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In this work, we employ a soft-sphere discrete element method with a cohesion implementation to model the dynamical process of sub-km-sized cohesive rubble piles under continuous spinup. The dependencies of critical spin periods $T_c$ on several material parameters for oblate rubble piles with different bulk diameters $D$ are explored. Our numerical simulations show that both the increase of interparticle cohesion and particle shape parameter in our model can strengthen the bodies, especially for the smaller ones. In addition, we find there exists some critical diameter $D_{cri,ρ}$ at which the variation trend of $T_c$ with the bulk density $ρ$ reverses. Though a greater static friction coefficient $μ_S$ can strengthen the body, this effect attains a minimum at a critical diameter $D_{cri,ϕ}$ close to $D_{cri,ρ}$. The continuum theory (analytical method) is used for comparison and two equivalent critical diameters are obtained. The numerical results were fitted with the analytical method and the ratio of the interparticle cohesion $c$ to the bulk cohesion $C$ is estimated to be roughly 88.3. We find this ratio keeps constant for different $c$ and $ρ$, while it strongly depends on the friction angle $ϕ$. Also, our numerical results further show that the dependency of $T_c$ on $ϕ$ is opposite from that predicted by the continuum theory when $D$ < $D_{cri,ϕ}$. Finally, we find that the two critical diameters happen to be close to the diameter when the mean normal stress of the body equals zero, which is the separation between the compressive regime and the tensile regime.