Diffusion-model-based risk assessment of moisture originated wood deterioration in historic buildings

• Assessment of damaging effects in wood threatening from moisture variations.
• An original diffusion model developed for the moisture content and stress assessment.
• Analytical proof of only a surface layer response to fast environment variations.
• Risk assessment methodology is demonstrated on historic churches as case studies.

The paper deals with investigating the response of wood artefacts to relatively fast changes of ambient air humidity and temperature and with estimating the wood stress and strain variations due to the moisture content changes. The moisture content dynamics are described by a specially developed model based on the Fick's second law and further transformed into a state space model. The surface boundary conditions are tied up with a model of equilibrium moisture content. As the final objective of the diffusion model application the moisture induced stress and strain in the wood artefact is assessed. The obtained stress amplitudes are compared with the yield point stress as the boundary of elastic deformations. The model application has particularly confirmed that the concerned transfer phenomena have to do with only a thin surface layer of wood while the deeper layers are not touched by them. For a given set of data provided from unheated historical churches the stress and strain responses are evaluated and compared with their admissible limits in order to estimate the risk of potential moisture originated damage.