地铁车站地震破坏机理及密贴组合结构的地震响应研究
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摘要
随着轨道交通的发展和地铁施工技术的日臻成熟，车站和区间隧道断面形式逐渐演化，换乘车站逐渐增多，车站的空间交叉现象愈来愈普遍。地铁结构形式的多样化及空间结构组合的普遍性是未来地铁发展的必然趋势。对于地铁换乘站或交通枢纽，车站-车站、车站-区间隧道相互空间交叉，再加上其间的连接通道，构成了错综复杂、相互影响的地下空间结构体。地震作用下，由于在交叉、连接等部位的地基位移分布不同，较一般地下结构更易产生较大变形和附加内力；此外，地震波在结构上引起的横向剪切变形，会导致连带结构处于纵向拉压或弯曲的复杂应力状态，即整个地下立体式交叉结构在地震作用下的变形受力状态更加复杂，且相互作用更加显著。
本文依托国家973课题―城市地下基础设施的地震破坏与抗震理论（2007CB714203）‖和北京市自然科学基金重点项目―地铁车站立体交叉结构地震响应及抗震设计方法研究（8111001）‖，根据北京地区地质条件、地铁车站结构形式、车站-隧道典型组合形式等特点，主要从地震作用下地铁车站典型结构的破坏机理、破坏模式和车站-隧道不同组合条件下的地震响应等两个方面进行了相关的分析与研究，具体的研究内容和研究成果如下：
以土体电镜扫描为研究对象，把数字图像处理技术引入土体的细观结构观察和定量分析中，求解土颗粒孔隙度、颗粒粒径及颗粒形状等细观颗粒组成参数，为建立颗粒流离散元细观模型提供物理参数。在基础上，对土样的三轴试验进行模拟，并研究细观力学参数（包括：摩擦系数、平行连接强度及刚度比）对宏观性质的影响。
建立基于典型地铁车站结构大型振动台试验的有限差分-颗粒流离散元耦合模型，对车站结构模型在地震中的地震响应和破坏现象进行模拟分析。在耦合计算模型中，土体采用连续模型、结构采用颗粒流离散元模型模拟，在FLAC边界节点处建立接触面，将FLAC在大应变模式计算的位移通过接触面传输给颗粒流离散元；并将颗粒与接触面计算的相互作用力传输给FLAC，作为施加在各节点上的力，从而实现耦合运算。结果表明，数值模型的计算结果与试验结果能够较好的拟合；地震加载过程中，柱板、墙板节点为地铁车站模型结构的薄弱部位；模型的整个破坏过程和能量转化过程可分为3个阶段；结构的破坏过程可以通过颗粒孔隙率、配位数和接触力的变化以及能量的转化规律反映出来。
设计并开展地铁车站-隧道不同密贴组合结构的振动台试验，建立以覆土厚度为主要控制因素的相似关系处理方法，对不同的组合结构形式输入不同的地震作用，主要研究：自由场振动特性和模型振动前后的动力性质变化以及物性演变过程；单层连拱形地铁结构的地震受力和变形特征以及土-结构相互作用的土压力和位移变化规律；并行隧道结构的地震受力和相互影响规律；地铁车站及隧道结构在不同空间组合形式下的地震响应影响规律。
基于试验结果和建立在振动台试验基础上的FLAC模型模拟分析得到以下规律：模型在振动激励下，土体的自振频率不断降低，阻尼比增加。模型箱的顶部反应位移大于底部，反应加速度则底部大于顶部。模型箱的边界吸波效果良好，且土体具有明显的滤波性质；结构的存在对上部土体的反应加速度具有减弱作用；结构与土的相互作用较为明显，且与埋深，结构尺寸等呈现不同的分布规律；结构墙柱应变大于梁板，节点处应力集中；车站倾斜放置时，结构-土相互作用力受竖向土压力控制；相对于单体车站，结构的应变幅值由墙柱向顶板转移，且分布趋于平均分布；并行隧道结构的存在加剧了对土体剪切波的反射和集中，对单体隧道的反应加速度、动土压力、动应变幅值等均具有放大效应；底部隧道结构的存在对传来的地震波具有吸收作用，使得上部车站的地震响应减弱，且减弱幅度随夹层土体厚度的增加而减小。
With the development of subway and maturation of construction technology, thecross-section form of station and tunnel has been changed. The transfer station hasbeen gradually increased, the phenomenon of space cross-station been increasingcommon. The diversification of subway station structure form and universality ofspace cross-station is the development trend of the future subway. The space-cross ofstation-station and station-tunnel and the connecting channel between them of Metrotransfer station or transport hub constitute a complex interaction of underground spacestructure. A greater deformation and additional internal forces will be generated in theconnection point under earthquake. In addition, the transverse shear deformationcaused by seismic waves in the structure will make another structure in a complexstress state of longitudinal tension or bending. In short, the deformation and stressstate of underground three-dimensional structure under earthquake is more complexand more significant interaction.
This work was financially supported by a grant from the Major State BasicResearch Development Program of China (973Program),‖the earthquake damageand seismic theory of unban underground infrastructure‖. No.2007CB714203, andsupported by Beijing Municipal Natural Science Foundation.‖Study on seismicresponse and design method of three-dimensional intersected underground subwaystructures‖. No.8111001. According to the geological conditions in Beijing, thesubway station structure, and the typical combination of characteristics of station andtunnel, this article focuses on two aspects of analysis and research related to failuremechanism and mode of typical subway station structure and seismic response ofthree-dimensional intersected underground subway structures. The specific researchcontents and results are as follows:
Taking silt soil image photographed by scanning electron microscope as theresearch object, use image treatment technology for microstructure observation andquantitative analysis of soil, solve the parameter of particle composition of soil, suchas porosity, grain diameter and granular shape. These works provide physicalparameters for granular flow model developing. And then simulate the tri-axial test ofthe soil and study the variation rules of property of silt soil with micro-parameters,such as friction coefficient, parallel-bond and stiffness ratio.
A continuum-discrete element coupled model is built based on a large-scaleshaking table test of typical subway station in Beijing, to simulate the seismicresponses and the damage process of subway station structure model. In the couplingmodel, the soil is simulated by finite-difference method, and the structure is simulatedby particle flow code. Interfaces are built between the adjacent nodes on the boundaryof FLAC model and used as walls in PFC. Displacement calculated by FLAC inlarge-strain model transfer to PFC through interfaces, and the interaction force between particle and walls transfer to FLAC, so as to approach the couplingcalculation. The result shows that the experimental results can be well fitted. Theinterior column and nodes of column and plates are weak parts of subway stationstructure model during inputting earthquake waves. The whole damage process andenergy conversion process of structure model can be divided into three phases. Thechange of porosity, average number of contacts and contact force and the energyconversion law can response the damage process of structure model.
Design and carry out shaking table test of different combinations of subwaystation and tunnel. Establish the treatment method of similar ratio with mainlycontrolling factors of over burden quality. Enter the different types of seismic waves.The main contents are as follows: the vibration characteristic of free field and itsdynamic nature of change and evolution of physical properties during the vibration,seismic force and deformation characteristics of arch station and the variation of earthpressure and deformation of soil-structure interaction, seismic force and interactionlaw of parallel tunnels, interaction law of seismic response of different combinationsof subway station and tunnel.
The following laws are obtained by the analysis of shaking table test results andnumerical simulation by FLAC based on the shaking table test. The natural frequencyof soil decreases and damping ratio increases in the process of vibration. The topdisplacement of model box is larger than the bottom, and the distribution law of theacceleration is contrary. The effect of absorbing seismic waves of model boxboundary is good. The filtering nature of soil is obvious. The acceleration response ofshallow soil is weakened with the structure buried. The interaction force between soiland structure is comparatively large, and the distribution law is obviously differentaccording to different depths and structure sizes. The strains of columns and walls arelarger than which of beams and plates. The structure stress concentration is located onnodes. The interaction force is controlled by vertical earth pressure. The distributionof maximum strain value is transfer from columns and walls to beams and plates andtends to uniform. The existence of parallel tunnel structure intensifies the reflectionand exacerbates of shear waves in the soil, which amplify the response of acceleration,earth pressure, and strain of single tunnel. About the combinations of subway stationand tunnels, the bottom tunnels structure can absorb the earthquake waves comingfrom shaking table test, and reduce the seismic response of the upper station structure.The week effect reduces with soil thickness increasing.
本文依托国家973课题―城市地下基础设施的地震破坏与抗震理论（2007CB714203）‖和北京市自然科学基金重点项目―地铁车站立体交叉结构地震响应及抗震设计方法研究（8111001）‖，根据北京地区地质条件、地铁车站结构形式、车站-隧道典型组合形式等特点，主要从地震作用下地铁车站典型结构的破坏机理、破坏模式和车站-隧道不同组合条件下的地震响应等两个方面进行了相关的分析与研究，具体的研究内容和研究成果如下：
以土体电镜扫描为研究对象，把数字图像处理技术引入土体的细观结构观察和定量分析中，求解土颗粒孔隙度、颗粒粒径及颗粒形状等细观颗粒组成参数，为建立颗粒流离散元细观模型提供物理参数。在基础上，对土样的三轴试验进行模拟，并研究细观力学参数（包括：摩擦系数、平行连接强度及刚度比）对宏观性质的影响。
建立基于典型地铁车站结构大型振动台试验的有限差分-颗粒流离散元耦合模型，对车站结构模型在地震中的地震响应和破坏现象进行模拟分析。在耦合计算模型中，土体采用连续模型、结构采用颗粒流离散元模型模拟，在FLAC边界节点处建立接触面，将FLAC在大应变模式计算的位移通过接触面传输给颗粒流离散元；并将颗粒与接触面计算的相互作用力传输给FLAC，作为施加在各节点上的力，从而实现耦合运算。结果表明，数值模型的计算结果与试验结果能够较好的拟合；地震加载过程中，柱板、墙板节点为地铁车站模型结构的薄弱部位；模型的整个破坏过程和能量转化过程可分为3个阶段；结构的破坏过程可以通过颗粒孔隙率、配位数和接触力的变化以及能量的转化规律反映出来。
设计并开展地铁车站-隧道不同密贴组合结构的振动台试验，建立以覆土厚度为主要控制因素的相似关系处理方法，对不同的组合结构形式输入不同的地震作用，主要研究：自由场振动特性和模型振动前后的动力性质变化以及物性演变过程；单层连拱形地铁结构的地震受力和变形特征以及土-结构相互作用的土压力和位移变化规律；并行隧道结构的地震受力和相互影响规律；地铁车站及隧道结构在不同空间组合形式下的地震响应影响规律。
基于试验结果和建立在振动台试验基础上的FLAC模型模拟分析得到以下规律：模型在振动激励下，土体的自振频率不断降低，阻尼比增加。模型箱的顶部反应位移大于底部，反应加速度则底部大于顶部。模型箱的边界吸波效果良好，且土体具有明显的滤波性质；结构的存在对上部土体的反应加速度具有减弱作用；结构与土的相互作用较为明显，且与埋深，结构尺寸等呈现不同的分布规律；结构墙柱应变大于梁板，节点处应力集中；车站倾斜放置时，结构-土相互作用力受竖向土压力控制；相对于单体车站，结构的应变幅值由墙柱向顶板转移，且分布趋于平均分布；并行隧道结构的存在加剧了对土体剪切波的反射和集中，对单体隧道的反应加速度、动土压力、动应变幅值等均具有放大效应；底部隧道结构的存在对传来的地震波具有吸收作用，使得上部车站的地震响应减弱，且减弱幅度随夹层土体厚度的增加而减小。
With the development of subway and maturation of construction technology, thecross-section form of station and tunnel has been changed. The transfer station hasbeen gradually increased, the phenomenon of space cross-station been increasingcommon. The diversification of subway station structure form and universality ofspace cross-station is the development trend of the future subway. The space-cross ofstation-station and station-tunnel and the connecting channel between them of Metrotransfer station or transport hub constitute a complex interaction of underground spacestructure. A greater deformation and additional internal forces will be generated in theconnection point under earthquake. In addition, the transverse shear deformationcaused by seismic waves in the structure will make another structure in a complexstress state of longitudinal tension or bending. In short, the deformation and stressstate of underground three-dimensional structure under earthquake is more complexand more significant interaction.
This work was financially supported by a grant from the Major State BasicResearch Development Program of China (973Program),‖the earthquake damageand seismic theory of unban underground infrastructure‖. No.2007CB714203, andsupported by Beijing Municipal Natural Science Foundation.‖Study on seismicresponse and design method of three-dimensional intersected underground subwaystructures‖. No.8111001. According to the geological conditions in Beijing, thesubway station structure, and the typical combination of characteristics of station andtunnel, this article focuses on two aspects of analysis and research related to failuremechanism and mode of typical subway station structure and seismic response ofthree-dimensional intersected underground subway structures. The specific researchcontents and results are as follows:
Taking silt soil image photographed by scanning electron microscope as theresearch object, use image treatment technology for microstructure observation andquantitative analysis of soil, solve the parameter of particle composition of soil, suchas porosity, grain diameter and granular shape. These works provide physicalparameters for granular flow model developing. And then simulate the tri-axial test ofthe soil and study the variation rules of property of silt soil with micro-parameters,such as friction coefficient, parallel-bond and stiffness ratio.
A continuum-discrete element coupled model is built based on a large-scaleshaking table test of typical subway station in Beijing, to simulate the seismicresponses and the damage process of subway station structure model. In the couplingmodel, the soil is simulated by finite-difference method, and the structure is simulatedby particle flow code. Interfaces are built between the adjacent nodes on the boundaryof FLAC model and used as walls in PFC. Displacement calculated by FLAC inlarge-strain model transfer to PFC through interfaces, and the interaction force between particle and walls transfer to FLAC, so as to approach the couplingcalculation. The result shows that the experimental results can be well fitted. Theinterior column and nodes of column and plates are weak parts of subway stationstructure model during inputting earthquake waves. The whole damage process andenergy conversion process of structure model can be divided into three phases. Thechange of porosity, average number of contacts and contact force and the energyconversion law can response the damage process of structure model.
Design and carry out shaking table test of different combinations of subwaystation and tunnel. Establish the treatment method of similar ratio with mainlycontrolling factors of over burden quality. Enter the different types of seismic waves.The main contents are as follows: the vibration characteristic of free field and itsdynamic nature of change and evolution of physical properties during the vibration,seismic force and deformation characteristics of arch station and the variation of earthpressure and deformation of soil-structure interaction, seismic force and interactionlaw of parallel tunnels, interaction law of seismic response of different combinationsof subway station and tunnel.
The following laws are obtained by the analysis of shaking table test results andnumerical simulation by FLAC based on the shaking table test. The natural frequencyof soil decreases and damping ratio increases in the process of vibration. The topdisplacement of model box is larger than the bottom, and the distribution law of theacceleration is contrary. The effect of absorbing seismic waves of model boxboundary is good. The filtering nature of soil is obvious. The acceleration response ofshallow soil is weakened with the structure buried. The interaction force between soiland structure is comparatively large, and the distribution law is obviously differentaccording to different depths and structure sizes. The strains of columns and walls arelarger than which of beams and plates. The structure stress concentration is located onnodes. The interaction force is controlled by vertical earth pressure. The distributionof maximum strain value is transfer from columns and walls to beams and plates andtends to uniform. The existence of parallel tunnel structure intensifies the reflectionand exacerbates of shear waves in the soil, which amplify the response of acceleration,earth pressure, and strain of single tunnel. About the combinations of subway stationand tunnels, the bottom tunnels structure can absorb the earthquake waves comingfrom shaking table test, and reduce the seismic response of the upper station structure.The week effect reduces with soil thickness increasing.
引文
1邵伟民，郭建国．北京地铁规划概述[J]．铁道建筑，1997.(1)：19-21．
2郭村安．北京城市轨道交通线网络调整规划[J]．城市交通，2004.2(1)：33-38．
3于翔．地铁建设中应充分考虑抗地震作用－阪神地震破坏的启示[J]．铁道建筑技术，2000.06：32-36．
4赵成刚，冯启民．生命线地震工程[M]．地震出版社，1979：1-87．
5Youssef M.A. Hashasha， Jeffrey J. Hooka， Birger Schmidtb， John I-Chiang Yaoa，Seismic Design and Analysis of Underground Structures [J]．Tunnelling and UndergroundSpace Technology，2001， Vol.16：247-293．
6Kaneshiro, J.Y.， Power, M.， Rosidi, D.， Empirical Correlations of Tunnel PerformanceDuring Earthquakes and Aseismic Aspects of Tunnel Design[C]．Proceedings of theConference on Lessons Learned From Recent Earthquakes－On Earthquakes in Turkey1999， November8-11，2000．
7Hidenao Hayashi，Tamotsu Marui，Nobuhiko Taniguchi，Shigeru Kayano．Restoration ofHanshin Expressway after Kobe/Awaji Earthquake Challenge of623days beforeOpening[J]．Cement&concrete composites，2000，22(2)：29-38．
8Somerville, P.(1995)．Kobe Earthquake[J]．An Urban Diasaster．1995. Vol.76：49-51．
9于翔，赵跃堂，郭志昆．人防工程的抗地震问题[J]．地下空间，2001,21(1)：28-32．
10Tang, Y. K.，et. al．1991，The Hualien large-scale Seismic Test for Soil-structure InteractionResearch[C]．SMIRT11，Transactions，1991，Vol. K：69-74．
11Power,M.,Rosidi,D.,Kaneshiro,J.,SeismicVulnerability of Tunnels-revisited[C]．Proceedingsof the North American Tunneling Conference．Elsevier，Long Beach，CA，USA，1998．
12Igor A. Beresnev．Empirical Constraints on Nonlinear Site Response Using Data from1999Chi-chi, Taiwan, earthquake, U.S. Geological survey[R]．1999.05．
13宋胜武．汶川大地震工程震害分析与研究[M]．科学出版社，2009.04：1-34．
14陶连金．512汶川大地震后震区城市轨道交通调研报告[R]，中国土木工程学会城市轨道交通技术推广委员会，2008.06．
15庄海洋．土-地下结构非线性动力相互作用及大型振动台试验研究[D]，南京工业大学博士学位论文，2006：2-8．
16王越．北京地震历史资料汇编[M]．专利文献出版社，1998.06：34-55．
17关于印发《市政工程设施抗震设防专项论证技术要点（地下工程篇）》的通知，中华人民共和国住房和城乡建设部．2011．
18胡聿贤．地震工程学[M]．北京，地震出版社，1988：71-72．
19林皋．地下结构抗震综述(上)[J]．世界地震工程，1990(2)：1-10．
20林皋．地下结构抗震综述(下)[J]．世界地震工程，1990(2)：1-10．
21孙超．地铁地下结构抗震性及分析方法研究[D]．中国地震局工程力学研究所博士学位论文，2009：1-10．
22Lee, VW.and Trifunae, M.D. Response of Tunnels to Ineident SH Waves[J]．Joumal ofEnglneering Mechanics，1979，6：643-659．
23Mow,C.C.， Pao, A.H.，著弹性波的衍射和动应力集中[M]．刘殿魁、苏先抛译，北京：科学出版社，1993．
24Datta，S.K.andShah，A.H.，W6ng，K.C.，Dynamic Stresses and Displaeements InburiedPipe [J]． Joumal of Engineering Mechanies，1985，10：1451-1466．
25Stamos，A.A.andBeskos，D.E.3Dseismic Rresponse Analysis of Long Lined Tunnels inHalf-space [J]．Soil Dynamics and Earthquake Engineering，1996，15(2)：111-118．
26付鹏程，王刚，张建民[J]．地铁地下结构在轴向传播剪切波作用下反应的简化计算方法[J]．地震工程与工程振动，2004.24(3)：44-50．
27J.P.瓦尔夫著，吴世明译．土-结构动力相互作用[J]．北京：地震出版社，1989．
28Guin, J.， et al． Coupled Soil Piles Struetures Interaetion Analysis Under SeismicExcitation[J]．Joumal of Structural Engineering，1998，124(4)：434-444．
29Wegner,J.L, Dynamic Waves-Soil-Structure Interaetion Analysis in the TimeDomain[J]．Computers and structures，2005，83：2206-2214．
30李建波等．结构-地基动力相互作用时域数值计算模型研究[J]．地震工程与工程振动，2005，25(2)：169-176．
31JohnPW，SongC Dynamic-Stiffness Matrix of Unbounded Soil by Finite-element MulticellCloning[J]．Earthquake Engineering and Structural Dynamics，1994，V23：233-250．
32林皋，梁青槐．地下结构的抗震设计[J]．土木工程学报，1996(l)：15-24．
33CHEN Guo-xing, ZHUANG Hai-yang, SHI Guo-long， Analysis on the EarthquakeResponse of Subway Station Based on the Substructure Subtraction Method[J]．Journal ofDisaster Pnevention and Mitigation Engineering，2004.04：397-401．
34John Lysmer，Farhang Ostadan，Chih Cheng Chin．A system for analysis of soil-structureinteraction[J]． Geotechnical engineering，Berkeley.2000：1~8．
35Jun Seong Choi. Jong She Lee. Member ASCE，Jae Min Kim. Nonlinear EarthquakeResponse Analysis of2-D Underground Structures with Soil-structures InteractionIncluding Separation and Sliding at Interface [A]．15th ASCE Engineering MechanicsConference[C]，June2-5，2002，Columbia University New York，NY，1-8．
36Huo Hong-bin, Bobet A. Seismic Design of Cut and Cover Rectangular Tunnels-evaluationof Observed Behavior of Dakai Station During Kobe Earthquake,1995[A]. Proceedings of1st World Forum of Chinese Scholars in Geotechnical Engineering, August20-22,2003[C],Tongji University, Shanghai,456-466．
37刘晶波，李彬，谷音等．地铁盾构隧道地震反应特性研究[J]．现代隧道技术（增刊）2004，4：251-257．
38Chen Guo-xing, Zhuang Hai-yang. Analysis on the Earthquake Response of Subway StationBased on the Substructure Subtraction Metho[C]．Proceedings of the Third InternationalConference on Earthquake Engineering．2004，19~20October，195-199．
39刘如山．强地震动作用下地铁结构与土脱开滑移的研究[J]．地震工程与工程振动，2004，24(6)：136-141．
40Liu Hua-bei, Song Er-xiang. Seismic Response of Large Underground Structures inLiquefiable Soils Subjected to Horizontal and Vertical EarthquakeExcitations[J]．Computers and Geotechnics，2005，32：223-244．
41Liu Hua-bei, Song Er-xiang. Working Mechanism of Cutoff Walls in Reducing Uplift ofLarge Underground Structures Induced by Soil Liquefaction[J]．Computers and Geotechnics,2006，33：209-221．
42An Xue-hui, Ashraf A. The Collapse Mechanism of a Subway Station During the GreatHanshin Earthquake[J]．Cement and Concrete Composites，1997，19：241-257．
43庄海洋，陈国兴等．土体动非线性黏弹性模型及其ABAQUS软件的实现[J]．岩土力学，2007，28（3）：436-441．
44车爱兰，岩碷敞广，葛修润．关于地铁地震响应的模型振动试验及数值分析[J]．岩土力学，2006，27(8)：1293-1298．
45林利民，陈建云．软土中浅埋地铁车站结构的抗震性能分析[J]．防灾减灾工程学报，2006，26(3)：268-273．
46Kirzhner，F，and Rosenhouse，G. Numerical Analysis of Tunnel Dynamic Response to EarthMotions[J]．Thnneling and Underground spaeeTechnology，2000，15(3)：249-258．
47Franeisco，J.Site effects in Parkway Basin Comparison Between Observations and3DModeling．Applied Geophysies，2003，154：633-646．
48边金．地铁地下结构的地震动力响应[D]．北京工业大学博士学位论文，2006：1-11．
49李海波，马行东，李俊如等．地震荷载作用下地下岩体洞室位移特征的影响因素分析[J]．岩土工程学报，2006.28（3）：358-362．
50杨林德，王海波等．地铁车站结构振动台试验及地震响应的三维数值模拟[J]．岩土力学与工程学报，2007.26（8）1439-1445．
51蒋英礼，赵伯明，胡晓勇．软土地铁车站中柱在强震作用下的响应研究[J]．防灾减灾工程学报，2009.29（4）：405-410．
52Cundall P A. A Computer Model for Simulating Progressive Large Scale Movements inBlocky Systems[J]．Proceedings of Rock Mechanics，1971,Vol.1：1-8．
53Cundall P A. The Measurement and Analysis of Acceleration in Rock Slopes. Ph. D.Dissertation, University of London, Imperial College of Science and Technology，1971．
54Strack O.D.L, Cundall P.A．The Distinct Element Method as a Tool for Research inGranular Media[R]．Part I. Report to the Nation Science Foundation, Minnesota：Universityof Minnesota，1978．
55Cundall P.A, Strack O.D.L. The Distinct Element Method as a Tool for Research inGranular media[R]．Part II. Report to the Nation Science Foundation, Minnesota: Universityof Minnesota，1979．
56Cundall P.A, Strack O.D.L. A Discrete Numerical Model for GranularAssembles[J]．Geotechnique，1979，29(1)：47-65．
57Cleary P.W．DEM Simulation of Industrial Particle Flows：Case Studies of DraglineExcavators，Mixing in Tumblers and Centrifugal mills[J]．Powder Technology，2000，109(1-3)：83-104．
58陶连金，常春．节理岩体的动力响应分析及工程应用[J]．黑龙江矿业学院学报，2000.4：6-10．
59伍永田，张旭生，李晓芸等．地震作用对采空区塌陷的UDEC模拟[J]．矿业工程，2007，5(6)：1439-1445．
60周家文，徐卫亚，石崇．基于3DEC的节理岩体边坡地震影响下的楔体稳定性分析[J]．岩石工程与力学学报，2007，26(1)：3402-3407．
61Kim，M.K，et.Seismic Analysis of Base-Isolated Liquid Storage Tanks Using the Be-FE-BECoupling Technique[J]．Soil Dynamics and Earthquake Engineering，2002，22：1151-158．
62Spyrakos， C.C.and Xu,C.J. Seismic Soil-strueture Interaction of Massive FlexibleStrip-Foundations Embedded in Layered Soil by Hybrid BEM-FEM[J]．Soil Dynamic sandEarthquake Engineering，2003，23：383-389．
63Celso Pomanel and Tribokram Kundu A Hybrid Modeling of Soil-structure InteractionProblems for Deeply Embedded Structures in a Multi-layered Medium[J]．EarthquakeEngineering and Structure Dynamics，1993.Vol.22：557-571．
64Hongbin Huo. Antonio Bobet. Seismic Design of Cut and Cover RectangularRunnels-evaluation of Observed Behavior of Dakai Station during KobeEarthquake[C]．Proceedings of1st World Forum of Chinese Scholars in GeotechnicalEngineering．Tongji University. Shanghai．1995August：20-22．
65金峰，贾伟伟，王光纶．离散元-边界元动力耦合模型[J]．水利学报，2001.01：22-26．
66杨光，刘曾武．地下隧道工程地震动分析的有限元-人工透射边界方法[J]．工程力学，1994.4：122-130．
67姜忻良，徐余，郑刚．地下隧道-土体系地震反应分析的有限元和无限元耦合法[J]．地震工程和工程振动，1999.3：22-26．
68赵伯明，蒋英礼，陈靖．软土地铁车站结构在三维强地震动作用下的响应分析[J]．中国铁路科学，2009，30(3)：45-49．
69刘如山，邬玉斌，杜修力．用纤维模型对地下结构地震破坏的数值模拟分析[J]．北京工业大学学报．2010，36(11)：1488-1495．
70Cundall P A. PFC2D user’s Manual (version3.1)，Itasca Consulting Group，Inc,2004．
71周健，贾敏才等．土工细观模型试验与数值模拟[M]．北京：科学出版社，2008：46-55．
72M．Celebi, J. Lysmer, J. E. Luco, Recommendations for a Soil-structure InteractionExperiment Report Based on a Workshop Held at San Francisco， California on February7，1992．
73G. Gazetas, N. Gerolymos, I. Anastasopoulos, Response of Three Athens MetroUnderground Structures in the1999Parnitha earthquake[J]．Soil Dynamics and EarthquakeEngineering，2005，25：617-633．
74Y. Shojia, K. Taniib, M. Kamiyama, A Study on the Duration and Amplitude Characteristicsof Earthquake Ground Motions[J]．Soil Dynamics and Earthquake Engineering，2005，25(1)：505-512．
75Tang, H. T., et. al, A Large-scale Soil Structure Interaction Experiment[C]．Part I--Designand construction，SMIRT9，1987，Vol. K2：177-182．
76M. elebi, C.B. Crouse, Recommendations for Soil-structure Interaction Instrumentation，COSMOS (Consortium of Organizations for Strong-Motion Observation Systems)Workshop on Structural Instrumentation Emeryville，Ca.2001，November14-15．
77Tang, Y. K., et. al．The Hualien Large-scale Seismic Test for Soil-structure InteractionResearch[C]．SMIRT11，Transactions,1991, Vol. K：69-74．
78Jun Matsui, Keizo Ohtomo, Kensei Kanaya．Development and Validation of NonlinearDynamic Analysis in Seismic Performance Verificationof Underground RCstructures[J]．Journal of advanced concrete technology，2004，Vol.2：25-35．
79季倩倩．地铁车站结构振动台模型试验研究[D]．同济大学博士学位论文，2002．
80宫必宁，赵大鹏．地下结构与土动力相互作用试验研究[J]．地下空间，2002，22(4)：320-326．
81尚昊，郭志昆，张武刚．大断面地下结构抗震模型试验[J]．岩土工程界，2002，5(10)：60-62．
82左熹，陈国兴，王志华等．近远场地震动作用下地铁车站结构地基液化效应的振动台试验[J]．岩土力学，2010，31（12）：3733~3738．
83Shigeki Unjoh, Takaaki Kusakabe, Sho-ichi Nakatani, Takeshi Ohshita, Yasuhiko Wakizaka,Kei-ichi Tamura and Jiro Fukui, Site-specific Design Earthquake Ground Motion andSeismic Design Technology in Next Generation．
84St. John, C.M., Zahrah, T.F., Aseismic Design of Underground Structures[J]．TunnelingUnderground Space Technol，1987，Vol.22：165-197．
85W.D.L. Finn, State-of-the-art of Geotechnical Earthquake Engineering Practice[J]．SoilDynamics and earthquake Engineering，2000，Vol.20：1-15．
86Wang, J.-N．Seismic Design of Tunnels: A State-of-the-Art Approach[M]．Monograph,monograph7. Parsons，Brinckerhoff，Quade and Douglas Inc，New York,1993．
87Penzien, J., Seismically-Induced Racking of Tunnel Linings[J]．Earthquake Eng. Struct.Dyn.2000，Vol.29：683~691．
88Mark Aschheim, M.EERI, Seismic Design Based on the Yield Displacement[J]．EarthquakeSpectra，2002，18(4)：581–600．
89Seishi Nakagawa, Naotaka Shikida, Tsutomu Tanaka, Shogo Ohtake, Behaviour of theTunnel in the Rugged Hard Ground in the Event of Earthquake, and Earthquake ResistantDesign Method. Towards News Worlds in Tunneling[J]． Vieitez-Utesa&Montanez-CartaxoBalkema, Rotterdam,1990：437-444．
90L. M. Gil, E. Hernandez, P. De la Fuente, Simplified Transverse Seismic Analysis of BuriedStructures[J]．Soil dynamics and earthquake engineering，2001，Vol.21：735~740．
91川岛一彦．地下结构耐震设计[M]．日本，鹿岛出版社，1994.28．
92福季耶娃著，徐显毅译．地震区地下结构支护的计算[M]．北京，煤炭出版社，1986．
93Thoms R, Kuesel F, ASCE, Earthquake Design Eriteria for Subways[J]．Journal of theStructural Division Proceedings of the American Society of Civil Engineers.1969(6)：1213-1331．
94黄先锋．地下结构的抗震计算[J]．铁道建筑，1999(6)：3-6．
95Shukla D K Pizzo P C，Stephenson DE Earthquake load analysis of tunnels and shafts[R]． Proceeding of the Seventh world Conefernce on Earthquake Engineering1980，8：20-28．
96林皋．地下结构抗地震问题[C]．第四届全国地震工程会议，1994．
97John C.M.S.，Zahrah T.F. A Seismic Design of Underground Surtcutres[J]．Tunneling andUndegrround Space Technology1987,21：65~197．
98Campbell C.S, Brennen C.E. Computer Simulation of Granular Shear Flows[J]．J FluidMech,1985,151：167-188．
99Campbell C.S, Brennen C.E. Chute Flows of Granular Materials: Some ComputerSimulations. J Appl Mech，1985，52：172-178．
100An, B.(2006) A Study of Energy Loss During Rock Impact Using PFC2D,[D]．Department of Civil&Environmental Engineering, University of Alberta,Spring．
101An, B., and D. D. Tannant. Discrete Element Method Contact Model for DynamicSimulation of Inelastic Rock Impact[J]． Comput. Geosci，2007，33(4)：513-521．
102Bortal-Nafaa, S., and D. Gouvenot.(2003)"Fine Cement Grout Injection: DiscreteNumerical Modeling," in Numerical Modeling in Micromechanics Via ParticleMethods (1st International PFC Symposium, Gelsenkirchen, Germany, November2002)：165-171．
103Dolezalová, M., P. Czene and F. Havel.(2003)"Micromechanical Modeling ofStress Path Effects Using PFC2D Code," in Numerical Modeling inMicromechanics Via Particle Methods (1st International PFC Symposium,Gelsenkirchen, Germany, November2002)：173-181．
104曾远，周健．砂土的细观参数对宏观性质的模拟研究[J]．地下空间与工程学报，2008，4（3）：499~503．
105周健，余荣传，贾敏才．基于数字图像技术的砂土模型试验细观参数测量[J]．岩土工程学报，2006，28（12）：2047~2052．
106周健，池毓蔚，池勇等．砂土双轴试验的颗粒流模拟[J]．岩土工程学报，2000，22（6）：701~704．
107汪成兵．软弱破碎隧道围岩渐进性破坏机理研究[D]．同济大学，2007．
108张敏政．地震模拟试验中相似率应用的若干问题[J]．地震工程与工程震动，1997.6，17（2）：52~58．
109周健，金炜枫．基于耦合方法的挡土墙地震响应的数值模拟[J]．岩土力学，2010.31（12）：3949-3956．
110Riemer.M.，et al，1-g Modeling of Seismic Soil-Pile-superstucture Interaction in softClay[C]．Proc.4thCaltrans Seismic Researth Workshop．Sacramento，1996.7．
111杜修力，李霞，李立云．用于地下结构振动台试验的悬挂式层状多向剪切模型箱装置[P]．CN201010128793.7.发明专利，2010.07.
112《北京地铁十六号线工程场地地震安全性评价报告》
113FLAC说明书[M]．．Itasca Consulting Group． Inc. USA，2001．
2郭村安．北京城市轨道交通线网络调整规划[J]．城市交通，2004.2(1)：33-38．
3于翔．地铁建设中应充分考虑抗地震作用－阪神地震破坏的启示[J]．铁道建筑技术，2000.06：32-36．
4赵成刚，冯启民．生命线地震工程[M]．地震出版社，1979：1-87．
5Youssef M.A. Hashasha， Jeffrey J. Hooka， Birger Schmidtb， John I-Chiang Yaoa，Seismic Design and Analysis of Underground Structures [J]．Tunnelling and UndergroundSpace Technology，2001， Vol.16：247-293．
6Kaneshiro, J.Y.， Power, M.， Rosidi, D.， Empirical Correlations of Tunnel PerformanceDuring Earthquakes and Aseismic Aspects of Tunnel Design[C]．Proceedings of theConference on Lessons Learned From Recent Earthquakes－On Earthquakes in Turkey1999， November8-11，2000．
7Hidenao Hayashi，Tamotsu Marui，Nobuhiko Taniguchi，Shigeru Kayano．Restoration ofHanshin Expressway after Kobe/Awaji Earthquake Challenge of623days beforeOpening[J]．Cement&concrete composites，2000，22(2)：29-38．
8Somerville, P.(1995)．Kobe Earthquake[J]．An Urban Diasaster．1995. Vol.76：49-51．
9于翔，赵跃堂，郭志昆．人防工程的抗地震问题[J]．地下空间，2001,21(1)：28-32．
10Tang, Y. K.，et. al．1991，The Hualien large-scale Seismic Test for Soil-structure InteractionResearch[C]．SMIRT11，Transactions，1991，Vol. K：69-74．
11Power,M.,Rosidi,D.,Kaneshiro,J.,SeismicVulnerability of Tunnels-revisited[C]．Proceedingsof the North American Tunneling Conference．Elsevier，Long Beach，CA，USA，1998．
12Igor A. Beresnev．Empirical Constraints on Nonlinear Site Response Using Data from1999Chi-chi, Taiwan, earthquake, U.S. Geological survey[R]．1999.05．
13宋胜武．汶川大地震工程震害分析与研究[M]．科学出版社，2009.04：1-34．
14陶连金．512汶川大地震后震区城市轨道交通调研报告[R]，中国土木工程学会城市轨道交通技术推广委员会，2008.06．
15庄海洋．土-地下结构非线性动力相互作用及大型振动台试验研究[D]，南京工业大学博士学位论文，2006：2-8．
16王越．北京地震历史资料汇编[M]．专利文献出版社，1998.06：34-55．
17关于印发《市政工程设施抗震设防专项论证技术要点（地下工程篇）》的通知，中华人民共和国住房和城乡建设部．2011．
18胡聿贤．地震工程学[M]．北京，地震出版社，1988：71-72．
19林皋．地下结构抗震综述(上)[J]．世界地震工程，1990(2)：1-10．
20林皋．地下结构抗震综述(下)[J]．世界地震工程，1990(2)：1-10．
21孙超．地铁地下结构抗震性及分析方法研究[D]．中国地震局工程力学研究所博士学位论文，2009：1-10．
22Lee, VW.and Trifunae, M.D. Response of Tunnels to Ineident SH Waves[J]．Joumal ofEnglneering Mechanics，1979，6：643-659．
23Mow,C.C.， Pao, A.H.，著弹性波的衍射和动应力集中[M]．刘殿魁、苏先抛译，北京：科学出版社，1993．
24Datta，S.K.andShah，A.H.，W6ng，K.C.，Dynamic Stresses and Displaeements InburiedPipe [J]． Joumal of Engineering Mechanies，1985，10：1451-1466．
25Stamos，A.A.andBeskos，D.E.3Dseismic Rresponse Analysis of Long Lined Tunnels inHalf-space [J]．Soil Dynamics and Earthquake Engineering，1996，15(2)：111-118．
26付鹏程，王刚，张建民[J]．地铁地下结构在轴向传播剪切波作用下反应的简化计算方法[J]．地震工程与工程振动，2004.24(3)：44-50．
27J.P.瓦尔夫著，吴世明译．土-结构动力相互作用[J]．北京：地震出版社，1989．
28Guin, J.， et al． Coupled Soil Piles Struetures Interaetion Analysis Under SeismicExcitation[J]．Joumal of Structural Engineering，1998，124(4)：434-444．
29Wegner,J.L, Dynamic Waves-Soil-Structure Interaetion Analysis in the TimeDomain[J]．Computers and structures，2005，83：2206-2214．
30李建波等．结构-地基动力相互作用时域数值计算模型研究[J]．地震工程与工程振动，2005，25(2)：169-176．
31JohnPW，SongC Dynamic-Stiffness Matrix of Unbounded Soil by Finite-element MulticellCloning[J]．Earthquake Engineering and Structural Dynamics，1994，V23：233-250．
32林皋，梁青槐．地下结构的抗震设计[J]．土木工程学报，1996(l)：15-24．
33CHEN Guo-xing, ZHUANG Hai-yang, SHI Guo-long， Analysis on the EarthquakeResponse of Subway Station Based on the Substructure Subtraction Method[J]．Journal ofDisaster Pnevention and Mitigation Engineering，2004.04：397-401．
34John Lysmer，Farhang Ostadan，Chih Cheng Chin．A system for analysis of soil-structureinteraction[J]． Geotechnical engineering，Berkeley.2000：1~8．
35Jun Seong Choi. Jong She Lee. Member ASCE，Jae Min Kim. Nonlinear EarthquakeResponse Analysis of2-D Underground Structures with Soil-structures InteractionIncluding Separation and Sliding at Interface [A]．15th ASCE Engineering MechanicsConference[C]，June2-5，2002，Columbia University New York，NY，1-8．
36Huo Hong-bin, Bobet A. Seismic Design of Cut and Cover Rectangular Tunnels-evaluationof Observed Behavior of Dakai Station During Kobe Earthquake,1995[A]. Proceedings of1st World Forum of Chinese Scholars in Geotechnical Engineering, August20-22,2003[C],Tongji University, Shanghai,456-466．
37刘晶波，李彬，谷音等．地铁盾构隧道地震反应特性研究[J]．现代隧道技术（增刊）2004，4：251-257．
38Chen Guo-xing, Zhuang Hai-yang. Analysis on the Earthquake Response of Subway StationBased on the Substructure Subtraction Metho[C]．Proceedings of the Third InternationalConference on Earthquake Engineering．2004，19~20October，195-199．
39刘如山．强地震动作用下地铁结构与土脱开滑移的研究[J]．地震工程与工程振动，2004，24(6)：136-141．
40Liu Hua-bei, Song Er-xiang. Seismic Response of Large Underground Structures inLiquefiable Soils Subjected to Horizontal and Vertical EarthquakeExcitations[J]．Computers and Geotechnics，2005，32：223-244．
41Liu Hua-bei, Song Er-xiang. Working Mechanism of Cutoff Walls in Reducing Uplift ofLarge Underground Structures Induced by Soil Liquefaction[J]．Computers and Geotechnics,2006，33：209-221．
42An Xue-hui, Ashraf A. The Collapse Mechanism of a Subway Station During the GreatHanshin Earthquake[J]．Cement and Concrete Composites，1997，19：241-257．
43庄海洋，陈国兴等．土体动非线性黏弹性模型及其ABAQUS软件的实现[J]．岩土力学，2007，28（3）：436-441．
44车爱兰，岩碷敞广，葛修润．关于地铁地震响应的模型振动试验及数值分析[J]．岩土力学，2006，27(8)：1293-1298．
45林利民，陈建云．软土中浅埋地铁车站结构的抗震性能分析[J]．防灾减灾工程学报，2006，26(3)：268-273．
46Kirzhner，F，and Rosenhouse，G. Numerical Analysis of Tunnel Dynamic Response to EarthMotions[J]．Thnneling and Underground spaeeTechnology，2000，15(3)：249-258．
47Franeisco，J.Site effects in Parkway Basin Comparison Between Observations and3DModeling．Applied Geophysies，2003，154：633-646．
48边金．地铁地下结构的地震动力响应[D]．北京工业大学博士学位论文，2006：1-11．
49李海波，马行东，李俊如等．地震荷载作用下地下岩体洞室位移特征的影响因素分析[J]．岩土工程学报，2006.28（3）：358-362．
50杨林德，王海波等．地铁车站结构振动台试验及地震响应的三维数值模拟[J]．岩土力学与工程学报，2007.26（8）1439-1445．
51蒋英礼，赵伯明，胡晓勇．软土地铁车站中柱在强震作用下的响应研究[J]．防灾减灾工程学报，2009.29（4）：405-410．
52Cundall P A. A Computer Model for Simulating Progressive Large Scale Movements inBlocky Systems[J]．Proceedings of Rock Mechanics，1971,Vol.1：1-8．
53Cundall P A. The Measurement and Analysis of Acceleration in Rock Slopes. Ph. D.Dissertation, University of London, Imperial College of Science and Technology，1971．
54Strack O.D.L, Cundall P.A．The Distinct Element Method as a Tool for Research inGranular Media[R]．Part I. Report to the Nation Science Foundation, Minnesota：Universityof Minnesota，1978．
55Cundall P.A, Strack O.D.L. The Distinct Element Method as a Tool for Research inGranular media[R]．Part II. Report to the Nation Science Foundation, Minnesota: Universityof Minnesota，1979．
56Cundall P.A, Strack O.D.L. A Discrete Numerical Model for GranularAssembles[J]．Geotechnique，1979，29(1)：47-65．
57Cleary P.W．DEM Simulation of Industrial Particle Flows：Case Studies of DraglineExcavators，Mixing in Tumblers and Centrifugal mills[J]．Powder Technology，2000，109(1-3)：83-104．
58陶连金，常春．节理岩体的动力响应分析及工程应用[J]．黑龙江矿业学院学报，2000.4：6-10．
59伍永田，张旭生，李晓芸等．地震作用对采空区塌陷的UDEC模拟[J]．矿业工程，2007，5(6)：1439-1445．
60周家文，徐卫亚，石崇．基于3DEC的节理岩体边坡地震影响下的楔体稳定性分析[J]．岩石工程与力学学报，2007，26(1)：3402-3407．
61Kim，M.K，et.Seismic Analysis of Base-Isolated Liquid Storage Tanks Using the Be-FE-BECoupling Technique[J]．Soil Dynamics and Earthquake Engineering，2002，22：1151-158．
62Spyrakos， C.C.and Xu,C.J. Seismic Soil-strueture Interaction of Massive FlexibleStrip-Foundations Embedded in Layered Soil by Hybrid BEM-FEM[J]．Soil Dynamic sandEarthquake Engineering，2003，23：383-389．
63Celso Pomanel and Tribokram Kundu A Hybrid Modeling of Soil-structure InteractionProblems for Deeply Embedded Structures in a Multi-layered Medium[J]．EarthquakeEngineering and Structure Dynamics，1993.Vol.22：557-571．
64Hongbin Huo. Antonio Bobet. Seismic Design of Cut and Cover RectangularRunnels-evaluation of Observed Behavior of Dakai Station during KobeEarthquake[C]．Proceedings of1st World Forum of Chinese Scholars in GeotechnicalEngineering．Tongji University. Shanghai．1995August：20-22．
65金峰，贾伟伟，王光纶．离散元-边界元动力耦合模型[J]．水利学报，2001.01：22-26．
66杨光，刘曾武．地下隧道工程地震动分析的有限元-人工透射边界方法[J]．工程力学，1994.4：122-130．
67姜忻良，徐余，郑刚．地下隧道-土体系地震反应分析的有限元和无限元耦合法[J]．地震工程和工程振动，1999.3：22-26．
68赵伯明，蒋英礼，陈靖．软土地铁车站结构在三维强地震动作用下的响应分析[J]．中国铁路科学，2009，30(3)：45-49．
69刘如山，邬玉斌，杜修力．用纤维模型对地下结构地震破坏的数值模拟分析[J]．北京工业大学学报．2010，36(11)：1488-1495．
70Cundall P A. PFC2D user’s Manual (version3.1)，Itasca Consulting Group，Inc,2004．
71周健，贾敏才等．土工细观模型试验与数值模拟[M]．北京：科学出版社，2008：46-55．
72M．Celebi, J. Lysmer, J. E. Luco, Recommendations for a Soil-structure InteractionExperiment Report Based on a Workshop Held at San Francisco， California on February7，1992．
73G. Gazetas, N. Gerolymos, I. Anastasopoulos, Response of Three Athens MetroUnderground Structures in the1999Parnitha earthquake[J]．Soil Dynamics and EarthquakeEngineering，2005，25：617-633．
74Y. Shojia, K. Taniib, M. Kamiyama, A Study on the Duration and Amplitude Characteristicsof Earthquake Ground Motions[J]．Soil Dynamics and Earthquake Engineering，2005，25(1)：505-512．
75Tang, H. T., et. al, A Large-scale Soil Structure Interaction Experiment[C]．Part I--Designand construction，SMIRT9，1987，Vol. K2：177-182．
76M. elebi, C.B. Crouse, Recommendations for Soil-structure Interaction Instrumentation，COSMOS (Consortium of Organizations for Strong-Motion Observation Systems)Workshop on Structural Instrumentation Emeryville，Ca.2001，November14-15．
77Tang, Y. K., et. al．The Hualien Large-scale Seismic Test for Soil-structure InteractionResearch[C]．SMIRT11，Transactions,1991, Vol. K：69-74．
78Jun Matsui, Keizo Ohtomo, Kensei Kanaya．Development and Validation of NonlinearDynamic Analysis in Seismic Performance Verificationof Underground RCstructures[J]．Journal of advanced concrete technology，2004，Vol.2：25-35．
79季倩倩．地铁车站结构振动台模型试验研究[D]．同济大学博士学位论文，2002．
80宫必宁，赵大鹏．地下结构与土动力相互作用试验研究[J]．地下空间，2002，22(4)：320-326．
81尚昊，郭志昆，张武刚．大断面地下结构抗震模型试验[J]．岩土工程界，2002，5(10)：60-62．
82左熹，陈国兴，王志华等．近远场地震动作用下地铁车站结构地基液化效应的振动台试验[J]．岩土力学，2010，31（12）：3733~3738．
83Shigeki Unjoh, Takaaki Kusakabe, Sho-ichi Nakatani, Takeshi Ohshita, Yasuhiko Wakizaka,Kei-ichi Tamura and Jiro Fukui, Site-specific Design Earthquake Ground Motion andSeismic Design Technology in Next Generation．
84St. John, C.M., Zahrah, T.F., Aseismic Design of Underground Structures[J]．TunnelingUnderground Space Technol，1987，Vol.22：165-197．
85W.D.L. Finn, State-of-the-art of Geotechnical Earthquake Engineering Practice[J]．SoilDynamics and earthquake Engineering，2000，Vol.20：1-15．
86Wang, J.-N．Seismic Design of Tunnels: A State-of-the-Art Approach[M]．Monograph,monograph7. Parsons，Brinckerhoff，Quade and Douglas Inc，New York,1993．
87Penzien, J., Seismically-Induced Racking of Tunnel Linings[J]．Earthquake Eng. Struct.Dyn.2000，Vol.29：683~691．
88Mark Aschheim, M.EERI, Seismic Design Based on the Yield Displacement[J]．EarthquakeSpectra，2002，18(4)：581–600．
89Seishi Nakagawa, Naotaka Shikida, Tsutomu Tanaka, Shogo Ohtake, Behaviour of theTunnel in the Rugged Hard Ground in the Event of Earthquake, and Earthquake ResistantDesign Method. Towards News Worlds in Tunneling[J]． Vieitez-Utesa&Montanez-CartaxoBalkema, Rotterdam,1990：437-444．
90L. M. Gil, E. Hernandez, P. De la Fuente, Simplified Transverse Seismic Analysis of BuriedStructures[J]．Soil dynamics and earthquake engineering，2001，Vol.21：735~740．
91川岛一彦．地下结构耐震设计[M]．日本，鹿岛出版社，1994.28．
92福季耶娃著，徐显毅译．地震区地下结构支护的计算[M]．北京，煤炭出版社，1986．
93Thoms R, Kuesel F, ASCE, Earthquake Design Eriteria for Subways[J]．Journal of theStructural Division Proceedings of the American Society of Civil Engineers.1969(6)：1213-1331．
94黄先锋．地下结构的抗震计算[J]．铁道建筑，1999(6)：3-6．
95Shukla D K Pizzo P C，Stephenson DE Earthquake load analysis of tunnels and shafts[R]． Proceeding of the Seventh world Conefernce on Earthquake Engineering1980，8：20-28．
96林皋．地下结构抗地震问题[C]．第四届全国地震工程会议，1994．
97John C.M.S.，Zahrah T.F. A Seismic Design of Underground Surtcutres[J]．Tunneling andUndegrround Space Technology1987,21：65~197．
98Campbell C.S, Brennen C.E. Computer Simulation of Granular Shear Flows[J]．J FluidMech,1985,151：167-188．
99Campbell C.S, Brennen C.E. Chute Flows of Granular Materials: Some ComputerSimulations. J Appl Mech，1985，52：172-178．
100An, B.(2006) A Study of Energy Loss During Rock Impact Using PFC2D,[D]．Department of Civil&Environmental Engineering, University of Alberta,Spring．
101An, B., and D. D. Tannant. Discrete Element Method Contact Model for DynamicSimulation of Inelastic Rock Impact[J]． Comput. Geosci，2007，33(4)：513-521．
102Bortal-Nafaa, S., and D. Gouvenot.(2003)"Fine Cement Grout Injection: DiscreteNumerical Modeling," in Numerical Modeling in Micromechanics Via ParticleMethods (1st International PFC Symposium, Gelsenkirchen, Germany, November2002)：165-171．
103Dolezalová, M., P. Czene and F. Havel.(2003)"Micromechanical Modeling ofStress Path Effects Using PFC2D Code," in Numerical Modeling inMicromechanics Via Particle Methods (1st International PFC Symposium,Gelsenkirchen, Germany, November2002)：173-181．
104曾远，周健．砂土的细观参数对宏观性质的模拟研究[J]．地下空间与工程学报，2008，4（3）：499~503．
105周健，余荣传，贾敏才．基于数字图像技术的砂土模型试验细观参数测量[J]．岩土工程学报，2006，28（12）：2047~2052．
106周健，池毓蔚，池勇等．砂土双轴试验的颗粒流模拟[J]．岩土工程学报，2000，22（6）：701~704．
107汪成兵．软弱破碎隧道围岩渐进性破坏机理研究[D]．同济大学，2007．
108张敏政．地震模拟试验中相似率应用的若干问题[J]．地震工程与工程震动，1997.6，17（2）：52~58．
109周健，金炜枫．基于耦合方法的挡土墙地震响应的数值模拟[J]．岩土力学，2010.31（12）：3949-3956．
110Riemer.M.，et al，1-g Modeling of Seismic Soil-Pile-superstucture Interaction in softClay[C]．Proc.4thCaltrans Seismic Researth Workshop．Sacramento，1996.7．
111杜修力，李霞，李立云．用于地下结构振动台试验的悬挂式层状多向剪切模型箱装置[P]．CN201010128793.7.发明专利，2010.07.
112《北京地铁十六号线工程场地地震安全性评价报告》
113FLAC说明书[M]．．Itasca Consulting Group． Inc. USA，2001．