Performance of wildlife fence systems under animal impact load

Abstract

Wildlife fence protection systems specifically designed for animal protection are critical in mitigating wildlife-vehicle collisions and preserving animal habitats. These systems are quite similar to rockfall barrier systems, which are well studied and developed, however, few studies are specifically oriented toward investigating structural performance of these systems. Despite the similarities, results of studies related to rockfall barriers may not be directly applicable to design and performance evaluation of wildlife barrier systems due to differences in a range of size, shape, and velocity of impactors and structural details. This study aims to bridge this gap by analyzing performance and capacity of wildlife structures in more detail through parametric study with consideration of a wide range of properties and structural details appropriate for these systems, such as mesh type (square and inclined), mesh size, and wire diameters. The behavior of these systems under impact loads is simulated using nonlinear finite element models with consideration of ductile damage and element removal techniques to accurately capture wire rupture and changes in the impactor-fence system interface. The results demonstrate that the response of the system is highly influenced by factors such as mesh type, opening size, wire diameter, and impactor size. Notably, the system utilizing an inclined mesh type exhibits a 35 % higher failure velocity, 50 % greater energy dissipation, and 21 % less maximum displacement compared to the square mesh system. The detailed results and discussions in this study provide valuable insights into the influence of individual parameters on the behavior of wildlife fence systems, aiding in the design of more efficient wildlife barrier systems with enhanced performance.

1. Introduction

The detrimental consequences of natural hazards on infrastructure, properties, and human lives have long been a major concern for engineers. One specific risk involves the potential for falling rocks, which can pose a threat to infrastructure such as roads and expressways, endangering the safety of passing trains, cars, and individuals. In recent years, significant efforts have been made to analyze and develop structural countermeasures to mitigate the destructive effects of rockfall hazards.

However, it is important to recognize that the risk to roads extends beyond falling rocks. The construction of large-scale infrastructure projects, such as expressways, within natural habitats has resulted in the fragmentation and destruction of ecosystems. This, in turn, disrupts the movement patterns of wildlife, forcing animals to cross roads and creating numerous dangers for humans. The social and economic costs of such encounters, combined with the increased risk of secondary traffic accidents caused by drivers swerving to avoid wildlife, are collectively referred to as “Roadkill” [1]. Furthermore, wildlife often causes extensive damage to agricultural areas, not only by consuming crops but also through destructive play. Additionally, wildlife can contribute to the spread of infectious diseases like African Swine Fever (ASF). Therefore, studying the relationship between human infrastructure and ecological changes can provide valuable insights into human impacts on the environment and contribute to the improvement of global environmental policies [2] aimed at preventing terrestrial wildlife from accessing human infrastructure.

Apart from the ecological impacts on animal species, substantial attention has been devoted to studying these structures due to the significant effects they have on both human lives and finances resulting from wildlife collisions with infrastructure. To mitigate accidents involving wild animals on expressways, the installation of dynamic barriers and retention steel networks has gained popularity. These measures are favored due to their wide range of capacities and adaptability to diverse topographies. Innovative forms of fences aimed at reducing wildlife-vehicle collisions have been proposed in several regions including North America and Europe [3,4].

Animal barriers, similar to falling rock protection barriers depicted in Fig. 1(a), (b), and (c), are metallic structures designed as passive measures to prevent wild animals from passing through. These barriers typically consist of wire nets, structural steel posts, and specialized connecting components that effectively impede and block animal movement. When studying wildlife fences, three distinct perspectives can be explored.

• I)Animals create passages by digging the ground and pushing the fence upwards. This phenomenon can be considered a “passing” problem and may be addressed in future studies.
• II)Animals attempting to jump over the fence using slopes to cross it. Consequently, the effectiveness of the fencing system is compromised in areas with rugged terrain, as it provides more opportunities for animals to either “underpass” or “overpass” the barrier.
• III)Animals rushing towards the fence and colliding with it, resulting in an impact effect. This impact effect has been thoroughly investigated and documented in this paper.

Fig. 1.

Actual examples of wildlife fences showing animal crossing [23].

Furthermore, when an animal collides with the fence, there is a potential risk of the animal getting trapped in the wires. In such cases, the animal may attempt to escape, leading to dynamic interactions such as twisting, swaying, tearing, and other movements. It is important to note that these dynamic interactions typically started after the impact, as the duration of the impact itself is relatively short.

The impact problem extends beyond the specific case of grid structural systems affected by rockfall and animals. It encompasses a broad range of scenarios, including heavy objects falling on beam and plate structures [5,6] and the impact of storms on marine structures, such as tidal current turbines [[7], [8], [9], [10]]. It is important to note that each case involves distinct properties of impactors and target structures, necessitating comprehensive studies tailored to the specific circumstances of each scenario.

These barriers are designed to withstand impacts from large and fast-moving objects, such as animals or blocks, with velocities exceeding 13 m/s. These types of barriers are designed to dissipate the energy of high-impact loads by facilitating significant plastic deformation within the system, particularly within the wire net component. In the study conducted by Ref. [1], wildlife fences were categorized into rhombic, square, and barbed-wire types. Fence systems offer advantages such as rapid installation and easy maintenance. However, it is crucial to continuously monitor these systems to ensure their proper and long-term functionality, as highlighted by Ref. [11].

Fence systems have been developed recently in many countries, including China, Australia, Spain, Japan, Italy, Switzerland, France, and the United States. China, with its extensive mountainous terrain covering more than two-thirds of the land area, has a long history of dealing with mountain hazards, including frequent rockfalls. The 2008 Wenchuan earthquake further emphasized the need to address these hazards. In recent years, the rapid development of transportation infrastructure has highlighted the significance of protecting highways and railroads in mountainous areas from rockfalls. Yu et al. [12] examined the performance of 20,000 m² flexible rockfall barriers installed along a mountain road in western China. They identified five failure modes, analyzed the underlying failure mechanisms, and proposed design strategies. To enhance the system, an improved barrier system was developed and validated through a full-scale impact test with 5000 kJ of energy. Additionally, the dynamic behavior of the barrier was investigated through numerical simulations. Xu et al. [13] introduced a practical design methodology for rapidly determining the specification, size, and quantity of components needed for a flexible rockfall protection barrier structure. This approach relied on dependable numerical modeling, validated through a series of experimental tests encompassing both component-level and full-scale impact tests. The effectiveness of the proposed design procedure was evaluated by applying it to a barrier structure with a nominal energy level of 3500 kJ. A subsequent full-scale impact test demonstrated the reliability and efficiency of the design approach.

In Europe, the protection of structures in mountainous areas against rockfalls has necessitated the development and construction of various types of barrier devices. These efforts have resulted in practical design and construction solutions, along with guidelines for the approval of rockfall protection kits [[14], [15], [16]]. In Japan, numerous scholars have conducted impact tests to determine the ultimate capacity of protection fence systems [[17], [18], [19], [20]]. Recently, the Japan Road Association [21] published a revised version of the handbook on rockfall measures, which embraces the concept of performance-based design [22]. These developments signify a shift towards considering the performance and effectiveness of rockfall protection measures in design practices.

Several experimental tests have been conducted to ascertain the failure mechanism of impact load on protection barrier systems [[24], [25], [26], [27], [28]]. Buzzi et al. [29] conducted experimental testing of rockfall barriers designed for the low range of impact energy which is a particular case in New South Wales, Australia, because of the nature of the geological environments. They focused on the influence of the system's stiffness on the transmission of load to components of the barrier such as posts and cables.

However, physical testing is not always an efficient and preferred method due to the high cost and time-consuming processes. The repetitions at various block sizes and the necessary iterations to determine the block speed inducing failure at a particular block size cause to apply a more efficient approach requiring fewer tests or lower experimental costs [30]. Prina Howald and Abbruzzese [31] introduced a methodological framework for the preliminary evaluation of the performance of rockfall protection systems to determine their performance and understand how their effectiveness impacts hazard zoning in areas impacted by rock falls.

Developing designs based on the use of various computer programs plays a crucial role in studying and designing the structure of protection fences. The overall response and dynamic characteristics of the protection fences can be satisfactorily reproduced in numerical simulations. Moreover, consistent information on the actual behavior and the value of the safety factors can be achieved by employing numerical models. These simulations can be performed by various finite element software based on the requirements [32]. The models also can be used to run preliminary parametric studies on different parameters such as block size, speed, and position within a realistic range [33]. A variation of the block dimension and its effect on the response of the semi-rigid type of protection fence was investigated by Mentani et al. [34,35]. Douthe et al. [36] investigated the behavior of protection barriers against the fall of boulders and rocks using a non-linear spring-mass equivalence model for dynamically simulating the barrier deformation under impact. The research explores the variability due to block-related parameters and net-related parameters, highlighting the role of the cables’ geometric stiffness in the global response of the fence.

ABAQUS, a highly developed software, is used to model a specific dynamic event of a net barrier against rockfall [30,37,38]. Al-Budairi et al. [39] developed a three-dimensional finite element model in Abaqus/Explicit to analyze double-twisted wire mesh. The model's accuracy was verified through both quasi-static loading and impact tests. The findings emphasized the significance of precise geometric representation for accurately simulating wire deformation modes and the interaction between double-twisted wires. Additionally, the model allows for the incorporation of the actual stress-strain relationship of an individual steel wire in constitutive models.

FARO software is also used to simulate the impact of falling rock as a rigid body with a special contact algorithm for the interaction with the barrier. In this model, the connection between net elements and rope elements can be addressed effectively [40]. LS-DYNA is one of the most common programs used to analyze the dynamic behavior of protective barrier structures which is able to simulate the characteristic values of collision, such as the impact force, displacement, and kinetic energy [17,[41], [42], [43], [44]].

While there are similarities between rockfall and wildlife fence systems, it is important to note that certain specific considerations need to be taken into account. One significant distinction lies in the design requirements for impactors with different shapes as well as mass and velocity ranges. In addition, wildlife fence systems are typically simpler in structure, with fewer appurtenances, resulting in less damping. As a result, energy dissipation through plastic deformation becomes the primary means of dissipating the impactor's energy. Because of these differences, the results of studies related to rockfall barrier systems cannot be directly utilized for design of wildlife animal systems.

Despite these crucial differences, there are only a limited number of studies focusing on the behavior of these systems with structural properties proper for impact load imposed by animals. The objective of this study is to bridge this gap by considering the structural characteristics of wildlife fence systems and exploring a range of expected impactor velocities and masses. In this study, the dynamic response of fence systems subjected to the impact of wildlife animals is investigated using numerical simulations. A three-dimensional numerical model based on the finite element method (FEM) is employed to accurately replicate the dynamic behavior of fences under highly nonlinear conditions. The ABAQUS software [45] is utilized for the simulations. An extensive parametric study is conducted to examine the influence of various parameters on the performance and capacity of the system. The study focuses on elucidating the role of these influential parameters through numerical analysis.

The subsequent sections of the paper provide a comprehensive explanation of the examined system's characteristics, including its geometry, mechanical properties, and boundary conditions. The procedure and assumptions employed to develop the finite element model are also outlined in detail. Finally, the results of the parametric study are presented and thoroughly discussed, shedding light on the findings obtained from the analyses.

2. Research significance

Three-dimensional (3D) numerical simulations have been performed by means of a finite element code involving the dynamic event of a running animal against a wire net barrier. To the best of the authors’ knowledge, such analysis has not been sufficiently researched for the wildlife barrier systems. Most research and data are available on the effect of the impact energy of blocks on protection fences whose goal is to stop the boulder propagation after the cliff collapse. Despite similarities between all barrier systems, wildlife fence systems have fewer components than rock fall systems, and the energy dissipation mechanism mainly relies on plastic deformation. In addition, the range of size, mass, and velocity of impactors are different. This research can open a new perspective for researchers by testing the performance of a new, multipurpose fence to prevent terrestrial wildlife from accessing the human infrastructure. Moreover, developing designs based on the use of a powerful computer program plays a pivotal role in studying and designing these structures under dynamic events. ABAQUS software was used to make a detailed 3D finite element model with the inclusion of all nonlinearity sources, which contributes to the impact loading problem. Its suitability and ability for design or redesign purposes are shown by performing a large number of parametric analyses on the effects of impact load, such as size, shape, velocity, and the impact point of the impactor. Results and discussions of the comprehensive parametric study presented in this paper elucidate the effects of each design parameter on the behavior of the system and also can be used prior to or supplement real-scale impact tests.

3. Numerical modeling assumptions

The objective of this study is to investigate the impact of influential parameters on the behavior of fence structures, particularly focusing on determining the critical state formed by the combination of mass and velocity. To achieve accurate predictions regarding barrier behavior, a combination of experimental and numerical studies is necessary. Comprehensive experimental tests are typically required to explore the effect of impactor size on fence behavior during an impact event. However, conducting physical experiments can be time-consuming due to the need for multiple repetitions involving various block sizes and speeds to determine the specific size that leads to failure. To address this challenge and improve efficiency, it is essential to employ a more efficient method that reduces the number of tests or computational costs [30]. In addition to impactor size, other parameters, including animal velocity and mass, impact location, and wire mesh size and diameter, also influence the results. Conducting a comprehensive parametric study using numerical simulations can significantly reduce the initial costs associated with physical experiments and facilitate the optimization process. In this study, extensive series of numerical simulations have been conducted to thoroughly characterize the performance of a fence system under the influence of various parameters.

Modeling the response of barrier systems under impact load is a complex task. The response of the impacted structure rapidly changes in a short duration. Therefore, an intended numerical model used for analysis should be simple and flexible, while it can run the analysis quickly and provide reliable numerical evaluation results regarding the upon remarks [32]. The solution for the simulation of the barrier systems implies the simultaneous study of three nonlinearity sources: (1) material nonlinearity (inelastic behavior), (2) geometry (large deformation), and (3) boundary conditions (contact surfaces). A computer program to meet these requirements and solve the problem is needed. For this purpose, the commercially available computer program ABAQUS [45] has been employed. This program is suitable for dynamics applications (e.g., crash tests, impacts, explosions, etc.) and can solve all sources of nonlinearities [38]. In this study, a three-dimensional model has been developed to simulate the dynamic response of wildlife fence systems through dynamic/implicit analysis. The assumptions and details of numerical implementation for the fence structure and animals are explained in the following sections.

3.1. Modeling of the wildlife fence system

In general, a barrier system consists of several key components, including a flexible wire mesh (interception structure), rigid steel posts, anchors, and various connecting components, with or without energy-dissipating devices. The frame structure is primarily composed of steel posts, such as beams and columns, which provide support and maintain the integrity of the net. One key aspect is the height of fence structures. Different species of wildlife exhibit varying levels of jumping or climbing abilities. Therefore, the height of fences should be tailored to the specific target species, ensuring it serves as an effective deterrent. For instance, deer and elk may require higher fences to prevent them from leaping over, while smaller animals like rabbits may necessitate different barrier designs. The connecting components encompass various elements such as energy-dissipating devices (in certain cases), clamps, studs, and other joining devices that facilitate the integration of different parts of the barrier system. The interception structure is typically comprised of a metallic net that directly withstands and absorbs the impact forces. There are various technologies and patterns utilized for wire nets, including simple wire nets, double-twisted wire nets, cable nets, chain-link nets, and ring nets [46]. These different types of wire nets offer specific characteristics and performance capabilities, providing flexibility in designing barrier systems based on the specific requirements of the application.

When selecting an appropriate net for a barrier system, it is crucial to determine the maximum pressure that the system will be exposed to over its lifetime. Several methods can be employed to calculate this pressure, including classical methods of global stability, methods of extreme equilibrium, and finite element methods. Additionally, the yield strength obtained from laboratory tests is often assumed as the maximum value that the system can bear, without considering a safety factor [47]. According to the aforementioned descriptions, the initial model developed in this study was made of continuous steel frames with three spans on the horizontal axis and two different openings on the vertical axis. The structure used in the modeling is depicted in Fig. 2. The model is considered the representative barrier system used in practice to prevent terrestrial wildlife such as wild boar, deer, and wild bears from accessing human infrastructures (roads, agricultural lands, livestock farms, etc.).

Fig. 2.

Geometrical details of the system components.

In the developed model, the columns (or pillars) have a height of 1.88 m and are installed at a distance of 2.05 m from each other. These columns are connected with horizontal beams. The cross-sections of both the columns and beams are box profiles, the dimensions of which are specified in Fig. 2.

For the fence structure, two types of mesh are considered: a square mesh and an inclined mesh. The diameter of the wires used in both mesh configurations is variable, ranging from 2.5 mm to 5 mm. Additionally, the size of the mesh openings, or mesh size, is investigated within the range of 5 cm–15 cm. By exploring these variations in wire diameter and mesh size, the study aims to assess their influence on the behavior and performance of the barrier system under dynamic conditions.

In common practice, the connection between beams and columns is typically achieved through the use of bolts, welding, or a combination of both methods to ensure enhanced safety. Similarly, the wires are connected to the beams and columns either by welding, anchoring, or a combination of these techniques. The wires themselves can be interconnected using local ties, such as double-twisting, or through welding. For the purpose of this study, a detailed comparison of different connection types is not within its scope. Instead, it is assumed that all connections, including the beam-to-column, wire-to-beam and column, and wire-to-wire connections, are appropriately made. Furthermore, it is assumed that the connections possess greater strength than the connected components, such as the beam, column, and wire. As a result, the connections between these components are treated as rigid connections. To represent this assumption, the entire model is made as a single part, where the intersection nodes and corresponding degrees of freedom between the components are automatically shared. This approach simplifies the modeling process and allows for the assumption of rigid connections between components within the simulation.

All components of the system are made by wire geometry and discretized with B33 element, which is Euler-Bernoulli beam element with two nodes and cubic interpolation function. Due to the small cross-section of the wires used in the mesh, its flexural strength is negligible. However, the choice of beam element with rotational degrees of freedom for the wire net results in a more accurate emulation of the actual behavior and deformed shape under impact load.

In the simulation, boundary conditions are deemed influential in response and should be carefully considered to be consistent with the actual condition of the structure. The base support (below each pillar) and connection of the right and left sides of the frame were the two main boundary conditions. For the 3D model, active degrees of freedom (DOF) were translational (u_x, u_y, u_z) and rotational (ur_x, ur_y, ur_z). Based on the connection details between frames (continuous frames), the nodes located at the intersection of beams and the column on the right and left sides of the frame were restricted in the longitudinal direction (u_x) to represent the stiffness of spans implicitly continued toward the left and right of the model. It means that the frame (barrier system) can freely move toward the z-direction under the impact load. Rotational DOFs also partially restrained in reality due to flexural and torsional stiffness of connected beams, however, they were not restrained in the model to be conservative. Considering the rigidity of the base support, all translational and rotational DOFs of the bottom node of all columns, which are sunk into the ground, were restained.

The material used for the interception structure was mild steel (SRT355, KS D 3568) for the box profile (beams and columns) and Zinc-coated low-carbon steel (SWMGS-4) for the wire mesh. The detail of the material properties of the steel used for both the wire net and frame is shown in Table 1.

Table 1.

Material properties of wildlife fence components.

Material (steel)	Density ρ (Kg/m3)	Modulus of elasticity E (GPa)	Poisson's ratio υ	Yield stress σy (MPa)
Wire	7850	200	0.3	1200
Beam/column	7850	200	0.3	355

Elastic-perfectly plastic behavior was assumed for the steel material of the wire mesh and box profiles. However, rupture may happen in the wire when the plastic strain at failure (ε^f_pt) is reached. Therefore, it is crucial to use appropriate techniques for modeling possible ruptures in the wires. For this reason, ductile damage model in the software with a linear damage evolution function was also adopted to express the rupture in the model. This ductile damage model takes into account the undamaged material behavior (introduced as elastic-perfectly plastic form), damage initiation criteria, and damage evolution response. In this model, it is assumed that damage is characterized by stiffness degradation, and use degraded stiffness to calculate stress in the damaged part. Damage initiation criteria to predict the onset of damage (ε^f_p0) are defined by the ductile criterion which assumes that the equivalent plastic strain at the onset of damage is a function of stress triaxiality defined as η = -p/q, where p and q are pressure and Mises equivalent stress, respectively. For elements with essentially uniaxial stress such as beam elements, η is equal to 1/3. In case the criterion is met, the model uses damage evolution to calculate degraded stiffness by (1 - d)E, where E and d are modules of elasticity and damage parameters. Where d is equal to zero at the onset of fracture and equal to one at fracture strain. Damage evolution was introduced as a linear function based on the equivalent energy concept. The strain at the onset of fracture and fracture strain is set to be 5 % and 10 % for ductile damage in the simulations to capture fracture. These assumed values are defined based on the calibration against the experimental results of tests performed by Buzzi et al. [48] and the analysis conducted by Spadari et al. [30].

In order to model the rupture and its consequence on the system more realistic, the element deletion technique was utilized to allow the software to remove the fully damaged elements (i.e., d = 1) from the domain. This technique enables a more precise assessment of the reduced contact area, which is particularly crucial in cases where a high-energy impactor can tear through the wire net and penetrate it.

3.2. Modeling of the projectile (impactor)

Two primary approaches can be considered for simulating the impact load of a projectile on the wildlife fence system, irrespective of its shape and size.

The first approach involves explicitly incorporating the projectile into the numerical model, wherein the dynamic behavior of the system is directly assessed based on the interaction between the projectile and the fence system during the analysis. The projectile can be modeled as either deformable or rigid. The interaction between the projectile and the fence system can be defined based on two main factors: i) The nature of the normal behavior, determining whether there is separation of the projectile and wire net after the impact event or not, and ii) The type of tangential behavior during contact, which can be categorized as frictionless (free sliding), frictional, or fully rough (no sliding).

The second approach does not involve directly incorporating the projectile into the model, but rather its effects are implicitly accounted for. In this simplified modeling approach, the mass of the projectile is attached to a group of nodes in the model that represent the projected area of the assumed projectile. This approach shares similarities with the first approach but operates under the following assumptions: the projectile has zero stiffness, it cannot be separated from the system, and fully rough tangential behavior is considered.

In this study, the projectile or impactor was explicitly modeled using a 4-node 3-D rigid quadrilateral shell element (R3D4). As a result, there is no need to define the material of the impactor in the numerical simulations. The mass of the animal, acting as the impactor, as well as its speed, were assumed to be variable, ranging from 50 to 200 kg and 5–20 m/s, respectively. This variation allows for the consideration of uncertainty in the size and speed of the animal, providing a more comprehensive understanding of the structure's behavior. The front shape of the projectile was assumed to be a hemisphere, which serves as a representative model for an animal's head (Fig. 3).

Fig. 3.

Cross-section and 3D numerical model of the wildlife fence system showing the direction and position of the impact load.

The following assumptions were considered for the boundary condition of projectile and contact behavior. The projectile is restricted to move only in a straight path, with other translational and rotational degrees of freedom (DOFs) being restrained. The projectile has the potential to separate from the wire net after the impact event. Therefore, the behavior of the contact surface between the wire net and the impactor in the normal direction was defined using hard contact with the permission of the separation option. The tangential behavior of the contact surface was modeled using the penalty method with a friction coefficient (μ) of 0.4, which is the average value obtained in the literature [22,30,32,34,38]. The impactor was placed near the barrier structure in the simulations (to reduce the initial time) and given a prescribed initial velocity in the normal direction to the fence to reproduce the impact load.

Based on the Swiss design guidelines [15], multiple block dimensions must be analyzed for the approval of the safe and practical design of fence modules. In practice, a small block impacting at high speed may puncture a barrier despite having lower kinetic energy than the critical value obtained for a large block due to the “bullet effect”. The “bullet effect” has been studied by many researchers [38,40,48,49,50,51], which shows the effect of the impactor size on the behavior of barrier systems. Therefore, impactors with diameters of 25 cm, 50 cm, and 100 cm are examined in this study to consider the effect of impactor size on the response of the system.

The system's response to the impact load can vary significantly depending on the location of the impactor. Through preliminary evaluation, four critical impact locations were identified and considered as follows: fence-center (FC), column-center (CC), beam-center (BC), and column-beam intersection (CBI). These locations are depicted in Fig. 4. The corresponding models for each impact location are named FC, CC, BC, and CBI, respectively. For further reference, detailed information regarding the parameters associated with the projectile is provided in Table 2.

Fig. 4.

Different positions of the projectile on the FE model.

Table 2.

Parameters and range for projectile.

Parameters	Range	Units
Velocity	5–20	m/s
Vertical location (Δy)	0.75–1.5	m
Horizental location (Δx)	3.0375–4.05	m
Initial distance of the projectile (Δz)	25	cm
Diameter	25–100	cm
Mass	50–200	kg

4. Discussion of FEM results

The primary objective of this study was to assess the dynamic behavior of fence systems utilized for protecting infrastructures and to predict the overall and local responses of the barriers. The corresponding finite element (FE) model was analyzed to evaluate the performance and capacity of the fence system against impact loads caused by animals, while also examining the influence of each parameter on the system's behavior. The investigation focuses on various aspects of the system's behavior after experiencing the impact load, including elongation and dissipated energy. The simulation results are examined from two specific perspectives: when the impact is directed at the frame (column, beam, and the intersection of column and beam) and when the impact affects the wire mesh itself. Special attention is given to describing the dynamic behavior of the wire mesh throughout the analysis.

4.1. Impact on frame

Concerning various weights for the impactor, the dynamic behavior of the frame subjected to impact load at different velocities in terms of displacement-time curves is shown in Fig. 5 for CC, BC, and CBI models. All analysis was done for about 3 s.

Fig. 5.

The displacement-time curve of frame members under different impact loads.

Based on the provided figure, it can be observed that significant vibration is not evident in the displacement-time curve after approximately 0.15 s for all models. This period can be considered as the final elongation of the member under the impact load. The elongation value varies depending on the loading conditions and the specific modeling cases. Incremental changes in displacement are observed with a gradual increase in velocity and mass for all models. However, the magnitude of displacement change at different velocities differs based on the position of the impact load. This variation is attributed to the column's greater strength and stiffness compared to the beam, resulting in the BC model exhibiting weaker performance during loading due to its less robust profile.

Table 3 presents the key distinctions among the simulated FE models with varying masses and kinetic energies, focusing solely on the maximum displacements reached for comparative analysis. The highest displacement value observed is 0.61 m, which corresponds to the BC model with a mass of 200 kg and a velocity of 20 m/s. On the other hand, the lowest displacement value is associated with the CC model at a velocity of 5 m/s for a mass of 50 kg.

Table 3.

Maximum displacement (m) of the frame under different impact loads.

Weight (kg)	Velocity (m/s)	FE model
		CC	BC	BCI
50	V = 5 m/s	0.0280	0.0951	0.0779
	V = 10 m/s	0.0736	0.1667	0.1345
	V = 15 m/s	0.1282	0.2302	0.1851
	V = 20 m/s	0.1777	0.2934	0.2318
100	V = 5 m/s	0.0553	0.1459	0.1190
	V = 10 m/s	0.1416	0.2503	0.2065
	V = 15 m/s	0.2252	0.3424	0.2830
	V = 20 m/s	0.2939	0.4326	0.3593
150	V = 5 m/s	0.0795	0.1799	0.1479
	V = 10 m/s	0.1968	0.3085	0.2554
	V = 15 m/s	0.2949	0.4243	0.3539
	V = 20 m/s	0.1777	0.5310	0.4504
200	V = 5 m/s	0.1021	0.2081	0.1728
	V = 10 m/s	0.2409	0.3546	0.2995
	V = 15 m/s	0.3420	0.4852	0.4165
	V = 20 m/s	0.4083	0.6076	0.5199

As a matter of fact, the maximum displacement at the impact moment for model CC is about 14.5 times greater for kinetic energy E_k equal to 40 kJ (related to the larger mass and velocity) than the minimum kinetic energy equal to 0.625 kJ (related to the smaller mass and velocity). This value is obtained for the BC and CBI models at about 6.38 and 6.67, respectively. Furthermore, it is observed that the impact energy dissipates more rapidly in the CC model compared to the other two models, regardless of the masses involved. This behavior can be attributed to the greater capacity of the CC model, which benefits from a stronger profile.

Considering the average velocity of a wild boar to be approximately 15 m/s, weighing around 100 kg, these values are considered realistic impact load conditions for this study. Fig. 6 illustrates the deformed shape of the fence system when subjected to the impact load applied to the frame members. The maximum principal plastic strain for multiple section points can be observed for all models, which is 5.62 × 10⁻², 7.61 × 10⁻², and 3.67 × 10⁻², respectively, for CC, BC, and CBI models. Though maximum strain in CBI is the smallest among all cases, the damaged area is more extensive than in other cases. Overall, the level of damage observed in all cases is not significant, suggesting that the system demonstrates an acceptable performance when the impactor strikes the frame component.

Fig. 6.

The deformed shape of the frame under impact load at V = 15 m/s and W = 100 kg (maximum principal plastic strain).

4.2. Impact on wire net

In this section, the focus shifts to the results of the impact load on the wire mesh itself, which is notably weaker compared to the frame. The performance of the system was assessed by varying the velocities and masses of the impactors, while also considering the influence of mesh types (square or inclined mesh), mesh size (opening size), wire diameter, and impactor size.

4.2.1. Mesh type and opening size

The performance of the wire net with a square mesh type under impact load was assessed by considering impactors with varying masses and velocities. To quantify the effect of mesh size, opening sizes of 5 cm, 10 cm, and 15 cm were examined, which are representative dimensions commonly used in wildlife systems.

The deformed shape and maximum plastic strain of the system with square mesh at maximum elongation under impact load (mass of 100 kg and velocity of 15 m/s) are compared in Fig. 7. According to the results, the maximum plastic strain of the system with an opening size of 5 cm is about 5.3 % which is about 38 % and 50 % less than that of the system with an opening size of 10 and 15 cm, respectively. Additionally, as depicted in the figure, the impacted area of the system with a smaller opening size is significantly smaller compared to that of a system with a larger opening size. This observation emphasizes the significant influence of the opening size on the behavior and performance of the wire net under impact load. The findings highlight the importance of carefully considering the opening size when designing wildlife protection systems, as it directly impacts the affected area and the effectiveness of the system in preventing animal penetration.

Fig. 7.

The deformed shape of the square fence with different mesh sizes under impact load at V = 15 m/s and W = 100 kg (maximum principal plastic strain).

Fig. 8 displays the displacement-time curves of the fence system under different impact loads focused on the center of the fence (FC) using square mesh with various opening sizes. The results demonstrate that the maximum elongation of the system is strongly influenced by the kinetic energy of the impactor across all cases. When the kinetic energy of the impactor increases through larger mass and higher velocity, the maximum displacement of the system notably increases. This indicates that the impact energy directly affects the extent of deformation experienced by the fence system.

Fig. 8.

The displacement-time curve of impact load on different square mesh size.

Due to the impactor being positioned at a slight distance from the fence, there is a short period at the beginning of the displacement-time curves where no elongation is observed. The duration of this period is dependent on the velocity of the impactor. Once the impactor reaches the fence, the elongation of the system begins to increase until it reaches its peak value, at which point the kinetic energy of the impactor is fully dissipated, resulting in the impactor coming to a complete stop. Subsequently, the system pushes the impactor back as there is no rupture in the system, leading to a decrease in elongation. In cases where the system is subjected to an impactor with high kinetic energy, significant residual elongation is observed due to plastic deformation within the system. These results highlight the notable influence of mesh size on the system's performance under impact load. It is evident that both the peak and residual elongation of systems with smaller opening sizes are less pronounced compared to those with larger opening sizes.

Fig. 9 presents a comparison of the deformed shape and maximum plastic strain between the system with inclined mesh and the system with square mesh at their respective maximum elongations under impact load (using a mass of 100 kg and a velocity of 15 m/s). By comparing Fig. 7 (related to the square mesh) and Fig. 9, a distinct difference in the load transfer path becomes evident between the two systems. In the case of the system with a square mesh, the load is primarily transferred to the middle sections of the beams and columns. However, in the system with an inclined mesh, the load is predominantly transferred to the corner points of the frame, owing to the diagonal arrangement of the wires. This distinct load transfer mechanism leads to variations in the distribution of strain and deformations within the systems.

Fig. 9.

The deformed shape of the inclined fence with different mesh size under impact load at V = 15 m/s and W = 100 kg (maximum principal plastic strain).

According to the results, the maximum plastic strain of the system with an opening size of 5 cm is about 7.7 % which is about 3 % and 25 % less than that of a system with an opening size of 10 and 15 cm, respectively. In comparison to the maximum strain of the system with an opening size of 10 cm, the square mesh has about 30 % smaller than the inclined mesh. However, for the system with an opening size of 10 and 15 cm, the maximum strain of inclined mesh is smaller, which implies a better performance of inclined mesh for larger mesh size in terms of maximum strain.

A relatively similar pattern to Fig. 8 was observed for displacement-time curves of the system with inclined mesh. However, the peak and residual elongation of inclined mesh were notably less than square mesh. The results of comparing different mesh sizes and shapes on the maximum displacement of wire mesh under impact loading are shown in Fig. 10.

Fig. 10.

Comparison of maximum displacement for different mesh sizes and shapes.

Based on the obtained results, it is observed that the relationship between maximum displacement and velocity can be approximated by a linear function for both square mesh and inclined mesh configurations. However, the maximum displacement of the inclined mesh exhibits a substantially smaller slope with respect to velocity compared to the square mesh.

On average, the maximum displacement of the system with inclined mesh is approximately 21 % less than that of the system with square mesh across all opening sizes. This indicates that the performance of the system with inclined mesh, in terms of maximum displacement, is significantly better than that of the system with square mesh.

In the aforementioned parts, the performance of the system under impact load was evaluated for a range of expected velocity and mass of the impactors. It is of particular interest to find the ultimate capacity of the system which is necessary for the appropriate design of an engineered system with consideration of safety margin against the expected load. Fig. 11 presents the deformed shape of the system with both square mesh and inclined mesh when subjected to an impactor with a mass of 200 kg and a velocity of 20 m/s. It can be observed that in the system with square mesh, some wires in the impact area were ruptured. However, the extent of the failure area was not extensive, and the impactor was unable to pass through the fence. In contrast, no ruptures were observed in the system with inclined mesh, indicating that it possesses a greater capacity compared to the square mesh configuration.

Fig. 11.

The deformed shape at the limit state of impact load with opening size = 10 cm, V = 20 m/s, and W = 200 kg (maximum principal plastic strain).

From a conservative perspective and considering the uncertainty in structural properties, the ultimate capacity of the system can be defined as the limit state at which the first wire rupture occurs in the net. To determine this limit state, a comprehensive set of analyses has been conducted for each combination of impactor mass, mesh type, and opening size. For each case, the velocity of the impactor was incrementally increased with an increment of 1 m/s to find the failure.

Failure velocity of square and inclined mesh with respect to the mass of impactor and mesh size are presented in Fig. 12. The results reveal that failure velocity is substantially smaller for larger masses. The capacity of the system reduces by increasing mesh size, and the amount of reduction for square and inclined mesh are comparable. Based on the results, the capacity of the system with mesh sizes of 10 and 15 cm is about 63 % and 46 % of the capacity of the system with the mesh size of 5 cm.

Fig. 12.

The comparison of velocity at the first failure for different fence shape and size under different impact mass.

According to the results, the failure velocity of inclined mesh with different opening sizes is, on average, 35 % larger than square mesh, which implies the capacity of inclined mesh is remarkably larger than square mesh. The energy dissipation through viscous damping and frictional damping at contact surfaces was negligible in comparison with other components for all models. In Fig. 13, a comparison of the components of internal energy between square mesh and inclined mesh is presented for a representative case. The results indicate that the dissipation of energy through plastic deformation at failure velocity is approximately 50 % greater in the inclined mesh compared to the square mesh. This observation highlights that the inclined mesh configuration possesses a significantly higher energy dissipation capacity. As a result, the inclined mesh can be considered a more effective system in terms of its ability to absorb and dissipate energy under impact load.

Fig. 13.

Energy versus velocity for W = 100 kg and opening size = 10 cm.

4.2.1.1. Wire diameter

In the previous sections, a wire diameter of 2.5 mm was assumed for all cases. However, it is important to note that wire diameter has a significant impact on the stiffness and strength of the system. In systems with smaller wire diameters, the flexural stiffness is negligible, and the out-of-plane stiffness primarily relies on axial stiffness. Consequently, the undeformed shape of the net has zero out-of-plane stiffness, and the system needs to deform to activate its stiffness. On the other hand, in systems with larger wire diameters, the flexural stiffness becomes significant, and the system exhibits considerable out-of-plane stiffness even in its undeformed state. As a result, the response mechanism differs substantially between systems with different wire diameters. Additionally, in practical applications, wire diameters larger than 5 mm are rarely used in wildlife fence systems. Thus, to investigate the effect of wire diameter on system capacity, the analysis focused on two wire diameter cases: 2.5 mm and 5 mm.

Fig. 14 compares the maximum displacement of the fence for both square and inclined mesh configurations with varying wire diameters. The results demonstrate that increasing the wire diameter significantly reduces the maximum displacement for both square and inclined mesh. Furthermore, the reduction in displacement is more pronounced at higher impactor velocities, particularly for the inclined mesh configuration. This suggests that increasing the wire diameter can enhance the system's resistance to deformation and reduce the maximum displacement, leading to improved performance and capacity under impact load conditions.

Fig. 14.

Maximum displacement of the fence with different wire diameters for W = 100 kg.

Table 4 presents the maximum and residual elongation values of the system, providing a comprehensive evaluation of the effect of wire diameter for different mesh sizes and shapes. The results highlight the impact of wire diameter on the maximum displacement of the system.

Table 4.

Maximum and residual displacements of fence at V = 15 m/s and W = 100 kg.

Mesh size (cm)	Wire diameter (mm)	Residual displacement (m)		Max. displacement (m)
		Square mesh	Inclined mesh	Square mesh	Inclined mesh
5	2.5	0.3054	0.2156	0.4018	0.2959
	5	0.1783	0.1163	0.3068	0.1976
10	2.5	0.3535	0.2825	0.4421	0.3588
	5	0.2841	0.1616	0.3691	0.2374
15	2.5	0.3875	0.3229	0.4670	0.4033
	5	0.3186	0.1800	0.3936	0.2635

Specifically, for the square mesh configuration with a size of 5 cm, the maximum displacement of a system with a 5 mm wire diameter is approximately 24 % smaller than that of a system with a 2.5 mm wire diameter. It is important to note that the reduction effect becomes less significant as the mesh size increases. For instance, for a mesh size of 10 cm, the reduction in maximum displacement between the two wire diameter cases is approximately 17 %, and for a mesh size of 15 cm, the reduction is approximately 16 %.

A relatively similar pattern can be observed for residual displacement, where the amount of reduction is 42 %, 20 %, and 18 % for mesh sizes of 5 cm, 10 cm, and 15 cm, respectively. In regard to the effect of diameter, the results disclose two promising points for inclined mesh. First, the reduction percentages in all cases for inclined mesh are quite larger than square mesh. Second, the reduction effect for inclined mesh seems to be almost independent of mesh size in comparison with the square mesh. This issue is particularly more important where the mesh size is not uniform. According to these observations, wire diameter size is a very influential parameter on the maximum and residual response, and it is more effective for a system with an inclined mesh.

4.2.2. Impactor size

The kinetic energy of the impactor is transferred to the system through the contact interface with the fence. Therefore, the smaller the impactor size is, the higher energy is transferred to a single element, and the overall response should be more significant. In a limit case, a very small impactor with low kinetic energy can tear the fence due to the concentration of energy at smaller contact surfaces, which is known as the bullet effect. It is also trivial that frictional dissipation is reduced by decreasing impactor size and results in enlarging the response. On the other hand, normal stress at the contact surface is increased by reducing impact size, which raises frictional dissipation. Therefore, the response is affected by a combination of energy concentration and changes in frictional dissipation. These effects could be easily observed in Fig. 15, where the maximum deformation of the system with the same properties but different impactor sizes are compared.

Fig. 15.

Comparison of animal size at V = 15 m/s and W = 100 kg (maximum principal plastic strain).

To show how strongly the impactor size influences the maximum capacity, fence properties were assumed to be constant, and velocity increased incrementally to reach the first rupture in the wire net for each impactor size. The displacement-time curves of failed models are shown in Fig. 16. It can be seen that increasing impactor size exceedingly raises the failure velocity. According to the results, the velocity at failure becomes about 1.8 times larger by doubling the diameter of the impactor for both mesh types of square and inclined. This issue emphasizes that the size of the impactor should be carefully selected for actual design to be a realistic representation of the target impactor and avoid extreme over or under-estimations.

Fig. 16.

Maximum displacement for W = 100 kg with different sizes of impactor at the velocity of the first failure.

5. Conclusion

In this paper, the performance of the fence system subjected to animal impact load was evaluated by FEM simulation. A comprehensive parametric study has been done to assess the capacity of the system and the effect of influential parameters, including mesh type, opening size, wire diameter, and impactor size for the expected range of velocity and mass of the impactor.

The results highlight that the performance of the system is substantially better for smaller opening sizes. It was found that the maximum plastic strain of the system with square mesh and an opening size of 5 cm is about 5.3 % which is about 38 % and 50 % less than that of the system with an opening size of 10 and 15 cm, respectively, Moreover, the capacity of the system of systems with mesh sizes of 10 cm and 15 cm is about 63 % and 46 % of system with the mesh size of 5 cm.

The capacity of the system with inclined mesh is noticeably larger than that of square mesh for all examined opening sizes due to a more efficient dissipation energy mechanism. It was shown that the maximum displacement of systems with inclined mesh is 21 % on average less than square mesh. Also, the failure velocity and energy dissipation of systems with inclined mesh are about 65 % and 50 % larger than square mesh. This implies that for a specified opening size, the inclined mesh can be a better option to be used.

The effect of increasing wire diameter for both square and inclined mesh was considerable. It was found that the effect of increasing the wire diameter for impactors with larger kinetic energy is even more significant, especially for inclined mesh. For square mesh, the maximum and residual displacement of the system with a mesh size of 5 cm and 5 mm wire diameter, is about 24 % and 42 %, respectively, less than the system with 2.5 mm wire diameter. By the way, the amount of reduction for the larger panel size was found to be smaller. In the case of inclined mesh, the results show that the reduction is larger than square mesh and also the reduction has a weaker dependency on mesh size.

The size of the impactor was found to be very influential on the behavior and capacity of the system. It was found that by doubling the diameter of the impactor for both mesh types, the velocity at failure becomes about 1.8 times larger. Therefore, it is crucial to rationally consider the impactor's size to be a realistic representation of animal size for a proper design.

The results of the comprehensive parametric study presented in this paper can significantly assist engineers in understanding the behavior of wildlife fence systems subject to impact load imposed by animals. With in-depth analyses of crucial factors like strain, displacements, and capacity across diverse scenarios, these findings in combination with regional statistical data and cost-benefit models empower engineers to design the system with higher performance.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.