Prediction of low-temperature fracture resistance curves of unmodified and crumb rubber modified hot mix asphalt mixtures using a machine learning approach

Highlights

• R-curves of asphalt concrete mixtures were determined by a modified SE(B) test.

• Crumb rubber incorporation impacts the R-curves, particularly in the unstable crack growth phase.

• The MLP-ANN method is used for the prediction of R-curves of asphalt concrete mixtures.

• MGGP is used to develop the equation between the asphalt mixture properties and the corresponding low-temperature R-curve.

Abstract

Fracture resistance curves (R-curves) provide a robust tool for a comprehensive insight into the crack propagation regime in engineering materials. In this paper, an extensive research program is conducted to determine R-curves for hot mix asphalt (HMA) mixtures with varying properties. The experimental results are then used to develop R-curve prediction models following a machine learning approach. Three-point single-edge notched beam (SE(B)) experiments were conducted on HMA mixtures incorporating 0%, 5%, 10%, 15%, and 20% crumb rubber at low temperatures. The temperature ranged from + 5 °C to −20 °C while limestone and siliceous aggregate with two gradations were used in developing mixtures with two base bitumen having performance grades of PG58-22 and PG64-22. It was observed that as the temperature is declined to −20 °C, the stable crack growth region is significantly diminished in the R-curves, and the mixtures undergo a brittle fracture with abrupt failure of the specimen. A temperature of −15 °C could be determined where the transition from quasi-brittle to brittle fracture occurs. Mixtures fabricated incorporating 20% crumb rubber exhibited a progressively rising R-curve at the lowest test temperature (−20 °C) even in the unstable crack propagation phase, which is a desirable material characteristic. Two prediction models were developed for R-curves. Artificial neural networks (ANN) were used in the first model resulting in an R-square value of 0.965. Due to the black-box nature of the ANN, the multi-gene genetic programming approach was also applied in the prediction of the R-curves to derive a mathematical equation between the input data and the outputs. The R-square equaled 0.870 in this method. R-curves could successfully be predicted by both methods considering the negligible to fair errors.

Introduction

Fracture mechanical insight into the low-temperature cracking of asphalt concrete (AC) has gained extensive attention for the past two decades. Researchers have adopted and amended the fundamental fracture mechanics concepts to characterize low-temperature cracking in AC. Kim and El Hossein in 1997 [1] used the linear elastic fracture mechanics and determined low-temperature fracture toughness (K_IC) values for asphalt concrete mixtures in the earliest efforts. Later, Marasteanu and Labuz [2] applied the single-edge notched beam (SE(B)) test protocol for metals based on ASTM E399-20a to obtain critical fracture toughness values of the mixtures at low temperatures using linear elastic material behavior. Regarding the nonlinear and inelastic behavior of the AC in intermediate to low temperatures, a plastic zone forms near the crack tip. Hence, the singularity dominated zone could be violated, and the classical stress intensity factor could not describe the stress distribution in the crack tip [3]. In 2010, Li and Marasteanu [4] investigated the fracture process zone (FPZ) dimensions in hot mix asphalt (HMA) mixtures using acoustic emissions. They carried out semicircular bend (SC(B)) testing of variable mixtures in three temperature levels of high (−6 °C), middle-low (−18 °C), and low (−30 °C). It was found in their study that the FPZ size is significantly increased at the crack tip in HMA as the temperature is reduced to intermediate and thereafter. Another research by Doll et al. [5] used the digital image correlation (DIC) technique to study the FPZ development of the notched specimen in SC(B) test and reemphasized the presence of large scale yielding and considerable FPZ size. Consequently, the use of other crack tip parameters along with energy concepts such as the J-integral [6], C* integral [7], and fracture energy [8] have become widely appreciated in recent years. A large body of research is currently available in the literature measuring fracture energy of normal and modified asphalt mixtures as a low-temperature fracture resistance parameter [9], [10]. However, despite all the benefits of indices such as the critical J-integral or the fracture energy, single-parameter fracture characterization of HMA mixtures is still far from the required detailed knowledge of fracture of HMA mixtures. Fracture toughness values (whether K_c or J_c) relate to the threshold magnitude of applied load, while fracture energy itself is a combination of crack initiation and crack propagation energies. The fracture resistance curve (R-curve) concept expressing the variation of the crack tip parameter as a function of crack extension can serve as a robust method to characterize the entire fracture process of AC mixtures. However, research on R-curve characterization of asphalt mixtures has been very limited to date due to experimental costs and intricacies. Ghafari and Nejad, in 2015 [11], constructed J-R curves for HMA and evaluated the crack propagation process sensitivity to aggregate type, binder content, and temperature. They observed a progressively rising J-R curve for the mixtures from + 5 °C to −15 °C which is a desirable characteristic, while the propagation phase appeared distinctly flat (unstable) at −20 °C. They also derived magnitudes of fracture instability toughness (J_inst) and the critical crack length initiating unstable crack propagation in HMA for mixtures in 6 temperature levels. Yang and Braham [12] derived R-curves for HMA with three different levels of ageing in addition to moisture-conditioned samples. They found that long-term ageing of asphalt could reduce the mixtures' cohesive energy, fracture rate, and general fracture energy. They concluded that the R-curves could be used as an effective tool in characterizing various phases of cracking in asphalt concrete.

Using R-curves, in addition to observing the crack growth trend, one can derive fracture parameters such as the fracture energy, blunting and cohesive energy, fracture initiation toughness, fracture instability toughness, etc. However, experimental costs and complexities have seriously restricted the R-curve approach towards fracture analysis of materials such as asphalt concrete. Therefore, the prediction of the resistance curves could significantly contribute to the conservation of experimental time and expenses. Efficient prediction of pavement performance indices has been among the challenges engineers, and researchers have faced for the past decades [13]. Such indices are primarily determined experimentally in laboratory-scale or field samples. Derivation of comprehensive indices entails substantial experimental costs, while ample time also has to be considered. In the recent years, researchers have widely welcomed methods such as machine learning to predict pavement performance parameters [14]. The application of machine learning could significantly contribute to the consistent prediction of pavement performance indices and model developments while avoiding the experimental issues. Machine learning has recently been successfully incorporated in the prediction of fracture properties of asphalt mixtures [15]. In 2009, Tasdemir [16] used the general linear model and the multi-layer perceptron neural network to predict low-temperature fracture performance of asphalt mixtures. The research used admixture type, binder content, ageing, and air voids as the input variables and could predict the corresponding values of fracture temperature and strength for modified mixtures. In 2017, Ling et al. [17] investigated the top down cracking by means of the fracture parameter, J-integral. The finite element method (FEM) was used in their research to determine the values of J-integral for a propagating crack. Finally, incorporating the FEM input variables into the ANN, six models were trained to predict the J-integral. The trained ANNs consisted of an input layer, two hidden layers, and an output layer resulting in an R-square value of 0.99. Majidifard et al. [18] used the gene expression programming method with a combination of the simulated annealing and ANN in order to predict the fracture energy magnitude of asphalt mixtures. Fifty-seven data points from the disk-shaped compact tension (DC(T)) test were used. Input variables included: binder performance grade (PG), binder content, nominal maximum aggregate size (NMAS), reclaimed asphalt shingles (RAS) content, crumb rubber (CR) content, and temperature. The fracture energy was predicted by means of the gene expression programming and the simulated annealing methods with ANN by R-square values of 0.96 and 0.92, respectively. Ziari et al. [19], in 2020, used reclaimed asphalt pavement (RAP) content, glass fiber content, and test temperature as input variables to predict fracture energy and the critical J-integral by means of a multiple regression model. Semi-circular bend (SC(B)) test data for 250 experiments were used and the R-square value for fracture energy and critical J-integral was obtained to be 0.72 and 0.63, respectively. In 2020, Moniri et al. [20] considered RAP content, fiber content, as well as SCB test temperature and used the multiple regression analysis accompanied by ANN to predict the fracture energy and the critical J-integral. It was shown in this study that the ANN results in better accuracy than the multiple regression methods.

As can be inferred from the available literature, all the modeling efforts to date have focused on predicting one or two single fracture parameters of the asphalt concrete mixtures. As pointed out earlier, more detailed insight into the entire fracture regime of asphalt concrete is required, improving further mixture research and design. In this research, SE(B) fracture experiments accompanied by capturing and analyzing images were conducted at six temperature levels of + 5 °C, 0 °C, −5 °C, −10 °C, −15 °C, and −20 °C on unmodified and modified mixtures fabricated by limestone and siliceous aggregates at three binder contents of 4%, 4.5%, and 5%. Two gradations with NMAS of 19 mm and 25 mm were considered, and PG 58–22 and PG64-22 bitumen were used in the mixtures for the entire scope of test variables. Crumb rubber contents of 5%, 10%, 15%, and 20% by weight of bitumen were incorporated for modified samples. Due to substantial experimental costs and difficulties in deriving R-curves for asphalt concrete mixtures, this paper aims to predict the fracture resistance curves and the relevant key parameters about the fracture regime of the mixtures using machine learning methods conserving experimental time and expenses. In the next stage, R-curves are predicted by converting the metaheuristic genetic optimization algorithm to multi-gene genetic programming (MGGP) with a multi-layer perceptron ANN. This method is superior to the common machine learning procedures which perform black-box predictions since it can output globally usable prediction equations. Model training and predictions are implemented by the vast range of input parameters, i.e., aggregate type, binder content, nominal maximum aggregate type, binder performance grade, and mixture modification with crumb rubber contents. To construct an unabridged space of variables for modeling, additional samples of mixtures with 6% and 6.5% binder content from PG52-16, PG52-34, PG76-10, PG58-28, and PG76-28 bitumen, as well as 25% and 30% crumb rubber incorporation, were also considered in the experiments. The fracture parameters include the magnitude of the applied load during each test, loading time, crack mouth opening displacement (CMOD), load-line displacement (LLD), crack extension, and fracture energy.