## 1 Introduction  
Skid resisting performance is the primary factor affecting traffic safety, specifically during vehicle braking where the anti-skid deficiencies found in pavement will prolong braking time and increase braking distance [1]. Due to this concern, highway authorities and researchers have been exploring the anti-skid properties of pavement through the frictional contact analyses of three key factors. The first factor is water. In the early 1960s, [PERSON] and [PERSON] 1963 [2] put forward the famous National Aeronautics and Space Administration (NASA) hydroplaning equation, which is used to calculate the hydroplaning speed of a tire. Later, [PERSON] 1966, [PERSON] 1967, and [PERSON] et al. 1968 [3; 4; 5] also simulated the hydroplaning of a tire, but in only two dimensions. In the following thirty years, both the NASA equation and the two-dimensional contact model were promoted by [PERSON] et al. 1986 [6] on the applicable conditions and accuracy. In the 21 st century, a three-dimensional frictional model of inflated tire and rigid pavement contact, simulating moist conditions, was developed by [PERSON] et al. 2007, 2008, 2010, 2012 [7; 8; 9; 10]. With this model, the degradation mechanism of wet-pavement skid resistance and the subsequent effects of tire slip velocity on rigid pavement under different degrees of wetness were examined. The second factor is the frictional property of tire rubber. The friction between tire and pavement is mainly determined by adhesive and hysteretic friction. Hysteric friction is enhanced with rise in temperature. For this analysis, [PERSON] 2001 [11] chose to use the rubber friction model based upon the tire rubber's viscoelasticity. Coupling thermos-mechanics with the finite element method, [PERSON] and [PERSON] 2013 [12; 13] estimated the variations in hysteretic friction during tire-pavement contact due to differences in temperature. This estimation was calculated by simulating a tire rolling on rigid pavement in CAPA-3D (developed and dated by the group of Mechanics of Infrastructure Materials at Delft University of Technology, The Netherlands) Finite Element system. The third final component in exploring the anti-skid properties of pavement is the surface texture of the pavement. Both the macro-texture and micro-texture are typically used to represent the skid resistance of pavement. The correlation between pavement texture and skid resisting ability are often evaluated via various test methods ([PERSON] 1990, [PERSON] 2014, [PERSON] 2015 [14; 15; 16]). For instance, [PERSON] and [PERSON] 2013 [12; 13] captured morphological data reflecting the surface of asphalt pavement through X-ray tomography. Furthermore, they reconstructed the texture of the pavement in CAPA-3D and analyzed their simulation of the kinetic contact of tires rolling on the rough, rigid-pavement [17]. After analyzing the aforementioned literature, we found that research on skid resistance primarily focuses on the macro or micro-texture of the pavement, by which the anti-skid property could be achieved. In addition, there are two methods to model asphalt pavement in the finite element analysis. One approach is modeling the pavement as a flat rigid surface, while the other one is an analytical rigid body with a macro-texture surface. It is apparent that both means of modeling consider the asphalt pavement as a rigid body, disregarding its elasticity. In the field of terrain vehicle mechanics, the fundamental source of vehicle braking is the friction between the tires and pavement. As illustrated in Figure 1a, the pedal force \(F_{p}\) is delivered to the wheel brake the moment the driver steps on the pedal, forming the frictional moment \(T_{\mu}\) opposite the momentum of the tire. This moment could be regarded as the circumferential component \(F_{\mu}\), which is applied to the tire-pavement contact region to prohibit the rotation of the tire.