中文摘要：

以甘肃省266个黄土自然极限状态坡为研究对象,将其按地形地貌、地层岩性等特征划分为4个亚区,对每个亚区的极限状态坡高与坡宽进行双对数线性模型回归和不同置信度下的统计分析,给出4个亚区不同置信度下坡高与坡宽的相关关系。以1 024组黄土物理力学指标统计结果作为计算参数,用Bishop法的稳定系数计算公式建立极限状态方程,利用Monte Carlo法对各亚区不同置信度下的边坡进行可靠度模拟,系统分析了坡高、坡度、参数变异性对失效概率的影响,以及失效概率与稳定系数的关系。结果表明,临洮-永靖亚区边坡坡度低于31.5,失效概率可控制在10%以下;陇东亚区、兰州-定西-会宁亚区和天水-秦安-通渭亚区在强度参数变异系数取当地平均水平,稳定系数为1.3情况下失效概率在10%以内,稳定系数为1.2情况下,失效概率多在20%以内。

英文摘要：

In order to analyze reliability of loess high slopes, 266 natural ultimate stat~ slopes are measured in Gansu area. According to the characteristics of topography and lithology, the studied region is divided into 4 subareas. The correlations of ultimate state 1 slope height and width are given by means of double log-linear regression in different confidences for the 4 subareas respectively. Meanwhile, 1 024 groups of physico-mechanieal indices obtained from reports are statistically analyzed. Based on the above, the ultimate state equation is built by means of Bishop＇s method. Reliability analysis for slopes under different confidences in 4 subareas is carried out with the Monte Carlo method. The effects of slope height, slope ratio and variability of parameters on the probability of failure are systematically analyzed. The results show that the slope ratio in Lintao-Yongjing subarea is smaller than 31.5° if the probability of failure（Pf） is kept within 10%. In the condition of the average coefficient of variation in Longdong subarea, Qin＇an Lanzhou-Dingxi-Huining subarea and Tianshui-Qin＇an-Tongwei subarea, the maximum of Pf of loess slopes is less than 10% with safety factor（Fs） of 1.3, as well as Pfless than 20% with Fs =1.2.