An XFEM strategy to analyse the scale-slenderness-reinforcement failure mode transitions in RC beams

Reinforced concrete beams in flexure exhibit three different collapse mechanisms by varying the mechanical and geometrical parameters. The limit cases are: tensile failure for low steel percentages and/or small and slender beams, and crushing failure for high steel percentages and/or large and stocky beams. The intermediate collapse mechanism is represented by diagonal tension failure, in which the collapse is dominated by the unstable propagation of one or more shear cracks. In the present contribution, the results of a comprehensive experimental research program are presented. A total of 48 three-point-bending tests have been performed on beams having longitudinal reinforcement amounts varying from 0.10% to 3.39%, different structural sizes varying in the ratio 1:16, and different slendernesses varying from 3 to 24. The obtained results confirm the original insight by Carpinteri on the effects of the size, slenderness and reinforcement ratio on the collapse transitions. More in details, transitions from tensile-to-shearing-to-crushing failures have been obtained in the following cases: by increasing the reinforcement percentage, by increasing the beam size with constant reinforcement ratio, by decreasing the beam size with constant reinforcement area, and by decreasing the beam slenderness. Further progress in the numerical modeling are also presented, with the proposal of a more refined approach, based on the XFEM. With respect to previous models, the new one takes into account all the forms of nonlinearity, included those of concrete, with the implementation of the Cohesive and the Overlapping Crack models. Such an effective tool permits to consider more than one crack along the beam span, and to evaluate the actual crack trajectory step-by-step, on the basis of a stress criterion of propagation.