Effective strength of saturated double porous media with a Drucker–Prager solid phase |
| |
| Authors: | Wanqing Shen Zheng He Luc Dormieux Djimédo Kondo |
| |
| Institution: | 1. Laboratoire de Mécanique de Lille‐UMR 8107 CNRS, , USTL, 59655 Villeneuve d'Ascq, France;2. Unité de Recherche Navier, , UMR 8205 CNRS, 6/8 Avenue B. Pascal, 77455 Champs sur Marne, France;3. Institut D'Alembert, , UMR 7190 CNRS, UPMC (Paris 6), 75005 Paris, France |
| |
| Abstract: | This study aims at determining the macroscopic strength of porous materials having a Drucker–Prager solid phase at microscale and two populations of saturated pores with different pressures at both micro and meso scales. To this end, and taking account of the available results by Maghous et al. (2009), we first derive a closed‐form expression of approximate criterion for a dry porous medium whose matrix obeys to a general elliptic criterion. The methodology to formulate this criterion is based on limit analysis of a hollow sphere subjected to a uniform strain rate boundary conditions. The obtained results are then implemented in a two‐step homogenization procedure, which interestingly delivers analytical expression of the macroscopic criterion for dry double porous media whose solid phase at microscale obeys to a Drucker–Prager criterion. After a brief discussion of the results, we propose an extension to double porous saturated media, allowing therefore to quantify the simultaneous effects of the different pore pressures applied on each voids population. The results are discussed in terms of the existence or not of effective stresses. Finally, they are assessed by comparing them to recently available results. Copyright © 2013 John Wiley & Sons, Ltd. |
| |
| Keywords: | double porous materials ductile behavior macroscopic strength lastic compressibility pore saturated media Drucker– Prager solids |
|
|
