考虑沥青路面材料参数空间差异性的解析计算及影响分析

复杂服役环境下沥青路面的材料参数存在明显的空间差异性,具体表现为沿深度的模量梯度分布与非连续层间接触以及横观各向同性,实现其解析计算对现有的沥青路面力学响应分析及结构设计方法具有重要的参考价值。为此,从弹性力学基本方程出发,基于状态空间法,推导了具有指数模量梯度的横观各向同性弹性层状体系通解;在此基础上,基于波传递方法,将状态向量转换为波向量,并结合边界条件和层间条件,建立了考虑沥青路面材料参数差异性的多层路面结构解析解;然后借助MATLAB平台编制了数值计算程序,采用文献对比、BISAR程序以及有限元软件ABAQUS验证了该解析解的精度与效率;最后结合典型数值算例,阐述了该解析解在沥青Top-Down开裂和传统路面疲劳损伤分析中的应用。理论推导和数值计算结果表明：该解析解摆脱了弹性力学问题求解对应力函数的依赖性,并且借助波传播方法,避免了求解中正指数过大对求解精度的影响,并使得边界条件和不同层间接触关系的描述更加便捷;沥青路面材料参数的空间差异性不可忽视,沥青面层连续模量梯度会造成更大的路表拉应力和最大剪应力,进而加剧沥青路面的Top-Down开裂;而横观各向同性和层间接触状态间存在耦合效应,从而会加剧沥青路面的疲劳损伤。

Analytical Solution and Effect Analysis of Asphalt Pavement Considering the Spatial Difference of Material Parameters

Under the influence of the environment and loads, pavement materials exhibit modulus gradients, imperfect contact conditions, and transverse isotropies. These characteristics are termed as spatial differences in material parameters. Moreover, it is critical to establish an analytical solution for the response analysis and structural design approach considering the spatial differences in asphalt pavements. For this purpose, based on the fundamental equations of elastic mechanics, the integral transformation and state-space approach were adopted in the derivation of the general solution of transversely isotropic elastic layered media with exponential modulus gradient. Then, based on the wave propagation approach, the state vector was transformed into a wave vector, and the boundary conditions and interlayer conditions were employed to establish the analytical solution of the multi-layered pavement structure considering the spatial difference of material parameters. Subsequently, the corresponding software was compiled using the MATLAB platform. The accuracy and efficiency of this analytical solution were verified by means of the reference, BISAR program, and finite element software ABAQUS. Finally, based on typical numerical examples, the application of the analytical solution in the top-down crack and traditional fatigue damage analysis of asphalt pavements was illustrated. The theoretical derivation and results of the numerical examples reveal that the proposed analytical solution does not rely on stress functions, and the influence of large exponential functions on the solution accuracy can be avoided with the help of the wave propagation approach. Meanwhile, the proposed solution can facilitate the description of the boundary conditions and different interlayer conditions. The spatial difference of the material parameters in asphalt pavements cannot be ignored, and the continuous modulus gradient of asphalt pavements will result in higher surface tension and maximum shear stress in the pavement surface, thus aggravating the top-down cracking in asphalt pavements. Additionally, there is a coupling effect between the transverse isotropy and contact state between the layers, which intensifies the fatigue damage of the asphalt pavement.