Physical and geometric non-linear analysis using the finite difference method for one-dimensional consolidation problem

Abstract This article presents a numerical model based on the finite difference method for the physical and geometric non-linear analysis of a one-dimensional consolidation problem regarding a saturated, homogeneous and isotropic soil layer with low permeability and high compressibility. The problem is formulated by adopting the void ratio as the primary variable, considering a Lagrangian movement description. The physical non linearity is introduced on the formulation by the constitutive law defined as effective stress and permeability void ratio functions. Based on this numerical model, a computational system named AC-3.0 was developed, which has been verified and validated in terms of the temporal variation of the void ratio distribution throughout the soil layer, by comparing the numerical results with analytical and numerical solutions found in literature for some specific scenarios. Knowing the void ration distribution,it is possible to obtain secondary variables such as: superficial settlement, effective stress and excess of pore water pressure.The importance of the non-linear formulation is highlighted for the analysis of problems related to material presenting high compression and a very high initial void ratio.

摘要 本文提出一种基于有限差分法（Finite Difference Method）的数值模型，用于开展低渗透性、高压缩性饱和均质各向同性土层一维固结问题的物理与几何非线性分析。本研究以孔隙比作为主变量，采用拉格朗日（Lagrangian）运动描述方式构建该问题的控制方程。模型的物理非线性通过本构关系引入，该本构关系将有效应力与渗透性均定义为孔隙比的函数。基于该数值模型，本研究开发了一款名为AC-3.0的计算系统。通过将数值结果与文献中特定场景下的解析解及数值解进行对比，针对孔隙比在土层内的时空分布变化特征，对该系统完成了验证与校核。在获取孔隙比分布后，便可推导得到地表沉降、有效应力以及超孔隙水压力等次级变量。针对高压缩性且初始孔隙比极高的岩土材料相关问题的分析而言，非线性本构建模的重要性在本文中得到了充分凸显。