滑坡演化的非线性动力学与突变分析

NONLINEAR DYNAMIC MODEL AND CATASTROPHE ANALYSIS OF SLOPE EVOLUTION

基于对任一连续函数 ,至少在较小的邻域内可以用多项式任意逼近的数学理论 ,运用改进的Backus广义线性反演理论 ,以斜坡位移时间序列为基础 ,反演建立了斜坡演化的非线性动力学模型。并利用自治梯度系统与突变模型的等价性 ,通过变量代换得到标准的尖点突变模型。以黄茨及卧龙寺滑坡为例对滑坡的发展孕育过程进行分析 ,结果表明 :该非线性动力学模型不仅预测效果十分理想 ,而且具有较高的自我调整适应能力 ;斜坡临滑前都以突变特征值D的突降至零为前兆特征 ,可作为一个具有物理意义的前兆指标。

On the basis of displacement-time series of the slope, a nonlinear dynamic model is set up according to Backus generalized linear inversion theory in this paper. Due to the equivalence between autonomous gradient system and catastrophe model, a standard cusp catastrophe model can be obtained through variable substitution. The method is used in analysis of displacement data of Huangci landslide and Wolongsi landslide and in understanding how slopes evolve before sliding. The result shows that the nonlinear dynamic model can make satisfactory prediction results. Is it most important that there is a sudden fall of D, which indicates the occurrence of catastrophe (when D=0).