Fuzzy Parameters Analysis of Time--Dependent Fracture of Concrete Dam Models

In order to apply the mechanical properties (measured on material specimens or laboratory-sized models) to large structures (such as concrete dams), a non-linear theory able to predict the size-scale effect has to be used. One of these theories was first proposed by Hillerborg and co-workers (fictitious crack model) and is based on the earlier works by Barenblatt and Dugdale for metals (cohesive crack model). It is based on the existence of a fracture process zone (FPZ), where the material undergoes strain softening. The behaviour of the material outside the FPZ is linear elastic. A large number of short-time laboratory tests were executed, by varying the load, under crack mouth opening displacement control. Since concrete exhibits a time-dependent behaviour, an interaction between creep and micro-crack growth occurs in the FPZ. Therefore, different testing conditions can be applied: rupture can be achieved by keeping the load constant before peak value (pre-peak tests), or after peak value and after an unloading and reloading procedure (post-peak tests). The crack propagation rate is shown to be small enough to neglect inertial forces and large enough to keep the time-dependent behaviour of the process zone as dominant compared to the behaviour of the undamaged and viscoelastic zone. Due to the variability in material microstructure from one specimen to another, experimental data show large ranges of scatter. Well established methods in probability theory require sufficient experimental data in order to assume a probability density distribution. The objective of this study is to investigate the ranges of variation of the time response under constant load in simple structural elements associated with pre-selected variation (fuzziness) in the main material parameters. For situations where the values of the material parameters are of a non-stochastic nature, the fuzzy set approach to modelling variability has been proposed as a better and more natural approach