Application of Rigid-plastic Finite Element Method to Geotechnical Engineering

塑性有限元法是结构极限分析的一种数值方法，要求不高，但刚塑性有限元法的程序编制比一般的有限元法稍复杂一些。因此，这种方法并没有被广泛使用。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法的巨大优势和有效性。本文的主要研究成果如下：1）弹性区的处理在刚塑性有限元法中，假定所有区域都处于塑性状态，这意味着即使远离载荷，也不存在弹性区。这种假设会导致一定数量的数值误差和数值不稳定性。因此，解决弹性区域的处理问题是刚塑性有限元法的难点之一。在这项研究中，我们有E 关于我们 通过假设弹性区域是完全刚性的，没有任何变形率，建立了解决这个问题的新方法。这种思想直接遵循刚塑性理论，并能使数值过程稳定。2）考虑地下水的土结构极限分析一般假定土结构周围存在地下水，地下水对地基的稳定性影响很大。这是由于地下水改变了地基的重力，降低了有效应力，使地基强度降低。因此，地下水的处理必须考虑土结构的极限状态。在极限状态分析中，将土结构的临界状态与地下水的影响相结合的研究，至今尚未见到。在这项研究中，我们成功地联合收割机孔隙水压力的影响，以及重力的变化与平衡方程在整个区域的极限状态。少

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