具有黏弹性衬砌的深埋圆形隧洞饱和土动力响应

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Abstract Since the concrete lining has viscoelastic properties，the whole process of its creep can not be described well by the previous theories such as elastic curved beam，elastic shell and so on. In this paper，the soil and concrete lining are considered as saturated viscoelastic porous medium and viscoelastic material with fractional derivative constitutive relation，respectively. The coupled vibration characteristics of the saturated viscoelastic soil and the lining system with a deep circular tunnel are investigated in frequency domain. Based on the Biot?s theory and viscoelastic theory，analytic solutions of displacement，stress and pore water pressure of the saturated soil and the lining under harmonic loads are obtained by displacement potential function，respectively. Besides，the expressions of undetermined coefficients are presented according to the inner boundary conditions of the lining as well as the displacement and stress continuous conditions at the interface between the saturated soil and the lining. At last，the effects of the physical and geometric parameters of the saturated soil and the lining on the system dynamic behavior are investigated. It is shown that the dynamic characteristics of the saturated viscoelastic soil and fractional derivative viscoelastic lining system are obviously different from those of the saturated viscoelastic soil and classic viscoelastic lining system. Furthermore，the response amplitudes decrease gradually as the damping ratio of the soil skeleton increases.

Key words： tunnelling engineering porous medium circular tunnel viscoelastic lining fractional derivative dynamic responses

Received: 22 April 2011

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https://rockmech.whrsm.ac.cn/EN/Y2012/V31/I2/413

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