Abstract：The dynamic characteristics of tunnel lining-soil interface are very complex and affected by many factors. The propagation of subway vibration is spatial，and it will change greatly at the interface. A viscoelastic interface model was proposed to simulate the dynamic interaction between the tunnel lining and soil. The analytical expressions of the dimensionless spring coefficient and damping coefficient of the viscoelastic interface model were derived with the propagation law of cylindrical P-wave. And the low frequency limits and high frequency limits of the dimensionless spring coefficient and damping coefficient were given. The results showed that the viscoelastic interface model can effectively simulate the loss of wave energy at the interface of lining-soil compared with the continuous interface model. The dynamic response amplitude of the soil increases with the increase of the shear modulus ratio of lining-soil. The density ratio of lining-soil has little effect on the soil stress amplitude，and the radial displacement amplitude near the fundamental frequency increases as the density ratio increases. The Poisson's ratio of soil has little effect on the radial displacement amplitude when and ，and the corresponding radial displacement amplitude near the fundamental frequency decreases with the increase of the Poisson?s ratio of the soil.
[1] JENKINS H H，STEPHENSON J E，CLAYTON G A，et al. The effect of track and vehicle parameters on wheel/rail vertical dynamic forces[J]. Railway Engineering Journal，1974，3(1)：2–16.
[2] ZHAI W，CAI Z. Dynamic interaction between a lumped mass vehicle and a discretely supported continuous rail track[J]. Computers and Structures，1997，63(5)：987–997.
[3] LEI X，NODA N A. Analyses of dynamic response of vehicle and track coupling system with random irregularity of track vertical profile[J]. Journal of Sound and Vibration，2002，285(1)：147–165.
[4] 夏 禾. 车辆与结构动力相互作用[M]. 北京：科学出版社，2002：1–16.(XIA He. Vehicle-structure dynamic interaction[M]. Beijing：Science Press，2002：1–16.(in Chinese))
[5] 翟婉明. 车辆–轨道耦合动力学研究的新进展[J]. 中国铁道科学. 2002，23(2)：1–14.(ZHAI Wanming. New advance in vehicle-track coupling dynamics[J]. China Railway Science，2002，23(2)：1–14.(in Chinese))
[6] KNOTHE K L，GRASSIE S L. Modelling of railway track and vehicle/track interaction at high frequencies[J]. Vehicle System Dynamics，1993，22(3)：209–262.
[7] 陈功奇，高广运. 层状地基中填充沟对不平顺列车动荷载的隔振效果研究[J]. 岩石力学与工程学报，2014，33(1)：144–153.(CHEN Gongqi，GAO Guangyun. Vibration screening effect of in-filled trenches on train dynamic loads of geometric irregular track in layered grounds[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(1)：144–153.(in Chinese))
[8] 盛 曦，赵才友，王 平，等. 地铁隔振措施对钢轨声功率特性影响测试分析[J]. 振动与冲击，2018，37(8)：206–212.(SHENG Xi，ZHAO Caiyou，WANG Ping，et al. Measurements and analysis of effects on rail sound power characteristics from metro vibration- reduction measures[J]. Journal of Vibration and Shock，2018，37(8)：206–212.(in Chinese))
[9] 包汉营，陈文化. 衬砌隧道中移动轴向激励作用下两相多孔介质动力响应[J]. 岩土力学，2018，39(10)：3 735–3 742.(BAO Hanying，CHEN Wenhua. Dynamic response of a saturated poroelastic medium due to a moving axial excitation in a lining tunnel[J]. Rock and Soil Mechanics，2018，39(10)：3 735–3 742.(in Chinese))
[10] 袁宗浩，蔡袁强，史 吏，等. 移动简谐荷载作用下饱和土体中圆形隧道和轨道结构的动力分析[J]. 岩土工程学报，2016，38(2)：311–322.(YUAN Zonghao，CAI Yuanqiang，SHI Li，et al. Response of rail structure and circular tunnel in saturated soil subjected to harmonic moving load[J]. Chinese Journal of Geotechnical Engineering，2016，38(2)：311–322.(in Chinese))
[11] 张 谦，陈文化. 地铁列车出、进站加、减速的轴向激励引起出平面振动[J]. 振动与冲击，2016，35(24)：96–101.(ZHANG Qian，CHEN Wenhua. Out-of-plane vibration induced by axial excitation while a metro train arriving at or leaving a station[J]. Journal of Vibration and Shock，2016，35(24)：96–101.(in Chinese))
[12] 曾 晨，孙宏磊，蔡袁强，等. 饱和土体中衬砌隧道在移动荷载下的动力响应[J]. 浙江大学学报：工学版，2015，49(3)：511–521.(ZENG Chen，SUN Honglei，CAI Yuanqiang，et al. Dynamic response of lined tunnel in saturated soil due to moving load[J]. Journal of Zhejiang University：Engineering Science，2015，49(3)：511–521.(in Chinese))
[13] 黄晓吉，扶名福，徐 斌. 移动环形荷载作用下饱和土中圆形衬砌隧洞动力响应研究[J]. 岩土力学，2012，33(3)：892–898.(HUANG Xiaoji，FU Mingfu，XU Bin. Dynamic response of a circular lining tunnel in saturated soil due to moving ring load[J]. Rock and Soil Mechanics，2012，33(3)：892–898.(in Chinese))
[14] 姚署霖，闻敏杰. 黏弹性土中衬砌隧道振动响应的解析解[J]. 工程力学，2014，31(3)：109–115.(YAO Shulin，WEN Minjie. Analytical solutions of dynamic responses of a lined tunnel in viscoelastic soil[J]. Engineering Mechanics，2014，31(3)：109–115.(in Chinese))
[15] LU J F，JENG D S. Dynamic response of a circular tunnel embedded in a saturated poroelastic medium due to a moving load[J]. Journal of Vibration and Acoustics，2006，128(6)：750–756.
[16] 袁宗浩，蔡袁强，曾 晨. 地铁列车荷载作用下轨道系统及饱和土体动力响应分析[J]. 岩石力学与工程学报，2015，34(7)：1 470–1 479. (YUAN Zonghao，CAI Yuanqiang，ZENG Chen. Dynamic response of track system and underground railway tunnel in saturated soil subjected to moving train loads[J]. Chinese Journal of Rock Mechanics and Engineering. 2015，34(7)：1 470–1 479.(in Chinese))
[17] 黄 强，黄宏伟，张 锋，等. 饱和软土层地铁列车运行引起的环境振动研究[J]. 岩土力学，2015，36(增1)：563–567.(HUANG Qiang，HUANG Hongwei，ZHANG Feng，et al. Research on environmental vibration response of soft saturated soil due to moving metro train[J]. Rock and Soil Mechanics，2015，36(Supp.1)：563–567.(in Chinese))
[18] 张 波，李术才，张敦福，等. 岩石介质中地铁列车运行引起的环境振动响应研究[J]. 岩石力学与工程学报，2011，30(增1)：3 341– 3 347.(ZHANG Bo，LI Shucai，ZHANG Dunfu，et al. Research on rock environments vibration response induced by metro trains in rock media[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(Supp.1)：3 341–3 347.(in Chinese))
[19] 包汉营，陈文化，张 谦. 基于薄层法和移动坐标系法的地铁竖向振动在成层土层中传播[J]. 岩土力学，2018，39(9)：3 277–3 284. (BAO Hanying，CHEN Wenhua，ZHANG Qian. Propagation of subway vertical vibration in layered soils based on thin layer method and moving coordinate system method[J]. Rock and Soil Mechanics，2018，39(9)：3 277–3 284.(in Chinese))
[20] 杨文波，陈子全，徐朝阳，等. 盾构隧道与周围土体在列车振动荷载作用下的动力响应特性[J]. 岩土力学，2018，39(2)：537–545.(YANG Wenbo，CHEN Ziquan，XU Zhaoyang，et al. Dynamic response of shield tunnels and surrounding soil induced by train vibration[J]. Rock and Soil Mechanics，2018，39(2)：537–545.(in Chinese))
[21] 葛世平，姚湘静，叶 斌，等. 列车振动荷载作用下隧道周边软黏土长期沉降分析[J]. 岩石力学与工程学报，2016，35(11)：2 359–2 368.(GE Shiping，YAO Xiangjing，YE Bin，et al. Analysis of long-term settlement of soft clay under train vibration[J]. Chinese Journal of Rock Mechanics and Engineering，2016，35(11)：2 359–2 368.(in Chinese))
[22] 杜修力. 工程波动理论与方法[M]. 北京：科学出版社，2009：283–285.(DU Xiuli. Theories and methods of wave motion for engineering[M]. Beijing：Science Press，2009：283–285.(in Chinese))
2019, Vol. 38 
