3.1. Statistical Analysis of Measured Data
Figure 5 presents the values of moisture content, modulus of elasticity and failure stress obtained for the three environments for all specimens extracted from the beams (
Figure 2). The MOE and FS presented in this figure were adjusted by Equation (3) to consider an equivalent moisture content of 12%. In general, it is observed that all parameters vary for each beam and exposure conditions. Therefore, a statistical analysis will be first carried out to study the influence of the exposure conditions.
The data is first gathered per beam/zone and analyzed for each kind of exposure. The histograms for each considered parameter and each beam are summarized in
Figure 6. These histograms show different patterns of average values and dispersion of data for each exposure. The mean, standard deviation, and coefficient of variation (CoV) for each exposure/beam/zone are given in
Table 3. Concerning moisture content, it is observed that the lower mean value was obtained for the beams under unsheltered exposure. This behavior is due to the fact that the beam was exposed to a dried period before the tests. For the modulus of elasticity and the failure stress, it is noted that higher mean values for beams are estimated for the air-conditioned exposure. This means that the strength of the beam was preserved when it was subjected to controlled environmental conditions. For MOE and FS, the dispersion of the values for the sheltered beams covers almost all the range of the values for air-conditioned and unsheltered exposure conditions (
Figure 6).
The mean values of the module of elasticity and failure stress are compared to those obtained by Manfoumbi [
28] that are also presented in
Table 3. The average MOE values were estimated from the instantaneous deflection of the beams measured after loading. The average FS values were computed from samples extracted from the beams but without any differentiation concerning its exposure. For this reason,
Table 3 provides the same values for all exposures. It is noted that the mean values of MOE for all beams are lower than that the indicated by Manfoumbi [
28]. This decrease of the wood rigidity can be explained by the shrinkage-swelling, creep and mechano-sorptive phenomena, which are more accentuated in environments exposed to the weather than in the air-conditioned environment. Indeed, loss or absence of water in the wood leads to the disappearance of some links [
35] such as low-energy (van Der Waals) bonds between water molecules and wood polymers (cellulose, hemicellulose, and lignin); therefore, timber unlinked fibers could be cracked due to water loss. The results obtained partly explain this observation since we observed a very low loss of rigidity (2%) in an air-conditioned environment, compared to sheltered outdoor environments (21%) and unsheltered (35%) in which the surrounding conditions change during the year. Further analysis of the timber microstructure will be very useful to better understand the mechanisms leading to the wood rigidity reduction. Concerning the FS, our values are in average 12 to 16% higher than the reported by Manfoumbi [
28]. Nevertheless, the values reported by Manfoumbi [
28] are in the range of those found in this work.
Comparing the average values of the parameters in the zones, it is observed in
Table 3 that most part of minimum values for each exposure are in the upper zone. Conversely, most maximum values are in the middle zone. The lower zone mainly contains medium average values. Any pattern was identified for the CoV because the range of variation for each zone is not very large. The difference between the zones could be related to the long-term behavior where tensile/compressive stresses reduced the resistance in the upper/lower zones, respectively. The middle zone, that is normally less loaded, preserving the maximum resistance.
The reduction of MOE and FS for the unsheltered and sheltered exposure is due to timber aging, loading duration, and exposure conditions [
36,
37,
38,
39,
40,
41,
42]. All these parameters considerably influence the resistance of wood due to its nature and anisotropic behavior [
43,
44]. More particularly, the variations in the moisture content, associated with the exposure and loading, play a key role in the longevity of the wooden structure, because they influence its aging process. The loss of secondary metabolites [
45] such as tannins (polyphenols) would also be the cause of decrease in rigidity of the test samples since the tannins act as defender of wood structure by limiting the growth of wood biological agents [
46] and the influence of climatic variations (modification of the conformation of molecular structures) which can alter the main polymers of wood [
47]. However, other chemical mechanisms such as the strong crystallization of celluloses [
48] in wood can greatly reduce the stiffness of the material. Further analysis of chemical changes will provide additional information allowing to better understand their role on the loss of rigidity.
Determining the potential correlation between the parameters is important when the information will be after used for probabilistic modeling purposes. The Pearson correlations and
p-values for the studied parameters (MC, MOE, and FS) are given in
Table 4. It is noted that the absolute values of the correlations
and
are lower than 0.56 with
p-values larger than 5% for the most part of the cases. This indicates the moisture content is not linearly correlated with the mechanical parameters (MOE and FS). This is explained by the fact that the moisture contents depend on the surrounding weather conditions at the time when the tests were realized. Contrarily, it is possible to state that there is a positive correlation between the mechanical parameters MOE and FS because the values of
are close to 1 with
p-values lower than 5% for most part of cases. This positive correlation should be considered for propagating uncertainties or spatial variability for these parameters.
3.2. Spatial Variability Analysis
The spatial distribution of the measured parameters given in
Figure 5 shows that there exists significant spatial variability for all collected data. The LB test was carried out to confirm the existence of a spatially correlated database. The statistics and
p-values for the LB test applied to the data obtained in this work are given in
Table 5. By considering a significance level of 0.05, it is observed that in all cases the
p-values are larger than this value confirming that autocorrelation is statistically significant for all spatial data series.
Figure 5 also shows that there are particular values in the areas of support and application of loads. To better illustrate these particular behaviors,
Figure 7 provides the spatial variability of each parameter estimated by doing an average of the three values per location
x estimated for upper, middle, and lower zones for each exposure. An average value gathering all measurements (nine values per location
x) is also shown in this figure (green line). Lower values are observed close to the support zones for the moisture content. This behavior is due to the fact that the beams are more exposed to the environment in the support areas. Some trends with low values of MOE and FS are also observed in the support zone close to 2 m. These trends could be related with the loading conditions that induced more concentrated stresses in these support zones. Since these trends could imply that the spatial variability of the studied parameters is not stationary, statistical tests will be carried out to evaluate the stationarity of these random fields.
The analysis of autocorrelation of a spatial database allows to quantify the spatial regularity of a phenomenon and to determine the extent of the spatial dependence [
49].
Figure 8 presents the autocorrelation of the residuals for all beams and exposure conditions. It is observed in all cases that the autocorrelation decreases when the measurements are distant (larger lag #). This suggests that exists a spatial dependency structure [
50,
51]; however, in several cases, the autocorrelation values are significantly larger/lower than zero indicating a complex autocorrelation structure. Therefore, ADF tests were carried out to confirm the existence of the autocorrelation and to determine if the random fields are stationary. The statistics and
p-values for the ADF tests are also provided in
Table 5. For the same significance level (0.05) the estimated
p-values indicate that the data series is not stationary. This result is not surprising considering the trends observed in
Figure 7 for the support or loading areas.