土岩变化地层长隧道纵向地震响应解析解
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摘要
土岩地层交界面是制约长隧道结构抗震安全的关键控制节点,但现有设计方法均未考虑隧道沿其纵向的地层变化。基于隧道的动力响应特点提出力学模型,将隧道沿纵向简化为两段处于不同地层条件中的半无限长弹性地基梁。通过求解结构的位移微分控制方程,推导出土岩变化地层长隧道纵向地震响应的解析表达式,并引入位移相位角模拟行波效应,提出了面向工程设计的土岩变化地层长隧道纵向抗震简化分析方法。通过与有限元基准模型在相同条件下的对比分析,验证了该方法的有效性。最后应用该解析公式进行参数敏感性分析,揭示了结构刚度、地层剪切波速比等关键因素对土岩变化地层隧道结构地震响应的影响规律:隧道结构刚度越大,结构内力响应越剧烈,隧道地层突变段的内力峰值差越大,地层突变的影响范围也随之变宽;地层剪切波速比越大,隧道地层突变段的内力峰值差越大,但地层突变的影响范围却不受影响。
The contact between soil and rock is the controlling point in the seismic design of long tunnels, which has not been considered in any design methods yet. The mechanical model for a long tunnel crossing soil-rock stratum is proposed with assumptions based on its dynamic response characteristics, in which two semi-infinite elastic foundation beams in different soils are assumed to model the behaviors of the tunnel. An analytical solution for longitudinal seismic responses of tunnels crossing soil-rock stratum is derived by solving the displacement differential governing equations. The simplified method for longitudinal seismic responses of tunnels crossing soil-rock stratum is proposed. The traveling wave effect can be considered by introducing the displacement phase angle. A benchmark model, a finite element model for a long tunnel crossing soil-rock stratum, is used to calibrate the proposed method. Comparison under the same parameters shows a high degree of consistency between them, which verifies the efficiency of the innovative method. Finally, sensitivity analyses of parameters are carried out using the proposed analytic formulas, and the influences of parameters on seismic response of tunnels crossing soil-rock stratum are revealed. The results suggest that with the increase of the structural stiffness, the internal force response of the tunnel becomes larger, the difference of the values of the peak internal forces becomes greater, and the zone of influence of the transition becomes wider. With the increase of shear velocity ratio of soils, the difference of the values of the peak internal forces becomes greater but the zone of influence of the transition remains unchanged.
The contact between soil and rock is the controlling point in the seismic design of long tunnels, which has not been considered in any design methods yet. The mechanical model for a long tunnel crossing soil-rock stratum is proposed with assumptions based on its dynamic response characteristics, in which two semi-infinite elastic foundation beams in different soils are assumed to model the behaviors of the tunnel. An analytical solution for longitudinal seismic responses of tunnels crossing soil-rock stratum is derived by solving the displacement differential governing equations. The simplified method for longitudinal seismic responses of tunnels crossing soil-rock stratum is proposed. The traveling wave effect can be considered by introducing the displacement phase angle. A benchmark model, a finite element model for a long tunnel crossing soil-rock stratum, is used to calibrate the proposed method. Comparison under the same parameters shows a high degree of consistency between them, which verifies the efficiency of the innovative method. Finally, sensitivity analyses of parameters are carried out using the proposed analytic formulas, and the influences of parameters on seismic response of tunnels crossing soil-rock stratum are revealed. The results suggest that with the increase of the structural stiffness, the internal force response of the tunnel becomes larger, the difference of the values of the peak internal forces becomes greater, and the zone of influence of the transition becomes wider. With the increase of shear velocity ratio of soils, the difference of the values of the peak internal forces becomes greater but the zone of influence of the transition remains unchanged.
引文
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[10]LI P,SONG E X.Three-dimensional numerical analysis for the longitudinal seismic response of tunnels under an asynchronous wave input[J].Computers and Geotechnics,2015,63:229-243.
[11]HASHASH Y M A,HOOK J J,SCHMIDT B,et al.Seismic design and analysis of underground structures[J].Tunnelling and Underground Space Technology,2001,16(4):247-293.
[12]JOHN C M S,ZAHRAH T F.Aseismic design of underground structures[J].Tunnelling and Underground Space Technology,1987,2(2):165-197.
[13]李鹏.饱和地基中隧道纵向地震反应的数值分析[D].北京:清华大学,2013.(LI Peng.Numerical analysis for longitudinal seismic response of tunnels in saturated soils[D].Beijing:Tsinghua University,2013.(in Chinese))
[14]廖少明.圆形隧道纵向剪切传递效应研究[D].上海:同济大学,2002.(LIAO Shao-ming.Study on the longitudinal shear transfer effect of circular tunnels[D].Shanghai:Tongji University,2002.(in Chinese))
[15]IDRISS IM,SUN J.User’s manual for SHAKE91?Acomputer program for conducting equivalent linear seismic response analyses of horizontally layered soil deposits center for geotechnical modeling[R].Davis:Department of Civil and Environmental Engineering,University of California,1992.
[16]YU H T,CHEN J T,YUAN Y,et al.Seismic damage of mountain tunnels during the 5.12 Wenchuan earthquake[J].Journal of Mountain Science,2016,13(11):1958-1972.
[17]YU H T,CHEN J T,BOBET A,et al.Damage observation and assessment of the Longxi tunnel during the Wenchuan earthquake[J].Tunnelling and Underground Space Technology,2016,54:102-116.
[18]禹海涛,袁勇.长大隧道地震响应分析与试验方法新进展[J].中国公路学报,2018,31(10):19-35.(YU Hai-tao,YUAN Yong.Review on seismic response analysis and test methods for long and large tunnels[J].China Journal of Highway and Transport,2018,31(10):19-35.(in Chinese))
[2]川岛一彦.地下构筑物の耐震设计[M].鹿岛:鹿岛出版会,1994.(KAWAJIMA K.Aseismic design of underground structure[M].Kajima:Kajima Institute Publishing Co,Ltd.1994.(in Chinese))
[3]赵武胜,何先志,陈卫忠,等.盾构隧道与竖井连接处管片及接头震害分析[J].岩石力学与工程学报,2012,31(增刊2):3847-3854.(ZHAO Wu-sheng,HE Xian-zhi,CHENWei-zhong,et al.Analysis of seismic damage of segments and joints at the junction of shield tunnel and shaft[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(S2):3847-3854.(in Chinese))
[4]张景,何川,耿萍,等.穿越软硬突变地层盾构隧道纵向地震响应振动台试验研究[J].岩石力学与工程学报,2017,36(1):68-77.(ZHANG Jing,HE Chuan,GENG Ping,et al.Shaking table tests on longitudinal seismic response of shield tunnel through soft-hard stratum junction[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(1):68-77.(in Chinese))
[5]STAMOS A A,BESKOS D E.Dynamic analysis of large 3-Dunderground structures by the BEM[J].Earthquake Engineering and Structural Dynamics,1995,24(6):917-934.
[6]STAMOS A A,BESKOS D E.3-D seismic response analysis of long lined tunnels in half-space[J].Soil Dynamics and Earthquake Engineering,1996,15(2):111-118.
[7]PARK D,SAGONG M,KWAK D Y,et al.Simulation of tunnel response under spatially varying ground motion[J].Soil Dynamics and Earthquake Engineering,2009,29(11/12):1417-1424.
[8]YU H T,YUAN Y,BOBET A.Multiscale method for long tunnels subjected to seismic loading[J].International Journal for Numerical and Analytical Methods in Geomechanics,2013,37(4):374-398.
[9]YU H T,YUAN Y,QIAO Z Z,et al.Seismic analysis of a long tunnel based on multi-scale method[J].Engineering Structures,2013,49(2):572-587.
[10]LI P,SONG E X.Three-dimensional numerical analysis for the longitudinal seismic response of tunnels under an asynchronous wave input[J].Computers and Geotechnics,2015,63:229-243.
[11]HASHASH Y M A,HOOK J J,SCHMIDT B,et al.Seismic design and analysis of underground structures[J].Tunnelling and Underground Space Technology,2001,16(4):247-293.
[12]JOHN C M S,ZAHRAH T F.Aseismic design of underground structures[J].Tunnelling and Underground Space Technology,1987,2(2):165-197.
[13]李鹏.饱和地基中隧道纵向地震反应的数值分析[D].北京:清华大学,2013.(LI Peng.Numerical analysis for longitudinal seismic response of tunnels in saturated soils[D].Beijing:Tsinghua University,2013.(in Chinese))
[14]廖少明.圆形隧道纵向剪切传递效应研究[D].上海:同济大学,2002.(LIAO Shao-ming.Study on the longitudinal shear transfer effect of circular tunnels[D].Shanghai:Tongji University,2002.(in Chinese))
[15]IDRISS IM,SUN J.User’s manual for SHAKE91?Acomputer program for conducting equivalent linear seismic response analyses of horizontally layered soil deposits center for geotechnical modeling[R].Davis:Department of Civil and Environmental Engineering,University of California,1992.
[16]YU H T,CHEN J T,YUAN Y,et al.Seismic damage of mountain tunnels during the 5.12 Wenchuan earthquake[J].Journal of Mountain Science,2016,13(11):1958-1972.
[17]YU H T,CHEN J T,BOBET A,et al.Damage observation and assessment of the Longxi tunnel during the Wenchuan earthquake[J].Tunnelling and Underground Space Technology,2016,54:102-116.
[18]禹海涛,袁勇.长大隧道地震响应分析与试验方法新进展[J].中国公路学报,2018,31(10):19-35.(YU Hai-tao,YUAN Yong.Review on seismic response analysis and test methods for long and large tunnels[J].China Journal of Highway and Transport,2018,31(10):19-35.(in Chinese))
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