Limit Analysis Method And Its Application To Geotechnical Engineering With Linear And Nonlinear Failure Criteria

The methods for calculating bearing capacity of foundation and stability of slope in geotechnical engineering are studied by many investigators. These methods may generally be classified into the following four categories: (1) the limit equilibrium method including vertical slice approach, (2) the slip line method, (3) numerical methods based on either elasto-plastic finite element technique or finite difference method, and (4) limit analysis method on the basis of classical plastic theory. This dissertation generalizes the previous achievements, and reviews the advanced development and application of limit analysis method in geotechnical engineering. The open problems unsolved in limit analysis method are pointed out in Chapter One. The further studies are also given in Chapter Six at the end of the dissertation. The main contributions of the dissertation are as follows.The objective of the research presented in Chapter Two is to develop a computational method for limit analysis problems that involve the determination of lower and upper bound analytical solutions of bearing capacity for circular footing under external loads. In general, the lower bound limit analysis is characterized by construction of two-dimensional stress fields. However, the concept of three-dimensional stress leg is proposed to construct statically admissible stress fields according to the theory of stress .field overlapping, and the lower bound solutions of circular footing bearing capacity are obtained under situations of different numbers of stress legs. By suitable choice of a kinematically admissible velocity field, the upper bound answers are obtained from the dissipated power. The results are approximate to the Shield's (1955) achievements, and are checked by the results of SPT experiments, which demonstrates the efficiency and correctness of computational method presented.Based on Sloan's (1995) achievements, discrelization of soil and rock into triangular elements is an efficient way to construct kinematically admissible linear velocity field within elements. Functions subject to associated flow rule within elements, associated flow rule along discontinuities and boundary conditions are solved by the method of mathematical programming such as the steepest edge active set algorithm proposed by Sloan (1989) and augmented Lagrangian method proposed by Jiang (1994). The algorithms mentioned above can solve the optimal problem with a few hundreds of elements efficiently. However, it will take much time to solve the problem with thousands of elements and discontinuities using the above methods. This objective of Chapter Three is to develop a computational method for large-scale optimal problem that involves plenty of kinematical elements and velocity discontinuities. First, the original problem is transformed into standard form adopted for interior-point approach using slack variables. Then, feasible range of original problem is converted to unit spheroid range, and converted optimal solution is obtained by moving converted objective function along first-order decent direction in converted range. Finally, inverse conversion is employed to obtain optimal result. From the results calculated, it can be seen that number of iterations of interior-point approach is less than that of steepest edge active set algorithm proposed by Sloan (1989), corresponding to the same problem.Chapter Four of the dissertation describes a technique for computing rigorous upper bounds on slopestability factors, passive earth pressure of rigid retaining wall and bearing capacity of a strip foting under the condition of plane strain. The method assumes a perfectly plastic soil, whose failure is governed by nonlinear Mohr-Coulomb (MC) yield criterion, and employs sequential quadratic programming (SQP) in conjunction with the limit analysis of classical plasticity theory. A new kinematically admissible velocity field is constructed. On operating with a linear failure criterion that exceeds the actual nonlinear failure criterion, the objective function fo...