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SUMMARYIn this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second-order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro-macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data.

SUMMARYA new formulation is proposed to model pounding between two adjacent structures, with natural periods T 1 and T 2 and damping ratios 1 and 2 under harmonic earthquake excitation, as non-linear Hertzian impact between two single-degree-of-freedom oscillators. For the case of rigid impacts, a special case of our analytical solution has been given by Davis ('Pounding of buildings modelled by an impact oscillator' Earthquake Engineering and Structural Dynamics, 1992; 21:253-274) for an oscillator pounding on a stationary barrier. Our analytical predictions for rigid impacts agree qualitatively with our numerical simulations for non-rigid impacts. When the di erence in natural periods between the two oscillators increases, the impact velocity also increases drastically. The impact velocity spectrum is, however, relatively insensitive to the stando distance. The maximum relative impact velocity of the coupled system can occur at an excitation period T * n which is either between those of the two oscillators or less than both of them, depending on the ratios T 1 =T 2 and 1 = 2 . Although the pounding force between two oscillators has been primarily modelled by the Hertz contact law, parametric studies show that the maximum relative impact velocity is not very sensitive to changes in the contact parameters.