The effect of grain crushing during one dimensional compression and triaxial compression tests is investigated in a double-porosity granular material using the Discrete Element Method (DEM). Experimental tests results from the literature on a porous crushable soil (pumice sand) were simulated in 3-D using a large number of particles and without the use of agglomerates. The numerical simulations show the importance of incorporating internal porosity as a material characteristic. The variation of internal porosity with particle dimensions is of fundamental importance while describing the mechanical behavior of the material. The contact model parameters were calibrated using low confinement triaxial compression experimental tests while the particle failure criteria was calibrated using high pressure one dimensional compression tests. Particle strength size effect was assumed equal to that observed in other porous geomaterials and ultimately derived from the variation of internal porosity. The good fit to experimental macroscopic observations thus attained lends credibility to numerical inferences about the evolution under loading of porosity fractions (intergranular and intragranular).