Biot齐次固结方程的通解

THE GENERALIZED SOLUTIONS OF HOMOGENEOUS BIOT'S EQUATIONS OF CONSOLIDATION

从考虑土颗粒和流体体积压缩的Biot固结方程出发,求得一般Biot固结方程的势函数通解和齐次Biot固结方程的势函数通解。当达西渗透系数趋向无穷大时,齐次Biot固结方程的通解退化为经典弹性静力学的帕普科维奇通解。当颗粒和流体的体积模量趋向无穷大时,Biot固结方程退化为不考虑土颗粒和流体体积压缩的简化Biot固结方程,从而得到一般简化Biot固结方程的势函数通解和齐次简化Biot固结方程的势函数通解。获得Biot固结方程和简化Biot固结方程的位移、应变和应力的势函数通解表达式。

The generalized potential solutions of the generalized and homogeneous Biot＇s equations of consolidation are obtained. The soil grain and fluid compressibilities are taken into account. It is found that when Darcy＇s seepage coefficient approaches infinitely, the generalized potential solutions of Biot＇s homogeneous equations degenerate into Papkovich＇s solutions in classical static elasticicity. When grain and fluid bulk moduli approach infinitely, the simplified Biot＇s theory of consolidation that does not consider soil grain or fluid volumetric compressibility are obtained. Therefore the generalized potential solutions of the generalized and homogeneous Biot＇s equations of consolidation degenerate into those of the simplified ones. The generalized expressions of displacements, strains and stresses for general and simplified Biot＇s equations of consolidation are expressed in terms of the potential functions.