基于均匀分布的滑坡数值模拟参数取值概率研究--以甘肃黑方台黄土滑坡为例

针对数值模拟参数选取主观性强、量化难度大的问题,在高精度无人机地形数据的基础上,通过对11起滑坡案例进行了407组参数反演实验,对结果准确度定量评价后,得到基于Massflow数值软件关键参数λ0的分布范围,进而运用小样本极大似然估计理论,分析区间边界长度对反演精度的影响,最终提出基于均匀分布的参数取值概率模型,并选用案例验证该模型的准确性。结果表明:地形约束会导致反演过程中所需的内聚力减小,反演获得的11组最优λ0的极差和方差分别为0.29、0.01,在置信度为95%下,极大似然法得到区间边界估计长度仅为0.0998,表明参数λ收敛性较好;反演过程中质心滑动距离ψ准确度优于堆积面积重叠率η,在λ0±0.05的范围,参数估计区间内任意值对模拟误差影响较小,评价指标ψ、η与λ0对应案例的相对误差不超过15%;所选案例验证了在置信度为95%下,以反演得到的最优参数区间边界中点构建概率分布函数的可行性和准确性,研究方法可为单体滑坡数值模拟风险评价提供理论支撑。

Parameters Probability of Landslide Numerical Model Based on uniform Distribution--a Case Study on the Heifangtai Terrace

The value of parameter in numerical simulation is selected subjectively and difficult to quantify at present.In order to establish probabilistic model,the maximum likelihood theory is used to perform interval estimation in this paper.11 loess landslides which located in Heifangtai terrace and occurred in the past 5 years were taken as cases and samples.The back-analysis can generate the optimal parameters with Massflow numerical model.Simulation results were quantitatively evaluated by two evaluation indicators,including centroid slip distanceψand stacking area overlap ratioη.The optimal pore pressure rationλ0 of different cases can be acquired,and the interval estimate of the parameterλwas obtained by the maximum likelihood method.Comparison of the relative errors between the non-optimal parameters and the corresponding evaluation indicators ofλ0,discussion on the error of the length of the interval estimation value on the simulation,a uniform distribution probability model of landslide parameter values is proposed,and the accuracy of the probability model was verified by another case.It was found in this paper that terrain constraints could cause the cohesion difference during the back-analysis.The range and variance from the 11 optimalλ0 are 0.29 and 0.0112,respectively,which indicated that the optimal pore pressure rationλrange has better convergence.Furthermore,interval length of the interval boundary a and b obtained by maximum likelihood method are 0.0998.The non-optimal parameters are in the range ofλ0±0.05 with relative errors of the evaluation indicators under 15%,which implies that the interval lengths a and b have minor influence on the simulation results.Besides,the case with a confidence level of 95%verifies the accuracy of the probabilistic model.The uniform distribution function was constructed by the midpoints of the interval estimates a and b,which could obtain the feasibility of the probability of parameter values,and the model can support for the quantitative risk assessment of site-specific landslide.