非饱和半无限多孔介质一维瞬态响应积分解

发布时间：2018-04-10 17:12

本文选题：土力学 + 非饱和多孔介质　；参考：《岩石力学与工程学报》2015年S1期

【摘要】：基于非饱和多孔介质动力方程,研究了充满2种流体的非饱和多孔介质动力响应问题,并分别给出了2种边界条件作用下非饱和半无限多孔介质一维瞬态响应积分形式解。首先,运用正弦与余弦变换法将偏微分方程组变换为常微分方程组。然后,运用状态空间法求解此常微分方程组,得到变换域内解析解。最后,通过正弦与余弦反变换,给出非饱和半无限多孔介质一维瞬态响应积分形式解。该方法的优点是积分解中被积函数为实函数,给数值计算带来极大的方便。通过算例分析,验证了本文结果的正确性,证实了非饱和多孔介质内存在3种类型压缩波,分析了3类压缩波作用下多孔介质内固体和2种流体间的相位关系。
[Abstract]:Based on the dynamic equations of unsaturated porous media, the dynamic response of unsaturated porous media filled with two kinds of fluids is studied, and the integral solutions of one-dimensional transient response of unsaturated semi-infinite porous media under two boundary conditions are given respectively.Firstly, the system of partial differential equations is transformed into ordinary differential equations by sine and cosine transformation.Then, the state space method is used to solve the ordinary differential equations, and the analytic solution in the transform domain is obtained.Finally, the integral solution of one-dimensional transient response of unsaturated semi-infinite porous media is obtained by inverse transformation of sine and cosine.The advantage of this method is that the integrable function in the integral solution is a real function, which brings great convenience to the numerical calculation.An example is given to verify the correctness of the results in this paper. It is proved that there are three types of compressible waves in unsaturated porous media. The phase relationship between solid and two kinds of fluids in porous media under the action of three kinds of compressible waves is analyzed.
【作者单位】：中国地震局工程力学研究所中国地震局地震工程与工程振动重点实验室;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;
【基金】：中国地震局工程力学研究所基本科研业务专项(2013B04) 国家自然科学基金资助项目(51308512,51278451)
【分类号】：TU43

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