HYBRID REINFORCED CONCRETE ELEMENTS (HRC): BRIDGED CRACK MODEL DETERMINATION OF MINIMUM REINFORCEMENT CONDITIONS

In the framework of Fracture Mechanics, this Master Thesis aims to analyze the behaviour of Hybrid Reinforced Concrete (HRC) structural elements, in which the reinforcing secondary phase consists in a combination of ordinary steel rebars and short discontinuous fibres. Analogously to the case of Fibre Reinforced Concrete (FRC) members, experimental campaigns suggest to subdivide the flexural behaviour of HRC beams into three different stages. Considering a notched HRC element subjected to bending the related applied load versus deflection diagram starts with a linear elastic branch (Stage I), up to the initiation of the fracturing process. Then, the post-cracking regime of the composite takes place, which depends on the amount of ordinary steel rebars and of reinforcing fibres. In the first part of this regime (Stage II), both fibres and steel rebars provide their contribution in terms of closing action against crack propagation. Finally, the toughening contribution of the fibres gradually decreases with the crack propagation, leading to a final plastic plateau (Stage III), which depends only on the amount of traditional steel rebars. As reported in Chapter 2, the Bridged Crack Model is proposed as a Fracture Mechanics approach able to describe the evolution of the crack propagation process at the notched (or critical) cross-section of HRC members subjected to monotonically increasing flexural loading. The model assumes an elastic-perfectly brittle behaviour of the concrete matrix, whose toughening contribution is described by the concrete fracture toughness, KIC. On the other hand, appropriate constitutive laws describe the toughening contribution of the reinforcing secondary phase, which relates to the yielding of the steel rebars and to the slippage of the steel fibres, respectively. The numerical model has been extended in order to simultaneously consider the effect of these two different bridging mechanisms, as described in Chapter 3. In Chapter 4, parametric sets of numerical simulations are presented, showing that the abovementioned post-cracking regimes are actually governed by three scale-dependent dimensionless numbers: (i) two reinforcement dimensionless numbers, and , which are directly related to the steel area percentage, ρ, and to the fibre volume fraction, Vf, respectively; (ii) the dimensionless number, , which depends on the fibre embedment length, wc. The focus of the present analysis is on the combination of these three dimensionless numbers, which provides the minimum reinforcement condition, i.e., the minimum percentage steel area, ρmin, or minimum fibre volume fraction, Vf,min, required to obtain a stable post-cracking response, together with its scale-dependence. Finally, in Chapter 5 the model is validated on the basis of different experimental campaigns reported in the scientific literature, in which flexural tests were carried out on HRC beams. It is shown that the identification of the mechanical properties of the composite leads to an effective superposition between experimental data and numerical predictions, thus promoting the model as an effective tool to predict the flexural behaviour of HRC structural members together with the minimum reinforcement condition.