基于随机场理论的土石混合体边坡稳定性

边宏光; 王顺; 马海善; 辛鹏

doi:10.19509/j.cnki.dzkq.tb20240183

基于随机场理论的土石混合体边坡稳定性

doi: 10.19509/j.cnki.dzkq.tb20240183

边宏光^{1a, 1b,},
王顺^{1a, 1b, ,},
马海善²,
辛鹏³

1a.
武汉大学水资源工程与调度全国重点实验室, 武汉 430072
1b.
武汉大学水利水电学院, 武汉 430072
2.
青海省环境地质勘查局, 西宁 810001
3.
中国地质科学院地质力学研究所, 北京 100081

基金项目:

国家自然科学基金项目 42472355

详细信息

作者简介:
边宏光, E-mail: hongguang@whu.edu.cn

通讯作者:
王顺, E-mail: shun.wang@whu.edu.cn

中图分类号: TU43
计量
- 文章访问数: 376
- PDF下载量: 56
- 被引次数: 0
出版历程
- 收稿日期: 2024-04-24
- 录用日期: 2024-08-13
- 修回日期: 2024-05-15

Stability of soil-rock mixture slopes based on random field theory

BIAN Hongguang^{1a, 1b
,},
WANG Shun^{1a, 1b
, ,},
MA Haishan²,
XIN Peng³

1a.
State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan 430072, China
1b.
School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, China
2.
Qinghai Bureau of Environmental Geology Exploration, Xining 810001, China
3.
Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China

More Information

Author Bio:
BIAN Hongguang, E-mail: hongguang@whu.edu.cn

Corresponding author: WANG Shun, E-mail: shun.wang@whu.edu.cn

摘要

摘要:
土石混合体边坡在我国分布范围广, 且其材料组成复杂, 受到了众多学者的关注。为了科学合理地评估土体参数的空间变异性对土石混合体边坡稳定性的影响, 基于随机场理论, 选取有效抗剪强度参数黏聚力c和内摩擦角φ作为随机变量, 采用局部平均法模拟随机场, 在MATLAB中实现随机场参数生成, 在考虑土石混合体块石真实形状和块石含量基础上, 采用Python语言脚本方式, 将随机场参数映射到有限元软件中的土石混合体边坡, 应用强度折减法计算边坡稳定安全系数。计算结果显示, 土石混合体边坡的稳定安全系数符合正态分布, 随着土石混合体边坡块石含量增加, 边坡稳定安全系数的均值从1.005增长至1.095, 边坡也由浅层破坏逐渐发展为深层破坏。块石质量分数均为35%时, 块石粒径较大土石混合体边坡稳定性安全系数为1.334, 块石粒径较小土石混合体边坡稳定安全系数为1.064。相比于确定性计算结果, 考虑土体参数空间变异性的稳定安全系数更高。因此, 在进行土石混合体边坡稳定性分析时, 应充分考虑土体有效抗剪强度参数空间变异性, 避免出现设计过于保守的情况。
- 土石混合体 /
- 随机场理论 /
- 边坡稳定性分析 /
- 有限元法 /
- 强度折减法
Abstract: <p>The extensive distribution and complex material composition of soil-rock mixture slopes in China have attracted significant attention from scholars.</p></sec><sec> <title>Objective
This study aims to scientifically and rationally assess the impact of the spatial variability of soil parameters on the stability of soil-rock mixture slopes.
Methods
Based on the random field theory, the effective shear strength parameters cohesion c and internal friction angle φ are selected as random variables. The local averaging method is used to simulate the random field, with random field parameter generation conducted in MATLAB. Python scripts are employed to map the random field parameters to the soil-rock mixture slope via finite element software, accounting for the actual shape and content of block rocks in the soil-rock mixture. The strength reduction method is then applied to calculate the slope stability safety factor.
Results
The results reveal that the stability safety factor of soil-rock mixture slopes follows a normal distribution. As the block stone content increases, the mean value of the stability safety factor rises from 1.005 to 1.095, reflecting a transition from shallow to deep failure. For block stone content of 35%, the stability safety factor reaches 1.334 for larger block stones and 1.064 for smaller ones. Compared to deterministic calculation results, incorporating the spatial variability of the soil parameters yields higher stability safety factor.
Conclusion
Therefore, in soil-rock mixture slope stability analyses, the spatial variability of effective shear strength parameters must be fully considered to prevent overly conservative designs.
- soil-rock mixture /
- random field theory /
- slope stability analysis /
- finite element method /
- strength reduction method
注释:

所有作者声明不存在利益冲突。

HTML全文

图 1 二维局部平均单元A和A′的相对位置参数(字母含义见正文)

Figure 1. Relative position of 2D local average element A and A′

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图 2 不规则形状块石生成过程

Figure 2. Process for generating irregularly shaped rock blocks

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图 3 土石混合体边坡模型示意图(单位：m)

Figure 3. Schematic of slope model for soil-rock mixtures

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图 4 有限元计算模型

Figure 4. Finite element computation model

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图 5 有效抗剪强度参数黏聚力c和内摩擦角φ的分布示意图

a, b.均质土坡; c, d.块石质量分数35%

Figure 5. Schematic of distribution of effective shear strength parameters cohesion c and internal friction angle φ

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图 6 强度折减系数ω-位移图

Figure 6. Strength reduction factor ω vs displacement

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图 7 土石混合体边坡破坏路径传播图

Figure 7. Propagation diagram of failure path of soil-rock mixture slope

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图 8 确定性计算结果的塑性应变云图

Figure 8. Plastic strain cloud map for deterministic calculation results

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图 9 随机场计算结果统计图

Figure 9. Statistics of random field calculation results

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图 10 稳定安全系数最大(a~e)和最小(f~j)时对应的塑性应变云图

Figure 10. Plastic strain cloud map for maximum and minimum of stability safety factors

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表 1 二维随机场常用的相关函数

Table 1. Correlation functions for a 2D random field

函数名称	相关函数
指数函数	$\rho\left(\tau_1, \tau_2\right)=\exp \left(-2 \sqrt{\frac{\tau_1^2}{\delta_1^2}+\frac{\tau_2^2}{\delta_2^2}}\right)$
高斯函数	$\rho\left(\tau_1, \tau_2\right)=\exp \left[-\pi\left(\frac{\tau_1^2}{\delta_1^2}+\frac{\tau_2^2}{\delta_2^2}\right)\right]$
可分离的指数函数	$\rho\left(\tau_1, \tau_2\right)=\exp \left[-2\left(\frac{\left\|\tau_1\right\|}{\delta_1}+\frac{\left\|\tau_2\right\|}{\delta_2}\right)\right]$
注：字母含义见正文

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表 2 土石混合体边坡模型参数

Table 2. Parameters for the soil-rock mixture slope model

组成成分	密度/(kg·m^-3)	弹性模量/MPa	泊松比v	黏聚力c/kPa	内摩擦角φ/(°)	本构模型
块石	2 700	15 000	0.25	—	—	理想弹性模型
土体	2 000	50	0.30	12.38	20	摩尔-库伦破坏准则

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表 3 有效抗剪强度参数的分布特征参数

Table 3. Distribution characteristic parameters of effective shear strength parameters

分布特征参数	黏聚力c/kPa	内摩擦角φ/(°)
均值μ	12.38	20.00
标准差σ	2.47	4.00

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表 4 稳定安全系数

Table 4. Stability safety factor

块石质量分数/%	确定性计算结果	均值	标准差	最小值	最大值
0	0.997	1.005	0.033	0.917	1.138
5	0.997	1.008	0.058	0.910	1.127
15	1.005	1.012	0.082	0.917	1.137
25	1.061	1.079	0.062	0.915	1.151
35	1.064	1.095	0.033	1.000	1.153
#35	1.334	—	—	—	—
注：块石质量分数0为均质土坡；块石质量分数#35%相较于其他情况，块石粒径增大；下同

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