Application of Rigid-plastic Finite Element Method to Geotechnical Engineering

塑性有限元法是一种用于结构极限分析的数值技术，需要很少的编程。然而，刚塑性有限元法的编程比通常的有限元法稍微复杂一些。因此这种方法没有被广泛使用。本研究的主要目的是通过重新建立理论背景和改进计算技术来展示刚塑性有限元方法的巨大优势和有效性。研究结果如下：1)弹性区域的处理在刚塑性有限元方法中，假设所有区域都处于塑性状态，这意味着即使远离加载，也不存在弹性区域。该假设会导致一定程度的数值误差和数值不稳定。因此解决弹性区域的处理是刚塑性有限元法的问题之一。在这项研究中，我们通过假设弹性区域完全刚性而没有任何变形率，建立了解决该问题的新技术。这一思想直接遵循刚塑性理论，可以使数值过程稳定。2）含地下水土结构的极限分析一般认为土结构周围存在地下水，严重影响地基稳定性。这是由于地下水改变了地面重力，降低了有效应力，使地面强度下降。因此，地下水的处理必须考虑土壤结构的极限状态。目前尚未发现将土结构临界状态与地下水影响之间的关系结合到极限状态分析中的研究。在这项研究中，我们成功地将孔隙水压力的影响以及重力的变化与整个区域极限状态下的平衡方程结合起来。较少的

The plastic finite element method is a numerical technique for the limit analysis of structures which requires very few The programming of the rigid-plastic finiete element method is, however, a little bit more complicated than the usual finite element method. Therefore this method is not being used popularly. The main object of this research is to show the great advantages and effectiveness of the rigid-plastic finite element method by re-establishing the theoretical background and improving the computational techniques. The findings from this research are as follows.1)Treatment of elastic regionIn the rigid-plastic finite element method, all the region is assumed to be in plastic state, which means no elastic region exists even if it is far from loading. This assumption results in some amount of numerical error and numerical instability. Therefore it is one of the problems in the rigid-plastic finite element method to solve the treatment of elastic region. In this research, we have e … More stablished the new technique for this problem by assuming the elastic region to be completely rigid without any deformation rate. This idea follows directly the theory of rigid-plasticity and can make the numerical process stable.2)Limit analysis of soil structure with groundwaterIt is general to assume that there exists the groundwater around the soil structures which affects the stability of ground severely. This is due to the fact that the groundwater changes the gravity force of the ground and decrease the effective stresses which makes the ground strength decreased. Therefore the treatment of the groundwater is essential to consider the limit state of the soil structures. Thus far no research cannot be found which combines the relationship between the critical state of soil structures and the effect of the groundwater in the limit state analysis. In this research, we have succeeded to combine the effect of pore water pressure as well as the change of gravity force with the equations of equilibrium at the limit state of the whole region. Less