Abstract: 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.

Key words: Verhulst model, landslide forecast, criterion, velocity, acceleration, accelerated acceleration, residual sliding force