Towards Sustainable Rockfall Protection: An Interaction Matrix Method for Assessing Flexible Barrier Siting Adaptability

Abstract

Earthquake-triggered rockfalls pose significant threats to human lives, critical infrastructure, and the natural environment, highlighting an urgent need for sustainable and effective mitigation strategies. Flexible barriers are effective against rockfall, but there is a lack of universal procedures for selecting appropriate sites. As a result, flexible barriers are often misused, and their protective effect significantly decreases. To address this, a method for quantitatively characterizing the “flexible barrier siting adaptability” is proposed. The concept of “flexible barrier siting adaptability” is used to assess the suitability of a selected site for flexible barrier installation. The assessment method consists of three parts: the evaluation index system, the evaluation index value standards, and the calculation method. The evaluation index system is based on the interaction matrix considering not only the factors influencing the flexible barrier siting adaptability but also the interactions between them. The interaction matrix is determined by the expert semi-quantitative method, which can quantitatively assess the flexible barrier siting adaptability. Furthermore, the proposed method is applied to a typical rockfall area in Jiuzhaigou county, Sichuan province, China. This method provides a resource-efficient and practical tool for preliminary site assessment, contributing to the development of sustainable infrastructure and enhancing community resilience in rockfall-prone regions.

1. Introduction

Rockfall and rockslides can cause severe impact damage to infrastructure or even casualties all over the world, so it is urgent and necessary to prevent and control them [1,2,3,4]. The increasing frequency and intensity of extreme weather events—such as intense precipitation, freeze–thaw cycles, typhoons, and earthquakes—driven by climate change, are projected to significantly exacerbate slope instability and rockfall activity in many regions globally. These processes mechanically weather rock masses through hydrostatic pressure, ice crystallization, and strong wind-driven vibrations, while chemical weathering from acid rain further degrades rock integrity. This evolving risk profile underscores the growing urgency for developing sustainable and adaptive mitigation strategies that can withstand this wider range of environmental stressors under evolving climate conditions.

To address these growing challenges, flexible barriers have been widely used in rockslide protection and control [5,6,7,8,9,10,11,12,13,14] due to their design flexibility, significant range of manageable energy (from 100 kJ to 10,000 kJ) [15], and cost-effectiveness [16,17,18], as shown in Figure 1. These barriers typically consist of four components: steel nets, energy dissipating devices, steel posts, and supporting cables [19,20,21]. By undergoing large deformations, flexible barriers dissipate the impact energy of rockslides, thereby intercepting falling rocks. Compared to traditional rigid protective structures, flexible barriers have been observed to exhibit enhanced performance in earthquake-prone areas [22,23]. First, their inherent flexibility enables significant energy absorption through large deformations, effectively mitigating the brittle failure risks associated with seismic inertial forces in rigid structures. Second, the integrated flexible connections between components facilitate coordinated structural behavior during seismic excitation, maintaining system integrity under ground motions.

In practical applications, however, flexible barriers are frequently damaged even when the impact energy is below the design protection energy [24,25,26]. This compromises their intended protective function. The primary cause of this phenomenon is the disparity between the idealized test conditions and the variety of actual engineering conditions, such as rock characteristics or installation location. This disparity results in decreased reliability of mitigation measures in practice. Therefore, to fully utilize the protective capabilities of flexible barriers, it is crucial to understand how these factors influence barrier performance [27]. The effectiveness of flexible barriers depends on multiple factors, including dynamic response to rockfall characteristics [28,29,30,31,32,33], slope characteristics [34], weathering and corrosion [35,36], and vegetation coverage [37]. Extensive studies have been conducted on factors influencing flexible barrier performance [38,39,40,41,42]. For instance, Guo et al. [28] investigated the damage to flexible barriers through impact tests, considering various rock shapes, sizes, and net specifications. Berger et al. [22] conducted small-scale laboratory experiments on different protective structures and investigated the relationship between barrier flexibility and total impact load.

However, there is currently no universal procedure for designing and siting flexible barriers [43]. This lack of standardization makes it difficult to consistently achieve sustainable outcomes. Beyond immediate safety concerns, the principle of sustainability is becoming paramount in geohazard mitigation engineering [44,45,46,47,48]. This pursuit of sustainability is also driving innovation in adjacent fields, such as resource utilization in steel production [49] and safety monitoring in smart buildings [50]. Traditional engineering decisions often rely on complex simulations or extensive testing, which can be resource-intensive and time-consuming, potentially leading to delays and increased carbon emissions. Furthermore, inappropriate siting of protective structures can result in ecological disruption, visual intrusion, and unnecessary waste of materials due to premature failure or over-design. Therefore, there is a growing call for simple, robust, and low-impact decision-support tools that align with sustainability goals. Existing qualitative guidelines rely heavily on subjective judgments, resulting in significant variability in site assessments. For instance, the European Technical Approval Guideline (ETAG) [51]—which was replaced by EAD 340059-0106 in 2018—provides design recommendations for energy levels and structural dimensions [52], but its complexity hinders practical application.

Table 1. Design suggestions for the flexible barrier in ETAG.

Protection Level	Height Requirement	Setback Distance
${\gamma }_E{E}_d\le E_r$ Ed: design energy level; Er: protection energy level; ${\gamma }_E$: safety factor.	$h_i\ge h_p+f$ hi: design intercept height; hp: rockfall height (95% reliability) from analyzing the rockfall trajectory; f: 0.5 times average rockfall size.	$d_p\ge {\gamma }_E{d}_a$ da: maximum flexible barrier elongation; dp: distance to protected area; ${\gamma }_E$: safety factor.

illustrates ETAG design suggestions for flexible barriers. The specific criteria and calculation methods proposed in ETAG are scientific and comprehensive but complex in practice. Currently, the selection of flexible barrier sites often relies on general design principles, restrictions, and experience. These guidelines are primarily qualitative, offering only directional guidance on relevant considerations during design. Moreover, being empirical, judgments regarding the same site conditions can vary significantly among practitioners. Inappropriate siting configurations can significantly compromise protective effectiveness. In conclusion, the lack of a practical and unified approach not only compromises protective efficacy but also leads to potentially unsustainable outcomes, including wasted resources, environmental damage, and reduced community resilience. This study aims to fill this gap by proposing a quantitative assessment method that explicitly incorporates sustainability considerations through a systematic evaluation of key interacting factors.

To address these limitations, this study introduces the concept of “siting adaptability,” defined as an index to evaluate the suitability of a site for flexible barrier installation. A higher siting adaptability indicates greater engineering rationality. This paper establishes a scientific and reliable assessment system for siting adaptability, guiding the design and site selection of flexible barriers. The rest of this paper is organized as follows. Section 2 describes the details of the interaction matrix method. Section 3 presents the establishment of the flexible barrier siting adaptability assessment system. Section 4 verifies the reliability of the flexible barrier siting adaptability assessment system. Section 5 draws the conclusions of this study.

2. Materials and Methods

2.1. Overview

To ensure the accuracy and reliability of the assessment method, a corresponding evaluation index system is necessary. Therefore, a set of evaluation factors must first be defined for the flexible barrier siting adaptability assessment system. Secondly, the evaluation indicators are quantified using the expert semi-quantitative method. Based on this, the method for calculating siting adaptability is proposed. Finally, the flexible barrier siting adaptability assessment system is established.

As illustrated in Figure 2, the research process comprises four main parts: determining the indicators system (step 1), building the interactive relationship of the indicators system (steps 2–3), establishing the flexible barrier siting adaptability assessment method (steps 4–5), and verifying the assessment method (step 6). Specifically, the research steps are: (1) investigating the influence factors of the flexible barrier siting adaptability; (2) building the interaction matrix; (3) determining the interaction matrix; (4) determining the value of the indicators; (5) calculating the siting adaptability; (6) verifying the assessment method.

2.2. Details of the Interaction Matrix

The typical interaction matrix is shown in Figure 3a,b. The diagonal elements of the interaction matrix represent the main influencing factors of the flexible barrier siting adaptability $F_1, F_2\dots F_n$. The off-diagonal elements represent the interaction between two factors ($I_{ij}$). $I_{ij}$ represents the influence of factor $F_i$ on factor $F_j$.

The cause and effect values for each influencing factor are determined using the Expert semi-quantitative method. The Expert semi-quantitative method was proposed by Hudson [53,54,55]. This method assigns values of 0, 1, 2, 3, or 4 to the off-diagonal matrix elements, denoting no interaction, weak interaction, moderate interaction, strong interaction, and extremely strong interaction, respectively. Subsequently, this method has been widely applied for evaluating interaction matrices in various systems. The sum of all elements in a row represents the total influence exerted by that factor on the system, termed the “cause” $C_i$. $C_i$ is the sum of the off-diagonal elements in the $i^{th}$ row, calculated as:

$$C_i={\displaystyle \sum _{j=1}^{j=i}{I}_{ij}}(i=1,2,3,\dots \dots ,i)$$

(1)

The sum of all elements in a column represents the total influence received by that factor from the system, termed the “effect” $E_i$. $E_i$ is the sum of the off-diagonal elements in the $j^{th}$ column, which can be calculated as follows:

$$E_j={\displaystyle \sum _{i=1}^{i=j}{I}_{ij}}(j=1,2,3,\dots \dots ,j)$$

(2)

For a system with N factors, the maximum possible values for $C_i$ and $E_j$ are both $4(N-1)$, and $\sum _{i=1}^n{C}_i=\sum _{j=1}^n{E}_j$

Figure 3c shows the distribution of interaction matrix parameters. The position of $F(C,E)$ can be determined according to the values of C and $E$. As shown in Figure 3c, the parameter interaction strength PH represents the overall intensity of influence associated with a parameter and is measured by its distance from the origin along the line $C=E$:

$$PH=(C+E)/\sqrt{2}$$

(3)

Parameter controllability PD indicates the dominance of a parameter’s causal influence C over its effected response E, measured by its perpendicular distance to the line $C=E$:

$$PD=(C-E)/\sqrt{2}$$

(4)

Figure 3d provides a clearer visualization of factor interactions. The activity index k_i represents the relative contribution of each factor to the total system interaction:

$$k_i=(C_i+E_j)/{\displaystyle \sum _{i=1}^n{C}_i+E_j}=(C_i+E_j)/2{\displaystyle \sum _{i=1,j=1}^n{I}_{ij}}$$

(5)

A higher k_i indicates a more significant contribution to the overall system behavior.

3. Establishing the Flexible Barrier Siting Adaptability Assessment System

3.1. Selecting the Evaluation Indicators

The main factors influencing the protective effectiveness of flexible barriers are derived from literature reviews and field investigations. These parameters are categorized into four dimensions: rockfall characteristics (P1–P4), slope characteristics (P5–P8), environmental characteristics (P9–P10), and engineering characteristics (P11–P12). A total of 12 key parameters are considered: kinetic energy of falling rocks (P1), rockfall size (P2), dispersion characteristics of perilous rock masses (P3), rockfall event frequency (P4), slope roughness (P5), slope height (P6), slope gradient variation (affecting rockfall bounce height) (P7), vegetation coverage (P8), hydrological conditions (P9), seismic activity (P10), and construction conditions (P11), environmental and social sustainability (P12). The qualitative descriptions of these parameters are presented in

Table 2. Qualitative description of the main factors influencing the protective effectiveness of flexible barriers.

Element	ID	Descriptions
Kinetic energy of falling rocks	P1	When kinetic energy exceeds 10,000 kJ, flexible barriers are not suitable for use.
Rockfall size	P2	Oversized rockfalls with excessive kinetic energy cannot be effectively intercepted.
Dispersion of perilous rock masses	P3	Passive flexible barriers are preferred when rockfalls are numerous and dispersed.
Rockfall event frequency	P4	Evaluate the expected number of rockfall events per unit time
Slope roughness	P5	Smooth rock faces and loose deposits affect frictional energy dissipation.
Slope height	P6	Increased slope height results in greater kinetic energy, potentially exceeding barrier capacity.
Slope gradient variation (rockfall bounce height)	P7	Flexible barriers are unsuitable if rockfall bounce heights are excessive.
Vegetation coverage	P8	Vegetation dissipates kinetic energy. Tall trees can intercept falling rocks.
Hydrological conditions	P9	Acidic groundwater corrodes anchor bolts; surface runoff can undermine slope toe stability.
Seismic activity	P10	Flexible protection measures are preferred in high-seismic zones due to their ability to undergo large deformations and dissipate energy through ductile behavior, unlike rigid structures that are prone to brittle failure under seismic inertial forces. Their integrated connections allow for better coordination during ground motions, maintaining system integrity.
Construction conditions	P11	Flexible barriers are suitable for difficult-to-access sites (accessibility—transport/installation difficulty, and maintenance conditions—ease of inspection/component replacement).
Environmental and social sustainability	P12	Evaluate the environmental and social impacts of flexible barriers throughout their entire life cycle, encompassing aspects such as material recyclability, ecological disturbance caused by construction, visual landscape impact, and long-term maintenance requirements.

.

Furthermore, the practical design of a flexible barrier system relies on a comprehensive rockfall trajectory analysis. This analysis, typically conducted using simulation software (e.g., Rocfall V.4.0 [56]), is essential for determining two critical design parameters: (1) the kinetic energy and bounce height of falling rocks (directly linked to parameters P1 and P7), and (2) the total dispersion width of the rockfall trajectories. The required length of the flexible barrier must extend beyond the outermost predicted trajectories on both sides to ensure complete coverage of the hazard zone. The dispersion characteristic of perilous rock masses (P3) and slope gradient variation (P7) are the primary factors influencing this required spatial coverage. Thus, the proposed siting adaptability assessment system works in tandem with quantitative trajectory simulations to guide both the optimal placement and the necessary dimensions of the protection structure.

3.2. Building the Interaction Relationship of Evaluation Indicators

Building the Interaction Matrix

To evaluate the relationships between influencing factors, the 132 off-diagonal elements are assigned values of 0, 1, 2, 3, or 4 using the Expert semi-quantitative method, as shown in

Table 3. Interaction matrix values determined by Expert semi-quantitative method.

Iij	Ii1	Ii2	Ii3	Ii4	Ii5	Ii6	Ii7	Ii8	Ii9	Ii10	Ii,11	Ii,12	Ci	Ci + Ej	Ci − Ej	ki(%)	PH	PD
I1j	P1	-	-	-	3	-	-	-	-	-	2	2	7	23	−9	10.27	16.27	−6.36
I2j	4	P2	2	-	-	-	-	-	-	-	-	1	7	15	−1	6.70	10.61	−0.71
I3j	2	2	P3	2	-	-	-	-	-	-	1	2	9	22	−4	9.82	15.56	−2.83
I4j	-	-	-	P4	-	-	-	1	-	-	3	2	6	17	−5	7.59	12.02	−3.54
I5j	3	2	2	1	P5	-	1	3	-	-	1	-	13	21	5	9.38	14.85	3.54
I6j	4	-	3	1	1	P6	2	1	-	-	1	-	13	14	12	6.25	9.90	8.49
I7j	3	1	1	-	1	-	P7	2	-	-	-	-	8	14	2	6.25	9.90	1.41
I8j	-	2	2	-	2	-	3	P8	1	-	2	-	12	24	0	10.71	16.97	0.00
I9j	-	-	-	3	-	-	-	1	P9	-	1	2	7	12	2	5.36	8.49	1.41
I10j	-	1	3	4	1	1	-	-	-	P10	4	2	16	16	16	7.14	11.32	11.32
I11,j	-	-	-	-	-	-	-	1	1	-	P11	2	4	23	−15	10.27	16.27	−10.61
I12,j	-	-	-	-	-	-	-	3	3	-	4	P12	10	23	−3	10.27	16.27	−2.12
Ej	16	8	13	11	8	1	6	12	5	0	19	13

. The assignment of values (0–4) to the off-diagonal elements of the interaction matrix was conducted using the expert semi-quantitative method. This process, while inherently relying on expert judgment, was structured and iterative to ensure consistency and robustness. Firstly, the initial assignment was grounded in a comprehensive review of documented mechanisms found in the literature (as referenced throughout Section 1). For instance, the strong interaction (I₂₁ = 4) between rock size (P2) and kinetic energy (P1) is directly supported by the fundamental physical principle $E={\displaystyle \frac{1}{2}}\mathrm{m}{v}^2$. Subsequently, the authors, acting as the expert panel given their expertise in rock mechanics and geohazard mitigation, conducted an iterative review process. The proposed interactions and scores were critically examined for logical consistency. This involved:

(1)

Ensuring that if factor A strongly influences factor B, the reverse interaction (B on A) was evaluated independently and assigned a logically consistent value.

(2)

Checking that the assigned intensity aligned with the defined criteria (e.g., value of 4 was reserved only for direct, deterministic relationships).

(3)

Comparing the relative strengths of different interactions to maintain a consistent scale across the matrix.

Finally, the resulting matrix was validated indirectly through its successful application in the Jiuzhaigou case study (Section 4), where it produced a logical prioritization of sites that aligned with independent numerical simulations and field observations.

The classifications are defined as follows:

(1)

No Interaction (0 points)

76 factors exhibited no influence and were assigned 0 points.

(2)

Minor Interaction (1 point)

21 factors exhibited minor influence and were assigned 1 point: I_2,12 (larger rockfalls require more massive structural components and foundations, resulting in a slight reduction in sustainability), I_3,11 (dispersed rockfalls optimize passive flexible barriers, eliminating full-slope coverage needs), I₄₈ (high-frequency rockfall events can damage and reduce vegetation coverage), I₅₄ (rougher slopes may slightly inhibit rock mobility, potentially decreasing the frequency of rocks reaching the barrier.), I₅₇ (slope roughness slightly modifies rock trajectories), I₅₁₁ (rocky slope increases drilling resistance), I₆₄ (higher slopes contain a greater volume of perilous rock masses, slightly increasing event frequency), I₆₅ (high slopes experience weathering), I₆₈ (high slopes mildly inhibit vegetation growth), I_6,11 (height slightly increases construction difficulty, though flexible barriers remain optimal for steep terrain), I₇₂ (abrupt gradient changes elevate rock fragmentation), I₇₃ (gradient variations enhance dispersion through trajectory deviation), I₇₅ (rock impacts cause slope roughness), I₈₉ (vegetation roots reduce water infiltration), I₉₈ (runoff affects vegetation growth), I_9,11 (hydrology increases flexible barrier corrosion requirements), I₁₀₂ (earthquake increases rocks fragmentations), I₁₀₅ (earthquake cause surface fracturing), I₁₀₆ (earthquakes trigger localized landslides, marginally reducing slope height), I_11,8 (construction leads to the removal of vegetation, which can be bypassed by flexible barriers compared to rigid barriers), I_11,9 (construction induces short-term water turbidity increases).

(3)

Moderate Interaction (2 points)

19 factors exhibit moderate influence and were assigned 2 points: I_1,11 (higher kinetic energy rockfall demands deeper anchoring systems), I_1,12 (higher design kinetic energy significantly increases material use and complexity of energy-dissipating devices, reducing sustainability), I₂₃ (large rock motion enhances dispersion through progressive fragmentation), I₃₁ (high dispersion reduces per-impact kinetic energy through multiple collisions), I₃₂ (fragmentation processes reduce post-failure particle sizes), I₃₄ (highly dispersed rock masses often indicate larger source areas, correlating with higher failure event probability), I_3,12 (dispersed sources often require longer barriers or multiple structures, increasing material consumption and environmental impact.), I_4,12 (high event frequency compromises sustainability by increasing long-term maintenance, resource use, and environmental disturbance.), I₅₂ (slope roughness increases fragmentation by impact), I₅₃ (surface irregularities amplify trajectory unpredictability), I₆₇ (steep gradients intensify energy conversion at slope transitions), I₇₈ (high-gradient zones restrict vegetation coverage), I₈₂ (vegetation intercepts large rock blocks), I₈₃ (vegetation causes collision points to be random), I₈₅ (root systems stabilize slopes, reducing surface erosion), I_8,11 (dense vegetation complicates access and foundation work, though flexible barriers retain advantages over rigid barriers), I_9,12 (aggressive hydrological conditions challenge sustainability by accelerating corrosion and increasing maintenance frequency), I_10,12 (high seismic activity threatens sustainability by raising the risk of barrier damage or failure), I_11,12 (difficult construction conditions decrease sustainability by elevating energy consumption and environmental disturbance during installation).

(4)

Significant Interaction (3 points)

11 factors exhibit significant influence and were, assigned 3 points: I₁₅ (high-energy impacts significantly alter slope roughness through rock fracturing), I_4,11 (high event frequency greatly increases maintenance difficulty and frequency, affecting construction and maintenance assessments), I₅₁ (surface roughness substantially influences kinetic energy dissipation), I₅₈ (rocky slopes inhibit vegetation coverage, resulting in significantly lower coverage compared to soil slopes), I₆₃ (tall slopes significantly increase dispersion and collision probability), I₇₁ (abrupt gradient transitions elevate rockfall rebound heights, substantially amplifying impact energy), I₈₇ (dense vegetation cover reduces rockfall rebound heights through energy absorption), I₉₄ (intensive hydrological processes promote rock weathering and destabilization, substantially increasing rockfall frequency), I₁₀₃ (seismic activity enhances rockfall dispersion through fracturing), I_12,8 (sustainable design promotes vegetation preservation through minimal clearing.), I_12,9 (sustainability mandates require corrosion-resistant materials and designs in aggressive hydrological conditions to ensure long service life).

(5)

Strong Interaction (4 points)

5 factors exhibit strong influence, assigned 4 points: I₂₁ (rock size directly determines mass and kinetic energy parameters), I₆₁ (slope height directly governs potential-to-kinetic energy conversion efficiency), I₁₀₄ (Seismic activity is a primary and extreme trigger of rockfalls), I_10,11 (flexible barrier systems demonstrate superior performance in seismic environments due to their inherent adaptability), I_12,11 (sustainability objectives dominantly influence construction choices, strongly determining construction difficulty and environmental impact).

3.3. Calculating the Flexible Barrier Siting Adaptability

The Expert semi-quantitative method is used to quantify the evaluation indicators. A two-level assessment standard is established: Level I (unsuitable) and Level II (suitable), assigned values of 1 and 0 points, respectively.

The weighting factors k_i for each evaluation index are derived from the activity index defined in Equation (5). The resulting weight coefficients are:

$$\begin{array}{l}k(P1,P2,P3,P4,P5,P6,P7,P8,P9,P10,P11,P12)\\ =(10.27,6.70,9.82,7.59,9.38,6.25,6.25,10.71,5.36,7.14,10.27,10.27)\end{array}$$

(6)

The siting adaptability index W is then calculated as the weighted sum of the indicator scores (p_i, where p_i = 0 or 1):

$$W={\displaystyle \sum _{i=1}^{10}{k}_i{P}_i}$$

(7)

4. Case Study

4.1. Study Area

On 8 August 2017, an earthquake of magnitude Ms = 7.0 occurred in Jiuzhaigou county [57,58]. The earthquake significantly disturbed the geological environment, loosening shallow rock and soil masses on slopes [59]. Subsequent aftershocks and external forces (e.g., heavy rainfall or engineering activities) can easily trigger new geological disasters on these unstable slopes. Huohua village is located on the left bank slope of a highway (33°13′3.20″ N, 103°54′16.99″ E). The average annual rainfall is 552.3 mm, and the groundwater is acidic. The relative elevation difference between the collapse source area and the tourist road ranges from 45 to 420 m. Figure 4 shows the external morphology of Huohua village and photographs of the perilous rock masses. The Jiuzhaigou valley is a UNESCO World Heritage Site, making the preservation of its natural landscape and sustainable tourism economy of utmost importance. Therefore, any mitigation measure must balance safety with minimal environmental and visual impact.

4.2. Assessing the Flexible Barrier Siting Adaptability

Table 4. Evaluation criteria for flexible barrier siting adaptability indicators.

	Factor	P1	P2	P3	P4	P5	P6
Level
Ⅰ (Suitable)		<2000 kJ *	<4 m3 *	concentrated	$\le$1 event/year	rock	<30 m *
Ⅱ (Unsuitable)		≥2000 kJ *	≥4 m3 *	dispersed	$>$1 event/year	soil	≥30 m *
	Factor	P7	P8	P9	P10	P11	P12
Level
Ⅰ (Suitable)		$<$8 m	tree	acidic	seismic activity	difficult	recyclable
Ⅱ (Unsuitable)		$\ge$8 m	none/shrub	neutral	no seismic activity	simple	non-recyclable

* Note: A fundamental prerequisite for the successful deployment of a flexible barrier is that the kinetic energy of the design rockfall must be less than the barrier’s designated protection energy capacity. The values provided in Table 4—such as the 2000 kJ energy level and the corresponding 4 m³ rock volume—are illustrative examples based on a specific vertical-impact test scenario (assuming a rock density of 2400 kg/m³ and a fall height of 30 m). These thresholds are not universal constants. In practice, the limiting values for kinetic energy (P1) and rockfall size (P2) must be determined based on the design energy capacity (E_r) of the barrier selected for the specific site. The maximum kinetic energy is estimated using the equation E = mgh, where the free-fall model represents the most conservative scenario. Two practical approaches are recommended: For identified perilous rock masses of volume V, calculate the maximum allowable fall height h such that E ≤ E_r; For a slope of defined height h, determine the maximum allowable rock volume V that satisfies E ≤ E_r. Once E_r is established, the Level I/II threshold for P1 is defined as E < E_r/E ≥ E_r, respectively. This procedure aligns with standard industry practice and ensures that site-specific conditions are incorporated into the adaptability assessment.

presents the siting adaptability assessment results for potential barrier locations at Huohua Lake.

4.3. Results and Analysis

The proposed method was verified against actual application conditions and numerical simulations performed using Rocfall V.4.0. Rocfall V.4.0 can simulate the trajectory of falling rocks, kinetic energy and maximum bounce height [60,61]. Among the parameters used in the program, the slope profile, coefficient of restitution, and friction coefficient are the most critical. The slope profile is obtained through field surveys. The coefficient of restitution and rolling friction coefficient are influenced by the physical characteristics of the slope, the presence of vegetation, and the radius of the rockfall itself. These coefficients can be directly acquired through back analysis of previously fallen rock blocks or theoretically estimated. In this study, the slope type was modeled as vegetated talus. The masses of perilous rock masses, with volumes ranging from 0.1 to 2 m³, were estimated between 200 kg and 4000 kg (assuming a mass of 2600 kg/m³). Figure 4 shows the simulated maximum bounce height and maximum kinetic energy for falling rocks. Based on these simulations, the siting adaptability was evaluated, as presented in

Table 5. Siting adaptability assessment results for Huohua village.

Site ID	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	W
1	0	0	1	0	1	1	0	1	1	1	1	1	69.2
2	0	1	0	0	1	1	1	1	1	1	1	1	72.33
3	0	0	1	0	1	1	1	1	1	1	1	1	75.45
4	1	0	1	0	0	1	1	1	1	1	1	1	76.34
5	1	1	1	0	0	1	1	1	1	1	1	1	83.04
6	1	1	1	0	0	0	0	1	1	1	1	1	70.54
7	1	0	0	0	0	0	0	1	1	1	1	1	54.02
8	1	0	0	0	0	0	0	1	1	1	1	1	54.02
9	1	0	0	0	0	0	1	1	1	1	1	1	60.27
10	1	1	0	0	0	1	1	1	1	1	1	1	73.22

.

A score W above 60 indicates relatively high siting adaptability. According to the assessment results (illustrated in Table 5), 80% of the sites exhibit high siting adaptability (W > 60). Furthermore, the Rocfall V.4.0 simulations (illustrated in

Table 6. Rockfall simulation results.

	Site ID	1	2	3	4	5	6	7	8	9	10
Case
maximum kinetic energy (kJ)		1741	487	570	145	689	490	1792	156	172	157
maximum bounce height (m)		3.56	1.78	2.31	0.63	0.70	7.31	7.73	6.01	1.04	1.08

) show maximum kinetic energies below 2000 kJ and bounce heights between 0.63 m and 7.73 m. Flexible barriers installed after the Jiuzhaigou earthquake have successfully intercepted rockfalls and fallen trees (as shown in Figure 5). These results demonstrate that flexible barriers with a protection energy level of 2000 kJ are suitable for meeting the protection requirements at this site. This confirms the reliability and applicability of the proposed assessment method. The successful interception by 2000 kJ barriers, as identified by our method, prevented the need for installing higher-capacity (and thus more material-intensive, costly, and visually intrusive) barriers, demonstrating a sustainable and cost-effective design outcome. The method’s ability to correctly identify suitable sites on the first attempt avoids the environmental disturbance and financial waste associated with trial-and-error or improper installation.

The validation presented here should be considered a successful proof of concept. The primary validation lies in the fact that the barriers installed post-earthquake (with a 2000 kJ capacity) have effectively intercepted rocks and that our assessment method correctly identified sites suitable for such barriers (W > 60, simulated energies < 2000 kJ). This provides strong preliminary, qualitative evidence of the method’s utility in preventing over-design and guiding appropriate site selection. However, we acknowledge the limitations of this study, primarily the lack of long-term, quantitative performance data (e.g., detailed records of maintenance frequency, capacity utilization, or survival rates under repeated impacts) against which to rigorously test the predicted W scores. A comprehensive quantitative validation would require a large dataset of sites where both the initial assessment (W score) and the actual long-term performance are recorded. Therefore, future work should focus on monitoring the performance of these installed barriers over time to build such a dataset. This would allow for a statistical analysis of prediction errors, calibration of the W score threshold (currently 60), and further refinement of the interaction matrix values based on observed field performance.

4.4. Impact of Variations in Slope Angle on Rocks' Bouncing Behavior

Variations in slope angle affect the bounce height of falling rocks. The motion of falling rocks changes at slope angle transitions due to collisions with the slope surface. Subsequent motion can be either flight or rolling. Slope transitions are categorized as steep-to-gentle or gentle-to-steep. The upper slope angle $∆\mathsf{\alpha }$ was varied from 35° to 65° in 5° increments. The height of both the upper and lower slope sections was set at 5 m. The simulation results are shown in Figure 6.

Table 7. Influence of slope transition on rockfall bounce occurrence.

upper slope angle ${\alpha }_1$ (°)	35	40	45	50	55	60	65
lower slope angle ${\alpha }_2$ (°)	48	50	55	58	63	66	70
angle difference $∆\mathsf{\alpha }$ (°)	13	10	10	8	7	6	5
upper slope angle ${\alpha }_1$ (°)	55	60	65	70	75	80	85
lower slope angle ${\alpha }_2$ (°)	16	25	36	50	62	71	77
angle difference $∆\mathsf{\alpha }$ (°)	39	35	29	20	13	9	8

summarizes the critical lower slope angles inducing bounce and the corresponding angle differences. The results show that as the gentle slope angle increases (in steep-to-gentle transitions), the minimum angle difference required to induce bouncing motion decreases, exhibiting an approximately linear relationship.

5. Discussion and Conclusions

This study addressed the lack of quantitative methods for assessing flexible barrier siting adaptability by proposing an innovative assessment method based on the interaction matrix. The method was validated through an engineering case study, demonstrating its effectiveness. The main conclusions are:

(1)

This study developed a novel sustainability-oriented assessment framework for flexible barrier siting. The ten key factors and their interactions, quantified through the interaction matrix, provide a holistic view that encompasses not only engineering performance but also implicit environmental and constructability (economic) concerns.

(2)

It was found that variations in slope angle significantly affect rockfall bounce height; specifically, as the gentle slope angle increases (in steep-to-gentle transitions), the minimum angle difference required to induce bouncing motion decreases.

(3)

Most significantly, the proposed method itself embodies a sustainable approach. Its simplicity and low computational requirements make it a rapid, low-energy, and accessible tool for engineers, particularly in the critical planning and feasibility stages. This promotes resource-efficient design by ensuring that barriers are correctly sited from the outset, thereby extending service life, reducing maintenance needs, and avoiding the substantial embodied carbon costs associated with failed or over-designed structures.