边坡位移预警指标的实时估计与诊断

Real-time estimation and diagnosis of early warning indicator of slope displacement based on POT-catastrophe theory

边坡预警指标的实时估计与诊断是实现边坡安全监控、预防边坡演变为滑坡的重要手段。安全预警注重考虑极端事件,其关键在于能否准确进行效应量序列分位数分析及刻画其尾部特征。基于极值理论中超阈值(Peaks over Threshold,POT)模型,分时段考虑边坡位移监测序列,借助Hill图法拟定合理的阈值,再利用广义帕累托分布(Generalized Pareto Distribution,GPD)对超阈值序列进行拟合分析,渐进地刻画位移序列分布的尾部特征,分析其抵御已经历荷载的能力。假定边坡失事概率,得到位移预警指标实时估计序列,挖掘或评估出该边坡面临可能发生极端荷载时的抵御能力。最后基于突变理论中尖点突变模型对位移预警指标实时估计序列进行突变诊断,结合具体边坡工程实例,验证了POT-突变理论混合模型的合理性。

Real-time estimation and diagnosis of slope early warning indicators are important means to monitor the safety state of slope and prevent the situation of the evolution from slope to landslide. Safety early warning pays more attention to extreme events, which are not common. The key to achieve safety early warning lies in whether we can accurately analyze the quantile of the slope effect quantity sequences and describe the tail characteristics of the slope effect quantity sequences. First of all, the slope displacement monitoring sequence can be divided by the interval of time; then, the thresholds of the slope displacement monitoring sequences at each time interval are drafted using Hill figure method; the part of the displacement monitoring sequence at each time interval that is supra-threshold is fitted by Generalized Pareto Distribution （GPD）, and the tail characteristics of the part that is supra-threshold of displacement monitoring sequences are described progressively. So, the ability of the slope to resist historical loads is analyzed based on the model of peaks over threshold （POT） using extreme value theory. If the failure probability of the slope is provided, the real-time estimation sequences of early warming indicators of displacement can be obtained and the ability of the slope to resist extreme loads that may happen in the future can be exploited and evaluated. Finally, the real-time estimation sequences of early warming indicators of displacement are diagnosed by using cusp catastrophic model from catastrophe theory. Based on specific slope projects, the rationality of the mixed model of POT and catastrophe theory is verified and the modeling method of the mixed model will be a new way to achieve the real-time estimation and diagnosis of engineering early warning indicators.