基于因素空间的露天采坑边坡稳定性评价

易富; 孟兴涛; 赵文华; 杜常博

doi:10.19509/j.cnki.dzkq.tb20210773

基于因素空间的露天采坑边坡稳定性评价

doi: 10.19509/j.cnki.dzkq.tb20210773

a.
辽宁工程技术大学建筑与交通学院, 辽宁阜新 123000
b.
辽宁工程技术大学土木工程学院, 辽宁阜新 123000

基金项目:

国家自然科学基金项目 51774163

鞍钢科研基金项目 2019-科A02

辽宁工程技术大学首批“双一流”学科建设创新团队项目 LNTU20TD-26

详细信息

作者简介:
易富(1978-), 男, 教授, 博士生导师, 主要从事环境岩土与道路工程方面的研究。E-mail: yifu9716@163.com

通讯作者:
孟兴涛(1998-), 男, 现正攻读岩土工程专业硕士学位, 主要从事露天矿边坡稳定性研究。E-mail: a397252273@163.com

中图分类号: TD854⁺.6
计量
- 文章访问数: 452
- PDF下载量: 137
- 被引次数: 0
出版历程
- 收稿日期: 2021-12-09
- 录用日期: 2022-03-16
- 修回日期: 2022-03-02

Evaluation of slope stability of open pit based on factor space

a.
College of Architecture and Transportation, Liaoning Technical University, Fuxin Liaoning 123000, China
b.
College of Civil Engineering, Liaoning Technical University, Fuxin Liaoning 123000, China

摘要

摘要:
影响露天采坑边坡稳定性因素具有复杂性和模糊性, 采用数学及力学的分析方法较难有效评价其稳定性。根据露天采坑的实际工程特点, 在现场勘查和研究的基础上, 确定了包括地形地貌、地质构造、岩体性质、赋存环境4个一级评价指标, 17个二级评价指标, 建立了基于因素空间的露天采坑边坡稳定性评价模型。首先利用层次分析法和熵权法计算主客观权重, 赋予露天采坑边坡稳定性影响因素的组合权重。进而利用未确知测度理论构造测度函数, 计算评价边坡稳定性的单因素测度矩阵, 通过因素合成完成因素空间的降维, 生成合因素测度向量。最后采用置信度识别准则实现对露天采坑边坡的稳定性评价, 并以辽宁齐大山露天铁矿东帮典型边坡剖面为例, 将因素空间评价结果与极限平衡法和有限差分法计算结果进行对比分析, 对所建边坡评价模型的可靠性进行验证。结果表明: 因素空间模型评价结果与现场情况基本吻合, 且与极限平衡法、有限差分法计算结果相一致, 验证了所建因素空间评价模型的准确性与科学性; 综合分析了因素空间评价结果和其他方法计算结果, 给出了4个边坡剖面的防护及治理建议。因素评价模型简化了边坡稳定性评价过程, 提高了模型评价结果的精度, 可为同类型地质条件露天采坑边坡稳定性评价工作提供一定借鉴。
- 因素空间 /
- 露天采坑 /
- 边坡稳定性评价 /
- 未确知测度理论
Abstract: Objective
The factors affecting the stability of an open pit slope are complex and fuzzy. Hence, it is difficult to evaluate the stability through mathematical and mechanical analysis methods.
Methods
According to the actual engineering characteristics and in-situ investigation of an open pit, four first-class evaluation indexes including landform, geological structure, rock mass properties and occurrence environment and 17 second-class evaluation indexes were determined. The stability evaluation model of open pit slope based on factor space is established. Firstly, the analytical hierarchy process(AHP) and entropy weight method are used to calculate the subjective and objective weights, and the combined weights of the factors affecting the stability of the open pit slope are given. Then, the unascertained measure theory is used to construct the measure function, calculate the single factor measurement matrix to evaluate the slope stability, reduce the dimension of the factor space through factor synthesis, and generate the combined factor measure vector. Finally, the stability of the open pit slope is evaluated through the confidence recognition criteria. Taking the typical slope profile of the eastern slope of Qidashan open pit iron mine as an example, the factor space evaluation results are compared with the calculation results of the limit equilibrium method and the finite difference method, and the reliability of the slope evaluation method is verified.
Results
The results show that the evaluation results of factor space model are basically consistent with the results obtained from the field investigation, and are consistent with the calculation results of limit equilibrium method and finite difference method, which verifies the accuracy and scientificity of the established factor space evaluation model. Based on the comprehensive analysis of the factor space evaluation results and the calculation results of other methods, four slope profile protection and treatment suggestions are given.
Conclusion
The factor evaluation model simplifies the process of slope stability evaluation, improves the accuracy of the evaluation results of the model, and can provide a reference for the stability evaluation of an open pit slope with similar geological conditions.
- factor space /
- open pit /
- slope stability evaluation /
- unascertained measure theory
注释:

(所有作者声明不存在利益冲突)

HTML全文

图 1 特征值为具体数值对应的测度函数

Figure 1. Measurement function corresponding to the specific value of the eigenvalue

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图 2 属性识别规则图

Figure 2. Attribute identification rule diagram

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图 3 特征值为区间数对应的测度函数

Figure 3. Measure function corresponding to the interval number of eigenvalues

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图 4 模型求解流程

Figure 4. Model solution process

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图 5 剖面位置图

Figure 5. Sectional position diagram

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图 6 典型边坡地质剖面图

Figure 6. Geological profile of a typical slope

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图 7 剪切应变增量云图及安全系数

Figure 7. Contour diagram of shear strain increment and safety factor

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图 8 极限平衡法计算结果

Figure 8. Calculated result obtained from limit equilibrium method

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表 1 露天采坑边坡稳定性分级评价体系

Table 1. Graded evaluation system for slope stability of open pit

条件因素(▲为定性因素)		评价指标分级标准
一级指标	二级指标	稳定M₁	较稳定M₂	基本稳定M₃	欠稳定M₄	不稳定M₅
C₁ 地形地貌	d₁边坡高度/m	< 100	[100, 200)	[200, 300)	[300, 400]	>400
C₁ 地形地貌	d₂坡角/(°)	< 20	[20, 30)	[30, 45)	[45, 60]	>60
C₂ 地质构造	▲ d₃地质构造	95	85	70	60	40
	▲ d₄结构面结合程度	95	85	70	60	40
	▲ d₅结构类型	95	85	70	60	40
	d₆结构面走向和边坡坡面走向夹角/(°)	[90, 75)	[75, 60)	[60, 45)	[45, 30)	[30, 0]
	▲ d₇软弱夹层性质	95	85	70	60	40
C₃ 岩体性质	d₈岩体强度/MPa	[200, 150)	[150, 120)	[120, 90)	[90, 40)	[40, 10]
	d₉岩体质量指标RQD/%	[100, 90)	[90, 75)	[75, 50)	[50, 25)	[25, 0]
	d₁₀内摩擦角/(°)	>45	[45, 40)	[40, 35)	[35, 30]	< 30
	d₁₁黏聚力/kPa	>300	[300, 200)	[200, 150)	[150, 100]	< 100
	▲ d₁₂风化程度	95	85	70	60	40
C₄ 赋存环境	d₁₃年降雨量/mm	< 400	[400, 600)	[600, 800)	[800, 1 000]	>1 000
	▲ d₁₄工程扰动	95	85	70	60	40
	▲ d₁₅开挖方式	95	85	70	60	40
	▲ d₁₆地下水	95	85	70	60	40
	d₁₇地震烈度	< 3	[3, 5)	[5, 7)	[7, 8]	>8

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表 2 定性因素属性量化规则

Table 2. Qualitative factor attribute quantification rules

边坡稳定性属性	稳定M₁	较稳定M₂	基本稳定M₃	欠稳定M₄	不稳定M₅
量化评价特征值	95	85	70	60	40
d₃地质构造	运动微弱、几乎无断裂	运动较弱、只有少量小型断裂	运动不强烈、只有小型断裂	运动强烈、大型断裂带，断裂较密集	运动强烈、巨大断裂带，断裂密集
d₄结构面结合程度	无充填物	表面粗糙，钙质或铁质胶结	岩屑充填	表面平直光滑、无胶结	强分化的小型断层破碎带
d₅结构类型	整体结构	整体块状	层状	破碎状	散体状
d₇软弱夹层性质	无夹层	软岩、岩块	岩屑	岩屑夹泥	泥夹岩屑或泥质
d₁₂风化程度	未风化	微风化	中风化	强风化	全风化
d₁₄工程扰动	无扰动	微扰动	弱扰动	较强扰动	强扰动
d₁₅开挖方式	自然边坡	预裂爆破	光面爆破	一般或机械开挖	欠缺爆破
d₁₆地下水	完全干燥	潮	湿	淋水	涌水

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表 3 典型边坡剖面在因素空间的映射向量

Table 3. Mapping vectors of typical slope profiles in factor space

边坡剖面	d₁	d₂	d₃	d₄	d₅	d₆	d₇	d₈	d₉	d₁₀	d₁₁	d₁₂	d₁₃	d₁₄	d₁₅	d₁₆	d₁₇
P1	150	36	68.8	64.2	67.4	35	67.7	78.5	58.6	32.5	748	88.6	715	72.5	90.2	73.7	5
P2	185	34	88.7	84.3	64.6	68	90.2	85.6	83.3	42.1	422	82.3	715	75.3	89.1	84.3	5
P3	265	49	76.5	84.2	81.3	58	65.6	72.2	71.8	31.4	162	78.5	715	66.7	82.6	82.4	5
P4	290	41	82.3	80.6	84.0	51	85.6	85.9	75.0	38.0	556	76.3	715	73.2	79.2	75.0	5

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表 4 剖面Ⅰ条件因素集的组合权重

Table 4. Combined weights of conditional factor sets of Section Ⅰ

	d₁	d₂	d₃	d₄	d₅	d₆	d₇	d₈	d₉	d₁₀	d₁₁	d₁₂	d₁₃	d₁₄	d₁₅	d₁₆	d₁₇
W′	0.042	0.080	0.073	0.031	0.061	0.053	0.173	0.075	0.172	0.033	0.080	0.062	0.023	0.078	0.094	0.081	0.046
W″	0.057	0.080	0.049	0.046	0.092	0.069	0.099	0.157	0.034	0.094	0.104	0.080	0.043	0.085	0.080	0.046	0.041
W	0.050	0.080	0.060	0.039	0.077	0.061	0.134	0.118	0.099	0.065	0.093	0.072	0.034	0.082	0.087	0.062	0.043

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表 5 岩体物理力学参数表

Table 5. Physical and mechanical parameters of the rock mass

岩性	容重/(kN·m^-3)	内聚力/kPa	内摩擦角/(°)	弹性模量/MPa	剪切模量/MPa
含铁石英岩	26.57	1 053.76	40.00	6 375	2 510
混合岩	25.29	748.64	32.40	5 462	2 134
绿泥片岩	27.32	304.31	30.93	2 465	1 809

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表 6 边坡稳定性评价结果

Table 6. Slope stability evaluation results

边坡剖面	边坡稳定性					本文模型概念提取	结果	稳定性系数
边坡剖面	m₁	m₂	m₃	m₄	m₅	本文模型概念提取	结果	极限平衡法	有限差分法
P1	0.164 16	0.188 78	0.542 61	0.346 29	0.014 16	m₁₁+m₁₂+m₁₃=0.895 55>0.7	基本稳定	1.223	1.214
P2	0.454 99	0.280 93	0.184 12	0.102 36	0.033 15	m₂₁+m₂₂=0.744 29>0.7	稳定	1.535	1.531
P3	0.052 83	0.151 96	0.279 82	0.266 34	0.253 58	m₃₁+m₃₂+m₃₃+m₃₄=0.750 95>0.7	不稳定	0.993	0.966
P4	0.096 66	0.440 55	0.439 11	0.231 24	0.031 86	m₄₁+m₄₂+m₄₃=0.976 32>0.7	基本稳定	1.187	1.174
注：m_ik为在条件因素作用下，研究对象被评价为m_k时的测度

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参考文献(20)

[1]	黄丹, 史秀志, 邱贤阳, 等. 基于多层次未确知测度-集对分析的岩质边坡稳定性分级体系[J]. 中南大学学报: 自然科学版, 2017, 48(4): 1057-1064. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201704028.htm Huang D, Shi X Z, Qiu X Y, et al. Stability gradation of rock slopes based on multilevel uncertainty measure-set pair analysis theory[J]. Journal of Central South University: Science and Technology, 2017, 48(4): 1057-1064(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201704028.htm
[2]	徐建, 董杰华, 徐中来, 等. 基于改进AHP-模糊综合评判方法的露天矿边坡稳定性评价[J]. 水利与建筑工程学报, 2020, 18(6): 213-218. https://www.cnki.com.cn/Article/CJFDTOTAL-FSJS202006036.htm Xu J, Dong J H, Xu Z L, et al. Open-pit mine slope stability evaluation based on improved AHP-fuzzy comprehensive evaluation method[J]. Journal of Water Resources and Architectural Engineering, 2020, 18(6): 213-218(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-FSJS202006036.htm
[3]	冯忠居, 朱彦名, 高雪池, 等. 基于熵权-灰关联法的岩质开挖边坡安全评价模型[J]. 交通运输工程学报, 2020, 20(2): 55-65. https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202002005.htm Feng Z J, Zhu Y M, Gao X C, et al. Safety evaluation model of excavating rock slope based on entropy-grey correlation method[J]. Journal of Taffic and Tansportation Engneering, 2020, 20(2): 55-65(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202002005.htm
[4]	张旭, 周绍武, 林鹏, 等. 基于熵权-集对的边坡稳定性研究[J]. 岩石力学与工程学报, 2018, 37(增刊1): 3400-3410. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2018S1030.htm Zhang X, Zhou S W, Lin P, et al. Slope stability evaluation based on entropy coefficient-set pair analysis[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(S1): 3400-3410(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2018S1030.htm
[5]	李建林, 周宜红. 基于AHP的模糊评判法在边坡稳定性评价中的应用[J]. 岩石力学与工程学报, 2007, 26(增刊1): 2627-2632. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2007S1005.htm Li J L, Zhou Y H. Application of fuzzy analysis based on AHP to slope stability evaluatioan[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(S1): 2627-2632(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2007S1005.htm
[6]	仝德富, 谭飞, 苏爱军, 等. 基于多源数据的谭家湾滑坡变形机制及稳定性评价[J]. 地质科技通报, 2021, 40(4): 162-170. doi: 10.19509/j.cnki.dzkq.2021.0432 Tong D F, Tan F, Su A J, et al. Deformation mechanism and stability evaluation of Tanjiawan landslide based on multi-source data[J]. Bulletin of Geological Science and Technology, 2021, 40(4): 162-170(in Chinese with English abstract). doi: 10.19509/j.cnki.dzkq.2021.0432
[7]	杨灿, 刘磊磊, 张遗立, 等. 基于贝叶斯优化机器学习超参数的滑坡易发性评价[J]. 地质科技通报, 2022, 41(2): 228-238. doi: 10.19509/j.cnki.dzkq.2022.0059 Yang C, Liu L L, Zhang Y L, et al. Machine learning based on landslide susceptibility assessment with Bayesian optimized the hyperparameters[J]. Bulletin of Geological Science and Technology, 2022, 41(2): 228-238(in Chinese with English abstract). doi: 10.19509/j.cnki.dzkq.2022.0059
[8]	汪培庄, Sugeno M. 因素场与模糊集的背景结构[J]. 模糊数学, 1982(2): 45-54. Wang P Z, Sugeno M. The factors field and background structurefor fuzzy subsets[J]. Fuzzy Mathematics, 1982(2): 45-54(in Chinese with English abstract).
[9]	崔铁军, 马云东. 基于因素空间的煤矿安全情况区分方法的研究[J]. 系统工程理论与实践, 2015, 35(11): 2891-2897. https://www.cnki.com.cn/Article/CJFDTOTAL-XTLL201511017.htm Cui T J, Ma Y D. Research on the classification method about coal mine safety situation based on the factor space[J]. Systems Engincering-Theory & Practice, 2015, 35(11): 2891-2897(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-XTLL201511017.htm
[10]	李辉, 易富, 张佳. 基于因素空间的尾矿坝稳定性综合评价[J]. 中国安全科学学报, 2019, 29(12): 28-34. https://www.cnki.com.cn/Article/CJFDTOTAL-ZAQK201912005.htm Li H, Yi F, Zhang J. Comprehensive stability evaluation of tailing dam based on factor space[J]. China Safety Science Journal, 2019, 29(12): 28-34(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-ZAQK201912005.htm
[11]	王光远. 论未确知性信息及其数学处理[J]. 哈尔滨建筑工程学院学报, 1990, 23(4): 52-58. Wang G Y. Uncertainty information and its mathematical treatment[J]. Journal of Harbin Architecture and Engineering Institute, 1990, 23(4): 52-58(in Chinese with English abstract).
[12]	刘开第, 吴和琴, 庞彦军. 不确定信息数学处理及应用[M]. 北京: 科学出版社, 1999. Liu K D, Wu H Q, Pang Y J. Mathematics treatment and application of unascertained information[M]. Beijing: Science Press, 1999(in Chinese).
[13]	丁丽宏. 基于改进的灰关联分析和层次分析法的边坡稳定性研究[J]. 岩土力学, 2011, 32(11): 3437-3441. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201111042.htm Ding L H. Research on estimation of slope stability based on improved grey correlation analysis and analytic hierarchy process[J]. Rock and Soil Mechanics, 2011, 32(11): 3437-3441(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201111042.htm
[14]	陈云超, 杨平庆. 模糊综合评判在山区公路边坡稳定性分析中的应用[J]. 水利与建筑工程学报, 2018, 16(6): 202-206, 229. https://www.cnki.com.cn/Article/CJFDTOTAL-FSJS201806038.htm Chen Y C, Yang P Q. Application of fuzzy comprehensive evaluation in slope stability analysis of mountain roads[J]. Journal of Water Resources and Architectural Engineering, 2018, 16(6): 202-206, 229(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-FSJS201806038.htm
[15]	赵军, 宋扬. 改进熵权-正态云模型在边坡稳定性评价中的应用[J]. 水电能源科学, 2016, 34(4): 120-122, 165. https://www.cnki.com.cn/Article/CJFDTOTAL-SDNY201604031.htm Zhao J, Song Y. Slope stability evaluation based on improved entropy weight-cloud model[J]. Water Resources and Power, 2016, 34(4): 120-122, 165(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-SDNY201604031.htm
[16]	周洪福, 冯治国, 石胜伟, 等. 川藏铁路某特大桥成都侧岸坡工程地质特征及稳定性评价[J]. 水文地质工程地质, 2021, 48(5): 112-119. https://www.cnki.com.cn/Article/CJFDTOTAL-SWDG202105012.htm Zhou H F, Feng Z G, Shi S W, et al. Slope engineering geology characteristics and stability evaluation of agrand bridge to Chengdu bank on the Sichuan-Tibet Railway[J]. Hydrogeology & Engineering Geology, 2021, 48(5): 112-119(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-SWDG202105012.htm
[17]	中华人民共和国住房和城乡建设部. 工程岩体分级标准: GB/T 50218-2014[S]. 北京: 中国计划出版社, 2014. Mimistry of Housing and Urban-Rural Devel Opment of the People's Republic of China. Standard for engineering classification of rock mass: GB/T50218-2014[S]. Beijing: China Planning Press, 2014(in Chinese).
[18]	徐琛, 刘晓丽, 王恩志, 等. 基于组合权重-理想点法的应变型岩爆五因素预测分级[J]. 岩土工程学报, 2017, 39(12): 2245-2252. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201712015.htm Xu C, Liu X L, Wang E Z, et al. Prediction and classification of strain mode rockburst based on five-factor criterion and combined weight-ideal point method[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(12): 2245-2252(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201712015.htm
[19]	中华人民共和国住房和城乡建设部. 非煤露天矿边坡工程技术规范: GB 51016-2014[S]. 北京: 中国计划出版社, 2014. Mimistry of Housing and Urban-Rural Devel Opment of the People's Republic of China. Techmcal code for non-coal open mine slope engineening: GB/T 51016-2014[S]. Beijing: China Planning Press, 2014(in Chinese).
[20]	杜时贵. 大型露天矿山边坡稳定性等精度评价方法[J]. 岩石力学与工程学报, 2018, 37(6): 1301-1331. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201806001.htm Du S G. Method of equal accuracy assessment for the stability analysis of large open-pit mine slopes[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(6): 1301-1331(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201806001.htm