土质边坡的单元失效概率与失效模式研究

彭普; 李泽; 张小艳; 申林方; 许芸

doi:10.6052/j.issn.1000-4750.2022.02.0192

土质边坡的单元失效概率与失效模式研究

彭普^1,,
李泽^1, ,,
张小艳^2,,
申林方^1,,
许芸^3,

1.
昆明理工大学建筑工程学院，云南，昆明 650500
2.
昆明理工大学电力工程学院，云南，昆明 650500
3.
长江勘测规划设计研究有限责任公司，湖北，武汉 430010

基金项目: 国家自然科学基金项目(12162018，12262016)；昆明理工大学引进人才科研启动基金项目(KKSY201904006)

详细信息

作者简介:
彭　普(1995−)，男，湖北人，博士生，主要从事结构可靠度方面的科研工作(E-mail: pengpu@stu.kust.edu.cn)

张小艳(1981−)，女，湖北人，讲师，博士，主要从事结构可靠度方面的教学和科研工作(E-mail: zhangxiaoyan@kust.edu.cn)

申林方(1982−)，女，湖南人，副教授，博士，主要从事岩体力学领域的教学与研究工作(E-mail: linfangshen@126.com)

许　芸(1984−)，女，湖北人，工程师，学士，主要从事岩土工程方面的科研工作(E-mail: xuyun@cjwsjy.com.cn)

通讯作者:
李　泽(1981−)，男，云南人，教授，博士，主要从事岩土力学领域的科研工作(E-mail: lize@kust.edu.cn)

中图分类号: TU43
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出版历程
- 收稿日期: 2022-02-26
- 修回日期: 2022-06-29
- 网络出版日期: 2022-07-28
- 刊出日期: 2024-01-24

RESEARCH ON ELEMENT FAILURE PROBABILITY AND FAILURE MODE OF SOIL SLOPE

1.
Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, Yunnan 650500, China
2.
Faculty of Electric Power Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650500, China
3.
Changjiang Institute of Survey, Planning and Research Co., Ltd, Wuhan, Hubei 430010, China

摘要

摘要:
土质边坡系统失效概率与土体抗剪强度参数以及地下水位息息相关，在传统边坡可靠度分析中一般只考虑了土体抗剪强度参数的变异性，忽略了地下水位随机性带来的影响。该文将有限元离散技术、上限法理论、相关非高斯随机场模拟方法以及随机规划理论结合起来研究随机地下水位作用下考虑参数空间变异性的边坡系统失效概率。采用有限单元离散边坡土体，将边坡地下水位作为随机变量并考虑土体抗剪参数的空间变异性，基于塑性极限分析上限法构建边坡可靠度分析的随机规划模型；采用基于蒙特卡洛的迭代方法进行求解，得到边坡稳定性系数和速度场；根据边坡中单元的失效信息首次采用AP聚类分析方法来估算边坡的系统失效概率，发展了边坡系统可靠度分析理论。对一个经典的边坡算例进行了系统分析并与极限平衡分析方法、有限元方法结果进行对比，结果表明：随机地下水位作用下考虑参数空间变异性时，边坡存在多种失效模式，AP聚类分析方法可以根据失效单元的位置信息识别出边坡所有失效模式以及对应的失效概率；基于Matlab编制了高效的上限法并行程序，大大提高了计算效率。
- 边坡 /
- 可靠度 /
- 空间变异性 /
- 随机地下水位 /
- 上限法
Abstract:
The failure probability of a soil slope system is strongly related to soil shear strength parameters and groundwater level. In the traditional slope reliability analysis, only the variability of soil shear strength parameters is generally considered, and the influence of random groundwater level is ignored. Finite element discrete technique, upper bound method theory, relevant non-Gaussian random field simulation method and, stochastic planning theory are combined to study the failure probability of the slope system under the effect of stochastic groundwater level considering the spatial variability of parameters. A stochastic programming model for slope reliability analysis is constructed upon the upper bound method for plastic limit analysis by using a finite element discrete slope soil body, taking the groundwater level of the slope as a random variable and considering the spatial variability of the soil shear parameters, and then the model is employed to obtain the stability safety coefficient and velocity field of the slope upon Monte Carlo simulation; the AP clustering analysis method is used for the first time to the system failure probability of the slope estimated based on the failure information of the elements in the slope, and the reliability analysis theory of the slope system is developed. A classical slope calculation case is systematically analyzed and compared with the results of Limit Equilibrium Analysis Method and Finite Element Method. The results show that: there are multiple failure modes of slopes under the action of random groundwater level considering the spatial variability of parameters, and the AP cluster analysis method can identify all the failure modes of slopes and the corresponding failure probabilities based on the location information of failed elements; an efficient parallel program of upper bound method is prepared upon Matlab, which greatly improved computing efficiency.
- slope /
- reliability /
- spatial variability /
- random groundwater level /
- upper bound method

HTML全文

图 1 边坡随机地下水位作用示意图

Figure 1. Schematic diagram of random groundwater level of soil slope

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图 2 边坡可靠度上限法流程图

Figure 2. Flow chart of reliability analysis using upper bound method for slope

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图 3 AP聚类算法选点过程

Figure 3. AP clustering algorithm selection process

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图 4 均质边坡计算模型　/m

Figure 4. Homogeneous slope calculation model

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图 5 地下水位随机数分布直方图

Figure 5. Histogram of random distribution of groundwater level

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图 6 边坡稳定渗流场

Figure 6. Steady seepage field of slope

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图 7 关键点处孔隙水压力随机变化情况

Figure 7. The pore water pressure of the monitoring points

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图 8 边坡抗剪强度参数随机场

Figure 8. Random Field of Slope Shear Strength Parameters

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图 9 边坡稳定性系数分布特征

Figure 9. Distribution characteristics of slope safety factor

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图 10 边坡稳定性系数概率密度曲线

Figure 10. Probability density curve of safety factor of slope

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图 11 边坡稳定性系数累积概率密度曲线

Figure 11. Cumulative probability density curve of safety factor of slope

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图 12 边坡稳定性系数的均值与地下水位的关系

Figure 12. The relationship between the slope safety factor and groundwater

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图 13 边坡稳定性系数的频数分布直方图

Figure 13. Frequency distribution histogram of safety factors

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图 14 边坡失效模式AP聚类结果

Figure 14. Schematic diagram of AP clustering results of slope failure mode

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图 15 边坡整体失效概率与地下水位的关系

Figure 15. The relationship between slope failure probability and groundwater

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图 16 单元失效概率等值线

Figure 16. Element failure probability contour

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图 17 单元失效概率与地下水位的关系

Figure 17. The relationship between the element failure probability and groundwater

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表 1 土体参数统计特性

Table 1 Statistics of soil parameters

土体参数	均值	变异系数	分布类型	波动范围	相关系数
黏聚力c/kPa	10	0.3	对数正态	L_h=40 m	ρ_c,φ=−0.5
摩擦角φ/(°)	30	0.2	对数正态	L_v=4 m	ρ_c,φ=−0.5

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表 2 不同方法的边坡可靠度结果对比

Table 2 Comparison of slope reliability results of different methods

计算方法	水平坐标方向波动范围L_h/m	竖直坐标方向波动范围L_v/m	均值 u_k	标准差 σ_k	失效概率 $P_{\rm{f}}^Z$ /(%)
本文方法	40	4	1.201	0.096	1.10×10⁻²
K-L法^[37]			1.199	0.106	1.71×10⁻²
LHS法^[32]			1.184	0.102	1.80×10⁻²
FEM法			1.225	0.099	0.40×10⁻²

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表 3 三种水位作用下边坡的可靠度指标

Table 3 Calculation results of reliability index

水位	计算方法	均值u_k	标准差σ_k	失效概率 $P_{\rm{f}}^Z$ /(%)
t_w=1	UBM	1.201	0.096	1.10×10⁻²
	LEM	1.199	0.106	1.71×10⁻²
	FEM	1.226	0.097	0.60×10⁻²
t_w=25	UBM	1.143	0.090	4.50×10⁻²
	LEM	1.143	0.097	5.60×10⁻²
	FEM	1.168	0.090	2.40×10⁻²
t_w=50	UBM	0.894	0.070	92.70×10⁻²
	LEM	0.892	0.069	93.40×10⁻²
	FEM	0.916	0.071	89.40×10⁻²

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表 4 边坡失效模式以及对应的失效概率

Table 4 Slope failure mode and the corresponding failure probability

失效模式	失效面积/m²	失效次数	失效概率 $P_{\rm{f}}^Z$ /(%)
模式1	5.45~7.41	526	1.052
模式2	10.35~15.52	667	1.334
模式3	48.72~53.44	3342	6.684
模式4	69.43~72.42	1088	2.176
模式5	89.45~92.91	122	0.244
模式6	110.05~112.65	64	0.128
总和	−	5809	11.618

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表 5 不同地下水位作用下边坡失效模式以及对应的失效概率

Table 5 Slope failure modes and corresponding failure probabilities under the action of different groundwater levels

地下水位	失效模式	失效次数	失效概率 $P_{\rm{f}}^Z$ /(%)
t_w=1	模式3	8	0.800
t_w=25	模式3	13	1.300
t_w=25	模式4	12	1.200
t_w=50	模式1	219	2.190
	模式2	178	1.780
	模式3	340	3.400
	模式4	155	1.550
	模式5	26	0.260
	模式6	9	0.090

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土质边坡的单元失效概率与失效模式研究

通讯作者: 李 泽(1981−)，男，云南人，教授，博士，主要从事岩土力学领域的科研工作(E-mail: lize@kust.edu.cn)

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RESEARCH ON ELEMENT FAILURE PROBABILITY AND FAILURE MODE OF SOIL SLOPE

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通讯作者:
李　泽(1981−)，男，云南人，教授，博士，主要从事岩土力学领域的科研工作(E-mail: lize@kust.edu.cn)