Fuzzy logic based approach to FRP retrofit of columns

Current design approaches for seismic retrofit use deterministic variables to describe the geometry, material properties and the applied loads on the bridge column. Using a mechanistic model that considers nonlinear material behavior, these deterministic input variables can be directly mapped to the design parameters. However the results often give a false sense of reliability due to neglecting uncertainties related to the input variables of the analysis (data uncertainty), unpredictable fluctuations of loads and natural variability of material properties, and/or the uncertainty in the analytical model itself (model uncertainty). While methods of reliability analysis can provide a means for designing so as not to exceed specific levels of “acceptable” risk, they do not consider the uncertainty in the assumption of distribution functions for each of the input variables and are built on the basic assumption that the models used perfectly describe reality. This, however, still results in significant unknowns and often design models that are not truly validated across their response space. This paper describes the application of a fuzzy probabilistic approach to capture the inherent uncertainty in such applications. The application of the approach is demonstrated through an example and results are compared to those obtained from conventional deterministic analytical models. It is noted that the confidence in the achieved safety of the retrofit system that is based on the use of the fuzzy probabilistic approach is much higher than that achieved using the deterministic approach. This is due to the consideration of uncertainty in the material parameters as well as the consideration of uncertainty in the assumed crack angle during the design process.