Sixty-two trees of Mountain pine (Pinus uncinata Ramond ex DC.) were harvested in nine representative forest plots (Table 1). For each tree a bottom log (2 m long), a middle log (1 m long) and a top log (2 m long) were crosscut (Figure 1). The logs were through-and-through sawn into 50 x 100 mm planks dried further in a conventional kiln to a mean moisture content of approx. 11%.

Figure 1:
Sample preparation from tree to logs sawn to boards, rods and dedicated specimens for standard characterisations.

Table 1:
Provenance of trees and visual grading of boards. Altitude (m), trees, boards, rods (number), VG 1 to 4 and R (% of total boards) with VG₁ to VG₄: visual grades of boards from best (almost no defects) to worst (large knots) and R: rejected (mostly severe warping).

All 2 m long samples were graded using the French standard NF B 52-001-1 2011 employing four classes for visual grading (VG₁ to VG₄) based on combined criteria like ring width, knot diameter, position, splits, warp, rot etc. Boards that do not fulfil these criteria for any reason are rejected (R). Table 1 describes the differences in visual grading both for each plot and between bottom and top logs. Only the graded boards (945 in total) were used for the measurement of density and mechanical properties.

Ninety-eight short boards were selected to cover the whole range of densities and provenances (around 10 boards per forest plot). These boards were cut to clear wood specimens for mechanical and physical tests. From each board, one to three rods, a mean of two per board, were cut to obtain 183 clear wood rods, free of compression wood (450 mm x 20 mm x 20 mm in the L, R, T directions). Each rod was then cut into 3 sub-samples (Figure 1) for physical and mechanical measurements. These rods were placed in a climatic chamber with regulated standard conditions (20°C +/- 2°C, 65% +/- 5% RH).

Mass (M), length (L), width (W) and thickness (T) were measured on all boards and density was calculated using the ratio: D = M / (L*W*T), in kg/m³.

In order to measure both longitudinal MOE and MOR in the central third of the beam an edgewise bending test in accordance to the European standard NF EN-408 (2010) was performed on each board. Specific modulus (SM) for the board was calculated using the ratio: SM = MOE / D.

Small wood cobbles measuring 10 mm x 20 mm x 20 mm (L, R, T) extracted from rods ends were measured to quantify ring width, mass, R and T dimensions on all these specimens at equilibrium moisture content in the standard climate. All samples were then fully saturated using a vacuum/pressure process. At that stage, mass (Msat), R, T dimensions (Rsat, Tsat) were measured. The samples were successively placed in hygroscopic equilibrium under three different climates leading to usual wood equilibrium moisture contents, 18%, 14%, 8%. They were finally dried completely in an oven at 103°C. At each moisture content i, mass (Mi), R and T dimensions (Ri, Ti) were measured and the RT area calculated as Ai = Ri*Ti.

At the end, the following parameters were calculated:

ii00sat0satsat0satsat0satisati

The fibre saturation point (FSP) is calculated as the intercept of the linear relationship Hi / ΔAi and the moisture content axis (Choong 1969) (Figure 2).

Figure 2:
Fibre Saturation Point (FSP) calculation using surface variation. FSP is the intercept with the Y axis, i.e. the constant value in linear regression.

The sample dimensions were 60 mm x 20 mm x 20 mm (L, R, T). The mass and dimensions of the small rod were measured first and the specimen compressed between plates in a universal testing machine (Adhamel Lhomargy DY 36 of 100 kN capacity) until rupture in accordance with the French standard NF B51-007 (1985). The maximum force was recorded and the crushing strength (CS) was measured from that force and the transverse dimensions of the sample. The density of the sample (Dco) was also calculated for the sample under standard equilibrium moisture conditions.

This measurement was carried out on long samples (360 mm x 20 mm x 20 mm, L, R, T directions) under standard equilibrium moisture conditions. The dimensions in the three directions and the mass of the specimen were measured. Each rod was placed in free vibration on elastic supports at the level of the first vibration mode in bending condition, induced by knocking one end of the rod. The values of the three highest resonance frequencies were recorded using a Fast Fourier Transform analysis. The specific modulus SM (m²/s²) was calculated using the Timoshenko solution (Brancheriau and Baillères 2002).

The density of the sample (Dflex) was calculated using the values of the mass and dimensions of the rod. The longitudinal modulus of elasticity (MOE) was calculated as the product of density and specific modulus: MOE = Dflex*SM.

When the crushing strength and MOE are known, their ratio, SL = CS/MOE (SL: strain limit), is an interesting parameter which has the dimension of a strain. It is a lower limit for the real strain at rupture and can be considered as a proxy for the strain limit in compression for clear wood.

Table 1 gives the results for visual grading and shows that 10% to 30% of the boards, according to plot, were rejected (17% at a mean, with low differences between top and bottom logs). The percentage of top class logs (VG₁) is always low (6% at a mean, varying from 0% to 11% between plots) and the difference is remarkable between top (3,2%) and bottom (7,6%) logs. Among the classed boards, bottom logs generally give higher grades (VG₁ and VG₂ ) than top logs.

Table 2 and Table 3 give the results for the mean properties of the 945 boards that were not rejected.

At plot level (Table 2), VG_m is the mean value of visual notation (from 1 to 4), low values signifying better classification for the plot. There is consistent concordance between this mean visual classification and the mean strength (MOR) for the different plots, but this is not the case for mean density or mean stiffness of the boards (Table 3). The same concordance occurs between bottom and top logs: a 15% reduction in mean visual class (VG_m ) leads to a 20% reduction for mean MOR but only 6% for MOE, 4% for D and 2% for SM.

From grade 4 to grade 1 there is a 33% increase in mean MOE or SM and 64% increase in mean MOR.

Table 2:
Mean properties of graded boards per forest plot. Nb: number of boards in the plot, VGm: mean of visual grade (1 to 4) for the boards in the plot, D: density in kg/m³, MOR: flexure strength in MPa, MOE: modulus of elasticity in MPa, SM: specific modulus in 10⁶m²/s².

Table 3:
Mean properties of boards per visual grade. Nb: number of boards in the visual grade, 1 & 2: grouping of visual grades 1 and 2, 3&4: grouping of visual grades 3 and 4.

Histograms of D, MOR, MOE and SM (Figure 3) show that these values have a distribution close to a normal one.

Figure 3:
Histograms of graded boards properties. Continuous line: normal distribution associated to the population of boards.

Table 4 gives the correlation coefficient between properties of the all listed boards. There is a significant negative correlation between the visual grade and the mechanical properties of the boards. Density was not correlated to visual grade; however, there are also significant positive correlations between density, strength and stiffness. Variations in MOE help to predict 55% of MOR, which is rather usual in mechanical grading (Hanhijärvi et al. 2005, Srpčič et al. 2009).

Table 4:
Correlation between board properties. Lower triangle: coefficient of correlation r, higher triangle p-values. Bold characters: significant correlation (here always better than 0,001).

Using a linear regression model between MOR and MOE a predictive formula for the 5-percentile (5% MOR) is found at 5% MOR=5,6858*MOE-23,15 (MOR in MPa, MOE in GPa). This formula ensures that less than 5% of experimental MOR remains below the predicted value.

European rules for structural timber, NF EN-338 (2016), NF EN-384 (2016) are based on characteristic values (5-percentile) for MOR, MOE and density that must be determined by experimental tests on at least 900 timber pieces. Classes named C14-C50, based on the 5-percentile MOR (14 MPa-50 MPa) give references for both characteristic (5-percentile) and mean values for MOE and density (Table 5). The values for specific modulus (SM = MOE/D) and a tentative estimation of prices for each grade are added in Table 5.

Table 5:
Reference values for 5-percentile and mean value (D and MOE) for softwood grades in NF EN-338 (2016) SM: specific modulus calculated as MOEm/Dm, Price: Estimation of putative prices for the different grades in €/m³.

By using the table above, it is possible to propose a grading for all boards non-rejected by visual grading, or grade by grade, or by grouping the two best and the two worst grades (Table 6a and Table6b). This was done using all characteristic values (left portion of the table) or using mean MOE instead of 5-percentile MOE.

Table 6a:
Mechanical grading correlated to visual grading, using 5-percentile values only. Legend as in Table 5. Value: product of unit price by percentage of the boards in the grade in €. Mean value is 200 €/m³ for all boards graded C18, 218 €/m³ if all visual grades are mechanically graded, 207 €/m³ for grouping visual grades.

Table 6b:
Mechanical grading correlated to visual grading, using mean MOE instead of its 5-percentile values. See legend of Table 6a. Mean value is 200 €/m³ for all boards graded C18, 198 €/m³ if all visual grades are mechanically graded, 207 €/m³ for grouping visual grades.

It should be noted that grade is always determined using MOE (5-percentile or mean value) and 5-percentile MOR remains well above the reference for each grade.

Taking all visually graded timber as a population, C18 grade can be applied both using characteristic or mean values for MOE. Hence the value will be 200 €/m³ for all the population.

Class by class (or grouping 2 classes), grading using mean MOE is more severe than grading using characteristic MOE values. Characteristic or mean density is always far above established references. Using grouped visual graded classes gives around 43% C22 (VG₁ and VG₂) together with 57% C16 (VG₃ and VG₄), with a mean putative value of 207 €/m³ which means only 3,5% more than without difference among visually graded populations. The significance of this result remains to be determined.

3,3. Machine grading

Measuring both density and MOE of a board can be done either by flexure test (MOEf) or by vibration techniques (MOEv). MOEf gives the MOE for the central third of the board while MOEv gives the MOE for the entire board. The regression coefficient (r²) between the values obtained by both methods on the same population of boards is usually above 0,8 and vibration method is used most often.

In order to grade the boards in this population, we use the predictive model for 5-percentile MOR based on MOEf measurements. Cxx grade is given for a softwood population having a predicted MOR above xx MPa. For each graded population, characteristic (5-percentile) and mean values are calculated for MOR, MOE and density (Table 7). In each graded population, characteristic values are well above standards but mean values for MOE are well below specified ones. With this machine grading, mean value for the population of boards (945 boards), using 100 €/m³ as the price for non graded boards (MOR <14 MPa), will be 262 €/m³, a value 30% higher than the C18 grade for all boards.

If mean MOE value for the population should necessarily be above specification, regardless of the machine grading, the solution is to grade all the visually graded population (without rejected pieces) in C18 class and machine grading becomes unnecessary. It should be noted that the mean specific modulus for mountain pine boards in the classes are very low when compared to the values in NF EN 338 (2016).

Table 7:
Machine grading (NDT measurement of D and MOE) of the 945 boards, using 5-percentile reference. Same legend as Table 6a. Mean value is 262 €/m³ for this kind of machine grading.

Table 8 gives the statistical description of these parameters. The rings are narrow (a mean of 1,6 mm), but ring width variations were rather large (CV = 47%), which is usual (Koch 1972, Zhang 1995). On the other hand, the density or basic density variations were low (CV < 10%), but the values were in the usual range for pine wood (Koch 1972, Kretschmann 2010). Variability for the specific modulus was higher (CV = 14%) than for density, with a twofold range in this sampling. But specific modulus has low values, nearly 20% lower than the values for southern pines in the US (Kretschmann 2010). This is probably a result of adaptive growth due to windy conditions in these mountains (Telewski 1989).

Volumetric, tangential and radial shrinkage were within the usual range of values for pines (Glass and Zelinka 2010) and variability was much higher for radial shrinkage (CV = 19%) than it was for volumetric or tangential shrinkage. FSP had very low variability (CV = 5%) but its range was nonetheless from 25% to 30%, a range founded by Choong (1969) on sample of ten different pines growing in the southern US.

Variability in compressive strength was the lowest among mechanical properties, while MOE variability was significantly higher (19%). All mechanical properties were in the usual range for pines (Kretschmann 2010).

Table 8:
Statistical description of parameters and properties for the 183 specimens of clear-wood Min.: minimum value, Max.: maximum value, Mean: mean value, C.V.: coefficient of variation. D12: mean density (kg/dm³) in a standard climate (20°C, 65% RH), RW: ring width (mm), SM: specific modulus (m²/s²), BD: basic density (kg/dm³), VS: volumetric shrinkage (%), RS: radial shrinkage (%), TS: tangential shrinkage (%), T/R: shrinkage anisotropy, FSP: fibre saturation point (%), CS: compressive strength in longitudinal direction (MPa), MOE: modulus of elasticity in longitudinal direction (GPa), SL: strain limit from compression test (‰), MOR: bending strength in longitudinal direction (MPa).

Table 9 gives the results of the correlation analysis. Significant correlation at levels better than 5% probability are very numerous, as expected for a large number of data in this field. The basic density (BD) and density at moisture equilibrium for the standard climate (D12) were very strongly correlated (R2=93%) in a proportional way (Figure 4)

and the formula D12=1,2*BD can be used for these mountain pines.

Table 9:
Correlation coefficients for clear-wood. See legend as in Table 8; lower triangle: coefficient of correlation (R) values, bold numbers: correlation significant at the 5% level or better; upper triangle: coefficient of determination (R²) values for over the 5% level only (significant at the 0,1% level); bold numbers: R² value over 50%.

Figure 4:
Relationship between density and basic density D12: mean density value measured under standard climate conditions on compression and bending tests.

Among the parameters, although it had the highest C.V., ring width (RW) was not correlated to density. This has also been found for pines in natural stands with a ring width smaller than 3 mm (Koch 1972). Ring width was only significantly negatively correlated to the specific modulus (R²=6%). This kind of negative correlation between ring width and specific modulus is usual in typical radial patterns of juvenile wood for softwoods (Lachenbruch et al. 2011) however in this case it is rather weak.

Density is only weakly correlated with the specific modulus and this is unusual for softwood. It may be the result of the following: i) a very small ring width in general and ii) a small radial expansion of juvenile wood for these slow growing trees.

Among the shrinkage properties there were the usual strong links (R2>80%) between volumetric and transverse shrinkage, but a rather weak link between radial and tangential shrinkage (R2=46%). Moreover, radial shrinkage variations explained most of the shrinkage anisotropy (R2=72%).

Despite its low level of variability, FSP was correlated with all the shrinkage properties and a rather high coefficient of determination (R2=21% to 30%) was observed.

As expected there was very significant positive correlation between MOE and CS.

The strain limit was very strongly negatively correlated with SM (and to a lesser extend to MOE as a consequence), which is the case for flexure wood (Telewski 1989).

Looking at the relationship between parameters (ring width, density, and specific modulus) and mechanical properties, there were highly significant correlations (P<0,1%) for both density and specific modulus as related to the mechanical properties, except for the strain limit (which depends only on specific modulus). On the other hand, ring width only had a slightly significant negative correlation with mechanical properties, CS (P<5%) and MOE (P<1%), which is not usual for pines (Zhang 1995).

Density had the best coefficient of determination for strength properties: 76% (D) compared to 22% (SM) for CS. On the other hand, the specific modulus was the best for stiffness and flexibility: 75% (SM) compared to 41% (D) for MOE, 67% (SM) compared to 1% (D) for the strain limit. The fact that the specific modulus had a better determination coefficient than density for MOE in this experiment was merely a consequence of the greater variations in specific modulus (higher C.V.).

There was no significant correlation between ring width and shrinkage except for a slightly positive significant correlation with FSP (5% level).

There were highly significant correlations (P<0,1%) for density (positive) and specific modulus (negative) with all shrinkage properties except for FSP. The specific modulus had the best coefficient of determination for shrinkage properties (except for shrinkage anisotropy). Models of wood behaviour based on cell wall structure also explain the influence of these two parameters (Cave 1968, Neagu and Gamstedt 2007, Yamamoto et al. 2001).

The primary wall (P) and S1 layer of the secondary wall while very thin have microfibril orientation nearly perpendicular to the tracheid direction and will limit transverse shrinkage (Abe and Funada 2005, Donaldson and Xu 2005). On the other hand, the S2 layer is thick and the microfibrils limit longitudinal shrinkage more than transverse shrinkage. The thicker is the S2, the lower will be the efficiency of the P+S1 layer in limiting transverse shrinkage, thus explaining the positive influence of density on transverse shrinkage.

An increase in MFA in the S2 layer (lower values for the specific modulus) induces a restriction of transverse shrinkage in that layer and thus a lessening of global transverse shrinkage, regardless of the thickness (and density) of S2. The respective influence of the density and specific modulus on shrinkage variation will depend on both the C.V. of each layer (pure mathematical effect) and on the structural organisation of the cell wall.

Ring width, density and specific modulus are parameters that are easy to measure by non-destructive techniques such as X-ray tomography and vibration or ultrasound techniques (Freyburger et al. 2009, Van Den Bulcke et al. 2009). These parameters are also linked to the wood formation inside of the tree during cambial activity and cell wall thickening.

The different properties were predicted by stepwise linear regression. The combined influence of density and specific modulus can be additive or multiplicative (as for MOE) as a result, the product between these two parameters was introduced as an option in the analysis.

Table 10 gives the global results of these regression calculations providing for each property, the parameter involved with its entry rank and the cumulative determination coefficients (R2) obtained after each addition of a parameter (F to enter 0,05; F to remove 0,1).

Table 10:
Prediction of properties for clear-wood See legend as in Table 8, bold characters: best prediction.

Compressive strength was well predicted using density and specific modulus alone (R²=73%), with ring width contributing very little to variability. Strain limit was also well predicted by the specific modulus alone (R²=67%).

The product of density and specific modulus (MOE) was the best predictor of all shrinkage properties, often alone (VS and TS) and sometimes with a small contribution (less than 2%) from the specific modulus per se. Radial and volumetric shrinkage were rather well predicted (R²=62% and 58%) but tangential shrinkage and shrinkage anisotropy were poorly predicted by the parameters (R²=40% and 31%). In pine wood, variations in tracheid geometry follows a radial trend so that the successive hard and soft layers of late and early wood act as serial components for radial shrinkage, while they acting as parallel components for tangential shrinkage. In a study to predict anisotropic shrinkage of softwood (Pang 2002) found that radial shrinkage grows linearly with the proportion of late wood in the ring width, like mean density, while tangential shrinkage is mostly dependent on the late wood density value.

FSP could not be predicted (R²=6%). FSP describes the maximum amount of bound water of the cell wall. The results suggested that variations in FSP were not linked to structural parameters like cell wall thickness or MFA. The occurrence of extractives in pine is rather frequent (Choong 1969) and varies substantially between a single tree and within individual trees. It could be a major factor accounting for both FSP and shrinkage variations in addition to hemicellulose content variations between species.

^♠Corresponding author: cedric.montero@umontpellier.fr