Permanent deformation analysis of asphalt mixtures using soft computing techniques

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Abstract

This study presents two branches of soft computing techniques, namely multi expression programming (MEP) and multilayer perceptron (MLP) of artificial neural networks for the evaluation of rutting potential of dense asphalt-aggregate mixtures. Constitutive MEP and MLP-based relationships were obtained correlating the flow number of Marshall specimens to the coarse and fine aggregate contents, percentage of bitumen, percentage of voids in mineral aggregate, Marshall stability, and Marshall flow. Different correlations were developed using different combinations of the influencing parameters. The comprehensive experimental database used for the development of the correlations was established upon a series of uniaxial dynamic creep tests conducted in this study. Relative importance values of various predictor variables of the models were calculated to determine the significance of each of the variables to the flow number. A multiple least squares regression (MLSR) analysis was performed to benchmark the MEP and MLP models. For more verification, a subsequent parametric study was also carried out and the trends of the results were confirmed with the experimental study results and those of previous studies. The observed agreement between the predicted and measured flow number values validates the efficiency of the proposed correlations for the assessment of the rutting potential of asphalt mixtures. The MEP-based straightforward formulas are much more practical for the engineering applications compared with the complicated equations provided by MLP.

Research highlights

► New prediction models derived by means of multi expression programming (MEP) and multilayer perceptron (MLP) of artificial neural networks give reliable estimates of the flow number of dense asphalt-aggregate mixtures. The MEP-based straightforward formulas are much more practical for the engineering applications compared with the complicated equations provided by MLP. ► The proposed models correlate the flow number of Marshall specimens with the coarse and fine aggregate contents, percentage of bitumen, percentage of voids in mineral aggregate, Marshall stability, and Marshall flow. ► Sensitivity and parametric analyses were performed to verify the validity of the derived models. The obtained results were confirmed with the experimental study results and those of previous studies. ► The proposed MEP and MLP-based models perform superior than the developed regression models. ► The derived design equations can reliably be used as a quick check on solutions developed by more time consuming and in-depth deterministic analyses.

Introduction

Permanent deformation is one of the considerable load-associated distress types affecting the performance of asphalt concrete pavements. The repetitive action of traffic loads results in accumulation of permanent deformations in asphalt pavements (Kaloush, 2001). One of the principal causes of pavement rutting is the permanent deformation. Rutting in asphalt pavement develops progressively with increasing numbers of load application. It usually appears as longitudinal depression in the wheel paths accompanied by small upheavals to the side (Pardhan, 1995). Rutting decreases the useful service life of the pavement and, by affecting vehicle handling characteristics, creates serious hazards for highway users (Alavi et al., 2010, Gandomi et al., 2010, Sousa et al., 1991). It can decrease drainage capacity of pavements resulting in accumulation of water. Rutting also causes a phenomenon called “Bleeding” where the asphalt binder rises to the surface resulting in a very smooth pavement. Another effect of rutting is the reduction in thickness of pavement which increases the occurrence of the pavement failure through fatigue cracking (Bahuguna, 2003). These depressions or ruts are of major concern for at least two reasons: (1) if the surface is impervious, the ruts trap water and hydroplaning is a definite threat particularly for passenger cars, and (2) as the ruts develop in depth, steering increasingly becomes difficult, leading to added safety concerns. Previous studies show that rutting can have remarkable impacts on trucks operational cost (Sousa et al., 1991). The above considerations indicate that rutting is the most harmful distress mechanism in asphalt pavements. According to a comprehensive survey, rutting was considered to be the most serious distress mechanisms in pavements, followed by fatigue cracking and then thermal cracking (FHWA, 1998). As a result, it is important to fully characterize the permanent deformation behavior of asphalt mixes under repeated loading and identify the problematic mixes before they are placed in roadways (Alavi, Ameri, et al., 2010; Sousa et al., 1991, Zhou et al., 2004).

Evaluation of the rutting potential of asphalt mix has been the focus of much research in pavement engineering over the last decades. Majority of the available permanent deformation models are empirical or semi-mechanistic with limited fundamental material characterization. Unsatisfactory correlations with actual field performance are the common result. Some of the empirical models are derived from limited sets of materials and environmental conditions. Thus, they lack robustness and are not transferable to other conditions. The available rutting evaluation procedures are generally categorized into three main groups: (1) mechanistic-empirical modeling approaches, (2) advanced constitutive modeling approaches, and (3) development of a simple performance test to identify the rutting potential of mixtures during design based on measured fundamental engineering properties and response (Alavi, Ameri, et al., 2010; Kim, 2008, Chap. 11).

The mechanistic-empirical procedures for the rutting prediction couple mechanistic computations of pavement stresses and strains with empirical predictions of the consequent rutting. The earliest mechanistic-empirical rutting models explicitly considered only the strains in the subgrade (e.g., Shook, Finn, Witczak, & Monismith, 1982). Chen, Zaman, and Laguros (1994) provided concise summaries of the evolution of early models for predicting the number of cycles to permanent deformation failure as a function of the vertical compressive strain at the top of the subgrade. Timm and Newcomb (2003) adapted a new model of the form of the earliest models for predicting the asphalt rutting. Permanent strain models are a division of the mechanistic-empirical models by which the permanent vertical compressive strain at the mid-thickness of an asphalt sublayer is related to the number of load cycles, temperature, induced stress level, and other parameters. One of the earliest permanent strain models was that implemented in the VESYS program by different researchers (e.g., Kenis, 1977). Permanent to resilient strain ratio models are another class of the mechanistic-empirical models. The rationale for the permanent to resilient strain ratio models is essentially to consolidate some of the influences of temperature and stress level. Both of these parameters influence the resilient elastic and permanent strains. The permanent strains are normalized with the elastic strains to capture most of the temperature and stress effects. The asphalt rutting model implemented in the NCHRP Project 1–37A mechanistic-empirical design methodology (NCHRP, 2004) is based on this concept. The model has its origins in an extensive laboratory study by Leahy (1989) of the repeated load permanent deformation response of several asphalt concrete specimens. Kaloush (2001) further improved the robustness of the rutting model by combining Leahy’s original data with very large number of repeated load permanent deformation test results. Among the mechanistic-empirical procedures, regression models are similar to the permanent strain and strain ratio models since they usually have some mechanistic content such as a computed strain or deflection level (Alavi, Ameri, et al., 2010; Kim, 2008). Many other terms are also included to account for mixture characteristics, environmental variables, and other factors. The most well known of the regression approaches are the Highway Development and Management Model-III (HDM-III) rutting performance models (Kannemeyer & Visser, 1995).

The overall accuracy and robustness of the mechanistic-empirical rutting models still rely heavily upon the quantity and quality of the empirical data used for calibrating the empirical distress model component. Fully mechanistic distress prediction overcomes this limitation. This requires much more sophisticated constitutive models for asphalt concrete behavior (Alavi, Ameri, et al., 2010; Kim, 2008). Recently, significant efforts have been made on material models that capture the viscoelastic, viscoplastic, and damage response components needed to simulate the behavior of asphalt concrete over its full range of temperatures, loading rates, and stress conditions. These models are implemented into three-dimensional nonlinear finite element codes and applied to realistic test and field scenarios. Gibson, Schwartz, Schapery, and Witczak (2003) and Gibson (2006) proposed one approach toward viscoplastic modeling of asphalt concrete in compression in combination with a Schapery-type viscoelastic continuum damage model (Schapery, 1999). Many researchers also applied the Schapery’s model to various aspects of the asphalt concrete behavior (e.g., Chehab, Kim, & Witczak, 2004). The limitation of the finite element-based models is that they are sensitive to the individual cases. Also, a prior knowledge about the nature of the relationships between the data is needed to develop these models.

Another important element in the design of the rut-resistant pavements is screening of asphalt mixtures for the rut susceptibility during mix design. The time to tertiary flow failure is thought to be a good indicator of the rutting resistance of a given mixture (Alavi, Ameri, et al., 2010; Kim, 2008). This can be quantified via the flow number as measured in a repeated load permanent deformation test. Dynamic creep test is found to be one of the best methods for assessing the permanent deformation potential of asphalt mixtures (Kaloush & Witczak, 2002). The curve of accumulated strain against number of load cycles is the most important output of the dynamic creep test. Witczak, Kaloush, Pellinen, El-Basyouny, and Von Quintus (2002) defined the flow number as loading cycle number where tertiary deformation starts. The flow number is more analogous to field conditions since loading of pavement is not continuous. It can be used to identify a mixture’s resistance to the permanent deformation by measuring the shear deformation that occurs due to haversine loading (Williams, Robinette, Bausano, & Breakah, 2007). The dynamic creep test is a sensitive and costly test. Thus, it is not always possible to conduct the test. Therefore, developing a relationship between the flow numbers obtained from the dynamic creep test and parameters from the Marshall mix design leads to considerable savings in construction cost and time (Alavi, Ameri, et al., 2010; Gandomi et al., 2010).

Several alternative computer-aided data mining approaches have recently been developed. An instance is pattern recognition systems. These systems learn adaptively from experience and extract various discriminators. Artificial neural networks (ANNs) (Haykins, 1999) are one of the most widely used pattern recognition methods. There have been some researches with the specific objective of applying ANNs to the evaluation of the asphalt pavements performance characteristics. Tarefder, White, and Zaman (2005) constructed ANN-based models to determine a mapping associating mix design and testing factors of asphalt concrete samples with their performance in conductance to flow or permeability. Recently, Tapkin, Cevik, and Usar (2009) utilized ANN for the prediction of the accumulated strain values obtained at the end of repeated creep tests for polypropylene (PP) modified asphalt mixtures. Xiao, Amirkhanian, and Hsein Juang (2009) used a multilayer feed-forward ANN to predict the fatigue life of rubberized asphalt concrete mixtures containing reclaimed asphalt pavement. Ceylan, Schwartz, Kim, and Gopalakrishnan (2009) successfully applied ANNs to the estimation of dynamic modulus of hot-mix asphalt. In spite of the successful performance of ANNs, they usually do not give a deep insight into the process which they use the available information to obtain a solution. In the present study, the approximation ability of one of the most widely used ANN architecture, namely multilayer perceptron (MLP) (Cybenko, 1989) is investigated. In order to provide a better form of relationships between input and output data, the derived MLP models are expressed in explicit forms.

Genetic programming (GP) (Banzhaf et al., 1998, Koza, 1992) is another alternative approach for the analysis of the rutting potential. GP may generally be defined as a supervised machine learning technique that searches a program space instead of a data space. Many researchers have employed GP and its variants to find out any complex relationships between the experimental data (e.g., Cevik and Cabalar, 2009, Cevik, 2007, Gandomi, Alavi et al., 2009, Johari et al., 2006). Recently, Gandomi et al. (2010) developed new models to predict the flow number of asphalt mixtures utilizing gene expression programming. Also, Alavi, Ameri, et al. (2010); combined the GP and simulated annealing algorithms to obtain new prediction equations for the flow number of Marshall specimens. Multi expression programming (MEP) (Oltean & Dumitrescu, 2002) is a recent variant of GP using a linear representation of chromosomes. MEP has a special ability to encode multiple computer programs of a problem in a single chromosome. Applications of MEP to civil engineering tasks are quite new and restricted to a few areas (e.g., Alavi and Gandomi, in press, Alavi, Gandomi and Sahab et al., 2010, Baykasoglu et al., 2008).

In this study, the MEP and MLP techniques are utilized to evaluate the rutting potential of dense asphalt mixtures in the form of the flow number. Generalized relationships were obtained to correlate the flow number to the particle size distribution of natural soil, bitumen, voids in mineral aggregate, Marshall stability, and Marshall flow. The proposed correlations were developed based on several uniaxial dynamic creep tests on standard Marshall specimens conducted at Iran University of Science and Technology civil engineering laboratories. The experimental database covers a wide range of aggregate gradation. A linear regression analysis was performed to benchmark the MEP and MLP-based correlations.

Section snippets

Rutting mechanisms characterization

Rutting can take place in different times of pavement service life. Basically, there are two mechanisms for rutting. The first mechanism that happens in the first years of pavement life is “initial rutting”. This mechanism is caused by the densification of asphalt mixture especially for loosely compacted pavements. The initial rutting is followed by the second mechanism called “shear deformation”. This mechanism, also named “secondary rutting”, is the primary mechanism of rutting in well

Experimental study

A comprehensive research study was conducted by NCHRP to develop a simple mechanical test to supplement the Superpave volumetric method of mixtures design. Among the five laboratory tests investigated, the dynamic creep test had very good correlation with measured rut depth and a high capability to estimate the rutting potential of asphalt layers (Kaloush & Witczak, 2002). On the basis of the results of the previous research (Alavi et al., 2010, Kaloush and Witczak, 2002), the dynamic creep

Soft computing techniques

Soft computing includes evolutionary algorithms and all of their different branches combined with ANNs and fuzzy logic. Soft computing techniques have wide-ranging applications as important tools for approximating the nonlinear relationship between the model inputs and corresponding outputs. Developments in the computer hardware during the last two decades have made it much easier for these techniques to grow into more efficient frameworks. In addition, it has been proven that several soft

Development of models for rutting potential evaluation and analysis

Evaluation of the field rutting potential of asphalt mix has traditionally been a complicated task. Rutting is mainly influenced by several factors. An element of asphalt layer subjected to traffic loading transfers the load from the surface to underlying layers through intergranular contact and resistance to flow of the binder matrix. The stress pattern induced in a three-dimensional pavement structure due to traffic loading is complex. The stresses are transient and change with time as the

Comparison of the rutting potential predictive models

As described above, four different formulas were obtained for the assessment of the flow number of asphalt mixtures by means of MEP and MLP. Overall performance of the MEP, MLP and MLSR-based models on the whole of data are summarized in Table 6. Comparisons of the flow number predictions obtained by these models are also visualized in Fig. 18. No rational model to predict the flow number of asphalt mixes has been developed yet that would encompass the influencing variables considered in this

Parametric analysis

For further verification of the models, a parametric analysis was performed in this study. The main goal is to find the effect of each parameter on the flow number (Fn). Fig. 19 presents the predicted values of the flow number obtained by the proposed MEP and MLP-based correlations as a function of each parameter. The tendency of the Fn predictions to the variations of C/S, FP (%), BP (%), VMA (%), and M/F can be determined according to these figures.

As can be seen in Fig. 19(a) and (b), Fn

Conclusions

In this study, a robust variant of GP, namely MEP and MLP of ANNs were utilized to assess the flow number of asphalt-aggregate mixtures. Four different correlations were developed for the flow number prediction using different combinations of the affecting parameters. On the basis of an extensive trial study and literature review, the coarse aggregate to fine aggregate ratio (C/S), filler (FP), bitumen (BP), voids in mineral aggregate (VMA), and Marshall quotient (M/F) were identified to be

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