西安建筑科技大学学报(自然科学版)

受诸多因素的影响,边坡失效概率不是定值,实际上是具有一定置信度水平的置信区间分布的.以无限边坡为例,借助Bootstrap法判定抗剪强度参数最优边缘分布函数,采用Copula函数描述抗剪强度参数间互相关性,构建抗剪强度参数的联合分布函数,并从分布特性的角度研究了抗剪强度参数联合分布函数、边坡稳定性设计控制标准及参数变异水平对边坡失效概率的影响.研究表明:针对本算例,五类联合分布函数所得失效概率相近,其中No.16函数所得失效概率相对较大,Gaussian函数所得结果相对较小, Copula加权组合函数所得失效概率精确度相对较高; 随着边坡设计控制标准的提高,则边坡稳定安全系数取值不断增加,边坡失效概率逐渐减小且趋近于0; 边坡失效概率均随δφ的增加而增加,随δc的增加呈“增加 - 减小 - 增加”的趋势,并且边坡失效概率对内摩擦角φ的变异水平较黏聚力c更为敏感.

Affected by many factors, slope failure probability is not a fixed value, but a confidence interval distribution with a certain level of confidence. Taking the infinite slope as aexample, the optimal edge distribution functions of the shear strength parameters are determined by the Bootstrap method, the cross-correlation between the parameters is described by Copula function and the joint distribution function is constructed. The influence of the joint distribution functions, the slope stability safety factor and the variation level of shear strength parameters on slope failure probability are studied from the aspect of distribution characteristics. The research shows that the slope failure probabilities obtained by five joint distribution functions are similar. Specifically, the failure probability obtained by No.16 function is larger relatively, of which Gaussian Copula function is smaller, and Copula weighted combination function is more accurate; With the improvement of the slope design control standard, the value of the slope stability safety factor increases continuously, and the slope failure probability gradually decreases and approaches 0; The slope failure probability increases with the increase of δφ, and there is a tendency of “increasing-decreasing-increasing” with the increase of δc; The slope failure probability is more sensitive to the internal friction angle φ than the variation of cohesion c.

引言
1 失效概率计算方法及算例模型
2 联合分布函数类型对边坡失效概率的影响
3 边坡设计控制标准对边坡失效概率的影响
4 不同抗剪强度参数变异水平对边坡失效概率的影响
5 结论

图1 计算边坡失效概率置信区间的流程图<br/>Fig.1 Flow chart forcalculating the confidence interval of the slope failure probability

图1 计算边坡失效概率置信区间的流程图
Fig.1 Flow chart forcalculating the confidence interval of the slope failure probability

图2 无限边坡稳定性分析模型<br/>Fig.2 Stability analysis model of infinite slope

图2 无限边坡稳定性分析模型
Fig.2 Stability analysis model of infinite slope

表1 抗剪强度参数试验数据[20]<br/>Tab.1 Test data of shear strength parameters

表1 抗剪强度参数试验数据[20]
Tab.1 Test data of shear strength parameters

表2 5类Copula的分布函数、参数表达式及参数范围<br/>Tab.2 Five distribution functions, expressions and value ranges of their parameters

表2 5类Copula的分布函数、参数表达式及参数范围
Tab.2 Five distribution functions, expressions and value ranges of their parameters

表3 四类Copula的权重系数<br/>Tab.3 Weight coefficients of the four Copulas

表3 四类Copula的权重系数
Tab.3 Weight coefficients of the four Copulas

表4 基于五类联合分布函数所得失效概率统计表<br/>Tab.4 Failure probability statistics table with different distribution functions

表4 基于五类联合分布函数所得失效概率统计表
Tab.4 Failure probability statistics table with different distribution functions

图3 不同联合分布函数所得边坡失效概率分布图<br/>Fig.3 Slope failure probability distribution with different joint distribution functions

图3 不同联合分布函数所得边坡失效概率分布图
Fig.3 Slope failure probability distribution with different joint distribution functions

图4 不同Fst下所得失效概率均值<br/>Fig.4 Means value of slope failure probabilitywith different Fst

图4 不同Fst下所得失效概率均值
Fig.4 Means value of slope failure probabilitywith different Fst

表5 土体抗剪强度参数的变异水平划分<br/>Tab.5 The division of the variation level of soil shear strength parameters

表5 土体抗剪强度参数的变异水平划分
Tab.5 The division of the variation level of soil shear strength parameters

表6 不同δφ下所得边坡失效概率统计表<br/>Tab.6 Slope failure probability statistics table with different δφ

表6 不同δφ下所得边坡失效概率统计表
Tab.6 Slope failure probability statistics table with different δφ

图5 不同δφ下失效概率均值<br/>Fig.5 Means value of failure probability with different δφ

图5 不同δφ下失效概率均值
Fig.5 Means value of failure probability with different δφ

图6 不同变异系数δφ下失效概率变异系<br/>Fig.6 Standard deviation of failure probability with differentδφ

图6 不同变异系数δφ下失效概率变异系
Fig.6 Standard deviation of failure probability with differentδφ

表7 不同δc下所得边坡失效概率统计表<br/>Tab.7 Slope failure probability statistics table with different δc

表7 不同δc下所得边坡失效概率统计表
Tab.7 Slope failure probability statistics table with different δc

图7 不同δc下失效概率均值<br/>Fig.7 Means value of failure probability with different δc

图7 不同δc下失效概率均值
Fig.7 Means value of failure probability with different δc

图8 不同δc下失效概率标准差<br/>Fig.8 Standard deviation of failure probability with different δc

图8 不同δc下失效概率标准差
Fig.8 Standard deviation of failure probability with different δc

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备注

引言

1 失效概率计算方法及算例模型

2 联合分布函数类型对边坡失效概率的影响

3 边坡设计控制标准对边坡失效概率的影响

4 不同抗剪强度参数变异水平对边坡失效概率的影响

5 结论

期刊信息