Looking at the long-time behaviour of a dam, it is necessary to assume that the water can penetrate a possible crack washing away some components of the concrete. This type of corrosion reduces the tensile strength and fracture energy of the concrete compared to the same parameters measured during a short-time laboratory test. This phenomenon causes the so called sub-critical crack propagation. That is the reason why the International Commission of Large Dams recommends to neglect the tensile strength of the joint between the dam and the foundation, which is the weakest point of a gravity dam. In these conditions a shear displacement discontinuity starts growing in a point, called Fictitious Crack Tip (shortened FCT), which is still subjected to a compression stress. In order to manage this problem, in this paper the cohesive crack model is re-formulated with the focus on the shear stress component. In this context, the classical Newton-Raphson method fails to converge to an equilibrium state. Therefore the approach used is based on two stages: (a) a global one in which the FCT is moved ahead of one increment; (b) a local one in which the non-linear conditions occurring in the Fracture Process Zone are taken into account. This two-stage approach, which is known in the literature as a Large Time Increment method, is able to model three different mechanical regimes occurring during the crack propagation between a dam and the foundation rock. [ABSTRACT FROM AUTHOR]