## 1 Introduction
All of them have similar deck composed of 48 \(\times\) 233 mm lamellas treated with creosote excepting the footbridge in Sorliveien (Figure 1), which has a deck of untreated spruce and a deck height of 333 mm, made of vertically sawn gulam beams. The SLT deck protecting the whole bridge structure is shown for Sorliveien Bridge (Norway) in Figure 1a. In addition, Figure 1b shows a detail of the SLT deck with the view of the wood lamellas and the steel bars for the same bridge. Figure 1: Sorliveien Bridge. (**a**) Side view of the whole bridge structure. (**b**) Detail of the stress-laminated timber (SLT) deck protecting the bridge. The efforts to promote timber bridges continued also after the end of Nordic Timber Bridges Programme. For instance, the Wood Building Programme (2016-2021) was launched in Finland as a government undertaking to increase the use of wood in urban development, public buildings, bridges and halls [8]. The programme is also seen as an efficient way of attaining the energy and climate targets to reduce Finland's carbon footprint by 2030. However, the number of laminated wooden deck bridges for vehicle traffic in Finland is still relatively small. One such bridge, carrying significant vehicle traffic, is the highway crossing recently erected in the Tapiola district of the city of Espoo. The Tapiola Bridge is now being permanently monitored under the supervision of the Finnish Transport Infrastructure Agency. In addition to the durability problems, a common effect of moisture variation in SLTDs is the cupping deformation, which is usually measured as the uplift at the corner in the bottom surface of the deck [9]. A sharp increase of cupping is usually observed during wetting and only a partial decrease during drying. For the details, the reader is referred to Section 4.3 of the Durable Timber Bridges report [9]. The above review about performance of bridges shows that control of the \(MC\) in wooden parts is not only essential for the durability of the material, but for the whole superstructure as well. Variation of the \(MC\) directly affects structural integrity, serviceability and loading capacity of the bridge. Therefore, the monitoring techniques have a fundamental role in controlling the health of large structures exposed to outdoor climates, such as timber bridges. However, measurements obtained by the usual monitoring techniques based, e.g., on integrated humidity-temperature sensors, provide hygro-thermal measurements only in specific locations of the wood components. As shown in the recent literature [10; 11; 12], advanced multi-phase models are an effective tool to assist the hygro-thermal monitoring of timber bridge components such as gulam beams. Compared to the single-phase (or single-Fickian) models for transient moisture transport in wood [13; 14; 15], where the \(MC\) is the only variable of a Fick's second law equation, the multi-phase models below the fibre saturation point (FSP) analyse two different water phases, i.e., the water vapour in lumens and the bound water in wood-cell walls. Starting from the seminal works of [PERSON] [16] and [PERSON] [17], there was a strong effort to develop a multi-phase theory (often called multi-Fickian) for moisture transport in wood that includes the conversion rates between the different water phases. The multi-Fickian theory below the FSP is based on the identification of three phenomena occurring in cellular wood during moisture transfer, i.e., the diffusion of water vapour in the lumens, the sorption of bound water and the diffusion of bound water in the cell walls. In the multi-phase models available in the current literature, the two water phases are separated and the coupling between them is defined through a sorption rate [10; 11; 12; 17; 18; 19; 20]. Recently, [PERSON] et al. [21], developed a whole multi-Fickian model including also the transport of free water in the lumens above the FSP.