基于博弈论-云模型的露天矿岩质边坡稳定性分析

Analysis of the rock slope stability for the open-pit mine based on the game theory and the cloud model

针对露天矿岩质边坡稳定性具有随机性和模糊性的特点,建立了基于博弈论-云模型的边坡稳定性分级评价方法。首先,通过分析边坡稳定性影响因素,构建了包括地质、环境和工程条件等多方面的综合指标评价体系;其次,采用改进层次分析和熵权理论分别确定指标的主观和客观权重,基于博弈论计算指标综合权重;最后,通过计算综合确定度,基于最大隶属度原则确定边坡的稳定性等级。将所建立的评价模型应用到某露天矿边坡稳定性评价中,结果显示该模型的评价结果与实际情况完全符合,与未确知测度和可拓学理论的评价结果一致,表明该模型具有一定可靠性和实用性。

The present paper intends to establish a new analysis method for the rock slope stability based on the game theory and the cloud theory in view of the fuzziness and randomness of the slope stability of such open-pit mines.For the said purpose,we have first of all made a thorough analysis of the chief factors affecting the slope stability,mainly including the following 12 factors,that is,the compressive strength of the rock mass,the status-in-situ of the elasticity,the Poisson ratio,the rock quality designation,the cohesion,the internal friction angle,the maximum daily precipitation,the groundwater state situation,the height and the inclining degree of the rock slope,the intensity of the likely taking-place earthquake and vibration velocity of the blasting particles based on the relevant geological,environmental and engineering factors.All of the above mentioned factors under study should be categorized into 5 levels,that is,the stability level,the sub-stability level,the less stability level,the instability level,and last of all,the extremely instable one.And,next,we have identified and determined the digital cloud features on the basis of the above categorization rule and work out the corresponding cloud model via the normal cloud generator.Besides,the certainty degree of all the indexes in correspondence with each evaluation degree can be deduced based on the said cloud models.Besides,what is also worth to mention is that,in the given paper,we have also managed to improve the analytic hierarchical process and the entropy weight theory for determining the subjective and objective weights for each index,and introduced the game theory to find the comprehensive weights of each index,so that we can work out the comprehensive determination degree of the slope stability degrees on the basis of each index weight and certainty degree,as well as the slope stability degree on the maximum membership degree principle.Thus,finally,the slope stability level has been determined by using the analysis model with the analysis results demonstraitng that the stability degree of the aforementioned 3 slopes turn out to be respectively of 3 levels,that is,stable,sub-stable,and,less stable,which are fully consistent with the results of uncertainty measurement and extenics theory in line with the actual investigation on the spot.Therefore,it can be concluded that the evaluation model of the slope stability proves to be feasible and fully applicable as a novel reliable method for rock slope stability analysis.