Frequency Response of a Fractional Derivative Viscoelastic Type Lined Tunnel with Partial Sealing
Based on Biot saturated soil theory, steady state dynamic response of the system is studied in the frequency domain when the inner boundary of a fractional derivative viscoelastic type circular lined tunnel is under the axisymmetric load and fluid pressure respectively. On the basis of introducing a partial permeable boundary condition, the solutions of stress, displacement and pore pressure of the lining and saturated soil are obtained by the inner boundary of the lining and continuity conditions of the interface, besides, the stress-displacement constitutive behavior of the lining is described by fractional derivative viscoelastic constitutive model. The influence of physical parameter on the system response is investigated. It is shown that the order of fractional derivative model has a great influence on the system dynamic response, and it depends on material parameter of the lining when the inner boundary of lining is subjected to axisymmetric load. The permeability parameter of lining has significant effects on system response induced by fluid pressure.
Qing Yang, Li Hua Zhu, Jing Jing He, Zeng Feng Yan and Rui Ren
H. X. Gao et al., "Frequency Response of a Fractional Derivative Viscoelastic Type Lined Tunnel with Partial Sealing", Advanced Materials Research, Vols. 368-373, pp. 2692-2697, 2012