Probabilistic techniques are used in various fields including risk assessment and economic optimisation and they offer advantages over the alternative, but more traditional, deterministic methods that might otherwise be employed. In deterministic methods, uncertainty in the quantitative information available on the physical processes is considered, but accounted for by, for instance, intuitive safety factors. In this way, conservative and therefore safe answers are aimed for. The uncertainties themselves are not used in any quantitative manner. In deterministic methods therefore, part of the information available is not inherently exploited. By contrast in probabilistic methods, these uncertainties are direct input and utilised to the fullest.
Nowadays in more and more building sectors, behaviour assessments like for instance the assessment of tunnel safety or the durability of a structure, are being based on a probabilistic concept of limit state functions. In using such limit state functions, the loads applied to structures and their capacity to withstand them, are already couched in probabilistic terms. Generally the models used in these functions describe the load and behaviour of the structures, for instance a fire model in tunnel safety, or a chloride ingress model in a concrete structure durability study. Often it suffices to use analytical expressions for these models, like fire curves or Fick’s solution for chloride diffusion. These analytical models can then be used with probabilistic tools to calculate the failure probability. However, there is often a demand for more sophisticated models than these analytical functions, e.g. models based on the Finite Element (FE) method. The demand for such models is driven by the need for mechanisms to be described and for higher certainty in the outcome of the calculations, important for instance in economic optimisation.
Many models, describing loads were developed in the past and are available at the moment. But coupling of these models to probabilistic tools was hereto not intended and therefore often not provided. To overcome this deficiency and provide for coupling, TNO have been developing a generic toolbox called ProBox.
Frequently used tools to model the load and behaviour of a structure are based on the (FE) method in which the governing partial differential equations are solved numerically, while at the same time complex geometries can be accounted for. One of the finite element packages used is FEMLAB, a 3D multiphysics modelling tool. With this tool, a broad range of physical phenomena can be described1. The coupling of FEMLAB through the toolbox ProBox to numerical probabilistic techniques, opens the opportunity to perform probabilistic calculations in any of these fields directly. Hence, the coupling between ProBox and FEMLAB is part of the development.
One of the test cases for the ProBox module and its coupling with FEMLAB, consisted of evaluating the limit state functio