非饱和多孔介质一维瞬态响应半解析研究

发布时间：2018-07-07 20:35

本文选题：非饱和多孔介质 + 一维问题　；参考：《浙江大学》2013年硕士论文

【摘要】：多孔介质的波动问题是岩土工程、地震工程、海洋工程、环境工程等领域的重要基础课题,而瞬态响应是波动理论中的重要一环。本文即单层多孔介质的一维瞬态响应问题开展了半解析研究,并得到了一些成果。针对单层非饱和多孔介质一维瞬态响应问题,采用Zienkiewicz基于Biot理论提出的非饱和多孔介质波动方程,考虑两相流体和固体颗粒的压缩性以及惯性、粘滞和机械耦合作用,采用半解析的方法获得了十类典型非齐次边界条件下单层非饱和多孔介质的一维瞬态响应解。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,得到了一系列仅粘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,运用改进后的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本文结果的正确性并探讨了不同渗透系数、荷载频率、流体饱和度以及边界条件下单层非饱和多孔介质一维瞬态动力响应的特点。该方法不受材料参数和边界条件的限制,具有良好的计算精度、稳定性和适用性。针对单层非饱和多孔介质瞬态响应求解过程中遇到的动力矩阵不可逆问题,对原有的精细时程积分法进行了一定改进。这一改进拓宽了精细积分法的适用范围,使其能应用于刚度矩阵奇异或接近奇异的情形,从而满足本文各类边界条件下的瞬态响应问题求解。
[Abstract]:The wave problem of porous media is an important basic subject in geotechnical engineering, seismic engineering, ocean engineering, environmental engineering and so on, and the transient response is an important part of wave theory. In this paper, the one-dimensional transient response of single-layer porous media is studied by semi-analytical method, and some results are obtained. In view of the one-dimensional transient response of single layer unsaturated porous media, Zienkiewicz's wave equation based on Biot's theory is used to consider the compressibility of two-phase fluid and solid particles, as well as the inertial, viscous and mechanical coupling effects. The one-dimensional transient response solutions of monolayer unsaturated porous media under ten kinds of typical inhomogeneous boundary conditions are obtained by semi-analytical method. First, the governing equations expressed by displacement after dimensionless are derived and written in matrix form. Then the boundary conditions are homogeneous and the eigenvalue problem corresponding to the governing equation is solved. 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 improved precise time integration method. Finally, several examples are given to verify the correctness of the present results and the characteristics of one-dimensional transient dynamic response of single-layer unsaturated porous media under boundary conditions are discussed, such as different permeability coefficient, load frequency, fluid saturation and boundary conditions. The method is not limited by material parameters and boundary conditions, and has good accuracy, stability and applicability. In order to solve the irreversible problem of dynamic matrix in the process of solving the transient response of single layer unsaturated porous media, the original fine time integration method is improved. This improvement broadens the scope of application of the precise integration method and enables it to be applied to the singular or near singular cases of stiffness matrix, thus satisfying the solution of transient response problems under various boundary conditions in this paper.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TU435;O357.3

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