正态分布下边坡稳定性二元指标体系研究

安全系数是边坡稳定性评价中的常用方法,在长期的工程实践中积累了丰富的经验,其最大的缺点是不能考虑边坡岩土体中实际存在的不确定性。可靠性理论可有效地考虑边坡系统内实际存在的不确定性和相关性,但是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。取影响参数的平均值,计算得到最大可能安全系数(中值安全系数)。设安全系数服从正态分布,取系列的最大可能安全系数和变异系数,计算得到边坡在不同最大可能安全系数和变异系数下的破坏概率Pf。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。从折减后安全系数的极限状态中,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。根据不同的最大可能安全系数及它的临界破坏概率,绘制出边坡稳定性分区图。选择典型的安全系数及相对应的可靠性,建立传统安全系数与可靠性耦合的边坡稳定性二元指标体系,由安全系数和可靠性共同度量边坡系统的稳定性。提供了小样本条件下,利用矩估计原理计算参数方差的方法,研究实例表明,边坡稳定性判别的二元指标体系是可行的。

STUDY ON SLOPE STABILITY BY DUAL INDEX SYSTEM BASED ON NORMAL DISTRIBUTION

The traditional method of slope stability analysis is safety factor,and its applications have long time,broad prospects and abundant experience. However,the weakness of safety factor is that it can not consider uncertainties of parameters and models,for which,especially uncertainty of parameters,has a great influence on slope stability. Reliability theory can effectively solve uncertain and correlative problems in slope system. However,reliability theory is complicated and short of abundant experience. Therefore,it is necessary to build dual index system of slope stability coupling safety factor and reliability. Most likely safety factor (mean safety factor) was calculated with average value of parameters,and reliability of slope was calculated with variability of safety factor. Supposing that safety factors obey normal distribution in different maximum possible safety factors and variation coefficients,a series of most likely safety factors and variation coefficients of safety factor were taken,and failure probabilities of slope Pf were calculated. In this way,a series of most likely safety factors and failure probabilities were obtained. Multiplied most likely safety factor by corresponding reliability,reduced most likely safety factor,reliability safety factor of slope was obtained. From limit state of reduced safety factor,critical failure probabilities and variation coefficients corressponding different maximum possible safety factors were calculated. According to different maximum possible safety factors and their failure probabilities,divisional chart of slope stability was drawn. Choosing representative safety factor and its reliability,dual index system of slope stability coupling safety factor and reliability was built,by which slope stability could be measured. As a research example,stability of Yancun landslide was assessed with dual index system of slope stability;and research result shows that dual index system of slope stability is feasible method. Estimation of variance with moment estimation was expounded in little sample size.