孔隙介质的时域BEM计算.docVIP

集中力作用任意有限空间的饱和土动力反应分析与计算 丁伯阳1 蒋佳琪1 1. 浙江工业大学建筑工程学院 浙江杭州 310014 摘要：集中力作用下饱和土动力反应分析在无限空间是Biot方程的基本解，在半无限空间是两相介质的Lamb问题。在任意有限空间Somigliana表象积分结果。本文阐述以解耦的独立快纵波，慢纵波解答；结合独立的横波及流相简明基本解答，形成完整的Stokes状态的Biot孔隙动力方程-解答体系；在Somigliana表象积分计算中简化了BEM奇异性处理，给出集中力的表面源与埋置源作用下的饱和土有限空间时域分析的计算实例，并与相应单相结果作了比较。 关键词： 集中力 饱和孔隙介质 时域BEM 动力响应 任意空间 The dynamic analysis in arbitrary space of saturated soil subjected to a concentrated force and numerical implementation Boyang Ding[1] Jiaqi Jiang[1] 1. College of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, China Abstract: The results of dynamic analysis for an infinite space of saturated soil subjected to a concentrated force are the fundamental solutions of Biot’s dynamic equation; the results for a half-space are the solutions of Lamb’s problem in a two-phase medium; the results for arbitrary space are the integration for Somigliana’s representation. With achievements of decoupling for the fast and slow dilational waves; combining Holmholtz’s solution of independent distortional wave and the concise forms of fundamental solutions for the flow-phase, the authors complete the fundamental solutions in - formulation of Stokes’s state for Biot dynamic equation in this paper. The simplified methodology of treatment to singularity in BEM numerical implementation is presented, the calculation results in an arbitrary space subjected to a surface and embedment sources of concentrated forces are shown respectively for example. The comparison results of response computation in time domain for saturated soil and single phase soil are shown also. Keywords: Concentrated force; Porous medium; Time-domain BEM; Dynamic response; arbitrary space 引言 集中力作用下饱和土动力反应分析在无限空间是Biot方程的基本解[1]，在半无限空间是两相饱和介质的Lamb问题解答[2,3]；在有限空间Somigliana表象空间积分结果[4]，它的数值计算一般由BEM(边界元法)完成。由于FEM(有限元法)难以精确模拟饱和土中固相颗粒与流相间的相互作用，而BEM只需在边界积分，对域内架构要求较低；。并还有着降维和辐射自动满足优势；BEM在饱和孔隙问题(如土动力)响应分析中日益受到重视。 Biot(1941)是为研究土的固结 [5]提出具有耦合扩散变形，又充满自