Investigation of three-dimensional soil-structure interaction, 1979

The response to seismic excitation of a three-dimensional rigid foundation embedded into an elastic half space is analyzed. The analysis is separated into two physically meaningful subproblems: the first deals with the determination of the restraining forces acting on the foundation; the second deals with the evaluation of driving forces induced by seismic waves on the fixed foundation. This analysis is applied to the case of a hemispherical foundation embedded in a homogeneous elastic half space. The exact series solutions of the mixed boundary value problem are presented. The results are compared with those of a circular flat foundation. The comparison indicates that the embedment may have a marked influence of foundation response. The impedance components of the embedded hemispherical foundation are generally larger than those of the disc foundation. For incident plane P, SV and SH waves, scattering due to embedment reduces the foundation translational motion at high frequencies, but leads to significant rocking and torsional motions.

本文针对嵌入弹性半空间的三维刚性基础的地震激励响应展开分析。本次分析被拆分为两个具备物理意义的子问题：其一用于确定作用于基础的约束反力；其二用于评估固定基础上由地震波诱发的驱动力。将该分析方法应用于均匀弹性半空间内嵌入的半球形基础场景，本文给出了混合边值问题的精确级数解。将所得结果与圆形平板基础的结果进行对比，对比结果表明，基础埋置对其响应具有显著影响。嵌入式半球形基础的阻抗分量整体大于圆盘形基础。针对入射平面P波、SV波与SH波的场景，埋置作用引发的散射会在高频段降低基础的平动位移，但会引发显著的摇摆与扭转运动。