水平简谐荷载作用下层状饱和土体动力响应

Dynamic responses of a layered saturated soil subjected to harmonic horizontal loads

根据Biot波动理论,采用传递、反射矩阵(TRM)方法研究了水平简谐荷载作用下层状饱和土动力响应问题。由Helmholtz矢量分解求出基本解,再利用TRM法推导了层状饱和土动力响应,并由数值Hankel逆变换得到层状土地基位移、应力及孔压在空间域内的解。利用计算结果与已有结果相比较,二者相吻合,验证了算法的正确性。算例分析表明,水平简谐荷载作用在有软弱夹层的层状土体中比均质土中具有更显著的动力响应,尤其是软夹层上下有硬土层时,会引起软弱夹层土体孔隙水压升高、位移幅值增大、土体波动性增强;而荷载作用硬夹层及夹层上下有软土层时,情况则相反。

Based on the Biot＇s theory, the dynamic responses for a multilayered poroelastic soil subjected to harmonic horizontal load is developed with the transmission and reflection matrices （TRM） method. Applying the Helmholtz vector decomposition and Hankel transformation, the general solutions for the displacements, the stresses and the pore pressure are derived from the governing equations of Biot＇s theory. Utilizing the transmission and reflection matrices （TRM） method, the transformed domain solutions for the multilayer saturated poroelastic soil subjected to harmonic horizontal load are established. Numerical results for the displacements, the pore pressures and the stresses are obtained by performing inverse Hankel transformation in the space domain. Some numerical examples and corresponding analysis are presented. The present methodology is validated by comparing solutions with some known results. According to the analysis, it is concluded that the occurrence of a softer middle layer subjected to a harmonic horizontal load in the layered half space enhances the horizontal displacement and pore pressure. Comparing with the homogeneous case, the response of the multi-layered half space tends to contain higher frequency components and exhibits larger magnitude.