Unravelling Mangrove Storm Damage Resistance for Sustainable Flood Defense Safety Using 3D-Printed Mimics

Abstract

Mangrove forests are vital for flood reduction, yet their failure mechanisms during storms are poorly known, hampering their integration into engineered coastal protection. In this paper, we aimed to unravel the relationship between the resistance of mangrove trees to overturning and root distribution and the properties of the soil, while avoiding damage to natural mangrove forests. We therefore (i) tested the stability of 3D-printed tree mimics that imitate typical shallow mangrove root systems, mimicking both damaged and intact root systems, in sediments representing the soil properties of contrasting mangrove sites, and subsequently (ii) tested if the existing stability models for terrestrial trees are applicable for mangrove tree species, which have unique shallow root systems to survive waterlogged soils. Root systems of different complexities were modeled after Avicennia alba, Avicennia germinans, and Rhizophora stylosa, and printed at a 1:100 scale using material densities matching those of natural tree roots, to ensure the geometric scaling of overturning moments. The mimic stability increased with the soil shear strength and root plate surface area. The optimal root configuration for mimic stability depended on the sediment properties: spreading root systems performed better in softer sediments, while concentrating root biomass near the trunk improved stability in stronger sediments. An adapted terrestrial tree resistance model reproduced our measurements well, suggesting that such models could be adapted to predict the stability of shallow-rooted mangroves living in waterlogged soils. Field tree-pulling experiments are needed to further confirm our conclusions with real-world data, examine complicating factors like root intertwining, and consider mangrove tree properties like aerial roots. Overall, this work establishes a foundation for incorporating mangrove storm damage into hybrid coastal protection systems.

1. Introduction

Mangrove forests offer sustainable solutions for flood safety in the 21st century, gaining attention as alternatives or nature-based complements to traditional flood protection structures like breakwaters or embankments [1,2]. Similar to coastal defense structures, mangroves reduce waves [3,4,5], currents [6], and coastal erosion through sediment accumulation [7]. However, unlike hard coastal structures, mangroves can adapt to environmental changes [8], regenerating after damage [9] and adjusting to rises in the sea level by accumulating sediment and modifying their root systems [10]. Moreover, mangroves contribute to carbon sequestration [11], serve as nurseries for many fish species [12], and support local livelihoods [13]. Despite these advantages, mangrove forests cannot easily be implemented into coastal protection features yet as they lack design formulas like those used to predict the safety levels (i.e., failure chance) of engineered structures. Such formulas are needed to link extreme weather events to mangrove persistence (or failure). For instance, trees can fail during storms due to trunk breakage [14] or overturning [15], resulting in reduced wave attenuation [16,17], thus diminishing a forest’s protective capacity. In addition, storm impacts like wind, erosion [18], burial [19], and inundation can damage mangroves and cause long-term mortality effects [9]. While attempts are being made to capture these failure mechanisms and implement them into design formulas, especially tree overturning mechanisms—where extreme canopy drag forces [20,21] overpower soil–root anchorage [22,23,24]—mangrove failure modes remain understudied. To assess mangrove resilience, it is hence necessary to unravel the components that enhance the resistance of mangrove trees to overturning during extreme weather events.

Ideally, mangrove tree overturning resistance would be measured directly in the field with tree loading experiments [25], where a winch is used to mimic wind loading and measure its impact on the root–soil system and stability of the tree. However, obtaining measurements of mangrove overturning in the field is challenging. Mangrove anchorage is a complex system with interacting environmental factors that can convolute overturning measurements. This includes, for instance, variations in soil properties, which can vary significantly within a single field site [26], or variations in root properties, like the architecture of aerial roots [27] and the spread and density of belowground roots, and material properties, such as root strength and flexibility [2]. Acquiring a sufficiently large dataset to develop design formulas would imply the destruction of large numbers of trees, while mangroves are already under threat in many places around the world [28]. Moreover, the purpose of this study is to ultimately use mangrove forests in sustainable nature-based coastal protection, which does not align with the destruction of many trees. As large-scale field measurements are not realistic, alternative approaches are needed.

The current study therefore aims to (i) serve as a pilot study to inform the design of future field experiments that investigate mangrove resistance to overturning, and to (ii) support the development of design formulas that capture mangrove tree overturning resistance. Using small-scale 3D-printed (Nylon 12) mangrove mimics, this study aims to assess which sediment and root properties require priority in field measurements, hereby minimizing the number of trees damaged for research purposes, and explore to what extent we can apply our knowledge of overturning terrestrial trees to mangrove trees, which grow in dynamic, water-logged sediments [29] and develop shallower roots [28]. The 3D-printed mangrove tree mimics were designed to represent the shallow belowground portion of mangrove root systems of Avicennia and Rhizophora spp. We tested these mimics in sediment conditions representing natural contrasting mangrove sites. The mimics were geometrically scaled at 1:100 and the Nylon 12 material was selected for the trees and sediment densities to match those of natural trees and soils, ensuring that the measured forces were also scaled at 1:100 relative to the field conditions. Overall, our experiments aim to provide a first step towards understanding how root distribution influences mangrove stability across diverse soil conditions, while the strengths and limitations of this study are discussed.

2. Materials and Methods

2.1. Sediment Preparation and Properties

As mangroves can grow in diverse sedimentary environments, we aimed to cover the range of coastal sediments found in the literature (shown in Table S1). Based on this overview, we prepared five sediment types by mixing various sand, silt and water contents (

Table 1. The five sediment types we mixed and their properties, ordered by shear strength τs for easy comparison with the figures in Section 3.

Saturation State	Sediment	Sand Content (%)	Silt Content (%)	Average Grain Size (µm)	Water Content (% of Dry Weight)	Bulk Density ρs (kg m−3)	Penetration Resistance Pens (kPa)	Shear Strength τs (kPa)
Undrained	Silt	0	100	30	100	1498	0.5	0.7
Undrained	Sand	100	0	400	30	1732	64.3	7.6
Undrained	Silty sand	50	50	215	50	1738	6.5	9.1
Drained	Silt	0	100	30	70	1537	20.0	15.0
Drained	Silty sand	50	50	215	30	1903	53.7	40.7

). Each sediment was mixed with water, as dry sediment is not usually found at the seaward forest fringe, the zone where most uprooting takes place [30,31].

We mixed homogenous sediments to ensure that our measurements were as consistent as possible. For sand, we used aquarium sand with a grain size of 0.2–0.6 mm (JBL Sansibar, Neuhofen, Germany). For silt, we used kaolin powder with a grain size of 25–35 µm (Al₂Si₂O₅(OH)₄, Colpaert–Van Leemputten, Nevele, Belgium). To characterize the properties of each mixture, we measured the bulk density ρ_s (kg m⁻³), penetration resistance pen_s (kPa) and shear strength τ_s (kPa; Table 1).

The bulk density ρ_s was measured by weighing a disk filled with a known volume of sediment. The penetration resistance pen_s was measured by pushing down a 60° cone with a surface area of 50 mm² using a precise automated extenuator (INSTRON, Norwoord, MA, USA) with a speed of 60 mm min⁻¹.

The sediment shear strength τ_s was measured by placing a plate with a diameter of 8 cm below a 0.7 cm layer of sediment (i.e., same size and depth as the mimics in the pulling test; Section 2.3) and pulling the plate upward with a speed of 60 mm min⁻¹. The maximum load before failure was used to calculate the sediment shear strength τ_s, where we first subtracted the weight of the root–sediment plate from the maximum load and then divided it by the surface area of the sediment edge (i.e., perimeter of the plate $\times$ depth of the plate).

2.2. Root Plate and Mimic Design

We designed mangrove mimics with 3D-printed roots for five root mass distributions (Figure 1 and Figure 2b) and various root breakages (Figure 2b). The root mass distributions were inspired by photos of uprooted or eroded mangrove roots of Avicennia germinans, Avicennia alba, and Rhizophora stylosa (shown in Figure 1a–c).

We developed idealized versions for reproducible testing, with some more realistic and detailed (Figure 1h–j) and some more extreme and simplified root mass distributions (Figure 1g,k), to test the entire realm of possible root mass distributions, such that some have biomass closely centered around the stem (SimInn), some have biomass evenly spread out (DetInn, DetMid, DetOut), and some have biomass far away from the stem (SimOut). In this naming system, ‘Sim’ stands for simple and ‘Det’ stands for detailed.

The root plates were designed with equal surface areas A_r (Figure 2), but they differed slightly in their actual surface area because of the 3D printing process (Figure 3). Therefore, in this paper, the root plate areas A_r (cm²) will be represented by the proxy root plate weight W_r (g).

To assess the effect of root breakage, we removed a part of the root plate. We did this at two distances from the edge of the root plate, at 25% and 45% of the total diameter of the plate (2 and 3.5 cm of 8 cm diameter, respectively) and on the windward side (25W, 45W), leeward side (25L, 45L) or both sides (25B; Figure 2b). As the root distributions varied in the location of their biomass, the reduction in area (proxy weight W_r) was higher for some (e.g., SimOut) than for other root distributions (e.g., SimInn; Figure 3).

We opted to design rigid mangrove tree mimics that were scaled approximately 1:100 in terms of size compared to real mangrove trees (see Table 2), resulting in a root plate diameter of 8 cm and a height of 3 cm to facilitate the quick subsequent pulling tests.

2.3. Root Plate 3D-Printing Process and Assemblage

We drew the root systems using a browser-based 3D modelling program, namely Tinkercad (Autodesk, San Rafael, CA, USA), and 3D printed them with Nylon 12 plastic using Selective Laser Sintering (Shapeways, Eindhoven, The Netherlands).

The mimics were constructed by attaching the 3D-printed root plates with nuts to a tree trunk made of a M4 stainless steel rod and a canopy made of a M4 stainless steel eye nut held firmly in place with parafilm (Figure 2a). The Nylon 12 material has a density of 1.02 kg/m³ and a tensile modulus of elasticity of 1800 N/mm² [32]. The 3D-printed mimics did not deflect during the experiments and any flexibility effects can therefore be neglected in the interpretation of the results.

Table 2. Properties of mangroves trees and mimics, and mimics scaled up 100×. Tree data are from Njana et al. [33,34], where the root plate radius is based on the length of the belowground (cable) roots.

Tree/Mimic	Tree Height, m (Mean ± SD)	Root Plate Radius, m (Range)	Root Depth, m (Range)
Avicennia marina	9.6 ± 5.4	1.4–16.1	0.2–1.4
Rhizophora stylosa	7.4 ± 6.4	1.6–5.1	0.3–1.0
Mimic	0.105	0.04	0.007
Mimic upscaled 100×	10.5	4	0.7

Table 2. Properties of mangroves trees and mimics, and mimics scaled up 100×. Tree data are from Njana et al. [33,34], where the root plate radius is based on the length of the belowground (cable) roots.

Tree/Mimic	Tree Height, m (Mean ± SD)	Root Plate Radius, m (Range)	Root Depth, m (Range)
Avicennia marina	9.6 ± 5.4	1.4–16.1	0.2–1.4
Rhizophora stylosa	7.4 ± 6.4	1.6–5.1	0.3–1.0
Mimic	0.105	0.04	0.007
Mimic upscaled 100×	10.5	4	0.7

2.4. Weight Scaling of Tree-Soil System

The geometric scaling of both the soil layer and trees also implies the weight scaling of both the soil and trees, since the density of the soil is natural, and the density of the mimic material (Nylon 12) is the same as that of mangrove trees (slightly above 1 kg/m³). Since these experiments aimed to explore how varying sediment cohesions influence the failure of a block of rooted sediment, the sediment grain size was not scaled. Scaling the particle size would be relevant if we were entraining particles using a flow but is irrelevant in an experiment where the adhesion of a substance is key. To account for the effect of sediment consolidation, which modifies both weight and cohesion, a wide range of sediment weights and cohesion values were tested.

2.5. Pulling Tests to Measure Overturning Moments

We carried out pulling tests with all sediments, root mass distributions and root breakages. In total, 345 pulling tests were conducted. Each test was carried out three times, where we replaced the sediment in the pot after each test and placed the same mimic in it again (explained below). We carried out tests in each sediment type using each root mass distribution with the unbroken root plates (5 sediments × 5 root distribution × 3 repetitions = 75 tests).

Each pulling test was prepared by ‘planting’ the mimic in a pot filled with one of the sediments. An 80-micron plastic bag with a watertight seal (to avoid water leakage from sediments) was placed in a 9.6 cm tall pot made out of a PVC pipe with a diameter of 15.5 cm. The plastic bag was filled with sediment and levelled off evenly at the top. The pot had a 1 cm PVC disk at the bottom. To ensure that each mimic was placed at a 1 cm depth, we removed the disk so that the sediment ‘sunk’ 1 cm. The mimic was then placed on top of the sediment and the remaining gap was filled and levelled off evenly at the top, so that the mimic was now 1 cm belowground with an effective sediment depth of 7 mm (as the root plate was 3 mm tall, equal to 0.7 m belowground in the field; Table 2).

The mimics were attached to the pulling mechanism of a universal testing machine fitted with a 10 N load cell (INSTRON, Norwoord, MA, USA) by tying a polyester string (with a diameter of 0.75 mm and a tensile strength of 17 kg; Paracord Nano, Atwood Rope MFG, Millersport, OH, US) to the ‘crown’ of the mimic (the eye nut) with a Davy knot (Figure 2a). The other side of the string was looped through a pulley that was placed at a distance of 45 cm and attached with a bowline knot to the universal testing machine (INSTRON, Norwoord, MA, USA).

Pulling tests were carried out by moving the pulling mechanism upward, so that the mimic that was attached moved forward (Figure 4a). During each pulling test, we measured the load F (N) per extension ε (mm) continuously (Figure 4b) and pulled until the windward side of the root plate was fully uprooted. The pulling mechanism moved upwards at an extension speed of 60 mm min⁻¹. The extension ε (mm) was converted to a mimic angle θ_M (°) that moved with approximately 0.5 ° mm⁻¹ (i.e., 30° min⁻¹).

2.6. Calculation of Overturning Moments

We calculated the overturning moment $M_t$ (N∙m) according to Urata et al. [20]:

$$M_t=M_p+M_s$$

(1)

where M_p (N∙m) and M_S (N∙m) are the moments of the pulling load and self-loading (i.e., the turning moment generated by the weight of the mimic as it topples), respectively. The pulling load is the sum of its horizontal and vertical components:

$$M_p=H_{L}Fcos{\theta }_L+{\delta }_{L}Fsin{\theta }_L$$

(2)

where H_L is the pulling height (m), F is the pulling load (N), ${\theta }_L$ is the angle of pulling (rad) and ${\delta }_L$ is the horizontal displacement of the stem at pulling height (m). We calculated the pulling angle ${\theta }_L$ (rad) and the horizontal displacement of the stem at pulling height ${\delta }_L$ (m) using basic trigonometric calculations (Table S2). The self-loading moment M_s (N$·$m) is defined as follows:

$$M_s={\delta }_G{W}_{T}g$$

(3)

wherein ${\delta }_G$ is the horizontal stem displacement at the center of gravity of the above-ground part (m), which is, in our case, the same as the horizontal displacement of the stem at pulling height ${\delta }_L$ (m); W_T is the aboveground biomass (kg); and g is the gravity (9.81 N kg⁻¹). An overview of all parameters can be found in

Table A1. All properties with symbols, units, their meaning and the source where the values can be found.

Symbol	Unit	Meaning	Source
Soil parameters
${\tau }_s$	N m−2	Shear strength	Table 1
${\rho }_s$	kg m−3	Bulk density	Table 1
pens	N m−2	Penetration resistance	Table 1
Root parameters
Pr	%	Half surface parameter	Figure A2a
pivb	#	Number of root breakages	Figure 2b
$A_r$	m2	Root plate area	Figure 3, Table S3
$W_r$	kg	Root plate weight, proxy for area Ar	Figure 3, Table S3
$D_s$	m	Sediment/rooting depth	0.007; Table 2
Overturning components
Mt; Mtmax	N m	(Maximum) overturning moment	$M_t=M_p+M_s$
Mp	N m	Pulling moment	$M_p=H_{L}Fcos{\theta }_L+{\delta }_{L}Fsin{\theta }_L$
Ms	N m	Self-loading moment	$M_s={\delta }_G{W}_{T}g$
$H_L$	m	Pulling height	See Figure 4a
$F$	N	Pulling load	See Figure 4a
${\theta }_L$	rad	Angle of pulling	See Figure 4a
${\delta }_L$$, {\delta }_G$	m	Horizontal displacement of the stem at pulling height	See Figure 4a
$W_T$	kg	Aboveground biomass	0.02
Anchorage components
Ma	N m	Anchorage moment	$M_a=M_w+M_r$
Mw	N m	Weight moment	$M_w=y_1\left(W||r+W_s\right)g$
Mr	N m	Resistance moment	$M_r={\tau }_s{D}_s{C}_p{y}_2$
$y_1$	m	Distance from hinge to the center of gravity of root–sediment plate	Table S3, Figure A1 of the Appendix A
$W_s$	kg	Weight of the sediment cylinder above the roots	$W_s=D_s{A}_r{\rho }_s$
$g$	N kg−1	Gravitational constant	9.81
$C_p$	m	Perimeter of windward side of the root plate	Table S3, Figure A1 of the Appendix A
$y_2$	m	Distance from hinge to the center of gravity of the arc	Table S3, Figure A1 of the Appendix A

of Appendix A.

2.7. Statistical Methods

We used R (version 4.1.1) with packages rstatix (0.7.0), corrplot (0.92), FactoMiner (2.4), factoextra (1.0.7) and MuMIn (1.46.0) to carry out all statistical analyses. We calculated the maximum overturning moment Mt_max (N∙m) as the highest overturning moment M_t (N∙m) that was measured during a pulling test before failure, i.e., the moment just before the root plate was uprooted (Figure 4b). First, we tested the effect of sediment on mimic stability. We used a Kruskal–Wallis test to check if there were any significant differences in the maximum overturning moment Mt_max (N∙m) between sediments; this was followed by a post-hoc Dunn’s test to compare any differences between sediments.

We then tested the effect of root breakage on mimic stability. We normalized the maximum overturning moments Mt_max (N∙m) for the sediment effect on stability by dividing the average Mt_max per sediment by the Mt_max. We then fitted, per sediment, a linear model between the normalized moments and root breakage, which was represented by the root plate weight W_r (g) as a proxy for the change root plate area A_r (cm²), and we also calculated the Pearson correlation coefficient.

2.8. Mangrove Stability Model

We aimed to find out if mangrove (mimic) stability can be modelled mechanistically by adapting a model developed for terrestrial, shallow-rooted pine trees by Achim and Nicoll [22]. We used this model to predict the anchorage moment of our mangrove mimics and compared this to the measured maximum overturning moment Mt_max. Here, we assume that the maximum overturning moment Mt_max before failure is equal to the anchorage moment of the mimic.

We adapted this model at one point. In the original model, the resistance moment M_r is the resistance of the root–sediment matrix, which requires a resistance constant ‘A₁’ (N m⁻¹) to be estimated per sediment type based on the pulling tests. There is effectively no root resistance in our setup because the 3D-printed Nylon 12 material is too strong to break under the test circumstances, so that the only limiting factor is the resistance of the sediment.

Hence, we argue that the constant A₁ used in their model can be replaced with sediment resistance, measured as the sediment shear strength ${\tau }_s$ (N m⁻²). Thus, we define the anchorage moment M_a as follows:

$$M_a=M_w+M_r$$

(4)

where M_a is the anchorage moment, M_w is the moment of the root–sediment plate weight and M_r is the moment of the root–sediment resistance. The moment representing the root–sediment plate weight is as follows:

$$M_w=y_1{W}_{s}g$$

(5)

where M_W is the moment of the root–sediment plate, y₁ is the distance from the hinge to the center of gravity of the root–sediment plate (m; lever arm length, Figure 4), and W_s is the weight of the sediment in the root–sediment plate: $W_s=D_s{A}_r{\rho }_s$; here, A_r is the area of the root–sediment plate, D_s is the sediment depth, ${\rho }_s$ is the bulk density of the sediment (kg m⁻³) and g is the gravity (9.81 N kg⁻¹). Furthermore,

$$M_r={\tau }_s{D}_s{C}_p{y}_2$$

(6)

where ${\tau }_s$ (N m⁻²) is the sediment shear strength (as measured in Section 2.1), $D_s$ (m) is the sediment depth, $C_p$ (m) is the circumference/perimeter of the windward edge of the root–sediment plate, and $y_2$ (m) is the distance from the hinge to the center of gravity of the arc (Figure 4 and Table S2).

To assess the model fit of the anchorage model (Equation (4)), we compared the predicted anchorage moment M_a to the observed maximum overturning moment Mt_max for the full anchorage model M_a (Equation (4)), the weight model M_w (Equation (5)) and the resistance model M_r (Equation (6)). For each of these models, we compared the Akaike information criterion (AIC) and Akaike weight [35], correlation r, intercept ${\beta }_0$ (which should be 0 for a perfect prediction) and slope ${\beta }_1$ (which should be 1 for a perfect prediction). For the best-fitting model, we then left out each of the non-constant model components (e.g., for the resistance model, leave out ${\tau }_s$, then C_p, then y₂) to assess the role of each component.

3. Results

3.1. General Patterns in Mimic Stability

The overturning curves varied between sediment types, root mass distributions and root breakage (Figure 5). The maximum overturning moment withstood by the soil–root system (proxy of tree stability) was largest for drained soils with a low water content and a relatively larger sediment size. This can be seen in the larger stability values for Drained Silty Sand compared to the smaller values for Undrained Silts in Figure 5. The relationship between tree stability and the sediment type has been explicitly illustrated in Figure 6, which shows how the maximum overturning moment increases with the sediment shear strength.

The distribution of the belowground root plate also significantly influences the resistance of mangroves to overturning but, interestingly, the optimum (most stable) distribution changes per sediment type (Figure 5). For instance, root systems where cable roots spread radially from the center (DetOut) are most stable in relatively weak soils (Undrained Silt). For stronger sediments (Drained Silty Sand), root systems that increase their biomass near the center of the root system show higher stability (like DetInn).

There is a limit on increasing biomass near the center, though, as the root system with the most condensed biomass near the center (SimInn) is the least stable in all soil types. This implies that Avicennia sp. trees, which inspired the schematized root systems, DetInn and DetOut, could increase their stability in weak soils by spreading their biomass (DetOut) and increase their stability in stronger sediments by developing biomass closer to the center in stronger soils (DetInn) until reaching an optimum root configuration.

Figure 5 also suggests that the belowground root plate inspired by Rhizophora sp. trees is relatively more advantageous in terms of stability compared to the other root systems, due to its well-drained sandy soils. Moreover, the stilt roots of Rhizophora sp. mangroves could increase their stability even more with respect to the results of Figure 5 (see Section 4). Overall, these results suggest that mangroves could adjust their root plate morphology to the sediment they grow in to maintain optimal stability, as previously observed for various terrestrial tree species [36].

The pulling experiments also support that root plates with a larger area increase tree stability, implying that the breakage and detachment of part of the root system largely reduce stability, as shown in Figure 7. The role of breakage seems to be relatively more relevant for better drained soils, as indicated by the steeper curves for Drained Silt and Drained Silty Sand compared to Undrained Silty Sand.

3.2. Anchorage Predictions and Model Fitting

We compared the measured maximum overturning moments M_tmax (N∙m) to the anchorage moments M_a (N∙m) predicted with the anchorage model (Equation (4)) and found that the resistance model M_r (Equation (6)) best fit our data (

Table 3. Parameters of mechanical model variations. The sediment depth Ds and gravitational constant g are constants and not considered in the calculated df.

Prediction Equation	df	AIC (Mt~Ma)	Wi	r (p < 0.01)	${\mathit{\beta }}_0$	${\mathit{\beta }}_1$
$M_a=y_1{W}_{s}g+{\tau }_s{D}_s{C}_p{y}_2$	5	−507.08	0.06	0.84	0.03	0.56
$M_a=y_1{W}_{s}g$	2	−153.08	0	0.2	0.17	14.07
$M_a={\tau }_s{D}_s{C}_p{y}_2$	3	−512.6	0.94	0.84	0.04	0.56
$M_a={\tau }_s{D}_s{y}_2$l	2	−491.76	0	0.83	0.03	0.07
$M_a=D_s{C}_p{y}_2$	2	−145.53	0	0.13	0.18	3065.44
$M_a={\tau }_s{D}_s{C}_p$	2	−433.52	0	0.79	0.03	0.02

). Furthermore, we observed that the model overestimated stability slightly in most cases, such that the average ratio Mt_max/M_a = 0.71 (Figure 8). The model’s accuracy was quite variable across sediment types, but was more consistent for root breakage (Figure 8a,b). Across root mass distributions, the model was more accurate for more widespread distributions (Figure 8c).

4. Discussion

In this study, we aimed to understand the effect of the sediment type, root mass distribution and root breakage on mangrove tree stability using 1:100-scaled 3D-printed mimics. We observed higher mimic stability with a higher sediment shear strength and larger root plates (i.e., with less mimicked root breakage). Moreover, we found that the optimal root distribution for stability depended on the sediment type, and that the effect of root breakage on mimic stability also depended on the sediment type. Finally, we showed that the mechanistic anchorage model developed for terrestrial trees provided useful mechanistic principles for estimating mangrove tree stability, with the specification of the sediment resistance through the sediment shear strength being a useful alteration to this model.

4.1. Strengths and Limitations of the Experimental Set Up

Given the limited existing research on mangrove overturning, we used schematized root systems to isolate overturning processes, starting with the belowground root distribution. While being oversimplified, this approach does enable us to (i) derive the first generic patterns for shallow rooting mangrove species, and (ii) test the applicability of a terrestrial tree model for mangrove-like root systems. Future studies could incorporate additional processes and gradually increase complexity. Aerial roots were omitted in this study, but they can play a key role in stability; for example, Hill et al. [37] found that detaching aerial roots from the soil halved the force required to tilt a Rhizophora stylosa tree. Mangrove canopies are often offset from the trunk due to competition and wind stress [38], which also alters the overturning moment—a factor that could be investigated in future experiments. Follow-up studies could investigate materials that replicate not only the density but also the strength of natural mangrove roots to test root failure. Future studies could also include prototypes with multiple trees and varying root interconnection between trees, as intertwined roots may enhance overall forest stability [39].

A key limitation in developing mimic designs is the scarcity of studies mapping belowground mangrove root systems. Field surveys of fallen trees, like those by van Bijsterveldt et al. [10], could help expand our database of root typologies. Advanced tools like laser scanners and radars could map both the aboveground and belowground root systems of healthy trees. Comparing the root systems of healthy and fallen trees after storms, along with sediment sampling at fallen tree sites, could reveal the factors contributing to vulnerability. Additionally, field measurements could highlight species-specific differences in the extent of roots (as those presented in Table 2) and their impact on mangrove stability.

4.2. Validation with Field Experiments

Field tree-pulling experiments are recommended to validate the behaviors observed in scaled experiments. Scaled experiments could in turn guide the selection of environments and trees, focusing on root and soil types with distinct behaviors. A systematic approach—such as starting with a specific species or multiple species in a single soil type—can help minimize confounding factors. This ensures that the lessons learned from destructive field studies are more easily extrapolated to model development and enhance our conceptual understanding of tree stability.

4.3. Additional Drivers of Mangrove Root Development

Our experiments testing a root plate with a constant radius revealed that the most stable root configuration depended on the sediment type, consistent with findings for terrestrial trees [36]. However, factors beyond sediment type also influence root development. For instance, wind loading can induce thigmomorphic growth, increasing root mass on the leeward side [40], and waterlogging can inhibit root growth while promoting eutrophication shoots [41,42]. To better understand mangrove stability in coastal environments, field studies are needed to investigate the factors that influence the belowground root morphology of various mangrove species.

4.4. Failure Models

The mechanistic tree stability model for terrestrial trees by Achim and Nicoll [22] predicts mimic anchorage with reasonable precision (see AIC comparisons in Table 3 and

Table A2. Model comparison, showing model fits with Akaike Information Criterium AIC, Akaike weights Wi. and adjusted R2 with its p-value. Note that the root plate weight Wr functions as a proxy for the root plate area Ar.

Statistical Model	df	AIC	Wi	Adj. R2	p-Value
Mtmax~1	2	−142.78	0	0	NA
${\mathrm{Mt}}_{\max }~{\tau }_s$	3	−399.28	0	0.58	<0.001
${\mathrm{Mt}}_{\max }~W_r$	3	−146.48	0	0.02	0.017
Mtmax~Pr2	4	−142.9	0	0.01	0.13
${\mathrm{Mt}}_{\max }~{\tau }_s$$+W_r$	4	−451.16	0	0.64	<0.001
${\mathrm{Mt}}_{\max }~{\tau }_s$+ Pr2	5	−405.13	0	0.59	<0.001
Mtmax~${\tau }_s$+ $W_r$ + ${\tau }_s:W_r$	5	−490.85	0	0.69	<0.001
Mtmax~${\tau }_s$+ $W_r$ + Pr2	6	−466.51	0	0.66	<0.001
Mtmax~${\tau }_s$+ $W_r$ + ${\tau }_s:W_r$ + Pr2	7	−513.12	0	0.71	<0.001
Mtmax~${\tau }_s$+ $W_r$ + ${\tau }_s:W_r$ + Pr2 + ${\tau }_s:$Pr2	9	−519.52	0.03	0.72	<0.001
Mtmax~${\tau }_s$+ $W_r$ + ${\tau }_s:W_r$ + Pr2 + $W_r:$Pr2	9	−516.17	0.01	0.72	<0.001
Mtmax~${\tau }_s$+ $W_r$ + ${\tau }_s:W_r$ + Pr2 + ${\tau }_s:$Pr2 + $W_r:$Pr2	11	−526.62	0.97	0.73	<0.001

) and provides simple, useful principles for understanding mangrove stability. However, the model excludes root–sediment resistance and does not differentiate between root distributions. As a result, it cannot account for the effective windward perimeter (Cp) and leeward arm (y2) (see Figure A1 in the Appendix A), which vary with sediment type and root morphology interactions. Field validation with mangroves is needed to assess the model’s reliability across different sediment types, root morphologies, and species.

4.5. Implications for Mangrove Stability in Coastal Settings

Our experimental data revealed the strong influence of the sediment’s shear strength on mimic stability, with greater stability observed in sediments with higher upward shear strength, consistent with findings for terrestrial trees [43,44]. Since waterlogged sediments generally exhibit lower shear strength [45], mangrove trees at the seaward fringe, where waterlogging is more frequent or prolonged, may be less stable.

Mangroves rooted in waterlogged, silty, or clayey sediments—which erode more easily [46]—are at a higher risk of overturning compared to those in sandy sediments. When present in shallow sediments (0.1 m depth), Rhizophora species have been observed to produce more prop roots [47], which increases their belowground biomass and stability. By trapping sediment [9], mangroves can potentially enhance their root depth and protect against erosion and uprooting. The impact of soil depth on tree stability is further discussed in the following section.

4.6. Frameworks to Implement Mangrove Failure in Coastal Protection

This study provides a critical foundation for estimating vegetation failure in nature-based or hybrid flood protection systems, such as embankments combined with mangrove forests. Our findings suggest that stability models for terrestrial trees can be adapted for mangroves, though additional processes (discussed earlier) must be explored, and field validation is essential before application.

Once validated with field data, these failure models could predict tree instability during storms using Equations (4)–(6) and various forest data, including the species distribution, height, surface area, root dimensions, and local sediment characteristics. These equations can complement existing wave reduction models, such as those by Mendez and Losada [48], by accounting for vegetation failure and its impact on wave attenuation. Similarly, mangrove failure formulations could be applied using the output of wind models.

The wave heights propagating through damaged forests can then inform the design of coastal protection structures, such as revetments for embankments. As illustrated in Figure 9, neglecting mangrove failure due to wind and waves in design calculations risks underestimating the structural requirements, potentially compromising the flood safety of the hinterland.

Lastly, Equations (4)–(6) can be integrated into models estimating the changes in bed level (sediment) that occur during storms to assess how tree stability varies under extreme conditions. For example, in Figure 10, we used these equations to demonstrate the influence of sediment depth on tree stability, expressed through the anchorage moment provided by vegetation. The results indicate that greater root depths (i.e., a sediment layer with a greater thickness over the root plate) enhance mangrove stability by increasing the anchorage moment.

5. Conclusions

Our study provides valuable insights into the factors influencing mangrove tree stability under storm conditions. The results show that tree stability is strongly influenced by the sediment type, with drained soils offering higher stability due to an increased shear strength. The root mass distribution also plays a critical role, with optimal configurations varying depending on the soil conditions—the radial spread of roots enhances stability in weaker soils, while concentrated biomass is more beneficial in stronger soils. Additionally, larger root plate areas improve stability, highlighting that a reduction in stability is caused by root breakage. The anchorage model developed in this study provided reasonable predictions of the overturning moments, though it slightly overestimated the stability in most cases. These findings suggest that mangroves can adjust their root morphology to optimize their stability in response to varying soil conditions, offering a foundation for future research and applications in coastal protection systems. This study has limitations, notably the exclusion of aerial roots and root intertwining, which are crucial for mangrove stability. Future research should explore the effects of wind loads and waterlogging on root development and include field tree-pulling experiments to validate our findings. Expanding the database of root systems using field surveys and advanced mapping techniques could provide valuable insights into species-specific root morphology and stability, helping guide more complex future models.