饱和分数导数型粘弹性土深埋圆形隧洞衬砌系统的动力特性-工程力学.pdfVIP

29 卷 12 期 Vol.29 No.12 工 程 力 学 2012 年 12 月 Dec. 2012 ENGINEERING MECHANICS 248 文章编号：1000-4750(2012)12-0248-08 饱和分数导数型粘弹性土 深埋圆形隧洞衬砌 系统的动力特性 杨 骁，闻敏杰 (上海大学土木工程系，上海 200072) 摘 要：在频率域研究了分数导数型粘弹性饱和土体和深埋圆形隧 弹性衬砌相互作用的耦合简谐振动。将土骨 架视为具有分数阶导数型本构的粘弹性体，基于饱和多孔介质理论和平面弹性理论，分别给出了饱和粘弹性土、 弹性衬砌简谐振动的解析解。通过弹性衬砌和饱和土接触面处的连续性条件和衬砌内边界条件，得到了饱和粘弹 性土-衬砌系统的稳态动力响应，给出了衬砌和饱和粘弹性土位移、应力和孔隙压力的解析表达式。在此基础上， 进行了参数研究，讨论了物理和几何参数对系统响应的影响。研究表明：饱和分数导数型粘弹性土-衬砌系统的动 力响应与经典饱和弹性/粘弹性土-衬砌系统的动力响应差异很大。 关键词：分数导数模型；粘弹性饱和土；圆形隧 ；弹性衬砌；参数研究 中图分类号：O327; TU441.8 文献标志码：A doi: 10.6052/j.issn.1000-4750.2011.05.0283 DYNAMIC CHARACTERISTICS OF SATURATED FRACTIONAL DERIVATIVE TYPE VISCOELASTIC SOIL AND LINING SYSTEM WITH A DEEPLY EMBEDDED CIRCULAR TUNNEL YANG Xiao , WEN Min-jie (Department of Civil Engineering, Shanghai University, Shanghai 200072, China) Abstract: The coupled harmonic vibration of the saturated fractional derivative type viscoelastic soil and elastic lining of a deeply embedded circular tunnel is investigated in the frequency domain. Regarding the soil skeleton as a viscoelastic medium with a fractional derivative constitutive relation and based on the theory of saturated porous medium and plane elasticity, analytical solutions of the harmonic vibrations of the saturated viscoelastic soil and the elastic lining are presented, respectively. The steady-state dynamic responses of the saturated viscoelastic soil and lining system are obtained by the inner boundary conditions of the lining and the continuity conditions on the interface between the saturated soil and the lining, and the analytical expressions of the d