Bipolar coordinate solving method of ground displacement caused by shallow tunnel excavation
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摘要: 基于双极坐标系和Mohr-Coulomb准则，考虑剪胀特性，在Jeffery和Massinas半无限空间圆形隧道围岩应力解的基础上联立平衡方程，推导了浅埋隧道施工拱顶方向的地层位移弹塑性解，并通过Peck公式、Park公式、Loganathan-Poulos公式和实测数据进行验证，揭示了地层变形机理和既有研究之间的联系，给出了考虑地层参数和施工因素影响的经验参数(地层损失率和间隙参数)定量取值方法。研究结果表明：弹塑性解的假定条件更少，与Peck公式、Park公式的差值在2%以内，与Loganathan-Poulos公式的差值为9.5%；双极坐标求解法从弹塑性分析的角度进一步解释了地层变形机理、Peck公式和各类修正弹性公式，即浅埋隧道开挖也会引起地层弹性和塑性变形，以Peck公式为代表的经验公式法在计算地层变形时，地层损失率在不同地区和施工控制条件下的取值分别对应着不同地层参数(黏聚力、内摩擦角、泊松比、重度和弹性模量)和施工边界条件(埋深、开挖半径、支护力)下的地层弹塑性变形；以Park公式、Loganathan-Poulos公式为代表的各类修正弹性解也可近似看作通过断面椭圆化和下沉等手段的修正来抵消理想弹性解与弹塑性解之间的差值。可见，弹塑性解与既有公式结合能更好地指导现场施工。Abstract: Based on the bipolar coordinate system and Mohr-Coulomb criterion, the elastoplastic solution of ground displacement caused by the shallow tunnel excavation in vault direction was derived by considering the characteristic of dilatancy and combining the surrounding rock stress solution of Jeffery and Massinas semi-infinite spatial circular tunnel with the equilibrium equations. The new solution was further verified by the Peck formula, Park formula, Loganathan-Poulos formula, and measured data. The relationships between the ground deformation mechanism and existing solutions were revealed. The quantitative methods for determining the empirical parameters (ground loss rate and gap parameter) subjected to ground parameters and construction factors were provided. Research results show that fewer hypotheses are needed by the elastoplastic solution. An difference of less than 2% is presented in comparison with the Peck formula and Park formula, and an difference of 9.5% is shown in comparison with the Loganathan-Poulos formula. The ground deformation mechanism, Peck formula, and various modified elastic formulas are further elucidated from the perspective of elastoplastic analysis by the bipolar coordinate solving method. In other words, both the elastic and plastic deformations can be caused by the shallow tunnel excavation. When the ground deformation is calculated by the empirical formula methods, typified by the Peck formula, the values of ground loss rate in diverse regions and construction conditions correspond to the ground elastoplastic deformations under different ground parameters (cohesion, internal friction angle, Poisson's ratio, weight, and elastic modulus) and construction boundary conditions (buried depth, excavation radius, and support force). Various modified elastic solutions, typified by the Park formula and Loganathan-Poulos formula, can also be deemed as the modifications offsetting the discrepancy between the ideal elastic solution and the elastoplastic solution by the approximate means of the cross-section ovalization and sedimentation. Therefore, the field construction can be better guided by combining the elastoplastic solution with the existing formula.
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图 2 双极坐标系中的半无限空间隧道模型
Figure 2. Semi-infinite space tunnel model in bipolar coordinate system
图 4 不同隧道支护力下的最大地表沉降对比
Figure 4. Comparison of maximum ground settlements under different tunnel support forces
图 5 弹性、塑性和剪胀工况下隧道拱顶沉降
Figure 5. Tunnel vault settlements under elastic, plastic and dilatant conditions
图 9 黄土地层中地表最大沉降和间隙参数的关系
Figure 9. Relationship between maximum surface settlement and ground gap parameter in loess strata
表 1 采用不同公式计算的地表最大沉降结果
Table 1. Maximum ground settlements calculated by different formulas
公式名称 地表沉降/cm 与本文弹塑性解的相对误差/% 本文弹塑性解 2.64 理想弹性解 1.75 33.7 Peck公式 2.61 1.1 Loganathan-Poulos公式 2.39 9.5 Park公式 2.69 1.9 
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表 2 地层损失率统计及计算值对比
Table 2. Comparison of ground loss ratios between statistic and calculation
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表 3 中国部分地区地铁施工间隙参数的经验取值
Table 3. Empirical values of ground gap parameter in subway construction in some areas of China
地区 样本数 地层特征 g/mm 北京 81 砂土、黏性土互层 4.2~146.5 广州 31 黏性土、砂土、风化岩 8.9~97.6 深圳 27 淤泥质土、粉质黏土、风化岩 17.0~341.0 武汉 37 黏性土、软土、砂土 15.2~164.1 南京 25 淤泥质黏土、粉质黏土 2.0~187.4 西安 54 黄土 4.6~134.1
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[1] 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. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201005054.htmHUANG Fu, YANG Xiao-li. Analytical solution of circular openings subjected to seepage in Hoek-Brown media[J]. Rock and Soil Mechanics, 2010, 31(5): 1627-1632. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201005054.htm [2] 夏才初, 徐晨, 刘宇鹏, 等. 基于GZZ强度准则考虑应变软化特性的深埋隧道弹塑性解[J]. 岩石力学与工程学报, 2018, 37(11): 2468-2477. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201811005.htmXIA Cai-chu, XU Chen, LIU Yu-peng, et al. Elastoplastic solution of deep buried tunnel considering strain-softening characteristics based on GZZ strength criterion[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(11): 2468-2477. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201811005.htm [3] 侯公羽, 牛晓松. 基于Levy-Mises本构关系及Hoek-Brown屈服准则的轴对称圆巷理想弹塑性解[J]. 岩石力学与工程学报, 2010, 29(4): 765-777. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201004016.htmHOU Gong-yu, NIU Xiao-song. Perfect elastoplastic solution of axisymmetric cylindrical cavity based on Levy- Mises constitutive relation and Hoek-Brown failure criterion[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(4): 765-777. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201004016.htm [4] 陈春来, 赵城丽, 魏纲, 等. 基于Peck公式的双线盾构引起的土体沉降预测[J]. 岩土力学, 2014, 35(8): 2212-2218. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201408013.htmCHEN Chun-lai, ZHAO Cheng-li, WEI Gang, et al. Prediction of soil settlement induced by double-line shield tunnel based on Peck formula[J]. Rock and Soil Mechanics, 2014, 35(8): 2212-2218. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201408013.htm [5] PECK R B. Deep excavations and tunneling in soft ground[C]// ISSMGE. Proceedings of 7th International Conference of Soil Mechanics and Foundation Engineering. Mexico: ISSMGE, 1969: 225-290. [6] 王剑晨, 张顶立, 张成平, 等. 北京地区浅埋暗挖法下穿施工既有隧道变形特点及预测[J]. 岩石力学与工程学报, 2014, 33(5): 947-956. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201405010.htmWANG Jian-chen, ZHANG Ding-li, ZHANG Cheng-ping, et al. Deformation characteristics of existing tunnels induced by excavation of new shallow tunnel in Beijing[J]. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(5): 947-956. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201405010.htm [7] LITWINISZYN J. The theories and model research of movements of ground masses[J]. Colliery Engineering, 1958, 35(416): 437-444. [8] 韩煊, 李宁. 隧道开挖不均匀收敛引起地层位移的预测模型[J]. 岩土工程学报, 2007, 29(3): 347-352. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200703006.htmHAN Xuan, LI Ning. A predicting model for ground movement induced by non-uniform convergence of tunnel[J]. Chinese Journal of Geotechnical Engineering, 2007, 29(3): 347-352. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200703006.htm [9] PARK K H. Elastic solution for tunneling-induced ground movements in clays[J]. International Journal of Geomechanics, 2004, 4(4): 310-318. doi: 10.1061/(ASCE)1532-3641(2004)4:4(310) [10] LOGANATHAN N, POULOS H G. Analytical prediction for tunneling-induced ground movements in clays[J]. Journal of Geotechnical and Geoenvironmental Engineering, 1998, 124(9): 846-856. doi: 10.1061/(ASCE)1090-0241(1998)124:9(846) [11] HOU Yan-juan, ZHOU Mo-zhen, ZHANG Ding-li, et al. Analysis of four shield-driven tunnels with complex spatial relations in a clay stratum[J]. Tunnelling and Underground Space Technology, 2022, 124: 104478. doi: 10.1016/j.tust.2022.104478 [12] TANG Xiao-wu, LIANG Jia-xin, LIU Wei, et al. Modification of Peck formula to predict ground surface settlement of twin tunnels in low permeability soil[J]. Advances in Civil Engineering, 2021, 2021: 6698673. [13] 唐正, 王洪新, 孙德安, 等. 大断面管幕法隧道群管顶进的地表位移规律研究[J]. 岩土力学, 2022, 43(7): 1933-1941.TANG Zheng, WANG Hong-xin, SUN De-an, et al. Surface displacement during pipe roof construction of pipe-jacking group with large section[J]. Rock and Soil Mechanics, 2022, 43(7): 1933-1941. (in Chinese) [14] 韩煊, 李宁, STANDING J R. Peck公式在我国隧道施工地面变形预测中的适用性分析[J]. 岩土力学, 2007, 28(1): 23-28, 35. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200701005.htmHAN Xuan, LI Ning, STANDING J R. An adaptability study of Gaussian equation applied to predicting ground settlements induced by tunneling in China[J]. Rock and Soil Mechanics, 2007, 28(1): 23-28, 35. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200701005.htm [15] 韩煊, 李宁, STANDING J R. 地铁隧道施工引起地层位移规律的探讨[J]. 岩土力学, 2007, 28(3): 609-613. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200703034.htmHAN Xuan, LI Ning, STANDING J R. Study on subsurface ground movement caused by urban tunneling[J]. Rock and Soil Mechanics, 2007, 28(3): 609-613. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200703034.htm [16] 朱才辉, 李宁. 隧道施工诱发地表沉降估算方法及其规律分析[J]. 岩土力学, 2016, 37(增2): 533-542. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX2016S2068.htmZHU Cai-hui, LI Ning. Estimation method and laws analysis of surface settlement due to tunneling[J]. Rock and Soil Mechanics, 2016, 37(S2): 533-542. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX2016S2068.htm [17] 朱才辉, 李宁. 地铁施工诱发地表最大沉降量估算及规律分析[J]. 岩石力学与工程学报, 2017, 36(增1): 3543-3560. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2017S1049.htmZHU Cai-hui, LI Ning. Estimation and regularity analysis of maximal surface settlement induced by subway construction[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(S1): 3543-3560. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2017S1049.htm [18] 魏纲, 张世民, 齐静静, 等. 盾构隧道施工引起的地面变形计算方法研究[J]. 岩石力学与工程学报, 2006, 25(增1): 3317-3323. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2006S1111.htmWEI Gang, ZHANG Shi-min, QI Jing-jing, et al. Study on calculation method of ground deformation induced by shield tunnel construction[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(S1): 3317-3323. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2006S1111.htm [19] 魏新江, 张金菊, 张世民. 盾构隧道施工引起地面最大沉降探索[J]. 岩土力学, 2008, 29(2): 445-448. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200802049.htmWEI Xin-jiang, ZHANG Jin-ju, ZHANG Shi-min. Grope for shield tunnel construction induced ground maximal settlement[J]. Rock and Soil Mechanics, 2008, 29(2): 445-448. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200802049.htm [20] VERRUIJT A. Deformations of an elastic half plane with a circular cavity[J]. International Journal of Solids and Structures, 1998, 35(21): 2795-2804. [21] 朱宁, 施建勇, 陈海丰. 一种半无限土体中圆孔扩张的分析方法[J]. 岩土力学, 2006, 27(2): 257-260, 267. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200602018.htmZHU Ning, SHI Jian-yong, CHEN Hai-feng. A method for cavity expansion in semi-infinite soil[J]. Rock and Soil Mechanics, 2006, 27(2): 257-260, 267. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200602018.htm [22] VERRUIJT A, BOOKER J R. Surface settlements due to deformation of a tunnel in an elastic half plane[J]. Géotechnique, 1996, 46(4): 753-756. [23] GONZALEZ C, SAGASETA C. Patterns of soil deformations around tunnels. Application to the extension of Madrid Metro[J]. Computers and Geotechnics, 2001, 28(6): 445-468. [24] 韩凯航, 张成平, 王梦恕. 浅埋隧道围岩应力及位移的显式解析解[J]. 岩土工程学报, 2014, 36(12): 2253-2259. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201412017.htmHAN Kai-hang, ZHANG Cheng-ping, WANG Meng-shu. Explicit analytical solutions for stress and displacement of surrounding rock in shallow tunnels[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(12): 2253-2259. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201412017.htm [25] JEFFERY G B. Plane stress and plane strain in bipolar co-ordinates[J]. Philosophical Transactions of the Royal Society A: Mathematical Physical and Engineering Sciences, 1921, 221(582/583/584/585/586/587/588/589/590/591/592/593): 265-293. [26] MASSINAS S A, SAKELLARIOU M G. Closed-form solution for plastic zone formation around a circular tunnel in half-space obeying Mohr-Coulomb criterion[J]. Géotechnique, 2009, 59(8): 691-701. [27] VERRUIJT A, BOOKER J R. Discussion on surface settlements due to deformation of a tunnel in an elastic half plane[J]. Géotechnique, 1998, 48(5): 709-713. [28] 张常光, 赵均海, 张庆贺. 基于统一强度理论的深埋圆形岩石隧道收敛限制分析[J]. 岩土工程学报, 2012, 34(1): 110-114. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201201010.htmZHANG Chang-guang, ZHAO Jun-hai, ZHANG Qing-he. Convergence-confinement analysis of deep circular rock tunnels based on unified strength theory[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(1): 110-114. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201201010.htm [29] 王凤云, 钱德玲. 基于统一强度理论深埋圆形隧道围岩的剪胀分析[J]. 岩土力学, 2019, 40(5): 1966-1976. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201905040.htmWANG Feng-yun, QIAN De-ling. Dilatancy analysis for a circular tunnel excavated in rock mass based on unified strength theory[J]. Rock and Soil Mechanics, 2019, 40(5): 1966-1976. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201905040.htm [30] 赵星光, 蔡明, 蔡美峰. 剪胀对地下工程岩体位移的影响——以加拿大Donkin-Morien隧道为例[J]. 岩石力学与工程学报, 2010, 29(11): 2185-2195. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201011004.htmZHAO Xing-guang, CAI Ming, CAI Mei-feng. Influence of dilation on rock mass displacement around underground excavation—a case study of Donkin-Morien Tunnel in Canada[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(11): 2185-2195. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201011004.htm [31] 来弘鹏, 谢永利, 刘苗, 等. 黄土地区浅埋暗挖地铁隧道衬砌受力分析[J]. 岩土工程学报, 2011, 33(8): 1167-1172. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201108005.htmLAI Hong-peng, XIE Yong-li, LIU Miao, et al. Mechanical characteristics for linings of shallow excavation metro tunnel in loess region[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(8): 1167-1172. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201108005.htm [32] 韩煊. 隧道施工引起地层位移及建筑物变形预测的实用方法研究[D]. 西安: 西安理工大学, 2007.HAN Xuan. The analysis and prediction of tunneling-induced building deformations[D]. Xi'an: Xi'an University of Technology, 2007. (in Chinese) [33] 何川, 曾东洋. 砂性地层中地铁盾构隧道管片结构受力特征研究[J]. 岩土力学, 2007, 28(5): 909-914. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200705010.htmHE Chuan, ZENG Dong-yang. Research on mechanical characteristics of metro shield tunnel segment in sandy strata[J]. Rock and Soil Mechanics, 2007, 28(5): 909-914. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200705010.htm [34] 肖中平, 何川, 林刚, 等. 粘性地层地铁盾构隧道管片结构力学特征研究[J]. 现代隧道技术, 2006, 43(6): 18-22. https://www.cnki.com.cn/Article/CJFDTOTAL-XDSD200606003.htmXIAO Zhong-ping, HE Chuan, LIN Gang, et al. Study on the mechanical behavior of segmental structure of metro shield tunnels in viscous stratum[J]. Modern Tunnelling Technology, 2006, 34(6): 18-22. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XDSD200606003.htm [35] 江英超, 何川, 方勇, 等. 盾构施工对黄土地层的扰动及管片衬砌受荷特征[J]. 中南大学学报(自然科学版), 2013, 44(7): 2934-2941. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201307043.htmJIANG Ying-chao, HE Chuan, FANG Yong, et al. Soil disturbance caused by shield tunneling and segment lining loading characteristics in loess strata[J]. Journal of Central South University (Science and Technology), 2013, 44(7): 2934-2941. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201307043.htm -
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