3D model for the evaluation of multiaxial fracture behaviour of reinforced concrete members

Reinforced concrete exhibit a complex mechanical behavior even at low load levels; the main sources of a highly non-linear response are: non-linear compressive stress-strain relations, low tensile strength and cracking, post cracking softening and interaction effects between concrete and reinforcing bars, etc. In addition, 3D analysis is always complicated by a marked anisotropy behavior due to the arrangement of the reinforcement. In this study a three-dimensional numerical model for the analysis of multi-axial fractured reinforced concrete is proposed. The model, named 3D-PARC [1], is an extension of the previous 2D-PARC [3,4] and is formulated in terms of secant stiffness for the implementation into Finite Element procedures. The uncracked phase of concrete is described by a non-linear elastic model, whose moduli are evaluated through equivalent nonlinear uniaxial relationships and the maximum stresses limited by a strength domain [1]. Singly and multiply cracked phases are simulated by adding to the deformability of the integer material, adequately degraded for cracking, the strain contributes of cracks. These contributes are evaluated through local analysis of a reinforced concrete element on basis of a strain decomposition procedure. The crack model is based on fixed, multi-directional cracking and smeared reinforcement approaches taking into account the effects of multi-axial stress states, cracking and interface interactions such as tension stiffening, dowel action and aggregate interlock. The model is implemented in a Finite Element framework and it is validated through the comparisons to significant experimental test results.