简谐振动下黏弹性土中衬砌的动力特性
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摘要
考虑土骨架和衬砌结构的动力相互作用,在频率域内研究了黏弹性土中衬砌结构的动力特性。根据黏弹性理论,把土骨架和混凝土衬砌视为饱和多孔黏弹性介质,通过引入势函数得到了简谐荷载作用下土骨架和衬砌的位移、应力的解析表达式。将衬砌结构等效为具有分数阶导数本构关系的黏弹性体,根据黏弹性理论推导了衬砌的简谐振动响应的完全解析解。根据界面连续性条件,确定了待定系数的具体表达式。将不同类型的黏弹性简谐动力响应进行了对比,并考察了分数导数本构参数、土体和衬砌结构各参数对系统动力特性的影响。结果表明:衬砌结构的黏性对系统动力响应有显著影响。随着衬砌厚度的增加,衬砌结构振动响应幅值减小;随着阶数的增加,系统共振效应逐渐减弱;随着材料参数T_σ/T_ε比的增加,系统响应幅值减小。
Considering the dynamic characteristics between lining structure and its soil, the dynamic characteristics of lining structure is presented in the frequency domain. Based on the viscoelastic theory, the analytical solutions for the displacement and stress of the soil are derived by the potential functions. The lining structure is treated as a viscoelastic medium with a fractional derivative constitutive relation. Based on the viscoelastic theory, the analytical solution for the dynamic response of lining structure is obtained. The specific expressions of undetermined coefficients are determined based on continuity conditions. The dynamic responses of different types of viscoelastic lining structure are compared, and the influences of the parameters for fractional derivative constitutive parameters, the soil and the lining structure on the system dynamic characteristics are analyzed. The results show that the viscous of a lining structure has a significant influence on the dynamic response of the system. The response amplitudes of a lining structure decrease gradually as the thickness of the lining structure increases. With the order increasing, the system-resonance effect is weakening. With the material parameter ratio T_σ/T_ε.increasing, the system-response amplitudes are decreasing.
Considering the dynamic characteristics between lining structure and its soil, the dynamic characteristics of lining structure is presented in the frequency domain. Based on the viscoelastic theory, the analytical solutions for the displacement and stress of the soil are derived by the potential functions. The lining structure is treated as a viscoelastic medium with a fractional derivative constitutive relation. Based on the viscoelastic theory, the analytical solution for the dynamic response of lining structure is obtained. The specific expressions of undetermined coefficients are determined based on continuity conditions. The dynamic responses of different types of viscoelastic lining structure are compared, and the influences of the parameters for fractional derivative constitutive parameters, the soil and the lining structure on the system dynamic characteristics are analyzed. The results show that the viscous of a lining structure has a significant influence on the dynamic response of the system. The response amplitudes of a lining structure decrease gradually as the thickness of the lining structure increases. With the order increasing, the system-resonance effect is weakening. With the material parameter ratio T_σ/T_ε.increasing, the system-response amplitudes are decreasing.
引文
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[2] 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): 37-44.
[3] ALUSLENDER F, COMBESCURE A. Spherical elastic-plastic structures under internal explosion approximate analytical solutions and application [J]. Engineering Structures, 2000, 22(8): 984-992.
[4] Kumar R, M iglani A, Debnath L. Radiadisplacements of an infinite liquid saturated porousmedium w ith cylindrical cavity [J ]. Computers andM athematics w ith Applications, 1999, 37(7): 117-123.
[5] 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(5): 481-488.
[6] LI X.Stress and displacement fields around a deepcircular tunnel with partial sealing[J].Computersand Geotechnics,1999,24(2):125-140.
[7] 刘干斌,顿志林,谢康和,等.饱和土体中半封闭压力隧洞的应力和位移场[J].科技通报,2004,20(1):45-50.
[8] 杨桂通,张善元.弹性动力学[M].北京:中国铁道出版社,1988:199―203.
[9] 高华喜,闻敏杰.具有黏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.
[10] 刘林超,闫启方.一维分数导数粘弹性饱和多孔介质层的稳态响应[J].工程力学, 2012,29(3):41-45.