Application of Rigid-plastic Finite Element Method to Geotechnical Engineering

塑性有限元法是一种要求很少的结构极限分析的数值方法，但刚塑性有限元法的编程比通常的有限元法要复杂一些。因此，这种方法并不普遍使用。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显示刚塑性有限元方法的巨大优势和有效性。本研究的结果如下：在刚塑性有限元法中，假定所有区域都处于塑性状态，即即使远离荷载也不存在弹性区域。这种假设导致了一定程度的数值误差和数值不稳定性。因此，如何解决弹性区域的处理问题是刚塑性有限元法中的难题之一。在本研究中，我们建立了一种新的方法来解决这一问题，即假设弹性区域是完全刚性的，没有任何变形率。这种思想直接遵循了刚塑性理论，可以使数值过程稳定。2)含地下水的土结构极限分析一般假设土结构周围存在地下水，地下水严重影响地面的稳定性。这是由于地下水改变了地面的重力，降低了有效应力，使地面强度降低。因此，地下水的处理必须考虑土体结构的极限状态。在极限状态分析中，目前还没有将土结构临界状态与地下水作用的关系结合起来的研究。在本研究中，我们成功地将孔隙水压力和重力变化的影响与整个区域极限状态的平衡方程结合起来。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