CHARACTERIZATION OF A TWO-LAYER SOIL SYSTEM …docs.trb.org/prp/10-1653.pdf · 2 LIGHTWEIGHT...

CHARACTERIZATION OF A TWO-LAYER SOIL SYSTEM USING A 1

LIGHTWEIGHT DEFLECTOMETER WITH RADIAL SENSORS 2 Paper # 10-1653 3

4

By 5

6 Christopher T. Senseney, P.E., Maj, USAF (Corresponding Author) 7

Ph.D. Student 8

Division of Engineering 9

Colorado School of Mines 10

1610 Illinois Street 11

Golden, CO 80401 12

Ph: (303)384-2153 13

F: (303)273-3602 14

email: [email protected] 15

16

Michael A. Mooney, Ph.D., P.E. 17

Associate Professor 18

Division of Engineering 19

Colorado School of Mines 20

1610 Illinois Street 21

Golden, CO 80401 22

Ph: (303)384-2498 23

F: (303)273-3602 24

email: [email protected] 25

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27

Word Count: 28

Abstract = 0218 29

Text = 4710 30

Tables (4 x 250) = 1000 31

Figures (6 x 250) = 1500 32

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Total = 7428 34

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39

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43

Re-submitted on November 10, 2009 for presentation and publication by Transportation 44

Research Board, 88th

Annual Meeting, January 2010, Washington, D.C. 45

TRB 2010 Annual Meeting CD-ROM Paper revised from original submittal.

Senseney, C.T. & Mooney, M.A. 2

ABSTRACT 46 47

Non-destructive tests to estimate stiffness modulus, such as the light weight 48

deflectometer (LWD), have experienced increased popularity, but very little research has been 49

performed to evaluate the LWD with radial sensors. Results are presented from LWD testing 50

with radial sensors that measured the deflection bowl on one- and two-layer field test beds 51

consisting of unbound materials. LWD testing produced a measureable deflection bowl on 52

medium stiffness granular materials to a radial sensor spacing of 750 mm (30 in). When limited 53

to a stiff over soft layered system, the LWD with radial sensors demonstrated the ability to 54

accurately backcalculate layered moduli. Backcalculated moduli closely matched laboratory 55

determined moduli from triaxial testing at a similar stress state as in the field. The measurement 56

depth for the LWD with radial sensors was found to be 1.8 times plate diameter versus the 57

measurement depth of conventional LWD testing of 1.0 to 1.5 times plate diameter. The LWD 58

with radial sensors was able to measure deeper than conventional LWD testing because the radial 59

geophones measure vertical surface deflections caused almost entirely by deeper material. As 60

compared to other configurations, the 300 and 600 mm (12 and 24 in) radial sensor configuration 61

is recommended for unbound materials because it produced the most accurate moduli 62

backcalculation results and captures deflections critical to the backcalculation process. 63

64

INTRODUCTION 65 66

The light weight deflectometer (LWD) was developed to estimate the in-situ stiffness 67

modulus of soils. The device can be used for quality control/quality assurance and structural 68

evaluation of compacted earthwork and pavement construction. Over the past decade or more, 69

resilient modulus, analogous to stiffness modulus, was established as the primary input 70

parameter for characterizing subgrade, subbase and base materials for highway pavement design 71

in the United States. As a result, non-destructive tests to estimate stiffness modulus, such as the 72

LWD, have experienced increased popularity [1-5]. Conventional LWD testing uses deflection 73

measured from a center geophone or accelerometer coupled with static, linear-elastic half space 74

theory to calculate one stiffness modulus for the composite soil system. 75

LWD manufacturers have recently begun offering an LWD with radial geophones. This 76

evolution suggests that layered soil systems may be characterized in a similar method as the 77

falling weight deflectometer (FWD). If so, a significant advancement would be achieved because 78

earthwork is often layered. The modulus obtained from conventional LWD testing represents the 79

composite modulus of the layers within the influence depth rather than the true modulus of the 80

tested layer [6]. Very little research has been performed to evaluate the LWD with radial sensors. 81

To the authors’ knowledge there is just one published study presenting actual LWD radial 82

deflection results [7] and no published studies of backcalculated moduli from radial sensors. 83

This paper presents results from LWD testing that employed radial sensors to measure 84

the deflection bowl of one- and two-layer soil systems. Layer moduli were then backcalculated 85

based on measured deflections. The objectives of this paper are to: (1) verify the LWD produces 86

a deflection bowl on unbound materials and describe the nature of the deflection bowl on one- 87

and two-layer systems, (2) assess the capability of LWD with two radial sensors to accurately 88

characterize moduli of known two-layer stratigraphies (limited to stiff over soft), (3) evaluate 89

measurement depth of LWD with two radial sensors and show how and why it is different than 90



conventional LWD testing, and (4) evaluate the influence of radial sensor spacing on 91

backcalculation. 92

93

BACKGROUND 94

95

LWD Characteristics 96

97 The LWD is a portable device that applies an impulse load from a drop weight impacting 98

a circular plate resting on the ground. The LWD consists of a circular load plate (150 mm, 200 99

mm or 300mm diameter), housing, urethane dampers, guide rod, drop weight and geophone 100

sensors (Figure 1a). During testing the drop weight releases from a variable height, slides down 101

the guide rod and applies a dynamic force impulse to the load plate lasting 15-25 ms. Surface 102

deflections (through integration of velocity) are measured from a geophone mounted in the 103

center of the load plate and from up to two radial geophones mounted on a support bar resting on 104

the soil. Applied force (P) is measured with a force transducer mounted within the housing. In 105

conventional LWD testing, the maximum deflection measured by the center geophone (d0) and 106

maximum measured P are coupled with homogeneous, isotropic, static linear-elastic half space 107

theory to calculate a conventional LWD modulus (Evd or ELWD) that follows as: 108

109

( )π

ν

0

21

ad

PAELWD

−= (1) 110

111

where ν is the Poisson’s ratio of the soil, A is the contact stress distribution parameter (A = 2 for 112

a uniform stress distribution, π/2 for an inverse parabolic distribution, 8/3 for a parabolic 113

distribution) and a is the plate radius. The user has the option to input values for ν and A. The 114

LWD is designed for an impact force and load plate diameter to deliver an average contact stress 115

of 100 to 200 kPa (14.5 to 29 psi) on the soil surface. This stress range mimics the approximate 116

stress level on a typical subgrade, subbase or base course due to vehicle loading on the pavement 117

surface [8]. Two commercial LWD devices that employ radial geophone sensors are the Prima 118

100 and Dynatest LWD produced by Grontmij - Carl Bro Pavement Consultants and Dynatest 119

International, respectively. Results from testing with the Prima 100 (Fig. 2b) along with 120

backcalculated moduli from Dynatest’s LWDmod program are presented in this study. The 121

Prima 100 utilizes seismic velocity transducer geophones with a resolution of 1 µm and a 122

frequency range of 0.2 to 300 Hz [9]. 123



124

125

FIGURE 1 (a) Schematic of LWD, (b) picture of Prima 100 LWD. 126

127

Forward-calculation and Backcalculation 128

129 Dynatest’s LWDmod program forward-calculates deflections using Odemark’s layer 130

transformation approach together with Boussinesq’s equations. The basic assumption of 131

Odemark’s layer transformation is that the layered structure can be transformed into an 132

equivalent uniform, semi-infinite material, to which Boussinesq’s equations may be applied to 133

calculate deflections. Two critical assumptions of the Odemark-Boussinesq method are: (1) layer 134

thicknesses should be more than one-half the radius of the loading plate, and (2) moduli should 135

decrease with each descending layer by at least a factor of two [10]. Accurate backcalculation 136

with the Odemark-Boussinesq method is limited to pavement profiles with stiff layers over soft 137

layers. Using Odemark’s layer tranformation, a two-layer linear elastic system may be 138

transformed to a semi-infinite space provided that layer one is replaced by an equivalent 139

thickness (he) of material having the properties of the semi-infinite space. Assuming the 140

Poisson’s ratio is the same for all layers, the transformed equivalent thickness may be 141

determined as: 142

143

3

2

11

E

Efhhe = (2) 144

145

where h1 is the thickness of the top layer, E1 and E2 are the moduli of the top and bottom layer 146

respectively, and f is a correction factor for better agreement with exact values [11]. 147

A significant advantage of the Odemark-Boussinesq method is the ability to 148

accommodate for the stress dependent non-linearity in dynamic deflection testing by 149

incorporating a non-linear relation for the subgrade modulus. The universal non-linear model for 150

resilient modulus (Mr) that reflects stress dependence [12] is given by: 151

152 32

1

kk

r qpkM = (3) 153

154

where p is the mean normal stress (� � �� 3⁄ ), q is the deviator stress, and k1, k2 and 155

k3 are best fit parameters determined by laboratory data. The k3 value is negative, typically in the 156



range of 0 to -0.2 for granular materials and 0 to -0.6 for cohesive materials [12]. As k3 becomes 157

more negative, a material exhibits greater stress softening behavior where the modulus decreases 158

with increasing deviator stress. Dynamic deflection testing, e.g. FWD and LWD testing, 159

produces a non-linear effect in a stress softening subgrade, where the subgrade stress levels 160

beneath the outer sensors are much lower than subgrade stress levels for the inner sensors. The 161

apparent subgrade modulus measured by outer sensor locations is therefore higher than the 162

apparent subgrade modulus measured by the inner sensors [13]. The variation of modulus with 163

radial distance due to dynamic deflection testing is similar to that given by k3 part of Equation 3. 164

To this end, the non-linear subgrade modulus (E2) for use in Odemark-Boussinesq calculations 165

[14] is expressed in the form: 166

167 n

apCE

= 1

2

σ (4) 168

169

where σ1 is the major principle stress from external loading, pa is atmospheric pressure, and C 170

and n are constants. As is the case with k3, a material exhibits greater stress softening behavior as 171

n becomes more negative. A material is considered linear elastic when n = 0. 172

LWDmod uses a Odemark-Boussinesq static analysis to forward-calculate deflections. 173

First, apparent subgrade moduli E(r) are determined from a Boussinesq equation (Equation 5) for 174

loading on a homogeneous, isotropic, linear elastic half-space where dr is the measured 175

deflection at distance r, and P is a point load representing the uniformly distributed load of the 176

LWD. At a radial distance beyond one diameter from the center of the load, a point load 177

produces approximately the same surface deflections as a distributed load [15]. Next, the non-178

linearity constant n is calculated (Equation 6) where E(r1) and E(r2) are the apparent subgrade 179

moduli determined from radial sensors at r1 and r2. The n value is essentially a measure of 180

subgrade non-linearity as E(r2) will be greater than E(r1) when testing on a non-linear subgrade 181

due to a lower stress state at r2. Then, Odemark’s transformation is modified to accommodate a 182

non-linear subgrade in which the equivalent thickness of layer one (he,1) is calculated (Equation 183

7) as follows: 184

185

rrd

PrE

π

ν )1()(

2−

= (5) 186

187

=

1

2

2

1

log2

)(

)(log

r

r

rE

rE

n (6) 188

189



n

n

a

e

p

PnC

Ehfh

23

1

13

11,

2

3)21(

−

⋅−

=

π

(7) 190

191

where f is an correction factor (= 1.05 for a 2-layer system with n ≤ -0.4, = 1.0 for n > -0.4) [16]. 192

Then, stresses are calculated with Boussinesq’s equations on the transformed system and are 193

used to calculate E2 (Equation 4). Finally, deflections are calculated as the sum of the 194

compression in the transformed layer one, plus the deflection at the top of the subgrade. The 195

compression of the transformed layer one is the difference between deflections at the top and the 196

bottom of the transformed layer one. The deflection at the top the subgrade is calculated using 197

E2. The calculated deflections are compared with measured deflections and assumed moduli are 198

adjusted in an iterative procedure until calculated and measured deflection bowls reach an 199

acceptable match [13]. 200

201

Field Test Beds 202

203 Two field test beds were constructed to investigate the ability of the LWD with radial 204

geophones to characterize layered stratigraphies. Figure 2 summarizes the geometry of test bed 205

one (TB1) and test bed two (TB2). TB1 was 4 m (13 ft) long and 2.5 m (8 ft) wide and TB2 was 206

4 m (13 ft) long and 2 m (6.6 ft) wide. TB1 was designed as a homogeneous, medium stiffness 207

soil profile with in-situ material excavated to a depth of 1500 mm (60 in) and subsequently filled 208

with medium stiff sand (SW-SM) compacted with a vibratory plate in 150 mm (6 in) lifts. TB2 209

was designed as a medium stiffness soil over soft soil profile with in-situ soft clay (CL) 210

excavated to a depth of 600 mm (24 in) and filled with SW-SM compacted with a vibratory plate 211

in 75 mm (3 in) lifts. Great care was taken to ensure vertical homogeneity of both test beds with 212

quality assurance testing conducted every 150 mm (6 in). LWD testing was conducted at two 213

locations in each test bed, herein referred to as TB1-1, TB1-2, TB2-1 and TB2-2. 214

215

216 FIGURE 2 Test bed schematics for (a) homogeneous stiff sand profile (TB1); (b) medium 217

stiff sand over soft clay profile (TB2). 218



Soil properties are summarized in Table 1. Average dry density, moisture content, DCP 219

penetration rate and surface seismic modulus were obtained from in-situ quality assurance testing 220

with the sand cone, DCP and surface seismic. The seismic modulus was determined from multi-221

channel analysis of surface wave (MASW) testing utilizing an instrumented hammer to generate 222

surface waves which were measured at 0.1 m (4 in) intervals along a 1 m (39 in) array. MASW 223

based methods typically produce moduli greater than moduli determined from conventional 224

methods due to the low strains associated with MASW testing [16]. In the laboratory, the triaxial 225

secant modulus was determined from a consolidated, drained triaxial test using 150 mm (6 in) 226

tall, 70 mm (2.8 in) diameter samples. 227

228

TABLE 1 Summary of soil properties from TB1 and TB2 229

230 parameter Medium stiffness sand Soft clay

USCS classification SW-SM CL

AASHTO Classification A-1-b A-6

Liquid limit N/A 17

Plasticity index N/A 11

Average dry density 1988 kg/m3 (124 pcf) 1890 kg/m

3 (118 pcf)

Average moisture content 3.5% 17%

Average DCP penetration rate 7 mm/blow 22 mm/blow

Average low strain seismic modulus 263 MPa (38,000 psi) 48 MPa (7000 psi)

Triaxial secant modulus 63 MPa (9100 psi) 9 MPa (1300 psi)

231

Testing using the Prima 100 LWD with a 300 mm load plate and radial sensors was 232

conduced on both test beds. The test protocol consisted of testing on two points with three initial 233

10 kg (22 lb) pre-load drops. Measurements were then taken using 10 kg drop weights for 3 234

drops with radial sensor spacing (r) at 300/600 mm (12/24 in), followed by 3 drops with r = 235

450/750 mm (18/30 in). The same protocol was then used for 15 kg (33 lb) and 20 kg (44 lb) 236

drop weights. Testing was first conducted on the surface of TB1 to establish a baseline modulus 237

for the medium stiff sand. Then, testing was conducted on each 75 mm (3 in) lift of medium stiff 238

sand in TB2 in order to assess the capability of LWD to characterize a known two-layer system 239

with increasing depth of a medium stiff soil over a soft subgrade. Results from 10 kg and 15 kg 240

drop weight loading are presented in the following section; results from 20 kg loading are not 241

presented. It was determined that the LWD is not robust enough to support the 20 kg drop weight 242

because the device jumps and rocks during loading with such a heavy weight. Because of the 243

rocking motion, data from 20 kg loading was inconsistent and deemed unreliable, especially 244

deflection data from the center geophone. 245

246

RESULTS 247

248

Radial Deflections 249

250 LWD testing on medium stiffness granular soil produced a measureable deflection bowl to a 251

radial sensor spacing (r) of 750 mm. For both test beds, a decrease in surface deflection with 252

increasing radial sensor spacing was evident with the rate of decay dependent on soil modulus 253

and layering. Measured deflections on points 1 and 2 were nearly identical for both test beds; 254

therefore, only results from TB1-1 and TB2-1 are presented. Measured deflections on the 255



homogeneous SW-SM profile of TB1-1 are presented in Figure 3a for r = 300/600 mm with 10 256

kg and 15 kg loading. TB1-1 deflections indicated a gradual rate of decay with an increase in 257

radius. The change in deflection from r = 0 to r = 150 mm radial spacing is constant and equal to 258

d0 because the plate is assumed to be rigid. Deflections for the two-layer profile, TB2-1, are 259

presented in Figure 4a and 4b for r = 300/450/600/750 mm with 10 kg loading. The deflections 260

on TB2 with 15 kg loading are not presented here since the contours of the 15 kg deflection 261

bowls were similar to the contours of the 10 kg deflection bowls. Because the LWD is limited to 262

two radial sensors per measurement, measurements on TB2 were recorded for r = 300/600 mm, 263

followed by measurements for r = 450/750 mm. TB2-1 deflections exhibited a steep rate of 264

decay from r = 150 to r = 450 mm at shallow h1 of 240 mm, 310 mm, 385 mm (9 in, 12 in, 15 265

in). The steep decrease is an indication of weak CL material below layer one that caused high 266

deflections at the center geophone, followed by significant decreases in deflections with an 267

increase in radius. As h1 increased, measured deflections decayed at a more gradual rate and 268

began to match the 10 kg measured deflections from TB1-1. 269

Measured deflections indicate that TB1 was representative of a homogenous, isotropic, linear 270

elastic half-space. This is supported by the Boussinesq equation for deflection on the surface a 271

homogenous, isotropic, linear elastic half-space (see Equation 5). With an assumed modulus of 272

63 MPa, Equation 5 was used to calculate the theoretical radial deflections presented in 273

conjunction with measured deflections in Figures 3a, 4a and 4b. The theoretical deflections 274

between r = 150 and 300 mm are labeled invalid because the assumption of P (Equation 5) 275

representing a uniformly distributed load is only valid one diameter and beyond from the center 276

of the load. Equation 1 was used to generate the theoretical deflections between r = 0 and 150 277

mm (Figures 3a, 4a and 4b) with a modulus of 63 MPa and A = 2. Assuming the load plate is 278

perfectly rigid, theoretical deflections beneath the 150 mm radius plate are equal. Measured 279

radial deflections from TB1 showed good correlation with theoretical radial deflections. Figures 280

3b, 4c and 4d show apparent subgrade moduli E(r) calculated at radial distances based on 281

measured deflections. If a given test bed was an ideal homogeneous, isotropic, linear elastic 282

halfspace all the moduli would be the same. In fact, the calculated E(r) in Figure 3b closely 283

match the assumed theoretical modulus of 63 MPa, indicating TB1 is nearly homogeneous. 284



285 286

FIGURE 3 (a) TB1-1 deflections at radial distances for 10 kg and 15 kg; (b) TB1-1 moduli 287

at radial distances for 10 kg and 15 kg. 288

Measured deflections indicate TB2 with h1 < 400 mm (16 in) was not representative of a 289

homogeneous, isotropic, linear elastic halfspace. Figure 4a shows that measured deflections with 290

h1 < 400 mm do not match theoretical deflections. A mismatch was expected because TB2 was 291

vertically heterogeneous with E1 = (5-7)E2. As h1 increased, the degree of homogeneity 292

measured by the LWD in TB2 increased (Figure 4b). At an h1 = 620 mm (24 in), measured 293

deflections converge on the theoretical deflection bowl. Also, Figure 4c shows that calculated 294

E(r) do not match the assumed theoretical modulus of 63 MPa at h1 < 400 mm, while Figure 4d 295

shows that calculated E(r) start to converge on the assumed theoretical modulus of 63 MPa at h1 296

> 400 mm. 297



298 299

FIGURE 4 TB2-1 deflections at radial distances for 10 kg and (a) h1 = 240 mm, 310 mm, 300

385 mm; and (b) h1 = 460 mm, 535 mm, 620 mm; TB2-1 moduli at radial distances for the 301

same h1 thicknesses (c-d). 302

303

Backcalculation Results 304

305 Moduli were backcalculated from measured deflections and compared to laboratory 306

triaxial moduli with the caveat that stress levels in the lab do not necessarily represent those 307

experienced in the field owing to the varying stress state with depth. For this study, the 308

comparison soil moduli for layer one and two (E1 and E2) were estimated to be 63 MPa and 9 309

MPa based on consolidated, drained triaxial testing. The triaxial E1 and E2 were dependent on the 310

mean normal stress of the chamber (p) and applied deviator stress (q) as evidenced in Equation 3. 311

When E1 was measured during triaxial testing of the SW-SM material, mean p and q were 38 kPa 312

(5.5 psi) and 24 kPa (3.5 psi). When E2 was measured during triaxial testing of the CL material, 313

mean p and q were 34 kPa (4.9 psi) and 12 kPa (1.7 psi). A separate study measured in-situ 314

stresses generated by LWD loading on a test bed with 470 mm (18.5 in) of SP-SM sand over a 315

CL subgrade [17]. Table 2 presents measured stresses from that study where p and q were 316

calculated assuming an at rest earth pressure coefficient (Ko) of 0.5 and where �� , �� 317

�� . Table 2 suggests that p and q from the SW-SM triaxial test correspond to stresses at a 318

depth of approximately 200 mm (8 in) from LWD loading. According to Equation 3, the 319



comparison E1 would be larger if derived from a lower stress state than the stress state observed 320

at 200 mm. Table 2 also suggests that the p and q from the CL triaxial test correspond to stresses 321

at a depth of approximately 250 mm (10 in). Again, the comparison E2 would be larger if derived 322

from a lower stress state than the stress state observed at 250 mm. 323

324

TABLE 2 In-situ stresses from LWD loading where �� , �� 325

326

depth (mm) ��(kPa) p (kPa) q (kPa)

0 125 84 42

190 70 47 23

240 50 34 17

310 35 23 12

385 25 17 8

460 18 12 6

535 15 10 5

327

LWDmod demonstrated the ability to accurately characterize the moduli and nonlinearity 328

of the stiff over soft layered system in TB2. Backcalculation results from TB2-1 are presented in 329

Table 3 where measured deflections are shown for r = 0, 300 and 600 mm along with the 330

backcalculated deflections from LWDmod. LWDmod attempts to minimize the root mean square 331

(RMS) of the absolute difference between measured and backcalculated deflections. E1 and E2 332

are the backcalculated moduli for layer one and layer two respectively. Percent error represents 333

the percent discrepancy from the comparison moduli. C and n (Equation 4) are the non-linear 334

subgrade modulus constants. ELWD (Equation 1) is also provided. The most accurate moduli 335

backcalculation results were generated in a range of h1 = 385 mm (15 in) to h1 = 535 mm (21 in). 336

The soft clay of layer two caused underestimation of E1 at shallow h1. At deep h1, it is proposed 337

in the next section that the LWD with radial sensors has reached the depth of influence or 338

measurement depth, resulting in an overestimation of E2. The value of n increases with 339

increasing h1, indicating the radial sensors measure more of the non-linear CL at shallow h1 and 340

measure more of the linear SM-SW at deep h1. 341

342

343



TABLE 3 TB2-1 Backcalculation results for 10 kg and 15 kg 344

345

parameter h1 = 245 mm 310 mm 385 mm 460 mm 535 mm 620 mm

10 kg

d0 (measured) (mm) 1047 854 442 444 441 439

d300 (measured) (mm) 276 239 190 149 117 94

d600 (measured) (mm) 28 52 59 58 53 42

d0 (back) (mm) 1111 875 464 454 439 433

d300 (back) (mm) 198 225 163 143 117 97

d600 (back) (mm) 31 53 62 60 53 41

RMS (%) 17.9 3.9 9 3.5 0.5 1.9

E1 (MPa) [% error] 23 [63.5] 32 [49.2] 67 [-6.4] 61 [3.2] 60 [4.8] 56 [11.1]

E2 (MPa) [% error] 6 [33.3] 7 [22.2] 10 [-11.1] 15 [-66.7] 37 [-311.1] 77 [-755.6]

C (MPa) 2 2 2 4 26 77

n -0.82 -0.71 -0.68 -0.52 -0.16 0

ELWD (MPa) 24.6 30.9 59.6 59.3 62.4 62.3

15 kg

d0 (measured) (mm) 1575 1304 786 699 689 688

d300 (measured) (mm) 407 355 328 253 184 150

d600 (measured) (mm) 28 63 93 83 79 75

d0 (back) (mm) 1671 1331 836 762 691 667

d300 (back) (mm) 263 323 284 231 183 159

d600 (back) (mm) 30 64 99 87 79 72

RMS (%) 21.2 5.5 9.5 6 0.6 4.3

E1 (MPa) [% error] 23 [63.5] 33 [47.6] 60 [4.8] 59 [6.35) 60 [4.76] 60 [4.76]

E2 (MPa) [% error] 5 [44.4] 7 [22.2] 9 [0.0] 12 [-33.3] 29 [-222.2] 71 [-688.9]

C (MPa) 2 2 2 3 16 71

n -1 -0.86 -0.77 -0.69 -0.3 0

ELWD (MPa) 24.8 31.6 54.6 58.1 63.4 64.4

346

Measurement Depth 347

348 The measurement depth of the LWD with radial sensors was found to be greater than the 349

measurement depth of conventional LWD testing. In conventional LWD testing, the depth of 350

influence or measurement depth reflected in ELWD has been shown to range from 1.0 to 1.5 times 351

the plate diameter (for a = 200 and 300 mm) [6, 8, 17]. An inspection of the ELWD data for TB2 352

(Table 3) and the corresponding d0 data (Figure 5) suggest the ELWD and d0 plateau at h1 = 385 353

mm for 10 kg and at h1 = 460 mm for 15 kg. These measurement depths (1.2a for 10 kg and 1.5a 354

for 15 kg) are consistent with those found in previous studies. The measurement depth for LWD 355

with radial sensors was found to be 535 mm or 1.8a for both 10 kg and 15 kg. Beyond the depth 356

of 1.8a at h1 = 620 mm, measured deflections from TB2 for r = 300 and 600 mm match 357

measured deflections from the homogeneous SW-SM profile in TB1 for r = 300 and 600 mm. 358

The matching deflections indicate that the radial sensors no longer measured the CL layer two 359

and only measured the SW-SM layer one. In addition, n = 0 at h1 = 620 mm, indicating the radial 360

sensors are only measuring the linear SW-SM material. Interestingly, radial deflections did not 361

plateau in this study (Figure 5). However, it is proposed that radial deflections would plateau at 362



h1 > 620 mm because measured deflections at h1 = 620 mm match theoretical deflections of a 363

homogeneous, isotropic, linear elastic halfspace with E = 63 MPa (Figure 4b). 364

365

366 367

FIGURE 5 TB2-1 deflection versus h1 for (a) 10 kg and (b) 15 kg. 368

The LWD with radial sensors was able to measure deeper than conventional LWD testing 369

because the radial geophones measure vertical surface deflections caused almost entirely by 370

deeper material. For a homogeneous, isotropic, linear elastic halfspace, the vertical deflection at 371

z = r is approximately equal to the vertical deflection at r [15]. Figure 6 displays deflection (dz) 372

versus depth based on Boussinesq analysis (Equation 8) 373

��

��√�� 2�1 # $ �%�

&��%�' (8) 374

where E = 63 MPa, ν = 0.35, r is the radial offset and z is the depth. Figure 6 indicates that dz is 375

representative of material deformation below the 45º line because there is little change in 376

deflection from the surface to the 45º line. The 45º angle would be shallower for the layered 377

system is this study, however, the same principles apply. For the materials in this study, the sand 378

below the outer geophones is not affected by the LWD-induced stress, so the sand does not 379

experience deformation. The clay below the outer geophones is affected by the LWD-induced 380

stress that is spread through the sand. The clay deforms due to this stress and the geophones 381

measure the deflection at the surface. 382



383 384

FIGURE 6 Vertical deflection versus depth for r = 0, 300 and 600 mm on a homogeneous, 385

isotropic, linear elastic halfspace. 386 387

Radial Sensor Spacing 388

389 As compared to other configurations, the r = 300/600 geophone configuration produced 390

the most accurate moduli backcalculation results and this configuration captures deflections 391

critical to the backcalculation process on unbound materials. Results from two h1 thicknesses 392

(Table 4) show that the r = 300/600 exhibits the lowest percent error. More importantly, r = 393

300/600 characterizes the non-linearity of the CL layer two with the largest n value. Previously 394

presented results (Table 2) indicated the CL layer is highly non-linear. An r = 300 mm is the 395

recommended radial spacing for the inner sensor. For backcalculation on unbound materials, the 396

inner sensor is critical because it captures the steepness of the deflection bowl. In the Odemark-397

Boussinesq method with a 300 mm load plate, a sensor could not be placed any closer than r = 398

300 mm because the point load assumption is only valid beyond a radial distance of one 399

diameter. Due to the 1 µm resolution of the geophone, an r = 600 mm is the recommended 400

spacing for the outer sensor. The smallest deflection measurement recorded in this study was 13 401

µm, measured by the r = 750 mm sensor, which is starting to approach an unacceptable signal to 402

noise ratio of 10 percent. The smallest deflection measurement recorded by the r = 600 mm 403

sensor was 22 µm, well within an acceptable signal to noise ratio. 404

405



TABLE 4 TB2-1 backcalculation results by radial sensor configuration for 10 kg 406

and h1 = 385 mm and 460 mm 407

408

radial sensor spacing (mm)

parameter 300/600 450/750 300/450 600/750

h1 = 385 mm

E1 (MPa) [% error] 67 [6.3] 65 [(3.2] 71 [12.7] 62 [-1.6]

E2 (MPa) [% error] 10 [11.1] 14 [55.6] 11 [22.2] 23 [155.6]

C (MPa) 2 5 3 14

n -0.68 -0.46 -0.54 -0.26

h1 = 460 mm

E1 (MPa) [% error] 61 [-3.2] 51 [-19] 55 [-12.7] 56 [-11.1]

E2 (MPa) [% error] 15 [66.7] 22 [144.4] 17 [88.9] 18 [100]

C (MPa) 4 11 6 7

n -0.52 -0.33 -0.45 -0.41

409

CONCLUSIONS 410 411

1. LWD testing with a 300 mm diameter load plate on medium stiffness granular materials 412

produced a measureable deflection bowl to a radial sensor spacing of 750 mm. The 413

measured deflection bowl may be investigated to determine the degree to which a soil 414

system is homogeneous, isotropic and linear elastic. The measured deflection bowl on 415

TB1 indicated the one-layer, medium stiff sand profile was homogeneous, isotropic and 416

linear elastic. The measured deflection bowl on TB2 at h1 < 400 mm indicated the two-417

layer stiff over soft profile was not homogeneous, isotropic and linear elastic. 418

2. When limited to a stiff over soft layered system, the LWD with radial sensors 419

demonstrated the ability to accurately backcalculate layered moduli. Backcalculated 420

moduli closely matched laboratory determined moduli from triaxial testing at a similar 421

stress state as in the field. The companion LWDmod program found the clay subgrade in 422

the two-layer profile to be highly non-linear. 423

3. The measurement depth for the LWD with radial sensors was found to be 1.8 times plate 424

diameter versus the measurement depth of conventional LWD testing of 1.0 to 1.5 times 425

plate diameter. The LWD with radial sensors was able to measure deeper than 426

conventional LWD testing because the radial geophones measure vertical surface 427

deflections caused almost entirely by deeper material. 428

4. As compared to other configurations, the r = 300/600 mm geophone configuration is 429

recommended for unbound materials because it produced the most accurate moduli 430

backcalculation results and captures deflections critical to the backcalculation process. 431

432

Acknowledgements 433

434 The authors thank the Air Force Research Lab for funding this study. John Siekmeier (MnDOT) 435

and Roger Surdahl (FHWA) are acknowledged for providing testing equipment critical to this 436

study. The authors also thank Gabriel Bazi, Norman Facas and Caleb Rudkin for helping to 437

analyze and process LWD data.438



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