A Mechanistic Prediction Model of Resistance to Uprooting of Coniferous Trees in Heilongjiang Province, China
Abstract
:1. Introduction
2. Results
2.1. Coarse Root Distribution
2.2. Soil Properties and Root Plate Mass
2.3. Assessment of Samples in Resistance to Uprooting Using Data on Tree Morphological Characteristics
3. Discussion
4. Materials and Methods
4.1. Study Site
4.2. GPR Equipment and Data Acquisition in the Field
4.3. Soil Physical Properties
4.4. GPR Data Collection and Analusis
4.5. Mechanistic Model of Tree Resistance to Wind-Included Uprooting
- The tree is upright and healthy, with the root plate strong enough to support the aboveground components in windless conditions. The shape of the crown is conical. The anchorage point of the tree under wind load conditions is at the base of the stem.
- The wind load is applied horizontally and only directly to the tree crown with the assumption that the wind speed (v) is constant. The wind load is positively proportional to the frontal area of the crown (Stc) [16]. The center of gravity of the wind load is located at 2/3 of the crown length from the crown top [68,69]. The overturning moment of the wind acts on the anchorage point of the tree through the stem.
- Due to elasticity, the stem bends when wind loads are applied to the crown of the tree. However, some of the wind load can be offset by the elastic restoring force of the stem, which is positively correlated with the stiffness of the stem. The most significant factors affecting the resistive moment of the stem are tree height and DBH [55,70,71,72].
- Tree resistance to uprooting is influenced by the support provided by the root plate anchorage, which depends on a combination of four factors: the root plate mass, the strength of the windward roots and root hinge, and the soil strength at the base of the plate [26]. The mechanistic model calculates the resistive moment of the root plate based on the predicted root plate mass, as the contributions of factors other than root plate mass are very complex. The percentage contribution of root plate mass to root anchorage is constant [73,74]. Therefore, the resistive moment of the root plate can be calculated from the root plate mass, as demonstrated in the study by Peltola et al. [55]. Considering the complexity of the tree’s underground component, the root plate, which consists of coarse roots and surrounding soil, is conceptualized as a half-ellipsoid. The center of gravity of the root plate is located at 4 Drp/3 of the depth from the bottom of the root plate [75]. The mass of the root plate is mainly composed of the mass of the coarse root (Gcr) and the mass of the soil in the root plate (Gs). Gs is proportionally correlated to the bulk density of soil () and the volume of the root plate (Vr) [62,76].
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Depth (cm) | Bulk Density (g·cm−3) * | Porosity (%) * | Water Content (%) * | Sand (%) * | Silt (%) * | Clay (%) * |
---|---|---|---|---|---|---|
0~15 | 1.02 ± 0.13 | 75.35 ± 2.84 | 42.53 ± 2.41 | 34.83 ± 2.56 | 59.23 ± 2.06 | 5.94 ± 0.81 |
15~30 | 0.92 ± 0.15 | 79.35 ± 3.17 | 44.17 ± 2.27 | 31.36 ± 1.73 | 63.49 ± 3.18 | 7.66 ± 1.01 |
30~45 | 1.17 ± 0.09 | 63.93 ± 1.55 | 37.00 ± 2.84 | 28.41 ± 1.86 | 60.73 ± 1.47 | 10.86 ± 1.18 |
>45 | 1.24 ± 0.18 | 70.6 ± 1.89 | 28.13 ± 3.66 | 30.02 ± 1.22 | 50.15 ± 1.36 | 19.83 ± 1.86 |
Samples | Root Plate Volume (m3) | Coarse Root Mass (kg) | Soil Mass in the Root Plate (kg) | Root Plate Mass (kg) | Percentage of Coarse Root Biomass in Root Plate Mass (%) |
---|---|---|---|---|---|
S1 | 0.28 | 40.01 | 310.29 | 350.30 | 11.42 |
S2 | 2.00 | 68.60 | 2175.40 | 2243.99 | 3.06 |
S3 | 1.46 | 64.73 | 1592.00 | 1656.73 | 3.91 |
S4 | 2.43 | 73.43 | 2652.98 | 2726.41 | 2.69 |
S5 | 2.44 | 89.29 | 2659.25 | 2748.54 | 3.25 |
S6 | 1.14 | 59.35 | 1246.59 | 1305.94 | 4.54 |
S7 | 2.55 | 105.22 | 2775.02 | 2880.24 | 3.65 |
S8 | 2.55 | 96.67 | 2775.02 | 2871.69 | 3.37 |
S9 | 3.77 | 111.02 | 4104.98 | 4216.00 | 2.63 |
S10 | 3.39 | 132.07 | 3695.04 | 3827.11 | 3.45 |
S11 | 3.81 | 142.63 | 4150.04 | 4292.67 | 3.32 |
S12 | 1.54 | 57.17 | 1675.97 | 1733.14 | 3.30 |
S13 | 2.04 | 70.78 | 2221.96 | 2292.75 | 3.09 |
S14 | 2.15 | 60.92 | 2344.52 | 2405.44 | 2.53 |
S15 | 2.55 | 78.24 | 2775.02 | 2853.26 | 2.74 |
S16 | 0.92 | 42.40 | 998.06 | 1040.45 | 4.07 |
S17 | 0.61 | 27.98 | 662.34 | 690.33 | 4.05 |
S18 | 2.21 | 68.78 | 2412.05 | 2480.83 | 2.77 |
S19 | 0.28 | 17.57 | 302.04 | 319.62 | 5.50 |
S20 | 2.29 | 70.14 | 2498.92 | 2569.06 | 2.73 |
Mean ± S.E. | 2.02 ± 0.23 | 73.85 ± 7.16 | 2201.38 ± 250.09 | 2275.26 ± 256.79 | 3.80 ± 0.43 |
S.D. | 1.03 | 32.02 | 1118.43 | 1148.4 | 1.94 |
K1 | 0.46 | 32.96 | 502.35 | 535.31 | 6.16 |
K2 | 1.43 | 40.01 | 1553.62 | 1593.64 | 2.51 |
K3 | 3.21 | 434.70 | 3504.05 | 3938.76 | 11.04 |
K4 | 0.30 | 23.66 | 322.81 | 346.46 | 6.83 |
K5 | 2.08 | 181.46 | 2265.70 | 2447.17 | 7.42 |
K6 | 4.18 | 1149.48 | 4556.20 | 5705.68 | 20.15 |
K7 | 1.95 | 75.64 | 2125.94 | 2201.58 | 3.44 |
K8 | 3.05 | 219.99 | 3329.27 | 3549.27 | 6.20 |
K9 | 3.06 | 250.79 | 3338.74 | 3589.53 | 6.99 |
K10 | 4.00 | 593.40 | 4360.00 | 4953.40 | 11.98 |
K11 | 4.16 | 1116.47 | 4534.40 | 5650.87 | 19.76 |
K12 | 3.45 | 497.85 | 3760.50 | 4258.35 | 11.69 |
K13 | 0.99 | 36.76 | 1079.50 | 1116.26 | 3.29 |
K14 | 0.64 | 34.18 | 695.34 | 729.52 | 4.69 |
K15 | 1.45 | 40.77 | 1575.18 | 1615.94 | 2.52 |
K16 | 0.57 | 29.37 | 624.60 | 653.97 | 4.49 |
K17 | 1.85 | 47.16 | 2018.83 | 2065.98 | 2.28 |
K18 | 0.66 | 35.86 | 714.07 | 749.93 | 4.78 |
K19 | 0.67 | 40.01 | 733.72 | 773.73 | 5.17 |
K20 | 1.76 | 41.03 | 1919.08 | 1960.11 | 2.09 |
Mean ± S.E. | 2.00 ± 0.30 | 246.08 ± 77.98 | 2175.70 ± 324.68 | 2421.77 ± 393.11 | 7.17 ± 1.18 |
S.D. | 1.33 | 348.73 | 1452.00 | 1758.04 | 5.30 |
Species | DBH (cm) | Tree Height (m) | Height to Crown Base (m) | Average Crown Width (m) | Root Plate Volume (m3) | Root Plate Mass (kg) |
---|---|---|---|---|---|---|
Spruce | 28.60 ± 14.50 | 19.73 ± 8.18 | 11.15 ± 0.65 | 6.54 ± 1.66 | 4.24 ± 1.72 | 3407.56 ± 137.51 |
Korean pine | 45.18 ± 11.90 | 24.30 ± 5.14 | 12.39 ± 0.62 | 7.71 ± 2.04 | 10.02 ± 2.04 | 1624.99 ± 248.14 |
Sample | Hazard Level of Uprooting | |
---|---|---|
S1 | 1.18 | High |
S2 | 1.01 | High |
S3 | 5.32 | High |
S4 | 0.17 | High |
S5 | 1.51 | Low |
S6 | 7.84 | Low |
S7 | 0.98 | High |
S8 | 2.73 | Low |
S9 | 1.40 | Moderate |
S10 | 2.82 | Low |
S11 | 1.32 | Moderate |
S12 | 1.65 | Low |
S13 | 0.70 | High |
S14 | 0.47 | High |
S15 | 1.10 | High |
S16 | 0.33 | High |
S17 | 2.15 | Low |
S18 | 0.31 | High |
S19 | 0.70 | High |
S20 | 0.43 | High |
K1 | 0.83 | High |
K2 | 0.90 | High |
K3 | 0.71 | High |
K4 | 1.72 | Low |
K5 | 1.13 | High |
K6 | 0.69 | High |
K7 | 0.89 | High |
K8 | 1.13 | High |
K9 | 0.81 | High |
K10 | 0.86 | High |
K11 | 0.77 | High |
K12 | 0.72 | High |
K13 | 1.89 | Low |
K14 | 1.59 | Low |
K15 | 2.39 | Low |
K16 | 1.56 | Low |
K17 | 0.96 | High |
K18 | 1.38 | Moderate |
K19 | 0.69 | High |
K20 | 1.38 | Moderate |
Tree Number | DBH (cm) | Height to Crown Base (m) | Tree Height (m) | Crown Width | Average Crown Width (m) | |
---|---|---|---|---|---|---|
East-West (m) | North-South (m) | |||||
S1 | 26.7 | 3.7 | 7.8 | 5.2 | 5.8 | 5.5 |
S2 | 34.3 | 6.6 | 12.9 | 7.4 | 6.9 | 7.2 |
S3 | 32.8 | 5.3 | 9.6 | 8.3 | 4.4 | 6.4 |
S4 | 34.8 | 6.1 | 13.4 | 8.2 | 8.7 | 8.5 |
S5 | 37.8 | 7.0 | 14.1 | 7.2 | 5.0 | 6.1 |
S6 | 31.7 | 5.1 | 8.4 | 8.2 | 9.6 | 8.9 |
S7 | 39.3 | 6.0 | 11.8 | 11.8 | 12.6 | 12.2 |
S8 | 37.8 | 5.5 | 10.2 | 11.3 | 8.2 | 9.8 |
S9 | 39.8 | 5.7 | 11.8 | 11.2 | 12.5 | 11.9 |
S10 | 42.8 | 6.4 | 12.0 | 10.2 | 8.8 | 9.5 |
S11 | 47.0 | 11.6 | 19.3 | 12.3 | 8.3 | 10.3 |
S12 | 34.1 | 10.9 | 17.8 | 6.3 | 7.8 | 7.1 |
S13 | 37.3 | 12.6 | 17.4 | 7.2 | 4.6 | 5.9 |
S14 | 35.2 | 11.9 | 16.9 | 5.3 | 6.2 | 5.8 |
S15 | 38.5 | 12.3 | 15.9 | 5.8 | 9.4 | 7.6 |
S16 | 30.0 | 8.7 | 14.9 | 6.4 | 8.3 | 7.4 |
S17 | 26.6 | 10.6 | 17.1 | 2.7 | 3.1 | 2.9 |
S18 | 36.8 | 12.2 | 18.6 | 3.3 | 10.2 | 6.8 |
S19 | 22.6 | 10.3 | 17.6 | 1.8 | 4.1 | 3.0 |
S20 | 36.1 | 9.7 | 18.8 | 8.3 | 11.5 | 9.9 |
Mean ± S.E. | 35.1 ± 1.28 | 8.41 ± 0.66 | 14.32 ± 0.81 | 7.42 ± 0.67 | 7.8 ± 0.62 | 7.64 ± 0.57 |
S.D. | 5.71 | 2.95 | 3.63 | 2.97 | 2.77 | 2.53 |
K1 | 25.1 | 7.3 | 16.7 | 4.1 | 3.7 | 3.9 |
K2 | 27.2 | 12.6 | 29.1 | 5.8 | 6.7 | 6.3 |
K3 | 64.5 | 16.5 | 35.6 | 8.6 | 8.7 | 8.7 |
K4 | 22.3 | 7.7 | 16.6 | 6.4 | 6.4 | 6.4 |
K5 | 46.8 | 11.8 | 24.2 | 4.8 | 8.3 | 6.6 |
K6 | 91.7 | 18.3 | 30.9 | 12.4 | 14.6 | 13.5 |
K7 | 34.3 | 14.6 | 29.7 | 8.6 | 8.2 | 8.4 |
K8 | 50.5 | 16.8 | 24.8 | 7.6 | 9.8 | 8.7 |
K9 | 52.9 | 16.2 | 33.4 | 12.8 | 13.6 | 13.2 |
K10 | 72.0 | 14.9 | 33.8 | 9.0 | 9.6 | 9.3 |
K11 | 90.8 | 18.9 | 35.9 | 14.7 | 15.9 | 15.3 |
K12 | 68.2 | 23.7 | 36.2 | 11.4 | 10.2 | 10.8 |
K13 | 26.1 | 7.2 | 16.2 | 4.1 | 5.6 | 4.9 |
K14 | 25.5 | 8.4 | 16.8 | 7.3 | 5.6 | 6.5 |
K15 | 27.2 | 8.9 | 14.9 | 5.8 | 6.4 | 6.1 |
K16 | 24.2 | 9.4 | 15.6 | 2.9 | 4.7 | 3.8 |
K17 | 28.8 | 11.4 | 17.3 | 6.9 | 5.2 | 6.1 |
K18 | 26.0 | 9.4 | 17.2 | 9.2 | 7.9 | 8.6 |
K19 | 26.9 | 7.1 | 17.2 | 8.6 | 7.8 | 8.2 |
K20 | 27.2 | 7.9 | 16.5 | 8.2 | 9.6 | 8.9 |
Mean ± S.E. | 42.9 ± 5.14 | 12.5 ± 1.07 | 23.9 ± 1.84 | 8.0 ± 0.69 | 8.4 ± 0.73 | 8.2 ± 0.69 |
S.D. | 22.98 | 4.80 | 8.22 | 3.10 | 3.27 | 3.11 |
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Xie, G.; Li, Y.; Wang, L.; Kan, X.; Zhang, P. A Mechanistic Prediction Model of Resistance to Uprooting of Coniferous Trees in Heilongjiang Province, China. Plants 2024, 13, 2377. https://doi.org/10.3390/plants13172377
Xie G, Li Y, Wang L, Kan X, Zhang P. A Mechanistic Prediction Model of Resistance to Uprooting of Coniferous Trees in Heilongjiang Province, China. Plants. 2024; 13(17):2377. https://doi.org/10.3390/plants13172377
Chicago/Turabian StyleXie, Guangqiang, Yaoxiang Li, Lihai Wang, Xiangcheng Kan, and Ping Zhang. 2024. "A Mechanistic Prediction Model of Resistance to Uprooting of Coniferous Trees in Heilongjiang Province, China" Plants 13, no. 17: 2377. https://doi.org/10.3390/plants13172377