摘要
基于u-p形式的饱和两相介质弹性波动方程,开展了饱和两相介质近场波动问题时域显式数值计算方法的研究。通过对波动方程中的质量矩阵和孔隙流体压缩矩阵进行对角化处理,消除了方程中的动力耦联,实现了波动方程的解耦。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速度,基于向后差分法求解孔隙流体压力,推导得到了饱和两相介质动力响应的时域显式逐步积分的计算列式,建立了饱和两相介质近场波动问题的一种新的时域全显式数值计算方法。进行了该文方法中矩阵对角化合理性的验证。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。将该文建立的时域数值计算方法与透射人工边界方法相结合,应用于饱和两相介质的近场波动问题,进行了饱和土场地地震响应的计算研究,计算结果符合弹性波动理论的基本规律,表明该方法对于饱和两相介质近场波动问题时域计算求解的适用性。基于该方法中时域递推计算格式的传递矩阵,进行了该方法稳定性特性的研究。该文建立的数值计算方法具有时域全显式算法的基本特征。方法中对动力响应的全部分量均采用递推和迭代的模式进行求解,避免了求解耦联的动力方程组。该方法具有较高的计算效率,是进行饱和两相介质近场波动问题时域计算求解的一种有效的算法。
The explicit numerical algorithm for the near-field wave motion of fluid-saturated porous media in time domain is investigated based on u-p dynamic formulation.The wave motion equations are decoupled,and dynamic coupling is eliminated by the diagonalization of the mass matrix and pore fluid compression matrix.Based on the decoupled wave motion equations,the central difference method and Newmark constant average acceleration method are adopted for the solution of solid-phase displacement and velocity,respectively.The formulation of pore fluid pressure is derived based on the backward difference method.Then the explicit staggered calculating formulas for the dynamic response of fluid-saturated porous media are derived,and a new full explicit numerical algorithm for the near-field wave motion of fluid-saturated porous media in time domain is developed.The rationality of matrix diagonalization in the algorithm is validated.The numerical results gained by the proposed algorithm accord well with the corresponding analytical results.This indicates the accuracy of the proposed algorithm.Combining the time domain numerical calculation method proposed with the transmission artificial boundary method,it is applied to the near field wave motion problem of fluid-saturated porous media,and the seismic response of saturated soil site is calculated and studied.The numerical results of the seismic response of saturated soil field accord with the elastic wave motion theory.This indicates the applicability of the developed algorithm to the near-field wave motion problem of fluid-saturated porous media.The stability characteristic of the developed algorithm is investigated based on the transfer matrix of the iterative calculating formulas of the algorithm.In the developed algorithm,all the variables of dynamic response are calculated in an iterative pattern.Thusly,this algorithm has the basic characteristic of the full explicit numerical algorithm in time domain.In the developed algorithm,all the components of the dynamic response a
作者
李亮
李果
杜修力
宋佳
LI Liang;LI Guo;DU Xiu-li;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)
出处
《工程力学》
EI
CSCD
北大核心
2020年第8期20-31,共12页
Engineering Mechanics
基金
国家自然科学基金创新群体项目(51421005)
国家自然科学基金青年科学基金项目(51808006)。
关键词
饱和两相介质
近场波动问题
u-p形式波动方程
时域全显式算法
动力响应
透射人工边界
fluid-saturated porous media
near-field wave motion
u-p dynamic formulation
full explicit algorithm in time domain
dynamic response
transmitting artificial boundary
