饱和土一维动力响应分析的弱式微分求积元法

基于伽辽金加权残值法,本文首先建立一维饱和土动力学控制微分方程的弱形式,而后分别采用微分求积法和有限元法将其空间坐标离散,得到以土体骨架位移、流体-土骨架相对位移和孔隙流体压力为自由度的单元离散方程,从而采用Crank-Nicolson法求解.数值算例一方面通过与解析解的对比,验证了离散方程和数值程序的正确性.另一方面,通过地表位移和基底孔隙压力的收敛性分析,检验了求积元和有限元法的收敛效率.数值结果表明:所建立的弱式微分求积法在饱和土动力分析中不仅具有显著优于常规有限元法的收敛效率,而且还具有可变阶的收敛性能,为今后高效率分析提供了一种可能.

Weak-Form Quadrature Element Method for One-Dimensional Dynamic Analysis of Saturated Soil

It is established the weak-form of differential equations that govern the one-dimensional dynamic behaviors of saturated soil, using the Galerkin weighted residual method, then the space coordinate is discretized by differential quadrature method and finite element method, respectively. The displacement of soil skeleton, fluid-skeleton relative displacement and pore fluid pressure are chosen as the degrees of freedom. The discretized equations are finally solved by Crank-Nicolson method. Numerical examples, on the one hand, verifies the proposed weak-form equations and numerical programs developed through the comparisons with the analytical solutions, on the other hand, the convergence performance is examined via the convergence test about the ground surface displacement and pore pressure. The numerical results show that the proposed weak-form quadrature element method (WQEM) not only possesses significantly faster computational efficiency than the conventional finite element method in the dynamic analysis of saturated soil, but the convergence rate of WQEM is also adjustable, which makes it possible for its future high-performance analysis.