考虑惯性耦合的两相介质动力反应显式数值计算方法  

Time⁃domain Full Explicit Numerical Algorithm of Fluid⁃saturated Porous Media Considering Inertial Coupling

作　　者：徐静茹 李亮[1] 宋佳 XU Jingru;LI Liang;SONG Jia(Key Laboratory of Urban Security and Disaster Engineering,Beijing University of Technology,Ministry of Education,Beijing 100124,China;School of Civil Engineering,North China University of Technology,Beijing 100144,China)

机构地区：[1]北京工业大学城市安全与灾害工程教育部重点实验室,北京100124 [2]北方工业大学土木工程学院,北京100144

出　　处：《防灾减灾工程学报》2023年第5期1009-1015,共7页Journal of Disaster Prevention and Mitigation Engineering

基　　金：国家自然科学基金项目(51808006)资助。

摘　　要：基于包含惯性耦合(耦合质量密度系数)的u‑p形式饱和两相介质弹性波动方程,开展了对饱和两相介质近场波动问题时域全显式数值计算方法的研究。通过对波动方程中的质量集中矩阵和流体压缩矩阵对角化处理,消除了方程中的动力耦联的影响。分别应用中心差分法和Newmark常平均加速度法求解固相位移和固相速度,基于向后差分法求解孔隙流体压力,建立了考虑惯性耦合的饱和两相介质的时域显式数值计算方法。将该方法的数值解与相应的解析解进行对比,二者符合良好,验证了该方法的正确性。将该方法应用于饱和两相介质自由场的地震反应问题,研究了惯性耦合对两相介质动力反应的影响。基于本文研究的两种情况表明,惯性耦合对饱和两相介质动力反应的影响程度有限。Based on the u-p dynamic formulation of saturated two-phase media with considering inertial coupling(coupled mass density),the fully explicit algorithm intime domain for the near-field wave problem of fluid-saturated porous media is studied.The dynamic coupling in the equation is eliminated by diagonalizing the mass matrix and fluid compression matrix in the equation.The center difference method and Newmark constant average acceleration method are used to solve the solid phase displacement and velocity respectively,and the backward difference method is used to solve the fluid pressure.The numerical solution of the proposed method is compared with the analytical solution,with a strong agreement confirming the accuracy of the method employed.The method is applied to the seismic response of free field in saturated two-phase media and analyze the influence of inertial coupling on the dynamic response of two-phase media.Based on the two cases studied in this paper,the results show that the effect of inertial coupling on the dynamic reaction of fluid-saturated porous media is limited.

关 键 词：饱和两相介质 动力反应 时域全显式数值算法 惯性耦合 u‑p形式波动方程 

分 类 号：TU435[建筑科学—岩土工程]