单层非饱和不可压缩多孔介质一维瞬态响应精确解  

Exact solution for the one-dimensional transient response of single-layer incompressible unsaturated porous media

作　　者：杨相如[1] 陈雪梅 赵云 YANG Xiangru;CHEN Xuemei;ZHAO Yun(Fujian Chuanzheng Communications College,Fuzhou 350007,Fujian,China;School of Civil Engineering,Henan University of Technology,Zhengzhou 450001,Henan,China)

机构地区：[1]福建船政交通职业学院,福建福州350007 [2]河南工业大学土木工程学院,河南郑州450001

出　　处：《地震工程学报》2025年第3期522-528,共7页China Earthquake Engineering Journal

基　　金：福建省自然科学基金(2021J01338);河南工业大学创新基金支持计划专项资助(2022ZKCJ07)。

摘　　要：针对现有研究尚未给出不可压缩非饱和多孔介质瞬态响应的精确解问题,根据Zienkiewicz等提出的非饱和多孔介质波动方程,假定三相均不可压缩,并考虑各相材料间的惯性、黏滞和机械耦合作用,获得一维情况下的单层非饱和多孔介质瞬态响应问题的精确解。以液相流体相对位移为自变量,首先推导出无量纲形式的控制方程,给出无阻尼系统的特征值和特征函数,再根据常数变异法和特征函数的正交性,将原问题转化为一组二阶常微分方程中的初值问题,并用状态空间法求解,进而获得原问题位移和应力的精确解答。通过与已有解析和数值结果对比,验证该解答的正确性。算例分析表明,在不可压缩非饱和多孔介质中,只有一种压缩波;在固定位移边界处,可产生与入射波相位相反的压缩波,且响应幅值随着饱和度的增加呈现减小趋势。The exact solution for incompressible and unsaturated porous media has not been provided in the current literature.Thus,an exact solution was derived in the present study for the transient response of single-layer,incompressible,and unsaturated porous media in one-dimension conditions with typical boundary conditions based on the wave equations for unsaturated porous media proposed by Zienkiewicz.The inertial,viscous,and mechanical couplings were considered in the proposed solution.Taking the relative displacement of the liquid phase fluid as an independent variable,the dimensionless governing equations were first derived,and the eigenvalue and eigenfunction of the undamped system were given.Then,the original problem was transformed into the initial value problem for a set of second-order ordinary differential equations based on the constant-transform method and the orthogonality of eigenfunctions.The resulting problem was then solved using the state-space approach.Through this process,the exact solutions for displacement and stress of the original problem were obtained.The correctness of the solutions was verified by comparing them with the existing analytical and numerical results.Specifically,the analytical results indicate that only one type of compression wave exists in the incompressible unsaturated porous media.The compression wave with an opposite phase to the incident wave was generated at the fixed displacement boundary,whose response amplitude revealed a decreasing tendency with the increase of porous medium saturation.

关 键 词：非饱和多孔介质 不可压缩 瞬态响应 精确解 

分 类 号：TU435[建筑科学—岩土工程]