## 3 Results and Discussion
### Relationship of Compressive Strength  
The mechanical properties of a log are often extrapolated from those of the standard specimens. The compressive strength ratio, \(\gamma_{\sigma}\), is calculated for each log sample in Table 1 using:  
\[\gamma_{\sigma}=f_{\rm m}/f_{\rm c} \tag{5}\]  
where \(f_{\rm m}\) is the parallel-to-grain compressive strength of segments of the log sample. The calculated \(\gamma_{\sigma}\) is separated into four groups, according to age of samples (\(t=0\) for the new CL and \(t=100\) years for the aged CL) and sampling position (\(\lambda=0\) for HW and \(\lambda=1.0\) for SW) of the standard specimens. The 3D plot and boxplot of \(\gamma_{\sigma}\) are shown in Figure 6. In the boxplot, symbols '\(\bullet\)' and '\(\times\)' outside the box represent the maxima and minima, respectively; the symbol '\(\square^{\prime}\) within the box represents the sample mean of the data; the upper and lower edges of the box represent the upper and lower quartiles of the data, respectively; the solid line within the box represents the median. Our results show that the distributions of \(\gamma_{\sigma}\) of the HW and SW in the aged CL are similar. The maxima and range of data of the HW in the new CL are significantly higher than those of the other three groups, which is shown in Figure 6b. The distribution of \(\gamma_{\sigma}\) of the SW in the new CL is relatively centralized. Figure 5: Parallel-to-grain compressive strength of aged and new logs. The scattered points of \(\gamma_{\sigma}\) in Figure 6a can be fitted to a linear plane distribution using the least-squares method:  
\[\gamma_{\sigma}=-0.052\lambda-0.002t+0.939 \tag{6}\]  
where \(\lambda\) denotes the relative distance between the sampling location of the standard specimen and the centroid of the timber cross-section. The equations defining the four edges of the plane (dashed lines in Figure 6a) are shown in Figure 7. The solid dots in the plots represent the sample means of the data groups. Each sample mean is close to one end of the straight line, indicating a good representation of the fitted plane. The fitted distribution can be used to estimate the parallel-to-grain compressive strength of the log samples in this study. The estimated results using Equations (5) and (6) are listed in Table 5. The average difference between the estimated and experimental compressive strengths of the HW and SW were 12.70 and 11.40%, respectively, and this was considered satisfactory given the large variability in the properties of the aged CL [34]. The relationship between the parallel-to-grain compressive strengths of the clear specimens and timber logs, recommended by the standard [35], is  
\[f_{\text{m-CABP}}=K\,\overline{f}_{\text{c}} \tag{7}\]  
where \(f_{\text{m-CABP}}\) is the estimated compressive strength of the log sample; \(\overline{f}_{\text{c}}\) is the sample mean strength of clear specimens obtained from the same log sample; \(K\) is the influence coefficient defined as  
\[K=K_{\text{P}}K_{\text{A}}K_{\text{Q}} \tag{8}\]  
where \(K_{\text{P}}\) is the equation accuracy affecting coefficient that is recommended in the design code. \(K_{\text{P}}=1.0\), as recommended in the design code. \(K_{\text{A}}\) is the ratio of the actual geometric quantity to the standard value of the same quantity. \(K_{\text{Q}}\) is the reduction factor of material strength, defined as the product of influence coefficient of natural defect, \(K_{\text{Q1}}\); drying defect, \(K_{\text{Q2}}\); size, \(K_{\text{Q3}}\); and a reduction factor due to long-term load, \(K_{\text{Q4}}\):  
\[K_{\text{Q}}=K_{\text{Q1}}K_{\text{Q2}}K_{\text{Q3}}K_{\text{Q4}} \tag{9}\]  
The recommended values for the above coefficients are shown in Table 6[35]. It is noted that the specimens have defects in this study; therefore, the coefficient of natural defect, \(K_{\text{Q1}}\), has the recommended value of 1.00 instead of 0.66 [35].