基于WUS概率密度权重法的边坡稳定系统可靠度分析

姬建; 王乐沛; 廖文旺; 张卫杰; 朱德胜; 高玉峰

doi:10.11779/CJGE202108014

基于WUS概率密度权重法的边坡稳定系统可靠度分析 English Version

姬建^{1, 2,},
王乐沛¹,
廖文旺¹,
张卫杰^{1, 2},
朱德胜³,
高玉峰^{1, 2, ,}

1.
河海大学土木与交通学院,江苏　南京　210029
2.
岩土力学与堤坝工程教育部重点实验室,江苏　南京　210029
3.
扬州大学建筑科学与工程学院,江苏　扬州　225127

基金项目:

国家自然科学基金面上项目 51879091

国家自然科学基金面上项目 52079045

国家自然科学基金面上项目 41772287

详细信息

作者简介:
姬建(1983— ),男,教授,博士生导师,主要从事边坡工程、地下工程、岩土工程可靠度分析等方面的教学和科研工作。E-mail：ji0003an@e.ntu.edu.sg; ji0003an@e.ntu.edu.sg

通讯作者:
高玉峰, E-mail：yfgao66@163.com

中图分类号: TU43
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- 文章访问数: 297
- HTML全文浏览量: 27
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出版历程
- 收稿日期: 2021-01-06
- 网络出版日期: 2022-12-02
- 刊出日期: 2021-07-31

System reliability analysis of slopes based on weighted uniform simulation method

JI Jian^{1, 2,},
WANG Le-pei¹,
LIAO Wen-wang¹,
ZHANG Wei-jie^{1, 2},
ZHU De-sheng³,
GAO Yu-feng^{1, 2, ,}

1.
College of Civil and Transportation Engineering, Hohai University, Nanjing 210029, China
2.
Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210029, China
3.
College of Civil Science and Engineering, Yangzhou University, Yangzhou 225127, China

摘要

摘要: 复杂边坡工程中由于边坡土体分层或土体参数的不确定性等因素,边坡失稳往往会发生在多个潜在失稳滑面,因此,采用单一临界确定性滑面或临界概率滑面对边坡系统可靠度进行分析会极大低估其失效概率。运用WUS（Weighted Uniform Simulation）方法对边坡系统可靠度进行了概率分析,运用4个多层边坡算例演示WUS对于边坡系统可靠度分析的良好适用性。分析结果表明,该方法对高维、隐式极限状态方程下的多层土边坡问题分析精度较高的同时,可极大减少边坡模型计算样本数,例如,对于边坡可靠度分析MCS通常需要10⁴以上的样本量,而WUS仅需500组左右即可满足精度要求。通过对原始WUS算法的修正,在样本量足够的情况下,修正WUS法能更加高效计算得到复杂边坡系统失效概率,并且可以自动摒弃冗余失效模式而得到较为准确的多失效模式所对应的多组可靠度参数设计点,即MPP（Most Probable Failure Point）,进而高效识别出多层土复杂边坡的代表性滑动面,为边坡安全及失稳灾害防治提供重要的参考价值。
- 边坡稳定 /
- 多滑裂面识别 /
- WUS抽样模拟 /
- 系统可靠度 /
- 蒙特卡洛模拟
Abstract: In practical engineering, due to the slope stratification or the spatial variability of soil properties, the slope will often fail along multiple potential sliding surfaces. Considering that using a single critical deterministic sliding surface or a critical probability sliding surface to analyze slope reliability will greatly underestimate the probability of failure, this study uses the weighted uniform simulation (WUS) method to analyze the system reliability of slopes. Four multi-layer slope cases are used to prove that the WUS has good applicability for system reliability analysis of slopes. High accuracy is obtained for multi-layer slope problems under high-dimensional and implicit limit state equations by this method, while the sample size is greatly reduced from 10⁴ samples required by the direct Monte Carlo simulation to only about 500 samples under the same accuracy requirements. By modifying the original WUS algorithm, when the sample size is sufficient, the modified WUS can efficiently obtain the system failure probability and effectively abandon redundant failure modes to obtain accurate most probable failure points corresponding to multiple failure modes. Furthermore, the representative sliding surfaces of the multi-layer slope can be effectively and automatically identified, which provides important reference value for the later maintenance and failure prevention of slopes.
- slope stability /
- multiple failure surfaces /
- weight uniform simulation /
- system reliability /
- Monte Carlo simulation

HTML全文

图 1 修正WUS法分析系统可靠度的计算流程图

Figure 1. Flow chart for system reliability analysis of slopes by modified WUS

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图 2 两层黏土边坡代表性滑动面

Figure 2. Representative sliding surfaces of two-layer clay slope

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图 3 可靠度指标β随样本数量变化情况（算例1）

Figure 3. Change of reliability index β with sample size (Case 1)

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图 4 样本点权重因子柱状示意图（算例1）

Figure 4. Columnar diagram of sample weight index (Case 1)

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图 5 芝加哥国会街切坡代表性滑动面

Figure 5. Representative sliding surfaces of Congress Street Cut

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图 6 失效概率P_f随样本数量变化情况（算例2）

Figure 6. Change of probability of failure P_f with sample size (Case 2)

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图 7 软土地基上的黏性土路堤代表性滑动面

Figure 7. Representative sliding surfaces of embankment resting on soft clay foundation

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图 8 失效概率P_f随样本数量变化情况（算例3）

Figure 8. Change of probability of failure P_f with sample size (Case 3)

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图 9 样本点分布（算例3）

Figure 9. Distribution of samples (Case 3)

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图 10 ACADS 1(c)边坡代表性滑动面

Figure 10. Representative sliding surfaces of ACADS 1(c) problem

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图 11 可靠度指标β随样本数量变化情况（算例4）

Figure 11. Change of reliability index β with sample size (Case 4)

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表 1 土体不确定性强度参数（算例1）

Table 1 Uncertain strength properties of soil (Case 1)

随机变量	分布类型	均值/kPa	变异系数
黏土1 c_u	对数正态分布	120	0.3
黏土2 c_u	对数正态分布	160	0.3

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表 2 MPP点随样本数量变化情况（算例1）

Table 2 Change of MPPs with sample size (Case 1)

样本数量	可靠度指标β	MPP (c_u1/c_u2)
100	2.25	(47.24, 251.34)	(76.39, 71.19)
200	2.69	(44.58, 160.79)	(102.70, 49.77)
300	2.59	(50.34, 125.51)	(72.45, 52.79)
400	2.66	(48.96, 119.39)	(77.43, 57.43)
500	2.68	(47.95, 177.87)	(75.67, 61.73)

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表 3 不同方法边坡的系统可靠度结果比较（算例1）

Table 3 Comparison of different system reliability analysis results of slopes (Case 1)

计算方法	失效概率P_f	MPP (c_u1/c_u2)	样本数量	来源
WUS	$μ_{P_{f}}$ $μ_{P_{f}}$ = 0.42%, $σ_{P_{f}}$ $σ_{P_{f}}$ = 0.058%	(47.95, 177.87)(75.67, 61.73)	500	本文
MCS	$μ_{P_{f}}$ $μ_{P_{f}}$ = 0.44%, $σ_{P_{f}}$ $σ_{P_{f}}$ = 0.067%±0.405%	——	1000020000	Ching等^[16]Ji等^[8]
重要性抽样方法	$μ_{P_{f}}$ $μ_{P_{f}}$ = 0.41%, $σ_{P_{f}}$ $σ_{P_{f}}$ = 0.027%	—	1000	Ching等^[16]
GSS广义子集模拟	0.44%		1643	杨智勇等^[13]
分层响应面法	{0.402%, 0.411%}	—	—	Ji等^[8]

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表 4 土体不确定性强度参数（算例2）

Table 4 Uncertain strength properties of soil (Case 2)

随机变量	分布类型	均值/kPa	变异系数
c_u1	正态分布	55	0.37
c_u2	正态分布	43	0.19
c_u3	正态分布	56	0.24

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表 5 MPP点随样本数量变化情况（算例2）

Table 5 Change of MPPs with sample size (Case 2)

样本数量	可靠度指标β	MPP (c_u1/c_u2 /c_u3)
100	0.32	(43.33, 36.05, 48.72)	(110.10, 47.72, 24.05)	(38.60, 44.87, 39.79)
200	0.37	(63.01, 34.28, 37.86)	(40.18, 41.04, 39.92)	(34.67, 36.44, 53.61)
300	0.35	(58.15, 31.30, 44.63)	(46.62, 52.08, 36.64)	(29.65, 35.54, 70.51)
400	0.38	(49.28, 36.93, 41.30)	(34.53, 46.96, 35.31)	(39.55, 37.42, 71.50)
500	0.34	(42.38, 36.90, 49.77)	(39.05, 44.96, 34.13)	(14.86, 49.61, 48.61)

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表 6 不同方法边坡的系统可靠度结果比较（算例2）

Table 6 Comparison of different system reliability analysis results of slopes (Case 2)

计算方法	失效概率P_f	MPP (c_u1/c_u2/c_u3)	样本数量	来源
WUS	$μ_{P_{f}}$ $μ_{P_{f}}$ = 34%, $σ_{P_{f}}$ $σ_{P_{f}}$ = 2%	(42.38, 36.90, 49.77)(39.05, 44.96, 34.13)(14.86, 49.61, 48.61)	500	本文
Slide V6.0 MCS	±36.76%	—	10000	Ji等^[8]
分层响应面法	{31.22%, 41.84%}	—	—	Ji等^[8]
Ditlevsen上下限法	{27.4%, 44.7%}	—	—	Chowdhury等^[7]

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表 7 土体不确定性强度参数（算例3）

Table 7 Uncertain strength properties of soil (Case 3)

随机变量	位置	分布类型	均值	变异系数
内聚力c/kPa	路堤	正态分布	10	0.20
内聚力c/kPa	软黏土基层	正态分布	40	0.20
摩擦角φ/(°)	路堤	正态分布	12	0.25

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表 8 MPP点随样本数量变化情况（算例3）

Table 8 Change of MPPs with sample size (Case 3)

样本数量	可靠度指标β	最可能失效点MPP (c_路堤/φ_路堤/c_基层)
100	0.24	(8.58,11.88, 31.60),	(11.42,16.04, 10.80)
200	0.52	(10.86,10.45,29.99),	(11.57, 15.35, 9.98)
300	0.46	(9.68, 8.07, 36.63)	(10.10, 15.90,13.09)
400	0.37	(9.68, 8.19, 44.93)	(10.68,15.03, 10.97)
500	0.35	(9.29, 8.53, 41.68)	(10.04,18.34, 13.65)

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表 9 不同方法边坡的系统可靠度结果比较（算例3）

Table 9 Comparison of different system reliability analysis results of slopes (Case 3)

计算方法	失效概率P_f	MPP (c_路堤/φ_路堤/c_基层)	样本数量	来源
WUS	$μ_{P_{f}}$ $μ_{P_{f}}$ = 32.38%, $σ_{P_{f}}$ $σ_{P_{f}}$ = 2.58%	(7.69, 10.09, 40.13)(11.46, 13.19, 12.19)	500	本文
Slide V6.0 MCS	±36.1%	—	2000	Ji等^[8]
分层响应面法	{31.22%, 41.84%}	—	—	Ji等^[8]
Ditlevsen上下限法	{27.4%, 44.7%}	—	—	Chowdhury 等^[7]

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表 10 土体不确定性强度参数（算例4）

Table 10 Uncertain strength properties of soil (Case 4)

随机变量		分布类型	均值	变异系数
黏聚力c/kPa	黏土1	正态分布	5.3	0.3
黏聚力c/kPa	黏土2	正态分布	7.2	0.3
摩擦角φ/(°)	黏土1	正态分布	23	0.2
摩擦角φ/(°)	黏土2	正态分布	20	0.2

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表 11 MPP点随样本数量变化情况（算例4）

Table 11 Change of MPPs with sample size (Case 4)

样本数量	可靠度指标β	最可能失效点MPP (c₁ /φ₁ / c₂ /φ₂ )
100	2.14	(14.27, 3.49, 12.33, 4.84)	(8.56, 5.74, 10.68, 14.30)	(8.65, 10.73, 8.77, 9.04)
200	2.12	(21.40, 5.47, 12.84, 2.27)	(4.34, 4.32, 14.77, 7.80)	(5.39, 10.53, 5.12, 4.37)
300	2.16	(20.50, 4.60, 11.40, 4.62)	(6.58, 5.26, 23.17, 5.83)	(6.14, 6.02, 4.33, 7.55)
400	2.12	(21.56, 7.20, 11.27, 4.95)	(5.22, 4.58, 18.31, 4.46)	(12.23, 5.54, 6.04, 13.98)
500	2.17	(17.73, 4.93, 10.58, 7.91)	(6.54, 2.21, 28.87, 5.85)	(9.38, 6.92, 9.56, 12.29)

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表 12 不同方法边坡的系统可靠度结果比较（算例4）

Table 12 Comparison of different system reliability analysis results of slopes (Case 4)

计算方法	失效概率P_f	MPP (c₁ /φ₁ / c₂ /φ₂)	样本数量	来源
WUS	$μ_{P_{f}}$ $μ_{P_{f}}$ = 1.49%, $σ_{P_{f}}$ $σ_{P_{f}}$ = 0.21%	(17.73, 4.93, 10.58, 7.91)(6.54, 2.21, 28.87, 5.85)(9.38, 6.92, 9.56, 12.29)	500	本文
MCS	1.33%	—	50000	Zhang等^[29]
Slide V6.0 MCS	±1.40%1.22%	——	200001000000	Ji等^[8]Zhu等^[30]
分层响应面法	{1.08%, 1.30%}	—	—	Ji 等^[8]

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