突变理论在地质力学模型试验失稳判据中的应用

地质力学模型试验是研究高坝工程稳定安全性的重要方法之一，如何较准确的通过测试结果建立大坝失稳判据，判断坝与地基的失稳破坏过程，得到综合稳定安全系数，是地质力学模型试验的关键技术问题。本文由突变理论及其相关性质，选用较为成熟的尖点突变模型及其标准势函数公式，推导出相应的失稳突变判别式，建立基于尖点突变理论的失稳判据，并通过相关算例进行有限元分析，依据计算成果的变位—超载倍数关系，提出超载安全系数，并与有限元塑性区贯通、计算不收敛等失稳判据对比分析，印证尖点突变模型失稳判据的可靠性和适用性。再将其应用于丹巴水电站地质力学模型试验中，试验结果给出了闸坝在正常蓄水位和降强之后超载作用下的位移场，获得了闸坝的变形及分布特征、揭示了裂缝发展的全过程及其破坏机制，得到降强系数为 1.18，超载系数为 1.8～2.0，确定了闸坝整体稳定安全系数为 2.12～2.36。根据尖点突变理论，由试验测试成果建立相关失稳判据，据此提出破坏过程及综合稳定安全系数，并与常规地质力学模型试验分析成果进行对比，分析结果验证了基于地质力学模型试验测试成果的尖点突变模型失稳判据的合理性。

Application of Catastrophe Theory to Determine the Instability Criterion for Geo-mechanical Model Test

Geo-mechanical model test is an important method to study the stability safety of high dams.How to establish the criterion of dam failure through the test result,to judge the failure process of the dam failure,and to obtain the compressive stability safety factor in geo-mechanical model test are the key technical problems.In this study,the more mature cusp-catastrophe model and its standard potential function formula were introduced to deduce the corresponding discriminant instability of mutations,and the criterion of instability based on cusp-catastrophe theory was established.Meanwhile,the finite element calculation and analysis were carried out by means of related calculation examples.According to the relationship between the displacement and the overload coefficient in the results of finite element calculation,the instability criterion of cusp-catastrophe model was established and the overload safety factor was proposed.By comparing the calculated results with the instability criterion based on the run-through of plastic zone and un-convergence of finite element calculation,the reliability and applicability of the instability criterion of cusp-catastrophe model was proven.It was then applied to the geo-mechanical model test of danba hydropower station.Based on the test results,the displacement field of gate and gravity dam section under the action of normal pool level load and overloading after strength-decreasing were obtained.The deformation distribution characters of gate and gravity dam section for typical measurement points were reached,and the overall developing process of displacement and crack and its failure mechanism were revealed.The safety evaluation of model experiment indicates that the strength margin coefficient was 1.18 and the overloading coefficient was 1.8~2.0;and the global stability safety factor for gate and gravity dam was 2.12~2.36.According to catastrophe theory,the instability criterion was established and the failure process and the compressive stability safety factor were proposed.Comparing with the results of instability criterion analysis based on the conventional geo-mechanical model test,the analysis result indicated the rationality of the instability criterion of cusp catastrophe model based on the results of geo-mechanical model test.