Analytical study of mine closure behaviour in a poro‐visco‐elastic medium

Abstract

SUMMARYThis paper is interested in the hydro-mechanical behaviour of an underground cavity abandoned at the end of its service life. It is an extension of a previous study that accounted for a poro-elastic behaviour of the rock mass (Int. J. Comput. Geomech. 2007; DOI: 10.1016 DOI: 10. /j.compgeo.2007. Deterioration of the lining support with time leads to the transfer of the loading from the exterior massif to the interior backfill. The in situ material has a poro-visco-elastic constitutive behaviour while the backfill is poroelastic, both saturated with water. This loading transfer is accompanied by an inward cavity convergence, thereby compressing the backfill, and induces an outward water flow. This leads to a complex space-time evolution of pore pressures, displacements and stresses, which is not always intuitive. In its general setting, a semi-explicit solution to this problem is developed, using Laplace transform, the inversion being performed numerically. Analytical inversion leading to a quasi-explicit solution in the time domain is possible by identifying the characteristic creep and relaxation times of volumetric strains with those of the deviatoric strains, on the basis of a parametric study. A few numerical examples are given to illustrate the hydro-mechanical behaviour of the cavity and highlight the influence of key parameters (e.g. stiffness of backfill, lining deterioration rate, etc.). Further studies accounting for more general material behaviours for the backfill and external ground are ongoing.

Hydromechanical Responses of a Decommissioned Backfilled Tunnel Drilled into a Poro-Viscoelastic Medium

“…7(a) that the characteristic relaxation time of the bulk modulus, tr * , only has a marginal eŠect on the pore pressure and by extension, on the convergence and stress responses. A similarˆnding is reported in Wong et al (2008a) regarding this eŠect for the spherical cavity. Conversely, the characteristic relaxation time of the shear modulus, ur * , has a more signiˆcant eŠect on the pore pressure ( Fig.…”

“…In the framework of the present study, the ground movements and increases of the support loading are caused by the creep of the host rock and thus, must be taken into account. In light of this and to include the possibility of creep eŠects, the behaviour of the porous structure of the surrounding medium of the tunnel, can be described by the following poro-viscoelastic functional constitutive equations (e.g., Coussy, 1991Coussy, , 2004Wong et al, 2008a;Dufour, 2008):…”

“…where tc, uc are the characteristic creep times which are related to the above relaxation times as follows (e.g., Wong et al, 2008a;Dufour, 2008):…”

“…The radius of the tunnel, a, is chosen as the characteristic length, the initial overburden stress S0 is the characteristic stress or pressure and the characteristic diŠusion time is taken as (Wong et al, 2008a),…”

“…For the purpose of the present study we have chosen the same set of reference parameter values adopted in our earlier paper (Wong et al, 2008a) and inspired by Gaombalet (2004):…”