基于突变理论的边坡监测预警概率性模型研究

为解决边坡系统演化过程中不确定因素的影响，得到非确定性的边坡预警结果。结合突变理论与广义胞映射理论提出了一种边坡监测预警概率性模型。该模型采用尖点突变理论识别边坡稳定状态；将边坡稳定性演化结果视为随机事件，基于广义胞映射理论计算滑坡在某一时刻准时发生、提前发生、滞后发生、滑坡不发生的概率，从而实现边坡概率性预警。利用该模型计算了某黄土区工程边坡在某时刻发生失稳的概率为100%,且滞后发生的概率为83.8%,判定边坡系统突变会在该时刻之后发生，预警结果与实际情况一致，验证了该模型的有效性。与传统模型相比，概率性预警模型可提供更丰富合理的信息，有助于提升监测预警的准确率，为边坡监测预警研究提供了一种新思路。

Probabilistic model of slope monitoring and warning based on catastrophe theory

In order to solve the influence of uncertain factors in the evolution of the slope system, the non-deterministic warning results are obtained. A probabilistic model for slope monitoring and warning is proposed combining catastrophe theory and generalized cell mapping theory. The model uses catastrophe theory to identify slope stability. The slope stability evolution results are regarded as random events, and the probability of landslide happening on time, in advance, lagging and not happening at a certain time is calculated based on the generalized cell mapping theory, so as to realize the slope probabilistic warning. The results of the case analysis show that the probability of a sudden change in the slope of a loess area is 100%, and the probability of lagging occurrence is 83.8 %, and it is decided that the slope will occur afterwards, and the warning result is consistent with the actual situation. Compared with the traditional deterministic model, the probabilistic early warning model can provide more abundant and reasonable information, which is helpful to improve the accuracy of monitoring and early warning. In addition, the proposed uncertainty warning model provides a new idea for the research of slope monitoring and warning.