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International audienceIn this paper, we focus on strength properties of double porous materials having a Drucker-Prager solid phase at microscale. The porosity consists in two populations of micropores and mesopores saturated with different pressures. To this end, we consider a hollow sphere subjected to a uniform strain rate boundary conditions. For the microscale to mesoscale transition, we take advantage of available results by Maghous et al. (2009), while the meso to macro upscaling is performed by implementing a kinematical limit analysis approach using Eshelby-like trial velocity fields. This two-step homogenization procedure delivers analytical expression of the macroscopic criterion for the considered class of saturated double porous media. This generalizes and improves previous results established by Shen et al. (2014). The results are discussed in terms of the existence or not of effective stresses. Some illustrations are provided