Heterogeneous materials with a random microstructure, such as reinforced concrete composites, are extensively used in many engineering areas. However, the natural process of the material ageing progressed by the unfavourable external actions, may jeopardize the composite's integrity by inducing the micro-scale damage. Initially unnoticeable and negligible cracks propagate over time leading to a more significant material degradation in terms of macroscopic cracks which represent a serious threat for structural durability and the service life-span. Cracking of the cement matrix not only allows entering of the harmful substances, but also greatly affects the integrity of the bond between concrete and steel, which is the main requirement for their mutual action.
Mechanical models able to realistically describe and predict behaviour of quasi-brittle materials make an important prerequisite for reliable prediction of cracking and failure in RC structures. However, such deterministic models are not able to take into account the deterioration of the structural properties. As we often do not have an insight into the material degradation over time, it is convenient to place the computation into stochastic framework, with mechanical propertiesconsidered as uncertain and modelled as random variables and random fields.
As the initial choice of the mechanical parameters influences the structural response in a great manner, the aim is to calibrate the model parameters given the experimental data by solving a stochastic inverse problem. Formulating the probabilistic problem in a Bayesian setting, an ill-posed inverse problem is transformed into a well-posed one by incorporating the prior knowledge about the random parameters.
The importance of parameter estimation is perhaps the most notable when observed in the context of structural safety of massive structures such as dams, bridges and nuclear power plants, as the consequences of failure of these structures may be fatal. With the help of Bayesian methods we can assess the actual level of safety of these structures and this estimate further provides a valuable information whether the structure maintains its functionality, it needs to be repaired or completely dismissed.