Consolidation of a double-porosity medium

The classical one!dimensional column consolidation boundary value problem is studied for a double!porosity material[ Uniaxial strain and constant vertical stress conditions are applied to a column that is drained at the top and undrained at the bottom[ An initial ~uid pressure di}erential develops between the matrix and fracture phases in response to surface loading when variations in the mechanical and ~ow parameters of the matrix and fracture exist[ The mean stress is shown to be a linear combination of the ~uid pressure in the matrix and the ~uid pressure in the fracture[ The time dependent general analytical solution is given for the matrix and fracture pressure histories and surface displacements using fracture and matrix storage coe.cients de_ned for constant stress "constant con_ning pressure# and the assumption that the cross!storage coe.cient at constant stress is negligible[ Pressure and displacement histories are controlled by the mechanical and ~ow properties of both the matrix and fracture and on the magnitude of the di}erences between the two phases[ The double!porosity solution approaches the equivalent single porosity solution for closely spaced fractures\ a small permeability contrast and a large cross!~ow term[ Pressures and dis! placements are also compared to previous results in the literature based on storage coe.cients de_ned at constant volumetric strain and the assumption that the constant strain cross!storage coe.cient is negligible[ The previous results included small matrix ~uid pressures and fracture ~uid pressures in excess of the applied stress[ The constant stress formulation of the double!porosity column consolidation problem produces physically intuitive results[ 0887 Elsevier Science Ltd[ All rights reserved