Efficient reliability analysis of concrete structures on the basis of non-linear finite element analysis under numerical noise

The analytical expressions for the ultimate load bearing capacity of the RC structures do not provide the generalized notion of ultimate load bearing capacity, which can be obtained through nonlinear finite element analysis (NLFEA). In order to obtain an accurate estimate of failure probability of a RC structure it is necessary to use NLFEA based limit state function in a reliability analysis. However, there is a relative lack of NLFEA based reliability analysis efforts in the literature. Whatever efforts there are, none of them explicitly attempts to account for the uncertainty introduced by the NLFEA model, called modeling uncertainty, in the reliability analysis. Nor has there been much effort to study the impact of the numerical noise from NLFEA on the accuracy and efficiency of the reliability algorithms. Since the run time of each NLFEA is high, for a NLFEA based reliability analysis to be practically feasible it is imperative that the reliability algorithm is efficient and capable of handling different kinds of limit state functions (with multiple failure modes, for example). Keeping this in mind two adaptive response surface based methods, directional adaptive response surface method (DARS) and adaptive Kriging Monte Carlo simulation (AK-MCS), are selected based on the preliminary literature survey, for the investigation of NLFEA based reliability analysis of RC structures. The key objective of this thesis is to study the strengths and limitations of these two algorithms for RC structures and make necessary modifications in the DARS algorithm to make it more suitable for the reliability analysis of RC structure. A NLFEA solution strategy is formulated for RC beams and the modeling uncertainty is quantified based on 53 experimental results. Three RC beams, are selected as demonstrative cases. One of these beams fails in shear, another in bending and the last one can switch in failure modes between shear and bending. Based on these three beams it is demonstrated in this thesis that there is pronounced numerical noise in the NLFEA predicted bearing capacity whenever the beams fail is shear failure mechanism. Whereas for the bending failure mechanism the NLFEA solution strategy produces a much more smooth capacity prediction. Clear indications are found to the effect that the shear failure mechanism is more sensitive to certain choices adopted in the NLFEA solution strategy.