Most of the small asteroids with sizes below a few km are believed to be rubble piles. In order to study the strength of such bodies, we have performed bulk measurements on simulant granular material, varying the grain size and surface properties in ambient conditions. The samples were prepared from a high-fidelity asteroid soil simulant and subjected to compression and shear stresses. We measured the material angle of repose, Young Modulus, its angle of internal friction, bulk cohesion, and tensile strength. Grain sizes were varied from 0.1 to 10 mm. Grain surface properties (friction and cohesive forces) were modified by adding a surface frost layer. We find that, in shear, larger grains increase the strength in confined samples, representative of regolith subsurface layers on asteroids, while they decrease strength in unconfined samples, representative of surface regolith. In compression, confined samples become weaker with increasing grain size, while unconfined samples are barely sensitive to it. We also find that increasing surface friction and intergrain cohesion increases the strength in all the samples. We measure bulk cohesion values between ∼400 and 600 Pa, internal friction between 25 and 45°, and tensile strengths between 600 and 900 Pa. The measured angles of repose varied between ∼25 and 45° in an opposite trend to the internal friction. We compare these values to spacecraft data and numerical simulations and discuss implications of our findings for rubble-pile composition and disintegration behavior. We find that grain size sorting with depth, depletion of fines at the surface, or presence of water ice in the core can provide a mechanism for regular surface shedding event on small asteroids. • We performed mechanical strength measurements on high-fidelity CI asteroid simulant. • Larger grains weaken samples in compression but strengthen it in shear. • Surface frosting on grains strengthens the samples in both compression and shear. • Measured compression and tensile strengths are in agreement with in-situ measurements at Ryugu and Bennu. • We propose potential mechanisms for regular surface shedding event on rubble-pile asteroids.