Non-local poromechanical coupling based on multi phase-fields
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Accurate and realistic modeling of the coupling between concrete cracking and water pressure is a major challenge for determining the residual strength of hydraulic structures such as dams or dykes. The cracking can result from a mechanical loading, a hydraulic pressure, or a pathology of concrete such as an internal swelling reaction. Often a combination of the latter occurs simultaneously. The cracking generates a change in local water pressure field which can increase the cracking and the chemical pathologies. That is the reason why the poro-mechanics of cracked concrete must be modeled. From a numerical point of view, the modeling of cracking is the consequence of strains localization. In one hand, several methods can be used to make objective the numerical solution of localization. Among these methods are the local methods and the non-local ones. On the other hand, the frequent use of quadratic finite elements for poromechanical formulations leads to forego the ease to implement local methods, and leads to choose a non-local formulation. In this work, a non-local method based on second gradient theory applied to a plastic strain tensor using a multi phase-fields formulation is applied to regularize the strain localization while preserving the anisotropy of the model on the damaged dams [1]. As the permeability depends nonlinearly on the crack openings and re-closings, a subject of concern is the link between the regularized plastic strain and the permeability tensor. The objective is to preserve the independence of the response to the mesh on the mechanical part, but also to conserve the flow in the cracked zones. In this work, a method for calculating permeability based on the non-local plastic strain tensor and on the balance equations is proposed. Case studies are then presented and discussed.
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