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基于Zienkiewicz提出的非饱和多孔介质波动理论,考虑两相流体和固体颗粒的压缩性以及惯性、黏滞和机械耦合作用,采用半解析的方法获得了一类典型边界条件下单层非饱和多孔介质一维瞬态响应解。首先推导出无量纲化后以位移表示的控制方程,并将其写成矩阵形式;然后,将边界条件齐次化,求解控制方程所对应的特征值问题,得到了满足齐次边界条件的特征值和相对应的特征函数。根据变异系数法并利用特征函数的正交性,得到了一系列仅黏滞耦合的关于时间的二阶常微分方程及相应的初始条件。在此基础上,运用精细时程积分法给出了常微分方程组的数值解。最后,通过若干算例验证了结果的正确性并探讨了单层非饱和多孔介质一维瞬态动力响应的特点。该方法可推广应用于其他典型的边界条件。
Based on the theory of unsaturated porous media proposed by Zienkiewicz, considering the compressibility, inertia, viscosity and mechanical coupling of two-phase fluid and solid particles, a semi-analytical method was used to obtain a class of monolayer unsaturated porous media with typical boundary conditions One-dimensional transient response solution. Firstly, the governing equations expressed in terms of displacements after the non-dimensionalization are deduced and written into a matrix form. Then, the boundary conditions are homogeneous and the eigenvalues corresponding to the governing equations are solved. The eigenvalues satisfying homogeneous boundary conditions And the corresponding eigenfunction. According to the coefficient of variation method and the orthogonality of the eigenfunction, a series of second order ordinary differential equations and corresponding initial conditions of time-only viscous-coupling are obtained. On this basis, the numerical solution of ordinary differential equations is given by using the method of precise time integration. Finally, several examples are given to verify the correctness of the results and to investigate the characteristics of one-dimensional transient dynamic response of single-layer unsaturated porous media. This method can be extended to other typical boundary conditions.