Civil engineers are aware that the fracture behavior of concrete is affected by uncertainties, i.e. identical structures with the same material undergoing identical loads exhibit a scatter in their toughness. Therefore, in order to properly deal with the problem, uncertainties must be taken into account and statistical information about material fracture resistance should be known. A Bayesian updating approach, coupled with the Boundary Element Method (BEM), is proposed to identify the distributions of the input parameters of fracture mechanics numerical models.

The BEM provides an appropriate framework to model fracture problems, as stress concentrations are represented accurately and as domain mesh is not required. Moreover, the mesh dimension reduction provided by BEM makes the remeshing procedures during crack growth a less complex task [1]. The cracks are modeled using cohesive zone elements, which consist of one dimension elements inserted at the interface of the traditional bulk elements (for bidimensional models). Such elements describe the cohesive force resisting to the creation of an interface in the material (e.g. a crack) and dissipate the energy related to crack propagation by means of a dedicated traction-displacement law.

Bayesian updating is subsequently used to identify the mechanical model leading to the best fit between numerical results and experimental data. Statistical hypotheses are formulated and subsequently tested against the experimental observations. The outcome of the Bayesian updating procedure may be interpreted as the plausibility of these hypotheses on the basis of the available reference data [2], which is quantified by means of the posterior distribution. This plausibility may be associated with parameter values, but it may also be used to compare multiple modeling strategies.

In this contribution, a Bayesian updating strategy is applied to identify the joint probability density function of the parameters associated with the softening law of the cohesive crack. The experimental data consists of load-deflection curves from three point bending fracture tests. Multiple formulations are possible for the cohesive elements and a procedure for the identification of the most plausible formulation is proposed; it relies on model class selection.