Application And Research Of Catastrophe Theory In Nonlinear Finite Element Analysis Of Deep Anti-sliding Stability Of Dam

In normal circumstances, dam foundation is not a complete rock but always contains complex geological structure joints, cracks and faults, etc, when these surfaces forming a sliding channel, it will lead to major projects accidents resulting in significant losses to life and property of the people as well as the construction of our country. So the research for deep anti-sliding stability of gravity dam has very important implications.In recent years, many scholars of our country have done lots of analysis on deep anti-sliding stability of gravity dam. But the deep anti-sliding stability of gravity dam is such a complex issue that there are no unified specification or objective and accurate method for theoretical evaluation. So further discussion and analysis of deep anti-sliding stability of gravity dam is needed.Applying catastrophe theory to analysis of deep anti-sliding stability of gravity dam in the paper. Using nonlinear finite element method,,with the software-ANSYS,to study.The main contents studied are as follows: Firstly, needs to get nodes number and relative displacement values in horizontal direction of two nodes up and down the mezzanine under dam toe by nonlinear finite element calculation, then to determine the cusp mutation model potential function of horizontal relative displacement X of the two nodes(mentioned above) and the strength reduction coefficient k based on cusps catastrophe theory, then transform the cusp catastrophe model potential function to standard form of cusp catastrophe model. Discriminant of gravity dam instability criterion can be obtained based on the cusp catastrophe theory. By some calculations, the stability of dam can be determined.Secondly, analysis the deep anti-sliding stability of Qingyu Reservoir dam by using nonlinear finite element strength reduction method. For different typical points,the results is not unique. Therefore, using displacement mutation of typical points as instability criterion does not have broad applicability.What’s more, by analysising the deep anti-sliding stability of Qingyu Reservoir dam by using nonlinear finite element method, safety factor can be obtained based on relative displacement cusp mutation model instability criterion of deep anti-sliding stability of dam. The safety factor is equal to that obtained based on plastic zone through instability criterion used commonly.Finally, Analysising the stability of dam using dual-slope method and three-slope method, the safety factor obtained based on this instability criterion is close to the result obtained by using dual-slope method and three-slope method. It proved that relative displacement cusp catastrophe model instability criterion of deep anti-sliding stability of dam is correct and applicable in projects.Relative displacement cusp catastrophe model of two nodes up and down the mezzanine under dam toe as instability criterion can reflect the mutagenicity of dam instability process and quantify the safety factor to a specific objective value and make the result unique. By establishing the standard potential function of model and comparing the magnitude relation between criterion and zero to determine instability of dam, It is clear in concept and well defined.