饱和土地下源u-P形式解答动力响应计算

Dynamic response calculation for u-P solution in saturated soil subjected to an underground point source

一直以来,由Biot孔隙弹性动力方程得到的饱和土地下源Green函数都是u-w形式(u为固相介质位移,w为流相相对于固相的平均位移)。应用两相介质纵波解耦理论,得到了饱和土半空间地下点源荷载的u-P形式(P为孔压)Green函数频域解答;克服了u-w形式Green函数在边界元(BEM)积分时的增根影响。再由Hankel反演,结合Somigliana表象积分,完成BEM计算。并以计算结果分析了地下集中力作用时,饱和土位移、孔压、排水量等动力特性,这对地铁等交通工程、地震工程、土-结构动力相互作用(SSI)的响应计算都具有较重要应用价值。

The Green functions of saturated soil derived from the Biot’s poroelastic dynamic equation are the results in u-wformulation, where u is a displacement of the solid phase medium, and w is an average displacement of the fluid phase relative to the solid phase. Decoupling fast and slow longitudinal waves with regard to Biot’s dynamic equation, the analytical solutions for the solid and fluid Green’s functions in u-P formulation, where P is the porous pressure of the fluid phase, subjected to an underground point source in a porous medium in frequency-domain are obtained respectively and readily in this paper. The effects of increasing roots of Green functions in the u-w formulation on BEM integration are eliminated. Through Hankel’s inversion and Somigliana’s representative integral over a half-space in numerical implementation, the displacement, porous pressure, water discharge and other corresponding results of dynamic response in the saturated soil are presented for discussing. It has important application value for the response calculation of subway and other traffic engineering, seismic engineering and structure-soil dynamic interaction(SSI).