DEM-simulated model cohesive assemblies of spherical grains of diameter d , with contact tensile strength F 0 , once prepared in loose states, are quasistatically subjected to growing isotropic pressure P , and then to triaxial compression, maintaining lateral stresses σ 2 = σ 3 = P while increasing axial stress σ 1 = P + q and strain є 1 . Reduced pressure P * = d 2 P/ F 0 varies from 0.1 (cohesion dominated case, for which systems typically equilibrate with solid fraction Ф ≃ 0.35), to large values for which the cohesionless behavior is retrieved. In triaxial compression, while the moderate strain response (є 1 ~ 0.1) is influenced by initial coordination numbers and mesoscale heterogeneities, the approach to the critical state, as both q (deviator) and Ф steadily increase, gets slower for smaller P * . Critical ratio q /P strongly increases for decreasing P * , as roughly predicted in an “effective stress” scheme. Anomalously small elastic moduli are observed in the gel-like structures. While extensive geometric rearrangements take place, no shear banding is observed. Loose cohesive granular assemblies are thus capable of large quasistatic stable plastic strains and ductile rupture.