3 confining 273

pressure, 41.4, 57.6 and 13.8 kPa (6, 4 and 2 psi); which provides 15 resilient modulus values 274

corresponding to each stress level. Hence for each specimen, 15 resilient moduli are measured at 275

different stress level. Fig. 9 shows the laboratory measured vs. predicted Mr, for ¾ of the 276

samples at 15 different stress levels. The analyses results, illustrated in Fig. 9, show that the 277

proposed model is able to compute the laboratory-measured Mr with a coefficient of 278

determination ( R2) of = 0.83. 279

Figure 9. Laboratory-measured Mr vs. that computed prediction 280

281

Model Validation 282

Fig. 10 shows laboratory-measured vs. model-computed resilient modulus values using the 283

remaining quarter of the data set which was not used in the initial statistical correlations, at 15 284

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different stress level. The best-fit line for the data plotted shows that the proposed model slightly 285

underestimates resilient modulus by 7% with a coefficient of determination of 0.83. The 286

performance of the proposed model was also evaluated by utilizing data available from two other 287

studies by White et al. (2007) and Mohammad et al. (2008). Data from White et al. (2007) 288

included LWD measurements as well as laboratory-measured Mr data at a confining pressure = 289

41.4 kPa (6 psi) and deviatoric stress = 69 kPa (10 psi), for A-6 (CL), sandy lean clay; and A-1-b 290

(SP) soil, poorly graded sand with silt and gravel. Mohammad et al. (2007) presented LWD and 291

Mr measurements at a confining pressure 13.8 kPa (2 psi) and deviatoric stress 41.4 kPa (6 psi), 292

for A-4(CL-ML) and A-6 (CL-ML) soils. In order to be able to utilize this data from the 293

literature, the ratio of σ

δvalues were back calculated using Equation 3. The parameters utilized 294

in the back-calculation were Poisson’s ratio of 0.35 and 0.4, for White et al. (2007) and 295

Mohammad et al. (2008), respectively, and shape factors of 2

π for cohesive soils and 2 for 296

cohesionless soils, as originally reported by the authors. As shown in Fig. 11, the proposed 297

model underestimates laboratory-measured Mr by 11% with a coefficient of determination of 298

0.96. 299

300

Figure 10. Laboratory-measured M r vs. that predicted for one quarter of data set. 301

302

Figure 11. Laboratory-measured Mr vs. that predicted using literature data. 303

304

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SUMMARY AND CONCLUSIONS 305

A model for estimating Mr on the basis of LWD data is presented in this paper. A performance 306

evaluation of existing models from the literature to assess Mr based on LWD data indicated a 307

limitation related to the ability of these model to predict Mr at only a single stress level. Using a 308

linear regression analyses approach, applied to laboratory measured Mr and field measured LWD 309

data, a new model is proposed to compute Mr at any desired stress state. The use of such a model 310

exclude uncertainties involved with the assumption of parameters needed for current LWD 311

modulus determination. In the proposed model, the ratio of applied stress to surface deformation 312

measured by LWD is used directly to compute MEPDG universal constitutive model coefficients 313

(k1, k2 and k3). Based on the results obtained in this study, the following conclusion can be 314

stated: 315

• The proposed model is capable of predicting Mr at various stress combinations with a 316

coefficient of determination of, (R2)0.83. Good agreement was obtained between the 317

LWD-predicted Mr and laboratory-measured data presented in other studies, with an 11% 318

average underprediction of Mr. values with R2 = 0.96. 319

• Examination of the ability of two existing models to predict Mr from in-situ LWD data, 320

showed a general trend toward overprediction, except for the higher plasticity soils tested 321

in this study. For this soil the Mohammad et al. correlation was seen to underestimate the 322

measured Mr. values. 323

• Input parameters needed to calculate elastic modulus by the LWD, such as Poisson’s ratio 324

and shape factor, can have a significant effect on the calculated ELWD. At a given 325

Poisson’s ratio, the ELWD can change by a factor of 2 depending on the shape factor 326

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selected. The effect of Poisson’s ratio was shown to increase with increasing shape 327

factor. 328

• The proposed model was demonstrated to predict the resilient modulus of A-1-b (SP), A-329

4 (ML, SM, CL), A-6 (CL-ML), and A-7-5 (MH) soil types using the measured ratio of 330

applied stress to surface deflection from a Prima 100 LWD device, employed in this 331

study. Further work will need to be performed to evaluate the applicability of the 332

proposed approach to other soil types as well. 333

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Terzaghi, K., and Peck, R. B. 1967. “Soil mechanics in engineering practice”. 2nd Ed., John

Wiley & Sons, Inc., New York.

Vennapusa, P.K., and White, D.J. 2009. “Comparison of light weight deflectometer

measurements for pavement foundation materials. Geotechnical Testing Journal, Vol. 32, No. 3,

pp. 1-13,

Witczak, M.W., and Uzan, J. 1988. “The Universal Airport Pavement Design System”. Report 1

of 4, Granular Material Characterization, University of Maryland, College Park.

White, D., Thompson, M., and Vennapusa, P. 2007. “Field Validation of Intelligent Compaction

Monitoring Technology for Unbound Materials”. Report No. MN/RC-2007-10.

Yau, A., and Von Quintus, H. 2002. “Study of laboratory resilient modulus test data and

response characteristics”, Rep. No. FHWA-RD-02-051, FHWA, U.S. Department of

Transportation, Washington, D.C.

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Draft


5

Figure captions

Figure 1. Definition of resilient modulus

Figure 2. Prima 100 sketch (after Vennapusa and White 2009)

Figure 3. Example of recorded applied stress and surface deflection during LWD

testing

Figure 4. Location of resilient modulus specimens and LWD tests (dimensions in cm).

Fig. 5. Grain size distributions of resilient modulus samples

Figure 6. Effect of Poisson ratio and shape factor on ELWD (specimen H1-1).

Figure 7. Laboratory-measured Mr vs. that predicted from existing models

Figure 8. (a) Computed k1 vs. σ/δ, (b) Computed k2 vs. σ/ δ, and (c) Computed k3 vs. σ/δ.

Figure 9. Laboratory-measured Mr vs. that computed prediction

Figure 10. Laboratory-measured Mr vs. that predicted for one quarter of data set.

Figure 11. Laboratory-measured Mr vs. that predicted using literature data.

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Figure 1. Definition of resilient modulus

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Draft

Figure 2. Prima 100 sketch (after Vennapusa and White 2009)

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Figure 3. Example of recorded applied stress and surface deflection during LWD

testing

-250

-200

-150

-100

-50

00

30

60

90

120

150

180

0 20 40 60 80

Sur

face

def

lect

ion

(μm

)

App

lied

str

ess

(kP

a)

Time (ms)

Applied stress

Surface deflection

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Figure 4. Location of resilient modulus specimens and LWD tests (dimensions in cm).

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Draft

Figure 5. Grain size distributions of resilient modulus samples

0

10

20

30

40

50

60

70

80

90

100

0.0010.010.1110

Per

cen

t F

iner

, P%

Particle Diameter, D (mm)

MH (H1-1)

CL (H5-2)

ML (H4-2)

SM (H3-1)

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Figure 6. Effect of Poisson ratio and shape factor on ELWD (specimen H1-1).

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5 3

ELW

D(M

Pa)

Shape factor, (f)

ν=0.20

ν=0.35

ν=0.50

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Draft

Figure 7. Laboratory-measured Mr vs. that predicted from existing models

0

30

60

90

120

150

180

0 30 60 90 120 150 180

Pre

dict

ed M

r (M

Pa)

Measured Mr (MPa)

White et al. (2007), A-4aWhite et al. (2007), A-7-5Mohammad et al. (2008), A-4aMohammad et al. (2008), A-7-51-1

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Draft

Figure 8. (a) Computed k1 vs. σ/δ, (b) Computed k2 vs. σ/ δ, and (c) Computed k3 vs. σ/δ.

k3 = 2.80(σ/δ) - 3.8R² = 0.55

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.00.0 0.5 1.0

Com

pute

d k 3

σ/δ

(c)

k1 = 1040(σ/δ) + 480R² = 0.71

0

200

400

600

800

1000

1200

1400

1600

0.0 0.5 1.0

Com

pute

d k 1

σ/δ

(a)

k2 = -0.90(σ/δ) + 1R² = 0.82

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0

Com

pute

d k 2

σ/δ

(b)

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Figure 9. Laboratory-measured Mr vs. that computed prediction

R² = 0.83

0

40

80

120

160

0 40 80 120 160

Com

pute

d M

r (M

Pa)

Laboratory-Measured Mr(MPa)

A-4a

A-7-5

1-1

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Figure 10. Laboratory-measured Mr vs. that predicted for one quarter of data set.

Mr-P. = 0.93Mr-M.R² = 0.83

0

30

60

90

120

0 30 60 90 120

Com

pute

d M

r (M

Pa)

Laboratory-Measured Mr(MPa)

1-1

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Figure 11. Laboratory-measured Mr vs. that predicted using literature data.

Mr-Pr. = 0.89Mr-M.R² = 0.96

0

40

80

120

160

0 40 80 120 160

Pre

dict

ed M

r (M

Pa)

Laboratory-Measured Mr (MPa)

Mohammad et al.(2008)

White et al. (2007)

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Table 1. Summary of Sample Properties

Sample

No. Depth

1 γtotal

2 w %

3 e

4 Gs

5 LL

6 PL

7 PI

8

P200%9

Clay%10

USCS AASHTO

H1-111

79 16.9 34.0 0.98 2.70 72 48 24 80 65 MH A-7-5

H2-2 86 17.7 27.8 0.80 2.66 58 36 22 72 46 MH A-7-5

H2-1 18 18.7 14.4 0.51 2.64 15 12 4 41 16 SM A-4a

H3-1 8 18.0 16.8 0.61 2.65 20 17 3 49 19 SM A-4a

H6-1 8 18.3 17.0 0.58 2.65 13 10 3 42 14 SM A-4a

H3-2 23 18.8 16.0 0.51 2.62 18 17 2 51 16 ML A-4a

H4-1 23 18.6 21.8 0.63 2.60 20 17 3 54 20 ML A-4a

H4-2 23 19.3 15.4 0.47 2.62 19 16 3 55 20 ML A-4a

H5-1 0 19.4 13.3 0.46 2.61 22 19 2 51 20 ML A-4a

H6-2 23 18.8 21.2 0.59 2.61 19 15 4 49 19 ML A-4a

H8-1 8 18.8 16.6 0.52 2.61 19 17 2 54 14 ML A-4

H5-2 30 19.7 16.5 0.44 2.64 25 16 8 42 16 CL A-4a 1 cm,

2 kN/m

3, 3natural water content,

4void ratio,

5specific gravity,

6Liquid limit,

7Plastic limit,

8Plasticity index,

9pass sieve No.200,

10Clay< 5µm ,

11Hi-j,

i:borhole number, j: sample number

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Table 2. Summary of LWD Measurements and Mr Model Parameters

Soil

Classification

Specimen

No.

MPa

k1 k2 k3 R2

MH (A-7-5) H1-1 154 8.92 3.8 0.87 1310 0.230 -1.04 0.96

H2-2 111 4.32 1.4 0.63 1440 0.329 -2.44 0.99

SM (A-4a) H6-1 32 3.03 3.8 0.18 567 0.808 -2.11 0.96

H3-1 41 1.03 1.3 0.23 513 0.970 -3.08 0.96

H2-1 64 3.07 2.7 0.36 634 0.882 -2.50 0.94

ML(A-4a) H5-1 48 2.94 4.7 0.27 680 0.910 -2.82 0.96

H4-1 21 2.07 4.2 0.12 666 0.879 -3.28 0.94

H8-1 35 3.05 4.0 0.20 555 0.925 -2.82 0.96

H4-2 30 1.72 3.08 0.17 646 0.896 -2.44 0.97

H6-2 20 0.51 2.1 0.11 717 0.673 -4.39 0.86

H3-2 56 2.40 3.6 0.32 593 0.874 -3.09 0.95

CL(A-4a) H5-2 20 3.31 9.2 0.11 897 0.897 -4.26 0.92

a

LWDE.Std %

vC ,b c

σ

δ

( )

( )

( )

a

LWD

b

c

E MPa

kPa

m

σ

δ µ

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Table 3. Constant Coefficients of Developed Model

C1 C2

k1 480 1040

k2 1.0 -0.9

k3 -3.7 2.8

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