Calculation method of stress and deformation of loess tunnel based on quadratic parabolic strength criterion of loess
CAO Zhouyang1, GUAN Xiaodi2, MA Di3, DOU Guotao1, ZHU Yongfeng4
1.School of Civil Engineering and Architecture, Zhengzhou University of Aeronautics, Zhengzhou 450046, Henan, China; 2.School of Civil Engineering and Architecture, Xi'an University of Technology, Xi'an 710048, Shaanxi, China; 3.School of Civil Engineering, Xi'an Traffic Engineering Institute, Xi'an 710300, Shaanxi, China; 4.School of Geological Engineering and Geomatics, Chang'an University, Xi'an 710061, Shaanxi, China
Abstract: The problem that the stress and displacement of surrounding rock in loess tunnels may cause large errors based on the Mohr-Coulomb strength criterion. A new solution for calculating the stress and displacement of the surrounding rock of the loess tunnel was derived based on the quadratic parabolic strength criterion, which could comprehensively consider the tensile and shear strength characteristics of the loess. The analysis showed that the peak value of tangential stress of tunnel surrounding rock appeared at the elastic-plastic interface. The peak value of tangential stress based on quadratic parabolic strength criterion was 6.1% lower than that based on Mohr-Coulomb strength criterion, and the stress in plastic zone of the former was smaller than that of the latter. The plastic zone radius of loess tunnel surrounding rock increased with the decrease of supporting force. When the supporting force was small, the plastic zone radius of the former was larger than that of the latter, and the smaller the supporting force, the greater the difference between the two. The peripheral displacement of loess tunnel increased with the decrease of supporting force, the former was larger than the latter, and the difference between the two increased gradually with the decrease of supporting force. By comparing the surrounding rock stress of the loess tunnel under different strength criteria with the model test results, it was found that the surrounding rock stress of the loess tunnel based on the quadratic parabolic strength criterion was in good agreement with the model test results. It showed that the surrounding rock stress, plastic zone radius and tunnel surrounding displacement of loess tunnel based on the quadratic parabolic strength criterion were closer to engineering practice.
曹周阳, 关晓迪, 马迪, 窦国涛, 朱勇锋. 基于黄土二次抛物线型强度准则的黄土隧道应力变形计算方法[J]. 隧道与地下工程灾害防治, 2022, 4(4): 20-27.
CAO Zhouyang, GUAN Xiaodi, MA Di, DOU Guotao, ZHU Yongfeng. Calculation method of stress and deformation of loess tunnel based on quadratic parabolic strength criterion of loess. Hazard Control in Tunnelling and Underground Engineering, 2022, 4(4): 20-27.
[1] 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. [2] 江金硕, 李荣建, 刘军定, 等. 基于黄土联合强度的黄土隧道围岩应力及位移研究[J]. 岩土工程学报, 2019, 41(增刊2): 189-192. JIANG Jinshuo, LI Rongjian, LIU Junding, et al. Stress and displacement of surrounding rock of loess tunnels based on joint strength[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(Suppl.2): 189-192. [3] 张强, 王红英, 王水林, 等. 基于统一强度理论的破裂围岩劣化弹塑性分析[J]. 煤炭学报, 2010, 35(3): 381-386. ZHANG Qiang, WANG Hongying, WANG Shuilin, et al. Deterioration elasto-plastic analysis of cracked surrounding rocks based on unified strength theory[J]. Journal of China Coal Society, 2010, 35(3): 381-386. [4] JAEGER J C, COOK N. Fundamentals of rock mechanics[M]. 3rd ed. London, UK: Methuen and Co., Ltd., 1979. [5] BROWN E T, BRAY J W, LADANYI B, et al. Ground response curves for rock tunnels[J]. Journal of Geotechnical Engineering, 1983, 109(1): 15-39. [6] WANG Y. Ground response of circular tunnel in poorly consolidated rock[J]. Journal of Geotechnical Engineering, 1996, 122(9): 703-708. [7] SHARAN S K. Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock[J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(1): 78-85. [8] 刘夕才, 林韵梅. 软岩扩容性对巷道围岩特性曲线的影响[J]. 煤炭学报, 1996, 21(6): 596-601. LIU Xicai, LIN Yunmei. Effect of dilatancy of soft rocks on rock characteristic curves of tunnels[J]. Journal of China Coal Society, 1996, 21(6): 596-601. [9] 侯公羽, 牛晓松. 基于Levy-Mises本构关系及D-P屈服准则的轴对称圆巷理想弹塑性解[J]. 岩土力学, 2009, 30(6): 1555-1562. HOU Gongyu, NIU Xiaosong. Perfect elastoplastic solution of axisymmetric circular openings in rock mass based on Levy-Mises constitutive relation and D-P yield criterion[J]. Rock and Soil Mechanics, 2009, 30(6): 1555-1562. [10] 张小波, 赵光明, 孟祥瑞. 基于Drucker-Prager屈服准则的圆形巷道围岩弹塑性分析[J]. 煤炭学报, 2013, 38(增刊1): 30-37. ZHANG Xiaobo, ZHAO Guangming, MENG Xiangrui. Elastoplastic analysis of surrounding rock on circular roadway based on Drucker-Prager yield criterion[J]. Journal of China Coal Society, 2013, 38(Suppl.1): 30-37. [11] 陈立伟, 彭建兵, 范文, 等. 基于统一强度理论的非均匀应力场圆形巷道围岩塑性区分析[J]. 煤炭学报, 2007, 32(1): 20-23. CHEN Liwei, PENG Jianbing, FAN Wen, et al. Analysis of surrounding rock mass plastic zone of round tunnel under non-uniform stress field based on the unified strength theory[J]. Journal of China Coal Society, 2007, 32(1): 20-23. [12] 蒋斌松, 张强, 贺永年, 等. 深部圆形巷道破裂围岩的弹塑性分析[J]. 岩石力学与工程学报, 2007, 26(5): 982-986. JIANG Binsong, ZHANG Qiang, HE Yongnian, et al. Elastoplastic analysis of cracked surrounding rocks in deep circular openings[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(5): 982-986. [13] ZHANG L M, WANG Z Q, LI H F, et al. Elastic-plastic analysis for surrounding rock of pressure tunnel with liner based on material nonlinear softening[M] //Geotechnical Engineering for Disaster Mitigation and Rehabilitation. Beijing:Springer Berlin Heidelberg, 2008: 1085-1092. [14] 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. [15] ZHANG Q, ZHANG H X, LAI J X. Finite element analysis for the displacement characteristics of loess tunnel with weak surrounding rock[J]. Advanced Materials Research, 2012, 487: 64-68. [16] 张瀚, 李英明, 任方涛, 等. 基于Zienkiewicz-Pande准则的隧道/巷道围岩弹塑性分析[J]. 现代隧道技术, 2015, 52(2): 30-35. ZHANG Han, LI Yingming, REN Fangtao, et al. Elasto-plastic analysis of the surrounding rock of a tunnel/roadway based on the Zienkiewicz-Pande criterion[J]. Modern Tunnelling Technology, 2015, 52(2): 30-35. [17] 苏雅, 苏永华, 赵明华. 基于Hoek-Brwon准则的软岩隧道围岩极限变形估算方法[J]. 岩石力学与工程学报, 2021, 40(增刊2): 3033-3040. SU Ya, SU Yonghua, ZHAO Minghua. An evaluation approach to ultimate deformation of tunnel surrounding rock in weak rocks based on the Hoek-Brown criterion[J]. Chinese Journal of Rock Mechanics and Engineering, 2021, 40(Suppl.2): 3033-3040. [18] 王衍汇, 倪万魁, 袁志辉. 原状黄土的联合强度理论探讨[J]. 合肥工业大学学报(自然科学版), 2015, 38(12): 1688-1692. WANG Yanhui, NI Wankui, YUAN Zhihui. Discussion on joint strength theory of intact loess[J]. Journal of Hefei University of Technology(Natural Science), 2015, 38(12): 1688-1692. [19] 王衍汇. 原状黄土的联合强度理论及其边坡工程应用[D]. 西安:长安大学, 2016. WANG Yanhui. Study on undisturbed loess joint strength theory and slope engineering applications[D]. Xi'an: Chang'an University, 2016. [20] 王衍汇, 倪万魁, 戴磊,等. 二次抛物线破坏准则下的黄土边坡稳定性分析[J]. 地下空间与工程学报, 2017, 13(3): 833-839. WANG Yanhui, NI Wankui, DAI Lei, et al. Loess slope stability analysis with quadratic parabola failure criterion[J]. Chinese Journal of Underground Space and Engineering, 2017, 13(3): 833-839. [21] 关晓迪, 马迪, 曹周阳, 等. 基于二次抛物线型强度准则的黄土被动土压力计算[C] //2021年全国土木工程施工技术交流会论文集(下册).[出版地不详] :[出版者不详] , 2021: 547-551. [22] 何盛东, 关晓迪, 张明飞, 等. 基于黄土二次抛物线准则的邓肯-张模型修正[J]. 郑州航空工业管理学院学报, 2022, 40(2): 92-96. HE Shengdong, GUAN Xiaodi, ZHANG Mingfei, et al. Modification of Duncan-Zhang model based on quadratic parabola criterion of loess[J]. Journal of Zhengzhou University of Aeronautics, 2022, 40(2): 92-96. [23] 国家铁路局. 铁路隧道设计规范: TB 10003—2016[S]. 北京: 中国铁道出版社, 2017. [24] 赵彭年. 松散介质力学[M]. 北京: 地震出版社,1995. [25] 关晓迪, 何盛东, 曹周阳, 等. 基于统一强度的非轴对称荷载隧道围岩弹塑性分析[J]. 建筑结构, 2021, 51(增刊2): 1728-1733. GUAN Xiaodi, HE Shengdong, CAO Zhouyang, et al. Elastoplastic analysis of tunnel surrounding rock under non-axisymmetric load based on unified strength[J]. Building Structure, 2021, 51(Suppl.2): 1728-1733.