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Original Research Paper

Sensitivity analysis of longitudinal cracking on asphalt pavement using MEPDG in permafrost region

Chen Zhang a, Hainian Wang a'*, Zhanping You b, Biao Ma a

a Key Laboratory for Special Area Highway Engineering of Ministry of Education, Chang'an University, Xi'an 710064, China b Civil and Environmental Engineering Department, Michigan Technological University, Houghton 49931, USA

ARTICLE INFO

ABSTRACT

Article history: Available online xxx

Keywords:

Road engineering

Asphalt pavement

Mechanistic-Empirical Pavement

Design Guide

Sensitivity analysis

Sensitivity spectrum

Longitudinal cracking is one of the most important distresses of asphalt pavement in permafrost regions. The sensitivity analysis of design parameters for asphalt pavement can be used to study the influence of every parameter on longitudinal cracking, which can help optimizing the design of the pavement structure. In this study, 20 test sections of Qinghai—Tibet Highway were selected to conduct the sensitivity analysis of longitudinal cracking on material parameter based on Mechanistic-Empirical Pavement Design Guide (MEPDG) and single factorial sensitivity analysis method. Some computer aided engineering (CAE) simulation techniques, such as the Latin hypercube sampling (LHS) technique and the multiple regression analysis are used as auxiliary means. Finally, the sensitivity spectrum of material parameter on longitudinal cracking was established. The result shows the multiple regression analysis can be used to determine the remarkable influence factor more efficiently and to process the qualitative analysis when applying the MEPDG software in sensitivity analysis of longitudinal cracking in permafrost regions. The effect weights of the three parameters on longitudinal cracking in descending order are air void, effective binder content and PG grade. The influence of air void on top layer is bigger than that on middle layer and bottom layer. The influence of effective asphalt content on top layer is bigger than that on middle layer and bottom layer, and the influence of bottom layer is slightly bigger than middle layer. The accumulated value of longitudinal cracking on middle layer and bottom layer in the design life would begin to increase when the design temperature of PG grade increased.

© 2015 Periodical Offices of Chang'an University. Production and hosting by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://

creativecommons.org/licenses/by-nc-nd/4.0/).

* Corresponding author. Tel.: +86 29 82334798. E-mail address: wanghnchd@gmail.com (H. Wang).

Peer review under responsibility of Periodical Offices of Chang'an University. http://dx.doi.org/10.1016/jotte.2015.01.004

2095-7564/© 2015 Periodical Offices of Chang'an University. Production and hosting by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Cracking is one of the most important types of distresses in asphalt pavement, especially in permafrost regions, and the performance and service quality of asphalt pavement descend because of cracking (Zhu et al., 2013). In many countries, the cracking performances are incorporated into pavement design and maintenance systems (Teltayev, 2014). Therefore, conducting the multi-position research to the cracking based on various parameters and data statistics in permafrost regions has some prominent meanings. Lu et al. (2014) used three-dimensional finite element (FE) model of the tire tread rubber-block to describe the stress-strain field of the pavement with TDC, and discussed the effect law of fracture characteristics for the longitudinal crack affected by the multiple loading parameters simultaneously. The result found there was a nonlinear relationship between the equivalent stress intensity factor of the pavement and the load parameters. The longitudinal distance has a great influence on the equivalent stress intensity factor. Chou and Sheng (2014) focused on how the sunny-shady slope contributed to longitudinal crack formation under different mean annual air temperatures, roadbed surface materials, embankment heights and strikes in permafrost regions. The results show the mean annual air temperature and embankment height were the main factors to the longitudinal crack, and the longitudinal crack position was related to the shady-sunny slope effect. The greater the shady-sunny slope effect, the nearer the longitudinal crack position to the embankment sunny shoulder. Park et al. (2014) verified the capability of the layered viscoelastic pavement analysis for critical distresses (LVECD) model to capture crack initiation locations, propagation propensity, and cracking severity by comparing the simulation results with the field core observations and the field condition survey of in-service pavements in North Carolina. The result shows the agreement rate between the result of field core observations and field condition survey and the predicted LVECD simulation result is about 78% in terms of cracking direction and severity. Dong and Huang (2014) used Weibull hazard function to evaluate the influence of different factors on the crack initiation of resurfaced asphalt pavement with long-term pavement performance (LTPP) data. It was found that traffic level was a significant factor for all four types of cracks. High traffic level accelerated the initiation of cracking. Thick overlay delayed the initiation of cracking except for the non-wheel path longitudinal crack, which was mainly caused by poor construction technique. Total pavement thickness only retarded the initiation of wheel path longitudinal cracking. Through reviewing the most recent research of the cracking of asphalt pavement in domestic and foreign, the research was mainly based on cracking evaluation model, cracking variation trend, traffic impact analysis of cracking and so on. Very few studies on how a particular parameter such as air voids content or percent binder were investigated for cracking during the service life.

There is widely distribution of frozen soil over northwest China and Qinghai-Tibet Plateau. The region annual mean temperature is -2 °C to -7 °C, and it has about 8 months frost period every year. The annual precipitation is about 400 mm in

Fig. 1 - Research technical route.

this region, mainly during the period from June to September. Longitudinal cracking is the main distress of asphalt pavement in permafrost regions, and the research of longitudinal cracking analysis of material parameter is rarer. This research takes the Qinghai-Tibet Highway as an example, and adopts Mechanistic-Empirical Pavement Design Guide (MEPDG), which was developed recently through the National Cooperative Highway Research Program (NCHRP) 1-37A project, to study the development rule of longitudinal cracking in permafrost regions. The Latin hypercube sampling (LHS) technique (Wu et al., 2010), Excel solver and multiple regression analysis were applied to conduct a single factorial sensitivity analysis of longitudinal cracking on material properties parameters (Orobio, 2010).

An introduction of MEPDG

The NCHRP 1-37A project according to the observation result of 2200 LTPP test section in USA and development of the 2002 guide for design of new and rehabilitated pavement structures was completed in 2004. The MEPDG and its software were obtained from this project. This mechanistic-empirical pavement design procedure is based on mechanistic-empirical analysis of the pavement structure to predict the performance of the pavement under different sets of conditions (traffic, structure and environment). MEPDG takes into account the advanced modeling concepts and pavement performance models in performing the analysis and design of pavement (NCHRP, 2004).

The predictive equation used in the MEPDG to predict cracking in the asphalt mixtures is based upon a field calibrated statistical analysis of laboratory repeated load tests. The final model is listed in Eq. (1)

C = 10.56

1 + eci_c2lgD

where C is longitudinal cracking (m/km), D is fatigue damage, c1, c2 and c3 are calibration coefficients which vary with

different regions. Therefore, when MEPDG is applied to predict the cracking, the first step is to calibrate it.

3. Methodology

The flow chart of this study is listed in Fig. 1. 3.1. Data collection

Table 2 - Test matrix for sensitivity analysis.

Variable of each layer Unit Range

Air void % 3-8

Effective binder content % 3-6

Temperature range of PG grade "C High temperature: 46-70 °C

Low temperature: —34 °C

Note: The air void of each layer is local air void.

With the typical model of asphalt pavement with semi-rigid base in Qinghai-Tibet Highway, for example, the pavement structure is listed in Table 1. Sensitivity test matrix and input variable ranges (Tarefder and Sumee, 2011) are listed in Table 2.

3.2. Input parameters of MEPDG

Three hierarchical input levels are considered in MEPDG. Level 1 requires the direct measurement of the parameters, Level 2 allows the estimation of the parameters from regression equations or correlations, and Level 3 uses typical values. These levels classify the inputs based on the experience of designers on each parameter. Level 1 is the most accurate and Level 3 is the least accurate. This research focuses on sensitivity analysis which belongs to a qualitative analysis method. Therefore, Level 3 is selected.

Climate file of MEPDG mainly includes the temperature, wind speed, precipitation, the sunshine duration and the relative humidity. The key factor determining the occurrence, existence and change of permafrost is climatic condition, and the corresponding climatic data are summarized in Table 3 (Chou et al., 2008; Yang, 2013).

Based on the above climatic data, this study obtains the more detailed data through China meteorological data sharing service system and makes them into a data file which is similar to climate file of MEPDG.

For the design guide procedure, the traffic data describes with axle load spectrum. It mainly includes traffic volume adjustment factors, vehicle class distribution, traffic growth factors and axle load distribution factors. Because of the hostile environment conditions in Qinghai-Tibet Plateau, to collect the traffic data of Qinghai-Tibet Highway is very difficult. This study focuses on the sensitivity analysis of material parameters, therefore, the default values of traffic parameter in MEPDG are used here.

Table 1 - Pavement structure.

Pavement structure Thickness Gradation

(cm) (accumulate residual rate)

Top layer of asphalt 4 0%-32%-51%-8%

concrete (AC-16)

Middle layer of asphalt 5 5%-40%-62%-6%

concrete (AC-20)

Bottom layer of asphalt 6 8%-46%-68%-7%

concrete (AC-25)

Lime-fly ash stabilized 20

aggregate base

Lime-ash soil sub-base 25

Subgrade

LHS was employed for data sampling in Table 2 according to variable ranges and the number of runs was defined as 10 times the number of parameters. 100 runs were defined for structure in Table 1. The other general parameters in MEPDG are listed in Table 4.

It is worth mentioning that cracking is considered only taking place in the AC layers on semi-rigid base (Sheikhmotevali and Ameri, 2014).

3.3. Calibration of longitudinal cracking prediction model in MEPDG

For conducting more accurate factorial sensitivity analysis of longitudinal cracking on material properties parameters, this study takes 20 test sections of Qinghai-Tibet Highway as example, and the length of each section is 1 km, and the measured data of longitudinal cracking is the accumulative value per kilometer. The survey field is shown in Fig. 2.

The Excel solver method is used to calibrate the longitudinal cracking prediction model in MEPDG. Use the measured value and predicted value of MEPDG as comparability factors (Wang et al., 2013). Use Eq. (1) as relation function, and use the least sum of square error (LSSE) of comparability factor as objective function in this process. A part of the results are listed in Table 5.

It is worth mentioning that the initial calibration coefficients of longitudinal cracking prediction model in MEPDG are default values, c1 = 7, c2 = 3.5, c3 = 1000.

From Table 4, the calculated correction coefficients are c1 = 6.34, c2 = 3.72, c3 = 1000. Substitute calculated correction coefficients in Eq. (1) and obtain Eq. (2) as follow:

C = 10.56

1 e6.34-3.72lgD

This research verifies calibration result by linear fit method in Origin software, and the results are shown in Fig. 3.

From Fig. 3, the fitting coefficient R2 of measured value and MEPDG predicted value without calibration is 0.463225, and the fitting coefficient R2 of measured value and MEPDG predicted value with calibration is 0.812793. Therefore, the longitudinal cracking prediction model after calibration is more accuracy.

3.4. MEPDG and multiple regression analysis

For structure in Table 1, the LHS was used as inputs to run MEPDG and the sensitivity of input parameters on longitudinal cracking was analyzed using multiple regression analysis with standardized regression coefficients (SRC). The 150 runs

Table 3 - Summary of climatic data from 2003 to 2012 along the Qinghai-Tibet Highway.

Year Average Average wind Precipitation (mm) Sunshine Relative humidity (%)

temperature (°C) speed (m/s) duration (h)

2003 -6.4 5.8 251.5 2858 56.1

2004 -5.8 5.9 398.7 2788 59.6

2005 -5.2 6.1 249.1 3122 54.7

2006 -4.2 4.8 277.5 2921 60.4

2007 -4.5 4.6 266.8 2763 57.4

2008 -5.6 4.3 252.1 2814 56.3

2009 -4.4 3.9 264.7 3084 57.3

2010 -3.8 3.4 285.5 2911 54.7

2011 -4.4 3.5 369.1 2799 53.6

2012 -4.9 3.8 376.4 3031 58.9

defined in the LHS for parameters in Table 3 are inputs in MEPDG and run using the batch mode.

MEPDG was performed to validate the result of sensitivity analysis in multiple regression process with single factorial sensitivity analysis method. In single factorial sensitivity analysis, the value of one input variable was varied in the MEPDG at a time to determine if that input variable had significant impact on predicted performance. As a result, a smaller number of input variables and MEPDG runs were chosen from the full set of input variables for carrying out detailed sensitivity analysis. MEPDG software version 1.1 was used for sensitivity analysis.

4. Result and discussion

4.1. Single factorial sensitivity analysis

In order to validate the sensitivity of longitudinal cracking on material parameters, the single factorial sensitivity analysis method was used to calculate the sensitivity at first, that is, keeping other parameters constant, changing the value of sensitive parameters to validate the result of multiple regression analysis. The results are shown in Fig. 4.

Fig. 4 shows that compared with middle layer and bottom layer, the material property of top layer plays an important role in improving the longitudinal cracking performance of asphalt mixture (Zegeye et al., 2012). Fig. 4(a) shows the influence of air void on longitudinal cracking of asphalt pavement. The influence of air void on top layer is bigger than that on middle layer and bottom layer. When the air void is lower than 4%, the change of longitudinal cracking accumulated value is not obvious. When the air void is higher than 4%, the accumulated value of longitudinal cracking has a great increase, and the growth rate is higher than 40%. The reason is that when asphalt content is constant, the asphalt binder still

keeps strong force with smaller air void, and the fatigue resistance of asphalt mixture is still good. As the air void increases, the asphalt membrane tends to be thin, and the binding power and fatigue life also gradually decay, and finally cracks occur (Dave et al., 2011). Fig. 4(b) shows the influence of effective asphalt content on longitudinal cracking. The influence of effective asphalt content on top layer is bigger than that on middle layer and bottom layer, and the influence of bottom layer is slightly bigger than middle layer. This result is in accordance with the result of multiple regressions. The reason is that the lower effective asphalt content and the smaller aggregates size of surface layer result in thin asphalt membrane, and it indirectly increases the air void of asphalt mixture, and finally cracks occur (Xu, 2010). Fig. 4(c) shows the influence of PG grade on longitudinal cracking. Based on the range of values in designed specifications (CCCC Highway Consultants, 2004), the accumulated values of longitudinal cracking of middle layer and bottom layer in the design life have begun to increase when the designed temperature of PG grade increases. But for top layer, the accumulated value of longitudinal cracking decreases, and the sensitivity to longitudinal cracking is not obvious compared to that on middle layer and bottom layer (Tan et al., 2012).

4.2. Result of multiple regression analysis

In order to have sufficient knowledge of how a material parameter affects the cracking, this paper uses Statistical Product and Service Solutions (SPSS) software with longitudinal cracking as dependent variable and LHS data as independent variable for multiple regression analysis with 150 group data. The results are listed in Table 6.

The above result was obtained from SPSS software through stepwise analysis method with rejecting the invalid variables, and Rsqu value is 0.974, therefore, the result of regression is remarkable. There are unstandardized coefficients, B, the standard error of unstandardized coefficients and standardized coefficients in Table 6. The major indicator of this research to evaluate the sensitivity of material parameter is standardized coefficient. The higher absolute value of standardized coefficient is, the stronger influence is on cracking. Some parameters have positive values which illustrate that the parameter and cracking have the positive correlation, which means cracking increases with the increase of the parameter. Also, some parameters have negative value which

Table 4 - General input parameters of MEPDG.

Parameter Value Reliability

Design life 20 years 90%

Terminal IRI 2.72 m/km 90%

Longitudinal cracking 189.43 m/km 90%

Alligator cracking 25% 90%

Cracking (AC only) 6.35 mm 90%

(a) Longitudinal cracking in road (middle) (b) Longitudinal cracking in road

Fig. 2 - Survey field of Qinghai-Tibet Highway.

Table 5 - Partial calibration data of longitudinal cracking prediction model in MEPDG.

Value Predicted value by MEPDG Predicted value by MEPDG Correction Objective Target value without calibration with calibration coefficient function

123.35 130.1 124.63 6.33679 1.6384

156.25 150.3 159.32 3.7210033 9.4249

179.21 183.3 177.50 1000 2.9241

201.45 210.4 206.50 25.5025

236.80 220.4 230.54 39.1876

134.50 150.0 143.38 78.8544

146.87 140.3 148.87 4.0000

170.52 183.2 176.50 35.7604

200.34 211.4 205.65 28.1961

220.67 226.5 223.50 8.0089

illustrates that cracking decreases with the increase of the parameter.

As Table 6 shows, the air void of top layer had the most important effect on the longitudinal cracking. The effective binder content of top layer and PG grade of bottom layer followed. The three parameters in descending order of their effect weights on longitudinal cracking are air void, effective binder content and PG grade. As a result of primary examination, the longitudinal cracking has a positive correlation with air void and PG grade, and has a negative correlation with effective binder content. As shown in Fig. 5, the longitudinal cracking prediction result of MEPDG is compared with cracking

prediction result of multiple regression analysis, and the linear fitting is obtained. The result shows they have linear correlation.

4.3. Sensitivity spectrum of material parameter of cracking

In Section 4.1, the multiple regression analysis is used to process the predict data of MEPDG and determine the remarkable influence factor of longitudinal cracking. In Section 4.2, the single factorial sensitivity analysis with MEPDG is conducted, and the feasibility of using multiple regression

Measured value of longitudinal cracking (m/km) Measured value of longitudinal cracking (m/km)

(a) Without calibration (b) With calibration

Fig. 3 - Comparison of MEPDG without calibration and MEPDG with calibration.

Fig. 4 - Single factorial sensitivity analysis based on MEPDG.

analysis to determine the remarkable influence factor when applying the MEPDG software in sensitivity analysis of longitudinal cracking has been validated. Because of the consistent result in Sections 4.1 and 4.2, this section establishes the sensitivities spectrum of material parameter on longitudinal cracking based on the result in Table 6, as shown in Table 7.

In Table 7, the "+" represents the effect of this parameter on longitudinal cracking, and the more this symbol, the more the sensitivity. The "+" and "-" represent this parameter has positive correlation relationship or negative correlation relationship with longitudinal cracking, respectively. The blank space represents this parameter has no correlation relationship with longitudinal cracking. The effect of each parameter

on longitudinal cracking was divided into three grades, "+", "**" and "***". Table 6 lists the six most significant factors for longitudinal cracking, and the effect weights of these parameters from high to low are air void of top layer, effective binder content of top layer, PG grade of bottom layer, air void of bottom layer, effective binder content of bottom layer and PG grade of top layer based on the standardized coefficients of them. Therefore, the material parameters on level "***" are the air void of top layer and effective binder content of top layer. Similarly, the material parameters on level "**" are PG grade of bottom layer, air void of bottom layer, effective binder content of bottom layer and PG grade of top layer, and the

Table 6 - Result of regression analysis.

Model Unstandardized Standardized

coefficient coefficient

B Std. error

Constant 198.220 2.014

Air void of top layer 0.677 0.122 0.983

Effective binder content of -1.194 2.973 -0.009

bottom layer

PG grade of bottom layer 0.008 0.008 0.016

PG grade of top layer -0.536 0.074 -0.007

Effective binder content of -2.540 3.796 -0.083

top layer

Air void of bottom layer -1.223 0.203 -0.012

R = 0.996; Rsqu = 0.974; F = 678.2; P < 0.01.

Fig. 5 - Comparison of MEPDG and regression on longitudinal cracking prediction.

Table 7 - Sensitivity spectrum of material parameter.

Material parameter Longitudinal cracking

Air void of top layer Correlation +

Sensitivity

Air void of middle layer Correlation +

Sensitivity +

Air void of bottom layer Correlation +

Sensitivity

Effective binder content of top layer Correlation -

Sensitivity

Effective binder content of middle layer Correlation

Sensitivity +

Effective binder content of bottom layer Correlation -

Sensitivity

PG grade of top layer Correlation -

Sensitivity

PG grade of middle layer Correlation +

Sensitivity +

PG grade of bottom layer Correlation +

Sensitivity

material parameters on level "+" are effective binder content of middle layer, PG grade of middle layer and air void of middle layer, which are the least sensitive parameters on longitudinal cracking in this study. The sensitivity spectrum can be used to determine input level of parameter in MEPDG, and improve the prediction accuracy of longitudinal cracking.

5. Conclusions

The air void of top layer has the most important effect on the longitudinal cracking, the effective binder content of top layer and PG grade of bottom layer follow it. The three parameters in descending order of effect weights on longitudinal cracking are air void, effective binder content and PG grade.

The influence of air void on top layer is bigger than that on middle layer and bottom layer. When the air void is lower than 4%, the change of longitudinal cracking accumulated value is not obvious. When the air void is higher than 4%, the accumulated value of longitudinal cracking has a great increase, and the growth rate is higher than 40%.

The influence of effective binder content on top layer is bigger than that on middle layer and bottom layer, and the influence of bottom layer is slightly bigger than middle layer. This result is in accordance with the result of multiple regressions.

Based on the range of values in design specifications, the accumulated values of longitudinal cracking of middle layer and bottom layer in the design life have begun to increase when the designed temperature of PG grade increases. But for top layer, the accumulated value of longitudinal cracking decreases, and the sensitivity to longitudinal cracking is not obvious compared to that on middle layer and bottom layer.

Multiple regression analysis can determine the remarkable influence factor more efficiently and process qualitative analysis when applying the MEPDG software in sensitivity analysis of longitudinal cracking in permafrost regions.

Acknowledgments

This research is supported by research project of Ministry of Science and Technology of China (2014BAG05B04), research project of Ministry of Transport of China (2012319495030) and the Special Fund for Basic Scientific Research of Central Colleges, Chang'an University (CHD2013G3212003).

REFERENCES

CCCC Highway Consultants, 2004. JTG D50-2004, Specifications for Design of Highway Asphalt Pavement. China Communications Press, Beijing.

Chou, Y.L., Sheng, Y., 2014. Longitudinal crack formation mechanism of embankment in permafrost regions. Electronic Journal of Geotechnical Engineering 19, 5961-5981.

Chou, Y.L., Sheng, Y., Wei, Z.M., et al., 2008. Calculation of temperature differences between the sunny slopes and the shady slopes along railways in permafrost regions on Qinghai-Tibet Plateau. Cold Regions Science and Technology 53 (3), 346-354.

Dave, E.V., Behnia, B., Ahmed, S., et al., 2011. Low temperature fracture evaluation of asphalt mixtures using mechanical testing and acoustic emissions techniques. Journal of the Association of Asphalt Paving Technologists 80, 193-220.

Dong, Q., Huang, B.S., 2014. Evaluation of influence factors on crack initiation of LTPP resurfaced-asphalt pavements using parametric survival analysis. Journal of Performance of Constructed Facilities 28 (2), 412-421.

Lu, Y.J., Yang, S.P., Wang, J.X., 2014. Research on pavement longitudinal crack propagation under non-uniform vehicle loading. Engineering Failure Analysis 42, 22-31.

NCHRP, 2004. Guide for Mechanistic-empirical Design of New and Rehabilitated Pavement Structures. National Research Council, Washington DC.

Orobio, A., 2010. Sensitivity Analysis of Flexible Pavement Performance Parameters in the Mechanistic-empirical Design Guide (PhD thesis). West Virginia University, Morgantown.

Park, H.J., Eslaminia, M., Kim, Y.R., 2014. Mechanistic evaluation of cracking in in-service asphalt pavements. Materials and Structures 47 (8), 1339-1358.

Sheikhmotevali, A.H., Ameri, M., 2014. Application of bitumen rheological parameters to predict thermal cracking behavior of polymer modified asphalt mixture. Construction and Building Materials 66, 259-267.

Tan, Y.Q., Zhang, L., Xu, H.N., 2012. Evaluation of low-temperature performance of asphalt paving mixtures. Cold Regions Science and Technology 70, 107-112.

Tarefder, R.A., Sumee, N., 2011. Evaluating sensitivity of pavement performance to mix design variable in MEPDG. In: Proceedings of 2011 GeoHunan International Conference Road Materials and New Innovations in Pavement Engineering, Changsha, 2011.

Teltayev, B., 2014. Evaluation of low temperature cracking indicators of hot mix asphalt pavement. International Journal of Pavement Research and Technology 7 (5), 343-351.

Wang, H.N., Zhang, C., You, Z.P., et al., 2013. Calibration of rutting prediction model in MEPDG based on mathematical statistics method. Journal of Chang'an University: Natural Science Edition 33 (6), 1-7.

Wu, Z.J., Wang, S.L., Ge, X.R., 2010. Application of Latin hypercube sampling technique to slope reliability analysis. Rock and Soil Mechanics 31 (4), 1047-1054.

Xu, A.H., 2010. A discussion about the relation between longitudinal embankment cracks and road trend in permafrost regions. Journal of Glaciology and Geocryology 32 (1), 121-125.

Yang, J.F., 2013. Study on the Changes of Moisture and Heat Impact on the Longitudinal Cracks of Subgrade in Qinghai-tibet Highway (PhD thesis). Chang'an University, Xi'an.

Zegeye, E., Le, J.L., Turos, M., et al., 2012. Investigation of size effect in asphalt mixture fracture testing at low temperature. Journal of the Association of Asphalt Paving Technologists 81, 219-238.

Zhu, D.P., Zhang, J.Z., Chen, J.B., et al., 2013. Experiment on road performance of diatomite modified asphalt mixture in permafrost regions. China Journal of Highway and Transport 26 (4), 23-28.