饱和土中任意形状衬砌对稳态压缩波的散射

Scattering around a liner of arbitrary shape in saturated soil under dilatational waves

采用不同的复平面间的保角映射法,对无限饱和土中任意形状的多孔衬砌结构对弹性压缩波的散射问题进行了研究。首先,通过引入位移势函数将饱和土和衬砌两种介质的Biot波动方程解耦成6个Helmholtz方程,并求出复平面极坐标下相应势函数的通解;之后,利用两个复平面间的极角变换关系,得到位移、应力和孔压在映像平面上势函数表达式。在此基础上,将原像平面中任意形状的衬砌内外边界处的边界条件代入到映像平面中圆环势函数的关系式中,从而求出饱和土中衬砌介质在弹性稳态体波作用下产生的动态响应。最后通过具体算例,变换不同的入射角及介质参数得出相应数值解及规律。

The method of conformal mapping between complex planes is used to solve the problem of the scattering around a poroelatic liner of arbitrary shape in saturated soil under harmonic plane dilatational waves. The equations of the Biot wave motion for saturated soil and liner are decoupled to Helmholtz equations and given by introducing potential function. Utilizing the polar angle transform, the expressions of the displacements, stresses and pore pressures of saturated soil and those of the liner in the mapping plane can be obtained. Based upon this, the dynamic response around the liner can be obtained by transform the boundary conditions of liner of arbitrary shape in the preimage plane into those of the cirque in the mapping plane. Some results and rules are oresented with different incident angle and parameter conditions of the liner.