Research On The Method Of Nonlinear FEM Reliability Analysis Of Slope Stability

Based on the review of the analysis methods of slope stability and a lot of knowledge, such as geomechnics, elasto-plastic mechanics, nonlinear finite element method (FEM), probability theory and mathematics statistics, reliability mathematics, computer science, some methods of nonlinear FEM reliability analysis of slope stability are studied in detail in this thesis. Main achievements and conclusions are as follows.A FEM reliability analysis method of slope stability which is based on the strength reduction method (SRM) is proposed. The advantage of this method is that it can calculate the overall reliability index instead of the calculation of each element's reliability index. Another advantage is that this method can make use of any definite FEM software, no matter the research object is linear of nonlinear. Therefore, it is very convenient for anyone to use it.Based on incremental initial stress method and partial differential technique, another FEM reliability analysis method of slope stability which is based on the slip surface stress analysis (SSA) is studied. The main problems of this method are the calculation methods of the overall reliability index and the location of the corresponding slip surface of a slope. It's concluded that the type of the limit state function has great influence to the overall reliability index, and the yielding function which can consider the sliding direction should be selected as the limit state function for it can reflect the influence of the sliding direction properly.The similarities and differences of the above two methods are compared. It's proved that the first method is simple in programming and can make use of any definite software, but the running speed is very slow. On the contrary, the programming procedure is very complicate in the second method, but the running speed is very quick. At the same time, it can also calculate the location of the slip surface in the second method. It's also testified that the above two methods are the same substantially, and the difference of the two methods may come from their different implementation procedures.An improved response surface method - FORM-RSM - is proposed in this thesis. This new method can overcome the shortcomings of the general used RSM, which is based on the iteration of response surfaces. The first step of this method is to calculate the reliability index and the design point by using first order reliability method, and the second step is to fit a response surface on the design point. Then, the reliability index can be calculated by using some normal first order reliability method. It's demonstrated from several examples that the accuracy and efficiency of this new method are better than that of the general used RSM.The sensitivity calculation method in the FEM reliability analysis is studied, and the formulas of the sensitivity of reliability index to the basic parameters in the original space when they arc correlated are derived. And then, a relative sensitivity analysis method and formula are suggested. It's showed that the transforming matrix, which is needed in the computation in the transformed space, is now unnecessary in this method. And the disturb of the different units of each parameter can now be eliminate in the relative sensitivity analysis method, so it's more proper to compare the influence of all kinds of parameters.In the reliability analysis of a slope using finite element method, what is usually considered is only the property of elasto-plasticity or material nonlinearity. However, there exists local large strain in most soil slopes. Therefore, the FEM reliability analysis method, which can consider both the material nonlinearity and the large deformation geometric nonlinearity, is studied, and the differences of the results of small and large deformation methods are compared. It's proved that the parameter of elastic module has little influence on the safety factor and the reliability index in the normally used small deformation FEM analysis. However, if there is some large deformation, the influence of elastic module to the safety factor and the reliability index will become large, and it should not be omitted.Based on the accelerating convergence method of Aitken and the method of incremental tangent stiffness method in the definite FEM analysis, a corresponding accelerating convergence method and its formulas are studied in the stochastic finite element analysis. Through the comparison of the methods which consider and don't consider the accelerating one, it's demonstrated that this new accelerating method can improve the convergence speed greatly.The application of the limit step length iteration method to the FEM reliability analysis of the slope stability is studied. Through many times of calculation, the influence of the initial step length and the step length adjustment coefficient to the iteration procedure of the reliability index and their range of values are studied. It's proved that this method can conquer the probably non-convergence phenomenon of the iteration of the normally used first order reliability method.