Analytical solution for surrounding rock of circular roadway based on generalized SMP criterion considering seepage and dilatancy

Authors

PAN Jiliang, School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China; Beijing Key Laboratory of Urban Underground Space Engineering(University of Science and Technology Beijing), Beijing 100083, China; Key Laboratory of Ministry of Education for Efficient Mining and Safety of Metal Mines(University of Science and Technology Beijing), Beijing 100083, China
REN Fenhua, School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China; Beijing Key Laboratory of Urban Underground Space Engineering(University of Science and Technology Beijing), Beijing 100083, China; Key Laboratory of Ministry of Education for Efficient Mining and Safety of Metal Mines(University of Science and Technology Beijing), Beijing 100083, ChinaFollow

Abstract

Based on the generalized spatially mobilized plane(SMP) criterion, considering intermediate principal stress, pore water pressure and dilatancy characteristics of surrounding rock, an ideal elastic-plastic model of roadway surrounding rock is established. According to the elastic-plastic theory, the unified analytical solutions of stress field, displacement field and radius of plastic zone under seepage flow are obtained. Then, the stress distribution of surrounding rock and the radius of plastic zone calculated by SMP criterion are compared with those calculated by Mohr-Coulomb(M-C) criterion, and the influencing factors such as pore water pressure and dilatancy angle of surrounding rock are analyzed. It is shown that the radius of plastic zone based on the SMP criterion are smaller than that of the M-C criterion, and the calculation results of M-C criterion are more conservative than those of generalized SMP criterion. The pore water pressure has a great influence on the displacement field of the roadway surrounding rock. The increase of displacement near roadway wall is influenced by the larger pore water pressure. Meanwhile, the change of radius of plastic zone of surrounding rock and the peak tangential stress variations at elastic-plastic interface are proportional to the pore water pressure. The strength of the surrounding rock will be underestimated by using the correlation flow rule, and the actual deformation of the surrounding rock will be underestimated without considering the dilatancy.

Keywords

circular roadway, seepage, dilatancy, intermediate principal stress, elastic-plastic analysis

DOI

10.3969/j.issn.1001-1986.2019.05.005

Recommended Citation

P R. (2019) "Analytical solution for surrounding rock of circular roadway based on generalized SMP criterion considering seepage and dilatancy," Coal Geology & Exploration: Vol. 47: Iss. 5, Article 6.
DOI: 10.3969/j.issn.1001-1986.2019.05.005
Available at: https://cge.researchcommons.org/journal/vol47/iss5/6

Reference

[1] 刘成学,杨林德,李鹏. 考虑应力重分布的深埋圆形透水隧洞弹塑性解[J]. 工程力学,2009,26(2):16-20. LIU Chengxue,YANG Linde,LI Peng. Elastic-plastic analytical solution of deep buried circle tunnel considering stress redistribution[J]. Engineering Mechanics,2009,26(2):16-20.

[2] 荣传新,程桦. 地下水渗流对巷道围岩稳定性影响的理论解[J]. 岩石力学与工程学报,2004,23(5):741-744. RONG Chuanxin,CHENG Hua. Stability analysis of rocks around tunnel with ground water permeation[J]. Chinese Journal of Rock Mechanics and Engineering,2004,23(5):741-744.

[3] 李宗利,任青文,王亚红. 考虑渗流场影响深埋圆形隧洞的弹塑性解[J]. 岩石力学与工程学报,2004,23(8):1291-1295. LI Zongli,REN Qingwen,WANG Yahong. Elasto-plastic analytical solution of deep-buried circle tunnel considering fluid flow field[J]. Chinese Journal of Rock Mechanics and Engineering,2004,23(8):1291-1295.

[4] 黄阜,杨小礼. 考虑渗透力和原始Hoek-Brown屈服准则时圆形洞室解析解[J]. 岩土力学,2010,31(5):1627-1632. HUANG Fu,YANG Xiaoli. Analytical solution of circular openings subjected to seepage in Hoek-Brown media[J]. Rock and Soil Mechanics,2010,31(5):1627-1632.

[5] 王睢,钟祖良,刘新荣. 基于D-P屈服准则考虑渗流影响的深埋有压圆形隧洞弹塑性解[J]. 现代隧道技术,2019,56(1):39-46. WANG Sui,ZHONG Zuliang,LIU Xinrong. D-P yield criterion based elastoplastic solution for a deep-buried and pressured circular tunnel considering seepage effect[J]. Modern Tunnelling Technology,2019,56(1):39-46.

[6] 张常光,胡云世,赵均海,等. 深埋圆形水工隧洞弹塑性应力和位移统一解[J]. 岩土工程学报,2010,32(11):1738-1745. ZHANG Changguang,HU Yunshi,ZHAO Junhai,et al. Elastic-plastic unified solutions for stresses and dis-placements of a deep buried circular hydraulic tunnel[J]. Chinese Journal of Geotechnical Engineering,2010,32(11):1738-1745.

[7] 张常光,张庆贺,赵均海. 考虑应变软化、剪胀和渗流的水工隧洞解析解[J]. 岩土工程学报,2009,31(12):1941-1946. ZHANG Changguang,ZHANG Qinghe,ZHAO Junhai. Analytical solutions of hydraulic tunnels considering strain softening,shear dilation and seepage[J]. Chinese Journal of Geotechnical Engineering,2009,31(12):1941-1946.

[8] 张常光,赵均海,杜文超. 岩石中间主应力效应及强度理论研究进展[J]. 建筑科学与工程学报,2014,31(2):6-19. ZHANG Changguang,ZHAO Junhai,DU Wenchao. Advances in rock for intermediate principal stress effect and strength theory[J]. Journal of Architecture and Civil Engineering,2014,31(2):6-19.

[9] 曾开华,鞠海燕,盛国君,等. 巷道围岩弹塑性解析解及工程应用[J]. 煤炭学报,2011,36(5):752-755. ZENG Kaihua,JU Haiyan,SHENG Guojun,et al. Elastic-plastic analytical solutions for surrounding rocks of tunnels and its engineering applications[J]. Journal of China Coal Society,2011,36(5):752-755.

[10] MATSUOKA H,NAKAI T. Stress-deformation and strength characteristics of soil under three different principal stresses[C]//Proceedings of the Japan Society of Civil Engineers,Tokyo,Japan:Japan Society of Civil Engineers,1974,232:59-70.

[11] 吴创周,杨林德,李秋实. 弹脆塑性围岩应力和位移的广义SMP准则解[J]. 工程力学,2013,30(8):223-228. WU Chuangzhou,YANG Linde,LI Qiushi. Perfect elas-tic-brittle-plastic solution of axisymmetric circular openings in rock mass on extended SMP criterion[J]. Engineering Mechanics,2013,30(8):223-228.

[12] 吕彩忠,孙亚丽. 软岩洞室最优支护的广义SMP准则解与对比研究[J]. 岩土力学,2016,37(7):1956-1962. LYU Caizhong,SUN Yali. A generalized SMP criterion for the optimal support of soft rock tunnel and its comparative analysis[J]. Rock and Soil Mechanics,2016,37(7):1956-1962.

[13] 朱建明,程海峰,姚仰平. 基于SMP强度准则的岩石残余应力与围压的关系[J]. 煤炭学报,2013,38(增刊1):43-48. ZHU Jianming,CHENG Haifeng,YAO Yangping. Relationship between the residual stress and the surrounding rock pressure based on SMP failure criterion[J]. Journal of China Coal Society,2013,38(S1):43-48.

[14] MATSUOKA H,YAO Y,ICHIMURA M. A transformed stress based on extended SMP criterion and its application to elastoplastic model for geomaterials[J]. Doboku Gakkai Ronbunshu,2001,2001(680):211-224.

[15] MATSUOKA H,YAO Y,SUN D. The Cam-clay models revised by the SMP criterion[J]. Soils and Foundations,1999,39(1):81-95.

[16] 朱建明,吴则祥,张宏涛,等. 基于Lade-Duncan和SMP两种强度准则的岩石残余应力研究[J]. 岩石力学与工程学报,2012,31(8):1715-1720. ZHU Jianming,WU Zexiang,ZHANG Hongtao,et al. Study of residual stress of rock based on Lade-Duncan and SMP strength criteria[J]. Chinese Journal of Rock Mechanics and Engineering,2012,31(8):1715-1720.

[17] 罗汀,姚仰平,MATSUOKA H. 基于SMP准则的土的平面应变强度公式[J]. 岩土力学,2000,21(4):390-393. LUO Ting,YAO Yangping,MATSUOKA H. Soil strength equation in plane strain based on SMP[J]. Rock and Soil Mechanics,2000,21(4):390-393.

[18] 郝冬雪,陈榕,许成顺,等. 基于广义SMP准则及应力路径法的柱孔扩张分析[J]. 岩土力学,2013,34(10):2781-2789. HAO Dongxue,CHEN Rong,XU Chengshun,et al. Analysis of cylindrical cavity expansion based on extended SMP criterion and stress path approach[J]. Rock and Soil Mechanics,2013,34(10):2781-2789.

[19] 高召宁,孟祥瑞,付志亮. 考虑渗流、应变软化和扩容的巷道围岩弹塑性分析[J]. 重庆大学学报,2014,37(1):96-101. GAO Zhaoning,MENG Xiangrui,FU Zhiliang. Elasto-plastic analysis on surrounding rock of roadways based on seepage,strain softening and dilatancy[J]. Journal of Chongqing University,2014,37(1):96-101.

[20] 潘继良,高召宁,任奋华. 考虑应变软化和扩容的圆形巷道围岩强度准则效应[J]. 煤炭学报,2018,43(12):3293-3301. PAN Jiliang,GAO Zhaoning,REN Fenhua. Effect of strength criteria on surrounding rock of circular roadway considering strain softening and dilatancy[J]. Journal of China Coal Society,2018,43(12):3293-3301.

[21] 蔡美峰,何满潮,刘东燕. 岩石力学与工程[M]. 北京:科学出版社,2002.

[22] 潘继良,高召宁,郑志伟,等. 考虑损伤与剪胀及中间主应力的巷道围岩弹塑性分析[J]. 中国安全生产科学技术,2017,13(2):40-45. PAN Jiliang,GAO Zhaoning,ZHENG Zhiwei,et al. Elasto-plastic analysis on surrounding rock of roadway consid-ering damage,shear dilation and intermediate principal stress[J]. Journal of Safety Science and Technology,2017,13(2):40-45.

[23] 王云飞,郑晓娟,焦华喆,等. 砂岩试验强度与强度准则预测结果对比分析[J]. 煤田地质与勘探,2016,44(5):122-125. WANG Yunfei,ZHENG Xiaojuan,JIAO Huazhe, et al. Comparative analysis of sandstone experiment strength and different strength criteria prediction results[J]. Coal Geology and Exploration,2016,44(5):122-125.