非饱和土-结构动力响应的多耦合周期性有限元法  

MULTI COUPLING PERIODIC FINITE ELEMENT METHOD FOR CALCULATING THE DYNAMIC RESPONSE OF UNSATURATED SOIL-STRUCTURE SYSTEM

作　　者：狄宏规[1,2] 郭慧吉 周顺华[1,2] 王炳龙[1,2] 何超[1,2] Di Honggui;Guo Huiji;Zhou Shunhua;Wang Binglong;He Chao(Key Laboratory of Road and Traffic Engineering of the Ministry of Education,Tongji University,Shanghai 201804,China;Shanghai Key Laboratory of Rail Infrastructure Durability and System Safety,Tongji University,Shanghai 201804,China;The Technical Center of Shanghai Shentong Metro Group Co.,Ltd.,Shanghai 201103,China)

机构地区：[1]同济大学道路与交通工程教育部重点实验室,上海201804 [2]同济大学,上海市轨道交通结构耐久与系统安全重点实验室,上海201804 [3]上海申通地铁集团有限公司技术中心,上海201103

出　　处：《力学学报》2022年第1期163-172,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(51808405);上海市自然科学基金(20ZR1459900)资助项目。

摘　　要：真实的地基土体-隧道系统中土体及结构性质往往沿线路纵向变化.为考虑土体与结构沿纵向的变化特性,提出了一种非饱和土-结构系统动力响应分析的多耦合周期性有限元法.首先基于非饱和土的实用波动方程,采用Galerkin法推导了单节点5个自由度的非饱和土u;-p;-p;格式有限元表达式,相比于单节点9个自由度的u;-v-w格式有限元表达式,节省了计算资源.其次引入复拉伸函数,构建完美匹配层边界单元截断无限域.最后采用多周期性模拟结构沿纵向的变化特性,引入自由波传播理论,结合各周期性结构间的连续性条件,实现纵向各周期性结构间的耦合.通过与既有的2.5维有限元-完美匹配层法和波函数法的计算结果进行对比,验证了本文方法的可靠性.该方法与既有的解析、数值方法相比,具有可高效考虑结构纵向变化特性的优点.基于该方法,以非饱和土-隧道-隔离桩系统为例,讨论了隔离桩的减(隔)振效果,结果表明:与咬合桩相比,考虑隔离桩桩间距后地表动力响应规律有所改变,因此在进行地铁隧道系统振动响应预测时,应考虑系统结构沿纵向的变化特性.In the actual foundation-tunnel system, the properties of soil and structures often change longitudinally along the tunnel line. In order to consider the longitudinal variation characteristics of structures, a multi coupling periodic finite element method for dynamic response analysis of unsaturated soil-structure system is proposed in this paper. Firstly,based on the practical wave equation of unsaturated soil, the finite element expression of ub-pl-pg scheme for unsaturated soil with 5 degrees of freedom at a single node is derived by Galerkin method, which can save the computing efficiency compared with the finite element expression of ub-v-w scheme with 9 degrees of freedom at a single node. Then, by introducing the stretching function with complex number, the perfectly matched layer boundary element is constructed to truncate the infinite domain. Finally, multi periodicity is used to simulate the longitudinal variation characteristics of the structure. By introducing the free wave propagation theory and combining the continuity conditions between periodic structures, the coupling between periodic structures can be realized. The results of the proposed method are compared with the results obtained by the existing 2.5 dimensional coupled FE-PML model and analytical method respectively,which verified the reliability of the proposed method. Compared with the existing analytical methods or numerical methods, the proposed method has the advantage of considering the longitudinal variation characteristics of the structure efficiently. Based on the proposed method, taking unsaturated soil-tunnel-isolation pile system as an example, the vibration reduction and isolation effect of isolation pile is discussed. The results show that compared with gnawing piles,the regular of surface dynamic response changes after considering the spacing between isolated piles. Therefore, in order to accurately predict the vibration response of subway tunnel system, the longitudinal variation characteristics of the system structure should

关 键 词：非饱和土 隧道 多耦合周期性有限元 完美匹配层 动力响应 

分 类 号：U451.3[建筑科学—桥梁与隧道工程]