Probabilistic modelling of concrete structures degradation

In the context of performance-based approaches for the design or assessment of concrete structures, time is the decisive variable and the durability issues are pronounced. Also, the reliability aspects are important as they is attribute to service life, maintenance, inspection, repair and the lifecycle cost – see also ISO 13823 (2008) and the fib Model Code (2010). Evidently, durability and reliability are often crucial structural performance characteristics and the reliability level for relevant limit states has to be analysed frequently utilising mathematical models for degradation prognosis. When doing this it can be useful to have a range of models available for the structural task in question. The engineer can then select a suitable one with respect to the type of relevant limit state, although frequently, for pragmatic reasons, the model choice is based on the availability of model data and effective software. Modelling of degradation processes may be based on models of different levels of sophistication: a) macro-level; b) simplified models, probabilistic approach; c) micro-level. The level a is the most simple, often being called a “deemed-to-satisfy” set of rules (mostly according to current codes), and does not allow for the design/assessment of a specified service life with a specified reliability level. The level b comprises simple models (often semi-empirical) verified by comparisons with results obtained from testing under experimental and real-life conditions; the variables are treated as random quantities, so the outputs are also capable of expressing statistical and probabilistic quantities (service life assessment). This is the level dealt with in the present work. The level c is the most refined one, where the models are complex and are developed making use of basic physical laws and often also the constitutive laws of mechanics, thus leading to the problem of needing to solve partial differential equations. This level of sophistication is too high for everyday design practice. Note that levels b and c may be viewed as performance-based design types. Many variables applied in the assessment of deteriorating concrete structures show random spatial variability. In contrast, the majority of published analyses deal with 1D representation, which enables the investigation of a “point in space” or “hotspot”. Because of this, only temporal variability is taken into account. However, numerous proposals for approaches which also facilitate the analysis of the spatial characteristics of deterioration processes have recently appeared – e.g. Darmavan & Stewart (2003), Straub (2011). Frequently, random fields in 2D space are used, often simulated by means of random variables generated for a chosen mesh in stochastic finite element analysis. The requirement for data concerning the correlation structure in space creates a challenge in real-life cases; therefore, monitoring/testing can be employed. A more appropriate and economical decision about the service life consequences can then be based on defining the limit states for a certain proportion of the structure, and not merely for an isolated hotspot. The spatial variability can also be captured by using e.g. cellular automata technique – for an example of this applied to chloride ingress see Podroužek & Teplý (2008). 2. Tool for practical applications