A wave numerical method for seismic response of tunnels in bedding strata
HU Hongyun1，2，ZHOU Xiaojun1，2，WANG Jinghe1，2
(1. Key Laboratory of Transportation Tunnel Engineering，Ministry of Education，Southwest Jiaotong University，Chengdu，Sichuan 610031，China；2. School of Civil Engineering，Southwest Jiaotong University，Chengdu，Sichuan 610031，China)
Abstract：The bedding rock mass is a common geological configuration in tunnel engineering. The seismic damage occurs frequently in the bedding strata，but there is no effective method of seismic response analysis. In this paper，a method of seismic wave input and a corresponding formula were established. The method combines the FEM with the analysis of the time-domain wave and adopts the visco-elastic artificial boundary. The transverse isotropic constitutive law of bedding rock mass is used with the consideration of the characteristics of polarization and phase velocity change of the seismic wave in rock mass. The method is applicable to the case of the oblique incidence direction of earthquake wave in parallel with the longitudinal section of the tunnel. In order to verify the feasibility of the method，the seismic response of a high-speed railway tunnel in a bedding rock mass was studied. The results show that，when the rock layer is horizontal or vertical，the qP wave causes the symmetric internal force envelope of lining. When the rock layer is inclined，the qP wave causes the asymmetric internal force envelope，and the amplitude of the asymmetry correlates to the dip angle of the rock layer. When the dip angles of rock layers are different，the difference of bending moments is larger. The maximum of hoop bending moment is located at the arch foot，while the maximum longitudinal bending moment is located at the vault and invert no matter the moment envelope is symmetrical or not. When the rock layer is simplified as the isotropic medium，the P wave causes the symmetric internal force envelope，which is close to the results when the rock layer is simplified as the transversely isotropic medium. The findings further verify the rationality and reliability of the method.
[1] OKAMOTO S. Introduction to earthquake engineering[M]. 2nd Edition. Tokyo：University of Tokyo Press，1984：1–571.
[2] SHARMA S，JUDD W R. Underground opening damage from earthquakes[J]. Engineering Geology，1991，30(3/4)：263–276.
[3] 吉随旺，唐永建，胡德贵，等. 四川省汶川地震灾区干线公路典型震害特征分析[J]. 岩石力学与工程学报，2009，28(6)：1 250–1 260. (JI Suiwang，TANG Yongjian，HU Degui，et al. Analysis of typical seismic damages of highways in Wenchuan earthquake-induced hazard areas in Sichuan province[J]. Chinese Journal of Rock Mechanics and Engineering，2009，28(6)：1 250–1 260.(in Chinese))
[4] ST JOHN C M，ZAHRAH T F. Aseismic design of underground structures[J]. Tunnelling and Underground Space Technology，1987，2(2)：165–197.
[5] YOUSSEF M A H，JEFFREY J H，BIRGER S，et al. Seismic design and analysis of underground structures[J]. Tunnelling and Underground Space Technology，2001，16(4)：247–293.
[6] MIRKO C，LAURA S，CARLO G，et al. Seismic analysis of deep tunnels in near fault conditions：a case study in Southern Italy[J]. Bull Earthquake Engineering，2011，19(4)：975–995.
[7] SHEN Y H，GAO B，YANG X M，et al. Seismic damage mechanism and dynamic deformation characteristic analysis of mountain tunnel after Wenchuan earthquake[J]. Engineering Geology，2014，180(8)：85–98.
[8] ESMAEILI M，VAHDANI S，NOORZAD A. Dynamic response of lined circular tunnel to plane harmonic waves[J]. Tunnelling and Underground Space Technology，2006，21(5)：511–519.
[9] PARK K H，TANTAYOPIN K，TONTAVANICHB，et al. Analytical solution for seismic-induced ovaling of circular tunnel lining under no-slip interface conditions：A revisit[J]. Tunnelling and Underground Space Technology，2009，24(2)：231–235.
[10] CILINGIR U，GOPAL MADABHUSHI S P. A model study on the effects of input motion on the seismic behaviour of tunnels[J]. Soil Dynamics and Earthquake Engineering，2011，31(3)：452–462.
[11] KOURETZIS G P，SLOAN SCOTT W，CARTER JOHN P. Effect of interface friction on tunnel liner internal forces due to seismic S- and P-wave propagation[J]. Soil Dynamics and Earthquake Engineering，2013，46(4)：41–51.
[12] 崔光耀，王明年，于 丽，等. 断裂黏滑隧道减震缝减震技术模型试验研究[J]. 岩石力学与工程学报，2013，32(8)：1 603–1 609.(CUI Guangyao，WANG Mingnian，YU Li，et al. Model test study of shock absorption joint damping technology of crossing stick-slip fracture tunnel[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(8)：1 603–1 609.(in Chinese))
[13] 徐 华，李天斌，王 栋，等. 山岭隧道地震动力响应规律的三维振动台模型试验研究[J]. 岩石力学与工程学报，2013，32(9)：1 762–1 771.(XU Hua，LI Tianbin，WANG Dong，et al. Study of seismic responses of mountain tunnels with 3D shaking table model test[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(9)：1 762–1 771.(in Chinese))
[14] 何 川，李 林，张 景，等. 隧道穿越断层破碎带震害机制研究[J]. 岩土工程学报，2014，36(3)：427–434.(HE Chuan，LI Lin，ZHANG Jing，et al. Seismic damage mechanism of tunnels through fault zones[J]. Chinese Journal of Geotechnical Engineering，2014，36(3)：427–434.(in Chinese))
[15] 仇文革，胡 辉，赵 斌. 长大隧道穿越断层带减震结构数值解析研究[J]. 岩土工程学报，2013，35(2)：252–257.(QIU Wenge，HU Hui，ZHAO Bin. Numerical analysis of damping structure of deep buried tunnel crossing fault zone[J]. Chinese Journal of Geotechnical Engineering，2013，35(2)：252–257.(in Chinese))
[16] 李育枢. 山岭隧道地震动力响应及减震措施研究——以国道318线黄草坪隧道为例[博士学位论文][D]. 上海：同济大学，2006.(LI Yushu. Study on earthquake responses and vibration-absorption measures for mountain tunnel——a case study of Huangcaoshan tunnel on NO.318 national highway[Ph. D. Thesis][D]. Shanghai：Tongji University，2006.(in Chinese))
[17] 黄 胜. 高烈度地震下隧道破坏机制及抗震研究[博士学位论文][D]. 武汉：中国科学院武汉岩土力学研究所，2010.(HUANG Sheng. Research on failure mechanism and aseismic measures for underground engineering under high intensity earthquake[Ph. D. Thesis][D]. Wuhan：Institute of Rock and Soil Mechanics，Chinese Academy of Sciences，2010.(in Chinese))
[18] 耿 萍，何 悦，何 川，等. 穿越断层破碎带隧道合理抗震设防长度研究[J]. 岩石力学与工程学报，2014，33(2)：358–365.(GENG Ping，HE Yue，HE Chuan，et al. Research on reasonable aseismic fortified length for tunnel through fault fracture zone[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(2)：358–365.(in Chinese))
[19] 李积栋，陶连金，吴秉林，等. 密贴交叉隧道在强震作用下的三维动力响应分析[J]. 现代隧道技术，2014，51(1)：26–31.(LI Jidong，TAO Lianjin，WU Binglin，et al. Analysis of 3D Dynamic response of closely overlapping tunnels during a strong earthquake[J]. Modern Tunnelling Technology，2014，51(1)：26–31.(in Chinese))
[20] 王峥峥，高 波，李 斌，等. 跨断层隧道振动台模型试验研究Ⅰ：试验方案设计[J]. 现代隧道技术，2014，51(2)：50–55.(WANG Zhengzheng，GAO Bo，LI Bin，et al. Experimental study using a shaking table model for a tunnel passing through faults(Part I)：test scheme design[J]. Modern Tunnelling Technology，2014，51(2)：50–55.(in Chinese))
[21] THOMSEN L. Weak elastic anisotropy[J]. Geophysics，1986，51(10)：1 954–1 966.
[22] 梁 锴. TI介质地震波传播特征与正演方法研究[博士学位论文][D]. 东营：中国石油大学，2009.(LIANG Kai. The study on propagation feature and forward modeling of seismic wave in TI media[Ph. D. Thesis][D]. Dongying：China University of Petroleum，2009.(in Chinese))
[23] 吴国忱，梁 锴，印兴耀. TTI介质弹性波相速度与偏振特征分析[J]. 地球物理学报，2010，53(8)：1 914–1 923.(WU Guochen，LIANG Kai，YIN Xingyao. The analysis of phase velocity and polarization feature for elastic wave in TTI media[J]. Chinese Journal of Geophysics，2010，53(8)：1 914–1 923.(in Chinese))
[24] 吴国忱，梁 锴，戚艳平. 三维TTI介质相速度和群速度[J]. 地球物理学进展，2009，24(6)：2 097–2 105.(WU Guochen，LIANG Kai，QI Yanping. Phase velocity and group velocity in 3D TTI media[J]. Progress in Geophysics，2009，24(6)：2 097–2 105.(in Chinese))
[25] 尤红兵，赵凤新，荣棉水. 地震波斜入射时水平层状场地的非线性地震反应[J]. 岩土工程学报，2009，31(2)：234–240.(YOU Hongbing，ZHAO Fenxin，RONG Mianshui. Nonlinear seismic response of horizontal layered site due to inclined wave[J]. Chinese Journal of Geotechnical Engineering，2009，31(2)：234–240.(in Chinese))
[26] 廖振鹏. 工程波动理论导论[M]. 北京：科学出版社，2002：141–155.(LIAO Zhenpeng. Introduction to wave motion theories in engineering[M]. Beijing：Science Press，2002：141–155.(in Chinese))
[27] 何建涛，马怀发，张伯艳，等. 黏弹性人工边界地震动输入方法及实现[J]. 水利学报，2010，41(8)：960–969.(HE Jiantao，MA Huaifa， ZHANG Boyan，et al. Method and realization of seismic motion input of viscous-spring boundary[J]. Journal of Hydraulic Engineering，2010，41(8)：960–969.(in Chinese))
[28] 徐海滨. 地震波斜入射对拱坝地震反应的影响[硕士学位论文][D]. 北京：北京工业大学，2010.(XU Haibing. Effect of oblique incidence of seismic wave on seismic response of arch dam[M. S. Thesis][D]. Beijing：Beijing University of Technology，2010.(in Chinese))
[29] 杜修力，赵 密，王进廷. 近场波动模拟的人工应力边界条件[J]. 力学学报，2006，38(1)：49–56.(DU Xiuli，ZHAO Mi，WANG Tingjin. A stress artificial boundary in FEA for near-field wave problem[J]. Chinese Journal of Theoretical and Applied Mechanics，2006，38(1)：49–56.(in Chinese))
[30] WINTERSTEIN D F. Velocity anisotropy terminology for geophysicists[J]. Geophysics，1990，55(8)：1 070–1 088.
[31] 刘晶波，杜义欣，闫秋实. 黏弹性人工边界及地震动输入在通用有限元软件中的实现[J]. 防灾减灾工程学报，2007，2(增)：37–42. (LIU Jingbo，DU Yixin，YAN Qiushi. Realization of viscoelastic boundary and seismic input in finite element software[J]. Journal of Disaster Prevention and Mitigation Engineering，2007，2(Supp.)：37–42.(in Chinese))
[32] 朱泽奇，盛 谦，梅松华，等. 改进的遍布节理模型及其在层状岩体地下工程中的应用[J]. 岩土力学，2009，30(10)：3 115–3 121. (ZHU Zeqi，SHENG Qian，MEI Songhua，et al. Improved ubiquitous- joint model and its application to underground engineering in layered rock masses[J]. Rock and Soil Mechanics，2009，30(10)：3 115–3 121. (in Chinese))
2017, Vol. 36 
