An analysis concerning the influence of time-dependent loads on the final lining is carried out using the finite element method. The loading induced by a drop in the bearing capacity of temporary support system and changes in the behaviour of geomaterials caused by swelling or creep phenomena is investigated and quantified. Two-dimensional plane strain models are employed for four Mohr-Coulomb types of geomaterials representative of characteristic RMR categories with deep circular openings under hydrostatic pressure.


The final lining of a tunnel is generally constructed after the temporary support system has reached conditions of equilibrium, the purpose of strongly reinforced final linings thus questioned. It is generally accepted that the final lining provides for increased safety as to the project lifetime and considers a number of load types of permanent, variable and accidental nature, such as, hydrostatic pressure, seismic forces, temperature changes. In addition, the final lining may be required to withstand loads resulting from deterioration of the preliminary support system, long term deformation of geomass and physical-chemical alterations of the rock/soil itself. Within this framework, an analysis concerning the influence of the above time-dependent loads of the final lining is carried out using the finite element method aiming to quantify the induced loading.

1.1 Swelling

The phenomenon of swelling concerns time dependent strains that are due to a combination of physicochemical activity related to water and stress regime. Grob (1972) provided the mathematical expression of the swelling rule and Einstein et al. (1972) assumed that the swelling rock behaves as an isotropic and linear elastic material and that results of onedimensional oedometer tests can be extrapolated to three dimensions. An extensive coverage of methods and models can be found in ISRM, 1994. In the current research the numerical approach combined with the three-dimensional extension shall be used.

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