Predicting Marshall parameters of flexible pavement using support vector machine and genetic programming
Graphical abstract
Introduction
The overall objective of mixture design is to determine the aggregate gradation and the amount of asphalt binder so that the mixture has the following characteristics [1] (1) sufficient asphalt content to ensure durability, (2) sufficient mixture stability to sustain traffic without distortion, (3) sufficient air voids in the total mix to prevent bleeding and loss of stability as a result of increased ambient temperature and traffic, (4) maximum void content to limit the permeability of water and air into the pavement, (5) sufficient workability to permit efficient placement of the mix without segregation, without sacrificing stability and performance, and (6) aggregate texture and hardness properties to provide skid resistance in unfavorable weather conditions.
Various methods have been proposed for the mix design of asphalt mixture, such as (1) Marshall method, which is a design procedure developed by Bruce Marshall of the Mississippi Highway Department in the 1930 s [1], (2) Modified Marshall method, which is an improved and modified the Marshall mix design procedure, which was developed by the US Corps of Engineers through extensive research and correlation studies in the 1950s, (3) Hveem mix design developed by Francis Hveem in the 1930s, which is similar to the Marshall mix design method. Meanwhile, Hveem introduced the kneading compactor and recognized the need to have a mechanical test to evaluate the performance of the mix, and (4) Superpave mix design method which uses a gyratory compactor to prepare the test specimens while measuring the volumetric properties to determine the optimum binder content. Before the development of the Superpave mix design in the 1990 s, approximately 75 percent of the state highway agencies were using the Marshall mix design.
The most common type of pavement used around the world is asphalt concrete pavement. Currently, Marshall mix design and modified Marshall mix design have been widely used in Pakistan, which is recommended by asphalt institute MS-2 respective of the general specifications of National Highway Authority (NHA) [2]. The Marshall mix design is a function of parameters including grading aggregates characteristics, the percentages, and types of bitumen. The analytical mathematical relationship for the variables and the Marshall mixture parameters are not presented so far, which are usually determined by several trial and error. Also, important features of the Marshall mix design that need to be determined include Marshall stability, the flow, and Marshall quotient. Stability is the most important property of asphalt mixture in the wearing course design, which reflects the ability of the pavement in terms of resisting shoving and rutting. The flow of the asphalt mixture is regarded as the opposite property of stability; it determines the elastic and plastic properties of asphalt concrete. Flow also represents the ability of the asphalt pavement for adjusting the gradual settlements and movements in the subgrade without cracking [3], [4]. The Marshall quotient is the ratio of the stability to the flow, Marshall quotient is the measurement of the material’s resistance to permanent deformation [5].
Marshall mixture design in the laboratory is time-consuming, costly process, and required skillful operators. On the other hand, only the stability and the flow values of the specimens can be obtained physically at the end of the Marshall mix design test. Other parameters, such as the specific gravity of the mixture, theoretical specific gravity, voids in mineral aggregate (VMA), voids filled with asphalt (VFA), and air voids (Va) can only be calculated by extra calculations. Therefore, the rest of the parameters can be determined by mathematical calculations given parameters of Marshall stability and flow of a standard mix.
The Marshall parameters specimen testing is an extremely complex procedure in traditional ways [5], which is required to be improved by state-of-the-art technologies, such as Artificial Intelligence (AI) approaches. Artificial Neural Networks (ANNs) can be a pattern recognition system that determines the pattern between different parameters, which is a computational approach that is increasingly used in the development of predictive models. The fundamental unit of an ANNs is the artificial neuron [6]. The function of the artificial neuron, which mimics the biological term, is to process input signals and modulate its own response through an activation function, which is called the transfer function, to determines the interruption of transmission of the outgoing impulse. Therefore, several studies have been conducted to evaluate the performance of the asphalt mixtures using ANNs. For example, in the study by Baldo et al [7], the laboratory data for modeling of hot mix asphalt (HMA) parameters for predicting the stiffness modulus, Marshall stability, and Marshall quotient were evaluated on ANNs multiple layer structures, which employed k-fold validation approaches to conduct the training of ANNs models. It was verified that developing multiple hidden layer structures depending on mechanical parameters can be very useful for the prediction of HMA parameters.
In another study by Khuntia et al. [8] the Marshall stability of polyethylene-modified asphalt samples was simulated by ANNs, and least-squares support vector machine (LS-SVM) methods. Laboratory results demonstrated that the incorporation of polyethylene improved the Marshall properties of asphalt samples such as stability, flow, and air voids. The two simulation methods used polyethylene, bitumen, and aggregate content as input parameters to predict three variables of Marshall mix specimens i.e., stability, flow, and the percentage of air voids. It was proved that ANN-based model had a much higher accuracy than the LS-SVM model. Back propagation Neural Network were applied to train the Neural Network for the prediction of the Marshall test results for polypropylene modified dense bituminous mixtures, which was analyzed by Tapkin et al. [9] The research shows that for a specific type of asphalt mixture and for predetermined testing conditions, the stability, flow and Marshall Quotient values obtained by Marshall design tests can be estimated without carrying out time-consuming and labor-insensitive destructive tests.
The main application attraction for using ANNs models is the acceptable performance. One of the drawbacks of the traditional ANNs-based model is facing problems with generalization [10]. ANNs can produce models that can overfit the data. Furthermore, the most difficult tasks in ANNs studies are to find the optimal network architecture such as numbers of optimal layers and neurons in the hidden layers by trial-and-error approach [9], [11].
Support vector machine (SVM) method introduced by Vapnik [10], can provide an effective novel approach to improve generalization performance of ANNs, and can achieve global solutions simultaneously [12]. Recently, with the progress and modification of SVM, SVM models has been derived to estimate and solve non-linear regression problems [12], [13]. In addition, SVM uses structural risk minimization principle (SRM), being able to result in simplification of complex patterns, and better generalization. SVM applications have been applied in pavement engineering field. Nguyen, et al. [14], developed hybrid AI approaches and SVM based regression model for predicting the Marshall parameters of stone matrix asphalt. The results indicated that SVM based method exhibited the best model compared to the other methods. In another study by Saif et al. [15], SVM and classical backpropagation neural networks (BPNNs) were used for the prediction of the stability of asphalt concrete mixes. They validated that SVM was superior to the other methods for evaluating the stability of asphalt mixes. Yan et al. [16] used SVM in comparison with Gene Expression Programming (GEP) and multiple least square regression (MLSR) for the prediction of flow numbers. The performance of SVM based model was more reliable than GEP and MSLR.
Genetic Programming (GP) developed by Koza [17] is alternative modeling for solving complicated problems [11], [18]. GP is a supervised machine-learning approach that searches for program space instead of data space. Therefore, many researchers have used GP for pavement problems in recent years. Multiple linear regression (MLR) models were used as base models to evaluate the performance of GP models, while GP was used to represent the Marshall test results of asphalt mixtures based on particle index, amount, and types of bitumen. Compared with MLR, GP model has the higher coefficient of determinations (R2) and least error. Research has concluded that GP models can be used for pavement design under diverse condition of materials characteristics [18]. Meanwhile, the fatigue performance of controlled and modified asphalt mixtures was evaluated by GP [19], [20]. Similarly, GP with the accurate predictions were also implemented by Gandomi et al. [21] and Alavi et al. [11] for the prediction of rutting performance (flow number) of asphalt mixtures, and the results were compared with MLSR models. Their results revealed that the models provided by GP were able to accurately predict the flow number.
The stability, the flow, and air voids are the primary parameters influencing the analysis and design of the asphalt mixtures. A comprehensive literature review shows that fewer AI models and empirical models are available for the prediction of asphalt mixture design’s stability, flow, and air voids parameters. Similarly, few studies are available for the prediction of Marshall parameters of the base and/or wearing course of the asphalt mixtures based on SVM and GP. However, these resulted models are also limited to the small database. Therefore, this research is focused in filling the gap and implementing SVM method for the prediction of Marshall parameters of the base course and wearing course of the asphalt mixtures. Meanwhile, GP based method is also employed to develop simplified empirical relationships for predicting the Marshall stability, flow, and air voids of the base course and wearing course, respectively with acceptable error. A comprehensive dataset of Marshall mix design has been established based on four road project sections. The implementation of diverse dataset ensures that the models are applicable on the unseen data. Several statistical criteria-based, as well comparison to regression methods, and parametric studies for GP based models were conducted to validate the performance of the models.
Section snippets
Mix design data collection
The data of Marshall mix design was compiled from four different road sections in Pakistan, which are implemented by projects entitled as, Dualization of Naguman Shabqadar Section of Provincial Highway S-1 A Peshawar, Northern Bypass Package 1 Peshawar, Mardan Ringroad Eastern Bypass, and Overlay and Modernization of Lahore Islamabad Motorway M−2. All the experimental procedure for determining the Marshall parameters of asphalt mixtures were carried out at National Engineering Services Pakistan
Model based on SVM
In this section, support vector machine, regression models are presented to predict the Marshall stability, flow, and air voids of the asphalt base and wearing courses, respectively.
The performance of the SVM models between the actual and prediction results, for both training and testing datasets are illustrated in Figs. 6 and 7. The expression for the regression lines between the model and actual results is also shown in the graphs. It can be seen that the developed model of Marshall stability
Conclusions
This research mainly focused on the applications of machine learning techniques in the field of pavement engineering. Two state-of-the-art techniques: support vector machine and genetic programming symbolic regression approach are implemented to analyze the Marshall parameters (i.e., Marshall stability (Kg), Marshall flow (0.01″), and air voids (%)) of flexible pavement, including both the base and wearing courses. For reliability, a comprehensive dataset of Marshall mix design was collected
CRediT authorship contribution statement
Weiguang Zhang: Conceptualization, Methodology, Software, Data curation, Writing – original draft, Supervision. Adnan Khan: Conceptualization, Methodology, Software, Data curation, Writing – original draft, Visualization, Investigation, Software, Validation, Writing – review & editing. Ju Huyan: Conceptualization, Methodology, Software, Visualization, Investigation, Supervision, Software, Validation, Writing – review & editing. Jingtao Zhong: Supervision, Software, Validation, Writing – review
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research is supported by the National Key Research and Development Project (grant number: 2020YFB1600102), the National Natural Science Foundation of China (grant number: 5210081588), and Intelligent monitoring of airport pavement status and rapid performance recovery technology, which are highly acknowledged.
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