饱和土中弹性波在双椭圆孔洞周围的散射

Scattering of elastic wave around double elliptic cavities in saturated soil

利用复变函数法和多极坐标法,研究了饱和土中弹性波在双椭圆孔洞周围的散射及动应力集中的问题。首先通过引入位移势函数,将二维稳态条件下Biot波动方程解耦成势函数所满足的3个Helmholtz方程,根据分离变量方法即可得Helmholtz方程在柱坐标下势函数的通解。利用土骨架和孔隙水的边界条件,确定波函数展开式中的未知系数,进而得到位移、应力和孔压的表达式。给出了弹性波对2个椭圆形孔洞的动应力集中系数的数值结果,并讨论了波数和孔距变化对动应力集中系数和孔压集中系数的影响。

The theory of complex variables methods and multi-polar coordinate systems are used to solve the problem of scatter and dynamic stress concentration of elastic waves around double elliptic cavities in saturated soil. The 2D steady state Biot wave equations are decoupled by introducing the potentials and reduced to three Helmholtz equations that the potentials satisfy. The solving of the Helmholtz equations by separating variable methods obtains general solutions of the potentials. The expressions of displacements, stresses and pore pressure can be obtained by determining the unknown coefficients in the potentials and utilizing the boundary conditions of soil and pore pressure. Numerical examples are provided to show the effect of wave number, distance between centers of cavities upon the dynamic stress concentration and pore pressure concentration around the cavities under incident steady elastic wave.