线性加速度显式积分格式的海岸两相介质场地地震反应分析  

Analysis on Using Linear Acceleration Explicit Integration Formula for Seismic Response of Two-Phase Media Site in Coastal

作　　者：陈学良[1] 张波 李铁飞[1] CHEN Xueliang;ZHANG Bo;LI Tiefei(Institute of Geophysics,China Earthquake Administration,Beijing 100081,China;School of Civil Engineering,Hebei University of Architecture,Zhangjiakou 075000,China)

机构地区：[1]中国地震局地球物理研究所,北京100081 [2]河北建筑工程学院土木工程学院,河北张家口075000

出　　处：《烟台大学学报(自然科学与工程版)》2025年第2期125-133,共9页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：基本科研业务专项(DQJB24Z01,DQJB24R31);国家重点研发计划(2023YFC3007305,2019YFC1509403);国家自然科学基金资助项目(52478566,51978633);河北省教育厅科学研究项目(QN2025419)。

摘　　要：为了建立覆水海岸两相介质地震反应分析的全显式有限元法,以饱和两相介质土力学模型为基础,对近场波动问题的时域显式数值算法进行研究。首先,采用伽辽金加权余量法对一维压缩波波动的动力方程实现空间离散;然后,分别应用中心差分和Newmark线性加速度法求解位移和速度,而加速度是由速度积分法求得,进而得到该动力方程自起步的时域逐步积分公式;最后,引入透射人工边界,得到饱和两相介质近场波动问题求解的全显式时域有限元法。基于时域递推公式的积分逼近算子矩阵,研究了该算法的稳定性条件。将该算法的数值解与相应的解析解进行比较,验证了算法的正确性和有效性。最后,将此方法应用于覆水海岸两相介质场地土层的地震反应分析中,研究了海水对其地震响应的影响。该方法具有计算量小、效率高、精度高的优势,可为结构动力方程和波动方程的求解提供借鉴。The paper presents a fully explicit finite element method for analyzing the seismic response of two-phase media sites in coastal areas.It develops a time-domain explicit numerical algorithm for near-field wave problems based on a soil mechanics model of saturated two-phase media.Initially,the Galerkin weighted residual method is applied for spatial discretization of the one-dimensional compressional wave motion dynamic equation.Subsequently,displacement and velocity are computed using the central difference and Newmark linear acceleration methods,respectively,with acceleration determined via velocity integration.This leads to the derivation of a time-domain stepwise integration formula for the dynamic equation.Finally,by incorporating a transmitting artificial boundary,the study establishes a fully explicit time-domain finite element method for solving near-field wave problems in saturated two-phase media.The stability conditions of the method are examined using the integral approximation operator matrix within the time-domain recursive formula.The algorithm's validity is confirmed by comparing numerical solutions with corresponding analytical solutions.The method is then applied to analyze the seismic response characteristics of two-phase media sites in coastal areas,highlighting the significance of seawater.This approach offers advantages in computational cost,efficiency,and accuracy,providing a valuable reference for solving structural dynamic and wave equations.

关 键 词：饱和两相介质 土力学模型 显式有限元 透射人工边界 线性加速度法 

分 类 号：O357.3[理学—流体力学] TU435[理学—力学]