基于解析层元法的成层半平面地基移动荷载动力响应研究

Dynamic response of a multilayered half-plane under moving loads with analytical layer-element method

解析层元法具有较高的计算效率和数值稳定性,为此基于解析层元法研究移动荷载作用下层状各向同性地基的平面应变动力响应问题。假定研究坐标系随移动荷载同步移动,移动荷载相对于移动坐标系处于相对静止状态,从而将移动荷载作用下的动力问题转化为准静态问题。结合移动坐标系下的控制方程和傅里叶变换方法,推导出单层有限厚度和半空间土体在傅里叶变换域内的解析层元。根据有限层法原理组装各土层的解析层元得到总刚度矩阵,再结合边界条件求解总刚度矩阵方程在积分变换域内的解。然后,利用傅里叶积分逆变换将变换域内的解答转换为物理域内的解。最后,通过算例验证本文理论的正确性,并分析荷载移动速度、荷载作用深度、成层性及地基加固厚度与加固效果等对成层地基动力响应的影响。研究表明：地基的竖向位移和竖向应力随荷载移动速度的提高而不断增大,当移动速度接近土体的剪切波速时,地基竖向位移和竖向应力均迅速增加;移动荷载作用下地基的成层性对土体的竖向位移有较大的影响,且主要受地基表层土体性质的影响;表层土体的加固对减小地基沉降有显著效果,随着加固效果的增加,地表沉降的减小量逐渐降低。

The analytical layer-element method owns higher computation efficiency and numerical stability. Hence, this method is utilized to analyze the dynamic response of an isotropic multilayered half-plane subjected to a moving load. It is assumed that the studied system moves synchronously with the moving load, therefore, the moving load is considered to be motionless relative to the moving system. Combining the governing equations of motion in the moving system and the Fourier transform, the analytical layer-elements for a single layer with a finite thickness and a half-plane are derived in the Fourier transform domain. The global matrix of the problem can be obtained by assembling the analytical layer-element of each layer. The solutions in the integral transform domain are obtained by combining with the boundary conditions. The corresponding solution in the frequency domain is further recovered by applying the inverse Fourier transform. Several examples are given to confirm the accuracy of the proposed method and to illustrate the influences of velocity, depth of the load, layering and reinforced thickness and effects on the dynamic response in layered soils. The following conclusions can be obtained. The vertical displacement and vertical stress increase with the increase of load velocity, and their increments increase rapidly when the load velocity gets close to the shear velocity of soils. Besides, the vertical displacement is affected by the layering of soils and the superstratum is the key factor. The reinforcement of the superstratum has a remarkable result in decreasing the settlement of foundation, but the decrease gets weak when the reinforcement effect increases.