1 LOCAL CALIBRATION OF THE MEPDG RUTTING …docs.trb.org/prp/16-3824.pdf · 1 LOCAL CALIBRATION OF THE MEPDG RUTTING MODELS FOR ONTARIO’S 2 FLEXIBLE ROADS: RECENT FINDINGS 3

Gautam, Yuan, Lee, Li 1

LOCAL CALIBRATION OF THE MEPDG RUTTING MODELS FOR ONTARIO’S 1

FLEXIBLE ROADS: RECENT FINDINGS 2

3

Gyan Prasad Gautam 4 Department of Civil Engineering, Ryerson University 5

350 Victoria Street, Toronto, ON, Canada 6

E-mail: [email protected] 7

8

Xian-Xun Yuan, Correspondence Author 9 Department of Civil Engineering & Ryerson Institute for Infrastructure Innovation, 10

Ryerson University 11

350 Victoria Street, Toronto, ON, Canada 12


14

Warren Lee 15 Pavement and Foundation Section, Ministry of Transportation of Ontario, 16

1201 Wilson Avenue, Toronto, ON, Canada 17


Ningyuan Li 19 Pavement and Foundation Section, Ministry of Transportation of Ontario, 20

1201 Wilson Avenue, Toronto, ON, Canada 21


23

Word Count: 6210 + 1250 (5 figures) = 7460 24

Submission Date: August 1, 2015 25

Revised: October 10, 2015 26

mailto:[email protected]





ABSTRACT 27

This paper summarizes the recent efforts for and major findings from local calibration of 28

the rutting models of the AASHTO mechanistic-empirical pavement design guide (MEPDG) 29

for Ontario’s practices in pavement design, construction and maintenance. Unlike many other 30

local calibration studies for rutting models, this study took a new calibration method built upon 31

the more recent rutting calibration results from NCHRP Project 9-30A. To reduce the 32

indeterminacy because of the unknown layer contributions of total rutting, two of the five local 33

calibration factors (the temperature and traffic exponents) were prefixed based upon statistical 34

analysis of the data obtained from Project 9-30A. The remaining three scale factors were 35

determined by using a two-objective optimization strategy that eliminates bias and reduces 36

residual errors. It was concluded that although the Superpave and Marshall-mixes share the 37

same set of traffic and temperature exponents, the scale factors are very different. A set of local 38

calibration factors were recommended for future flexible pavement design in Ontario. 39

40

Key Words: Mechanistic-empirical method; Local calibration; Rutting model; Multi-objective 41

optimization; Efficiency frontier 42


INTRODUCTION 43

Developed under multiple NCHRP projects including 1-37A[1], 1-40[2] and 9-30A [3] over 44

the past 15 years, the AASHTO Mechanistic-Empirical Pavement Design Guide (MEPDG) is 45

emerging as a mainstream pavement design method throughout North America. The method 46

established a direct tie between pavement distresses and various design inputs including 47

material properties, pavement structures, traffic loadings, climate, soil conditions, construction 48

quality, and so on. The design method has been packaged in a user-friendly working platform 49

now called the AASHTOWare Pavement ME software (originally DARWin-ME). As one of 50

the leading transportation agencies in Canada, the Ministry of Transportation of Ontario (MTO) 51

has been mandated to implement the MEPDG for future pavement design. 52

Preliminary studies for Ontario’s conditions have shown that the global (or default) 53

distress models in the MEPDG do not accurately predict the pavement distresses and 54

performance for Ontario roads. Rutting has been found to be drastically over-predicted, 55

whereas fatigue cracking is often under-predicted [4]. Three research projects have been 56

commissioned since 2010 under the support of the MTO Highway Infrastructure Innovation 57

Funding Program (HIIFP) to carry out a comprehensive local calibration study using the 58

pavement performance data from the MTO’s second-generation pavement management system 59

(PMS-2). The first HIIFP project focused on the development of a local calibration database 60

that included a number of typical pavement sections with accurate design input data as well as 61

high-quality performance and distress data. The second project was tasked mainly to perform 62

local calibration for the rutting models. The third project continued on the local calibration for 63

the cracking models and international roughness index (IRI) model by using more accurate 64

performance data collected by the new ARAN9000 system [5]. The challenges faced in the 65

database development were discussed in [6] and [7]. Some preliminary local calibration results 66

for the rutting models were reported in [8-10]. This paper presents major results from the more 67

recent rutting model calibration by the research team. 68

Two major results are reported in this paper. First, the local calibration was expanded to 69

cover pavement sections of Superpave mix. A major limitation of our previous local calibration 70

study was that it included only Marshall-type asphalt concrete (AC) mixes, which were called 71

Hot Laid or HL materials in Ontario, whereas Superpave AC has been widely used in Ontario 72

since the early 2000s. The Superpave mix is known to have much better rutting resistance than 73

Marshall mixes. From a design analysis point of view, however, the question is whether the 74

mechanistic part of the MEPDG (e.g., through the dynamic modulus model) fully captures the 75

difference of the two materials? In the context of local calibration, the question is rephrased as 76

follows: Do we need a separate set of local calibration parameters for the two materials? 77


FIGURE 1 illustrates four example rutting growth curves of four neighboring pavement 78

sections of Highway 403, a freeway in central Ontario. All four pavement sections have very 79

similar structural design, traffic loading and environmental and climatic conditions, except that 80

the top two sections (1189 & 1200) in FIGURE 1 are Marshall-mix design whereas the bottom 81

two (1240 & 1255) employed Superpave design. As shown in the figure, at the same pavement 82

age of six years, the rut depth in the two Superpave sections is less than one third of those in 83

the two Marshall sections. Moreover, the two Superpave sections show fairly good replication 84

in rutting and thus small residual error in the calibrated model is expected. With identical design 85

and under the very similar working conditions, however, the two Marshall sections disclose 86

relatively large variability in rutting. It was therefore speculated whether the MEPDG rutting 87

models would be able to capture these differences between the two types of asphalt materials. 88

89

FIGURE 1: Comparison of total rutting curves: Superpave versus Marshall sections. 90

The second major result of the study, which is more important for readers outside of 91

Ontario, is the improvement of the local calibration method. The rutting model in the MEPDG 92

contains three empirically determined transfer functions. Due to the lack of information for the 93

layer contribution to total rutting, the local calibration is challenged by the indeterminacy and 94

multiple local optima, as reported in [10]. This paper reports a new local calibration method 95

based on the findings from the third party’s recalibration work for NCHRP Project 9-30A. The 96

proposed method is featured by two key points: 1) the determination of traffic and temperature 97

factors of the AC model, and 2) the trade-off between minimization of residual sum of squares 98

(RSS) and elimination of bias. The proposed local calibration method is mathematically 99

rigorous and engineering sound. 100

The rest of the paper is organized as follows. The background of the MEPDG rutting 101

models is first presented and followed by a methodological review of the global and local 102

calibration. The subsequent two sections discuss the proposed local calibration method. The 103

0

2

4

6

8

10

12

0 2 4 6 8

Tota

l ru

t d

ep

th (

mm

)

Pavement age (years)

Marshall

SC1200

SC1189

SuperpaveSC1240

SC1255


proposed method is then applied to the local calibration for Ontario’s Superpave and Marshall-104

mix roads. The calibration database and results are discussed. Finally, conclusions are drawn 105

in the end. 106

RUTTING MODELS IN MEPDG 107

Background 108

The MEPDG relates rut depth to the vertical permanent deformation of different structural 109

layers. The mechanistic analysis starts with first calculating the resilient strain in each analysis 110

layer based on elastic layer theory. After the resilient strains are obtained, the plastic strain of 111

each analysis layer is then calculated by using one of the three empirical rutting models, 112

depending upon which material is used in the analysis layer. Since the three rutting models all 113

were established based on laboratory experiments, they are subject to further calibrations. 114

The AC rutting model is expressed as 115

𝜀𝑝,𝐴𝐶,𝑖

𝜀𝑟,𝐴𝐶,𝑖= 𝑘𝑧𝛽𝐴𝐶10−3.3541𝑇𝑖

1.5606𝛽𝑇𝑁0.4791𝛽𝑁 (1)

where 𝜀𝑟,𝐴𝐶,𝑖 denotes the resilient strain of AC at the mid-depth of the 𝑖𝑡ℎ analysis layer under 116

a specific traffic load; 𝜀𝑝,𝐴𝐶,𝑖 the corresponding accumulated plastic strain; 𝑘𝑧 the depth 117

confinement factor as a function of total asphalt layer thickness and depth to computational 118

point; 𝑇𝑖 the temperature at the 𝑖𝑡ℎ analysis layer in Fahrenheit degree; 𝑁 the number of load 119

repetitions; and finally 𝛽𝐴𝐶 , 𝛽𝑇 , 𝛽𝑁 represent the local calibration factors, which equal 1.0 by 120

default. Note that 𝛽𝐴𝐶 is also called AC-scale factor, and 𝛽𝑇 and 𝛽𝑁 are called temperature and 121

traffic exponents, respectively. 122

The rutting models for the unbound granular materials and fine-grained soil have the same 123

functional structure except for a different scale factor. The notations used in the MEPDG 124

documents for these two rutting models are very complicated and confusing. For the sake of 125

local calibration, the transfer function can be rearranged and expressed as the following: 126

𝜀𝑝,𝑖

𝜀𝑟,𝑖= 𝑘𝑠𝛽𝜙(𝑁, 𝛼) (2)

where 𝑘𝑠 represents the global calibration coefficient, which equals 1.673 for granular 127

materials (note that this 𝑘𝑠 is changed to 2.03 in the new 2015 MEPDG Manual of Practice and 128

this study does not reflect this new change) and 1.35 for fine-grained materials; and 𝛽 is the 129

local calibration factor and in this paper, we use 𝛽𝐺𝐵 and 𝛽𝑆𝐺 for the granular and fine-grained 130

materials, respectively, to differentiate the two models. The function 𝜙(𝑁, 𝛼), expressed as 131


𝜙(𝑁, 𝛼) = 0.075 exp (4.89285 ×1 − 𝑁−𝛼

1 − 10−9𝛼) + 10 exp (−4.89285 ×

𝑁−𝛼 − 10−9𝛼

1 − 10−9𝛼) (3)

lumps the effect of repetitive traffic loading and soil moisture. In Eq. (2) and (3), 𝛼 is a 132

transformed parameter describing moisture content (𝑊𝑐) in the soil and is evaluated from the 133

relationship expressed as log 𝛼 = −0.61119 − 0.017638𝑊𝑐. 134

Note that the calculation of the plastic strains in the AC layers also involves a so-called 135

‘strain-hardening procedure’, for details of which refer to [1]. Once the plastic strains are 136

obtained, the total rut depth at age 𝑡, denoted by 𝐷(𝑡), is then calculated from the following 137

summation expression: 138

𝐷(𝑡) = ∑ 𝜀𝑝,𝑖(𝑡) ℎ𝑖

𝑀

𝑖=1

(4)

where ℎ𝑖 is the thickness of the analysis layer, and 𝑀 the total number of analysis layers. The 139

above summation process is repeated for each traffic loading level, sub-season, and month of 140

the analysis period. For the detailed analysis procedure used to predict permanent deformation 141

for flexible pavements, refer to [1]. 142

Therefore, the MEPDG contains three rutting models, one for each type of pavement 143

material (AC, granular material, and subgrade soil). In total there are five calibration 144

coefficients that are subject to adjustment during local calibration: three in the HMA model 145

(𝛽𝐴𝐶 , 𝛽𝑇 , 𝛽𝑁), one in the unbound granular materials (𝛽𝐺𝐵), and one in the fine-grained materials 146

(𝛽𝑆𝐺 ). Note that 𝛽𝐴𝐶1, 𝛽𝐺𝐵, 𝛽𝑆𝐺 serve as a scaling factor that changes proportionally the 147

permanent deformation in each layer along the whole life. In contrast, 𝛽𝑁 is an exponent 148

parameter associated with 𝑁 and it changes the overall shape of the permanent deformation 149

curve of the AC layer. It is clear from the mathematical form that as 𝛽𝑁 increases, the absolute 150

value of rut depth will increase. Meanwhile, the other exponent parameter 𝛽𝑇 associated with 151

temperature 𝑇 serves only a localized adjustment of the overall performance curve because of 152

the seasonal variation of the temperature. Therefore, the effect of 𝛽𝑇 on the overall trend is 153

harder to assess. As for the rutting model of unbound materials, although the moisture content 154

would also change the permanent deformation rate, the coefficients in the function 𝜙(𝑁, 𝛼) are 155

not open for local calibration in the MEPDG. These observations are important because 156

otherwise one would not know which local parameter(s) should be adjusted in the local 157

calibration. 158

Global and Local Calibrations 159

NCHRP 1-37A used 88 sections from the Long Term Pavement Performance (LTPP) database, 160

387 data points with pavement life ranging from a few years to more than 20 years for the global 161


calibration of the three rutting models described above. Because the LTPP database included 162

only surface rutting depth and no trench rut depth was available, the global calibration assumed 163

that the proportion of the observed rut depth in different layers followed the same proportion 164

in the predicted rut depth. The calibration took a complicated four-step process, in which many 165

ad hoc decisions based on engineering judgment were made. 166

An independent review of the MEPDG was done under NCHRP project 1-40A [2]. The 167

review raised a number of issues that need to be resolved before effective implementation of 168

the design guide. One of them is the comparison of other transfer models and the possibility of 169

including them as alternative models for end users to select. This led to another NCHRP 170

project, 9-30A [3], in which three additional AC rutting models were investigated and 171

compared. The final report of that project (i.e., Report 719) was released in 2012. 172

A number of subsequent studies confirmed the essential need of local calibration before 173

the design tool can be used in local design practice. To facilitate local calibration, AASHTO 174

published a guide in 2010 [11]. Although this guide provides the general principles for local 175

calibration, it does not specify the exact optimization process. Many challenging issues in local 176

calibration were left for the local calibrator to address. 177

Many states or provincial transportation departments have initiated local calibration 178

studies based on either LTPP or PMS database. Generally these studies were focussed on 179

sensitivity analysis, design evaluation and assessment, and local calibration. Although the main 180

objective of all calibration is to reduce the bias and standard error, the calibration approaches 181

differ from one another in many ways. The following four major categories of approaches have 182

emerged from the diverse practice: 183

1) Simultaneous full calibration: This type of calibration aims to obtain a single set of 184

optimized value for all of the five local calibration parameters 𝛽𝐴𝐶, 𝛽𝑇, 𝛽𝑁, 𝛽𝐺𝐵 and 𝛽𝑆𝐺 185

simultaneously using some sort of optimization procedure. It has to be pointed out that 186

without trench investigation data or layer contribution information, mathematics dictates 187

that it is impossible to obtain a unique optimal solution. This indeterminate and non-188

unique nature of the rutting calibration, although it may have been previously realized, 189

has never been openly discussed and properly addressed. Rather, many researchers 190

relied, often blindly, on heuristic optimization procedures (e.g., generic algorithm) giving 191

a number of optimal solutions and then used ‘engineering judgment’ to pick the ‘best’ 192

combination of solutions. 193

2) Two-stage full calibration: This category of calibration is similar to the first one, except 194

the ‘optimal’ solution is found by using the two-step strategy that was used in the global 195

calibration. Specifically, the first step minimizes the RSS with a different set of 𝛽𝑇 and 196


𝛽𝑁 while taking all other betas constant to 1, whereas the second step utilizes the obtained 197

𝛽𝑇 and 𝛽𝑁 values for further reduction of RSS by changing 𝛽𝑟1, 𝛽𝐺𝐵 and 𝛽𝑆𝐺 [12]. This 198

approach is not essentially different than the first one. The reason is that the two steps 199

can iterate further, and there is no guarantee that they will converge. 200

3) Partially pre-set, partially optimized calibration: This method chooses to calibrate only a 201

subset of the five parameters through RSS minimization while keeping the rest in the 202

default value (i.e., 1.0) [13] and pre-set to zero (e.g., some studies pre-set the subgrade 203

rut depth to zero for rehabilitated sections based upon the argument that the subgrade rut 204

in those sections after many years of consolidation is negligible). 205

4) Full calibration through pre-set layer contribution [10]: This method attempts to 206

explicitly address the indeterminacy of rutting local calibration. The root cause of the 207

trouble was traced down to the unknown layer contribution to the total surface rut depth. 208

For that purpose, they investigated the possible range and distribution of the layer 209

contribution from a number of data sources. Using the pre-set layer contribution 210

combinations, they were able to uniquely determine the optimal solution of the five 211

parameters. 212

Based upon the investigation by Waseem and Yuan [10], the research team initiated a few 213

more studies, hoping to find a more solid determination of the layer contribution. It was 214

gradually realized that in the absence of trench studies, the layer rut percentage results were 215

hard to validate. Meanwhile, the recent NCHRP 9-30A project published some reliable 216

calibration results based on field performance and laboratory test data in NCHRP Report 719 217

(thereafter “Report 719”). The report has formed a solid ground to fix some of the local 218

calibration parameters before the RSS minimization process. The next section describes the 219

details of how the traffic and temperature exponents of the AC rutting model were determined. 220

221

TRAFFIC AND TEMPERATURE EXPONENTS IN THE AC RUTTING 222

MODELS 223

NCHRP Project 9-30A focused on the evaluation and recalibration of the MEPDG AC rutting 224

model. It contained both field tests and laboratory specimen tests. Unlike many previous 225

calibration studies, the field test results in this study were corroborated with forensic 226

investigations including trench cutting, core excavation, and falling weight deflection testing, 227

whereas the laboratory permanent deformation tests followed two testing protocols: the triaxial 228

test and the constant-height shear test. A total number of 60 field sections and 46 laboratory 229

specimens were used in the study. For each of those sections and specimens, a longitudinal 230

calibration was performed and the section- or specimen-specific temperature and traffic 231


exponents were determined. Here the temperature and traffic exponents both are a product of 232

the global and local calibration factors. The sections- or specimen-specific temperature and 233

traffic exponents were listed in the following tables of the original tables: 234

Tables 8 (p.37): Traffic exponents derived from field tests of 37 new constructed 235

sections 236

Table 9 (p.38): Traffic exponents derived from field tests of 23 overlay sections 237

Table 24 (p.78): Traffic and temperature exponents derived from repeated-load triaxial 238

test of 23 reconstituted specimens based on mixture designs of field test sections 239

Table 25 (p.78): Traffic and temperature exponents derived from constant-height shear 240

test of 23 reconstituted specimens based on mixture designs of field test sections 241

Table 26 (p.82): Traffic and temperature exponents derived from constant-height shear 242

test of 5 field-coring specimens. 243

By studying the range and distribution of those exponents we hope to find a reasonable 244

value for the two local calibration exponent factors that can be used for the subsequent local 245

calibration. 246

The Typical Traffic Exponent 247

The section- and specimen-specific traffic exponents in Report 719 invite a number of 248

interesting hypotheses. For example, by comparing the data in Tables 8 and 9 mentioned above, 249

one can determine whether the new pavement sections and the overlay sections should be 250

treated separately in calibration. Interestingly, the answer is no. The sample mean and standard 251

deviation of the traffic exponents in Table 8 for the new constructed sections are 0.305 and 252

0.071, respectively, whereas the mean and standard deviation of the data in Table 9 for the 253

overlay sections are 0.298 and 0.091, respectively. Both the means and standard deviations are 254

so close that a simple t test negates the null hypothesis. Similar conclusions are also drawn for 255

the comparison between the field-derived data and the laboratory specimens with reconstituted 256

mixture subject to constant-height shear test. However, the 𝑡 test suggests that the laboratory 257

test protocol matters in the determination of the traffic exponent. Although the sample mean 258

of the shear test specimens is 0.299, which is very close to the field-derived means mentioned 259

above, the sample mean of the triaxial test specimens is 0.226. According to the 𝑡 test, this 260

difference in sample means is so statistically significant (with 𝑝 value much lower than 1%) 261

lower that one has to reject the null hypothesis. For details of the statistical testing, refer to 262

[14]. These statistical testing concluded that 263

The new constructed sections and the overlay sections have the same traffic 264

exponent; 265


The field-derived traffic exponent can be the same as the laboratory test-derived 266

traffic exponent, provided that the test is performed under the constant-height 267

shear testing protocol; 268

The traffic exponents obtained from the triaxial test are significant different than 269

the field-derived traffic exponents and those from the shear tests. 270

In the end, the traffic exponent data from Tables 8, 9, 25 and 26 are combined and used to 271

draw the histogram, as shown in FIGURE 2. Ranging from 0.16 to 0.55, the 88 data points 272

have a mean value of 0.30 and standard deviation 0.08. Note that in the global calibration 273

model, the traffic exponent equals 0.4791, which is greater than the exponent of 84/88 cases, 274

or 95 per cent of the cases. This has partly explained why the AASHTOware Pavement ME 275

Design software under the default calibration factors always over predicts the rutting. 276

277

FIGURE 2: Histogram of the field- and laboratory test-derived traffic exponents (Data 278

source: Tables 8, 9, 25 and 26 of NCHRP Report 719) 279

280

A sensitivity analysis was performed to check the overall impact of the traffic exponent 281

(m) on rutting prediction. Under different 𝑚 values ranging from 0.17 to 0.57, fourteen 282

Superpave sections from the MTO database were analyzed. It was found that the predicted rut 283

depths do not change significantly when 𝑚 ≤ 0.35. 284

Report 719 also compared other three AC rutting models: the Asphalt Institute (AI) model, 285

the modified Leahy model, and the Verstraeten model, which all include a traffic term in 286

exponential form. The traffic exponent values of the three models are 0.4354, 0.25, and 0.25, 287

respectively. On the other hand, Waseem and Yuan (2013) performed a preliminary study on 288

Ontario’s Marshall-mix sections using longitudinal calibration and found the traffic exponent 289

varying from 0.11 to 0.57. With all of these considerations it was concluded that the traffic 290

0

5

10

15

20

25

30

0.16 0.20 0.25 0.29 0.33 0.38 0.42 0.46 0.51 >0.51

Nu

mb

er

of

cou

nts

Traffic exponent

Avg = 0.30St Dev = 0.08

Global calibration value = 0.4791


exponent be set at 0.30 (or 𝛽𝑁 = 0.30 0.4791⁄ = 0.6262) for the subsequent local calibration 291

study. 292

293

The Typical Temperature Exponent 294

Among the four rutting models considered in the NCHRP 9-30A project, only the MEPDG 295

model and the Asphalt Institute (AI) model include a temperature term. The AI model used a 296

temperature exponent (n) of 2.767 whereas the value is 1.5606 for the MEPDG model. The 297

other two rutting models do not explicitly contain a temperature term because, as the proponents 298

argued, the resilient modulus or other material characteristics used in the transfer function have 299

already included the temperature effects and thus adding another temperature term would risk 300

double counting. 301

302

FIGURE 3: Histogram of temperature exponents obtained from triaxial and shear tests 303

(Data source: Tables 24 and 25 of NCHRP Report 719). 304

305

Moreover, Report 719 found that the laboratory-derived temperature exponent is largely 306

dependent upon the material testing methods. The histograms of the triaxial and shear loading 307

test data reported in Tables 24 and 25 of the report, as described above, are depicted in FIGURE 308

3. The triaxial results are systematically smaller than those from the shear tests. The mean 309

value of the triaxial test results is 2.665, which is close to the exponent value set in the AI 310

model, whereas the mean of the shear test is 7.720. This large variation in the temperature 311

exponent blurs the issue. It is our belief that an intensive study of the temperature effect is 312

1.5 2 2.5 3 3.5 4 4.5 5 6 7 8 9 10 110

1

2

3

4

5

6

7

Temperature exponent

Num

ber

of

counts

Shear

Triaxial

MEPDG default

value: 1.5606

AI default

value: 2.767


required to settle down this issue. With consideration that many past local calibration studies 313

simply left the temperature exponent at the default value, this study also chose to fix the 314

temperature exponent at its global value of 1.5606. In other words the local calibration 315

coefficient 𝛽𝑇 is preset to 1.0 in this local calibration study. 316

LOCAL CALIBRATION METHOD 317

The study follows the general working procedure of the local calibration guide suggested by 318

[11], which includes development of a local calibration database that considers the proper 319

hierarchical input level of accuracy for each input parameter and includes an appropriate sample 320

size of pavement sections with sufficient length of performance data records. The details of 321

database development are discussed in the next section. This section focuses on the discussion 322

of the local calibration optimization procedure, as the method used in this study is not exactly 323

the same as suggested by the local calibration guide, and the authors believe that the method 324

proposed in the study is better than the vague two-step approach suggested in the local 325

calibration guide. 326

Using the two pre-set exponents discussed in the preceding section, the local calibration 327

needs to determine only the three scale factors (𝛽𝐴𝐶 , 𝛽𝐺𝐵, 𝛽𝑆𝐺 ), one for each material. To 328

determine them, the following two objectives are considered: (1) minimize the bias and (2) 329

minimize the Residual Sum of Squares (RSS), where the bias and RSS are defined as: 330

RSS = ∑(𝐷𝑖 − 𝑑𝑖)²

𝑛

𝑖=1

(5)

Bias = ∑(𝐷𝑖 − 𝑑𝑖)

𝑛

𝑖=1

(6)

where 𝑛 is the total number of rut depth measurements in the calibration set; 𝑑𝑖 the observed 331

rut depth; and 𝐷𝑖 the calculated total rut depth. These two objectives are usually compatible 332

in the sense that any additional bias will increase the RSS. In an ideal case, the RSS is 333

minimized only if the bias is zero. However, the natural constraint that the three scale factors 334

must be nonnegative cannot guarantee that the bias is eliminated when the RSS is minimized. 335

Since the three scale factors 𝛽𝐴𝐶 , 𝛽𝐺𝐵 and 𝛽𝑆𝐺 all are direct multipliers of the rutting 336

models, one can estimate the rut depth for each structural layer by using the rutting models with 337

the default value of 1.0 except 𝛽𝑁= 0.6262. Denote the rut depths that are so estimated by 338

𝐷𝐴𝐶𝑖,𝑔 , 𝐷𝐺𝐵𝑖,𝑔 and 𝐷𝑆𝐺𝑖,𝑔 for the AC, granular base/sub-base, and sub-grade soil layers, 339

respectively. Then the predicted (or calculated) rut depth is expressed as 340

𝐷𝑖 = 𝛽𝑟1𝐷𝐴𝐶𝑖,𝑔 + 𝛽𝐺𝐵𝐷𝐺𝐵𝑖,𝑔 + 𝛽𝑆𝐺𝐷𝑆𝐺𝑖,𝑔 (7)


If RSS is the only objective function of the local calibration, then it is readily shown that 341

the RSS minimization is equivalent to solving three simultaneous linear equations (similar to a 342

linear regression problem). Unfortunately, a few trial calibrations using the actual Ontario road 343

data suggested that this simple least square solution might lead to negative values for the three 344

calibration factors. Therefore, additional constraints should be added to the minimization 345

process. For this purpose the minimization of the absolute bias was introduced. In the end, the 346

local calibration problem is formulated as the following two-objective constrained optimization 347

problem: 348

minimize RSS and |Bias|

s.t. 𝛽𝐴𝐶 , 𝛽𝐺𝐵 , 𝛽𝑆𝐺 ≥ 0 (8)

The Excel Solver was used to solve the optimization. First, the RSS minimization and 349

bias elimination were solved separately. These two results would provide a general sense of 350

the range of the solutions. Using these two solutions as a guide, one could use a constrained 351

method (that is, minimize RSS while limiting the absolute bias to a certain prescribed number) 352

to find the Pareto efficiency frontier of the two-objective optimization problem. The final 353

solution was determined by weighing the relative importance of RSS and bias. Engineering 354

judgment would have to be used in the decision. Finally, the calibrated factors were validated 355

with the validation sections. It is important to note that since the predicted rut depth is a linear 356

function of the local calibration factors, as shown in Eq. (7), the optimization does not involve 357

repetitive MEPDG analyses using AASHTOware Pavement ME Design. In fact, for each 358

section, the one analysis that uses default values for the local calibration factors except 𝛽𝑁 =359

0.6262 is sufficient. This feature has greatly reduced the computational efforts involved in the 360

local calibration study. 361

CALIBRATION DATABASE 362

MTO started to introduce Superpave mix into pavement construction as the top asphalt layer(s) 363

in the year of 2001. For this study we selected 87 Superpave projects, which contains 140 364

pavement sections in the pavement management system. These projects have different 365

pavement structures and highway types, spreading over all of the five climatic zones of Ontario. 366

After a series of data cleansing, only 84 sections are qualified for calibration because the rest 367

lack reliable input information. The 84 pavement sections are further divided into a calibration 368

set of 42 sections and a validation set of 42 sections. This half-half calibration-validation 369

division scheme can be used because many of the Superpave projects include multiple sections, 370

and with very minor change in the environmental conditions the sections in the same project 371

can be considered as random replica. 372


The rutting data of the selected pavement sections were retrieved from MTO’s PMS-2 373

system. Although MTO has started to collect rut depth data since 2002, the data collection 374

technology has undergone a significant change in 2012. Starting in 2012, the rut depth was 375

collected using Fugro Roadware’s ARAN 9000 automated pavement data collection system. 376

ARAN 9000 contains a Laser XVP that uses two synchronized, laser-based devices to measure 377

the transverse profile of a 4.1 m (13.5 ft) lane width, with a lateral resolution of approximately 378

1,280 points. The rut depth measure accuracy is reported to be 1 mm [5], which represents a 379

significant improvement from the previous rut depth measurement system. For this reason, 380

only the rutting data of Year 2012 were used in the local calibration. This type of local 381

calibration is called cross-sectional calibration because only one-year of data are used. This is 382

in contrast with the so-called longitudinal calibration in which the multiple-year longitudinal 383

histories of rutting are used to track the prediction trend. Although the rutting data used in the 384

study were collected only in 2012, the data covers a wide range of pavement age from 1 year 385

to 11 years. Therefore, it can be stated that the rutting data have a good life-cycle 386

representation. 387

The local calibration method developed in this study was also applied to the calibration of 388

Marshall-mix sections in the previous database developed by Jannat [4]. The database includes 389

10 new/reconstruction sections and 19 rehabilitated sections. The 29 sections were divided into 390

a calibration set of 19 sections (mixed of new and rehabilitation sections) and a validation set 391

for the remaining. The same input data collection protocol for the Superpave database was 392

employed, except that the rutting data of the Marshall-mix sections were collected over the 393

years between 2002 and 2010. Note that the precision of the rut depth measurement technology 394

was not as good as the Laser XVP after 2012. This will affect the local calibration results that 395

are to be discussed subsequently. 396

CALIBRATION RESULTS & DISCUSSION 397

Results for Superpave Sections 398

The cross-sectional calibration was performed on 42 Ontario Superpave pavement sections by 399

comparing the observed and predicted rut depth in the year 2012. As described previously, the 400

calibration involves dual tasks: eliminate bias and minimize RSS. Initialized with the default 401

value 1.0 for all of the three local calibration factors, the bias elimination process gives the 402

following result: 403

𝛽𝐴𝐶 = 4.1565, 𝛽𝐺𝐵 = 0, 𝛽𝑆𝐺 = 0.1452 with |Bias| = 0 and RSS = 48.55; 404

whereas the RSS minimization yields: 405

𝛽𝐴𝐶 = 4.5679, 𝛽𝐺𝐵 = 0, 𝛽𝑆𝐺 = 0.1299 with |Bias| = 1.06 and RSS = 48.43. 406


It has to be pointed out that both processes are actually sensitive to the initial value fed into the 407

optimizer. For example, given another set of initial value, the bias elimination process ends up 408

with: 409

𝛽𝐴𝐶 = 0.9628, 𝛽𝐺𝐵 = 0.6310, 𝛽𝑆𝐺 = 0.0295 with |Bias| = 0 and RSS = 141.5, 410

which is drastically different than the previous result. This is explained by the indeterminacy 411

induced by the unknown layer contribution to rutting. Nevertheless, although both solutions 412

successfully eliminate the bias, the RSS is very different. Therefore, only the first solution is 413

considered a valid result. 414

But the results from the bias elimination and RSS minimization are still very different. To 415

decide which one is better, the constrained method described previously is used to construct the 416

Pareto efficiency frontier. Specifically, the two-objective optimization is converted to a single-417

objective optimization that minimizes the RSS while maintaining the nonnegative constraints 418

in Eq. (8) and adding an additional constraint that the absolute bias must be less than or equal 419

to some prescribed number. Since the previous two extreme cases provide the range of the bias 420

from 0 to 1.06, the prescribed number in the bias constraint can be set to be 0.1, 0.2, 0.3, 0.5 421

and 0.8. Solving these constrained optimization problems yields different solutions with the 422

minimized RSS. Plotting the minimized RSS against the prescribed bias, one obtains the 423

efficiency frontier of the two-objective optimization problem shown in FIGURE 4(a). FIGURE 424

4(b) shows the corresponding curve for the validation dataset using the solution from the 425

calibration results. 426

427

FIGURE 4: The efficiency frontiers of the two-objective calibration process 428

429

Both curves in Figure 4 suggest that the bias and RSS are two incompatible objectives: 430

decreasing one will necessarily increase the other. However, the sensitivities are different. 431

While the total bias of the calibration set increases from 0 to 1 and above, the total RSS reduces 432

by only 0.12, which is really negligible. Similar observation is made in the validation set. Also 433

48.42

48.44

48.46

48.48

48.5

48.52

48.54

48.56

48.58

0 0.2 0.4 0.6 0.8 1 1.2

RSS

(m

m2 )

Total Bias (mm)

(a) Calibration

53.35

53.4

53.45

53.5

53.55

53.6

53.65

53.7

53.75

53.8

1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9

RSS

(m

m2 )

Total Bias (mm)

(b) Validation


because bias is more important than RSS for design, it is concluded that the first solution is 434

taken as the final result of the cross-sectional local calibration for Ontario’s Superpave sections. 435

The corresponding standard deviation of residuals is estimated to be 1.10 mm, which is very 436

close to the measurement precision (1.0 mm) of the Laser XVP in ARAN 9000. 437

To validate, the corresponding mean bias and standard deviation of residuals of the 438

validation data are -0.03 mm and 1.16 mm. A simple F-test for the standard deviations of the 439

calibration and validation data provides a 𝑝 value of approximately 37%. This shows good 440

validation of the result. 441

442

FIGURE 5: Predicted versus observed rut depth for the Superpave sections 443

444

FIGURE 5 shows the scatterplot of the predicted versus the observed rut depth for 445

calibration and validation sets. Both sets of data showed a similar range of variation, and both 446

are scattered around the line of equality. 447

Results for Marshall-Mix Sections 448

Similar calibration and validation analyses were performed for the Marshall-mix sections with 449

preset exponent values 𝛽𝑁 = 0.6262 and 𝛽𝑇 = 1.0. Interestingly, very similar efficient frontier 450

curves are obtained as we have seen in for the Superpave sections. There are also two major 451

differences: 452

(1) The optimal scaling calibration factors are set at 𝛽𝐴𝐶 = 10.394, 𝛽𝐺𝐵 = 0.7116 and 453

𝛽𝑆𝐺 = 0. This is very different from the Superpave results in which 𝛽𝐺𝐵 is found to 454

be zero. Further discussion about this difference is made in the next subsection. 455

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Pre

dic

ted

ru

t d

ep

th (

mm

)

Observed rut depth (mm)

Calibration

Validation


(2) The resulted standard deviations of the residuals are greater than those for Superpave 456

sections. For the calibration sections, the standard deviation is 1.88 mm, whereas the 457

value increases slightly to 2.03 mm for the validation sections. Recall that the 458

Marshall-mix sections had the latest rut depth measurements in 2010, for which the 459

old-generation of measurement technology was used. The difference in the 460

measurement precision explains the difference in the standard deviation. 461

The calibration results are also well validated. The calibrated models yield very small bias 462

in the validation sections. An 𝐹 test for the two variances of the residuals gives a 𝑝 value of, 463

coincidently, also 37%. This again shows good validation of the calibration outcomes. 464

The local calibration results are comparable to, if not better than, the global calibration 465

results. Although the Ontario local calibration includes a smaller sample size, the standard 466

deviations achieved are close to the precision of the measurement technology. For both the 467

Superpave and Marshall-mix sections, the large overprediction of the global model has been 468

eliminated through the local calibration. 469

Discussions 470

Several interesting issues are discussed below. First, it has to be emphasized that the zero 𝛽𝑆𝐺 471

for Marshall-mix sections and the zero 𝛽𝐺𝐵 for the Superpave sections both are the result of the 472

nonnegative constraint posed on the calibration factors, as described in Eq. (8). Should this 473

constraint be removed, some negative values would be obtained, which does not make physical 474

sense, even though the negative values would bring the RSS to a further lower level. However, 475

the reason why for Marshall-mix roads 𝛽𝑆𝐺 is zero and for Superpave roads 𝛽𝐺𝐵 is zero is not 476

clear. This clearly invites a further study. Forensic investigations of a few pavement sections 477

would help address this issue. On the other hand, this vast difference of the calibrated models 478

for the two AC materials indicates that these two types of pavements have to be calibrated 479

separately. 480

Second, the percentage contribution of different layers to the total surface rutting is an 481

important indicator for the validation of local calibration results. For Marshall-mix pavements, 482

the AC layer contribution varies from 40% to 84% with an average of 60%, whereas in 483

Superpave pavements, the AC layer accounts for 29% to 62% of the total rut with an average 484

contribution of 47%. The greater contribution of the AC layer in Marshall-mix roads is 485

attributed to the greater 𝛽𝐴𝐶 value in this type of roads. This result seems reasonable, as the 486

Superpave AC is expected to be more rutting resistant than the Marshall-mixes. Moreover, 487

Salama et al. (2006) calibrated the VESYS mechanistic-empirical rut model and then used the 488

calibrated model to predict average layer contribution to rutting in 43 SPS-1 pavement sections 489

from the LTPP database [15]. On average 57% of the rutting came from the AC layer, and 43% 490


from the unbound materials. Zhou and Scullion (2002) studied the Accelerated Loading 491

Facility-Texas Mobile Load Simulator data and found the AC layer contribution was about 68% 492

on average [16]. 493

Finally, as mentioned earlier, this study represents a cross-sectional local calibration. 494

Although the calibration data covers a fairly wide range of pavement age (1 to 11 years), it is 495

interesting to check if the calibrated model is able to capture the life-cycle rutting trend for a 496

specific pavement section. To this end, the four sections shown in FIGURE 1 are evaluated 497

again using the calibrated models. The predicted results are depicted as broken lines in 498

FIGURE 1. It is clear that both the calibrated models predict the trend very well for both the 499

Marshall-mix and Superpave sections. 500

CONCLUSIONS 501

The study focuses on the location calibration of rutting models and covers both the Superpave 502

and Marshall-mix sections that have been used in the roads under the jurisdiction of the MTO. 503

The calibration method is featured with a pre-fixed set of traffic and temperature exponents of 504

the AC rutting mode. The two exponent calibration factors are determined based on a series of 505

secondary analyses of the results from the recalibration study of NCHRP 9-30A. The 506

calibration and validation results show that although the traffic and temperature exponents can 507

take the same values for the Superpave and Marshall-mix roads, the scale calibration factors 508

actually differ significantly between the two asphalt materials. With the common exponent 509

factors (𝛽𝑁 = 0.6262 and 𝛽𝑇 = 1.0), the three scale calibration factors are found to be as 510

follows: 511

For Superpave roads: 𝛽𝐴𝐶 = 4.1565, 𝛽𝐺𝐵 = 0.0004, 𝛽𝑆𝐺 = 0.1452 with standard 512

deviation of residuals equal to 1.10 mm; 513

For Marshall-mix roads: 𝛽𝐴𝐶 = 10.394, 𝛽𝐺𝐵 = 0.7116 and 𝛽𝑆𝐺 = 0 with the standard 514

deviation being 1.88 mm. 515

Although Marshall-mix asphalts are no longer used in new road construction in Ontario, 516

the existing Marshall-mix asphalts are often part of the surface layer of the overlay or other 517

types of rehabilitated pavements. As the AASHTO software allows for layer-specific transfer 518

models, the different AC rutting models for Superpave and Marshall-mix materials may further 519

improve the prediction accuracy of the mechanistic-empirical approach. 520

ACKNOWLEDGEMENT 521

This research is funded by a grant from the MTO under the Highway Infrastructure 522

Innovation Funding Program. The financial support of this organization is highly appreciated. 523


REFERENCES 524

1. NCHRP, Guide for Mechanistic Empirical Design of New and Rehabilitated Pavement 525

Structures, 2004: ARA, Inc., ERES Division 505 West University Avenue Champaign, 526

Illinois 61820. 527

2. Brown, S.F., M.R. Thompson, and E.J. Barenberg, Research Results Digest 307, in Research 528

Results Digest, National Cooperative Highway Research Program 2006. 529

3. Von Quintus, H.L., et al., NCHRP REPORT 719 Calibration of Rutting Models for 530

Structural and Mix Design, 2012, AASHTO: Washington, D.C. 531

4. Jannat, G.E., Database Development for Ontario's Local Calibration of Mechanistic-532

Empirical Pavement Design Guide (MEPDG) Distress Models, in Department of Civil 533

Engineering2012, Ryerson University. 534

5. Fugro Roadware, Laser XVP, 2013: http://www.roadware.com/related/Laser-535

XVP_2014.pdf. 536

6. Jannat, G., Database Development for Ontario’s Local Calibration of Mechanistic-537

Empirical Pavement Design Guide (MEPDG) Distress Model, 2012, Ryerson University. p. 538

163. 539

7. Jannat, G.E., et al., Database Development for Ontario's Local Calibration of the MEPDG 540

Distress Models for Flexible Pavements in The 9th International Transportation Specialty 541

Conference, CSCE2012: Edmonton, AB. 542

8. Jannat, G.E., X.-X. Yuan, and M. Shehata, Development of regression equations for local 543

calibration of rutting and IRI as predicted by the MEPDG models for flexible pavements 544

using Ontario's long-term PMS data. International Journal of Pavement Engineering, 2015. 545

17(2): p. 166-175. 546

9. Waseem, A., Methodology Development and Local Calibration of MEPDG Permanent 547

Deformation Models for Ontarios Flexible Pavements in Department of Civil Engineering 548

2013, Ryerson University. 549

10. Waseem, A. and X.-X. Yuan, Longitudinal local calibration of MEPDG permanent 550

deformation models for reconstructed flexible pavements using PMS data. International 551

Journal of Pavement Research and Technology, 2013. 6(4): p. 304-312. 552

11. AASHTO, Guide for the Local Calibration of the Mechanical-Empirical Pavement 553

Design Guide, ed. Joint Technical Committee on Pavements2010, Washington DC: 554

American Association of State Highway and Transportation Officials. 555

12. Tarefder, R. and J.I. Rodriguez-Ruiz, Local Calibration of MEPDG for Flexible 556

Pavements in New Mexico. Journal of Transportation Engineering, 2013. 139(10): p. 981-557

991. 558

13. Banerjee, A., J.P. Aguiar-Moya, and J.A. Prozzi, Calibration of mechanistic-empirical 559

pavement design guide permanent deformation models. Transportation Research Record, 560

2009. (2094): p. 12-20. 561

14. Gautam, G.P., Local Calibration of MEPDG Rutting Models for Ontario's Superpave 562

Pavements, in Department of Civil Engineering2015, Ryerson University. 563

15. Salama, H., K. Chatti, and S. Haider, Backcalculation of permanent deformation 564

parameters using time series rut data from in-service pavements. Transportation Research 565

Record, 2006. 1949: p. 98-109. 566

16. Zhou, F. and T. Scullion, VESYS5 Rutting Model Calibrations with Local Accelerated 567

Pavement Test Data and Associated Implementation, 2002, The Texas A&M University. 568

http://www.roadware.com/related/Laser-XVP_2014.pdf

http://www.roadware.com/related/Laser-XVP_2014.pdf

Documents

1 LOCAL CALIBRATION OF THE MEPDG RUTTING …docs.trb.org/prp/16-3824.pdf · 1 LOCAL CALIBRATION OF THE MEPDG RUTTING MODELS FOR ONTARIO’S 2 FLEXIBLE ROADS: RECENT FINDINGS 3