爆炸荷载作用下饱和土中隧道的瞬态动力响应
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摘要
用解析方法研究了爆炸荷载作用下饱和土中圆形隧道的动力响应问题。模型假定饱和土体中的圆形隧道中心处发生爆炸,爆炸荷载采用简化形式,衬砌运动方程基于Flügge壳体理论,饱和土采用Biot波动方程,通过引入两个势函数,在Laplace变换域中推导了爆炸荷载作用下圆形隧道位移和应力响应的表达式。利用Laplace数值逆变换得到爆炸荷载作用下衬砌与土体的时域计算结果,分析了排水条件对位移、应力变化的影响,并讨论了饱和土参数、衬砌和土的相对刚度的影响。数值结果表明,爆炸荷载作用下,不排水条件下应力和位移的响应幅值比排水条件下有所增大;饱和土参数b*对土体应力的幅值有明显的影响;衬砌与土的相对刚度越大,土体位移和应力响应的幅值越小,衰减的速度也越快。
Using an analytical method,the dynamic response of a circular tunnel in the saturated soil is investigated.Assuming that the blast occurs in the center of the tunnel,a model is established using simplified blast loads.The motions of the liner are considered specially based on the Flügge theory.The Biot's theory is used to describe the saturated soil.By introducing two potential functions,the analytical solutions of displacement and hoop stress induced by the blast loads are derived in Laplace transforms domain.Numerical results are obtained by inversion of Laplace transforms presented.The influences of permeable property of interface between the liner and soil on dynamic response of the tunnel are analyzed.Also,the influences of the parameters of the saturated soil and the relative rigidity of the liner are discussed.It is shown that the maximum stresses and displacements are both higher under impermeable conditions than those under permeable conditions.The parameter has a significant effect on the amplitude of hoop stress.What's more,the attenuation of the responses becomes more apparent as the rigidity of liner increases.
Using an analytical method,the dynamic response of a circular tunnel in the saturated soil is investigated.Assuming that the blast occurs in the center of the tunnel,a model is established using simplified blast loads.The motions of the liner are considered specially based on the Flügge theory.The Biot's theory is used to describe the saturated soil.By introducing two potential functions,the analytical solutions of displacement and hoop stress induced by the blast loads are derived in Laplace transforms domain.Numerical results are obtained by inversion of Laplace transforms presented.The influences of permeable property of interface between the liner and soil on dynamic response of the tunnel are analyzed.Also,the influences of the parameters of the saturated soil and the relative rigidity of the liner are discussed.It is shown that the maximum stresses and displacements are both higher under impermeable conditions than those under permeable conditions.The parameter has a significant effect on the amplitude of hoop stress.What's more,the attenuation of the responses becomes more apparent as the rigidity of liner increases.
引文
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[2]李忠献,刘杨,田力.单侧隧道内爆炸荷载作用下双线地铁隧道的动力响应与抗爆分析[J].北京工业大学学报,2006,32(2):173–181.(LI Zhong-xian,LIU Yang,TIAN Li.Dynamic response and blast-resistance analysis of double track subway tunnel subjected to blast loading within one side of tunnel[J].Journal of Beijing University of Technology,2006,32(2):173–181.(in Chinese))
[3]刘沐宇,卢志芳.接触爆炸荷载下长江隧道的动力响应分析[J].武汉理工大学学报,2007,29(1):113–117.(LIU Mu-yu,LU Zhi-fang.Analysis of dynamic response of Yangtze River tunnel subjected to contact explosion loading[J].Journal of Wuhan University of Technology,2007,29(1):113–117.(in Chinese))
[4]FELDGUN V R,KOCHETKOV A V,KARINSKI Y S,et al.Internal blast loading in a buried lined tunnel[J].International Journal of Impact Engineering,2007,74(1):2–12.
[5]SENJUNTICHAI T,RAJAPAKSE R K N D.Tranisent response of a circular cavity in a poroelastic medium[J].Int J for Numerical and Analytical Method in Geomechanics,1993,17:357–383.
[6]徐长节,蔡袁强.黏弹性饱和土中球空腔的动力响应.土木工程学报[J].2001,34(4):88–92.(XU Chang-jie,CAI Yuan-qiang.Dynamic response of spherical cavity in nearly saturated viscoelastic soils[J].Rock and Soil Mechanics,2001,34(4):88–92.(in Chinese))
[7]XIE Kang-he,LIU Gan-bin,SHI Zu-yuan.Dynamic response of partially sealed circular tunnel in viscoelastic saturated soil[J].Soil Dynamic and Earthquake Engineering,2004,24:1003–1011.
[8]高广运,高盟,冯世进.无限弹性介质中隧道内爆炸动力响应的解析解[J].西北地震学报,2008,30(2):124–127.(GAO Guang-yun,GAO Meng,FENG Shi-jin.Analytical solution for the dynamic response of tunnel to an internal explosion in infinite elastic medium[J].Northwestern Seismological Journal,2008,30(2):124–127.(in Chinese))
[9]WATSON G N.A treatise on the theory of Bessel Function[M].Cambridge:Cambridge University Press,1994.
[10]ZAKOUT U,AKKAS N.Transient response of a cylindrical cavity with and without a bonded shell in an infinite elastic medium[J].Int J Eng Sci,1997,35(12/13):1203–20.
[11]LI X,CHEN Y.Transient dynamic response analysis of orthotropic circular cylindrical shell under external hydrostatic pressure[J].Journal of Sound and Vibration,2002,257(5):967–976.
[12]DURBIN F.Numerical inversion of Laplace transforms efficient improvement to Durbin and Abate’s method[J].Computer Journal,1974,17(4):371–376.
[13]曹玉忠,卢泽生.抗爆容器内爆炸流场数值模拟[J].高压物理学报,1997,15(2):127–132.(CAO Yu-zhong,LU Ze-sheng.Nunerical simulations of blast flowfields in closed blast-resistant containers[J].Chinese Journal of High Pressure Physics,1997,15(2):127–132.(in Chinese))
[14]HONIG G,HIRDES U.A method for the numerical inversion of Laplace transforms[J].Journal of Computational and Applied Mathematics,1984,10(1):113–132.
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