Interplay of size effects in concrete specimens under tension studied via computational stochastic fracture mechanics

Abstract

We attempt the identification, study and modeling of possible sources of size effects in concrete structures acting both separately and together. We are particularly motivated by the interplay of several identified scaling lengths stemming from the material, boundary conditions and geometry. Methods of stochastic nonlinear fracture mechanics are used to model the well published results of direct tensile tests of dog-bone specimens with rotating boundary conditions. Firstly, the specimens are modeled using microplane material law to show that a large portion of the dependence of nominal strength on structural size can be explained deterministically. However, it is clear that more sources of size effect play a part, and we consider two of them. Namely, we model local material strength using an autocorrelated random field attempting to capture a statistical part of the complex size effect, scatter inclusive. In addition, the strength drop noticeable with small specimens which was obtained in the experiments is explained by the presence of a weak surface layer of constant thickness (caused e.g., by drying, surface damage, aggregate size limitation at the boundary, or other irregularities). All three named sources (deterministic-energetic, statistical size effects, and the weak layer effect) are believed to be the sources most contributing to the observed strength size effect; the model combining all of them is capable of reproducing the measured data. The computational approach represents a marriage of advanced computational nonlinear fracture mechanics with simulation techniques for random fields representing spatially varying material properties. Using a numerical example, we document how different sources of size effects detrimental to strength can interact and result in relatively complex quasibrittle failure processes. The presented study documents the well known fact that the experimental determination of material parameters (needed for the rational and safe design of structures) is very difficult for quasibrittle materials such as concrete.

Fracture characteristics of refractory composites containing metakaolin and ceramic fibers

“…Size effect of such organized tests is documented by the number of experimental research works. [32][33][34] Therefore, it is extremely important to clearly describe the testing methodology for better reproduction of obtained results. It was experimentally verified that the appropriate combination of aluminous cement with MK additive and natural crushed basalt aggregates ensures sufficient properties for practical utilization.…”

Computational modeling of size effects in concrete specimens under uniaxial tension

“…The most frequent combination in academic studies is the simultaneous randomization of G F and tensile strength f t . For example, it was shown previously by Vořechovský (2004b), Vořechovský and Novák (2004) that a strong positive correlation between these two parameters, when they are both randomly varying spatially, increases the slope of size effect curve in the transitional region between the two asymptotic limits (positive correlation, in fact, speeds up the convergence towards the classical Weibull statistical size effect).…”

“…Unfortunately, they did not consider more than one random property, and ignored its spatial correlation. The interplay of deterministic and statistical size effects is one of the central topics in PhD thesis by Vořechovský (2004b). Some analytical results supported by a large computational case study of the Malpasset dam failure are published by Vořechovský et al (2005), Bažant et al (2007b).…”

Interplay of probabilistic and deterministic internal length in simulations of concrete fracture

“…Even though there are several possible sources of random fluctuations, it is considered here that all of them can be approximately described by a single random field. This random field has its own characteristic length scale provided in a form of correlation length [14,15]. Incorporation of the random fluctuations into the present discrete model is closely described in [16,17].…”