DEVELOPMENT OF AN ARTIFICAL NEURAL NETWORK ......72 measurements of pavement deflection and surface...

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DEVELOPMENT OF AN ARTIFICAL NEURAL NETWORK MODEL

TO PREDICT SUBGRADE RESILIENT MODULUS FROM

CONTINUOUS DEFLECTION TESTING

Journal: Canadian Journal of Civil Engineering

Manuscript ID cjce-2017-0132.R1

Manuscript Type: Article

Date Submitted by the Author: 27-Apr-2017

Complete List of Authors: Elbagalati, Omar; Louisiana State University, Civil and Environmental

Engineering Elseifi, Mostafa; LSU, CEE Gaspard, Kevin; Louisiana Transportation Res Zhang, Zhongjie; Louisiana Transportation Research Center

Is the invited manuscript for consideration in a Special

Issue? : N/A

Keyword: subgrade resilient modulus, pavement deflection, rolling wheel deflectometer, network level

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

Canadian Journal of Civil Engineering

Draft

DEVELOPMENT OF AN ARTIFICAL NEURAL NETWORK 1

MODEL TO PREDICT SUBGRADE RESILIENT MODULUS FROM 2

CONTINUOUS DEFLECTION TESTING 3

4

5

Omar Elbagalati

Graduate Research Assistant

Department of Civil and Environmental Engineering

Louisiana State University

3316s Patrick Taylor Hall, Baton Rouge, LA 70803

e-mail: [email protected]

Mostafa A. Elseifi (Corresponding Author)

Associate Professor

Department of Civil and Environmental Engineering


3316s Patrick Taylor Hall, Baton Rouge, LA 70803


Kevin Gaspard

Senior Pavement Research Engineer

Louisiana Transportation Research Center


4101 Gourrier Ave., Baton Rouge, LA 70808


Zhongjie Zhang

Pavement Geotechnical Research Administrator

Louisiana Transportation Research Center


4101 Gourrier Ave., Baton Rouge, LA 70808


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7

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9

10

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Elbagalati, et al. 2

ABSTRACT: The subgrade resilient modulus is an important parameter in pavement 14

analysis and design. However, available Non-Destructive Testing devices (NDT) such as 15

the Falling Weight Deflectometer (FWD) have limitations that prevent their widespread 16

use at the network-level. This study describes the development of a model that utilizes 17

the Rolling Wheel Deflectometer (RWD) measurements to predict the subgrade resilient 18

modulus at the network level for flexible pavements. RWD and FWD measurements 19

obtained from a testing program conducted in Louisiana were used to train an Artificial 20

Neural Network (ANN) based model. The ANN model was validated using data from a 21

testing program independently conducted in Minnesota. The ANN model showed 22

acceptable accuracy in both the development and validation phases with coefficients of 23

determination of 0.73 and 0.72, respectively. Furthermore, the limits of agreement 24

methodology showed that 95% of the differences between the subgrade resilient modulus 25

calculated based on FWD and RWD measurements will not exceed the range of ±21 MPa 26

(±3 ksi). 27

28

Keywords; Subgrade Resilient Modulus, Pavement Deflection, Rolling Wheel 29

Deflectometer, network level 30

31

32

33

34

35

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INTRODUCTION 37

The subgrade resilient modulus (Mr) is an essential design parameter for stress-strain 38

analysis of pavement structures (Ping et al. 2012). In addition, the subgrade resilient 39

modulus is a key input in the AASHTO 1993 pavement design methodology and in all 40

three hieratical levels of design in the new AASHTOWare Pavement-ME design 41

procedure (Rahim 2005; Hossain et al. 2011). Recent studies have indicated high 42

sensitivity of Pavement-ME predicted distresses to the subgrade resilient modulus 43

(Schwartz et al. 2013; Abd El-Hakim et al. 2016). Furthermore, the subgrade resilient 44

modulus was found to have a significant effect on the design thickness of asphalt 45

overlays (Wu and Gaspard 2009; Wu et al. 2013). 46

For new construction, it is possible to measure the subgrade resilient modulus in 47

the laboratory after collecting sufficient soil materials from the field (Ahmed et al. 2016). 48

However, collecting a sufficient amount of soil materials from in-service pavement 49

sections by extracting cores is a tedious procedure that disturbs traffic, is costly, and can 50

have a significant impact on the integrity of the pavement structure (Tarefder et al. 2015). 51

To overcome these difficulties, many Non-Destructive Testing (NDT) and semi-52

destructive devices have been utilized to assess subgrade material properties in-situ such 53

as the Falling Weight Deflectometer (FWD) and the Dynamic Cone Penetrometer (DCP). 54

Yet, the DCP test requires drilling holes in the pavement section (Mohammad et al. 55

2009). On the other hand, the stationary nature of the FWD has limited the device 56

production rates and reduced its applicability for network-level surveys (Rada et al. 57

2011). To address these limitations, a number of continuous deflection measuring NDT 58

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devices were developed in recent years such as the Traffic Speed Deflectometer (TSD) 59

and the Rolling Wheel Deflectometer (RWD) (Flintsch et al. 2013). 60

OBJECTIVE 61

The objective of this study was to develop and validate a model to estimate subgrade 62

resilient modulus using RWD deflection measurements at the network-level for flexible 63

pavements. For model development, RWD and FWD measurements obtained from a 64

testing program conducted in Louisiana were used to train an Artificial Neural Network 65

(ANN) based model. After the learning process, the ANN model was validated using 66

RWD and FWD data from a testing program conducted independently at the MnROAD 67

facility in Minnesota. 68

BACKGROUND 69

The Rolling Wheel Deflectometer 70

The Rolling Wheel Deflectometer (RWD) is a pioneer test device for cost-effective 71

measurements of pavement deflection and surface properties at traffic speed, see Fig. 1. 72

On an Interstate, RWD can survey 400 lane-km (250 miles) per day compared to 64 lane-73

km (40 miles) per day for FWD. The most recent version of the RWD, which was 74

introduced in 2003, consists of a 16 m. (53-ft.) long semitrailer applying a standard 80 kN 75

(18,000-lbs.) load on the pavement structure by means of a regular dual-tire assembly 76

over the rear single axle (Briggs et al. 2000). The device operation speed can be as high 77

as 80 km/h (50 mph) causing no delays to the road users. Yet, the trailer is sufficiently 78

long to isolate the deflection basin produced by the RWD’s rear single axle from those 79

produced by the RWD tractor. 80

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FIGURE 1 81

82

Several modifications and upgrades were applied to the RWD since its first 83

introduction with respect to the laser sensors, data acquisition system, and software. The 84

laser collection system was moved between the tires, and a new procedure was 85

introduced for laser calibration. The laser sensors are set to collect a reading at a fixed 86

interval of 15.24 mm (0.6 in.) at all truck speeds. In 2009, a more accurate and stable 87

deflection measurement system customized for pavement applications was installed. The 88

upgraded system has a (101.1 mm) 4-in. measurement deflection range and has an 89

accuracy of ± 0.025 (0.001 in.). In the new system, four Selcom Model SLS 6000 laser 90

triangulation sensors are mounted at approximately 1.1 m. (3.6 ft.) above the roadway 91

surface with a 101.1 mm. measurement range. The laser sensors work simultaneously to 92

determine pavement deflections under the wheel load, with one sensor placed between 93

the dual tires to determine the maximum deflection. Two additional sensors are placed in 94

front of the wheels to measure a secondary pavement deflection at 457.2 mm (18 in.) 95

from the load. Prior to this research, no study has attempted to use the measurements 96

from the second sensor located 457.2 mm from the load in the analysis. 97

Typically, the RWD averages individual deflection readings over 160-meter (0.1 mile) 98

intervals, and reports the average deflection value along with its standard deviation. An 99

environmental chamber is utilized to maintain the measurement system at a constant 100

temperature. Further, the system includes a distance-measuring instrument (DMI) to 101

longitudinally reference collected data, an infrared thermometer to measure pavement 102

surface temperature, and a global positioning system (GPS) (ARA Inc. website). A 103

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Recent Strategic Highway Research Program 2 (SHRP2) study selected the RWD and 104

TSD as the most promising moving deflection measurement devices (Flintsch et al. 105

2013). 106

Calculating the Subgrade Resilient Modulus based on FWD data 107

In the 1993 AASHTO Guide, a detailed procedure is described to calculate the subgrade 108

resilient modulus based on FWD measurements as follows: 109

110 M� = C ∗ 0.24 ∗ Pd� ∗ r (1) 111

where Mr = subgrade resilient modulus (psi); C= Correction factor; P = FWD load (lb.); 112

dr = Deflection at distance r (in.); and r = Distance from the center of the FWD loading 113

plate (in.). 114

115

The relationship described in Equation (1) is valid at a distance r outside the pressure 116

bulb of the FWD load. Darter and co-authors recommended that the deflection used for 117

subgrade resilient modulus determination should be measured at a distance at least 0.7 118

times the radius of the stress bulb (ae), which can be calculated based on Equation 2 119

(Darter et al. 1991). For relatively thin pavements, the stress bulb was found to be 120

approximately 381 mm (15 in.), and for medium to thick pavements, the stress bulb 121

ranged from 660 to 840 mm (26 to 33 in.) (Darter et al. 1991): 122

123

a� =�a� + D� ∗ (E� M�� )�/�(2) 124

125

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where, a= FWD plate radius (in.); D= Total pavement thickness (in.); and Ep= effective 126

modulus of all pavement layers above the subgrade (psi), which can be calculated from 127

the following equation: 128

d� = 1.5pa� ! "1

M��1 + #$% &'()*+ ,�- + .1 − 0

&01234567 /E�8 9 : (3) 129

130

where, d0 = Deflection measured under the center of the loading plate (in). 131

Differences between FWD and RWD 132

Table 1 compares the general characteristics of FWD and RWD. Recent studies found 133

that the difference in deflection magnitude can be significant between a continuous 134

deflection measuring device such as RWD and FWD deflection measurements; yet, the 135

general trends were relatively the same when comparing pavements that were 136

structurally-sound or structurally-deficient (Katicha et al. 2013). Furthermore, both test 137

methods appear to properly reflect pavement conditions and structural integrity of the 138

road network by providing a greater average deflection and scattering for sites in poor 139

conditions. The effect of surface irregularities on the measurements of a moving device 140

(such as RWD), the difference in the load contact area between FWD and the RWD, and 141

the difference in loading mechanisms (rubber plate for the FWD and dual tire assembly 142

for the RWD), are all factors that may lead to deflection differences (Rada and Nazarian 143

2011). Therefore, the deflection basin characteristics for the RWD are not expected to 144

match with the ones from FWD. Accordingly, the approach presented in Equations (1) to 145

(3) cannot be directly applied to RWD measurements. To address this limitation, this 146

study made use of Artificial Neural Networks (ANNs). 147

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TABLE 1 148

149

Artificial Neural Networks 150

Artificial Neural Networks have commonly been used for solving complex engineering 151

problems in the last three decades (Ceylan et al. 2014). ANNs are parallel computing 152

schemes that imitate biological neural networks (Yet et al. 2014). They are effective and 153

accurate tools for solving complex nonlinear problems as they provide robust models that 154

can continuously be updated as new data become available. In addition, they can be used 155

in databases with either large or relatively small amount of data (Plati et al. 2015). Many 156

researchers have successfully used ANN-based models to backcalculate the layer 157

properties of in-service pavements, and they reported that ANNs are an effective tool for 158

backcalculation analysis (Kim et al. 2000; Gopalakrishnan et al. 2006; Bayrak et al. 2006; 159

Ceylan et al. 2005; genetic et al. 2006; Saltan et al. 2012). Therefore, ANN was selected 160

in the present study to backcalculate the subgrade resilient modulus from RWD 161

measurements. 162

DATA DESCRIPTION 163

Louisiana Testing Program 164

A two-phase comprehensive testing program was conducted in District 05 of Louisiana 165

(Abdel-Khalek et al. 2012). In the first phase, the complete asphalt road network (about 166

3,200 km [2,010 mi.]) was tested using the RWD deflection system based on the 167

manufacturer standard testing protocol. Researchers also selected 58 sections to be tested 168

using the FWD. In addition, 16 road-sections (2.4 km each [1.5 mi.]), referred to as 169

research sites, were selected and used for a detailed evaluation of RWD technology in the 170

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second phase (Elseifi et al. 2012). In addition to RWD testing, the field-testing plan in 171

Phase II conducted FWD testing on selected flexible and surface-treatment pavement test 172

sites. The testing plan specified that FWD testing should be conducted within 24 hours 173

following completion of RWD testing and at the same time of the day on the selected 174

sites, in order to maintain the same testing conditions. 175

Minnesota Testing Program 176

While the developed model was calibrated for the conditions pertinent to the Louisiana 177

road network, it was uncertain whether this model could be extended to different states 178

and varying road conditions and designs. To address this concern, FWD and RWD data 179

were obtained from a comprehensive testing program conducted at the MnROAD facility 180

in 2013. The testing program aimed at evaluating the accuracy of two continuous 181

deflection measuring devices (TSD and RWD) and to assess their use at the network level 182

(Sivaneswaran 2014). It is noted that the RWD prototype used in MnROAD was 183

measuring the secondary deflection (D1) at 381 mm (15 in.) instead of 457.2 mm (18 in.) 184

as it was the case in Louisiana. To assess the accuracy of these devices, 20 sensors were 185

installed in the MnROAD facility (strain gauges, pressure cells, geophones, 186

accelerometer, etc.). FWD was used to verify the performance of each sensor and to 187

evaluate the correlation between the continuous deflectometers and the FWD. Research 188

findings highlighted the benefits of using the RWD as well as the TSD for pavement 189

structural evaluation purposes at the network level. The flexible pavement test segments 190

at which both FWD and RWD measurements were conducted consisted of 16 road 191

sections that were used in the validation phase. 192

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METHODOLOGY 193

To develop the proposed ANN model, the FWD sensor D7 (1500 mm from the center of 194

the plate) measurements were used in Equation (1) to calculate the subgrade resilient 195

modulus for the tested pavement sections, Step 1. No temperature correction was applied 196

for the D7 measurements as they are only affected by the subgrade properties (Lukanen et 197

al. 2000; Kim et al. 2002). Second, statistical correlations were investigated between 198

RWD measurements and the subgrade resilient modulus calculated from Step 1. The 199

RWD measurements were corrected to a reference temperature of 20oC using BELLS 200

equation and the AASHTO 1993 procedure (Kim et al. 2002; Elseifi et al. 2012). Finally, 201

the RWD measurements and the subgrade resilient modulus values calculated from FWD 202

measurements were used to develop and validate the ANN model. 203

Correlations between RWD Measurements and the Subgrade Resilient Modulus 204

As described earlier, the RWD reports average deflections for 160 m intervals along with 205

standard deviations. Thus, four readings can be obtained from the device; the average 206

deflection at the rear axle (D0) and its standard deviation (σD0), and the average deflection 207

at 457.2 mm (D1) and its standard deviation (σD1). The statistical correlations between 208

these four parameters and the subgrade resilient modulus were investigated for the 209

measurements obtained from the Louisiana testing program. 210

An analysis of variance (ANOVA) was conducted between the subgrade resilient 211

modulus and the four RWD measurements using the SAS 9.4 software. Table 2 212

summarizes the results of the statistical analyses. As shown in this table, Parameters D0, 213

σD0, and D1 were found to be significantly correlated to the subgrade resilient modulus. 214

On the other hand, σD1 was not statistically correlated to the subgrade resilient modulus. 215

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The coefficient of determination (R2) between each parameter and the subgrade resilient 216

modulus was also calculated. Fig. 2. presents the correlations between the D1 and D0 217

with the Mr. As shown in Fig. 2, there is a downward trend between the decrease in 218

subgrade resilient modulus and the measured RWD deflections; yet, considering only one 219

deflection measurement is not sufficient to accurately predict the subgrade resilient 220

modulus as evident from the low R2 shown in this figure. 221

Based on these findings, the three RWD measurements (D0, σD0, and D1) were 222

considered in the ANN model for prediction of the subgrade resilient modulus. As 223

previously noted, the RWD prototype used in MnROAD measured the secondary 224

deflection (D1) at 381 mm (15 in.) instead of 457.2 mm (18 in.). To develop a model that 225

is compatible with measurements of both prototypes, “D1/r” was used in the model 226

instead of D1; where, r is the radial distance from the RWD rear axle. A multi-linear 227

regression model was developed using SAS 9.4 and showed an R2 of 0.6 and an RMSE of 228

15%; therefore, ANN was utilized in the present study to develop a model with better 229

accuracy. Comparing linear regression with ANN was not in the scope of this study as 230

recent studies concluded that comparison between linear regression models and ANN-231

based models is not adequate (Karlaftis and Vlahogianni 2011). 232

233

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TABLE 2 234

FIGURE 2 235

ANN Model Development 236

A multilayered feed-forward ANN using a back-propagation error algorithm was 237

developed with a tan-sigmoid transfer function and a linear activation function. The 238

simplest network topology that produces acceptable prediction accuracy was selected to 239

avoid overfitting of the model (Kim et al. 2014; Lawrence et al. 1997). The network 240

topology consisted of three layers of neurons and two layers of weights; an input layer (i) 241

of 3 neurons; a hidden layer (j) of 2 neurons; a target output layer (k) of 1 neuron, layer 242

of weights between neuron layers i and j (ij), and layer of weights between neuron layers 243

j and k (jk). Weights in layers ij and jk were named “Wij” and “W‵

jk”, respectively. In 244

addition, bias values were added to the sums calculated at each neuron (except layer i). 245

Biases in layers j and k were named “bj” and “Bk”, respectively (Leverington 2012). To 246

train the network, such that the proper weights and biases are calculated, the input layer 247

was fed with the three selected RWD measurements, and the target layer was fed with the 248

subgrade resilient modulus values. The network structure is shown in Fig. 3. 249

FIGURE 3 250

251

Data from the Louisiana testing program were used in the model development phase (124 252

road segments). The data were divided into 70% for training, 15% for validation, and 253

15% for testing, so that more than 25 data points are used for validation and testing 254

purposes as recommended in literature (Beleites et al. 2013). To avoid overfitting and to 255

increase the network generalization ability, training was halted when the validation set 256

error stopped decreasing, as shown in Fig. 4. Since the testing data set had no effect on 257

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the training phase, it was used to provide an independent measure of the network 258

performance. 259

FIGURE 4 260

261

RESULTS AND ANALYSIS 262

The regression plots of the ANN model for the training, validating, testing, and overall 263

sets are shown in Fig. 5. All data processing was performed off-line using a commercial 264

software package (MATLAB R2013a, The MathWorks Inc.). As shown in this figure, 265

the model had acceptable prediction accuracy with an R2 of 0.73. In addition, the RMSE 266

(%) was calculated at 12%. The RMSE (%) was calculated as follows: 267

268

RMSE% = 100 ∗ &∑ [@��ABCD�A)*(EF$)GH%ICJI%D�A)*(KF$)]6MN O /∑ C%ICJI%D�A)*MN O (4) 269

270

FIGURE 5 271

272

Network Description 273

At the end of the learning phase, proper weights were assigned to every connection, and 274

proper biases were assigned to each neuron as follows: 275

276 PQR = S−37.4 −42.8 −0.03−0.2 −0.35 −0.17W 277

278 bY = S22.49−0.47W 279 W′Y] = [0.0271.80] 280 B] = 0.415

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Forward Calculations 281

Artificial neural network models are considered by many researchers as "black-boxes" 282

(Attoh-Okine et al. 2009; Hsie et al. 2012; Benítez et al. 1997; Prechelt 1998). With a 283

complex network structure, it is difficult to explicitly describe the learned relationship 284

between the input and the output variables. However, the simplicity of the model 285

presented in this study (only one hidden layer with only 2 neurons) offers a chance to 286

describe the network in a form of a simple equation. The general equation of a 287

backpropagation algorithm-based neural network with one hidden layer, one output 288

variable, and a tan-sigmoid (tansig) transfer function can be described as follows: 289

290 k = (B` + ∑ tansig(bY1∑ aBWBY)Of0Og0 WY]) (5) 291

where k= the model output at layer k; nj = number of neurons in the hidden layer; ni = 292

number of neurons in the input layer; ai = the input variables; and The tansig function can 293

be described as follows: 294

295 tansig(x) = �iG�ji�i1�ji (6) 296

297

The tansig transfer function forces the neurons in the hidden layer to produce outputs in 298

the range of -1 to +1, which accelerates the back-propagation algorithm (Vogl et al. 1988; 299

Dorofki et al. 2012). A linear activation function was then utilized to transfer the output 300

in layer k to the final output (Mr). The following expression describes the model 301

developed utilizing ANN to predict the subgrade resilient modulus based on RWD 302

measurements: 303

M� = 119.7 ∗ S0.415 + 0.027 ∗ tansig 222.49 − 37.4D� − 42.8σ$l − 0.03 $N� 5 +304 1.80 ∗ tansig 2−0.47 − 0.2D� − 0.35σ$l − 0.17 $N� 5W + 195.2 (7) 305

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Model Evaluation and Analysis 306

Limits of Agreement 307

The limits of agreement (LoA) methodology, developed by Bland and Altman, is a 308

simple powerful methodology for assessing agreements between two devices or 309

procedures (Bland and Altman 1986). The methodology was successful to the extent that 310

the reference that introduced this method has become one of the most cited statistical 311

papers (Ryan and woodall 2005). Bland and Altman concluded that using only regular 312

regression could be misleading when comparing two devices or methodologies for two 313

reasons. First, correlation depends on the range and distribution of the variables. 314

Second, correlation ignores any systematic bias between the two variables (Bland and 315

Altman 2003). A recent study concluded the usefulness of the LoA methodology for 316

comparing TSD and the FWD measurements (Katicha et al. 2013). 317

The procedure of the LoA methodology consists of the following steps: (1) plot a 318

chart with the differences between measurements by two methods on the Y-axis, and the 319

mean of the two measurements on the X-axis, (2) calculate the mean and the standard 320

deviation (σ) of the differences, and (3) calculate the mean ± 1.96 σ. One would then 321

expect 95% of differences between measurements by two methods to lie within these 322

limits. Fig. 6 shows the LoA between the subgrade resilient modulus values calculated 323

based on FWD and RWD measurements; the chart is also known as the Bland and 324

Altman chart. 325

As shown in Fig. 6, 95% of the differences between the Mr values calculated 326

based on the FWD and the RWD measurements did not exceed the range of ± 21 Mpa (± 327

3 ksi), which is reasonable especially at the network level. The figure provides a better 328

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understanding of the model accuracy in predicting Mr based on RWD data. The figure 329

also shows that the error in the predicted subgrade resilient modulus is independent of the 330

Mr value. 331

FIGURE 6 332

333

Model Validation 334

The generalization ability of the presented ANN model was tested using measurements 335

obtained from the testing program conducted at MnROAD. RWD data from 16 flexible 336

pavement testing cells were used as inputs in the ANN model to predict the subgrade 337

resilient modulus. The Mr predicted values were then compared with those calculated 338

based on FWD measurements, see Equation 1. The model showed acceptable accuracy 339

with an R2 of 0.72 and RMSE of 8% as shown in Fig. 7. 340

FIGURE 7 341

SUMMARY AND CONCLUSIONS 342

The objective of this study was to develop a model to utilize RWD measurements in 343

predicting the subgrade resilient modulus for flexible pavements. RWD and FWD 344

measurements were obtained from two comprehensive testing programs conducted in 345

Louisiana and Minnesota and were used to develop and validate an ANN model for 346

predicting the subgrade resilient modulus. The Louisiana testing program data were used 347

for developing the model, and data from the Minnesota testing program were used in the 348

model validation. The ANN model showed acceptable accuracy in both the development 349

and validation phases with coefficient of determination of 0.73 and 0.72, respectively. 350

The RMSE was found to be 12% and 8% in the development and the validation phases, 351

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respectively. Furthermore, the limits of agreement methodology showed that 95% of the 352

differences between the Mr values calculated based on FWD and RWD measurements 353

will not exceed the range of ± 21 MPa (± 3 ksi), which is acceptable especially at the 354

network level. 355

The availability of additional RWD and FWD testing will allow feeding and 356

refining the developed ANN model and will enhance its generalization ability. The 357

model presented in this study was developed and validated based on testing conducted on 358

flexible pavements. Conducting additional RWD and FWD testing on rigid pavement 359

sections will allow assessing the validity of the presented approach in predicting the 360

subgrade resilient modulus using RWD testing data conducted on different types of 361

pavements. 362

ACKNOWLEDGMENTS 363

The financial support of the Louisiana Transportation Research Center (LTRC) is greatly 364

appreciated. The authors also acknowledge the help of Nadarajah Sivaneswaran from the 365

FHWA Turner-Fairbank Highway Research Center in providing the MnROAD data. 366

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List of Tables

Table 1. Comparison between RWD and FWD Characteristics

Table 2. Correlation between RWD measurements and the FWD Subgrade Resilient

Modulus

List of Figures

Fig. 1. General Layout of the Rolling Wheel Deflectometer

Fig. 2. Correlation between the Mr and (a) D1 and (b) D0

Fig. 3. Structure of the ANN Network

Fig. 4. ANN Model Performance

Fig. 5. Regression plots of the developed ANN model for (a) the training data set (b) the

validation data set (c) the testing data set and (d) All data

Fig. 6. Bland and Altman Chart for Mr calculated based on FWD and RWD

measurements

Fig. 7. Model Validation Using Data from the MnROAD Testing Program

368

369

370

371

372

373

374

375

376

377

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378

Table 1. Comparison between RWD and FWD Characteristics 379

Factor RWD FWD

Operational Speed Traffic Speed Stationary

Deflection Sensor

Accuracy

6.25 microns 0.254 microns

Number of Operators 2 1

Productivity (km/day) 160 to 320 4 to 40

Number of Sensors 1 to 2 7 to 9

Applied Load (kN) 80 26 to 80

Load Type Transient wheel load Impact circular plate

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

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402

Table 2. Correlation between RWD measurements and the FWD Subgrade Resilient 403

Modulus 404

Parameter P-Value R2

D0 <0.0001 0.2950

σD0 <0.0001 0.4023

D1 <0.0005 0.1933

σD1 0.9087 0.1679

405

406

407

408

409

410 411

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(a)

(b)

R² = 0.1933

0

20

40

60

80

100

120

140

160

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

MrMPa

D1 mm

R² = 0.2954

0

20

40

60

80

100

120

140

160

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Mr MPa

D0 mm

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-30

-20

-10

0

10

20

30

40 50 60 70 80 90 100 110 120 130

Mr difference

Mr mean

Mean difference Upper limit of agreement Lower limit of agreement

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R² = 0.7175

60

70

80

90

100

110

120

130

60 70 80 90 100 110 120 130

Mr (RWD) MPa

Mr (FWD) MPa

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DEVELOPMENT OF AN ARTIFICAL NEURAL NETWORK ......72 measurements of pavement deflection and surface...

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