半空间饱和土中圆柱形衬砌内荷载引起的动力响应解答

地下衬砌结构经常会受到内部动荷载的作用，内荷载引起的衬砌结构的动应力集中备受关注。采用Laplace变换和波函数展开法，对半空间饱和土中均布突加荷载作用下圆柱形衬砌结构的动力响应进行了研究。对以大半径凸圆弧来近似半空间表面，将半空间饱和土中的波动方程展开成无穷级数的形式，应用Graff加法公式进行坐标变换，根据连续条件和边界条件，确定波函数展开式中的未知系数，求得了半空间饱和土中均布突加荷载作用下圆柱形衬砌的动力响应解答，讨论了衬砌埋深对圆柱形衬砌动力响应的影响。该问题的求解，为地下结构的动力分析提供了一种有效方法。

THE TRANSIENT RESPONSE OF CYLINDRICAL LINING IN POROELASTIC SATURATED HALF-SPACE

Buried lined tunnels are often subject to internal dynamic loading,such as blast loading and impact loading.The dynamic stress concentration of lining structure due to various dynamic sources is a special concern in practical engineering.The transient dynamic response of a cylindrical lining subjected to sudden internal uniform loading has been investigated with the Laplace transform and the method of the separation of variables.The wave potentials in a homogeneous saturated half-space are expanded into Fourier-Bessel series using the wave function expansion method.A convex approximation is used to replace the straight boundary of the half-space.In terms of continuity conditions and boundary conditions of the problem,the unknown coefficients in potentials are determined by coordinate transform.The dynamic responses of the lining structure in saturated half-space are discussed for different buried depths of lining.This study provides an effective method for analyzing some similar problems about dynamic response of underground structure.