Simulation at the Meso-Scale of the Crack Induced Permeability in Concrete, Estimate of the Non Linear Evolution of the Flow Coefficient.
Résumé
The coupling between cracking and permeability of geomaterial members such as concrete and rock is of great interest for numerous problems. In most case the structure is wanted to be tight in order to prevent fluid or gas to migrate, this is as an example the case of nuclear waste disposals, nuclear plant confinement vessels, or other simple civil engineering infrastructures. In other cases, like hydraulic fracture for gas or geothermal welbores, the geomaterial is wanted to be permeable. If the material is uncracked, the overall permeability is driven by the migration into the porosity, in a case of macrocracking the flow into the cracks governs the overall permebility. The coupling between cracking and permeability can be introduced by the way of the damage variable \\cite\Picandet\₂001,chen\₂014\, but the application of this method must be restricted to the initiation of damage in particular conditions. An other way is to use directly the value of the crack width and to compute the permeability through the so called "cubic law". The crack width could be a direct result of the computation for discrete methods, embedded crack element or X-FEM methods, or the result of a post processing for continuous damage approches \\cite\Matallah\₂009\. In most cases the direct use of the cubic law overestimates the flow and authors use a tortuosity or flow coefficient which value ranges from 0.01 to 1. The computation of the cracking process at the mesoscopic scale allows to model the transition between difuse cracking and localized cracking \\cite\NGuyen\₂010\. We show that the cubic law directly applies at the mesoscopic scale and that it is possible to compute a non linear evolution of the flow coefficient that can be used at the macroscopic scale.