Advances in Materials Science and Engineering

Volume 2017 (2017), Article ID 4768718, 12 pages

https://doi.org/10.1155/2017/4768718

## Investigation on Reinforced Mechanism of Fiber Reinforced Asphalt Concrete Based on Micromechanical Modeling

School of Civil Engineering, Hebei University of Engineering, Handan 056038, China

Correspondence should be addressed to Qinglin Guo; nc.ude.uebeh@lqoug

Received 11 October 2016; Revised 3 December 2016; Accepted 25 December 2016; Published 18 January 2017

Academic Editor: Akihiko Kimura

Copyright © 2017 Ying Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Short fibers have been widely used to prepare the fiber reinforced asphalt concrete (FRAC). However, internal interactions between fiber and other phases of asphalt concrete are unclear although experimental methods have been used to design the FRAC successfully. In this paper, numerical method was used to investigate the reinforced mechanism of FRAC from microperspective. 2D micromechanical model of FRAC was established based on Monte Carlo theory. Effects of fiber length and content on stress state of asphalt mortar, effective modulus, and viscoelastic deformation of asphalt concrete were investigated. Indirect tensile stiffness modulus (ITSM) test and uniaxial creep test were carried out to verify the numerical results. Results show that maximum stress of asphalt mortar is lower compared to the control concrete when the fiber length is longer than 12 mm. Fiber reduces the stress level of asphalt mortar significantly. Fiber length has no significant influence on the effective modulus of asphalt concrete. Fiber length and content both have notable impacts on the viscoelastic performance of FRAC. Fiber length should be given more attention in the future design of FRAC except the content.

#### 1. Introduction

Asphalt concrete is a kind of composite including aggregate, asphalt, filler, and voids. It has been widely used for pavement construction in the world due to its good raveling performance. But pavement defects such as rutting, cracking, and moisture damage had plagued the designers and researchers all the way. In order to improve pavement service quality, many modifiers were added in asphalt concrete [1, 2]. Among these modifiers, fiber reinforced technique has got more and more attentions as a result of its convenience [3].

So far, many kinds of fibers had been applied in asphalt concrete. These fibers included the steel fibers [4, 5], basalt fibers [6], polypropylene fibers [7, 8], glass fibers [9], natural fibers [10, 11], and thermoplastic fibers [12]. Among these researches, Chen and Xu [13] and Qian et al. [14] determined effects of polyester fiber, polyacrylonitrile fiber, lignin fiber, and aramid fiber on the asphalt binder. Chen and Xu [13] indicated that rutting resistance of the binder was improved by the fibers formed spatial network. Result of Qian et al. [14] revealed that fiber reinforced asphalt binder had a good low temperature ductility. However, Herráiz et al. [11] thought that fibers’ behavior should be assessed in asphalt mixture although a general sight on the effect of fibers had been given by its characterization. So study on fiber reinforced binder only is an indirect evaluation.

In order to determine fibers’ effect on asphalt mixtures directly, Serin et al. [4, 5] used steel fiber to modify the mixture. They suggested that the reinforced mixture had the best performance when the bitumen and fiber content were 5.5% and 0.75%, respectively. Tapkin and Özcan [7, 15] and Kim and Park [8] carried out extensive analyses on polypropylene fibers reinforced mixture. Tapkin and Özcan [7, 15] indicated that polypropylene fibers not only reduced the accumulated creep strain but also improved the physical and mechanical properties of the mixture. Optimal fiber content for FRAC was 0.55% by the weight of aggregate. Kim and Park [8] proposed that optimal fiber content for recycled foamed asphalt concrete was 0.15%. Morova et al. [16] stated that the optimal content of polyparaphenylene terephtalamide fiber was 0.25%. Oda et al. [10] made a comparative analysis on the different FRACs. They indicated that natural fibers present excellent performance compared with polyester and cellulose fibers. Fiber increased the tensile strength and resilient modulus of asphalt mixture. On the study of crack resistance, Yoo and Kim [12] proposed an effective method to estimate the interfacial bond strength of plastic fibers. They indicated that interfacial bond strength between plastic fiber and the mixture was 0.12 Mpa, and fiber’s contribution to resisting the failure was 25.5% approximately.

In China, performances of FRAC also were studied extensively. Chen et al. [17] investigated effects of polyester fiber, polyacrylonitrile fiber, and lignin fiber on the strength and fatigue behavior of asphalt concrete. It demonstrated that all fibers improved the rutting resistance, fatigue life, toughness, and ultimate flexural strain of asphalt concrete. Besides, rutting resistance and indirect tensile strength were best when the fiber content was 0.35%. Xue et al. [18] studied the interface reinforced action and crack resistance of pavement straw composite fiber reinforced asphalt concrete. They thought that pavement straw composite fiber had a better interface reinforced action compared to the others. Ye et al. [19] pointed out that FARC had lower stiffness and higher flexibility. Few fibers reinforced mixtures had a better fatigue life than the control mixture. Fibers’ effect on fatigue resistance of low stress level was more significant than that of the high level [20].

Based on the previous literatures review, we can find that the fiber improves the high temperature property, fatigue property, crack resistance, and toughness of asphalt mixture. Optimal fiber content also was different for each type of fiber. But the reinforced effects of all fibers were similar. Besides, these investigations were mainly focused on the influence of fiber content. However, García et al. [21] indicated that properties of mixtures such as air void and particle loss were related to the length and diameter of fibers. They also suggested that fibers for dense asphalt concrete should have certain geometries. Chen and Xu [13] also stated that fiber shape, size, and tensile strength also had noticeable impact on asphalt. Morova [22] also pointed out that the optimal basalt fiber content was 0.50% for the fiber with a length of 3.94 mm. This was different from the result of Gao [23]. Gao [23] thought that the optimal fiber content was 0.07% and 0.15% for the ones of 9 mm and 6 mm, respectively. Results of Fu et al. [24] and Park et al. [25] both showed that long fiber had better bridging action than the short one. Therefore, it can be concluded that fiber length also influences its reinforced ability. But load transferring ability of the fiber is mostly inferred based on the macro test results. Interactions among the mortar, fiber, and aggregate were so complex that they could not be revealed by the traditional test directly. Reinforced mechanism of fibers in the mixture was unclear although we have obtained the fibers distribution in the mixture [21]. Fortunately, micromechanical method is an effective technique to evaluate the internal mechanical behaviors of composites. It had been applied in asphalt concrete successfully [26–37].

Currently, discrete element method (DEM) and finite element method (FEM) are mainly applied to investigate the internal mechanical response of asphalt concrete. On the one hand, You et al. [27], Liu and You [28, 29], and Dai and You [30] analyzed the dynamic and creep properties of asphalt concrete based on discrete element modeling. They indicated that 3D computation is extremely time-consuming. So frequency-temperature superposition principle was suggested for DEM by them. On the other hand, Wang et al. [31–33] determined the voids distribution in asphalt concrete by X-ray CT scanning. Then micromechanical FE model was reconstructed based on the scanned images. Their results showed that modulus ratio, air voids, and loading orientation had significant impact on the strain state of mastic. Results of discrete and finite element simulation both agreed with the experimental results. For FRAC, fiber diameter is so small that it is very difficult to establish the fiber model in the discrete element simulation. Therefore, FEM was utilized to investigate the fibers’ micromechanical reinforced mechanism in this study.

In this paper, micromechanical models of FRAC were established based on Monte Carlo theory. Effects of fiber length and content on the stress state of asphalt mortar, effective modulus, and viscoelastic deformation of mixture were investigated by finite element numerical analysis. Indirect tensile stiffness modulus test and creep test were carried out in order to verify the numerical results. Finally, variance analysis was made to determine the significant level of different factors.

#### 2. Theories and Methods

##### 2.1. Micromechanical Model Generation Algorithm

Until now, there are mainly two typical methods for micromechanical model establishment. One is based on digital image processing (DIP) technique [26–28, 30–32, 34, 35]. The other one is the random generated method which is based on Monte Carlo theory [36, 37]. For the first one, digital image from camera or X-CT scanner was processed and then vector data was used to establish the model. Image processing and vector processing are so complicated that we must spend a lot of time on them although image describes the actual structure. Fortunately, Song et al. [38] proposed that the generated work of micromechanical model could be finished in several minutes. Guo et al. [39] also indicated that aggregate can be assumed as ellipsoidal particle. Hence, the second method was employed to generate the micromechanical model of FRAC in this paper. According to the studies of Dai and You [30], Wang et al. [36], and Yin et al. [37], aggregate can be simulated as elliptical particle in 2D analysis. In addition, Ioannis et al. [40] and Yu et al. [41] suggested that the short fiber also can be simulated as elliptical particle which had high aspect ratio in fiber reinforced composite. Therefore, aggregate and short fibers were both simulated as elliptical shape in this study.

For the aim of fast generation, overlapping of different aggregates and fibers should be avoided. The overlapping checking theory which is proposed by Song et al. [38] was adopted in this paper. For an ellipse, its center is , length of major axes is* 2a*; length of minor axes is* 2b*, the angle between the major axes and -axis is (), and the rotate matrix of ellipse can be written as follows:General equation of ellipse is shown in (2). The checking function is defined as (3). Consider where, for any point , it locates outside of the ellipse if ; it locates on the ellipse if ; it locates inside of ellipse if . Positional relationships between two ellipses are tangent, intersect, and separate. These relationships can be determined using the distance from the point to the ellipse. In this paper, a numerical searching method was used to calculate the minimum distance considering the computing efficiency. Ellipse was discreted to points using the parametric equation of ellipse. Minimum distance from the point to these discrete points was used for distance checking approximately. Distance from the point to ellipse can be calculated with the following equations:

Moreover, the meshing of micromechanical model may be unsuccessful if the distance between two elliptical particles is very small. Considering the meshing need, distance between two elliptical particles was also checked. Micromechanical model of FRAC was established by two steps using the self-prepared program. Firstly, area percentages of aggregate and fibers were calculated according to the selected gradation. Then aggregates were randomly generated from the big to the small ones. Data of elliptical aggregate was stored when the generated aggregate did not overlap the previous particles. Secondly, short fiber was randomly generated and it was checked with previous generated aggregate and fibers until fiber fraction reached the set value. This process was conducted using the software MATLAB. Specific flowchart of self-prepared program was shown in Figure 1.