In nature, weakly cemented granular materials are encountered in the form of soft rocks such as limestone, sandstone, mudstone, shale, etc. The mechanical behaviour of these materials is quite different from the purely frictional granular materials. The presence of cementation between the grains causes a significant variation in mechanical response under complex boundary conditions. In order to understand the manifestation of this interparticle cohesion at the ensemble level, we have used a hollow cylinder torsional testing apparatus which is capable of independently controlling the magnitude and the direction of the three principal stresses. From this experimental programme, the small strain response, peak strength and post peak behaviour with changing intermediate principle stress ratio (b) and initial mean effective stress (I1) is studied. In addition to the analysis of stress strain behaviour at different b and I1, stress-dilatancy characteristics of these cohesive frictional material are also discussed. This experimental study is followed by calibration and validation of a single hardening constitutive model which considers cementation as additional confinement. Observations from validation exercises suggest that this consideration works well for stress-strain response whereas it fails to predict the volumetric behaviour. © Springer International Publishing AG 2017.