土壤的固结效应及精细积分数值求解

基于广义Biot固结理论，利用有限元离散方法，得到土层固结效应的u-p形式的基本方程，进而通过引入基本方程中原变量的对偶变量，在Hamilton体系下建立了土层固结效应的微分方程。在具体计算过程中，利用时程精细积分方法，对固结问题进行了计算，并通过数值算例说明了中方法的有效性。

Precise Numerical Solution of Soil Consolidation Effect and Its Possible Engineering Application

Numerical methods progressed by leaps and bounds since the days of Terzaghi, who pioneered in soil mechanics with a view to applying it to solution of engineering problems. The aim of this paper is to give an effective precise integration numerical method for soil consolidation effect in Hamilton system. Based on the generalized Biot theory and the finite element discretion method, for soil consolidation effect, the essential equation with u p form is obtained. Then by introducing into the dual variable of the original variable in the essential equation, the differential equation of soil consolidation effect in Lagrange system is established under Hamilton system. In the process of the concrete computation, the consolidation problem is computed with the help of established time precise integration method in linear dynamic system. Finally a numerical example is given. It is not a real engineering problem but may possibly be termed an idealized engineering problem. Fig.1 shows the finite element mesh of a soil foundation 20m long and 12.5 m high, with a beam 3.5 m long and lying on top of left end of soil foundation. Table 1 gives the soil settlements in meters of various mesh nodes at 5 day intervals after 5 to 50 days. Table 2 gives the final soil settlements of various mesh nodes for two cases: (1) with a 3.5m beam; (2) without a beam. The numerical examples show that the presented method is effective. This paper provides some important valuable conclusions , which will lay some foundations for the deep researches of theory, computation and engineering application of soil mechanics.