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Article

Modeling the Effect of High Soil Moisture on the Wind Resistance of Urban Trees

by
Chia-Cheng Fan
*,
Shu-Cheng Li
and
Jin-Zong Lu
Department of Construction Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 824, Taiwan
*
Author to whom correspondence should be addressed.
Forests 2022, 13(11), 1875; https://doi.org/10.3390/f13111875
Submission received: 27 September 2022 / Revised: 2 November 2022 / Accepted: 4 November 2022 / Published: 9 November 2022
(This article belongs to the Section Natural Hazards and Risk Management)
Browse Figures
Versions Notes

Abstract

:
In urban areas, typhoons frequently cause the tilting and uprooting of trees, resulting in damage to city infrastructure. During periods of intense rainfall, at shallow soil depths, soil water content is typically high, reducing the anchoring resistance of tree roots in the soil. Tree root systems play an important role in providing anchoring resistance against severe winds during typhoons. In this study, we examined the influence of high soil saturation on the turning resistance of trees by conducting winching tests on three tree species found in urban areas. In highly saturated soils, the maximum resisting moment of camphor trees (Cinnamomum camphora (L.) J. Presl.) is 35–50% lower than in soils with low saturation levels. A tree’s maximum resisting moment (TMmax) exhibits a linearly positive relationship with its diameter at breast height (DBH) in near-saturated soil conditions. The ratio of TMmax values to DBH in near-saturated soils is noticeably lower than in low-moisture soils. Our research establishes a relationship between the DBH of trees and the strength of the wind that they can resist during typhoons, as measured on the Beaufort scale.

1. Introduction

Severe winds and heavy rainfalls are fundamental characteristics of summer typhoons and hurricanes in the west Pacific and Atlantic regions. The high wind loads of such storms can result in uprooted and toppled trees in urban areas, which may damage houses and cause traffic problems. Subsequent restoration work can be labor-intensive and costly. The geometry of trees and the mechanics of their root systems are important factors to consider when assessing the ability of trees to resist severe winds during typhoons. The morphology of a tree’s root system exerts a more substantial influence on whether it survives or overturns than the material properties of the roots and soils [1]. The mechanics of root systems in trees subjected to severe winds are complicated [2]. The depths of taproots, the dimensions of the zone of rapid taper, and the basal diameter of the shallow windward roots all influence the turning resistance of trees subjected to pulling forces [2].
In recent decades, researchers have investigated the turning resistance of trees [3,4,5,6,7,8,9,10,11,12,13] and have conducted field experiments to estimate the turning resistance of trees [3,5,6,9,10,11,13]. The resisting moment of trees is greatly affected by the asymmetry of the root system [3,14] and is positively related to the geometric characteristics of the individual tree, i.e., its diameter at breast height (DBH) and the volume of its trunk [5,6,9]. Researchers in European countries found a close relationship between the resisting moment and DBH, and also between the resisting moment and crown biomass, in the case of fir trees [6]. Trees with a larger area in the soil–root plate exhibit a higher turning resistance [15]. The anchorage demonstrated by trees is mainly provided by taproots and sinker roots, while the resisting moment is mainly determined by the trunk diameter and not by the cross-sectional area of the lateral roots [4]. For urban trees, however, the root system after transplanting usually develops smaller regenerated branching roots at the cut end and a reduced root plate radius [16]. Moreover, compacted soils in urban areas often restrict the depth to which roots may develop [16], and underground structural components near sidewalks or alongside streets may restrict the growth of the tree root system and affect the tree’s turning resistance against the wind.
Soil moisture is an important factor that affects the roots’ anchorage in the soil [17,18,19,20,21,22,23,24]. Few researchers have considered the influence of soil water content on tree anchorage and stability [17,22]. Trees in areas that are characterized by a shallow water table exhibit lower turning resistance than those in areas with a deep water table [18]. Owing to capillary action, moisture may rise upward from the groundwater table in the soil [25]. The uptake of moisture by the root system may enhance moisture migration in the ground at shallow depths. High soil water content levels below the root plate noticeably reduce root anchorage. The maximum resisting moment of trees negatively correlates with the soil water content [19]. The anchorage of young Pinus pinaster trees in sandy soil does not noticeably lessen with soil wetting until the soil reaches complete saturation [17]. The high precipitation preceding winter storms contributes to the increased winter storm damage to forests [20]. Moreover, the centrifuge modeling of push-over tests on model trees showed that the root anchorage strength measured in dry soils was higher than that in saturated soils [22].
Factors influencing tree failure in wind events are categorized into two groups: intrinsic and extrinsic [26]. Intrinsic factors include tree size, wood density, structural defects, and foliage [26]. Tall trees [27,28], low wood density [27], and dense foliage [27,29] tend to result in lower resistance to wind events. In addition, extrinsic factors include site condition, management, and soil characteristics [26]. Trees growing in sandy soils tend to have higher resistance against wind loads compared with silty and clayey soils [30]. Trees growing in groups are more likely to show better resistance against wind loads [29]. Pruned trees have more significant survival rates than unpruned trees [27,29]. Climate change affects the pattern and intensity of environmental events, especially by increasing the frequency of high-intensity storms. This raises serious safety issues in inhabited environments such as cities, especially those built on sloping land. In the west Pacific region, typhoons with high-intensity rainfall are now a routine summer phenomenon [31]. During typhoons, trees are toppled or uprooted by strong winds because heavy rainfall reduces the anchorage provided by tree root systems [17,21,29,32]. Some researchers have considered this issue [18,19,33], but our knowledge of tree resistance to solid winds during typhoons remains limited.
In July and September of 2016, three moderate to severe typhoons hit southern Taiwan and brought heavy rainfall. In Kaohsiung city, 1075 mm of rain fell over the course of the three typhoon events. These typhoon events caused tens of thousands of trees to tilt and uproot on sidewalks and along the streets, which usually provides restricted root space. Species affected included samanea saman (Samanea saman (Jacq.) Merr.), mahogany (Swietenia mahagoniv (L.) Jacq.), amboyna wood (Pterocarpus indicus Willd.), and marabutan (Ficus microcarpa Linn. F.). The resulting damage required substantial financial resources to repair. Heavy rainfall caused by typhoons results in a considerable increase in soil water content at shallow depths. Any resulting effects upon root anchorage strongly affect the stability of trees subjected to high wind loads [17].
In this study, we investigated the effect of high soil moisture on the turning resistance of urban trees. We sought to simulate how anchorage changes during typhoons. We determined the turning resistance provided by the tree’s anchorage by conducting winching tests in near-saturated soil conditions. We focused on three species: the camphor tree, samanea saman, and amboyna wood, which are common in parks and along sidewalks in Kaohsiung city in southern Taiwan. In addition, we carried out winching tests on camphor trees in low-moisture soil conditions to assess how turning resistance is affected by increases in saturation. Trees with large DBH values tend to demonstrate the strength to resist higher wind load levels during typhoons. The results of the present study provide an experimental basis for assessing the stability of urban trees during typhoons. Our findings contribute to a better understanding of the strength of urban trees that are subjected to high wind loads during typhoons and may help tree managers in local governments to produce better policies and measures concerning the planting and maintenance of trees in urban areas.

2. Materials and Methods

2.1. Experimental Sites

We selected three test sites near the south gate of the Diyi campus of Kaohsiung University of Science and Technology, Kaohsiung, Taiwan. The winching tests on trees need an open space in which to set up the apparatus and to accommodate researchers for the experiment. The sidewalks and the area along the streets are restricted in terms of space, which may also bring up safety concerns. It is challenging to set up the apparatus in these areas. At the time of the study, the sites were near the road and in open spaces with flat ground surfaces. The shallow soil is primarily composed of silty sands with low proportions of clayey materials and gravel. We measured the soil properties and water content at the experimental sites by conducting laboratory tests using soil samples. Table 1 lists the physical properties of the soil at the experimental sites. The soil water content at the camphor trees site was 4–4.9% (saturation ratio = 5–10%). Prior to the winching tests, we measured the volumetric soil water content in the field to a depth of 12 cm, using a portable TDR soil moisture meter (Spectrum Inc., TDR100). The TDR reading was calibrated by the gravitational water content of soil samples, extracted at the site, and tested in the laboratory.

2.2. Tree Species

For the winching tests, we used three tree species, namely, the camphor tree (Cinnamomum camphora (L.) J. Presl.), samanea saman (also known as the rain tree) (Samanea saman (Jacq.) Merr.), and amboyna wood (Pterocarpus indicus Willd.). Trees at the testing site were transplanted from other areas and had been growing for more than 10–15 years. The height of the trees ranged from 6 to 12 m for camphor trees, 5 to 11 m for samanea saman, and 6 to 12 m for amboyna wood. These species are typically planted in open spaces and are common in urban areas of Kaohsiung. In our study, we used samples from 18, 19, and 23 trees of camphor, samanea saman, and amboyna wood, respectively. DBHs ranged from 13 to 27 cm for the camphor tree, 13 to 24 cm for samanea saman, and 13 to 24 cm for amboyna wood.
We measured the circumference (CR) of all sample trees at a height of 1.3 m and used a simple formula, π(DBH) = CR, to estimate the DBH of individual trees. We also determined the tree height and crown size on site, using a theodolite. Table 2 lists the geometric data for the three tree species.

2.3. Winching Tests

We carried out winching tests on the trees at the site to investigate their maximum turning resistance against wind loads. Figure 1 shows the experimental setup in the field. We attached the winched tree to an anchoring tree, using a steel wire rope at a height of 1.3 m. The distance between the winched and anchoring trees was about 6–9 m. We used a load cell with a capacity of 50 kN and a displacement sensor with a stroke of 100 cm. We continuously applied a pulling force to the tree, using a chain winch until the maximum value was attained. We recorded the pulling force and displacement of the wire rope using a data logger system. The distance between each tested tree is about 4 to 7 m at the site. Moreover, the pulling on the winching tree stops when the pulling force starts to drop, to avoid excessive tilting displacement on the tree. The ground surface surrounding the winched trees shows limited heave or displacement. Disruption of the soil-root interface for the winched tree from the previous winching tests is nominal in the study. During testing, we estimated the deflection angle of the tree, based on the lateral displacement of the winched tree, measured at a height of 1.3 m. We carried out 18, 19, and 23 winching tests for the camphor tree, samanea saman, and amboyna wood, respectively. For camphor trees, we carried out six winching tests in low-moisture soil conditions and twelve in near-saturated conditions. To create the near-saturated soil conditions, we poured water on the ground surrounding the winched trees. For camphor trees, the low-moisture soil water content was 4–4.9% (saturation ratio = 5–10%); in near-saturated conditions, the soil water content was 27.2–28.8% (saturation ratio = 73.5–77%). We carried out all winching tests for samanea saman and amboyna wood in near-saturated soil conditions. For samanea saman, the soil water content was 28–30.5% (saturation ratio = 92–98%); for the amboyna wood, the soil water content was 22–23.8% (saturation ratio = 77–84%).

2.4. Data Analysis

We determined the turning moment (TMapplied) of the winched tree, based on the pulling force applied and the deflection angle observed. Following [5], we calculated the applied turning moment (TMapplied) as follows:
TMapplied = Fx × cos(θ) × Hcable + Fy × sin(θ) × Hcable
Fx = F × cos(α); Fy = F × sin(α)
where Fx = applied force in the horizontal direction; Fy = applied force in the vertical direction; F = applied force in the wire rope; Hcable = height of the attachment point at the winched tree; θ = deflection angle of the winched tree; α = angle between the wire rope and the ground surface. We estimated most stem diameters to be approximately 18–25 cm, and we considered the tree stem to be a rigid element. We attached the extensometer to the wire rope close to its point attachment to the trunk, 1.3 m above the ground. We measured the lateral displacement of the trunk at the 1.3 m level, with reference to a metal rack anchored in the ground during the pulling test. The recorded displacement represents the tree’s lateral displacement at an angle α to the ground surface (as shown in Figure 1). During testing, we calculated the deflection angle θ of the winched tree at a given pulling displacement (dl), using the law of cosines.
We calculated the turning moment (TMweight) at the base of the tree, due to the weight of the leaning tree, as follows:
TMweight = W × Gx
where W = weight of the trunk and Gx = horizontal distance of the center of gravity of the trunk from its base. The maximum resisting moment of trees (TMmax) is the sum of TMapplied and TMweight.
We fitted a simple linear regression model to the data of the maximum resisting moment for trees and the tree geometries. The resulting coefficient of determination (R2) showed how well the fitted equation explained the data [34].

2.5. Wind Loads on Trees Subjected to Typhoons

Typically, information concerning winds during typhoons is forecast and released by the national meteorological offices of individual countries. Meteorologists use the Beaufort scale as an indicator of wind speed. The International Meteorological Organization classifies the Beaufort scale from levels 0 to 12 [35], but the central weather bureau in Taiwan extends the Beaufort scale to level 17 [36]. Maximum wind speeds near the center of mild-intensity typhoons are 17.2–32.6 m/sec, equivalent to 8–11 on the Beaufort scale. Moderate-intensity typhoons correspond to Beaufort scale levels of 12–15, with maximum wind speeds of 32.6–50.9 m/sec near their center [36]. Beaufort scale levels of 16 or above indicate severe typhoons, with maximum wind speeds in excess of 51 m/sec near their center [36].
According to Newton’s laws of motion and the properties of objects, and in line with the authors of [37], we can determine the wind force on trees as follows:
F = 0.5 × (ρCdaV2)A
where F is the drag force (N); Cd is the drag coefficient; ρ is the air density (=1.2 kg/m3); a is the reduction coefficient, taking into account the windward canopy density of the trees; V is the wind speed (m/sec); A is the area of the canopy of the trees (m2).
The moment of wind force acting on trees is proportional to the height of the trees. The drag force F is proportional to the drag coefficient, which depends on the object’s shape [38]. For a cone-shaped canopy, the drag coefficient is typically around 0.5, but the precise value is affected by the type and density of the tree leaves, the bending stiffness of the trunk, crown shape, wind direction, wind speed, planting density, and tree location [39]. The authors of [40] determined the overall drag coefficient (Cda) values of 0.2–0.8 for red alder, trembling aspen, black cottonwood, and paper birch trees at wind speeds of 5–20 m/s [40]. The Cda value decreases as the wind speed increases. For this study, we used a Cda value of 0.2 to estimate the toppling moment at the bottom of trees that are subjected to storms.

3. Results

3.1. Turning Resistance vs. the Deflection Angle of Trees

The winching tests resulted in the cracking and bulging of the ground surface around the winched trees. Figure 2 shows the relationships between the turning moments and the deflection angles obtained in this study for the camphor tree, samanea saman, and amboyna wood. We found that turning moments in low-moisture soil conditions were noticeably higher than in near-saturated soil conditions. In near-saturated soil conditions, the maximum turning moment occurred at a deflection angle of about 8–10°. However, tree samples in low-moisture soil conditions did not reach their maximum turning moment value, due to the capacity of the pulling system. Figure 3 plots the deflection angles (θmax) for trees at maximum pulling forces in near-saturated soil conditions, against DBH values for all three species; the θmax values ranged from 6° to 20° at DBHs of 12 to 26 cm, and the θmax values decreased with lower DBH values. Based on the test results obtained for camphor trees in near-saturated soil conditions, we found that most deflection angles were greater than 8–10° for trees winched at a height of 1.3 m that were subjected to the maximum pulling forces.

3.2. Relationship between the Maximum Resisting Moment and the Geometry of Trees

We estimated the maximum resisting moment for camphor trees in low-moisture soil conditions by extending the relationship between the turning moment and the deflection angle (θ) to a θ value of 9°, as shown in Figure 2. We anticipated a close relationship between the root anchorage and the age of the tree, as indicated by tree geometry [41]. For example, Saint Cast et al. (2019) [41] reported that the stump diameter of Pinus pinaster in France increases from 2.5 cm at the age of 3 years to 20 cm at the age of 13 years. Figure 4 shows the relationship between the maximum resisting moment (TMmax) and DBH for camphor trees in low-moisture and near-saturated soil conditions. The TMmax values increase with DBH, and TMmax correlates well with DBH. TMmax values in near-saturated soil conditions are about 40–45% lower than in low-moisture soil conditions, when measured at DBHs of 18–23 cm. This represents a considerable reduction in the turning resistance of trees, due to an increase in soil saturation ratio from about 10% to 77%. Moreover, the ratio of the maximum resisting moment to DBH in near-saturated soil conditions is about 35% of that seen in low-moisture soil conditions. The simple linear regression equations between TMmax and DBH for camphor trees are listed in Table 3.
Figure 5 illustrates the relationships between the maximum resisting moment (TMmax) and the DBH for the camphor tree, amboyna wood, and samanea saman in near-saturated soil conditions. For all three species, the TMmax values increase linearly with DBH, and the coefficients of determination (R2) are good. Differences in TMmax values and DBH correlations can also be observed for three plant species. TMmax values for the camphor tree and amboyna wood are slightly higher than for samanea saman. The soil water content at the samanea saman site was higher than at the camphor tree and amboyna wood sites. In the case of the camphor tree, our results show that soil water content considerably affects the maximum turning resistance of the plants. We consider the high soil water content at the samanea saman test site to be one of the reasons why this species exhibited the lowest maximum resisting moment among the three species studied. Table 4 lists the regression equations for the relationship between TMmax and DBH in near-saturated soil conditions.
Figure 6 shows the relationships between the maximum resisting moment and tree height (H) for a camphor tree, amboyna wood, and samanea saman in near-saturated soil conditions. The correlations between TMmax values and H are fair for amboyna wood and samanea saman but are poor for the camphor tree. These results suggest that DBH seems to be a better tree characteristic for estimating the turning resistance of trees compared with tree height. Table 5 lists the regression equations for the relationship between TMmax and H in near-saturated soil conditions.

4. Discussion

4.1. Turning Resistance of Urban Trees in Near-Saturated Soil Conditions

The occurrence of extreme weather events such as typhoons raises the need to study the behavior of urban trees subjected to high wind loads. Until now, researchers have focused on the turning resistance of urban trees against typhoons. Rahardjo et al. (2017) [32] found that a rainfall-induced decrease in matric suction caused a reduction in the resistive moment of trees against wind load. Theoretical calculations suggest that the maximum resisting moment of trees decreases by up to 80% when the matric suction decreases from 35 to 0 kPa. Défossez et al. (2021) [17] showed that soil-water content exerted a minimal influence on the maximum resisting moment of 14-year-old Pinus pinaster trees, except in simulated domains on completely saturated sandy soils. Simulations have also shown that the maximum resisting moment decreases by up to 40% when the ground is close to saturation, compared with the corresponding low-saturation value. The influence of soil saturation on turning resistance depends on the distribution of water within the mass of the soil–root system [17]. This study used winching tests to identify the relationships between TMmax and tree geometry for three trees that are commonly seen in urban settings in Taiwan. These tests replicated the conditions experienced by urban trees subjected to typhoons.
Our results demonstrate how the turning resistance of urban trees declines as a result of substantial increases in soil water content, which simulate the actual situation during typhoons. For urban trees planted in open spaces, such as parks, the decrease in turning resistance may be as high as 35–50% when the soil saturation increases from low to high levels. However, urban trees are commonly planted at the site on sidewalks or alongside city streets. In such cases, the surface and underground structural components near the sidewalk or close to the street may restrict the growth and lateral extent of the tree root system. This restricted growth of the root system may hinder the turning resistance development of the tree. The root system, DBH, tree height, and crown of the tree all tend to increase over time, meaning that the applied moment on an older tree may exceed that on a younger tree under the same wind conditions. The ability of urban trees on sidewalks or along streets to resist the levels of wind load induced by typhoons may decrease yearly. Therefore, trees in urban areas may now be more vulnerable to damage during typhoons. Our results highlight the need for the sustainable management of planting trees in urban areas, within the context of infrastructure design.
In line with previous research [4,6,15], our results show that the TMmax values correlate well with DBH measurements. Figure 7 presents the data obtained in this study and from similar previous studies in Asia and European countries [6,15]. Rahardjo et al. (2014) [15] also conducted pulling tests with samanea saman, and their data correlate well with ours. Correlations between TMmax and DBH for silver fir and European beech are close to the corresponding figures that we obtained for camphor trees with DBHs of 18–22 cm of soil in normal soil conditions. These data further support the results obtained in this study. Previous research [5,6,42] also supports our finding that TMmax has a closer association with DBH than with tree height, although TMmax also correlates well with stem volume [5,42]. In any case, the DBH of trees is easy to measure in the field and can be considered a suitable variable by which to estimate tree TMmax values.

4.2. Application in the Stability Assessment of Urban Trees against Typhoons

Figure 8 shows the turning moment applied at the bottom of trees subjected to various wind speeds, as represented by the Beaufort scale, at different tree heights for a frontal area of 12 m2. Figure 8 also shows the experimental result of the winching test for amboyna wood, with a frontal area of 12 m2. This datum indicates that the tested tree (amboyna wood) can resist winds at level 15 on the Beaufort scale, which corresponds to a moderate-intensity typhoon. In this study, we applied this procedure to all the experimental results obtained for samanea saman and amboyna wood to determine the tree resistance to typhoons, in terms of the Beaufort scale. We found that the maximum tolerable wind speed, expressed using the Beaufort scale, is related to DBH and to the canopy’s frontal area.
In this study, we sought to identify the relationships between wind resistance, DBH, and the frontal area of the tree canopy for both samanea saman and amboyna wood. However, this is a challenging task because the canopy’s frontal area may vary with time, due to the growth of the tree and the pruning of branches. To express matters more simply, Figure 9 shows the relationship between DBH and the level of wind strength, which samanea saman and amboyna wood trees can resist, and ignores the effect of the canopy’s frontal area. The data show that, as the DBH increases, the ability of these trees to withstand severe winds increases. The figure also plots the upper and lower bounds for the DBH data points against wind speed levels, recorded using the Beaufort scale. The Beaufort scale level for a specific DBH can be considered to be the likely maximum level at which that specific tree is able to resist the wind loads that are typical of typhoons. Figure 9 shows that the ability of amboyna wood to resist severe winds is greater than that of samanea saman. For example, samanea saman trees with a DBH of 17.5 cm can resist winds at levels 10–14 on the Beaufort scale, while amboyna wood trees with the same DBH can resist winds at levels 13–17.
For this paper, we proposed a method (Figure 9) for assessing the stability of urban trees in open spaces during typhoons, in terms of DBH, based on the experimental results obtained in this study. The research outcome may benefit the maintenance of urban trees to protect people during typhoons and mitigate the workforce and financial expenses to recover the damages and chaos caused by fallen trees in urban areas.

5. Conclusions

In this study, we carried out winching tests on urban trees in open areas to investigate the effect of high soil saturation on the maximum turning resistance against strong winds. The tilting or uprooting of urban trees, caused by strong winds during typhoons may damage city infrastructure. The stability of urban trees in regions affected by typhoons is an important issue for urban planners and policymakers.
We found that the maximum resisting moment of camphor trees in near-saturated soil conditions is 35–50% lower than in low-moisture soil conditions. The ratio of the maximum resisting moment to DBH in near-saturated soil conditions is about 34% of that in low-moisture soil conditions. DBH is a tree geometry indicator that is suitable for estimating the maximum resisting moment of urban trees during typhoons. Camphor trees and amboyna wood show greater resistance to typhoons than samanea saman in open spaces in urban areas. We also identified a relationship between DBH and tolerable wind speed, expressed on the Beaufort scale, for both samanea saman and amboyna wood. Our results provide new insight into the anti-tilting strength of urban trees during typhoons and offer a means to assess the wind loads which trees can resist during such events. The findings of this study may be beneficial for government officials responsible for managing tree stability during typhoons.

Author Contributions

Conceptualization, C.-C.F.; methodology, C.-C.F.; data curation, C.-C.F., S.-C.L. and J.-Z.L.; validation, C.-C.F., S.-C.L. and J.-Z.L.; formal analysis, S.-C.L. and J.-Z.L.; writing—original draft preparation, C.-C.F.; writing—review and editing, C.-C.F.; visualization, S.-C.L. and J.-Z.L.; supervision, C.-C.F.; funding acquisition, C.-C.F. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Ministry of Science and Technology of Taiwan under the grant numbers MOST 106-2221-E-327-008 and MOST 108-2221-E-992-014.

Data Availability Statement

The data that support the findings in the research are available upon reasonable request.

Acknowledgments

The assistance of Rui-peng Lee, Shi-quan Chou, Suan-Ce He, Jun-Hong Chang, Sheng-Zhi Lin, Hsin-Hong Chen, Bai-Yuan Tseng, You-Lun Jong, Guan-Ting Chen, and Cheng-Hao Yang in the field test and data processing is also gratefully acknowledged.

Conflicts of Interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

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Forests 13 01875 g001 550
Figure 1. Schematic diagram of the setup of the winching tests (redrawn from [5]).
Figure 1. Schematic diagram of the setup of the winching tests (redrawn from [5]).
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Figure 2. Experimental relationship of the turning moment vs. the deflection angle of the trees.
Figure 2. Experimental relationship of the turning moment vs. the deflection angle of the trees.
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Figure 3. Deflection angle (θmax) at maximum pulling forces vs. DBH in near-saturated soil conditions.
Figure 3. Deflection angle (θmax) at maximum pulling forces vs. DBH in near-saturated soil conditions.
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Figure 4. Maximum resisting moment vs. DBH for camphor trees in low-moisture and near-saturated soil conditions.
Figure 4. Maximum resisting moment vs. DBH for camphor trees in low-moisture and near-saturated soil conditions.
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Figure 5. The maximum resisting moment vs. DBH for different tree species in near-saturated soil conditions.
Figure 5. The maximum resisting moment vs. DBH for different tree species in near-saturated soil conditions.
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Figure 6. Maximum resisting moment vs. tree height (H) for different tree species in near-saturated soil conditions.
Figure 6. Maximum resisting moment vs. tree height (H) for different tree species in near-saturated soil conditions.
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Figure 7. The maximum resisting moment vs. DBH for different trees.
Figure 7. The maximum resisting moment vs. DBH for different trees.
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Figure 8. The relationship between the Beaufort scale and the turning moment, applied to trees with a canopy frontal area of 12 m2.
Figure 8. The relationship between the Beaufort scale and the turning moment, applied to trees with a canopy frontal area of 12 m2.
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Figure 9. Relationship between the Beaufort scale and the DBH scale for samanea saman and amboyna wood.
Figure 9. Relationship between the Beaufort scale and the DBH scale for samanea saman and amboyna wood.
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Table
Table 1. Soil properties at the experimental sites.
Table 1. Soil properties at the experimental sites.
Physical PropertiesSite of Camphor TreeSite of
Samanea Saman 		Site of
Amboyna Wood
Total unit weight (γm, kN/m3)18.6316.0116.31
Dry unit weight
(γd, kN/m3)		14.7014.1914.41
Specific gravity (Gs)2.622.622.56
Void ratio0.73~0.890.71~0.80.71~0.74
Unified Soil Classification System SM/SCSMSM
Table
Table 2. Geometry of the trees used in the experiment.
Table 2. Geometry of the trees used in the experiment.
Camphor TreeSamanea SamanAmboyna Wood
Tree no.DBHHTree no.DBHHTree no.DBHH
1113.110.23120.48.39116.68.31
1214.315.50317.58.66220.411.62
1315.37.24417.28.42318.58.36
1418.06.53517.58.15418.28.06
1515.310.29719.18.93516.99.97
1614.05.90820.18.43611.85.78
2013.96.651018.87.51714.38.21
2622.412.72.1119.99.32819.18.65
2728.012.061224.210.60918.59.00
2828.78.151319.49.251013.15.16
2926.710.91422.99.951114.87.26
3022.310.641513.15.021218.99.05
N-319.011.01621.79.561315.99.00
N-419.012.511724.510.11418.510.67
N-522.09.341817.87.441518.28.16
N-621.010.361919.19.781615.38.00
N-718.59.712018.39.571719.89.31
N-822.012.232119.17.711812.16.60
2220.48.191913.77.16
2012.427.18
2116.569.81
2216.247.87
2314.407.26
Note: H—tree height (in meters); DBH—diameter at breast height (in centimeters).
Table
Table 3. Regression equations for the relationship between TMmax and DBH for camphor tree.
Table 3. Regression equations for the relationship between TMmax and DBH for camphor tree.
In Low-Moisture Soil ConditionsIn Near-Saturated Soil Conditions
TMmax = 8018.9(DBH) – 91,250TMmax = 2834.9(DBH) – 15,433
R2 = 0.68; p = 0.042R2 = 0.83; p < 0.0001
Note: TMmax—maximum turning moment (in N·m); DBH—diameter at breast height (in centimeters).
Table
Table 4. Regression equations for the relationship between TMmax and DBH in near-saturated soil conditions.
Table 4. Regression equations for the relationship between TMmax and DBH in near-saturated soil conditions.
Camphor TreeSamanea SamanAmboyna Wood
TMmax = 2834.9(DBH) – 15,433TMmax = 3478.9(DBH) – 43,101TMmax = 4523(DBH) – 48,388
R2 = 0.83; p < 0.0001R2 = 0.70; p < 0.0001R2 = 0.67; p < 0.0001
Note: TMmax—maximum turning moment (in N·m); DBH—diameter at breast height (in centimeters).
Table
Table 5. Regression equations for the relationship between TMmax and tree height (H) in near-saturated soil conditions.
Table 5. Regression equations for the relationship between TMmax and tree height (H) in near-saturated soil conditions.
Camphor TreeSamanea SamanAmboyna Wood
TMmax = 2184.2(H) + 16,964TMmax = 6367.6(H) – 30,596TMmax = 7427.1(H) – 36,342
R2 = 0.15; p = 0.22R2 = 0.55; p = 0.0003R2 = 0.60; p < 0.0001
Note: TMmax—maximum turning moment (in N·m); H—tree height (in meters).
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Fan, C.-C.; Li, S.-C.; Lu, J.-Z. Modeling the Effect of High Soil Moisture on the Wind Resistance of Urban Trees. Forests 2022, 13, 1875. https://doi.org/10.3390/f13111875

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Fan C-C, Li S-C, Lu J-Z. Modeling the Effect of High Soil Moisture on the Wind Resistance of Urban Trees. Forests. 2022; 13(11):1875. https://doi.org/10.3390/f13111875

Chicago/Turabian Style

Fan, Chia-Cheng, Shu-Cheng Li, and Jin-Zong Lu. 2022. "Modeling the Effect of High Soil Moisture on the Wind Resistance of Urban Trees" Forests 13, no. 11: 1875. https://doi.org/10.3390/f13111875

APA Style

Fan, C. -C., Li, S. -C., & Lu, J. -Z. (2022). Modeling the Effect of High Soil Moisture on the Wind Resistance of Urban Trees. Forests, 13(11), 1875. https://doi.org/10.3390/f13111875

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