具有圆形隧道的准饱和黏弹性土振动响应
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摘要
采用解析方法在频率域内研究简谐荷载作用下具有分数导数黏弹性衬砌的圆形隧道准饱和黏弹性土振动响应.假定混凝土衬砌为黏弹性材料,利用分数导数模型描述动力学行为.将水-气混合物视为一种均匀流体,采用Biot波动理论模拟准饱和黏弹性土.利用分数导数黏弹性衬砌内边界以及准饱和黏弹性土和衬砌结构界面处的连续性条件,得到准饱和黏弹性土和分数导数型衬砌动力相互作用时土体和衬砌的位移、应力和孔隙水压力等的解析表达式.讨论饱和度、衬砌厚度及分数导数本构参数对系统动力响应的影响.数值结果表明,分数导数阶数对系统响应的影响与衬砌材料参数比有关;饱和度对衬砌和土体界面处孔隙水的渗透性有较大影响;弹性衬砌条件下的系统响应大于分数导数黏弹性衬砌条件下的系统动力响应.
The dynamic response of the nearly saturated viscoelastic soil with a fractional derivative viscoelastic lined circular tunnel subjected to harmonic load was investigated in the frequency domain by using an analytical method.Assuming that the concrete lining is a viscoelastic material,its dynamic behavior was described by the fractional derivative model.The mixture of water and gas was considered as a uniform fluid and the Biot'theory was used to describe the nearly saturated viscoelastic soil.By inner boundary conditions of the fractional derivative viscoelastic lining and the continuity boundary conditions on the interface between the nearly saturated viscoelastic soil and lining structure,the analytical expressions for the displacement,stress and pore water pressure of the soil and lining for the interaction of nearly saturated viscoelastic soil and fractional derivative viscoelastic lining were obtained.The influences of the saturation,lining thickness and the fractional derivative constitutive parameters on the system responses were discussed.Results show that the influences of the order of fractional derivative on the system responses relate to the material parameters;the saturation greatly influences on the permeability of pore water on the interface between the lining and soil.The system responses with the elastic lining are greater than those with the fractional derivative viscoelastic lining.
The dynamic response of the nearly saturated viscoelastic soil with a fractional derivative viscoelastic lined circular tunnel subjected to harmonic load was investigated in the frequency domain by using an analytical method.Assuming that the concrete lining is a viscoelastic material,its dynamic behavior was described by the fractional derivative model.The mixture of water and gas was considered as a uniform fluid and the Biot'theory was used to describe the nearly saturated viscoelastic soil.By inner boundary conditions of the fractional derivative viscoelastic lining and the continuity boundary conditions on the interface between the nearly saturated viscoelastic soil and lining structure,the analytical expressions for the displacement,stress and pore water pressure of the soil and lining for the interaction of nearly saturated viscoelastic soil and fractional derivative viscoelastic lining were obtained.The influences of the saturation,lining thickness and the fractional derivative constitutive parameters on the system responses were discussed.Results show that the influences of the order of fractional derivative on the system responses relate to the material parameters;the saturation greatly influences on the permeability of pore water on the interface between the lining and soil.The system responses with the elastic lining are greater than those with the fractional derivative viscoelastic lining.
引文
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[15]BARDET J P,SAYED H.Velocity and attenuation ofcompressional waves in nearly saturated soils[J].SoilDynamics and Earthquake Engineering,1993,129(7):397-401.
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[17]徐长节,马晓华.粘弹性准饱和土中球空腔的动力响应[J].岩土力学,2005,26(8):1189-1194.XU Chang-jie,MA Xiao-hua.Dynamic response ofspherical cavity in nearly saturated viscoelatic soils[J].Rock and Soil Mechanics,2005,26(8):1189-1194.
[18]BIOT M A.Theory of propagation of elastic waves in afluid-saturated porous media.I.low frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):168-178.
[19]BAGLEY R L,TORVIK P J.A theoretical basis forthe application of fractional calculus to viscoelasticity[J].Journal of Rheology,1983,27(3):201-210.
[20]朱正佑,李根国,程昌钧.具有分数导数本构关系的粘弹性Timoshenko梁的静动力学行为分析[J].应用数学和力学,2003,23(1):1-10.ZHU Zheng-you,LI Gen-guo,CHENG Chang-jun.Quasi-static and dynamical analysis for viscoelasticTimoshenko beam with fractional derivative constitu-tive relation[J].Applied Mathematics and Mechanics,2003,23(1):1-10.
[2]SENJUNTICHAI T,RAJAPAKSE R K N D.Transi-ent response of a circular cavity in a poroelastic medium[J].International Journal for Numerical and AnalyticalMethods in Geomechanics,1993,17(6):357-383.
[3]杨峻,宫全美,吴世明,等.饱和土体中圆柱形孔洞的动力分析[J].上海力学,1996,17(1):37-45.YANG Jun,GONG Quan-mei,WU Shi-ming,et al.Transient response of a cylindrical cavity in a saturatedsoil body[J].Shanghai Journal of Mechanics,1996,17(1):37-45.
[4]FELDGUN V R,KOCHETKOV A V,KARINSKI YS,et al.Internal blast loading in a buried lined tunnel[J].International Journal of Impact Engineering,2007,35(3):172-183.
[5]ALUSLENDER F,COMBESCURE A.Spherical elas-tic-plastic structures under internal explosion approxi-mate analytical solutions and application[J].Engineer-ing Structures,2000,22(8):984-992.
[6]GLENN L A,KIDDER R E.Blast loading of a sphericalcontainer surrounded by an infinite elastic medium[J].Journal of Applied Engineering,1983,50(4a):723-726.
[7]XIE K H,LIU G B,SHI Z Y.Dynamic response of par-tially sealed circular tunnel in viscoelastic saturated soil[J].Soil Dynamics Earthquake Engineering,2004,24(12):1003-1011.
[8]LIU G B,XIE K H.Transient response of a sphericalcavity with a partially sealed shell embedded in viscoe-lastic saturated soil[J].Journal of Zhejiang University:Science,2005,6A(3):194-201.
[9]蔡袁强,陈成振,孙宏磊.爆炸荷载作用下饱和土中隧道的瞬态动力响应[J].岩土工程学报,2011,33(3):361-367.CAI Yuan-qiang,CHEN Cheng-zhen,SUN Hong-lei.Transient dynamic response of tunnels subjected to blastloads in saturated soil[J].Chinese Journal of Geotechni-cal Engineering,2011,33(3):361-367.
[10]蔡袁强,陈成振,孙宏磊.黏弹性饱和土中隧道在爆炸荷载作用下的动力响应[J].浙江大学学报:工学版,2011,45(9):1657-1663.CAI Yuan-qiang,CHEN Cheng-zhen,SUN Hong-lei.Dynamic response of tunnel in viscoelastic saturated soilsubjected to blast loads[J].Journal of Zhejiang Universi-ty:Engineering Science,2011,45(9):1657-1663.
[11]高盟,高广运,王滢,等.饱和土与衬砌动力相互作用的圆柱形孔洞内源问题解答[J].固体力学学报,2009,30(2):481-488.GAO Meng,GAO Guang-yun,WANG Ying,et al.Asolution on the internal source problem of a cylindricalcavity considering the dynamic interaction between lin-ing and saturated soil[J].Chinese Journal of SolidMechanics,2009,30(2):481-488.
[12]高华喜,闻敏杰.具有粘弹性衬砌的深埋圆形隧洞饱和土动力响应[J].岩石力学与工程学报,2012,31(2):413-420.GAO Hua-xi,WEN Min-jie.Dynamic responses ofsaturated soil with a viscoelastic lined embedded circ-ualr tunnel[J].Chinese Journal of Rock Mechanics andEngineering,2012,31(2):413-420.
[13]周洪峰,朱陆明,徐长节,等.准饱和土地基刚性基础的竖向振动分析[J].哈尔滨工业大学学报,2006,38(4):603-606.ZHOU Hong-feng,ZHU Lu-ming,XU Chang-jie,etal.Vertical vibration of a rigid foundation on nearlysaturated soil[J].Journal of Harbin Institute of Tech-nology,2006,38(4):603-606.
[14]YANG J,SATO T.Influence of water saturation onhorizontal and vertical motion at a porous soil interfaceinduced by incident SV wave[J].Soil Dynamics andEarthquake Engineering,2000,19(5):339-346.
[15]BARDET J P,SAYED H.Velocity and attenuation ofcompressional waves in nearly saturated soils[J].SoilDynamics and Earthquake Engineering,1993,129(7):397-401.
[16]吴世明.土介质中的波[M].北京:科学出版社,1997:16-22.
[17]徐长节,马晓华.粘弹性准饱和土中球空腔的动力响应[J].岩土力学,2005,26(8):1189-1194.XU Chang-jie,MA Xiao-hua.Dynamic response ofspherical cavity in nearly saturated viscoelatic soils[J].Rock and Soil Mechanics,2005,26(8):1189-1194.
[18]BIOT M A.Theory of propagation of elastic waves in afluid-saturated porous media.I.low frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):168-178.
[19]BAGLEY R L,TORVIK P J.A theoretical basis forthe application of fractional calculus to viscoelasticity[J].Journal of Rheology,1983,27(3):201-210.
[20]朱正佑,李根国,程昌钧.具有分数导数本构关系的粘弹性Timoshenko梁的静动力学行为分析[J].应用数学和力学,2003,23(1):1-10.ZHU Zheng-you,LI Gen-guo,CHENG Chang-jun.Quasi-static and dynamical analysis for viscoelasticTimoshenko beam with fractional derivative constitu-tive relation[J].Applied Mathematics and Mechanics,2003,23(1):1-10.
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