Wood absorbs and desorbs moisture due to its hygroscopic behavior, leading to moisture gradients in timber elements as well as swelling and shrinkage. These processes are constrained due to the orthotropic material properties of wood, leading to moisture-induced stresses, which can cause crack initiation and propagation. A significant amount of the damage in timber constructions indoors can be related to changes of the moisture content (MC). However, more information is needed about the correlation between moisture changes or gradients and specific damage characteristics, like crack depths. Thus, based on numerical simulations, the crack depth development within two solid timber and one glued laminated timber (GLT) cross section over time for different relative humidity (RH) reductions and initial MCs is analyzed. For this purpose, a multi-Fickian transport model is used to determine moisture fields, which are then used as loads in a subsequent stress simulation, where linear elastic material behavior is considered. An extended finite element approach, supported by a multisurface failure criterion defining the failure behavior, allows for the simulation of moisture-induced discrete cracking. Based on simulation results, correlations between potential maximum crack depths and moisture gradients in indoor climate conditions are derived, which enables the prediction of crack depths in wood. Finally, it is shown that the initial MC level significantly influences the maximum crack depth that can be expected.

Wood has the property to absorb and desorb moisture due to its hygroscopicity resulting in dimensional changes. Due to constrained non-uniform direction-depending expansion caused by moisture changes and gradients, respectively, stresses are induced, which may lead to crack initiation and propagation, reducing the load-bearing capacity of timber structures. However, little is known about the correlation between moisture changes or gradients and crack depths, and no quantitative prediction exists of crack depths caused by moisture gradients. Thus, based on numerical simulations, the cracking process for different initial moisture contents (MC) and various relative humidity (RH) reductions is investigated for two solid timber and one glued laminated timber cross-section. As a result, correlations between moisture gradients and maximum crack depths are derived, thus enabling the estimation of crack depths. The investigation revealed that cross-section size significantly influences the relation. In addition, more significant moisture gradients occur in larger cross-sections, resulting in earlier crack initiation compared to smaller ones, and crack development in larger cross-sections tends to last longer.