基于集对分析的滑坡变形动态建模研究

Landslide deformation dynamic modeling research based on set pair analysis

滑坡是一个确定-不确定的动态系统,其变形表现出复杂的非线性演化特征。为了克服传统分析方法在处理系统不确定性方面的不足,将集对分析法(SPA)引入岩土变形监测分析领域,并结合层次分析法(AHP)提出了滑坡变形动态预测模型,给出了基于概率论的最优预测算法,提出并证明了集对论中最大同一度在等势条件下存在极限解,据此提出位移势的概念。在位移势的基础上,进行SPA二次建模,提出了基于SPA的滑坡变形与水库蓄水过程相关性动态分析模型。运用上述预测模型对新近发生的刘家沱滑坡进行变形监测定量分析,实践证明:最优预测值具有良好的短期预报精度;位移势能够表征系统当前状态下位移所能达到的最大潜力,可作为短期预测的上限值,其变化能够反映系统宏观层面上的演化特征,对滑坡演变加速预警具有指导意义;运用集对分析方法进行滑坡变形响应滞后效应的定量研究是一条可行的新思路,反演结果与实际情况吻合;该方法在岩土监测分析领域有良好的应用前景。

The landslide is a certain-uncertain dynamic system. As a explicit behaviors of this complicated nonlinear dynamic system, the deformation of landslide is characterized with many uncertain factors. In order to reduce the limitation of traditional methods, the set pair analysis （SPA） theory was introduced to describe the landslide dynamic system. Based on SPA theory combined with analytic hierarchy process （AHP）, a new displacement prediction model is suggested. The existence of limit value of maximum same degree for SPA theory in equal potential condition are also suggested and demonstrated. Based on this demonstration, the new SPA model and probability analysis, some new concepts, such as optimum displacement prediction and potential displacement, are suggested. Furthermore, the potential displacement is also used to set up the quadratic correlation SPA model to describe the dynamic correlation between landslide deformation and reservoir accumulation process. As a test, all these models are used to analyze the newly-happened Liujiatuo landslide in Qingjiang Shuibuya Reservoir. The results indicate following three main conclusions. First, the optimum displacement prediction is reliable and has high precision in short-term prediction ability. Second, the potential displacement is the maximal potential for landslide deformation, which can be regarded as an upper limit of displacement prediction in current status. Furthermore, the variation of it can describe the evolution track for landslide dynamic system in macro level. So, it has guiding significance in early warning for landslide deformation acceleration. Third, the dynamic correlation SPA model is the new way to quantitatively study the relationship between landslide response and reservoir accumulation process. It can be used for quantitative inverse the hysteresis effect on landslide deformation responded to the reservoir accumulation process. The lag time deduced by this back analysis model matches the observed information well. It was proved that these set of models are simple, efficient, and can be promoted in practical engineering.