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

1)圆柱内同轴与非同轴凸轮-粘土模型的分叉分析。本文给出了共轴和非共轴Cam-clay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，对于一个非共轴模型，所有模式的分叉载荷存在，几乎相等的压缩测试，然而，一个扩展的测试的负载采取其最小值在收缩模式。这些结果与饱和粘土的实验变形模式吻合较好。然后，我们发现，对于一个非共轴模型，从最大应变的分布，预测的网状滑移面与粘土压缩试验中观察到的滑移模式吻合得很好。我们还发现，对于一个同轴模型，轴对称胀形模式的分叉载荷，这是经常在实验中观察到的，不存在。这表明非共轴项在滑坡研究中是不可或缺的。2）采用隐式计算算法的土/水耦合问题有限元分析。我们开发了一种新的方法隐式，有限元分析的土/水耦合问题，在一个著名的剑桥模型。隐式返回映射方案是基于弹性预测和塑性校正。算例表明，隐式法计算精度高，大大减少了计算时间。3）非协调单元的有限元分析及精度检验。作为滑坡问题的基础研究，本文提出了一种单元内位移不连续的强不连续有限元分析方法，其解与网格无关。然后，我们估计的方法，通过使用E积分验证的断裂能的准确性。结果表明，从断裂能的角度考虑，强不连续性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.