**3. Results**

#### *3.1. Hygro-Thermal Response of the Deck of Sørliveien Bridge*

The outputs of the finite element model are the temperature, the moisture content and the vapour pressure in the wood material.

Since the *RH* and *T* in wood were measured directly by the monitoring system, reference results for the validation of the numerical model were available from all of the nine integrated humidity-temperature sensors installed in the wood lamellas. For the purpose of investigation of *MC*s and moisture gradients near the surface of untreated wood exposed to the external climate, data measured at 20 mm from the bottom surface were selected for comparison with the numerical results.

Figure 10 shows the comparisons in terms of vapour pressures between the measured and numerical data. The directly measured *RH* in wood was multiplied by the saturated vapour pressure by using the same Equation (9) adopted for the numerical model. Figure 11 presents the comparison between measured and numerical values of temperatures. The results of the FEM calculation show a good correlation to the yearly variation of the monitored temperatures and measurement-based vapour pressures.

**Figure 10.** Sørliveien Bridge. Comparison between measurement-based and numerical vapour pressures in wood at 20 mm from the bottom surface.

**Figure 11.** Sørliveien Bridge. Comparison between measured and numerical temperatures in wood at 20 mm from the bottom surface.

The numerical model assists the monitoring by allowing the evaluation of the *MC* from the bottom surface of the 3D slice until 20 mm, as shown in Figure 12. The numerical *MCs* close to the bottom surface are much higher than the ones at 20 mm from the surface that show small fluctuations (Figure 12a). The related moisture envelopes (minimum, maximum, average, 5th and 95th percentile), which show the trend of the moisture gradients, are presented in Figure 12b. A summary of the maximum and minimum *MC* values between the surface and 20 mm depth is shown in Table 4.

**Figure 12.** Sørliveien Bridge. Moisture content predicted by the finite element method (FEM) between the bottom surface and 20 mm depth. (**a**) *MC* vs. time. (**b**) Moisture envelopes (minimum, maximum, average, 5th and 95th percentile) from the external surface to 20 mm.


**Table 4.** Sørliveien Bridge. Numerical moisture content (MC) peaks at the bottom surface and 6, 12, 20 mm from the surface.

#### *3.2. Hygro-Thermal Response of the Deck of Tapiola Bridge*

In this case-study, in this case-study, the results of the FEM analysis are in good agreemen<sup>t</sup> with the yearly variation of the temperatures and vapour pressures monitored at 60 mm from the bottom surface in sensors KC1 and KC2 (Figures 13 and 14). The larger temperatures measured in KC1 are because this sensor is located on the bridge side exposed to sun while KC2 is in the shadow. Since the model does not include the effect of solar radiation, the better comparison is with the data provided by sensor KC2 that is installed from the bottom of the deck.

**Figure 13.** Tapiola Bridge. Comparison between numerical temperatures in wood and measurements in sensors KC1 and KC2 at 60 mm from the surface.

The *MC* history at 60 mm from the bottom surface shows very small daily fluctuations while the numerical results closer to the surface are larger (Figure 15a). Figure 15b shows the minimum and maximum moisture envelopes during the monitoring time, as well as the 5th and 95th percentile from the external bottom surface to 60 mm depth. For this thick deck, a summary of the maximum and minimum *MC* values between the surface and 400 mm depth is shown in Table 5.

**Figure 14.** Tapiola Bridge. Comparison between numerical vapour pressures in wood and measurements in sensor KC2 at 60 mm from the bottom surface. In red the vapour pressure measurements in sensor KC1 at 60 mm from the lateral side exposed to the afternoon sun.

**Figure 15.** Tapiola Bridge. (**a**) Moisture contents from the external surface of the deck until 60 mm depth. (**b**) Moisture envelopes (minimum, maximum, average, 5th and 95th percentile) from the external surface to 60 mm.

**Table 5.** Tapiola Bridge. Numerical MC peaks at the bottom surface and 20, 60, 200 and 400 mm from the surface.

