岩体都具有一定的与时间相关的流变特性,而渗流引起的孔隙压力变化对流变岩体工程的时变有效应力影响明显。对渗流作用影响下黏弹性岩体中任意大小和布置的双隧洞力场问题进行一定的简化,利用复变函数法、Schwartz交替法和弹性-黏弹性对应原理实现流固弱耦合问题解析求解并给出解答。从力学机制上,解答体现出渗流对力场影响的面力效应和流动效应。解析结果与数值结果和现场实测数据吻合,验证了模型的正确性。解析模型为数值模型提供验证手段,也为富水地区多隧洞在开挖、运营阶段与时间相关的稳定性问题提供一种快速分析和判定方法。基于解析模型,分析了隧洞净距和黏性系数对应力、位移随时间变化的影响。结果表明:尽管考虑了稳态渗流影响,岩体的有效应力仍随时间延长而增大;同一黏性系数下应力随时间的收敛速度快于位移;渗流的存在使双洞相互影响更加显著,当隧洞净距大于6.6倍洞半径时应力与单洞值差别小于10％,而无渗流情况为4倍洞半径。
Rock mass generally exhibits time-dependent rheological properties, while the changes in pore water pressure induced by seepage flow have a significant effect on the time-dependent effective stress field of rheological rock mass. After certain simplification of the force field problem of a twin tunnel of arbitrary size and arrangement in a viscoelastic rock body under the influence of seepage, the complex function method, the Schwartz alternation method, and the elastic-viscoelastic correspondence principle were used to achieve an analytical solution of the problem of weakly coupled fluid-solid coupling, and the solution was given. In terms of mechanical mechanism, the solution reflected the surface force effect and flow effect of seepage on the force field. The analytical results were consistent with the numerical results and field measurements, which verified the correctness of the model. The analytical model provided a means to validate the numerical model, and also provided a quick analysis and determination method for the time-related stability problems of multi-tunnels in water-rich areas during the excavation and operation phases. Based on the analytical model, the effects of tunnel clearances and coefficients of viscosity on stress and displacement over time were analyzed. The results show that: Even considering the steady-state seepage condition, the effective stress of the rock masses increases over time. For cases with the same viscosity properties, the convergence rate of stresses is faster than displacements. In addition, the existence of seepage flow can significantly increase the interactions between twin tunnels. Specifically, the difference in stress compared to the single tunnel value is less than 10% when the pillar width is greater than 6.6 times the tunnel radius, however, it is 4 times for purely mechanical problems.
[1] Wu D, Zhang Y L, Zhao R K, et al. A coupled thermal-hydraulic-mechanical application for subway tunnel[J]. Computers and Geotechnics, 2017, 84: 174-182.
[2] Lee I M, Nam S W. Effect of tunnel advance rate on seepage forces acting on the underwater tunnel face[J]. Tunnelling and Underground Space Technology, 2004, 19(3): 273-281.
[3] Cheng X S, Zhang S L, Zhou X H, et al. Parameter analysis of excavation face stability of shield tunnel under high water pressure seepage[J]. Physics and Chemistry of the Earth, Parts A/B/C, 2022, 128: 103218.
[4] Huang M, Li S, Yu J, et al. Continuous field based upper bound analysisfor three-dimensional tunnel face stability in undrained clay[J]. Computers and Geotechnics, 2018, 94: 207-213.
[5] 王华宁, 宋飞, 曾广尚. 隧道工程解析方法及解析模型研究进展[J].力学季刊,2023,44(2): 227-257.
[6] Zhang B Q, Chen F Q, Wang Q Y. Elastoplastic solutions for surrounding rock masses of deep-buried circular tunnels with non-darcian flow[J]. International Journal of Geomechanics, 2019, 19(7): 04019065.
[7] 张丙强, 王启云, 臧万军. 非达西渗流效应对深埋圆形隧洞弹塑性解的影响[J]. 铁道学报, 2018, 40(8): 139-145.
[8] 和晓楠, 周晓敏, 郭小红, 等. 深埋隧道注浆加固围岩非达西渗流场及应力场解析[J]. 中国公路学报, 2020, 33(12): 200-211.
[9] 汪优, 王星华, 陈俊儒.考虑渗流的海底隧道围岩弹塑性分析[J].公路交通科技, 2012, 29(5): 89-95.
[10] Carranza-Torres C, Zhao J. Analytical and numerical study of the effect of water pressure on the mechanical response of cylindrical lined tunnels in elastic and elasto-plastic porous media[J]. International Journal of Rock Mechanics and Mining Sciences, 2009, 46(3): 531-547.
[11] Zareifard M R, Shekari M R. Comprehensive solutions for underwater tunnels in rock masses with different GSI values considering blast-induced damage zone and seepage forces[J]. Applied Mathematical Modelling, 2021, 96: 236-268.
[12] Zhang Q, Shao C, Su H J, et al. A closed-form hydraulic-mechanical coupling solution of a circular tunnel in elastic-brittle-plastic rock mass[J]. European Journal of Environmental and Civil Engineering, 2020, 26(8): 3594-3611.
[13] 俞凯木, 俞缙, 周雨晴. 考虑孔隙水压劣化作用的围岩黏弹性变形解[J]. 铁道科学与工程学报, 2016, 13(6): 1046-1052.
[14] Zou J F, Xia Z Q, Xu Y. Nonlinear visco-elasto-plastic solution of surrounding rock considering seepage force and 3-D Hoek-Brown failure criterion[J]. International Journal of Geotechnical Engineering, 2017, 11(3): 302-315.
[15] Sokolnikoff I S, Mathematical Theory of Elasticity, 2nd ed[M]. McGraw-Hill, New York, 1956.
[16] Fu J Y, Yang J S, Yan L, et al. An analytical solution for deforming twin-parallel tunnels in an elastic half plane[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2015, 39(5): 524-538.
[17] Zhang L Q, Yue Z Q, Lee C F, et al. Stress solution of multiple elliptic hole problem in plane elasticity[J]. Journal of Engineering Mechanics, 2003, 129 (12): 1394-1407.
[18] Zhang L Q, Lu A Z, Yue Z Q, et al. An efficient and accurate iterative stress solution for an infinite elastic plate around two elliptic holes, subjected to uniform loads on the hole boundaries and at infinity[J]. European Journal of Mechanics A/Solids, 2009, 28 (1): 189-193.
[19] Lin L B, Lu Y P, Chen F Q. An analytical solution for stress and displacement field for arbitrarily positioned twin-tunnel excavation at great depth[J]. Mathematical Problems in Engineering, 2018, 2018: 2947970.
[20] Wang H N, Gao X, Wu L, et al. Analytical study on interaction between existing and new tunnels parallel excavated in semi-infinite viscoelastic ground[J]. Computers and Geotechnics, 2020, 120: 103385.
[21] Zeng G S, Wang H N, Wu L, et al. A generalized analytical model for mechanical responses of rock during multiple-tunnel excavation in viscoelastic semi-infinite ground[J]. International Journal of Geomechanics, 2021, 21(11): 04021202.
[22] Zareifard M R, Fahimifar A. A simplified solution for stresses around lined pressure tunnels considering non-radial symmetrical seepage flow[J]. KSCE Journal of Civil Engineering, 2016, 20(7): 2640-2654.
[23] Kargar A R, Rahmannejad R, Hajabasi M A. The stress state around lined non-circular hydraulic tunnels below the water table using complex variable method[J]. International Journal of Rock Mechanics and Mining Sciences, 2015, 78: 207-216.
[24] Do D P, Tran N H, Dang H L, et al. Closed-form solution of stress state and stability analysis of wellbore in anisotropic permeable rocks[J]. International Journal of Rock Mechanics and Mining Sciences, 2019, 113: 11-23.
[25] Bobet A, Yu H. Stress field near the tip of a crack in a poroelastic transversely anisotropic saturated rock[J]. Engineering Fracture Mechanics, 2015, 141: 1-18.
[26] Ying H W, Zhu C W, Shen H W, et al. Semi-analytical solution for groundwater ingress into lined tunnel[J]. Tunnelling and Underground Space Technology, 2018, 76: 43-47.
[27] Wang H N, Utili S, Jiang M J, et al. Analytical solutions for tunnels of elliptical cross-section in rheological rock accounting for sequential excavation[J]. Rock Mechanics and Rock Engineering, 2015, 48(5): 1997-2029.
[28] Wang H N, Zeng G S, Utili S, et al. Analytical solutions of stresses and displacements for deeply buried twin tunnels in viscoelastic rock[J]. International Journal of Rock Mechanics and Mining Sciences, 2017, 93: 13-29.
[29] Song F, Wang H N, Jiang M J. Analytically-based simplified formulas for circular tunnels with two liners in viscoelastic rock under anisotropic initial stresses[J] , Construction and Building Materials, 2018, 175: 745-767.
[30] 卿三惠, 黄润秋. 乌鞘岭特长隧道软弱围岩大变形特性研究[J]. 现代隧道技术, 2005, 42(2): 7-14.
[31] 陶波, 伍法权, 郭啟良, 等. 高地应力环境下乌鞘岭深埋长隧道软弱围岩流变规律实测与数值分析研究[J]. 岩石力学与工程学报, 2006(9): 1828-1834.
