Safety evaluation model of excavating rock slope based on entropy-grey correlation method
-
摘要: 根据边坡稳定性评价体系, 选取边坡岩体质量评分、边坡开挖方法调整系数、高度修正系数、结构面调整系数、结构面调整值5个评价指标反映边坡的整体稳定性, 并作为安全评价模型的序列变量; 建立了熵权-灰关联安全评价模型, 将目标边坡作为系统特征序列, 12处岩质边坡作为相关因素序列, 评价了京沪高速改扩建工程沿线典型岩质边坡的安全性, 并提出工程建议; 采用FLAC3D仿真软件, 分析了不同阶段机械开挖和不同炮孔处静力爆破条件下边坡的稳定性变化规律, 以验证安全评价模型的准确性。分析结果表明: 边坡稳定性评价指标可较好地反映边坡的稳定性特征; 熵权-灰关联安全评价模型充分发挥了灰关联法在小样本数据分析的优点, 且由熵权法计算的指标权重改善了传统灰关联分析中由专家打分或平均赋权的缺陷, 使评价结果更加客观; 三级边坡和一级边坡的开挖使边坡K593+260~K593+555的安全系数分别降至1.01和1.00, 和上一级边坡相比降幅分别为34.8%、9.1%, 说明缓倾顺层岩质边坡的开挖会使岩层沿结构面滑动, 使边坡失稳; 瞬时动荷载和荷载积累效应控制静力爆破条件下边坡的稳定性, 瞬时动荷载的出现使边坡安全系数下降了7.7%, 荷载积累效应的消散使安全系数平均回升3.6%, 说明爆破对边坡的松动作用明显, 荷载积累的消散使边坡的稳定性提升。
-
关键词:
- 岩质边坡 /
- 熵权-灰关联评价模型 /
- 安全评价 /
- 数值模拟 /
- 开挖方法
Abstract: According to slope stability evaluation system, five evaluation indexes, such as slope rock mass quality score, excavation method adjustment coefficient, height correction coefficient, structural surface adjustment coefficient, and structural surface adjustment value, were selected to reflect the overall stability of slope, and serve as the safety evaluation model sequence variables. The entropy weight-gray correlation safety evaluation model was established. Taking the target slopes as the system characteristic sequence and the 12 rock slopes as the correlation factor sequence, the safety of the typical rock slopes along the reconstruction and expansion project of Beijing-Shanghai Expressway was evaluated, and the engineering advices were provided. FLAC3 D simulation software was used to analyze the stability variation laws of the slopes under different stages of mechanical excavation and static blasting at different blastholes, and the accuracy of the safety evaluation model was verified. Analysis result shows that the evaluation indexes of the slope stability can well reflect the slope stability characteristics. The entropy weight-grey correlation safety evaluation model full plays the advantages of grey correlation method in the analysis of small sample data, and the index weights calculated by entropy weight method improve the defect of the traditional grey correlation analysis that the indexes are weighted by experts or average method, making the evaluation result more objective. The third-grade and first-grade slope excavations reduce the safety factor of the slope K593+260~K593+555 to 1.01 and 1.00, respectively, with decreases of 34.8% and 9.1% respectively compared with the upper grade slope. It shows that the excavation of rock slope with gently inclined bedding slope will cause rock layer slide along structural plane and makes the slope become unstable. Transients dynamic load and load accumulation effect control the stability of the slope under static blasting condition. The occurrence of transients dynamic load reduces the slope safety factor by 7.7%, and the dissipation of the load accumulation effect rises the safety factor by 3.6%. It shows that the blasting has obvious loosening effect on the slope, and the dissipation of load accumulation improves the slope stability. -
图 4 目标边坡在不同施工阶段下的安全系数
Figure 4. Safety coefficients of target slopes in different construction stages
表 1 边坡岩体质量分类
Table 1. Classification of slope rock masses
岩石单轴抗压强度 岩石质量指标 裂面间距 裂面特征 地下水 取值/MPa 评分 取值/% 评分 取值/cm 评分 状态 评分 状态 评分 < 25 0~2 < 25 0~5 < 6 < 5 软弱充填物厚度 > 5 mm或张开度 > 5 mm, 连续 < 8 涌水 0 25~50 2~5 25~50 5~10 6~20 5~8 光滑或充填物厚度 < 5 mm或张开 8~15 渗水 0~5 50~100 5~10 50~75 10~15 20~60 8~12 稍粗糙, 张开度 < 1 mm, 岩壁强风化 15~22 潮湿 5~8 100~250 10~13 75~90 15~18 60~200 12~15 稍粗糙, 张开度 < 1 mm, 岩壁微风化 22~28 湿润 8~11 > 250 13~15 90~100 18~20 > 200 15~20 很粗糙, 不连续, 未张开, 岩壁未风化 25~28 干燥 11~15 
下载: 导出CSV
表 2 边坡结构面调整系数
Table 2. Structural surface adjustment coefficients of slope
结构面类型 断层、夹泥层 层面、贯通裂隙 节理 λ 1.0 0.8~0.9 0.7
下载: 导出CSV
表 3 结构面与边坡走向关系系数
Table 3. Relationship coefficients between structural surface and slope trend
平面滑动破坏模式边坡倾角/(°): α1-α2 > 30 30~20 20~10 10~5 < 5 倾倒破坏模式边坡倾角/(°): α1-α2-180° > 30 30~20 20~10 10~5 < 5 F1取值 0.15 0.40 0.70 0.85 1.00
下载: 导出CSV
表 4 破坏模式与结构面倾角关系系数
Table 4. Relationship coefficients between failure mode and structural surface inclination
平面滑动破坏模式结构面倾角/(°): β1 > 30 30~20 20~10 10~5 < 5 倾倒破坏模式结构面倾角/(°): β2 > 45 45~35 35~25 25~15 < 15 F2取值 0.15 0.40 0.70 0.85 1.00
下载: 导出CSV
表 5 结构面倾角与边坡倾角关系系数
Table 5. Relationship coefficients between structural surface inclination and slope inclination
平面滑动破坏模式结构面与边坡夹角/(°): β1-β2 > 10 10~0 0 0~-10 < -10 倾倒破坏模式结构面与边坡夹角/(°): β1+β2 < 110 110~120 > 120 - - F3取值 0 6 25 50 60
下载: 导出CSV
表 6 边坡开挖方法调整系数
Table 6. Adjustment coefficients of slope excavation method
开挖方法 欲裂爆破 静力爆破 机械开挖 欠缺爆破 M 10 8 0 -8
下载: 导出CSV
表 7 系统特征序列
Table 7. System characteristic sequences
序号 工程名称 结构面倾向 a λ R/100 F/60 M/20 稳定状态 1 新滩滑坡 顺倾 0.74 1.00 0.38 0.21 0.75 失稳 2 李家峡坝Ⅰ号滑坡 逆倾 0.71 1.00 0.42 0.13 0.75 失稳 3 李家峡坝Ⅱ号滑坡 顺倾 0.73 1.00 0.35 0.02 0.50 失稳 4 抚顺西露天矿人卷车边坡 顺倾 0.85 1.00 0.35 0.02 0.50 失稳 5 公伯峡电站古奉群滑坡 逆倾 0.65 0.80 0.41 1.00 0.75 稳定 6 天生桥二级电站后山边坡 逆倾 0.82 0.80 0.51 0.08 0.40 稳定 7 天生桥水电站溢洪道边坡 顺倾 0.84 0.80 0.62 0.14 0.40 稳定 8 小峡石坪台滑坡 顺倾 0.86 0.70 0.36 0.08 0.50 稳定 9 积石峡4号滑坡 散体结构 0.67 0.70 0.50 0.21 0.75 稳定 10 漫湾石料场边坡 块状结构 0.75 0.70 0.76 0.07 0.50 稳定 11 三峡升船机及临时船闸边坡 顺倾 0.73 0.80 0.42 0.12 0.75 失稳 12 白灰厂滑坡 顺倾 0.86 0.80 0.71 0.01 0.50 失稳
下载: 导出CSV
表 8 目标边坡参数
Table 8. Parameters of target slopes
目标边坡桩号 地质情况 坡高/m 可能破坏模式 结构面 坡面 倾向/(°) 倾角/(°) 倾向/(°) 倾角/(°) K498+870~K499+200 溶洞, 中、强风化石灰岩 38.0 倾倒滑动 240 70 49 53 K503+585~K504+018 碎石, 中、强风化石灰岩 41.0 平面滑动 235 71 235 53 K551+714~K552+115 残积土, 中、强风化石灰岩 39.7 倾倒破坏 0 53 30 45 K565+914~K566+300 残积土, 中、强风化石灰岩 45.2 倾倒滑动 45 16 222 45 K593+260~K593+555 残积土, 中、强风化石灰岩 40.7 平面滑动 76 10 239 45
下载: 导出CSV
表 9 目标边坡评价指标
Table 9. Evaluation indexes of target slopes
目标边坡桩号 a λ R F M K498+870~K499+200 1.48 1.00 64.60 3.25 0 K503+585~K504+018 1.41 0.85 58.50 2.76 0 K551+714~K552+115 1.44 0.90 56.50 3.75 0 K565+914~K566+300 1.33 0.80 51.80 1.25 0 K593+260~K593+555 1.42 0.70 53.00 1.35 0
下载: 导出CSV
表 10 量纲为1的目标边坡评价指标
Table 10. Dimensionless evaluation indexes of target slopes
目标边坡桩号 a λ R/100 F/60 M/20 K498+870~K499+200 1.48 1.00 0.65 0.05 0 K503+585~K504+018 1.41 0.85 0.59 0.05 0 K551+714~K552+115 1.44 0.90 0.57 0.06 0 K565+914~K566+300 1.33 0.80 0.52 0.02 0 K593+260~K593+555 1.42 0.70 0.53 0.02 0
下载: 导出CSV
表 11 岩质边坡相关因素序列
Table 11. Correlation factor sequences of rock slopes
序号 工程名称 γ0i(1) γ0i(2) γ0i(3) γ0i(4) γ0i(5) 1 新滩滑坡 0.84 1.00 0.48 0.70 0.33 2 李家峡坝Ⅰ号滑坡 0.81 0.87 0.56 0.86 0.41 3 李家峡坝Ⅱ号滑坡 0.84 0.96 0.51 0.92 0.43 4 抚顺西露天矿人卷车边坡 0.93 0.51 0.44 0.87 0.56 5 公伯峡电站古奉群滑坡 0.77 0.43 0.55 0.84 0.33 6 天生桥二级电站后山边坡 0.90 0.43 0.88 0.39 0.48 7 天生桥水电站溢洪道边坡 0.92 0.43 0.93 0.82 0.54 8 小峡石坪台滑坡 0.94 0.33 0.45 0.98 0.33 9 积石峡4号滑坡 0.79 0.33 0.84 0.70 0.27 10 漫湾石料场边坡 0.85 0.33 0.48 1.00 0.43 11 三峡升船机及临时船闸边坡 0.83 0.43 0.56 0.87 0.33 12 白灰厂滑坡 0.94 0.43 0.57 0.89 0.43
下载: 导出CSV
表 12 系统评价指标权重
Table 12. Weights of system evaluation indexes
参数 a λ R F M wv/% 20.5 15.6 30.6 18.4 14.9
下载: 导出CSV
表 13 加权关联度计算结果
Table 13. Calculation results of weighted correlations
序号 稳定状态 K498+870~K499+200 K503+585~K504+018 K551+714~K552+115 K565+914~K566+300 K593+260~K593+555 1 失稳 0.130 0.132 0.143 0.132 0.131 2 失稳 0.137 0.138 0.132 0.138 0.138 3 失稳 0.153 0.154 0.151 0.154 0.149 4 失稳 0.151 0.158 0.172 0.158 0.201 5 稳定 0.112 0.114 0.126 0.114 0.114 6 稳定 0.150 0.157 0.184 0.195 0.158 7 稳定 0.114 0.173 0.162 0.145 0.146 8 稳定 0.164 0.115 0.122 0.115 0.116 9 稳定 0.109 0.126 0.117 0.121 0.117 10 稳定 0.134 0.127 0.132 0.126 0.121 11 失稳 0.113 0.115 0.118 0.114 0.115 12 失稳 0.152 0.144 0.139 0.135 0.135
下载: 导出CSV
表 14 不同施工方法安全性评价结果
Table 14. Safety evaluation result under different construction methods
目标边坡桩号 机械开挖 静力爆破 K498+870~K499+200 稳定 稳定 K503+585~K504+018 稳定 稳定 K551+714~K552+115 稳定 稳定 K565+914~K566+300 稳定 稳定 K593+260~K593+555 失稳 失稳
下载: 导出CSV
表 15 计算参数
Table 15. Computation parameters
参数 容重/(kN·m-3) c/kPa φ/(°) E/GPa 泊松比 强风化石灰岩 23.0 20 29 5 0.25 中风化石灰岩1 23.6 24 51 20 0.20 中风化石灰岩2 24.2 26 45 25 0.20 结构面 - 100 30 - -
下载: 导出CSV
表 16 边坡安全系数范围划分
Table 16. Range division of slope safety coefficient
安全系数范围 稳定状态 f < 1.00 不稳定 1.00≤f < 1.05 欠稳定 1.05≤f < 1.3 基本稳定 f≥1.3 稳定
下载: 导出CSV
表 17 爆破关键参数
Table 17. Key parameters of blasting
孔径/mm 90 排距/m 3.5 炮孔台阶高度/m 12 炸药消耗量/(kg·m-3) 0.20 超深/m 1 单孔药量/kg 38 孔深/m 13 填塞长度/m 4.5 底盘抵抗线/m 4 爆破孔数/m 38 炮孔密集系数/m 1 爆破总药量/kg 7 000
下载: 导出CSV
-
[1] 黄润秋. 20世纪以来中国的大型滑坡及其发生机制[J]. 岩石力学与工程学报, 2007, 26(3): 433-454. doi: 10.3321/j.issn:1000-6915.2007.03.001HUANG Run-qiu. Large-scale landslides and their sliding mechanisms in China since the 20th century[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(3): 433-454. (in Chinese). doi: 10.3321/j.issn:1000-6915.2007.03.001 [2] 王涛, 吴树仁, 石菊松, 等. 国内外典型工程滑坡灾害比较[J]. 地质通报, 2013, 32(12): 1881-1899. https://www.cnki.com.cn/Article/CJFDTOTAL-ZQYD201312002.htmWANG Tao, WU Shu-ren, SHI Ju-song, et al. A comparative study of typical engineering landslide disasters both in China and abroad[J]. Geological Bulletin of China, 2013, 32(12): 1881-1889. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZQYD201312002.htm [3] 徐世强, 折学森, 王思长. 高速公路边坡滚石自由飞落分析模型[J]. 交通运输工程学报, 2011, 11(2): 14-17. doi: 10.3969/j.issn.1671-1637.2011.02.003XU Shi-qiang, SHE Xue-sen, WANG Si-chang. Free rolling model of stone on expressway slope[J]. Journal of Traffic and Transportation Engineering, 2011, 11(2): 14-17. (in Chinese). doi: 10.3969/j.issn.1671-1637.2011.02.003 [4] 冯光乐, 凌天清, 许志鸿. 公路边坡支护方案优化设计[J]. 交通运输工程学报, 2002, 2(1): 43-47. doi: 10.3321/j.issn:1671-1637.2002.01.009FENG Guang-le, LING Tian-qing, XU Zhi-hong. Optimizing design method of highway slope[J]. Journal of Traffic and Transportation Engineering, 2002, 2(1): 43-47. (in Chinese). doi: 10.3321/j.issn:1671-1637.2002.01.009 [5] 郝建斌, 郭进扬, 张振北, 等. 地震作用下锚杆支护边坡动力响应[J]. 交通运输工程学报, 2017, 17(3): 46-55. http://transport.chd.edu.cn/article/id/201703005HAO Jian-bin, GUO Jin-yang, ZHANG Zhen-bei, et al. Dynamic response of anchors-supported slope under earthquake[J]. Journal of Traffic and Transportation Engineering, 2017, 17(3): 46-55. (in Chinese). http://transport.chd.edu.cn/article/id/201703005 [6] 周波. 道路改扩建边坡稳定性控制及支护措施研究[D]. 长沙: 中南大学, 2011.ZHOU Bo. Study on the stability control for the rebuilding roadside slope and its retaining measurements[D]. Changsha: Central South University, 2011. (in Chinese). [7] HU Qing-guo, XIE Wang-xiang, HE Zhong-ming. Risk evaluation index system for operation security in high slope construction on freeway reconstruction and extension[J]. Applied Mechanics and Materials, 2013, 438/439: 1983-1986. doi: 10.4028/www.scientific.net/AMM.438-439.1983 [8] GRAVANIS E, PANTELIDIS L, GRIFFITHS D V. An analytical solution in probabilistic rock slope stability assessment based on random fields[J]. International Journal of Rock Mechanics and Mining Sciences, 2014, 71: 19-24. doi: 10.1016/j.ijrmms.2014.06.018 [9] OZTEKIN B, TOPAL T, KOLAT C. Assessment of degradation and stability of a cut slope in limestone, Ankara-Turkey[J]. Engineering Geology, 2006, 84(1/2): 12-30. [10] 李炜. 边坡稳定性联合评价方法[J]. 交通运输工程学报, 2010, 10(5): 8-11. http://transport.chd.edu.cn/article/id/201005002LI Wei. Combined evaluation method of slope stability[J]. Journal of Traffic and Transportation Engineering, 2010, 10(5): 8-11. (in Chinese). http://transport.chd.edu.cn/article/id/201005002 [11] 孙东亚, 陈祖煜, 杜伯辉, 等. 边坡稳定评价方法RMR-SMR体系及其修正[J]. 岩石力学与工程学报, 1997, 16(4): 297-304. doi: 10.3321/j.issn:1000-6915.1997.04.001SUN Dong-ya, CHEN Zu-yu, DU Bo-hui, et al. Modifications to the RMR-SMR system for slope stability evaluation[J]. Chinese Journal of Rock Mechanics and Engineering, 1997, 16(4): 297-304. (in Chinese). doi: 10.3321/j.issn:1000-6915.1997.04.001 [12] 周志军, 牛涌, 张铁柱. 基于改进Sarma法的岩质边坡稳定性分析[J]. 交通运输工程学报, 2013, 13(1): 15-19. http://transport.chd.edu.cn/article/id/201301003ZHOU Zhi-jun, NIU Yong, ZHANG Tie-zhu. Stability analysis of rock slope based on improved Sarma method[J]. Journal of Traffic and Transportation Engineering, 2013, 13(1): 15-19. (in Chinese). http://transport.chd.edu.cn/article/id/201301003 [13] 陈昌彦, 王思敬, 沈小克. 边坡岩体稳定性的人工神经网络预测模型[J]. 岩土工程学报, 2001, 23(2): 157-161. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200102005.htmCHEN Chang-yan, WANG Si-jing, SHEN Xiao-ke. Predicting models to estimate stability of rock slope based on artificial neural network[J]. Chinese Journal of Geotechnical Engineering, 2001, 23(2): 157-161. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200102005.htm [14] 李胜伟, 李天斌, 王兰生. 边坡岩体质量分类体系的CSMR法及应用[J]. 地质灾害与环境保护, 2001, 12(2): 69-72. https://www.cnki.com.cn/Article/CJFDTOTAL-DZHB200102016.htmLI Sheng-wei, LI Tian-bin, WANG Lan-sheng. Application of the csmr system for slope stability evaluation[J]. Journal of Geological Hazards and Environment Preservation, 2001, 12(2): 69-72. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DZHB200102016.htm [15] HAO Yong-hong, CAO Bi-bo, CHEN Xiang, et al. A piecewise gray system model for study the effects of anthropogenic activities on Karst hydrological processes[J]. Water Resour Manage, 2013, 27: 1207-1220. [16] OLSON D L, WU De-sheng. Simulation of fuzzy multiattribute models for grey relationships[J]. European Journal of Operational Research, 2006, 175(1): 111-120. [17] 冯忠居, 陈思晓, 徐浩, 等. 基于灰色系统理论的高寒盐沼泽区混凝土耐久性评估[J]. 交通运输工程学报, 2018, 18(6): 18-26. http://transport.chd.edu.cn/article/id/201806003FENG Zhong-ju, CHEN Si-xiao, XU Hao, et al. Durability evaluation of concrete in alpine salt marsh area based on gray system theory[J]. Journal of Traffic and Transportation Engineering, 2018, 18(6): 18-26. (in Chinese). http://transport.chd.edu.cn/article/id/201806003 [18] 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.htmHUANG Dan, SHI Xiu-zhi, QIU Xian-yang, 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). https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201704028.htm [19] 李炜, 康海贵. 边坡稳定性模糊随机可靠度分析[J]. 交通运输工程学报, 2010, 10(1): 19-23. http://transport.chd.edu.cn/article/id/201001004LI Wei, KANG Hai-gui. Fuzzy-random reliability analysis of slope stability[J]. Journal of Traffic and Transportation Engineering, 2010, 10(1): 19-23. (in Chinese). http://transport.chd.edu.cn/article/id/201001004 [20] ABEDINI M, TULABI S. Assessing LNRF, FR, and AHP models in landslide susceptibility mapping index: a comparative study of Nojian watershed in Lorestan province, Iran[J]. Environmental Earth Sciences, 2018, 77(11): 1-13. [21] MONDAL S, MAITI R. Integrating the analytical hierarchy process(AHP) and the frequency ratio(FR) model in landslide susceptibility mapping of Shiv-Khola watershed, Darjeeling Himalaya[J]. International Journal of Disaster Risk Science, 2013, 4(4): 200-212. [22] 何海鹰, 胡甜, 赵健. 基于AHP的岩质高边坡风险评估指标体系[J]. 中南大学学报(自然科学版), 2012, 43(7): 2861-2868. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201207059.htmHE Hai-ying, HU Tian, ZHAO Jian. Risk assessment indexes system of high rock slope based on AHP[J]. Journal of Central South University (Science and Technology), 2012, 43(7): 2861-2868. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201207059.htm [23] 周宁, 傅鹤林, 袁勇. 基于模糊神经网络的边坡稳定性评价方法[J]. 地下空间与工程学报, 2009, 5(增2): 1826-1832. https://www.cnki.com.cn/Article/CJFDTOTAL-BASE2009S2084.htmZHOU Ning, FU He-lin, YUAN Yong. Evaluation approach of slope stability based on fuzzy neural network[J]. Chinese Journal of Underground Space and Engineering, 2009, 5(S2): 1826-1832. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-BASE2009S2084.htm [24] 王小兵, 夏晓舟, 章青. 基于正交试验和神经网络的堤防边坡抗滑稳定可靠度研究[J]. 长江科学院院报, 2019, 36(10): 89-93. https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB201910021.htmWANG Xiao-bing, XIA Xiao-zhou, ZHANG Qing. Reliability analysis on anti-sliding stability of levee slope based on orthogonal test and neural network[J]. Journal of Yangtze River Scientific Research Institute, 2019, 36(10): 89-93. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB201910021.htm [25] ACHARYYA R, DEY A. Assessment of bearing capacity of interfering strip footings located near sloping surface considering artificial neural network technique[J]. Journal of Mountain Science, 2018, 15(12): 2766-2780. [26] GRECO R, GIORGIO M, CAPPARELLI G, et al. Early warning of rainfall-induced landslides based on empirical mobility function predictor[J]. Engineering Geology, 2013, 153: 68-79. [27] ZENG Yao-xun, FAN Xiao-yi. Evaluation of seismic landslide runout distance based on the fuzzy mathematics and range analysis[J]. Applied Mechanics and Materials, 2013, 405-408: 2341-2345. [28] 赵怀鑫, 孙星星, 徐倩倩, 等. 基于灰熵法的公路货运量和货物周转量关联因素分析[J]. 交通运输工程学报, 2018, 18(4): 160-170. http://transport.chd.edu.cn/article/id/201804017ZHAO Huai-xin, SUN Xing-xing, XU Qian-qian, et al. Analysis of relavent factors for highway freight volume and freight turnover based on grey entropy method[J]. Journal of Traffic and Transportation Engineering, 2018, 18(4): 160-170. (in Chinese). http://transport.chd.edu.cn/article/id/201804017 [29] 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1): 3400-3410. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2018S1030.htmZHANG Xu, ZHOU Shao-wu, LIN Peng, 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). https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2018S1030.htm [30] 郑颖人, 赵尚毅, 邓卫东. 岩质边坡破坏机制有限元数值模拟分析[J]. 岩石力学与工程学报, 2003, 22(12): 1943-1952. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX200312000.htmZHENG Ying-ren, ZHAO Shang-yi, DENG Wei-dong. Numerical simulation on failure mechanism of rock slope by strength reduction fem[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(12): 1943-1952. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX200312000.htm -
点击查看大图
图(6) / 表(17)
计量
- 文章访问数: 785
- HTML全文浏览量: 154
- PDF下载量: 370
- 被引次数: 0
