Post-cracking behavior of reinforced concrete deep beams: A numerical fracture investigation of concrete strength and beam size

A significant number of failures in reinforced concrete structures initiate in tension regions promoted by stress risers such as areas of high-stress concentrations or pre-existing cracks. Stable growth of these tensile cracks until peak loads is associated with the development of large zones of fracture (fracture process zone (FPZ)). The growth of the FPZ until peak load is reached introduces the effect of structural size on the failure loads. An energy approach based on fracture mechanics concepts can be used to rationally analyze and design for size effects in brittle failures. Current design equations were developed based on strength analysis (as in current American Concrete Institute (ACI)) where the margin of safety will be higher for smaller structures compared to larger ones. It is also conceivable that this approach would lead to unconservative designs for some very large structures (e.g., deep slabs for underground storage tanks). Since the empirical formulations of the code are based on data for normal strength concrete, it places a limit on the maximum strength that can be effectively used in the design equations. As a result, promising high-performance concrete cannot be used to its fullest potential. Revisions to the shear design formulations are needed to ensure uniform margin of safety for members of all sizes, strength, and geometries.;The dissertation deals with the finite element analysis of reinforced concrete deep beams using nonlinear fracture mechanics. Development of a numerical model that incorporates compression and tension softening of concrete, bond slip between concrete and reinforcement, and the yielding of the longitudinal steel reinforcement is presented and discussed. The development also incorporates the Delaunay refinement algorithm to create a triangular topology that is then transformed into a quadrilateral mesh by the quad-morphing algorithm. These two techniques allow automatic remeshing using the discrete crack approach. Nonlinear fracture mechanics is incorporated using the fictitious crack model and the principal tensile strength for crack initiation and propagation. The model has been successful in reproducing the load deflections, cracking patterns, and size effects observed in experiments of normal- and high-strength concrete deep beams with and without shear reinforcement.