Augmented Finite Element Method And Its Application In Discontinuous Deformation Analysis In Geotechnical Engineering

Shear bands are common forms of geotechnical engineering disasters, and therefore accurate predictions of the onset and the propagation of the shear bands are very important to understand the mechanism of geotechnical engineering disasters, and to devise measures to prevent and control the disasters. The shear band is virtually a kind of cohesive crack growth problem. The modeling of the shear bands involves discontinuous deformation analysis and is a current research focus. Aiming at some key issues involved in the modeling of discontinuous deformation problems, this thesis proposes a mesh-separation-based approximation technique and an augmented finite element method. The description of discontinuous deformation and an adative mesh refinement strategy, which are suitable for arbitrary shear band growth problems, are presented based on the augmented finite element method. Then these two techniques are used to model the rupture of the deposits induced by fault movements.The research results are as follows:(1) A standard finite element mesh is separated into two geometrically independent meshes, namely mathematical mesh and physical mesh. The mathematical mesh is used to construct displacement approximation, and the physical mesh is obtained by subdividing the problem domain. By doing this, a finite element approximation technique with mesh-separation and mapping rules as the core is proposed, and an augmented finite element method which lies in the framework of the standard finite element method is also presented. The geometrical independence of the mathematical mesh and the physical mesh makes it easy for meshing and for the construction of high-quality displacement interpolations, and so the flexibility and applicability of the finite element method are improved greatly. The standard finite element method is a special case of the augmented finite element method, and the latter is an augmented form of the former.(2) A uniform mapping rule is presented by introducing a transitional element. The uniform mapping rule consists of a reconstruction rule Rr which bridges the nodal displacements of the transitional element and that of the mathematical element, and a covering rule Rc which bridges the displacement approximation of the physical element and that of the transitional element. The formulas of the augmented finite element method, the smoothing stress calculation, and the integration scheme of the element matrices are derived, and then the implementation of the augmented finite element method in existing finite elment codes is given.(3) Based on the uniform mapping rule, by learning the concepts of constructing displacement approximations in the meshfree methods, the semi-analytical finite element methods, etc, corresponding reconstruction rules are proposed. These rules enable the augmented finite element method to enjoy the advanteges of the meshfree methods, the semi-analytical finite element method, and the smoothed finite element method. Additionally, a method for solving the moving boundary problems with fixed mesh is presented.(4) The intra-element discontinuities can be represented by adding enriched transitional nodes and enriched mathematical nodes and subsequently defining proper transitional elements and mathematical elements, while the mapping rule is kept unchanged. This method is recursive and can be easily extended to cases with complex multiple cracks. This method is superior to the standard finite element method in which a crack must be aligned with element boundaries, and it overcomes the difficulties confronted by the XFEM and the Hansbo&Hansbo method in modeling multiple-crack problems.(5) A method to handle arbitrary-level hanging nodes at the element level is proposed. An element-subdivision based adaptive mesh refinement strategy is presented for modeling cohesive crack growth problems. This strategy empolys two indicators, the refinement radius and the crack-tip element size. The results show that the adapvite mesh refinement strategy greatly improves the accuracy of stresses in the vicinity of the crack tip and the results of the crack growth, e.g., the load-displacement curves and the crack path; the load-displacement curve is sensitive to the mesh refinement, whereas the crack path is not.(6) A method to model the shear band propagation in soils is proposed, in which the frictional cohesive zone model is used to represent the softening property of the relationship between the shear stress and the displacement and the mechanism of energy dissipation, and the discontinuous deformation is described by the augmented finite element method. The parameters of the cohesive zone model are determined by back-analyzing the direct shear tests. The centrifuge experiment result of the soil rupture induced by a reverse fault movement is reproduced numerically. The effects of the plastic flow rule and the softening property of the shear band on the soil rupture are studied. The results show that the propagation path of the shear band determined by the associated flow rule is more comparable to the experiemente results.