基于n维等效方法的岩质边坡楔体稳定体系可靠度分析

 提出岩质边坡楔体稳定体系可靠度分析的n维等效方法，建立考虑多失效模式相关的楔体稳定体系可靠度分析的概率故障树模型。采用四参数b 分布来描述可靠度分析中基本随机变量的分布。最后采用n维等效方法计算楔体稳定体系可靠度，并着重分析随机变量敏感性分析的3个层次及不同层次上的可靠度对基本随机变量的敏感性。结果表明，n维等效方法计算的楔体体系失效概率均在Cornell简单上下限法的范围内，它能够有效地评价楔体体系可靠度。概率故障树模型能够清晰直观地模拟多失效模式相关的楔体体系可靠度问题，忽略失效模式间的相关性将会明显高估楔体体系失效概率。此外，黏聚力和内摩擦角之间的负相关性对边坡的可靠度具有有利的影响。随机变量敏感性分为单一极限状态方程、单一失效模式以及体系可靠度3个不同的层次，在研究随机变量敏感性时必须明确相应的分析层次。水压力和结构面产状的敏感因子较大，因此布置良好的边坡排水系统以及进行详细的地质勘测工作是提高楔体可靠度有效的方法。研究成果为边坡风险分析奠定了一定的基础。

SYSTEM RELIABILITY ANALYSIS OF ROCK SLOPE WEDGE STABILITY BASED ON N-DIMENSIONAL EQUIVALENT METHOD

A probabilistic fault tree is presented to model system reliability of rock wedge with multiple failure modes. The versatile 4-parameter b distribution is used to describe the basic random variables in the rock wedge stability model. The n-dimensional equivalent method is employed to perform the system reliability analysis of rock wedge. Reliability sensitivities in three different levels are discussed. An example is investigated to illustrate the proposed method. The results indicate that the failure probabilities of system for rock wedge using the proposed method are fully within the bounds of failure probability obtained from the Cornell bound method. The system reliability of rock wedge can be efficiently evaluated using the proposed method. In addition，the system reliability of rock wedge with correlated multiple failure modes can be intuitively represented by the probabilistic fault tree. The failure probability of system will be overestimated if the correlations between different failure modes associated with rock wedge are not taken into account. The negative correlation between cohesion and internal friction angle has a positive effect on the system reliability of rock wedge. Reliability sensitivity analysis has three levels，namely single limit state function level，single failure mode level and system reliability level. The importance of reliability sensitivity level should be realized due to the significant differences in sensitivity coefficient associated with the aforementioned three levels. Results from sensitivity analysis indicate that the water-pressure parameter and the geometry of rock wedge are significant random variables with higher sensitivity coefficients，which have a significant impact on the calculated failure probabilities of system. Accordingly，to improve the rock wedge stability effectively，a good drainage system for the slope should be designed；and a good structural characterization of discontinuities in the rock mass should be conducted. The proposed conclusions and approaches can form a basis for risk analysis of rock slopes.