单层非饱和多孔介质一维瞬态响应半解析解

发布时间：2018-11-15 08:44

【摘要】：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。
[Abstract]:Based on the wave theory of unsaturated porous media proposed by Zienkiewicz, the compressibility, inertia, viscosity and mechanical coupling of two-phase fluid and solid particles are considered. The one-dimensional transient response of a class of monolayer unsaturated porous media under a typical boundary condition is obtained by semi-analytical method. Firstly, the governing equation expressed by displacement after dimensionless is deduced, and it is written into matrix form. Then, the homogenization of the boundary conditions is used to solve the eigenvalue problems corresponding to the governing equations, and the eigenvalues and the corresponding eigenfunctions satisfying the homogeneous boundary conditions are obtained. According to the variation coefficient method and the orthogonality of the eigenfunction, a series of second order ordinary differential equations about time and corresponding initial conditions are obtained. On this basis, the numerical solutions of ordinary differential equations are obtained by using the precise time integration method. Finally, some examples are given to verify the correctness of the results and the characteristics of one-dimensional transient dynamic response of monolayer unsaturated porous media are discussed. This method can be extended to other typical boundary conditions.
【作者单位】：浙江大学软弱土与环境土工教育部重点实验室;浙江大学岩土工程研究所;中国地震局工程力学研究所;
【基金】：国家自然科学基金(No.51278451) 浙江省自然科学基金重点项目(No.LZ12E09001)
【分类号】：TU435

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