Study On Sliding Stability Of Gravity Dam Using Catastrophe Theory

With the development of the nonlinear finite element technology, foundation surface for the gravity dam stability analysis against sliding is no longer confined to using rigid body limit equilibrium method or the linear finite element method and other methods.In view of the nonlinear finite element method, has now formed a variety of criteria (convergence criterion by criteria, etc.).In this paper, by using the mutation model common two application modes (data fitting and qualitative fitting) from two different angles of gravity dam foundation surface stability for this engineering problem studied, respectively.Specific work is as follows:(1) Made a introduction to the catastrophe theory, according to the five kinds of common has a single state variable mutation model of mathematics and geometry feature, using mathematical knowledge obtained common five kinds of mutation model of algebraic expressions of bifurcation set, and the problems arising from the catastrophe theory in practical application are expounded, with a single state variable of the reasonable application of five kinds of mutation model are proposed.(2) Combined with practical engineering, respectively based on rigid body limit equilibrium method of safety coefficient method, the partial coefficient method, reliability analysis method and nonlinear finite element method of the convergence criterion and paroxysmal criteria (including displacement, plastic zone area, criterion of mutant strain energy) for typical dam section was analyzed, and the calculation analysis shows that the mutant strain energy criterion is several other criteria have a certain advantage.(3) With the five kinds of a single state variable mutation model of numerical fitting method has made the preliminary elaboration, and combined with engineering example by the strain for instability of dam foundation system to investigate the five mutations model is used for calculation and analysis, preliminary to its foundation surface for the point mutation model for gravity dam stability analysis has stronger applicability conclusion, through the analysis and points out the deficiency of numerical fitting application way.(4) Use the mutations such as folding, sharp point, dovetail model to consider the stability of dam foundation surface of material damage theory and case analysis, and comparison with the conventional rigid body limit equilibrium method, points out the deficiency existing in the rigid body limit equilibrium method, and the applicability of various mutation model are analyzed. (5) The cusp catastrophic model is adopted to consider the material damage plastic coupling of gravity dam foundation surface stability are analyzed, and compared with the traditional rigid body limit equilibrium method, further points out the existing shortcomings of the rigid body limit equilibrium method, and analyzes the applicability of the cusp catastrophic model.