基于解析方法的半刚性基层沥青路面裂缝反射问题研究

Crack Reflection of Semi-rigid Base Asphalt Pavement Based on Analytical Method

针对沥青路面半刚性基层开裂且裂缝逐渐反射的问题,基于解析的方法开展开裂路面的力学响应研究。以断裂力学理论为基础,建立开裂沥青路面的理论分析模型,通过傅里叶积分变换求解偏微分方程组,引入位错密度函数表征裂缝力学特性,留数定理计算复杂积分,获得奇异积分方程,应用Lobatto-Chebyshev求积公式对奇异积分方程进行求解,求得路面内任一点位移、应力及应力强度因子的解析表达式及数值解。以工程实例为基础,分析影响基层裂缝反射的主要因素。计算结果表明:在车辆荷载作用下,剪切破坏是裂缝扩展的主要形式;半刚性基层的弹性是影响裂缝反射的主要因素。研究成果可为半刚性基层沥青路面的设计和施工提供理论参考依据。

Aiming at the cracking of semi rigid base of asphalt pavement and the gradual reflection of cracks, the mechanical response research on the cracked pavement was carried out on the basis of analytical method. Firstly, based on the theory of fracture mechanics, a theoretical analysis model of the cracked asphalt pavement was established. Then, the system of partial differential equations was solved by Fourier integral transform, and dislocation density function was introduced to characterize fracture mechanics. The residue theorem was used to calculate complex integrals and singular integral equations were obtained. Lobatto Chebyshev quadrature formula was applied to solve singular integral equations. Finally, the analytical expressions and numerical solutions of displacement, stress and stress intensity factors at any point of the road were obtained. Based on the engineering example, the main factors affecting the crack reflection of the base course were analyzed. The calculation results show that： under the action of vehicle load, shear failure is the main form of crack propagation, and the elasticity of semi rigid base is the main factor affecting crack reflection. The research results can provide theoretical reference for the design and construction of semi rigid base asphalt pavement.