基于解析方法的开裂水泥混凝土路面动力响应

水泥混凝土路面在使用过程中板底出现裂缝是一种常见的损坏形式.为分析影响水泥混凝土路面中板底裂缝扩展的主要因素,以断裂力学理论为基础,基于解析的方法对含裂缝水泥混凝土路面的动力响应进行研究.将水泥混凝土路面简化为Winkler 地基上的弹性板,通过Fourier积分变换和Laplace积分变换,将位移控制偏微分方程组转化为常微分方程组进行求解,引入位错密度函数并应用留数定理计算复杂积分,推导出奇异积分方程并获得路面动力响应的解析表达式.通过Lobatto-Chebyshev求积公式求解奇异积分方程,可以得到裂缝尖端应力强度因子的数值解.以工程实例计算结果为基础,分析影响水泥混凝土路面中板底裂缝向上扩展的主要因素.

Dynamic response of cement concrete pavement with crack under vehicle load based on analytic method

Bottom crack in cement concrete pavement is one of the major pavement diseases. The main purpose of this study is to propose the theoretical basis for evaluating the status of the pavement. In order to simplify the problem, the cement concrete pavement was modeled as an elastic plate on winkle foundation. To solve the governing equations, the Fourier transform and Laplace transform were introduced to transform the partial differential equations to ordinary differential equations. The residual theorem and dislocation density function were used to derive the singular integral equations. Lobatto-Chebyshev integration formula, as a numerical method, was used to gain the results of the singular integral equations. The numerical solution of dynamic stress intensity factor at the crack tip was obtained. In order to get the factors that affect the crack propagating, numerical analyses were carried out for a cement concrete pavement with a bottom crack.