Issue 35

S. Valente et alii, Frattura ed Integrità Strutturale, 35 (2016) 306-312; DOI: 10.3221/IGF-ESIS.35.35 307 called Fictitious Crack Tip (shortened FCT, see Fig.1), which is still subjected to a compression stress. The normal component of the displacement discontinuity (Crack Opening Displacement, shortened COD) will appear later on. Therefore it is not possible to apply the asymptotic expansion for a cohesive crack [2-4], or other techniques [5-9]. Therefore the cohesive crack model has to be re-formulated with the focus on the shear stress component [10]. In this context, the classical Newton-Raphson method fails to converge to an equilibrium state. Therefore the approach used is based on two stages. Figure 1 : Water pressure distribution and uplift pressure distribution applied to a gravity dam proposed as a benchmark by ICOLD [1]. T HE MODEL ne of the main difference between a model related to a specimen tested in the laboratory and a model related to a large structure is due to the effects of the self-weight. The analysis of the gravity dam shown in Fig.1 begins from an initial state, which is a steady-state equilibrium configuration of the dam and of an appropriate portion of the rock foundation. The equilibrium state includes both horizontal and vertical stress components in both materials (concrete and rock). It is important to establish these initial conditions correctly so that the problem begins from an equilibrium state. In this initial state the reservoir is empty , the only load applied is the self-weight and the dam/rock contact is frictionless [11]. Therefore the interface is free from tangential stresses. Traction-Separation law applied to the Fracture Process Zone Once the equilibrium state is achieved in this initial phase, following the classical hypothesis of the cohesive crack model, a critical condition at the FCT is looked for. With reference to Fig.1, the points on the right side of the FCT are tied, so that no displacement discontinuity can occur after this operation. With reference to the cohesive crack model, this portion of the interface plays the role of an undamaged ligament. On the contrary, the portion of the interface on the left side of the FCT is called Fracture Process Zone (shortened FPZ). All the non-linear phenomena occurring afterwards are localized into the FPZ. Concrete and rock outside the FPZ behave linearly. This implementation of the cohesive crack model 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 FPZ are taken into account. O