隧道纵向地震反应最不利时刻的确定及其应用
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摘要
《城市轨道交通结构抗震设计规范》(GB 50909―2014)建议的隧道结构纵向反应位移法,采用梁-地基弹簧计算模型,以自由场位移时程为等效地震作用,在一定程度上考虑了地震作用下土和结构之间相互作用,能够反映不同频谱成分地震波对结构纵向地震反应的影响。该文给出了根据自由场地震反应确定隧道结构纵向最不利变形和内力发生时刻,即最不利时刻的确定方法。采用规范纵向反应位移法,完成了出平面剪切波斜入射下北京某盾构隧道结构纵向地震反应计算,并应用最不利时刻的概念将规范方法在地震动持时内所有时间步的静力计算转化为单一时间步的静力计算,与动力时程法计算结果进行了对比。结果表明,规范方法得到的隧道结构位移值和弯矩值与动力时程法较为接近,但由于离散的地基弹簧不能有效模拟地基土对地下结构真实的约束条件,使得轴力和剪力结果存在较大误差;应用最不利时刻的概念,在一定程度上提高了计算效率,同时降低了隧道纵向地震反应(尤其是剪力)的计算误差。
The longitudinal response deformation method suggested by the "Code for Seismic Design of Urban Rail Transit Structures" is a kind of pseudo-static method, which can be introduced to seismic response analysis of tunnel structures. It builds a beam-foundation spring model, taking dynamic free-field displacement time-history as the equivalent input. This paper put forward a way of determining the critical moment when longitudinal maximal deformation and internal force of a tunnel structure occur. The standard method was adopted to obtain the longitudinal seismic responses of a certain shield tunnel construction under SH wave oblique incidence, with the dynamic time-history method being an accurate reference. Critical moments were then applied to simplify the computational procedure from all time steps to a single step during the seismic wave duration. Although the structural displacements and bending moments calculated by the standard were close to those obtained by the dynamic time-history method, it may bring large errors of structural axial and shear forces caused by the discrete foundation springs. The application of critical moments could increase the computational efficiency,simultaneously reducing the calculation error of structural internal forces, especially that of the shear forces.
The longitudinal response deformation method suggested by the "Code for Seismic Design of Urban Rail Transit Structures" is a kind of pseudo-static method, which can be introduced to seismic response analysis of tunnel structures. It builds a beam-foundation spring model, taking dynamic free-field displacement time-history as the equivalent input. This paper put forward a way of determining the critical moment when longitudinal maximal deformation and internal force of a tunnel structure occur. The standard method was adopted to obtain the longitudinal seismic responses of a certain shield tunnel construction under SH wave oblique incidence, with the dynamic time-history method being an accurate reference. Critical moments were then applied to simplify the computational procedure from all time steps to a single step during the seismic wave duration. Although the structural displacements and bending moments calculated by the standard were close to those obtained by the dynamic time-history method, it may bring large errors of structural axial and shear forces caused by the discrete foundation springs. The application of critical moments could increase the computational efficiency,simultaneously reducing the calculation error of structural internal forces, especially that of the shear forces.
引文
[1]GB 50909―2014,城市轨道交通结构抗震设计规范[S].北京:中国计划出版社,2014.GB 50909―2014,Code for seismic design of urban rail transit structures[S].Beijing:China Planning Press,2014.(in Chinese)
[2]何川,张景,封坤.盾构隧道结构计算分析方法研究[J].中国公路学报,2017,30(8):1―14.He Chuan,Zhang Jing,Feng Kun.Research on structural analysis method of shield tunnels[J].China Journal of Highway and Transport,2017,30(8):1―14.(in Chinese)
[3]刘晶波,王东洋,谭辉,等.隧道纵向地震反应分析的整体式反应位移法[J].工程力学,2018,35(10):17―26.Liu Jingbo,Wang Dongyang,Tan Hui,et al.Integral response displacement method for longitudinal seismic response analysis of tunnel structure[J].Engineering Mechanics,2018,35(10):17―26.(in Chinese)
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[7]刘晶波,王艳.成层半空间中平面内自由波场的一维化时域算法[J].工程力学,2007,24(7):16―22.Liu Jingbo,Wang Yan.A 1D time-domain method for in-plane wave motion of free field in layered media[J].Engineering Mechanics,2007,24(7):16―22.(in Chinese)
[8]刘晶波,王振宇,杜修力,等.波动问题中的三维时域粘弹性人工边界[J].工程力学,2005,22(6):46―51.Liu Jingbo,Wang Zhenyu,Du Xiuli,et al.Threedimensional visco-elastic artificial boundaries in three-domain for wave motion problems[J].Engineering Mechanics,2005,22(6):46―51.(in Chinese)
[9]刘晶波,吕彦东.结构-地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998(3):55―64.Liu Jingbo,LüYandong.A direct method for analysis of dynamic soil-structure interaction[J].China Civil Engineering Journal,1998(3):55―64.(in Chinese)
[10]李英民,王璐,刘阳冰,等.地下结构抗震计算地基弹簧系数取值方法研究[J].地震工程与工程振动,2012,32(1):106―113.Li Yingmin,Wang Lu,Liu Yangbing,et al.Analysis of methods for determining the spring constant of ground foundation in seismic design of underground structures[J].Earthquake Engineering and Engineering Dynamics,2012,32(1):106―113.(in Chinese)
[11]许成顺,许紫刚,杜修力,等.地下结构抗震简化分析方法比较研究[J].地震工程与工程振动,2017,37(2):65―80.Xu Chengshun,Xu Zigang,Du Xiuli,et al.Comparative study of simplified methods for seismic analysis of underground structure[J].Earthquake Engineering and Engineering Dynamics,2017,37(2):65―80.(in Chinese)
[2]何川,张景,封坤.盾构隧道结构计算分析方法研究[J].中国公路学报,2017,30(8):1―14.He Chuan,Zhang Jing,Feng Kun.Research on structural analysis method of shield tunnels[J].China Journal of Highway and Transport,2017,30(8):1―14.(in Chinese)
[3]刘晶波,王东洋,谭辉,等.隧道纵向地震反应分析的整体式反应位移法[J].工程力学,2018,35(10):17―26.Liu Jingbo,Wang Dongyang,Tan Hui,et al.Integral response displacement method for longitudinal seismic response analysis of tunnel structure[J].Engineering Mechanics,2018,35(10):17―26.(in Chinese)
[4]Idriss I M,Sun J I.SHAKE91:A computer program for conducting equivalent linear seismic response analysis of horizontally layered soil deposits[R].California:University of California,1992.
[5]Barder J P,Ichii K,Lin C H.EERA:A computer program for equivalent-linear earthquake site response analysis of layered soil deposits[R].Los Angeles:University of Southern California,2000.
[6]刘晶波,王艳.成层半空间出平面自由波场的一维化时域算法[J].力学学报,2006,38(2):219―225.Liu Jingbo,Wang Yan.A 1-D time-domain method for2-D wave motion in elastic layered half-space by anti-plane wave oblique incidence[J].China Journal of Theoretical and Applied Mechanic,2006,38(2):219―225.(in Chinese)
[7]刘晶波,王艳.成层半空间中平面内自由波场的一维化时域算法[J].工程力学,2007,24(7):16―22.Liu Jingbo,Wang Yan.A 1D time-domain method for in-plane wave motion of free field in layered media[J].Engineering Mechanics,2007,24(7):16―22.(in Chinese)
[8]刘晶波,王振宇,杜修力,等.波动问题中的三维时域粘弹性人工边界[J].工程力学,2005,22(6):46―51.Liu Jingbo,Wang Zhenyu,Du Xiuli,et al.Threedimensional visco-elastic artificial boundaries in three-domain for wave motion problems[J].Engineering Mechanics,2005,22(6):46―51.(in Chinese)
[9]刘晶波,吕彦东.结构-地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998(3):55―64.Liu Jingbo,LüYandong.A direct method for analysis of dynamic soil-structure interaction[J].China Civil Engineering Journal,1998(3):55―64.(in Chinese)
[10]李英民,王璐,刘阳冰,等.地下结构抗震计算地基弹簧系数取值方法研究[J].地震工程与工程振动,2012,32(1):106―113.Li Yingmin,Wang Lu,Liu Yangbing,et al.Analysis of methods for determining the spring constant of ground foundation in seismic design of underground structures[J].Earthquake Engineering and Engineering Dynamics,2012,32(1):106―113.(in Chinese)
[11]许成顺,许紫刚,杜修力,等.地下结构抗震简化分析方法比较研究[J].地震工程与工程振动,2017,37(2):65―80.Xu Chengshun,Xu Zigang,Du Xiuli,et al.Comparative study of simplified methods for seismic analysis of underground structure[J].Earthquake Engineering and Engineering Dynamics,2017,37(2):65―80.(in Chinese)