INTERACTIVE FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE; A FRACTURE MECHANICS APPROACH

One of the major complexities in the finite element modeling of post cracking behaviour of reinforced concrete structures is the proper representation of the structural discontinuity and stress singularity introduced by a crack. Ideally, the simulation of a crack in a finite element analysis should be accomplished by an interelement discontinuity. However the continuous modification of a mesh and its nodal renumbering have previously precluded such an approach. It has been found simpler to modify the material properties of a fixed mesh.; The purpose of this investigation is to solve the problems associated with interelement crack nucleation and propagation using an interactive computer code. The main advantage of this approach is its ability to properly model the stress singularity at the tip of a crack, and use fracture mechanics criteria for the stability and the length of the crack extension.; The applicability of linear elastic fracture mechanics to concrete has been confirmed by a proper reinterpretation of the extensive experimental program undertaken by Naus Kesler and Lott.; Although most of the individual components of this research program have been previously developed and used in different engineering fields, this is the first attempt to combine all those aspects on a multidisciplinary basis. In addition recent advances in the fields of finite element and fracture mechanics have been applied to reinforced concrete analysis for the first time. Numerical difficulties are overcome by using a state of the art mesh optimizer and equation solver algorithms, and the overall interactive analysis is greatly facilitated by using a medium-level computer graphics facility.; The computer program developed here is capable of automatically simulating discrete crack nucleation and extension through a finite element mesh as governed by an appropriate analysis. The user can interact with the program through a storage tube graphics display device. Throughout the multistep analysis, he is shown updated meshes and a number of intermediate results which will allow him to control, alter, or modify the computer decision making process based on his engineering judgment.; A parametric study of a reinforced concrete beam has been performed. The effects of fracture toughness, aggregate interlock and concrete non-linearity are assessed. The simple linear model gave a satisfactory correlation with the experimental results for up to half the failure load. An improvement in the correlation, up to failure, was achieved by modeling the concrete as a non-linear material. It was also found that while a large variation in the concrete fracture toughness resulted in a slightly stiffer response, the aggregate interlock model did play a crucial role.; Another problem, a tunnel opening in rock, was analyzed. It illustrates some of the code capabilities not fully exploited in the beam problem. Again results were found to be in good agreement with the available experimental evidence.; The major problems in the numerical application of fracture mechanics to structures in general, and reinforced concrete in particular, have been overcome. It is found that such an approach, thought for a long time to be inefficient and unfeasible, is indeed a very satisfactory one in terms of accuracy, reliability and execution time.