Materials
Figure 1 shows the experimental procedures followed in the present study. Ten Betula platyphylla Sukaczev trees were collected from a natural forest in Mandal, Selenge, Mongolia (36° 47ʹ N, 139° 29ʹ E; approximately 1100 m above the sea level). Although tree age was unknown, because these were naturally regenerated trees, the number of annual rings ranged from 33 to 70 at 1.8 m above the ground level (Fig. 1). The stem diameter measured at 1.3 m above the ground by a tape measure (F10-020DM, KDS, Kyoto, Japan) ranged from 13.2 to 23.0 cm (mean = 15.4 cm) (Fig. 1). After harvesting the trees, two disks (1 cm in thickness) and logs (ca. 50 cm in length) were obtained for each tree from 1.8 to 2.3 m above the ground (Fig. 1).
Annual ring width and cell length
Bark-to-bark radial strips, 10 mm in thickness, were obtained from 1-cm disks to measure the annual ring number and width (Fig. 1). The transverse sectional images (600 dpi) of radial strips in one direction from the pith to bark were captured using a scanner (GT-9300UF, Epson, Nagano, Japan). The annual ring width was measured using ImageJ (National Institutes of Health, Bethesda, MD, USA).
To determine the length of the wood fiber and vessel element, pith-to-bark radial strips (10 mm in thickness) were also obtained from the 1-cm disks (Fig. 1). Small stick specimens were obtained at 5-year intervals from the pith-to-bark radial strips. The stick specimens were collected from a total of 107 radial positions (eight to 15 radial positions × 10 trees). The stick specimens were macerated with Schultze’s solution (6 g of potassium chlorate in 100 mL of 35% nitric acid). A total of 50 wood fibers and 30 vessel elements at each radial position were measured using a micro projector (V-12, Nikon, Tokyo, Japan) and a digital caliper (CD-15CP, Mitutoyo, Tokyo, Japan).
Physical and mechanical properties
In the present study, the following physical and mechanical properties were determined: basic density, air-dry density, dynamic Young’s modulus, static bending, impact bending, compressive strength, and shearing strength (Fig. 1).
To determine the basic density, wedge-shaped specimens (30° at the central angle) were prepared from the disk (Fig. 1). The wedge-shaped specimens were then cut again into smaller specimens at 1-cm intervals from the pith. The basic density was calculated by dividing the oven-dried weight by the green volume measured using the water displacement method.
Physical and mechanical properties, except for basic density and air-dry density, were measured according to Japanese Industrial Standard Z 2101:2009 [21]. Radial boards about 3 cm in thickness were obtained from approximately 50-cm-long logs (Fig. 1). The boards were dried in the laboratory at 22 °C and 65% relative humidity for 3 months. After air drying, the boards were planed to a thickness of 20 mm in the tangential direction, and then stick specimens were obtained at 20-mm intervals from the pith. The following specimens were prepared: air-dry density specimens of approximately 20 (L) by 20 (R) by 20 (T) mm; dynamic Young’s modulus, static, and impact bending specimens of approximately 320 (L) by 20 (R) by 20 (T) mm; compressive strength specimens of approximately 40 (L) by 20 (R) by 20 (T) mm; and shearing strength specimens (chair shape) of approximately 20 (L) by 20 (R) by 20 (T) mm. A total of 30 specimens (two to four radial positions × 10 trees) were obtained from 10 sample logs.
To determine the air-dry density, small clear specimens were dried in the laboratory at 22 °C and 65% relative humidity for 2 weeks. Air-dried density was calculated by dividing the weight by the volume for the three measured dimensions. Moisture content at testing was also determined by the oven-dry method.
The dynamic Young’s modulus of small-clear specimens was measured by the lateral vibrational method [22]. A fast Fourier transform comparator (CF-4500, Ono Sokki, Yokohama, Japan) with a sound level meter (LA-4440, Ono Sokki, Yokohama, Japan) and microphone (MI-3110, Ono Sokki, Yokohama, Japan) were used to measure the first natural frequency of lateral vibration due to sound emitted by hitting the radial section of a specimen with a small steel hammer.
The static bending test was conducted using a universal testing machine (MSC-5/500-2, Tokyo Testing Machine, Tokyo, Japan). The load was applied to the radial surface at the center of the span (280 mm) at a rate of 5 mm/min. The MOE and MOR were calculated from the load and deflection data. The moisture content of the specimens at testing was 10.7 ± 0.2%.
The impact bending test was conducted using a Charpy impact testing machine with 98-J capacity at maximum pendulum height (162°; MC-10W, Maekawa Testing Machine MFG, Tokyo, Japan). The load was applied to the radial surface at the center of the specimens. The impact work in joules was obtained by the machine’s indicator. The absorbed energy during impact bending was calculated by dividing the impact work by the cross-sectional area of the specimen. The moisture content of the specimens at testing was 9.9 ± 0.3%.
The compressive strength test was conducted using a universal testing machine (RTF-2350, A&D, Tokyo, Japan) at a load speed of 0.5 mm/min. The compressive strength parallel to the grain was calculated by dividing the maximum load by the cross-sectional area of the specimen. The moisture content was 10.7 ± 0.2% at testing.
The shearing strength test was conducted using a universal testing machine (MSC-5/500-2) with a load rate of 0.5 mm/min. The shearing strength was determined by dividing the maximum load by the plane area. The moisture content of the specimens was 10.1 ± 0.2% at testing.
Statistical analyses
Statistical analyses were conducted using R software [23]. To evaluate the radial variations, data of the physical and mechanical properties determined at 1- or 2-cm intervals from the pith were converted to cambial age by the radial variation in the annual ring width. The annual ring number from the pith in a specimen was regarded as the annual ring number from the pith at the middle position of the 1- or 2-cm specimens.
To estimate the distance from the pith in relation to the annual ring number, a nonlinear mixed-effects model was developed using the nlme function in the nlme package [24]. The following model was developed:
$$y_{ij} = \alpha_{0} /\left\{ {1 + \left( {\alpha_{1} + a_{j} } \right) \cdot {\text{exp}}( - \alpha_{2} \cdot x_{ij} )} \right\} + e_{ij}$$
where yij is the estimated distance from the pith in relation to the ith annual ring number of the jth individual tree; xij is the ith annual ring number from the pith of the jth individual tree; α0, α1, and α2 are fixed-effect parameters; aj is a random effect parameter for the individual tree; eij is residual.
Linear and nonlinear mixed-effects models with random effects at the tree level were developed to determine radial variation in the wood properties in relation to the annual ring number from the pith using the lmer function in the lme4 packages [25] and the nlme function in the nlme package [24], respectively. The following models were developed:
$${\text{Model I}}:y_{ij} = \beta_{0} x_{ij} + \beta_{{1}} + u_{j} + e_{ij}$$
$${\text{Model II}}:y_{ij} = \beta_{0} {\text{ln }}\left( {x_{ij} } \right) + \beta_{{1}} + u_{j} + e_{ij}$$
$${\text{Model III}}:y_{ij} = \beta_{0} x_{ij}^{{2}} + \beta_{{1}} x_{ij} + \beta_{{2}} + u_{j} + e_{ij}$$
where yij is the measured value for the ith annual ring number from the pith of the jth individual tree; xij is the ith annual ring number from the pith of the jth individual tree; α0, α1, and α2 are fixed effect parameters; uj, is random effect parameter of the jth individual tree; eij is residual.
Model selection was performed using the Akaike Information Criterion (AIC) [26]. The best model (smallest AIC value) was selected from the developed models.
To evaluate the boundary between the core wood and outer wood, wood fiber length at each annual ring number was estimated using the regression formula based on the best model (selected by AIC value). The boundary was defined as the increase ratio of wood fiber length in the present year to one previous year reached 1.0% [9, 15]. In addition, each wood property was estimated at the annual ring number from the pith to the 70th annual ring number from the pith in each tree by the regression formula based on the best model. Mean values of each wood property in each tree were calculated for the core wood (from first to boundary annual ring number determined by the annual increment of wood fiber length) and outer wood (from boundary annual ring number to 70th annual ring). A significant difference in estimated wood properties between the core wood and outer wood was detected by conducting a paired t test for the mean values of 10 trees. The relationships among the examined wood properties of the small clear specimens were determined using Pearson’s correlation coefficient.