基于最短折减路径法的边坡安全系数研究

郑永来; 吴卓睿

doi:10.19509/j.cnki.dzkq.2022.0224

基于最短折减路径法的边坡安全系数研究

doi: 10.19509/j.cnki.dzkq.2022.0224

郑永来,
吴卓睿^,

同济大学土木工程学院, 上海 200092

基金项目:

水利部土石坝破坏机理与防控技术重点实验室开放基金项目 YK319002

详细信息

作者简介:
郑永来(1964-), 男, 教授, 主要从事海洋岩土工程及边坡稳定性研究。E-mail: zyll@tongji.edu.cn

通讯作者:
吴卓睿(1993-), 男, 现正读土木工程专业博士学位, 主要从事地下工程及边坡稳定性研究。E-mail: wuzr@tongji.edu.cn

中图分类号: P642.2
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出版历程
- 收稿日期: 2022-07-15

Estimation of slope safety factor based on trajectory reduction method

Zheng Yonglai,
Wu Zhuorui^,

College of Civil Engineering, Tongji University, Shanghai 200092, China

摘要

摘要:
使用双参数折减方法分析边坡稳定性的研究较多, 如何把两个折减系数定义为单一的综合安全系数是目前研究的一项重要内容。Isakov提出的最短折减路径法能够保证在不同工况下得到最小安全系数, 但是该方法的缺点在于计算复杂, 不适合工程应用。通过有限元数值模拟, 利用最短折减路径方法计算不同强度黏土构成的不同坡度均质土坡的最小安全系数和对应的折减系数, 探索了最小安全系数与土的初始黏聚力、内摩擦角以及边坡坡度的关系, 分析了初始强度对折减系数的影响。结果表明, 相同坡度下不同强度的黏土边坡在失稳时, 最小安全系数对应的临界破坏强度相同。临界破坏强度与坡度近似成线性正相关关系。由此基于最短折减路径法提出了一种新的计算最小安全系数的方法, 该方法得到的安全系数与目前常用的极限平衡方法所得结果相近, 并且计算简单, 因此可以用于边坡稳定性分析。
- 边坡稳定分析 /
- 双参数折减 /
- 最短折减路径法 /
- 安全系数 /
- 临界破坏强度
Abstract:
Currently, double reduction method (DRM) is widely used in the field of slope stability. However, one of the main challenges of the double reduction method is how to define the comprehensive safety factor based on two reduction parameters. The trajectory reduction method developed by Isakov can be used to ensure the minimum comprehensive safety factor on different conditions. However, its main shortcoming is that the method needs expensive calculation to determine the safety factor for a certain slope configuration. The paper examines the relationship between the comprehensive safety factor and cohesive and internal friction angle of soil, by using the FEM and trajectory method to calculate the minimum safety factor and corresponding reduction factor with respect to different inclinations of the slope. The initial strength effect on double reduction parameters are analyzed accordingly. The result shows for a certain slope configuration; the initial strength has little effect on the critical strength which is related to the minimum comprehensive safety factor. It means that for a slope with a certain inclination, even if the strength of soil is different, the critical strength is identical. The critical strength of soil slope is linear with the inclination of the slope, which means that every inclination corresponds to one critical cohesive and one critical internal friction angle. Consequently, a novel method to calculate the minimum safety factor is proposed in this paper. The result obtained by this method is close to the result which is from the limit equilibrium method, and compared with the original method by Isakov, this alternative method can simplify the calculation, and keep the result as accurate as the limit equilibrium method. Thus, it can be used to analyze the stability of slope.
- slope stability analysis /
- double reduction method /
- trajectory reduction method /
- safety factor /
- critical failure strength

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图 1 黏土边坡强度折减路径

M_min或M_k分别代表最短路径法或同步折减法的强度折减路径与临界状态线的交点, k_C, k_φ分别代表黏聚力和内摩擦角正切值的折减系数, (1, 1)点代表未折减的初始状态, 蓝线表示同步折减方法的折减路径, 而红线最短路径往往并非沿着45°线同步折减

Figure 1. Trajectories of soil strength reduction in embankment composed of clay

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图 2 有限元强度折减法计算中的最优边界条件

H.模型高度；h.坡高；L₁，L₂.坡顶及坡底的长度

Figure 2. Optimal condition in FEM of strength reduction method

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图 3 内摩擦角正切值与折减系数的关系

Figure 3. Relationship between tangent of internal friction and reduction parameter

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图 4 黏聚力与折减系数的关系

Figure 4. Relationship between cohesive strength and reduction parameter

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图 5 坡度与临界内摩擦角正切值的关系

Figure 5. Relationship between slope inclination and tangent of critical internal frictionangle

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图 6 坡度与临界黏聚力的关系

Figure 6. Relationship between slope inclination and critical cohesive strength

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图 7 不同坡度下的强度折减系数与路径(红线表示最短折减路径, 蓝线表示同步折减路径)

Figure 7. Reduction parameters and trajectory with various slope inclination

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表 1 坡度与安全系数的关系

Table 1. Relationship between slope inclination and the safety factor

坡度/(°)	30	35	40	45	50	55	60	65	70
安全系数	2.422	2.214	2.051	1.921	1.802	1.701	1.606	1.522	1.355

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表 2 不同黏性土在同一坡度下的最小安全系数对应的折减系数

Table 2. Reduction parameter of the minimum safety factor in the same slope inclination of various clay

不同黏土强度参数组合	tan20°		tan22°		tan24°		tan26°		tan28°
不同黏土强度参数组合	k_C	k_φ	k_C	k_φ	k_C	k_φ	k_C	k_φ	k_C	k_φ
C60	2.700	1.308	2.700	1.450	2.700	1.598	2.700	1.760	2.700	1.910
C55	2.475	1.308	2.475	1.450	2.475	1.598	2.475	1.760	2.475	1.910
C50	2.250	1.308	2.250	1.450	2.250	1.598	2.250	1.760	2.250	1.910
C45	2.025	1.308	2.025	1.450	2.025	1.598	2.025	1.760	2.025	1.910
C40	1.800	1.308	1.800	1.450	1.800	1.598	1.800	1.760	1.800	1.910
C35	1.575	1.308	1.575	1.450	1.575	1.598	1.575	1.760	1.575	1.910
C30	1.385	1.270	1.430	1.360	1.440	1.490	1.570	1.490	1.460	1.750
注：C和tanφ分别代表黏聚力和内摩擦角正切值, 如C60、tan20°分别表示初始黏聚力为60 kPa, 内摩擦角为20°的正切值

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表 3 不同黏性土在同一坡度下最小安全系数对应临界破坏强度

Table 3. Critical strength of the minimum safety factor in the same slope inclination of various clay

不同黏土强度参数	tan20°		tan22°		tan24°		tan26°		tan28°
不同黏土强度参数	C_c	tanφ_c	C_c	tanφ_c	C_c	tanφ_c	C_c	tanφ_c	C_c	tanφ_c
C60	22.2	0.278	22.2	0.279	22.2	0.279	22.2	0.277	22.2	0.278
C55	22.2	0.278	22.2	0.279	22.2	0.279	22.2	0.277	22.2	0.278
C50	22.2	0.278	22.2	0.279	22.2	0.279	22.2	0.277	22.2	0.278
C45	22.2	0.278	22.2	0.279	22.2	0.279	22.2	0.277	22.2	0.278
C40	22.2	0.278	22.2	0.279	22.2	0.279	22.2	0.277	22.2	0.278
C35	22.2	0.278	22.2	0.279	22.2	0.279	22.2	0.277	22.2	0.278
C30	21.7	0.287	21.0	0.297	20.8	0.299	19.1	0.327	20.5	0.304
注：C_c、tanφ_c分别为临界黏聚力(kPa)和内摩擦角正切值，而C60、tan20°分别表示初始黏聚力为60 kPa, 内摩擦角为20°的正切值

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表 4 不同坡度下的临界强度值

Table 4. Critical strength in the various slope inclination

坡度/(°)	C_c/kPa	tanφ_c
50	24.038	0.298
45	22.222	0.278
40	20.513	0.259
35	19.231	0.234
30	18.018	0.206
25	18.433	0.163

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表 5 不同方法计算的边坡安全系数结果对比

Table 5. Comparison of calculation results with different methods

坡度	35°	40°	45°
极限平衡法	1.70	1.61	1.50
最短折减路径法	1.652	1.525	1.436
本研究改进后的方法	1.668	1.538	1.422

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