边坡开挖支护时序有限元分析

闫强; 廉向东; 凌建明

doi:10.19818/j.cnki.1671-1637.2020.03.005

边坡开挖支护时序有限元分析

doi: 10.19818/j.cnki.1671-1637.2020.03.005

闫强^{1, 2,},
廉向东¹,
凌建明²

1.
广西交通投资集团有限公司, 广西南宁 530021
2.
同济大学交通运输工程学院, 上海 201804

基金项目:

国家自然科学基金项目 51878075

中国博士后科学基金项目 2019M663872XB

详细信息

作者简介:
闫强(1982-), 男, 山东菏泽人, 广西交通投资集团有限公司高级工程师, 工学博士, 从事道路工程研究

中图分类号: U416.14
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- 被引次数: 0
出版历程
- 收稿日期: 2020-01-07
- 刊出日期: 2020-06-25

Time series finite element analysis of support of slope excavation

1.
Guangxi Communications Investment Group Corporation Ltd., Nanning 530021, Guangxi, China
2.
School of Transportation Engineering, Tongji University, Shanghai 201804, China

Funds:

National Natural Science Foundation of China 51878075

China Postdoctoral Science Foundation 2019M663872XB

More Information

Author Bio:
YAN Qiang(1982-), male, senior engineer, PhD, yyqq023@163.com

摘要

摘要: 为研究公路改扩建工程边坡稳定性的影响因素, 寻求科学的支护方法, 以柳州至南宁高速K1456+800处左侧改扩建边坡为研究对象, 利用ANSYS建立了有限元数值模型, 选择未及时支护和及时支护2种支护方式, 模拟计算了改扩建工程中6级边坡开挖过程中坡体的剪应变增量及水平、竖向位移增量; 为定量分析2种支护条件下边坡开挖过程中位移及应力的变化趋势, 选取了6个特殊节点进行监测, 主要监测内容包括测点的位移(包括水平位移和竖向位移)以及主应力(包括最大主应力和最小主应力)随开挖时步的变化情况。分析结果表明: 无论是否及时支护, 每步剪应变增量最大值均位于坡脚, 但及时支护时, 分布面积及数值较未及时支护时小, 边坡发生失稳的可能性较低; 随着开挖推进, 水平位移增量先减小后小幅增大, 竖向位移增量先急剧增大后缓慢减小, 及时支护下各测点最终位移较未及时支护情况要小; 未及时支护时最终开挖安全系数接近1.0, 及时支护后每步安全系数均大幅提高, 基本大于1.35。综上所述, 及时支护能够有效减小边坡剪切应力, 限制水平与竖向位移, 降低整体应力水平, 提高边坡安全系数, 显著改善坡体稳定性。
- 公路边坡 /
- 改扩建 /
- 开挖 /
- 支护 /
- 位移 /
- 应力 /
- 安全系数
Abstract: In order to study the influence factors of slope stability of highway reconstruction and expansion project and to seek scientific support methods, the Liuzhou to Nanning Expressway K1456+800 left-hand reconstruction expansion slope was selected as the research subject, the finite element numerical model was built by using ANSYS, and two support methods were selected as the late support and timely support. The shear strain increment, horizontal and vertical displacement increments of the slope body during the excavation of 6-grade slope in the reconstruction and expansion project were simulated. For the quantitative analysis of the trend of displacement and stress during the excavation of slope under two support conditions, 6 special nodes were selected for the monitoring. The main monitoring contents include the displacement of measuring point(including the horizontal displacement and vertical displacement), and the change of principal stress(including the maximum principal stress and the minimum principal stress) with the excavation step. Analysis result shows that whether or not it is supported in time, the maximum shear strain at each step is at the foot of slope, however, the distribution area and shear strain increments of timely support are smaller than those of late support, and the probability of slope failure is low. With the excavation, the horizontal displacement increment decreases first and then increases slightly, the vertical displacement increment increases sharply first and then decreases slowly, and the final displacement of each measuring point under the timely support is smaller than the value under the late support. When it isn't supported in time, the safety factor is close to 1.0 finally. In case of timely support, the safety factor increases greatly at each step, basically greater than 1.35. As mentioned above, the timely support can reduce the shear strain of slope, limit the horizontal and vertical displacements, reduce the overall stress level, improve the safety factor, and significantly improve the stability of slope.
- highway slop /
- reconstruction and expansion /
- excavation /
- support /
- displacement /
- stress /
- safety factor

HTML全文

图 1 边坡工程

Figure 1. Slope engineering

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图 2 边坡开挖模型

Figure 2. Slope excavation model

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图 3 边坡数值计算网格模型

Figure 3. Grid model of slope numerical calculation

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图 4 剪应变增量

Figure 4. Shear strain increments

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图 5 水平位移

Figure 5. Horizontal displacements

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图 6 未及时支护测点U₁增量与开挖时步的关系

Figure 6. Relationships between U₁ increment of measuring point and time step under late support

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图 7 及时支护测点U₁增量与开挖时步的关系

Figure 7. Relationships between U₁ increment of measuring point and time step under timely support

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图 8 测点最终U₁增量曲线

Figure 8. Final U₁ increment curves of measuring points

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图 9 竖向位移

Figure 9. Vertical displacements

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图 10 未及时支护测点U₂增量与开挖时步的关系

Figure 10. Relationships between U₂ increment of measuring point and time step under late support

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图 11 及时支护测点U₂增量与开挖时步的关系

Figure 11. Relationships between U₂ increment of measuring point and time step under timely support

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图 12 测点最终U₂增量

Figure 12. Final U₂ increments of measuring points

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图 13 未及时支护测点最大主应力增量与开挖时步的关系

Figure 13. Relationships between maximum principal stress increment of measuring point and time step under late support

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图 14 及时支护时测点最大主应力增量与开挖时步的关系

Figure 14. Relationships between maximum principal stress increment of measuring point and time step under timely support

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图 15 未及时支护测点最小主应力增量与开挖时步的关系

Figure 15. Relationships between minimum principal stress increment of measuring point and time step under late support

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图 16 及时支护测点最小主应力增量与开挖时步的关系

Figure 16. Relationships between minimum principal stress increment of measuring point and time step under timely support

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图 17 测点最终应力增量

Figure 17. Final stress increments of measuring point

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图 18 安全系数与开挖时步的关系

Figure 18. Relationships between safety factor and time step

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表 1 模型建立参数

Table 1. Model building parameters

参数	宽度/m	高度/m	底部约束	两侧约束	节点变形	材料	屈服准则	收敛准则
数值	137	左侧73、右侧15	刚性约束	水平约束	竖向固定	莫尔-库仑弹塑性材料	莫尔-库仑准则	最大不平衡力趋近于10^-5 kN

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表 2 计算参数

Table 2. Calculation parameters

岩性	重度/(kN·m^-3)	黏聚力/kPa	内摩擦角/(°)	弹性模量/GPa	坡高/m	平均倾角/(°)	边坡分级/m
砾质黏性土	19.13	29	21.4	1.8	34	34.8	2
砂质黏性土	20.22	31	24.0	1.4	6	33.7	3
砂岩	25.10	46	45.0	2.8	17	39.5	1

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表 3 支护防护

Table 3. Support protection

边坡级数	第2级	第3级	第4级	第5级	第6级
支护防护	4排9 m长全长注浆锚杆(型号为HRB335, 直径28 mm)浅表支护	4排12 m长全长注浆锚杆(型号为HRB335, 直径32 mm)浅表支护	3排24 m长6束预应力锚索(直径15.2 mm)锚固10 m	4排12 m长全长注浆锚杆(型号为HRB335, 直径32 mm)浅表支护	4排9 m长全长注浆锚杆(型号为HRB335, 直径28 mm)浅表支护

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参考文献(33)

[1]	张坤勇, 杜伟, 王乾坤. 基于修正关口-太田模型的归一化变形量开挖边坡失稳判据[J]. 土木工程学报, 2019, 52(11): 86-96. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201911010.htm ZHANG Shen-yong, DU Wei, WANG Qian-kun. Criterion of normalized deformation for instability analysis of excavation slope based on modified Ohta-Sechiguchi anisotropic elastoplastic model[J]. China Civil Engineering Journal, 2019, 52(11): 86-96. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201911010.htm
[2]	刘广宁, 李聪, 卢波, 等. 降雨诱发全-强风化岩边坡浅层失稳模型试验研究[J]. 长江科学院院报, http://kns.cnki.net/kcms/detail/42.1171.TV.20191104.1013.002.html. LIU Guang-ning, LI Cong, LU Bo, et al. Model test of shallow failure of fully strong weathered rock slope induced by rainfall[J]. Journal of Yangtze River Scientific Research Institute, http://kns.cnki.net/kcms/detail/42.1171.TV.20191104.1013.002.html. (inChinese).
[3]	金磊, 曾亚武, 程涛, 等. 土石混合体边坡稳定性的三维颗粒离散元分析[J]. 哈尔滨工业大学学报, 2020, 52(2): 41-50. https://www.cnki.com.cn/Article/CJFDTOTAL-HEBX202002006.htm JIN Lei, ZENG Ya-wu, CHENG Tao, et al. Stability analysis of soil-rock mixture slope based on 3-D DEM[J]. Journal of Harbin Institute of Technology, 2020, 52(2): 41-50. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HEBX202002006.htm
[4]	蒋水华, 刘贤, 黄发明, 等. 考虑多参数空间变异性的降雨入渗边坡失稳机理及可靠度分析[J]. 岩土工程学报, http://kns.cnki.net/kcms/detail/32.1124.TU.20191115.1133.002.html. JIANG Shui-hua, LIU Xian, HUANG Fa-ming, et al. Failure mechanism and reliability analyses of soil slopes under rainfall infiltration considering spatial variability of multiple soil parameters[J]. Chinese Journal of Geotechnical Engineering, http://kns.cnki.net/kcms/detail/32.1124.TU.20191115.1133.002.html. (inChinese).
[5]	闫强. 高速公路改扩建工程高边坡开挖过程稳定性研究[D]. 西安: 长安大学, 2015. YAN Qiang. Study on the slope stability in the excavation process of reconstruction highway[D]. Xi'an: Chang'an University, 2015. (in Chinese).
[6]	殷德胜, 汪卫明, 陈胜宏. 岩质边坡开挖过程模拟的动态有限单元法[J]. 岩石力学与工程学报, 2011, 30(11): 2217-2224. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201111008.htm YIN De-sheng, WANG Wei-ming, CHEN Sheng-hong. Dynamic finite element method for excavation process simulation of rock slope[J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(11): 2217-2224. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201111008.htm
[7]	段钊, 唐皓, 党琪, 等. 边坡开挖诱发滑坡离散元模拟[J]. 长安大学学报(自然科学版), 2014, 34(5): 49-55. doi: 10.3969/j.issn.1671-8879.2014.05.008 DUAN Zhao, TANG Hao, DANG Qi, et al. Discrete element simulation of landslide induced by slope excavation[J]. Journal of Chang'an University (Natural Science Edition), 2014, 34(5): 49-55. (in Chinese). doi: 10.3969/j.issn.1671-8879.2014.05.008
[8]	林同立, 何忠明, 蔡军. 改扩建高速公路路堑边坡拓宽方案对比分析[J]. 矿冶工程, 2014, 34(6): 18-21. doi: 10.3969/j.issn.0253-6099.2014.06.005 LIN Tong-li, HE Zhong-ming, CAI Jun. Analysis and comparison of embankment widening schemes in highway renovation and expansion project[J]. Mining and Metallurgical Engineering, 2014, 34(6): 18-21. (in Chines). doi: 10.3969/j.issn.0253-6099.2014.06.005
[9]	王述红, 饶文杰, 关祥祥, 等. 复杂岩体边坡关键块体搜索及开挖支护[J]. 东北大学学报(自然科学版), 2013, 34(7): 1017-1021. doi: 10.3969/j.issn.1005-3026.2013.07.024 WANG Shu-hong, RAO Wen-jie, GUAN Xiang-xiang, et al. Search of key block in complex rock mass slope and support of excavated slope[J]. Journal of Northeastern University (Natural Science), 2013, 34(7): 1017-1021. (in Chinese). doi: 10.3969/j.issn.1005-3026.2013.07.024
[10]	周勇, 王旭日, 朱彦鹏, 等. 强风化软硬互层岩质高边坡监测与数值模拟[J]. 岩土力学, 2018, 39(6): 2249-2258. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201806041.htm ZHOU Yong, WANG Xu-ri, ZHU Yan-peng, et al. Monitoring and numerical simulation of an interbedding high slope composed of soft and hard strong-weathered rock[J]. Rock and Soil Mechanics, 2018, 39(6): 2249-2258. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201806041.htm
[11]	张媛, 董建华, 董旭光, 等. 季节性冻土区土钉边坡支护结构冻融反应分析[J]. 岩土力学, 2017, 38(2): 574-582, 592. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201702035.htm ZHANG Yuan, DONG Jian-hua, DONG Xu-guang, et al. Analysis of freezing and thawing of slope improved by soil nailing structure in seasonal frozen soil region[J]. Rock and Soil Mechanics, 2017, 38(2): 574-582, 592. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201702035.htm
[12]	王定伟, 伍法权, 马艾阳. 腊寨水电站坝址右岸边坡三维数值模拟分析[J]. 工程地质学报, 2013, 21(4): 641-648. doi: 10.3969/j.issn.1004-9665.2013.04.023 WANG Ding-wei, WU Fa-quan, MA Ai-yang. Three dimensional numerical simulation for right bank slope of Lazhai Hydropower Station[J]. Journal of Engineering Geology, 2013, 21(4): 641-648. (in Chinese). doi: 10.3969/j.issn.1004-9665.2013.04.023
[13]	赵晓彦, 胡厚田, 唐茂颖. 类土质高边坡开挖效应的离心模型试验及数值模拟研究[J]. 岩石力学与工程学报, 2006, 25(增2): 4046-4051. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2006S2110.htm ZHAO Xiao-yan, HU Hou-tian, TANG Mao-ying. Study on excavation effect of high soil-like slope by centrifugal model test and numerical simulation[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(S2): 4046-4051. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2006S2110.htm
[14]	赵川, 付成华, 何欢, 等. 锦屏水电站缆机平台高陡边坡开挖支护数值模拟[J]. 长江科学院院报, 2015, 32(8): 94-98. https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB201508022.htm ZHAO Chuan, FU Cheng-hua, HE Huan, et al. Numerical simulation on the excavation and support of high and steep slope of cable-crane platform of Jinping Hydropower Station[J]. Journal of Yangtze River Scientific Research Institute, 2015, 32(8): 94-98. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB201508022.htm
[15]	李安兴, 李杨秋, 王燕增, 等. 改建工程深基坑对地铁车站及区间隧道的影响分析[J]. 土木工程, 2019, 8(3): 821-829. LI An-xing, LI Yang-qiu, WANG Yan-zeng, et al. Effect of filling and grouting reinforcement on deep foundation pit support structure and adjacent tunnels[J]. Hans Journal of Civil Engineering, 2019, 8(3): 821-829. (in Chinese).
[16]	姚裕春, 姚令侃, 袁碧玉. 降雨条件下边坡破坏机理离心模型研究[J]. 中国铁道科学, 2004, 25(4): 64-68. doi: 10.3321/j.issn:1001-4632.2004.04.012 YAO Yu-chun, YAO Ling-kan, YUAN Bi-yu. Analysis of a centrifugal model of slope damage mechanism during rainfall[J]. China Railway Science, 2004, 25(4): 64-68. (in Chinese). doi: 10.3321/j.issn:1001-4632.2004.04.012
[17]	姚裕春, 姚令侃, 袁碧玉, 等. 施工时序对边坡稳定性影响的离心模型试验及数值分析[J]. 岩石力学与工程学报, 2006, 25(5): 1075-1080. doi: 10.3321/j.issn:1000-6915.2006.05.034 YAO Yu-chun, YAO Ling-kan, YUAN Bi-yu, et al. Centrifuge model test and numerical analysis of effects of excavation and support sequence on slope stability[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(5): 1075-1080. (in Chinese). doi: 10.3321/j.issn:1000-6915.2006.05.034
[18]	姚裕春, 姚令侃, 袁碧玉. 边坡开挖迁移式影响离心模型试验研究[J]. 岩土工程学报, 2006, 28(1): 76-80. doi: 10.3321/j.issn:1000-4548.2006.01.015 YAO Yu-chun, YAO Ling-kan, YUAN Bi-yu. Study of centrifuge model tests on transition effect of cut slopes[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(1): 76-80. (in Chinese). doi: 10.3321/j.issn:1000-4548.2006.01.015
[19]	赵朋辉, 刁文治, 周志林. 开挖与支护方法对边坡稳定性影响的数值模拟[J]. 路基工程, 2006(4): 16-18. doi: 10.3969/j.issn.1003-8825.2006.04.006 ZHAO Peng-hui, DIAO Wen-zhi, ZHOU Zhi-lin. Numerical simulation of the influence of excavation and support methods on slope stability[J]. Subgrade Engineering, 2006(4): 16-18. (in Chinese). doi: 10.3969/j.issn.1003-8825.2006.04.006
[20]	赵尚毅, 郑颖人, 唐树名. 路堑边坡施工顺序对边坡稳定性影响数值模拟分析[J]. 地下空间, 2003, 23(4): 370-374. doi: 10.3969/j.issn.1673-0836.2003.04.006 ZHAO Shang-yi, ZHENG Ying-ren, TANG Shu-ming. Numerical simulation analysis for the influence of construction process of deep cut slop on its stability[J]. Underground Space, 2003, 23(4): 370-374. (in Chinese). doi: 10.3969/j.issn.1673-0836.2003.04.006
[21]	朱彦鹏, 王立文. 边坡分级柔性支护数值模拟研究[J]. 建筑科学与工程学报, 2012, 29(4): 25-31. doi: 10.3969/j.issn.1673-2049.2012.04.005 ZHU Yan-peng, WANG Li-wen. Research on numerical simulation of slope grading flexible reinforcement[J]. Journal of Architecture and Civil Engineering, 2012, 29(4): 25-31. (in Chinese). doi: 10.3969/j.issn.1673-2049.2012.04.005
[22]	杨逾, 郭锐. 多台阶岩质边坡的稳定性分析及加固效应[J]. 辽宁工程技术大学学报(自然科学版), 2016, 35(6): 607-612. https://www.cnki.com.cn/Article/CJFDTOTAL-FXKY201606010.htm YANG Yu, GUO Rui. Research on the stability of multi-level rock slope and the reinforcement effect[J]. Journal of Liaoning Technical University (Natural Science Edition), 2016, 35(6): 607-612. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-FXKY201606010.htm
[23]	李韬, 徐奴文, 戴峰, 等. 白鹤滩水电站左岸坝肩开挖边坡稳定性分析[J]. 岩土力学, 2018, 39(2): 665-674. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201802034.htm LI Tao, XU Nu-wen, DAI Feng, et al. Stability analysis of left bank abutment slope at Baihetan Hydropower Station subjected to excavation[J]. Rock and Soil Mechanics, 2018, 39(2): 665-674. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201802034.htm
[24]	马国民, 李国锋, 杨磊, 等. 富龙石质高陡边坡下棚洞适用性及联合支护效果分析[J]. 中国公路学报, 2016, 29(9): 112-120. doi: 10.3969/j.issn.1001-7372.2016.09.015 MA Guo-min, LI Guo-feng, YANG Lei, et al. Analysis on applicability of shed-tunnel and effect of combined supporting under high and steep rocky slope condition of Funing-Longliu Expressway[J]. China Journal of Highway and Transport, 2016, 29(9): 112-120. (in Chinese). doi: 10.3969/j.issn.1001-7372.2016.09.015
[25]	刘军, 徐志军, 原方, 等. 立交桥桥台桩基托换基坑支护设计与监测[J]. 岩土工程学报, 2019, 41(增2): 217-220, 225. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2019S2056.htm LIU Jun, XU Zhi-jun, YUAN Fang, et al. Design and monitoring of foundation pit support project for pile foundation underpinning of abutment of interchange bridges[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(S2): 217-220, 225. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2019S2056.htm
[26]	陈乐求, 杨恒山, 林杭. 抗滑桩加固边坡稳定性及影响因素的有限元分析[J]. 中南大学学报(自然科学版), 2011, 42(2): 490-494. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201102035.htm CHEN Le-qiu, YANG Heng-shan, LIN Hang. Finite element analysis for slope stability and its influencing factors with pile reinforcement[J]. Journal of Central South University (Science and Technology), 2011, 42(2): 490-494. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201102035.htm
[27]	高春君, 张学富, 向立辉, 等. 深层排水孔堵塞对富水岩质高边坡稳定性的影响[J]. 土木建筑与环境工程, 2018, 40(5): 92-101. https://www.cnki.com.cn/Article/CJFDTOTAL-JIAN201805012.htm GAO Chun-jun, ZHANG Xue-fu, XIANG Li-hui, et al. Impact of deep drainage hole blockage on high slope stability in rich water formation[J]. Journal of Civil, Architectural and Environmental Engineering, 2018, 40(5): 92-101. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JIAN201805012.htm
[28]	WEI Zuo-an, YIN Guang-zhi, WANG J G, et al. Stability analysis and supporting system design of a high-steep cut soil slope on an ancient landslide during highway construction of Tehran-Chalus[J]. Environmental Earth Sciences, 2012, 67(6): 1651-1662. doi: 10.1007/s12665-012-1606-2
[29]	KAYA A, ALEMDAG S, DAG S, et al. Stability assessment of high-steep cut slope debris on a landslide (Gumushane, NE Turkey)[J]. Bulletin of Engineering Geology and the Environment, 2016, 75(1): 89-99. doi: 10.1007/s10064-015-0753-6
[30]	MEYER N, AHANGARI K. An investigation on stability and support of intake rock slopes of the Karun III Dam and power project[C]//KONIETZKY H. Numerical Modeling of Discrete Materials in Geotechnical Engineering, Civil Engineering, and Earth Sciences. New York: CRC Press, 2004: 229-234.
[31]	丁秀美, 刘光士, 黄润秋, 等. 剪应变增量在堆积体边坡稳定性研究中的应用[J]. 地球科学进展, 2004, 19(增): 318-323. https://www.cnki.com.cn/Article/CJFDTOTAL-DXJZ2004S1064.htm DING Xiu-mei, LIU Guang-shi, HUANG Run-qiu, et al. Shear strain increment applying in stability studying of debris slope[J]. Advance in Earth Sciences, 2004, 19(S): 318-323. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DXJZ2004S1064.htm
[32]	张伟. 边坡位移参数与稳定性变化关系[J]. 新疆交通运输科技, 2016(2): 15-19. ZHANG Wei. Relationship between slope displacement parameters and stability change[J]. Xinjiang Transportation Science and Technology, 2016(2): 15-19. (in Chinese).
[33]	饶运章, 张学焱, 利坚, 等. 边坡安全系数与滑坡概率关系分析[J]. 长江科学院院报, 2017, 34(5): 63-67. https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB201705015.htm RAO Yun-zhang, ZHANG Xue-yan, LI Jian, et al. Relationship between slope safety factor and landslide probability[J]. Journal of Yangtze River Scientific Research Institute, 2017, 34(5): 63-67. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB201705015.htm