Probabilistic slope stability analysis: A novel distribution for soils exhibiting highly variable spatial properties边坡随机稳定性分析: 高度空间变异性土的新分布
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Renaud V, Al Heib M, 2024. Probabilistic slope stability analysis: A novel distribution for soils exhibiting highly variable spatial properties. Probabilistic Engineering Mechanics, 76: 103586.DOI: 10.1016/j.probengmech.2024.103586
摘要 | Abstract
边坡稳定性计算需考虑土的性质 (黏聚力和摩擦角)。土木和矿业工程中，常观察到具有高度空间变异性的异质地形。基于案例研究的实测数据，本文对高黏聚力变异系数 (coefficient of variation, COV) 的高度异质地形进行了概率分析。现有的确定性和概率方法在计算边坡稳定性时，缺乏有效考虑地形显著异质性的能力。本文的目标是提出一种新的有界区间分布，其变异系数与黏聚力分布的变异系数一样高 (>150%)。使用这种新分布得到的结果与其它 4 种半无限分布进行比较。为考虑黏聚力和摩擦角之间的相关性，本文给出了一类特定公式，计算固定上下限之间变化的摩擦角，并满足所需的相关系数、均值和标准差。考虑了新的黏聚力和摩擦角分布并在概率数值模型中测试。这种新分布目前可应用于高度空间变异性地形和异质材性的岩土工程研究。关键词: 蒙特卡罗模拟, 边坡稳定性, 概率分布, 异质材料Slope stability calculation depends on the soil properties (cohesion and the friction angle) of the soil. Heterogeneous terrains are frequently observed in civil and mining projects where the properties are highly spatially variable. Based on a real data from case studies, this paper presents a probabilistic analysis of the slope stability of highly heterogeneous terrains with a very high coefficient of variation (COV) of the cohesion distribution. The existing deterministic and probabilistic approaches for calculating slope stability lack the capability to effectively consider the significant heterogeneity present in the terrain The objective of the paper is to develop a new bounded interval distribution having a COV that is as high (>150%) as the COV of the cohesion distribution The results obtained with this new distribution are compared to 4 other semi-infinite distributions. To consider the correlation between cohesion and the friction angle, a specific formulation was developed to generate friction angles varying between fixed minimum and maximum limits and having the desired correlation coefficient, mean, and standard deviation. The new cohesion and friction angle distributions were incorporated and tested in a probabilistic numerical model. The new distribution can presently be applied to geotechnical studies for terrains and heterogenous materials with properties exhibiting high spatial variability.Keywords: Monte-carlo simulation; Slope stability; Probability distribution; Heterogeneous materials创新点 | Highlights
- New bounded interval distribution for data with high coefficient of variation
- Probabilistic numerical simulation (Monte-Carlo) to compute global factor of safety
- New formulation to generate correlated variates varying between fixed limits
- New distribution for geotechnical studies of highly spatial variability properties
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Fig. 1. Normal distribution of the friction angle, before and after interval-censoring
图 2: 凝聚力初始参数下右删失后半无限区间定义的分布Fig. 2. Distributions defined on a semi-infinite interval with initial parameters (μ_C, σ_C) for the cohesion, and after right-censoring
图 3: 半无限区间定义的凝聚力的 5 个分布最佳拟合与有界分布的对比Fig. 3. Best fit of 5 distributions of the cohesion defined on a semi-infinite interval (right-censored parameters are computed in order to have μ~ = μ_c = 14.2 kPa and~ σ = σ_c = 20.3 kPa) compared to bounded distributions (Beta and RAFF)
图 4: 不同变异系数下有界区间定义的 4 个分布对比Fig. 4. Comparison of 4 distributions defined on a bounded interval, for different COV values
图 5: 洪水期最终坑道风险评估分布参数与上下界附近权重随变异系数的变化Fig. 5. Evolution of parameters α and β (RAFF distribution) and of weights near C_min and C_max as a function of the coefficient of variation (COV)
图 6: 洪水期最终坑道风险评估概率分布函数级数展开式的最大误差对比Fig. 6. Comparison of maximum errors for series expansions (original and modified) of the RAFF CDF
图 7: 复现 Masoudian 等人黏聚力数据的洪水期最终坑道风险评估概率分布函数与概率密度函数Fig. 7. Cumulative (CDF) and probability density functions (pdf) of the RAFF distribution that reproduces the cohesion data of Masoudian et al. (2019)
图 8: 不同连续分布的有效范围以及黏聚力与摩擦角变异系数的变化范围Fig. 8. Range of validity (μ/C_max, 2σ/C_max) of different continuous distributions (unbounded distributions having been censored), range of variation of the COV for cohesion (yellow) and friction angle (green)
图 9: 矿床边坡稳定性研究数值模型的几何与平均特性Fig. 9. Geometry and average properties of the numerical model for the study of slope stability of a deposit (Most lake example, Renaud et al. 2022)
Fig. 10. Distributions of cohesion C and friction angle φ in the deposit upper layer (Fig. 9): data taken from Masoudian et al. (2019)
图 11: 相关系数 -0.5 时黏聚力对安全系数分布的影响Fig. 11. Influence of C distributions on the FoS distribution (normal or Weibull), r = −0.5
作者信息 | Authors
Vincent Renaud, 通讯作者 (Corresp.) 法国工业环境研究所 (Institut National de L'environnement Industriel et des Risques)Email: vincent.renaud@ineris.fr
法国工业环境研究所 (Institut National de L'environnement Industriel et des Risques)
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
