Verhulst滑坡预测预报模型的改进及其应用

Verhulst生物生长模型是一种统计型的滑坡预测预报模型，针对原始Verhulst模型中把第一个数据点作为已知条件的理论依据不存在，可能导致预报精度较低问题，将前人改进Verhulst模型的方法应用到滑坡预测预报中，推导出用改进模型和速度最大值判据预报滑坡发生时间的计算公式。通过分析表明，原始Verhulst模型中以速度最大值作为预报滑坡发生时间的判据缺乏合理性，以加速度和加加速度最大值作为预报判据应更合理，并推导出用加速度和加加速度最大值判据预报的计算公式。基于推导的公式，编写Matlab程序进行计算，将原始和改进的Verhulst模型以及3种判据应用于一些滑坡实例的预报中。结果表明，（1）与原始Verhulst模型相比，改进模型的预报效果较好，其预报滑坡发生的时间更早，且更准确；（2）与速度最大值判据相比，加速度和加加速度最大值判据的预报效果较好，其预报时间较早，且较准确；（3）可把原始模型中单一的时间预报值拓展为一段预报的时间范围，该预报时间范围的上限是加速度最大值时刻，下限是加加速度最大值时刻；（4）用改进模型和该时间段范围判据进行预报能起到提前预报的作用，且预报结果较准确。此外，经讨论认为临近破坏时，裂缝的增多以及动摩擦系数小于静摩擦系数导致抗滑力降低，剩余下滑力增大，是使滑体产生加速度逐渐增大运动的原因。

Improvement of Verhulst forecast model of landslide and its application

The Verhulst biological growth model is a kind of statistical forecast model of landslide. According to the problem that there is no theoretical basis of taking the first displacement data as the known condition in the original Verhulst model; and a big error may be caused, the improved Verhulst model that other scholar proposed is firstly applied to the prediction and forecast of landslide. Based on the improved model and velocity maximum criterion, the calculation formula of displacement prediction and time forecast of landslide was deduced. Analysis of forecast results of different forecast criterions is another research content. Theoretical and case study indicates that taking maximum velocity as the forecast criterion of landslide time lacks rationality, and taking maximum of acceleration and accelerated acceleration as the forecast criterion is more in accordance with the mechanism of landslide. Then calculation formulas of forecast time based on the maximum criterion of acceleration and accelerated acceleration were deduced. Based on the deduced formulas above, the original and improved Verhulst model and the three kinds of criterion were applied to the time forecast of some actual landslides that had happened; and MATLAB software was used to calculate the time forecast. The forecast results indicate that, firstly, compared with the forecast results of the original Verhulst model, the forecast results of the improved Verhulst model are better, because the forecast time of improved model is closer to the actual occurrence time of landslide, and earlier than that of original Verhulst model. Secondly, as for the forecast results of three kinds of criterion, the forecast results of the acceleration and accelerated acceleration maximum criterion is better than that of the velocity maximum criterion, because the forecast time of acceleration and accelerated acceleration maximum criterion is closer to the actual occurrence time of landslide, and is earlier than the forecast time of velocity maximum criterion. Thirdly, it is suitable to substitute the single forecast time of the original Verhulst model with a forecast time range, and the upper limit of the rang is forecast time of the acceleration maximum criterion; and the lower limit is forecast time of the accelerated acceleration maximum criterion. Fourthly, the forecast time of the improved Verhulst model and the new time range criterion is more accurate than that of the original model, and it can play a role of early warning. In addition, the decrease of anti-slide force and increase of residual sliding force that is induced by increase of crack and decrease of friction coefficient is the reason why the acceleration of sliding mass increases gradually near failure.