Biot tensor

Abstract A new upscaling method has been developed using 3D numerical tools (RESOBLOK 3DEC). This method has been successfully compared with standard analytical approaches in the case of a simple fracture network. This method has been applied to determine the equivalent permeability, stiffness and Biot tensor of a real fracture rock-mass at different scales. The effects of the fracture network properties and of the state of stress on the result have been investigated. 

A new upscaling method has been proposed by INERIS to determine the equivalent hydro mechanical properties of a fractured rock-mass. This method is based on the 3D numerical simulations of the behaviour of a "sample" of fractured rock-mass submitted to different hydromechanical boundary conditions. The simulations are defined in order to determine the equivalent permeability, stiffness and Biot tensor of a fractured rock-mass. 

The macroscopic drained stiffness tensor Chom(f) and Biot s coefficient B( ) can then be expressed as a function of the average of A over the fluid saturated pore space (I=fourth identity tensor) ... 

The material properties to be homogenized and upscaled are drawn from Biot s theory extended for non-isothermal consolidation (Guvanasen and Chan 2000). The modified crack tensor theory of Oda (1986) has been modified to include other transport and thermoelastic properties specified by Guvanasen and Chan (2000). 

The stress tensor the elastic strain tensor Eu, the Biot s tensor Bg and the Biot coefficient G are linked by the Biot s equation ... 

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