弹性层状半空间中沉积谷地对入射平面SH波的放大作用

对Wolf理论进行拓展,使之可解决沉积谷地对波的散射问题,进而利用间接边界元法,求解了弹性层状半空间中沉积谷地对入射平面SH波的放大作用问题。通过自由场反应分析,求得假想边界上各点的位移和各单元的应力反应。施加虚拟均布荷载,求得位移和应力的格林函数。根据应力和位移连续边界条件确定虚拟分布荷载,将自由场反应和虚拟分布荷载产生的反应叠加起来,即得到问题的解答。最后,以基岩上单一土层中沉积谷地对入射平面SH波的放大作用为例进行了数值计算分析,结果表明,层状半空间中沉积谷地和均匀半空间中沉积谷地对波的放大作用存在显著差别。文中分析了造成差别的原因,并讨论了覆盖层厚度和刚度对放大作用的影响。

Surface motion of an alluvial valley in layered half-space for incident plane SH waves

Wolf's theory is extended to solve the problem of wave scattering by an alluvial valley.The indirect boundary element method(IBEM) is used to calculate the amplification of incident plane SH waves by an alluvial valley in layered half-space.The free-field response is carried out to give the displacements and the stresses on the line which forms the boundary of the valley.The fictitious uniform loads are applied on the same line to calculate the Green's functions for the displacements and the stresses.The amplitudes of the loads are determined by the boundary conditions of continuity of the displacements and the stresses.The displacements due to the free field and from the fictitious uniform loads have to be added to obtain the whole motion.Taking the amplification of incident plane SH waves by an alluvial valley in one layer over half-space as an example,the numerical results and analyses are performed.The results show that there exist distinct differences between the wave amplification by an alluvial valley in layered half-space and that in homogeneous half-space.The reasons for the difference are explained,and the effects of the thickness and the stiffness of the layer on the amplification are discussed.