牵引式滑坡后缘破裂面计算方法

孙立娟; 崔凯; 杨涛; 成启航

doi:10.3969/j.issn.0258-2724.20170873

牵引式滑坡后缘破裂面计算方法

doi: 10.3969/j.issn.0258-2724.20170873

孙立娟^1,2,,
崔凯^1,2,
杨涛^1,3, ,,
成启航¹

基金项目: 国家自然科学基金资助项目（51178402）；国家重点研发计划重点专项资助项目（2016YFC0802200）

详细信息

作者简介:
孙立娟（1982—），女，博士研究生，研究方向为岩土工程，E-mail：meiyao_sunshine@163.com

通讯作者:
杨涛（1973—），男，副教授，研究方向为岩土力学、边坡和滑坡，E-mail：03017003@163.com

中图分类号: V221.3
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- 文章访问数: 684
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- 被引次数: 0
出版历程
- 收稿日期: 2018-01-09
- 修回日期: 2018-05-16
- 网络出版日期: 2019-02-22
- 刊出日期: 2019-06-01

Calculation Method of Trailing Edge Failure Surface of Retrogressive Landslide

SUN Lijuan^{1,2
,},
CUI Kai^1,2,
YANG Tao^{1,3
, ,},
CHENG Qihang¹

摘要

摘要: 斜坡发生牵引式滑动破坏，形成后缘拉裂面，后缘面形态对滑坡稳定性分析及推力计算具有重要影响，但其在滑坡体内部的空间特征难以确定. 为探索后缘破裂面的形成机理和计算理论，建立合理的数学力学模型，提出后缘破裂面倾角的计算方法，确定各级滑块的最危险破裂倾角，并将其所在破裂面作为条分型式，计算各级滑块的稳定系数，实现滑坡渐进破坏过程的稳定性分析；同时，开展室内模型试验进行验证，研发了新的模型试验装置，其主体由若干渗透盒组成，能够构成各种几何形状的分段式滑面；通过向不同分段的渗透盒注水，实现牵引式滑坡的逐级失稳过程，并测试各级滑块最终形态的后缘破裂面倾角. 结果表明：后缘破裂面倾角计算值与试验值具有较高的一致性，主要集中在70° 左右，相对误差介于2%～4%之间；滑坡体失稳形成的各级滑块稳定性不同，第一级滑块的稳定程度最差，越向坡体后侧稳定性越好. 可为牵引式滑坡的稳定性分析提供新的思路.
- 牵引式滑坡 /
- 后缘破裂面倾角 /
- 稳定性分析 /
- 模型试验 /
- 计算方法
Abstract: Slope failure is induced by retrogressive slide, forming a trailing edge tension crack surface. The shape of the trailing edge surface has an important influence on landslide stability analysis and thrust calculation. However, it is difficult to determine the spatial characteristics of the landslide. In order to explore the formation mechanism and calculation theory of the trailing edge fracture surface, a reasonable mathematical and mechanical model was established. The calculation method of the trailing edge fracture inclination angle was put forward, from which the most dangerous fracture inclination angle of each level slider was found. Finally, the fracture surface was used as a stripe type to calculate the stability coefficient of each level slider and carry out the stability analysis of the landslide progressive failure process. Simultaneously, an indoor model test was conducted for verification. A new model test device was developed as well. Its main body was composed of a number of permeable boxes, thereby forming sectional sliding surfaces of various geometric shapes. By injecting water into different permeable boxes, step-by-step instability process of retrogressive landslide was realized. Then the trailing edge inclination of the final form of the sliders at each stage was measured. The results show that the calculated value of the inclination of the trailing edge is in good agreement with the test value. It is mainly concentrated at about 70°, with a relative error between 2% and 4%. The stability of the sliders is different at each level. Thus, the stability of the first stage is the worst, whereas the stability of the backside of the landslide body is better. These research results can provide a new procedure for conducting the stability analysis of retrogressive landslide.
- retrogressive landslide /
- inclination of trailing edge fracture plane /
- stability analysis /
- model test /
- calculation method

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图 1 牵引式滑坡概化模型

Figure 1. Retrogressive landslide generalisation model

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图 2 滑块划分及编号简图

Figure 2. Sketch of slice and block number

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图 3 牵引式滑坡体计算模型

Figure 3. Sliding-block computation model of retrogressive landslide

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图 4 试验模型计算简图（单位：m）

Figure 4. Calculation sketch of the test model (unit：m)

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图 5 滑块1计算简图

Figure 5. Calculation sketch of Block 1

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图 6 滑块1的安全系数曲线

Figure 6. Safety factor curve of Blcok 1

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图 7 滑块2计算简图

Figure 7. Calculation sketch of block 2

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图 8 滑块2的安全系数曲线

Figure 8. Safety factor curve of blcok 2

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图 9 滑块3计算简图

Figure 9. Calculation sketch of Block 3

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图 10 滑块3的安全系数曲线

Figure 10. Safety factor curve of Blcok 3

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图 11 后缘拉裂缝形态

Figure 11. Morphology of tension crack of trailing edge

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图 12 后缘面破裂倾角结果对比

Figure 12. Comparison results of the inclination of the trailing edge

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图 13 后缘面破裂倾角结果对比

Figure 13. Comparison results of the inclination of the trailing edge

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表 1 滑块1：后缘面破裂倾角计算结果

Table 1. Block 1: results of the fracture angle of the trailing edge

θ₁/（°）	A_era/m²	$l_{{B_1}{C_1}}$/m	F₁
30	0.189 8	0.955 6	2.475 0
40	0.131 2	0.630 8	1.226 3
50	0.114 2	0.494 0	0.975 9
60	0.086 3	0.416 3	0.895 7
65	0.079 3	0.390 2	0.882 9
70	0.073 2	0.355 1	0.878 0
71	0.072 2	0.349 6	0.877 9
72	0.071 1	0.344 9	0.878 3
75	0.068 2	0.328 4	0.879 4
76	0.067 2	0.323 8	0.880 4
78	0.065 5	0.315 3	0.882 9
80	0.063 7	0.307 6	0.886 3
90	0.056 2	0.283 4	0.923 7
100	0.051 2	0.247 7	0.936 1
110	0.045 4	0.230 9	0.973 6

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表 2 滑块2：后缘面破裂倾角计算结果

Table 2. Block 2: results of the fracture angle of the trailing edge

θ₂/（°）	A_rea/m²	$l_{{B_2}{C_2}}$/m	F₂
36	0.152 0	0.684 5	1.895 1
40	0.137 7	0.600 0	1.554 6
50	0.112 2	0.466 2	1.208 2
60	0.097 6	0.391 0	1.081 0
65	0.091 4	0.365 7	1.057 5
67	0.089 1	0.357 2	1.053 0
68	0.088 0	0.353 2	1.051 5
69	0.086 9	0.349 4	1.050 7
70	0.085 8	0.345 9	1.050 6
71	0.084 8	0.342 4	1.050 4
72	0.083 8	0.339 2	1.051 0
73	0.082 8	0.336 1	1.052 0
74	0.081 9	0.333 2	1.053 2
76	0.079 9	0.327 8	1.058 3
78	0.078 1	0.323 1	1.064 6
80	0.076 3	0.318 7	1.072 8
90	0.067 9	0.304 0	1.144 0
100	0.059 9	0.299 3	1.281 4
110	0.052 1	0.303 9	1.536 0
120	0.043 9	0.306 7	1.906 7
122	0.041 8	0.308 7	2.018 4

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表 3 滑块3：后缘面破裂倾角计算结果

Table 3. Block 3: results of the fracture angle of the trailing edge

θ₃/（°）	A_rea/m²	$l_{{B_3}{C_3}}$/m	F₃
39	0.085 7	0.493 1	1.524 7
50	0.061 0	0.375 1	1.373 5
60	0.050 7	0.316 4	1.275 9
61	0.049 9	0.312 0	1.269 8
62	0.049 0	0.307 8	1.267 7
63	0.048 2	0.303 8	1.264 3
64	0.047 4	0.300 0	1.262 1
65	0.046 6	0.296 4	1.261 0
66	0.045 9	0.293 0	1.258 3
67	0.045 2	0.289 7	1.256 6
68	0.044 4	0.286 6	1.258 8
69	0.043 7	0.283 7	1.259 2
70	0.043 0	0.280 9	1.260 5
80	0.036 7	0.260 6	1.300 5
90	0.031 1	0.248 4	1.388 6
100	0.025 8	0.245 3	1.542 4
105	0.023 6	0.245 9	1.627 8

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表 4 后缘面破裂倾角统计表

Table 4. Inclinations of the trailing edge

对象	工况1	工况2	工况3
渗透盒	2 + 3 + 4	5 + 6 + 7	8 + 9
破裂角/（°）	73	69	71
注：模型试验的第1级滑带长度（渗透盒2 + 3 + 4）即对应　图4中的AB₁段；第2级滑带长度（渗透盒5 + 6 + 7）对　应B₁B₂段；第3级滑带长度（渗透盒8 + 9）对应B₂B₃段. 　（比例1 : 1）

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