对数正态分布下边坡稳定性二元指标体系研究

安全系数不能考虑边坡系统中实际存在的不确定性,可靠性理论缺乏丰富的工程实践经验,因此,将工程实践经验丰富的安全系数与先进的可靠性理论相结合,建立传统安全系数与可靠性相耦合的二元评价体系具有重要的理论意义和应用价值.设安全系数服从对数正态分布,取系列的最大可能安全系数（中值安全系数）和变异系数,计算得到最大可能安全系数及在不同变异系数下的破坏概率Pfo从而可由最大可能安全系数和可靠性（R=1-Pf）共同度量边坡的稳定性.将最大可能安全系数与边坡可靠性相乘,对最大可能安全系数进行折减,得到边坡可靠的安全系数.根据折减后安全系数的极限状态,可计算出不同最大可能安全系数的临界变异系数和临界破坏概率.根据不同最大可能安全系数及它的临界破坏概率,绘出边坡稳定性分区图,并建立安全系数和破坏概率相结合的边坡稳定性判别的二元指标体系.文中提供了小样本条件下,利用3倍方差原理估计参数方差的计算方法,并给出了边坡稳定性二元指标体系的研究实例.

Study on Dual Index System of Slope Stability Based on Lognormal Distribution

Safety factor cannot consider uncertainty of parameters and models in slope system, reliability theory lacks abundant experience, therefore it is necessity to build dual index system of slope stability coupling safety factor and reliability theory. Suppose that safety factors obey lognormal distribution, we took a series of most likely safety factors (mean safety factors) and variation coefficient of safety factor, and computed failure probabilities of slope Pf in different most likely safety factors and variation coefficient of safety factor. Hence, we may measure slope stability using safety factor and reliability (R=1-Pf) together. In this way,we may obtain a series most likely safety factors and failure probabilities (or reliability). We multiply most likely safety factors by corresponding reliability and reduce most likely safety factors, and obtain reliability safety factor of slope. According to limit state of reduced safety factor, we can compute critical failure probability and variation coefficient corressponding different most likely safety factors. According to different most likely safety factors and their failure probabilities, we made a divisional chart of slope stability and set up dual index system of slope stability combing safety factor and reliability. We also provided a research example and expounded estimation of variance with Three-Sigma Rule in little sample size.