基于突变理论的土质边坡非线性演化分析

Nonlinear evolution analysis of soil slope based on catastrophe theory

应用突变理论对土质边坡稳定性进行研究,从系统能量的角度出发,综合考虑边坡土体的成层性、应变软化特性和水致弱化性质而建立了尖点突变模型。突变分析表明,系统内部多重参数(如应变软化程度mi、含水量iξ、剪切刚度比k、位移峰值强度ui)综合决定系统状态的控制变量a,b,并且内部参数受各外部激励因素的影响都是非线性的,边坡的孕育是一个复杂的非线性演化过程。同时,详细论述了3种典型边坡(稳定型边坡、外部因素持续作用下同步失稳的边坡和滞后失稳型边坡)的演化路径。

On the basis of catastrophe theory, a cusp catastrophe model for the stability anlysis of soil slope is developed form the system energy taking the inhomogeneity of soil mass, strain softening characteristics and water softening property into account. Through catastrophe analysis,it is indicated that multiple intemal paramenters of soil mass （such as the degree of strain softening m, water content ξi, shear stiffness ratio k, the strengh of displacement peak ui ） , which are influenced nonlinear by external factors, comprehensively determine the two control parameters of system state,a and b. The gestation of slope is a complex nonlinear evolution process. What＇s more, the evolution paths of three representational slopes （ stable slope, instable slope simultaneous sliping with external factors＇ persisting effort, retarded slope） are expatiated.