A Three-Dimensional Finite Element Approach For Contact Problems And Its Application In Geotechnical Engineering

The interfaces which extensively exist in the geotechnical problems, such as the joints in rock mass, sliding face in soil, the interface between the structure and geotechnical media and so on, will influence the mechanical behaviors of the geotechnical media and the structures significantly, so they shouldn't be ignored in the corresponding computations. So far, though the finite element method has been widely applied to geotechnical problems, it is still intractable to simulate the mechanical behaviors of these interfaces ideally in finite element method. The main intension of this thesis is to treat these uncontinuous problems as contact problems, and to develop a three-dimensional finite element approach which will be applicable to geotechnical problems, following the work in [1].At first, the present computational models to deal with the uncontinuous problems are analysed. Because they are not so perfect and rigorous, the author thinks that it is more reasonable to take the problems as a contact problem. Then, the principal characters of the interfaces can be reflected: (1) the contact interface is of shear strength which implies that a generic pair of contact points on the interface will displace coincidentally if the tangential force at this point has not reached the limit resistance, else, relative slide between the points will occur along the tangential direction. (2) No matter the relative slide occurs or not, the contact bodies cannot invade each other in any wise.To solve the contact problems by using finite element method, the method of variable degrees of freedom for contact problem is put forth by the author of [1], which can solve the contact problems more perfectly. However, only two-dimensional problems are solved in [1]. Based on the theory, the author will extend the method to three-dimensional contact problems in this thesis. The principle of virtual displacement is adopted to deduce the contact problem formulae of 3-D FEM directly instead of variational principle. Based on the forementioned work, one of the important topics is the programming of 3-D FEM code of contact problems. Because of the complex mechanical status in 3-D contact problems, it is not so easy to realize the corresponding 3-D FEM program. To achieve the object, the method of variable degrees of freedom for contactproblem is applied and the incremental iterative method is employed.At last the 3-D contact FEM program is applied to some typical geotechnical contact problems to verify the validity of the method. The successful solution of the examples concerning pressure distribution under rigid footing, proves correctness of the method. Furthermore, the method is applied to a landslide problem, and the satisfied computing result verifies the validity of the method to solve engineering problems. At the end of the thesis, some unsolved problems in this presented method are discussed briefly.