滑坡发生时间预报分析

系统论述了滑坡监测资料的整理方法：滤波和等时化。讨论了滑坡运动响应的主要组成成分。重点阐述了滑坡发生时间预报的理论基础，此基础不同于一般物理方程建立的思路，而是直接来源于观察和经验总结，并抽象为一定的数学模型。单次滑坡发生的整个过程包括孕育、如速、减速、停止等4个阶段，滑坡发生时间则指加速向减速转换的特征时间点，此点是滑坡爆发的峰值点，也是需要预报的特征时间。能够反映滑坡如此运动过程的典型数学函数是Pearl曲线，本质上此S型曲线与系统有阻尼的自由振动微分方程是一致的，也与生物群体演化的虫口方程一致，它们都共同反映了物质运动的一般规律，因此可以用来预测滑坡运动过程。直接运用一般力学报分方程描述滑坡运动过程的困难在于缺乏对滑体系统力学参数的精确把握，直接运用Logistic虫口微分方程则存在模型参数识别的困难，作者还发现某些误用灰色系统理论对Verbulst非线性方程，参数进行辩识。文末，为展示方法而不强调结果，以拥有10a监测资料的某滑坡为例，分析预报了滑坡活动过程，并进行了预测结果的数学检验。

Quantitative prediction of landslide using S-curve

A system method of processing of monitoring data of landslide,such as isochronal interpolation technology and filtering,was at first presented in the paper.Based on the observation and experience summary of landslide moving phenomena,then,the author has suggested a quantitative prediction equation of landslide by mathematic induction.The train of above thoughts was different from that of building general mechanic equations that are mostly based on debuctive method.A large of observations have shown that the whole process of landslide moving can be divided into four stages,start up,accelerate,decelerate,and end up,the characteristic time point when the accelerate stage turns into decelerate is referred as the occurring time of landslide.The function describing such relationship of deformation and time was typically Pearl curve that belongs to growth equations.The authors have found that the S|curve is consistent with general vibration differential equation with single degree of freedom and having damp that describes viscous|elasticity mechanic system,at least in form.The difficult of directly describing landsliding behavior using viscous|elasticity model existed in identifying mechanic parameters of landsliding system such as elastic consant and damper coefficient.The difficult is the same as to Logistic differential equation.However,directly using Pearl curve fitting the monitoring data can avoid the difficult and at the same time obtain the equivalent parameters.The author has also found that there are serious mistakes in some gray system theory application when identifying the parameters of verhulst equation and input raw data.Based on above considering,a set of spreadsheet template was designed to assist in conducting isochronal interpolation,filtering and S|curve estimating and forecasting.At the end of the paper,an example landslide of having been sliding in a reservoir,southwest China,with ten|years monitoring data is analyzed,in order to show the methodology.