INVESTIGATION OF POST-CRACKING BEHAVIOUR OF R.C. BOX-GIRDER BRIDGES

Abstract

The response of reinforced concrete on external loading is very complex and after reaching a certain amount of elastic deformation, elasto-plastic behaviour is observed and finally failure may be caused due to several possible mechanisms, such as concrete cracking, reinforcement yielding, bond slip between steel and concrete, concrete crushing and interface sliding. Constitutive modeling of concrete material in post-peak range is of great interest in engineering applications. Acquiring such knowledge may be of great significance to enable the engineers to understand the failure mechanism and to carry out life assessment studies of structures taking cognizance of past stress history of material. For the many years, the design of concrete structures is being carried out on the basis of working stress design method that considers only the linear elastic behaviour of materials. However, in practice, the response of structure remains linear within a very narrow range of loading and deformation, and subsequently a non-linear behaviour is observed. In view it, the Limit State Design (LSD) concept is gaining an ever-wider acceptance in the design codes as it enables the design to be more rational and accurate. Knowledge of the actual collapse mode and the ultimate strength of structures significantly improve the ability of the designer to construct the damage tolerant structures. Within the framework of LSD, the structures are commonly designed to satisfy two criterions, namely, the limit-state of serviceability and of collapse. The requirements for any mathematical model applied to engineering problems are to be able to predict response accurately and economically. For this reason mathematical models have to be carefully studied and fully understood before they can be applied. In this study, within the framework of finite element methodology, the theory of elasto-plasticity in conjunction with fracture energy based smeared cracking approach has been employed as the basic tool for the analysis. To achieve the objectives of the present work, the key issues identified in the context of non-linear finite element analysis of concrete structures are: • A robust Degenerated shell element formulation within the framework of mixed interpolation scheme • Modelling of concrete in compression including the computational aspects of elasto-plasticity, hardening hypothesis and the consistent iterative path independent solution algorithms. • Conceptual model for concrete cracking has been developed by using fixed smeared elastic approach and integrating the added features like fracture energy, tensionsoftening/ tension-stiffening phenomena and the adaptive strategies. The degenerated shell element proposed in this study is primarily is based upon the nine noded quadratic assumed strain element, which is simple to implement, robust and accurate for both thin and thick shell applications. In order to further enhance the performance of the assumed strain element, an element formulation based upon unification of a few existing methodologies has been proposed. The three techniques combined together in the proposed element are (i) an assumed interpolation of transverse shear strains in natural coordinate system to overcome the shear locking problem (ii) the reduced integration technique for in-plane strain components to avoid membrane locking behavior and (iii) addition of nonconforming displacement modes selectively to in-plane components. The nonlinear behavior of concrete material has been idealized by employing an elasto-plastic strain-hardening model. The Willam-Warnke five parameter model has beenusedto define the initial and subsequent yield surfaces. Within the framework of rate independent elasto-plasticity, the three integration schemes (forward Euler, semi/full backward Euler) for stress updating have been employed in the present work. The importance of employing consistent tangent modular in conjunction with Newton-Raphson iterative technique, in order to improve the convergence characteristics, has been re-emphasized. Though, the task of in evaluating the quantities like consistent tangent modular proves exceedingly laborious and is generally avoided, yet an attempt has been successfully made to derive an explicit expression for the modulus in context of five-parameter model. The accuracy analysis of various stress updating schemes have been demonstrated with the help of iso-error maps which suggest the superiority of consistent- full backward Euler technique to a large extent. Also a single constitutive model, which is the modification of original Willam- Warkne five-parameter model and is able to govern the non-linear behavior of concrete both in compression and tension including failure, has been proposed in the present study. A fixed crack smeared approach based upon fracture energy concept and nonlocal material softening law has been employed for the modelling of the tensile behavior of the concrete material. The methodology for the evolution of material damage produced by smeared cracking has also been presented. The motivation behind this method is to be able to circumvent some of the well-known problems of meshsensitivity and spurious modes associated even with energy based smeared crack model. Number of standard beam, plate and shell examples have been solved to demonstrate the validity of the proposed model. Studies are also being carried out to investigate the non-linear structural response of conventionally designed RC box-girder bridge structures loaded beyond the service load conditions. Effect of some pertinent design parameters on the post-peak response in general and overloading capacity in particular have also been investigated. IV