Three-dimensional numerical modeling of reinforced concrete behaviour

Reinforced concrete (RC) structures exhibit a complex behavior even for low load levels. Non-linear compressive stress-strain relations, tensile cracking, post cracking softening and interaction effects between concrete and reinforcing bars are the main sources of a highly nonlinear and complicated response. In order to capture the real structural behavior, sophisticated numerical tools are necessary to take into account all the remarkable phenomena and to perform the time-consuming non-linear calculations. In this doctorate dissertation, the three-dimensional (3D) constitutive model for non-linear analysis of RC structures 3D-PARC – Three-Dimensional Physical Approach for Reinforced Concrete, is presented. The 3D study started some years ago with the author's graduate thesis which laid the foundations of the model [34]. That work was an extension of PARC, a numerical model for membrane elements subjected to plane stress (Figure 1.1) developed at the Department of Civil Engineering of the University of Parma [8, 9]. The PARC formulation is based on some previous works [25, 14]. In the author's graduate thesis, the model was implemented in TRE, a computer code which can analyze the behavior of a single material point and therefore, also of simple structures subjected to uniform stress. The good results achieved were an encouragement to keep on working on this topic. The research carried out during the doctorate, deepens the investigation of the model theory and the development of numerical tools to provide efficacy and power to its application. Starting from the work already done, a new approach is developed and implemented. However, the basic philosophy does not change: the model remains as close as possible to the physical reality, without using numerical devices which are often “unphysical”. The starting point for the model formulation is the study of physical phenomena (concrete subjected to multiaxial stresses, aggregate bridging and interlock, tension stiffening, dowel action) through single basic studies which are assembled to build the model.The developed theory is implemented in a FORTRAN code which can be used within the commercial Finite Element (FE) code ABAQUS [1]. In this way, the model can be used to analyze structures subjected to complex stress states. In fact, the FE formulation gives the possibility to model a wide range of structures independently on the geometry. Subsequently, the theory formulation as well as the numerical implementation are validated by some significant comparisons with experimental tests taken from the literature. During a six-month collaboration with the Institute of Structural Engineering (IKI) of the University of Natural Resources and Applied Life Sciences – BOKU in Vienna, the software package SARA, which includes the RC-oriented FE code ATENA and the statistical module FREET, was also used. This research program produced the FE analysis of RC corbels reported in Chapter 5.