边坡稳定性分析的力矩和方法研究

陈文胜; 刘成; 徐彬; 尹平保

doi:10.11779/CJGE20231182

边坡稳定性分析的力矩和方法研究 English Version

长沙理工大学土木工程学院, 湖南长沙 410114

基金项目:

国家自然科学基金面上基金项目 52178311

国家自然科学基金面上基金项目 51778067

详细信息

作者简介:
陈文胜(1966—)，男，博士，教授，主要从事岩土工程方面的教学和科研。E-mail: 13319504070@126.com

中图分类号: TU43
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出版历程
- 收稿日期: 2023-12-03
- 网络出版日期: 2024-07-30
- 刊出日期: 2025-02-28

Torque sum method for slope stability analysis

School of Civil Engineering, Changsha University of Science & Technology, Changsha 410114, China

摘要

摘要: 提出了一种新的边坡稳定性分析方法，即力矩和方法。力矩和方法是在矢量和方法的基础上，考虑滑坡体作为刚体的位移模式，补充了滑坡体绕某点转动的位移趋势而提出来的。该方法对一确定的滑坡体与滑动面，假定滑坡体绕某点转动，通过求出滑坡体的转动力矩和与抗转动力矩和，从而求到滑坡体绕某点转动时的安全系数。给出了力矩和方法安全系数的定义，并结合条分模型的滑动面应力求解，推导了安全系数的求解公式与相应计算步骤。根据力矩和方法求解了两个ACADS考题，分别针对圆弧和非圆弧滑动面与其它代表性方法的结果进行了比较，结果显示力矩和方法得到了较传统方法较小的安全系数，该结果值得边坡稳定性分析时关注。力矩和方法的提出，是对矢量和方法仅考虑滑动体直线平移位移模式的一个补充，也为边坡稳定性分析，特别是滑坡体可能是转动位移模式提供了一种新的途径。
- 边坡 /
- 稳定性分析 /
- 力矩和方法 /
- 安全系数 /
- 矢量和方法
Abstract: A new method for analyzing slope stability, the torque sum method (TSM), is proposed. The TSM is on the basis of the vector sum method (VSM), considering the displacement mode of the landslide mass as a rigid body and supplementing the displacement tendency of rotating around a certain point. The TSM assumes, for a definite landslide mass and sliding surface, that the mass rotates around a certain point, and by calculating the sum of the rotating torques and the anti-rotating torques of the slide body, the factor of safety when the landslide mass rotates around a certain point is obtained. In this work, the definition of the factor of safety for the TSM is given, and the formula for solving the factor of safety as well as the corresponding calculation steps are derived based on the sliding surface stress of the slice method model. Two examples of ACADS are solved by the TSM, and the results of circular and non-circular sliding surfaces are compared with those of other representative methods. The results show that a smaller factor of safety is obtained by the TSM than by the traditional methods, which is worthy of attention in slope stability analysis. The proposed TSM is a supplement to the VSM which only considers the linear translational displacement mode of sliding body, and also provides a new way for slope stability analysis, especially the possible rotational displacement mode of landslide mass.
- slope /
- stability analysis /
- torque sum method /
- factor of safety /
- vector sum method

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图 1 转动点搜索示意图

Figure 1. Schematic diagram of rotating point searching

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图 2 安全系数求解示意图

Figure 2. Solution of factor of safety

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图 3 条分法安全系数求解示意图

Figure 3. Schematic diagram of solving factor of safety by slices method

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图 4 ACADS考题EX1(c)计算模型

Figure 4. Model of problem of EX1(c) of ACADS

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图 5 ACADS考题EX3(b)计算模型

Figure 5. Model of problem of EX3(b) of ACADS

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表 1 ACADS考题EX1(c)材料参数

Table 1 Material parameters of EX1(c) of ACADS

土层	c/kPa	φ/(°)	γ/(kN·m^-3)
1	0	38	19.5
2	5.3	23	19.5
3	7.2	20	19.5

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表 2 条方法计算过程

Table 2 Calculation process by slices method

条块i	基底长l_i/ m	条重W_i/ (kN·m^-3)	抗滑力 ${\tau _{{\text{f}}i}}{l_i}$ /(kN·m^-1)	基底反力P_i/ (kN·m^-1)
1	5.23	110.11	75.25	96.31
2	3.97	232.52	143.43	183.58
3	3.30	261.32	110.98	220.29
4	3.35	284.60	119.98	263.44
5	3.19	243.01	117.80	260.58
6	3.13	167.48	95.96	201.65
7	3.17	59.87	50.78	76.88

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表 3 安全系数计算结果

Table 3 Calculation results of safety factor

计算方法	圆心坐标/m	转动点坐标/m	安全系数
费伦纽斯法	(35.77, 23.54)		1.263
毕肖普法	(35.77, 23.54)		1.372
简布法	(35.77, 23.54)		1.296
M-P法	(35.77, 23.54)		1.379
矢量和法			1.375
力矩和法		(33.5, 4.6)	1.043

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表 4 ACADS考题EX3(b)材料参数

Table 4 Material parameters of EX3(b) of ACADS

土层	c/kPa	φ/(°)	γ/(kN·m^-3)
1	28.5	20	18.84
2	0	10	18.84

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表 5 滑动面控制点坐标

Table 5 Coordinates of control points for sliding surface

点号	X/m	Y/m
1	10.69	20.00
2	20.50	7.00
3	40.00	6.50
4	42.15	7.75

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表 6 条分法计算过程

Table 6 Calculation process by slices method

条块i	基底长l_i/m	条重W_i/ (kN·m^-3)	抗滑力 ${\tau _{{\text{f}}i}}{l_i}$ / (kN·m^-1)	基底反力P_i/ (kN·m^-1)
1	8.14	300.33	299.76	185.96
2	8.14	825.64	491.09	711.65
3	6.50	1158.27	207.78	1178.36
4	6.50	780.68	144.07	817.07
5	6.50	403.10	75.24	426.69
6	0.99	20.82	5.24	29.71
7	1.49	9.21	56.75	39.08

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表 7 安全系数计算结果

Table 7 Calculated results of factor of safety

计算方法		转动点坐标	安全系数
简布法			1.195
陆军工程师团法			1.364
M-P法			1.286
矢量和法			1.221
力矩和法	条间力函数为常数	(40, 6.5)	1.051
力矩和法	条间力函数为半正弦函数	(40, 6.5)	1.049

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参考文献(10)

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