动力固结问题的弱形式求积元分析

Dynamic consolidation analysis by the weak form quadrature element method

弱形式求积元法是一种新型的高阶方法,已经在岩土及结构分析中取得了成功的应用,本文对该方法进行进一步的发展和完善,将其应用于饱和土动力固结分析.首先基于Biot饱和土波动理论框架,以孔隙水压力和土体骨架位移为基本控制变量,建立饱和土波动问题控制方程弱形式描述,然后应用Lobatto积分和微分求积法进行数值积分和数值微分并采用Newmark方法进行时域逐步积分,建立饱和土波动问题求积元法求解列式.通过数值算例验证了本文方法的正确性,显示了方法的计算效率.

The weak form quadrature element method is a novel high order algorithm applied successfully in structural and geotechnical engineering.In the present study,it is reformulated for dynamic consolidation analysis of saturated soils.Based on Biot’s theory of dynamic consolidation,the pore pressure and soil displacement are chosen to be the control variables to establish the weak form governing equations.Then the Lobatto integration rule and the differential quadrature method are employed respectively to numerically integrate and differentiate the weak form governing equations,and the Newmark scheme is used for time integration.The established formulation is verified by numerical examples and its efficiency is highlighted.