We rely on 3D simulations based on the Lattice Element Method (LEM) to analyze the failure of porous granular aggregates under tensile loading. We investigate crack growth by considering the number of broken bonds in the particle phase as a function of the matrix volume fraction and particle-matrix adhesion. Three regimes are evidenced, corresponding to no particle damage, particle abrasion and particle fragmentation, respectively. We also show that the probability density of strong stresses falls off exponentially at high particle volume fractions where a percolating network of jammed particles occurs. Decreasing the matrix volume fraction leads to increasingly broader stress distribution and hence a higher stress concentration. Our findings are in agreement with 2D results previously reported in the literature.