The Role of Tree Size in Root Reinforcement: A Comparative Study of Trema orientalis and Mallotus paniculatus

Abstract

Root reinforcement in soil plays a critical role in maintaining forest slope stability. However, accurately estimating the reinforcement provided by the entire root system of a mature tree remains a time-intensive task. Previous experimental studies on root reinforcement have predominantly focused on small trees, leaving a knowledge gap concerning larger specimens. This study integrates field pullout test data of individual roots, analyses of root geometry distribution within root systems, and theoretical frameworks, including root distribution and Root Bundle Models, to develop methods for estimating root reinforcement across varying tree sizes. The findings indicate that root system reinforcement in large trees is substantially greater than in smaller counterparts. The methodology proposed herein provides forest management professionals with a practical tool for evaluating root reinforcement in dominant forest trees, thereby facilitating improved assessment of landslide risks in forested slopes.

1. Introduction

Forest conservation constitutes a critical component in safeguarding environmental integrity and maintaining ecological balance. Trees, as fundamental constituents of forest ecosystems, play a pivotal role in preserving biodiversity. Plant root systems contribute significantly to the protection of shallow soils against erosion and forest destabilization through both mechanical reinforcement [1,2] and hydrological regulation [3,4]. The loss of trees caused by deforestation and forest fires substantially compromises the stability of forested slopes. Root systems reinforce the surrounding soil matrix, thereby enhancing soil strength and contributing to slope stability. The spatial distribution of vegetation and their root systems is closely linked to slope stability and overall forest conservation. Consequently, root reinforcement represents a crucial parameter in the evaluation of forest slope stability [1,5,6].

Research on tree root reinforcement within soil matrices has been approached through both analytical [7,8,9,10] and experimental methodologies [11,12,13]. Early investigations predominantly addressed the shear resistance of root-permeated soils [7,8]. The tensile strength of roots plays a fundamental role in enhancing the shear resistance of these soils. Subsequent studies have developed theoretical frameworks focusing on root reinforcement based on the pullout resistance of individual roots within the soil [9,10,14,15]. Root system pullout resistance serves as the principal anchoring force that provides shearing resistance in the soil and has attracted considerable attention over the past decade due to its critical function in root anchorage [16,17,18,19,20].

Reasonable estimation of tree root reinforcement necessitates mechanical testing of roots alongside comprehensive investigations of root system distributions [6]. Quantifying root reinforcement is vital for assessing its quantitative contribution to shallow slope stability [6,21,22,23]. Furthermore, the geometric configuration of root systems provides essential insights for evaluating root reinforcement and environmental interactions [22,24]. The morphology of root systems varies considerably depending on species [25], terrain characteristics [26], age [27], local environmental conditions [23,25], hydrological factors [28], and climatic influences [29]. Root reinforcement contributed by larger roots is generally more significant than that of smaller roots [30,31]. Although mature large trees predominate in many forest ecosystems, investigations into their root system geometry and reinforcement remain limited due to the complexity and labor-intensive nature of fieldwork.

Assessing the root reinforcement in large trees via field tests is challenging. This study aims to address this gap by investigating root reinforcement in large trees. We conducted geometric analyses of the tree root systems and performed root pullout tests on Trema orientalis (L.) Blume (hereafter Trema) and Mallotus paniculatus (Lamm.) Müll. Arg. (hereafter Mallotus) under field conditions. Root reinforcement of the entire root system was estimated using the theoretical Root Bundle Model (RBMw) developed by Schwarz et al. (2013) [10]. Additionally, the root distribution model proposed by Giadrossich et al. (2016) [32] was calibrated based on collected root data to predict root system distributions in large trees. We expected that root reinforcement in large trees would increase substantially with diameter at breast height (DBH). Furthermore, the asymmetry of root distribution between the upslope and downslope sides of the tree was investigated based on field measurements of root biomass.

2. Materials and Methods

2.1. Test Site

The experimental sites are situated in the mountainous regions of Kaohsiung, Taiwan. Field investigations were conducted at two locations: the Duona and Sanping forest areas in northeastern Kaohsiung. A slope failure occurred at the study site in 2009 following Typhoon Morakot, which brought an accumulated rainfall of 2500 mm over three days. The resulting landslide affected an area of approximately 16.3 hectares.

The site is characterized by colluvial deposits containing numerous decomposed rock fragments and boulders within the shallow soil layer. The local topography is rugged, with the soil primarily composed of sand and decomposed slate. The unit weight of the shallow soil is approximately 16.2 kN/m³.

The average monthly temperature ranges from 10 °C in winter to 30 °C in summer. Annual precipitation is around 3536.1 mm, with the majority of rainfall occurring from May to September. The elevation of the test site is approximately 850 m above sea level and is predominantly covered with broadleaf forest. The geographic coordinates of the site are 22°53′24.3″ N latitude and 120°44′16.5″ E longitude.

2.2. Plant Species

Survey data collected eight years after the landslide, within a one-hectare plot in the study area, indicated that Mallotus and Trema accounted for 51.5% and 19.3%, respectively, of the stem density in the post-landslide plant community [33]. These heliophilous species were dominant during the early stages of vegetation recovery at the landslide site. The forest stand at the site had a canopy height of approximately 7–11 m, indicating an early successional stage. The root systems of Mallotus and Trema played a crucial role in stabilizing the failed slope, and they were therefore selected for this study to investigate their root system reinforcement capabilities.

2.3. Experiments

Root reinforcement for individual trees was calculated by integrating the results of root pullout tests with the root reinforcement model proposed by Schwarz et al. (2013) [10]. In this study, pullout forces of individual tree roots were measured using a motor-driven pullout apparatus. Root segments were excavated and exposed at a distance of approximately 20–30 cm from the tree stem. Pullout force and displacement were continuously recorded using a data-logging system (GW Instruments, INC., Charlestown, MA, USA), with a displacement rate of 10 mm/min during testing.

The motor system was mounted on a portable tripod, and the anchoring point was established at the base of the tree trunk. Steel wire ropes and rebar hooks were attached to the front end of the exposed root segment to apply the pulling force. The motor operates on battery power. Figure 1 illustrates the field setup of the pullout test. In total, 14 and 15 pullout test data points were obtained for Mallotus and Trema, respectively, covering a range of root diameters between 2 mm and 18 mm.

2.4. Investigation of Root Geometry Distribution

The soil surrounding the Mallotus and Trema trees was excavated in the field using shovels and rakes to fully expose their root systems. For each root system, the diameters of all roots extending from the tree stem were measured using a caliper. Additionally, the number of roots within different diameter classes was recorded along their length extending away from the stem.

Table 1. Geometry of the trees investigated in this study.

Tree No.	DBH (cm)	Tree Height (m)	Maximum Root Length (cm)
W1	8	4.8	200
W2	7	4.6	200
W3	6.7	4.5	170
S1	6	3.9	245
S2	5.7	3.7	310
S3	39	10	400

Remarks: W: Mallotus; S: Trema; Sample S3 is used for the validation of the parameters used in the root distribution model.

presents the geometric characteristics of the trees examined. The diameter at breast height (DBH) was estimated by dividing the stem circumference by π (3.14159). The DBHs of the three Mallotus trees were 6.7 cm, 7.0 cm, and 8.0 cm, while the DBHs of the two Trema trees were 5.7 cm and 6.0 cm. The root diameter classes in the root system were defined at 1 mm intervals.

2.5. Mathematical Models

2.5.1. Root Reinforcement Model

The mathematical model (RBMw) proposed by Schwarz et al. (2013) [10] was used to estimate the root reinforcement provided by individual trees. This model requires two key inputs: pullout test data for individual roots and the geometric distribution of the root system. According to the progressive failure framework employed in the model, external forces applied to individual roots within a system can mobilize either tensile (pulling) or anchorage forces. When a root fails due to breakage or pullout, the model assumes that the external force is redistributed among the remaining roots in the system.

The total reinforcement force of the root system is calculated as the sum of the tensile or anchorage forces mobilized by individual roots at varying displacement levels within the soil. A critical component of this model is the relationship between the pullout resistance of a single root and its diameter. This relationship is defined by Equation (1), as described by Schwarz et al. (2013) [10].

$$F_{max}=F_o{\left(\varphi \right)}^{\alpha }$$

(1)

where F_max = the maximum pullout force of single roots, F_o = the scaling factor, ϕ = the root diameter, and α = the shape factor for the maximum pullout force. The pullout stiffness (k, unit: force/length) of the root may rely on the root diameter and be expressed as follows:

$$k=k_o{\left(\varphi \right)}^{\beta }$$

(2)

where k_o = the scaling factor, and β = the shape factor for the pullout stiffness. The mathematical expression of the total force F_tot of a tree root system at a displacement Δx is given as follows:

$$F_{tot}\left(∆\mathrm{x}\right)=\sum _{i=1}^{i=max}{n}_{i}F\left({\varphi }_i, ∆x\right)S(∆x_i^{*})$$

(3)

where F(ϕ_i,Δx) = pullout force at a given displacement (Δx), ϕ_i = the mean root diameter of each root diameter class, ϕ_max = the maximum root diameter class, n_i = number of roots at root diameter class ϕ_i, $\mathsf{\Delta }{x}_i^{*}$ = normalized displacement of each root diameter class, and $\mathrm{S}(\mathsf{\Delta }{x}_i^{*}$) = Weibull survival function. The Weibull survival function depends on the pullout displacement; its value ranges from 0 to 1. It is the probability that roots survive in the root system when subjected to external forces. The survival function is determined as follows:

$$S\left(\mathsf{\Delta }{x}^{*}\right)=exp\left[-{\left({\displaystyle \frac{∆x^{*}}{\lambda }}\right)}^{\omega }\right]$$

(4)

where λ and ω are scaling and shape factors, respectively, and Δx* = the normalized displacement, defined as follows:

$$\mathsf{\Delta }{x}^{*}={\displaystyle \frac{\mathsf{\Delta }x}{\mathsf{\Delta }{x}_{max}^{fit}\left(\varphi \right)}}$$

(5)

where $\mathsf{\Delta }{x}_{max}^{fit}\left(\varphi \right)$ = the maximum displacement at the root’s failure based on pullout test data. The survival probability (S) of each root is calculated as follows:

$$S=1-{\displaystyle \frac{n_{AO}}{n_{tot}}}$$

(6)

where n_AO = the ranking of roots in ascending order, and n_tot = the total number of roots. The Root Bundle Model’s description refers to Schwarz et al. (2013) [10].

The root diameter class employed in the analysis of tree root reinforcement using the Root Bundle Model was set at 1 mm. The relationship between root reinforcement and displacement was established for Mallotus and Trema, providing insights into their mechanical contribution to slope stability. Tree root reinforcement was calculated using R-based computational tools, obtained in 2021 from the authors of the Root Bundle Model (RBMw).

2.5.2. Root Distribution Model

Previous studies [9,32,34] proposed models to estimate the geometric distribution of roots within tree root systems. The models employ the pipe theory to estimate root density intersecting a vertical soil profile at various distances from the stem. These root distribution models share a common framework, typically classifying roots into coarse and fine categories, with fine roots defined as those less than 1–2 mm in diameter.

Investigating the root systems of large trees in the field presents significant challenges. To address this, we calibrated the root distribution model proposed by Giadrossich et al. (2016) [32] to estimate the root geometry distribution of large Mallotus and Trema trees, using field data from trees with a DBH of 5–8 cm. The density of fine roots (ρ_fr), defined as roots with diameters less than 2 mm, intersecting a 1-m-wide vertical soil section at a distance d from the tree stem, is calculated according to Giadrossich et al. (2016) [32], as follows:

$${\rho }_{fr}(d)=\left({\displaystyle \frac{\mu \left({DBH}^2\frac{\pi }{4}\right)}{\left(2\pi d\right)d_{max}}}\right)\left({\displaystyle \frac{d_{max}-d}{d_{max}}}\right)$$

(7)

where d_max = the maximum rooting distance from the tree stem, DBH = diameter of the tree at breast height, and μ = piping coefficient (number of roots per square meter). The density of coarse roots at a distance d from the tree stem is calculated as follows:

$${\rho }_{cr}(d,{\varphi }_i)={\rho }_{fr}\left({\displaystyle \frac{\mathit{ln}\left(1+{\varphi }_{max}\right)-ln\left(1+{\varphi }_i\right)}{ln\left(1+{\varphi }_{max}\right)}}\right){\left({\displaystyle \frac{{\varphi }_i}{{\varphi }_0}}\right)}^{\gamma }$$

(8)

where γ = constant exponent, ϕ_i = root diameter class size i, ϕ_max = the diameter of the largest root at a distance d from the stem, and ϕ₀ = reference root diameter (1 mm). The ϕ_max decreases with d and is calculated as follows:

$${\varphi }_{max}={\displaystyle \frac{d_{max}-d}{\eta }}$$

(9)

where η = dimensionless constant. Three parameters (μ, γ, η) are needed in the root distribution model. Moreover, the maximum rooting distance (d_max) from the stem is proportional to the tree size and is calculated as follows:

$$d_{max}=\mathsf{\psi }\left(DBH\right)$$

(10)

where ψ = scaling factor.

2.5.3. Calibration of the Mathematical Models

The model parameters (μ, γ, η) were obtained by calibrating the model calculations using the root system geometry data collected in the field. To verify the accuracy of the root distribution model applied in this study, we excavated and examined the root system of a large Trema tree (DBH = 0.39 m) in the field. The root system geometry of this large tree was predicted using the calibrated root distribution model and parameter values derived from small Trema trees. The predicted root geometry was then compared with the measured data from the large Trema to evaluate the model’s reliability.

3. Results

3.1. Root System Distribution

Trema primarily developed lateral roots along with independent, large-diameter taproots. In contrast, Mallotus exhibited a more complex root architecture, including lateral roots, several oblique roots, and a large-diameter taproot. The maximum root lengths observed for Mallotus and Trema were 200 cm and 315 cm, respectively.

Figure 2 illustrates the exposed root system of Mallotus and the variation in root diameter along its length. Figure 2a is a photograph taken in the field, showing the excavated root structure. The root system of Mallotus includes oblique roots, multiple orders of branch roots, and a prominent taproot. The long dashed lines following root numbers 3-3 and 3-5 in Figure 2a represent the estimated length of unexcavated root segments, inferred based on the observed tapering trend of root diameter with distance from the stem. For a Mallotus tree with a DBH of 6.7 cm, the taproot diameter near the stem measured approximately 75 mm. Most Mallotus roots had lengths (L) ranging between 40 and 70 cm.

Figure 3 presents the exposed root system of Trema along with the variation in root diameter along its length. The root architecture comprised a taproot and lateral roots, both of which were densely populated with short, fibrous roots. Additionally, the system exhibited a hierarchical branching pattern with roots of various orders. The long dashed lines following root numbers 1-1 and 1-2 in Figure 3a represent the estimated length of root segments that remained unexcavated within the soil. Most Trema roots extended to lengths between 40 and 50 cm. A general trend of decreasing diameter with increasing root length was observed. Near the stem base, the taproot diameter measured approximately 77 mm for a tree with a diameter at breast height (DBH) of 5.7 cm. The study site was characterized by shallow layers of slate rock, which likely influenced the root growth pattern, particularly that of the taproot.

3.2. Reinforcement of the Tree Root System

The root reinforcement of the entire root system was estimated using the Root Bundle Model (RBMw) theory proposed by Schwarz et al. (2013) [10]. This approach integrated geometric survey data of the full root system with the pullout resistance of individual roots. Figure 4 illustrates the relationship between maximum pullout force and root diameter for Mallotus and Trema. Figure 5 presents pullout force–displacement curves for Mallotus and Trema roots of varying diameters.

Table 2. Parameters in the root reinforcement model for Mallotus and Trema.

Plant Species	Fo	α	k	β	λ	ω
Mallotus	50.7	1.15	600,529	1	1.1	3.04
Trema	14.19	1.61	1,282,281	1	1.02	6.22

summarizes the RBMw parameters derived from root data for Mallotus and Trema specimens with a diameter at breast height (DBH) ranging from 6 to 8 cm. Figure 6 illustrates the relationship between lateral root reinforcement and distance from the stem for entire root systems of Mallotus and Trema. Root reinforcement was calculated along the full perimeter at varying distances from the tree stem. Root reinforcement decreased progressively with increasing distance from the stem, approaching zero at distances between 150 cm and 200 cm. The maximum lateral root reinforcement values were 5.4 kN for Mallotus (DBH = 6.7 cm) and 6.4 kN for Trema (DBH = 6.0 cm). For Trema, the maximum root forces measured at 50 cm, 100 cm, and 150 cm from the stem were 3.83 kN, 1.62 kN, and 0.82 kN, respectively. Corresponding values for Mallotus were 3.76 kN, 0.515 kN, and 0.106 kN at the same distances.

3.3. Calibration of the Root Distribution Model

The root geometry data obtained in this study were used to calibrate the root distribution model proposed by Giadrossich et al. (2016) [32] for Mallotus and Trema, enabling the determination of model parameters. Specifically, we analyzed the number of roots with varying diameters at different radial distances from the tree stem. Parameters η and ψ were derived for Mallotus and Trema, as presented in

Table 3. Parameters in the root distribution model for Mallotus and Trema.

Mallotus				Trema
η	ψ	μ	γ	η	ψ	μ	γ
33.3	31.1	4488	−0.462	42.04	49.7	6987	−0.39

, based on the maximum root diameters observed at various distances and the maximum rooting extent. Parameters γ and μ in Equations (7) and (8) were calibrated using the distribution of root counts across diameter classes at multiple distances from the stem.

However, we observed that the values of γ and μ varied for the data set obtained for different distances from the stem (0.1 m, 0.5 m, 1.0 m, and 1.5 m) for a single tree species, although the model assumes a uniform parameter set for each species’ root system. We calibrated γ and μ values by using the data of root geometry distributions measured in the field, which led to one set of parameters (γ and μ). Figure 7 compares the measured and calibrated root distributions at different distances from the stem for both Mallotus and Trema, demonstrating a reasonable agreement. The calibrated γ and μ values for Mallotus and Trema were obtained and are shown in Table 3.

Further calibration of the root geometry distribution parameters was performed using root reinforcement values computed from the Root Bundle Model. Figure 8 presents the calculated root reinforcement for both species, using model-derived root data and field-measured root geometry. The favorable correspondence between modeled and measured results supports the reliability of the root distribution model in representing root system geometry, particularly for extrapolation to larger trees where direct measurement is impractical.

To further validate the root distribution model parameters established in this study, we conducted additional field investigations on a mature Trema tree with a diameter at breast height (DBH) of 0.39 m. The root geometry distribution was excavated and documented in detail. The measured root data were then compared with the root size distribution predicted by the root distribution model using the parameters listed in Table 3. Figure 9 presents a comparison of the measured and modeled number of roots at various distances from the stem for the large Trema specimen. Although some discrepancies were observed between the measured and computed values at specific distances, the overall trend demonstrated satisfactory agreement.

The calibrated parameters (γ and μ) for Mallotus and Trema were applied in Equations (7) and (8) to generate synthetic root geometry data for trees with a range of DBH values. This modeling approach supports the extrapolation of root system characteristics beyond the limits of direct field measurement.

The estimation of rooting depth at various distances from the stem was based on the methodology proposed by Tardio et al. (2016) [35], wherein the maximum rooting depth at the stem is assumed to be three times the tree’s average rooting depth (bm). The maximum horizontal rooting distance was taken as 18.5 times the tree’s diameter at breast height (DBH), following Schwarz et al. (2010a) [9]. For Trema, the average rooting depth was estimated to be 28.5 cm, based on the findings of Preti et al. (2012) [36].

Using the root distribution model developed in this study and the corresponding parameters listed in Table 3, we generated root number distributions at varying radial distances from the stem for Mallotus and Trema with large DBHs. Figure 10 illustrates the modeled number of roots located 50 cm from the stem for Mallotus and Trema across a range of DBH values. These modeled root distributions form the basis for estimating root system reinforcement in larger trees.

3.4. Root Reinforcement of Large Trees

Root system reinforcement for Mallotus and Trema trees with large DBHs was estimated using the Root Bundle Model, incorporating the predicted root geometry distributions described in the previous section. Root reinforcement was expressed as force per meter of stem circumference at a specified radial distance from the stem. Figure 11 and Figure 12 present the estimated root reinforcement per meter for Mallotus and Trema, respectively, across a DBH range of 10–50 cm.

The results indicate that trees with larger DBHs exhibit significantly greater root reinforcement compared to smaller trees.

Table 4. The root system reinforcement (kN/m) at a distance of 100 cm from the stem.

	DBH (cm)	10	20	30	40	50
Plant Species
Mallotus		0.6	1.1	6.3	10.1	15.4
Trema		0.3	2.4	12.1	28.7	55.1

summarizes the root system reinforcement values for Mallotus and Trema at 100 cm from the stem for DBHs of 10 cm, 20 cm, 30 cm, 40 cm, and 50 cm. These findings highlight the critical role of tree size (DBH) in contributing to root reinforcement and, consequently, slope or soil stability.

Additionally, Trema consistently exhibited higher root reinforcement than Mallotus across all DBH classes. This difference is attributed not only to variations in root geometry distribution but also to the higher pullout resistance observed in Trema roots with diameters exceeding 20 mm.

Figure 13 illustrates the lateral root reinforcement per meter of stem circumference for Mallotus and Trema at distances of 50 cm, 100 cm, and 200 cm from the stem, across a range of DBH values. At 50 cm from the stem, root system reinforcement for trees with a DBH of 30 cm was 19.4 kN/m for Mallotus and 65.1 kN/m for Trema.

For Mallotus, root reinforcement at 50 cm and 100 cm from the stem for a tree with a DBH of 30 cm was 8.8 and 10.3 times greater, respectively, than that of a tree with a DBH of 10 cm. In the case of Trema, reinforcement at the same distances increased by factors of 21.7 and 45.0, respectively, relative to the 10 cm DBH case.

These findings underscore the significant impact of tree size on root system reinforcement. The root reinforcement of large trees is substantially greater than that of smaller trees, confirming that DBH is a key factor in enhancing lateral root reinforcement and, by extension, soil stability.

4. Discussion

4.1. Evaluation of the Root Distribution Model

Researchers have investigated tree root distribution using trench wall excavations [32,37] or 360-degree trenching around the stem [24] in field settings. However, trees growing on slopes often develop asymmetric root systems, with a greater concentration of lateral roots on the upslope side [26,38]. In the present study, we also observed notable asymmetry in the root systems of five tree samples. Detailed characterization of root system morphology is essential for accurately assessing the reinforcement provided by tree roots on slopes. Nevertheless, conventional excavation methods to uncover entire root systems are labor-intensive, particularly for large trees. While indirect techniques such as ground-penetrating radar (GPR) have been used to detect extensive root systems [35,39,40], the reliability of GPR in detecting root distribution is influenced by factors such as root diameter, depth, and density [41].

Asymmetric root architecture on slopes often manifests in a bilateral-fan shape, which helps trees efficiently counteract soil body forces and wind loads on hillsides, thereby enhancing overall stability [26,35]. Previous research has shown that roots growing on the upslope side are generally more robust than those on the downslope side in various plant species [26,42,43]. The present study highlights the complexity and challenges involved in estimating root geometry within a single tree root system. The surrounding soil environment strongly influences tree root distribution on slopes. In this study, highly tortuous roots were observed, largely shaped by local soil conditions. Figure 14 illustrates the cross-sectional areas of first-order roots on the upslope and downslope sides for Mallotus and Trema. A clear asymmetry in root biomass was observed between the two sides; however, no consistent directional preference was identified. This irregularity in root distribution complicates the selection of appropriate parameters for modeling the overall root system geometry using root distribution models. Addressing this variability is critical for developing robust and reliable models for root system estimation.

4.2. Tree Root Reinforcement in Forests

Plantations play a significant role in mitigating the occurrence of shallow landslides on forested slopes, particularly when compared to areas lacking vegetation cover [44,45,46]. However, accurately quantifying tree root geometry and mechanical reinforcement remains a substantial challenge [23]. The present study integrates geometric data of root systems, in situ root pullout test results, and mathematical modeling to evaluate the reinforcement provided by large trees, offering a potential solution to these challenges. Our findings indicate that tree root reinforcement increases substantially with larger diameter at breast height (DBH). Despite this, previous research has provided limited quantitative insight into the influence of DBH on root reinforcement. Unpredictable root system development contributes to high variability in root reinforcement, complicating efforts to predict reinforcement at the stand or population level. Nevertheless, average values of root reinforcement across multiple trees tend to be consistent [24].

Giadrossich et al. (2020) [24] reported mean lateral root reinforcement values ranging from 8.86 to 14.46 kN/m (force per unit trench width) at 100 cm from the stem for Pinus radiata trees with DBHs of 47–61 cm. At 200 cm from the stem, reinforcement values ranged from 1.32 to 2.94 kN/m. In the same study, a minimum lateral root reinforcement of 0.75 kN/m was observed for 25-year-old Pinus radiata stands (400 stems per hectare), while values near the tree stem reached as high as 30–40 kN/m. For Populus deltoides with a DBH of 15.1 cm, calculated root reinforcement values were 28 kN/m, 8 kN/m, and 4.5 kN/m at 50 cm, 150 cm, and 250 cm from the stem, respectively [21]. For the same species with a DBH of 30 cm, predicted reinforcement increased to 37.5 kN/m and 21 kN/m at 150 cm and 250 cm, respectively [21]. Flepp et al. (2021) [31] reported that the lateral root reinforcement of spruce stands was expected to be linearly proportional to the mean DBH of the forest stand. According to data from the Swiss National Forest Inventory (NFI), root reinforcement for spruce trees was approximately 2–5 kN/m, 3–7 kN/m, and 4–14 kN/m for DBHs of 20 cm, 30 cm, and 50 cm, respectively [31].

In the present study, the predicted lateral root reinforcement for Mallotus with a DBH of 30 cm was 19.4 kN/m at 50 cm from the stem and 2.6 kN/m at 150 cm. For Trema with the same DBH, the corresponding predicted values were 65.05 kN/m and 3.75 kN/m at 50 cm and 150 cm, respectively. These findings underscore the importance of accurately characterizing the geometric distribution of the root system, the number of roots across different diameter classes, and the pullout resistance of individual roots. These factors are critical for reliably calculating and predicting tree root reinforcement.

In practical applications, incorporating the mechanical effects of vegetation and tree root reinforcement into slope stability analyses remains a challenge. The primary difficulties lie in accurately characterizing the spatial geometry of tree root systems of different species and conducting pullout tests for large-diameter roots—tasks that are both time-consuming and costly. Gehring et al. [47] proposed a formula for estimating maximum root reinforcement based on the diameter at breast height (DBH) and three species-specific coefficients. Tree root reinforcement generally comprises two key components: basal reinforcement, which anchors the tree in soil beneath the potential sliding surface, and lateral reinforcement, which stabilizes soil along the flanks of the sliding mass [1]. Schwarz et al. (2016) [23] proposed that the additional stabilizing force from vegetation could be incorporated into slope stability assessments by accounting for lateral root reinforcement along the upper scarp and 10% of the lateral root reinforcement across the landslip surface in the calculation of the slope’s factor of safety. The results of the present study highlight the substantial contribution that large trees can make to slope stability through root reinforcement, emphasizing their potential role in sustainable slope management and forested landslide mitigation strategies.

In addition, uncertainties and spatial variability in geotechnical and hydrological parameters used in slope stability analyses across large areas have been shown to significantly influence the distribution of slope instabilities [2,48,49,50]. The stabilizing role of vegetation in reducing slope failure is well established. However, capturing the spatial heterogeneity and variability of root reinforcement in forested slopes remains a significant challenge [51]. To address these limitations, several studies have explored the use of aboveground vegetation indicators, such as normalized difference vegetation index (NDVI) values [52] and canopy height data [53], to infer subsurface root characteristics. The methodology proposed in this study, which estimates root reinforcement of large trees based on diameter at breast height (DBH), provides a promising approach for leveraging aboveground vegetation data to approximate root reinforcement in forested slopes. Incorporating probabilistic approaches into landslide susceptibility assessments may help to account for the spatial uncertainty of root reinforcement, thereby enhancing the reliability of slope stability predictions and risk mitigation strategies in forested areas.

5. Conclusions

This study presents an integrated approach for estimating tree root system reinforcement in large trees. We conducted a geometric investigation of the root systems of two plant species, Mallotus and Trema, and performed field pullout tests on individual roots. Root system distributions were estimated using the model proposed by Giadrossich et al. (2016) [32], and the Root Bundle Model for woody roots (RBMw) developed by Schwarz et al. (2013) [10] was employed to evaluate root reinforcement. The main conclusions of this study are as follows:

• Tree size significantly influences root reinforcement: Diameter at breast height (DBH) is a critical factor in determining tree root reinforcement. For Trema, root reinforcement values at 100 cm from the stem were 0.3, 2.4, 12.1, 28.7, and 55.1 kN/m for DBHs of 10, 20, 30, 40, and 50 cm, respectively. For Mallotus, the corresponding values were 0.6, 1.1, 6.3, 10.1, and 15.4 kN/m.
• Large trees provide significantly greater root reinforcement than smaller ones: The root reinforcement of Mallotus with a DBH of 30 cm was 8.8 and 10.3 times greater than that of a tree with a DBH of 10 cm at 50 cm and 100 cm from the stem, respectively. For Trema, these values were even higher—21.7 and 45 times greater—at the same distances.
• Root distribution is strongly affected by slope and soil conditions: Root systems on slopes exhibited marked asymmetry, with substantial differences in root biomass between the upslope and downslope sides. Local slope geometry and soil conditions play a significant role in shaping root distribution patterns. Full excavation of the root system remains the most reliable method to accurately assess its geometry and mechanical contribution.

Understanding the reinforcement capacity of large tree root systems is essential for evaluating their mechanical role in enhancing slope stability in forested landscapes. However, acquiring such information remains a substantial challenge due to the time-consuming and labor-intensive nature of field investigations.