Investigation of the Landslip by the Bifurcation Theory and the Finite Element Method using Incompatible Elements

1)同轴和非同轴凸轮-粘土模型圆柱体的分叉分析。我们得到了同轴和非同轴凸轮-粘土模型在对称和反对称变形下所有扩散模的精确解.我们发现，对于非同轴模型，所有模的分叉载荷都存在，压缩试验的分叉载荷几乎相等，而扩展试验的分叉载荷在a-收缩模式下最小.这些结果与饱和粘土的实验变形规律吻合较好。对于非共轴模型，从最大应变的分布来看，预测的网状滑动面与粘土压缩试验中观测到的滑移形态吻合较好。我们还发现，对于同轴模型，实验中经常观察到的轴对称鼓包模式的分叉载荷是不存在的。这说明在研究滑坡问题时，非同轴项是不可缺少的。2)采用隐式算法进行土水耦合问题的有限元分析。在一个著名的凸轮-粘土模型中，我们发展了一种新的土/水耦合问题的隐式有限元分析方法。隐式返回映射格式是基于弹性预报器和塑性校正器的。算例表明隐式方法具有较高的计算精度，大大减少了总的计算时间。3)非协调单元的有限元分析及精度检验。作为滑坡的基础研究，我们发展了一种单元内部位移不连续的强不连续有限元分析，其解是网格无关的。然后，通过E积分验证断裂能的准确性，对该方法进行了估算。结果表明，从断裂能的角度考虑，强不连续面分析具有较高的精度。

1) Bifurcation Analysis in a Circular Cylinder of Coaxial and Non-coaxial Cam-clay Models. We obtain the exact solutions for all diffuse modes under symmetric and anti-symmetric deformation for coaxial and non-coaxial Cam-clay model., We find that, for a non-coaxial model, the bifurcation loads for all modes exist and nearly equal for a compressive test; however, the load for an extended test takes its minimum in a - constriction mode. These results agree well with the experimental deformation pattern of saturated clays. We then find that for a non-coaxial model, judging from the distributions of the maximum strain, the predicted net-like slip planes agree well with the observed slip pattern in the compressive test of clays. We find also, for a coaxial model, the bifurcation load for an ax symmetric bulging mode, which is often observed in the experiments, does not exist. This shows that the non-coaxial terms are indispensable to investigate the landslip.2) Finite Element Method Analysis of Soil/Water Couping Problems using an Implicit Calculation Algorithm. We develop a new method of implicit, finite element analysis of soil / water coupling problems in a well-known Cam-clay model. The implicit return mapping scheme is based on the elastic predictor and the plastic corrector. Some examples of the implicit method show the high accuracy and much reducing the total CPU time.3) Finite Element Analysis with the Incompatible Elements and the Examination of the Accuracy. As a basic research on the landslip, we developed a strong discontinuity finite element analysis with the displacement discontinuity inside the elements, which solutions are mesh-independent. We then estimate the method by means of verifying the accuracy of the fracture energy by using the E-integral. As a result, we find that the strong discontinuity analysis is high accurate in view of the fracture energy.