黏弹性边界对圆形衬砌隧道动力响应的影响

Effect of viscoelastic boundary on dynamic response of circular tunnel

引入黏弹性边界模型,研究了3种瞬态荷载形式下黏弹性边界上径向刚度系数Kr与阻尼系数Cr对饱和土体与衬砌的径向位移、应力的影响。当Kr趋向于无穷,Cr趋向于0,黏弹性边界退化为完美黏结边界,取退化条件下的黏弹性边界参数同完美黏结边界条件下土体径向位移、应力进行对比,验证了黏弹性边界条件下的解答。分析了突加荷载、阶跃荷载和三角脉冲荷载下不同Kr与Cr值对饱和土体与衬砌的影响,结果表明:3种荷载作用下,刚度系数对土体与衬砌的径向位移、应力影响较大,阻尼系数对土体与衬砌的径向位移、应力影响较小;3种瞬态荷载峰值相同的情况下,突加荷载引起的土体与衬砌的径向位移、应力大于阶跃荷载和三角脉冲荷载。

By introducing a viscoelastic boundary model,the effects of radial stiffness coefficient Kr and damping coefficient Cr on the radial displacement and stress of saturated soil and a liner are studied.When Kr tends to infinity and Cr approaches zero,the viscoelastic boundary degenerates to a perfect bounding boundary.The validity of the proposed method is verified through comparisons between two cases:one is to incorporate the viscoelastic boundary model in the above-mentioned degeneration case and the other is the perfect bounding boundary condition(without the viscoelastic boundary model).The radial displacement and stress of soil in the two cases should be the same.In the numerical results,the effects of Kr and Cr on the response of saturated soil and the liner under a suddenly applied load,a gradually applied step load,and a triangular pulse load are analyzed.It is shown that the stiffness coefficient Kr has a large effect on the radial displacement and stress of soil and the liner under three loading cases.When the three kinds of loads have the same maximum magnitude,the dynamic response in soil and the liner generated by the suddenly applied load are greater than those by the gradually applied step load and triangular pulse load.