Numerical Modelling of Rock Fragmentation in Landslide Propagation: A Test Case

Abstract

Landslides and rockfalls can negatively impact human activities and cause radical changes to the surrounding environment. For example, they can destroy entire buildings and roadway infrastructure, block waterways and create sudden dams, resulting in upstream flooding and increased flood risk downstream. In extreme cases, they can even cause loss of life. External factors such as weathering, vegetation and mechanical stress alterations play a decisive role in their evolution. These actions can reduce strength, which can have an adverse impact on the slope’s ability to withstand failure. For rockfalls, this process also affects fragmentation, creating variations in the size, shape and volume of detached blocks, which influences propagation and impact on the slope. In this context, the Morino-Rendinara landslide is a clear example of rockfall propagation influenced by fragmentation. In this case, fragmentation results from tectonic stresses acting on the materials as well as specific climatic conditions affecting rock mass properties. This study explores how different fragmentation scales influence both velocity and landslide propagation along the slope. Using numerical models, based on lumped mass approach and stochastic analyses, various scenarios of rock material fracturing were examined and their impact on runout was assessed. Different scenarios were defined, varying only the fragmentation degree and different random seed sets at the beginning of simulations, carried out using the Rock-GIS tool. The results suggest that rock masses with high fracturing show reduced cohesion along joints and cracks, which significantly lowers their shear strength and makes them more prone to failure. Increased fragmentation further decreases the bonding between rock blocks, thereby accelerating landslide propagation. Conversely, less fragmented rocks retain higher resistance, which limits the extent of movement. These processes are influenced by uncertainties related to the distribution and impact of different alteration grades, resulting from variable tectonic stresses and/or atmospheric weathering. Therefore, a stochastic distribution model was developed to integrate the results of all simulations and to reconstruct both the landslide propagation and the evolution of its deposits. This study emphasizes the critical role of fragmentation and the volume involved in rockfalls and their runout behaviour. Furthermore, the method provides a framework for enhancing risk assessment in complex geological environments and for developing mitigation strategies, particularly regarding runout distance and block size.

1. Introduction

This work is part of the LanDam project on the classification, prediction, and emergency management of landslides that could potentially occlude riverbeds. The project is funded by National Recovery and Resilience Plan (PNRR) funds as part of the extended partnership RETURN—Multi-risk Science for Resilient Communities in a Changing Climate—Spoke 2. This examines all the methodological issues relating to the characteristics that areas subject to potential landslides must have from the source area. Among the elements to be considered are the accumulations of debris from rockfalls collapse located at the top of the possible catchment area on which the debris flow phenomenon will then evolve. To this end, this work intends to focus on the behaviour upstream, i.e., on the source area of the materials that mobilize to form the occluding mass.

Landslides pose significant risks and challenges in risk assessment to the security of human life and resources, particularly in mountainous areas or in geological complexes system [1]. Landslides are defined as the movement of rock, soil or debris down a slope. Primarily driven by gravity, these mass movements usually occur along a distinct failure surface. They can vary significantly in terms of velocity, materials involved, and mechanisms by which they occur [2]. Rockslides, falls, and avalanches are a subset of these, where the mass movement involves blocks or masses of rock that slide down a slope [2]. These phenomena can be influenced by various factors such as mechanical weathering of rocks, hydrostatic pressure in the rock joints, changes in climatic conditions and increase in the tectonic stresses [3,4]. In this scenario, fragmentation is a key factor in determining the environmental impact of a landslide. The integrity of rock clusters is often compromised by external forces that alter their stability. Tectonic activity is the main cause of fracturing, creating planes of weakness such as faults and joints and making the rock vulnerable. Climatic agents also play a role, as temperature variations cause expansion and contraction, generating internal stresses that progressively widen cracks. The freeze–thaw cycle is even more incisive due to seepage water expanding into cracks and exerting cyclic pressure, which causes the entire mass to crumble [5,6]. These alterations usually result in a decrease in the rock’s mechanical properties, which compromises its overall strength and stability [6]. Additionally, they can alter rock mass characteristics, such as strength and rock mass rating (RMR) [7]. When altered rocks are involved in rock avalanches or falls, their behaviour upon impact with the ground can differ significantly from that of intact rock masses [8]. Altered rock may fracture into varying numbers of secondary blocks, either following natural fracture networks or breaking into smaller parts due to the heterogeneity in stress resistance. The degree to which a rock has been altered by processes such as weathering, mineralisation or the development of microfractures plays a significant role in determining how it will behave when subjected to external forces during a landslide [9]. The alteration of rock masses weakens the blocks and creates a complex fracture network that influences how the rock mass will break apart and propagate during a landslide [10]. Understanding these changes is important for predicting landslide behaviour and mitigating the risks associated with rock mass instability in vulnerable regions [11]. Understanding rock fragmentation is essential to understanding landslide dynamics. This is because the way rocks fragment directly influences several critical factors, such as the velocity, direction, and propagation distance of the landslide itself [12,13,14]. Fragmented rock, or rock that has broken into smaller parts, usually has a much larger surface area than intact rock. This increased surface area can significantly impact its behaviour, particularly in processes such as rockfalls and debris flows. The reduced structural integrity of fragmented rock allows it to move more fluidly, as individual parts can slide past one another more easily. This often leads to faster and more extensive movement, especially when saturated with water [15,16,17].

On the other hand, intact rock is usually stronger and more rigid, so it moves less easily. When it does move, it often breaks off in large, compact blocks [13]. This generally results in slower movement, as greater forces are needed to break or dislodge the blocks. Moreover, the distance that intact blocks can travel is often limited compared to fragmented rock, since significant geological forces or events are usually required to cause substantial displacement. This process is influenced by various factors, such as the properties of the block and the soil it impacts, the resistance of the materials involved, the presence of discontinuities and the rigidity and roughness of the impact surface. All these factors can influence the final arrest of the materials involved [14]. In fact, the fragmentation is a key factor to estimate the velocity and the sliding distance of landslides [15]. According to Matas et al. [15], fragmentation has three main consequences: a significant reduction in the size of the initial block, a divergence in the trajectories of the fragments, which fan out from the point of impact and a potentially increase in speed, known as the thrust effect, whereby smaller fragments can reach higher velocity. Although the most recent scientific literature, such as [16] and Ji [17], confirm the importance of also considering the effects of viscous friction and substrate roughness, in this work we have chose to focus the study only on the fragmentation effects. For this, an important tool to study this phenomenon is the Rock-GIS—a three-dimensional GIS-based model that incorporates the Fractal Fragmentation Model (RFFM) [18]. This tool uses a lumped mass approach, whereby the fragmentation process is triggered by the break-up of the detached rock mass just before it reaches the ground. The distribution of mass among the resulting fragments is stochastic and follows a power law. These fragments then follow trajectories within a maximum dispersion angle [18]. Overall, rock fragmentation plays a key role in slope dynamics, affecting how materials respond to increasing stress and how they are transported downslope. For example, smaller fragments may behave more like debris flows, while larger rock masses might move as block slides or rockfalls with different dynamics [19].

In this scenario, the Morino-Rendinara landslide represents a highly significant case study of a cascading event, distinguished by the differentiation in its failure mechanisms and the substantial extent of the surface involved (Figure 1) [20,21,22]. Located along the Ernici Mountains in the Abruzzo region, the study area is characterized by three distinct mechanisms that are interconnected from the upper to the lower part of the slope [21,23].

In this work, different scenarios of rock material fracturing were examined to assess their impact on the movement and runout of the landslide. The results show that, in a rock mass, cohesion along joints and fractures decreases as fracturing increases. This is because fracturing creates and spreads systems of discontinuity, which act as planes of weakness. As a result, the shear strength of a highly fractured rock mass is drastically reduced and becomes almost entirely dependent on the friction between the blocks and the normal pressure, making it much more vulnerable to triggering. In contrast, less fragmented rocks exhibit greater resistance, limiting the extent of the movement. Due to uncertainties in the initial spatial distribution of material alteration grades, a stochastic distribution model was developed. This model integrates all simulation results to reconstruct the landslide propagation and the evolution of the displaced material. This study presents an innovative approach to modelling rock fronts. Unlike traditional deterministic models, which fail to capture the natural variability of materials, our work integrates advanced stochastic analysis to evaluate different degrees of fragmentation. This demonstrates the effectiveness of a model that considers the intrinsic uncertainties of the fragmentation process in landslide evolution. The propagation of rockslides is particularly influenced by random factors such as rock mass quality, discontinuity presence and fracturing distribution and orientation. These elements significantly contribute to the intrinsic uncertainties of the phenomenon, often rendering traditional models unrealistic. Integrating a stochastic model that considers different possible distributions enables us to generate a significantly wider range of results and define how different fragmentation scales influence the velocity and propagation of landslides. Consequently, rather than providing a single prediction, the stochastic model reconstructs a series of plausible scenarios, greatly improving the reliability of risk assessments and enabling the development of more effective and resilient mitigation strategies.

2. Materials and Methods

2.1. Geological and Geomorphological Framework of the Study Area

The Rendinara municipality is in the upper Roveto Valley, which marks the boundary between the Abruzzo and the Lazio regions, in central Italy. The area sits on the southwestern slope, bordered by the mountain ranges, while on the eastern side, the Serra Lunga Mountain group separates it from Vallelonga. The valley’s most prominent peaks are Mount Viglio (2156 m above sea level) and Pizzo Deta (2041 m above sea level). The Roveto Valley itself is a depression running in NW-SE direction, carved by the Liri River, which collects the flow of numerous seasonal streams along its path [24]. The study area is primarily composed of Messinian siliciclastic deposits (Figure 2), which have been deformed by the active tectonics of the Apennines. Secondary components such as polygenic breccias and puddingstones are also present. The Ernici and Simbruini Mountains together form an overthrust ridge of Jurassic-Miocene carbonate units, which lie over the Messinian siliciclastic deposits in the valley.

The Miocene sections of these Jurassic-Miocene carbonate units, particularly in the area, show significant jointing due to active normal faults. These carbonate units overlie the siliciclastic deposits (clay and sandstone), forming the foundational structure of the Liri River. The tectonic contact between these layers is characterized by a low angle (10–20° with a W-SW dip component). Over time, this low-angle contact has been interpreted by several authors as the result of differential north-eastward displacement and anticlockwise rotation of the carbonate structure [13], with greater shortening occurring in the southern sector [21].

Along the main slope, the gradient transitions from 60° to an average of 18°. In areas with gentler inclines, fractured materials have led to sediment accumulation, resulting in the formation of slope deposits [16,17,18,19,20,21]. Additionally, the region includes Holocene fluvial deposits, as shown in Figure 2, which consist of fluvial terraces and detrital cone formations. In the study area, as in the broader region, the hydrogeological regime is influenced by active tectonics. There are numerous groundwater springs, especially on the slope affected by the landslide, in the contact zone where the more tectonically deformed marl-arenaceous formation is located. Some of these springs are brought to the surface by gravitational movements acting on the slope [19]. These high-flow springs contribute to material transport, adding clayey material to the deposits [18]. The slope and landslide can be further divided into three distinct sections; each associated with a dominant failure mechanism. The upper sector, which is the focus of this study, is primarily characterized by highly fractured limestones and is dominated by rockfall and avalanche processes. The morphologies in this area are strongly influenced by tectonics, as evidenced by fault scarps, and altered rock formations and complex jointing systems. The central sector is defined by the presence of a deep-seated rotational slide. This landslide develops along the contact zone between limestones and marls, where a significant detrital aquifer is present. This aquifer is fed by collapse blocks originating from the upper zone, further influencing the slope’s stability [18], because the highly tectonised material tends to create preferential detachment surfaces and is characterized by the presence of fractures that affect material stability [21]. The lower section is characterized by a significant debris flow, which was last reactivated in March 2021 due to a period of heavy rainfall, damming the Liri River [23].

2.2. Geomechanical: Surveys and Analytical Techniques

To assess the rock quality and characteristics of the upper sector, a detailed geomechanical survey was conducted [25]. A total of seven scanlines were conducted for the geomechanical survey of the rock face (Figure 3). The aim was to characterize the mechanical properties of the rock mass, considering the morphological complexity of the affected walls and the height of the rock masses [26]. Scanlines have enabled data to be acquired relating to the fracturing state of the rock slope by recording the main discontinuity systems, to define the geostructural characteristics of the mass [27,28]. Each scanline station has a length of between 10 and 13 m, and all measurements have been acquired according to the procedures proposed by the International Society for Rock Mechanics (ISRM) [29,30]. Based on the collected data, it was possible to define the quality of the rock mass, determine its classification index, and understand the possible kinematics of the slope. Rock masses were evaluated using Rock Mass Rating (RMR) [31], Slope Mass Rating (SMR) [32], and Geological Strength Index (GSI) [31]. Using the Schmidt Hammer test (rock sclerometer type L) [33], the stiffness of the rock was assessed through uniaxial compressive strength tests. For each discontinuity, at least sixty Schmidt Hammer tests were conducted, and the five highest values contributed to the final characterization. From these tests, the rebound index (R) was obtained, and the Joint Compressive Strength (JCS) was then determined [32,34,35,36]. For this study, particular attention was given to the rock volume. This value represents the amount of rock material that could potentially be involved in a rockfall. The volume of material was directly derived from the geomechanical survey, which provided precise measurements and data about rock masses and their discontinuities. This accurate volume estimation is essential for determining the potential dynamics of rock masses movement and predicting how far the material might travel during an event, enhancing the reliability of the runout estimation and contributing to a more comprehensive risk assessment.

The Rock-GIS tool was used to analyse rockfall runout by simulating rockfall trajectories and incorporating a fragmentation module based on references [36,37,38]. The tool uses a lumped mass approach to simulate block trajectories according to Newton’s second law and a simplified rebound model that does not consider air friction. The model calculates the post-impact trajectories of the fragments, which follow random paths within a cone-shaped area determined by the rebound velocity. The theory of Rock-GIS concerns rock mechanics during impact. In detail, the algorithm considers the impact angle and the energy required for rock breakage [39,40,41]. A correlation has been found between the number of blocks generated during breakage and the fractal dimension of their volumetric distribution. The tool incorporates different rock fragmentation models, including the Discrete Element Method (DEM), that simulates interactions between fragments based on pre-existing discontinuities [39]. In detail, in fragmentation modelling, the Rock-GIS tool is based on the energy threshold necessary for the breakage. This differs from other theories that use neural networks to model the process based on DEM simulations [40,41].

The Rockfall Block Size Distribution (RBSD) is used to analyse how the fragmentation process alters the original In Situ Block Size Distribution (IBSD) as the rock mass propagates downslope. Rock-GIS applies a stochastic method that incorporates fragmentation into GIS-based lumped mass models, with a focus on tracking volumetric changes in the IBSD during propagation. The model assumes that block disaggregation occurs when the blocks detach from the slope, without requiring additional energy input. Blocks are simulated individually, and collisions between blocks are ignored. Equation (1), calculates the kinetic energy before and after the impact block, accounting for energy dissipation during breakage [37]:

$$E_k^{bi}=E_k^{ai}+E_d+E_b$$

(1)

where:

$E_k^{bi}$ = kinetic energy before impact,

$E_k^{ai}$ = kinetic energy after impact,

$E_d$ = energy dissipated during the impact,

$E_b$ = energy dissipated due to the breakage process.

The energy loss during breakage is modelled as an uncoupled process from the block’s rebound, with a coefficient of breakage energy loss $C_b$ (2) used to estimate the energy dissipated during breakage:

$$E_b=C_b{E}_k^{bi}$$

(2)

The model checks if breakage will occur by comparing the block’s impact energy with a threshold value (3). If breakage occurs, fragments are generated based on a power law distribution of mass. The mass distribution for the generated fragments follows the power law

$$P_i=c{V}^{-b}$$

(3)

where:

$P_i$ = relative cumulative frequency,

$c$ and $b$ = parameters defining the power law,

$V^{-b}$ = volume of the blocks.

Random fragments are created until their volumes sum to the original block’s volume. The breakage criterion allows for some blocks to survive despite reaching the threshold energy, using a survival rate factor. The flowchart illustrating the theoretical framework of the Rock-GIS tool is shown in Figure 4.

To replicate the causality and uncertainty of natural phenomena, combined simulations for different fragmentation scenarios were integrated using stochastic methods [42]. The generation of pseudo-random numbers is governed using a seed, which is an initial value from which the entire numerical sequence is derived. To ensure reproducibility of the simulations and enable rigorous quantification of the variability inherent in the results, consistency in the application of the same seed is essential. The random numbers generated allow complex and non-deterministic scenarios to be simulated, such as those related to the fragmentation of rock material [43,44,45]. This helps to improve our understanding of the evolution and interaction of the natural forces that influence landslide phenomena. In this case, the code relies on a random combination of stop points obtained from different simulations, selecting the maximum volume in each case to ensure consistently high-volume estimates and reduce uncertainty in the results.

A numerical simulation of rock block fragmentation was carried out using the Rock-GIS model [15,29,30,46]. The input parameters (Kna, Knb, Kta, B1, B2, Na1 and Na2) were primarily derived from geomechanical field data, including RMR, GSI and JCS, as well as the spacing and orientation of discontinuities. The selection of numerical values was consistent with the physical behaviour of rock masses: more altered rocks or those with closely spaced discontinuities were associated with parameters that promoted higher fragmentation and energy dissipation, while more intact rocks received values that limited fragmentation. Specifically, Kna and Knb, which control normal energy restitution after impact, increase with rock strength and decrease for more altered masses, while Kta, related to tangential dissipation, assumes lower values for closely spaced discontinuities and higher values for compact rocks. B1 and b2, which are linked to fracture density and degree of alteration, govern the fractal distribution of fragments. Meanwhile, Na1 and Na2 determine surface increase and fragment generation based on block volume and geomechanical characteristics. The parameters were then unified and averaged across the different simulation scenarios to avoid introducing an additional degree of uncertainty into the models while varying only the degree of fragmentation. The fragmentation coefficient follows the same logic: values near zero indicate smaller blocks and high fragmentation, while values near 1 indicate larger blocks and reduced fragmentation. This dimensionless parameter reflects the rock mass’s susceptibility to fragmentation, and the distribution of fragments follows a fractal-type law consistent with the principles of self-similar geometry. The parameterisation was further refined using previous studies conducted in similar geological contexts, as well as by comparing it with the available literature on the Apennines [46]. This approach guarantees that the parameters are physically consistent and comparable with those of other studies, while also ensuring that the simulations realistically represent the propagation and fragmentation of blocks observed.

To accurately represent the different fragmentation grades seen during field activities, three distinct fragmentation scenarios were considered: no fragmentation, low/intermediate fragmentation and very high fragmentation. These scenarios were represented by the following values: −9999 for the no fragmentation scenario, 0.30 for low-medium fragmentation and 0.65 for extremely high fragmentation, with three different seed values used for each scenario. Also, the vegetation along the slope was derived using the difference between the DTM (Digital Terrain Model) and DSM (Digital Surface Model) with a resolution equal to 1.0 per 1.0 m. From this approach, nine different simulations were calculated, following the scheme outlined in

Table 1. Synthesis of parameters employed for the numerical simulations, derived following the procedure in [15,29,30].

Parameters	Set 1	Set 2	Set 3
Fragmentation	−9999 (off)	0.30	0.65
Kna [-]		19.50
Knb [-]		−1.03
Kta [-]		200
Rock Density [kg/m3]		2400
Na1 [-]		0.003
Na2 [-]		0.75
b1 [-]		0.92
b2 [-]		−0.52
q1 [-]		−0.51
q2 [-]		1.0
Cone [°]		45°
Seed	12345-56789-11111-12131	12345-56789-11111-12131	12345-56789-11111-12131

.

Parameters in Table 1 represent: Kna, the multiplier in the power-law relationship between the normal impact velocity and the normal restitution coefficient; it controls the energy restitution after the impact [46]; Knb is the exponent in the power-law relationship between the normal impact velocity and the normal restitution coefficient; Kta is the parameter that controls the hyperbolic function used to compute the tangential restitution coefficient; this parameter governs energy dissipation in the tangential direction [46]; Rock Density represents the rock material density, expressed in kg/m³, and influences the dynamic behaviour [47]; na1 and na2 are the parameters governing the power-law relationship between the remaining normal impact energy and the newly generated surface area during impact; these parameters govern how the fragmented blocks respond in terms of energy [37]; b1 and b2 are the parameters that influence the fractal dimension during fragmentation, depending on the newly created area. Fragmentation grade is a coefficient representing the ratio between the newly generated area and the total surface area, used as a threshold to trigger fragmentation. Cone [°] is the total opening angle of the material’s cone-shaped fragmentation pattern [46]. Finally, the seed is a stochastic factor used to introduce randomness and replicate the natural variability in the fragmentation process [48].

The values presented in Table 1 were used to compile the parameter profiles, which serve as the source points for the geomechanical stations. The areas around the geomechanical location were designated as the source zone, and a random distribution of one hundred points for zone was applied. The mean discontinuity distance, as defined by the geomechanical data, was used to determine the spacing required to build the unstable rock mass model. The initial volume was set using the values obtained from the geomechanical investigation. To keep the model simple and robust, variations in the initial block size distribution (IBSD) were not introduced. While this is theoretically possible, it would significantly increase the overall stochastic variability, making it difficult to distinguish the specific effects of the initial block size from those already induced by the model’s inherent stochasticity. This would cause the model to become more complex than is necessary for the stated objectives of the study, especially since the source area is already thoroughly parametrized using field data derived from in situ geomechanical analyses.

3. Results

The geomechanical survey consisted of seven stations. The aim was to collect the necessary data to precisely characterise the rock mass, identify potential kinematic behaviours and determine the mechanical properties of its discontinuities. Additionally, for each position, a criticality value was derived, expressed as the percentage of fractures or fracture intersections that fall within the instability area. Results were divided into two sections. The first section presents the results of the geomechanical campaign, while the second section focuses on the numerical simulation results.

Table 2. Summary table of the main results from the geomechanical analysis.

Station	Rock-Wall	Group	Trend/Plunge	Spacing	Volume	RMR	SMR	Class	Quality	Stability	GSI
	(°)		(°)	(m)	(m3)
ST1	360/88	K1	134/82	0.43	2	45	60	III	Moderate	Fairly stable	40–45
		K2	181/86	0.58
		K3	214/66	1.07
ST2	215/75	K1	125/8	1.10	2	60	31	IV	Moderate	Weak	50–55
		K3	211/71	0.41
		S	328/64	0.39
ST3	130/65	K1	120/79	0.26	3	40	55	III	Poor	Fairly stable	35–40
		K3	211/79	0.16
ST4	360/75	K2	182/87	0.81	5	54	60	III	Poor	Fairly stable	35–40
		S	282/24	0.85
ST5	030/82	K1	96/42	1.30	5	44	59	III	Poor	Fairly stable	35–40
		K2	350/85	0.17
		K3	235/74	0.44
ST6	360/62	K1	166/71	0.16	2	45	60	III	Poor	Fairly stable	35–40
		K2	31/67	0.15
		K3	359/70	0.16
ST7	360/80	K1	132/76	0.81	2	42	51	III	Poor	Fairly stable	35–40
		K2	179/85	0.39
		S	277/76	0.26

show the results, where for each station, the following information is provided:

• Rock-wall (°): The orientation of the rock wall in degrees.
• Group: Identifies different joint/structure groups (K1, K2, K3, S) present in the rock masses.
• Trend/Plunge (°): The orientation (direction and dip) of the joints or structures.
• Spacing (m): The average spacing between joints in m.
• Volume (m³): The volume associated with each station or joint.
• RMR: Rock Mass Rating.
• SMR: Slope Mass Rating.
• Class: The quality class of the rock mass.
• Quality: The qualitative description of the rock mass (e.g., “Very-poor”, “Poor”).
• Stability: The stability assessment (“Fairly stable”, “Weak”).
• GSI: Geological Strength Index.

The main rock face has a typically trends orientation north (360°) with a very steep plunge between 62° and 88°. However, there are a few exceptions, in fact at three specific stations, the rock face exhibits different alignments, with following readings: 130°/65°, 30°/82°, and 215°/75°. These variations are important to note as they could indicate localized structural complexities. The discontinuity spacing within the rock mass is generally quite limited. In fact, values range from 0.15 to 1.30 m, and the rock body is poor overall. However, there are parts where the spacing exceeds one meter, and we have estimated the rock volume to be between 12 and 15 m³. In the numerical model, these zones were highlighted as areas with a greater presence of rock material. Finally, the Geological Strength Index (GSI) consistently ranges from 35 to 55, indicating a very low-quality rock mass. According to the classification presented in the methodology, this corresponds to categories III and IV, highlighting its limited competence and stability. Overall, the results highlight extremely unstable conditions and poor rock mass quality. These are both significant factors that contribute to the area’s predisposition to instability. These poor conditions are further exacerbated by the area’s strong tectonic activity, which intensifies the rock mass’s structural weaknesses. In detail, of all the data, the ST2 station stands out as having the highest rock mass quality. However, this does not translate into high stability: in fact, the SMR value indicates a low level of stability, identifying the area as critical and prone to instability. By contrast, other stations demonstrate higher stability despite having lower rock mass quality. The geomechanical information from each station was used as input parameters in the Rock Lab program to compute the shear stress–normal stress curve of the rock mass. Specifically, the program processes the discontinuity data and mechanical parameters recorded during the geomechanical survey to derive the shear strength curve, based on standard models in rock mechanics. The resulting curves, shown in Figure 5 for each geomechanical station, represent the shear stress versus normal stress relationship and reflect the mechanical behaviour of the rock mass at the corresponding locations.

The curves in Figure 5 show a growing trend and are not linear, suggesting a typical rock behaviour characterized by an increase in shear stress with normal stress, as expressed by the Mohr-Coulomb criterion [44,45]. Normal stress values range from 0 to 1.2 MPa, while shear stress values range between 0 and 1.3 MPa. The observed differences among the geomechanical stations highlight spatial variability in rock mass properties, influenced by variations in discontinuity spacing and orientation. These results indicate that the materials are highly fractured, weathered, and potentially very sensitive to elevated water content. The curves associated with stations 4 and 2 show the highest levels of resistance, aligning with the results of the geomechanical survey, where ST2 and ST4 exhibited the largest spacing values and the best rock mass characteristics. Specifically, their GSI and RMR values (54 and 60, respectively) were the highest in the dataset, as expected. On the other hand, ST2 shows the lowest values, in line with the findings from the geomechanical survey, where GSI is 35–40 and RMR is 45. Additionally, the mean spacing is around 0.153 m, standing for the lowest recorded value. According to Rock Lab results, these values indicate that the rock mass associated with this geomechanical station is the weakest of the entire dataset and corresponds to the poorest part of the rock wall. Using the parameters presented in Table 1, that represent the range of geomechanical conditions observed in the field, multiple simulation sets were performed to investigate their influence on slope stability and failure mechanisms. For each scenario, three simulations were conducted to capture variability and reinforce the reliability of the outcomes. Figure 6 presents one representative result per scenario, selected to illustrate the main differences emerging from the parameter variation.

Figure 6a,d show the results of the analysis without considering the effects of fragmentation. In this scenario, smaller volume blocks stop at the top of the slope in proportion to their mass and the effect of acceleration. Conversely, larger blocks can roll further. Since mass remains unchanged, intact blocks achieve the maximum runout, which explains why the initial maximum volume is preserved in the output. Furthermore, the frequency of occurrence is highest in the impacted section of the slope, where the greatest accumulation of material has been recorded through field observations. Trajectories are less frequent in the lower part of the slope because fewer blocks can reach this area.

The maximum input volume is preserved in the output results because fragmentation was disabled during the simulation. In this configuration, the model generated an average of approximately 3350 sub-blocks by the end of the simulation. Figure 6b,e show the results for a low level of fragmentation (0.65); as in the previous scenario, the blocks exhibit a consistent trend. However, a key difference is that the total number of blocks reached 4597 by the end of the simulation. Due to the low fragmentation setting, the maximum volume was not preserved for all blocks. The longest recorded runout in this simulation was 422 m. Figure 6e, which shows the frequency, reveals higher passage values at the same points as Figure 6d. Combined with a larger affected area (due to the greater number of blocks produced), this resulted in the largest recorded runout of 525 m. Figure 6c,f show the results considering a high fragmentation level (0.30). As expected, the volume is exceptionally low and concentrated in the uppermost sector of the slope. The number of produced blocks is extremely high, reaching 85,942, largest recorded runout is 137 m. In this scenario all blocks are considered breakable, so no values of the initial volume are recorded. Additionally, the frequency is significantly higher compared to the other scenarios due to the substantial number of blocks involved in the model structure. According to the graphical results, a simple graph displaying all the conducted simulations illustrates the variation in the number of blocks and volume concerning the maximum runout (Figure 7). According to the numerical results, a simple ternary plot displaying all the conducted simulations illustrates the variation in the number of blocks and volume concerning the maximum runout (Figure 7).

Figure 7 shows a ternary diagram that visualises the normalised simulation results. This diagram clearly shows the relationship between rock fragmentation (represented by “n. Blocks” and “Volume max”) and the resulting “Runout max”. It illustrates how fragmentation affects runout and the number of produced blocks. Additionally, it shows that the combined results are independent of statistical influence, as the position of the point cloud for each simulation does not correlate with the red dot standing for the combined simulations. To integrate all simulations and replicate a scenario like field observations, where blocks are either completely fragmented or remain intact, a stochastic model was applied (Figure 8).

In this approach all simulations were combined in a single synthetic result, illustrating a propagation scenario influenced by fragmentation. This was achieved by randomly selecting points from the full set of generated simulations (Figure 8). A total of 21,237 blocks were recorded, reaching a maximum runout of 480 m. To confirm the model a simple comparison between field data and reach angle was carried out (Figure 9). The reach angle was calculated with Equation (4):

$$\mathrm{A}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\left({\displaystyle \frac{∆\mathrm{H}}{\mathrm{l}}}\right)$$

(4)

where:

$∆\mathrm{H}$: difference in height between the top of the source and the bottom of the deposits.

$\mathrm{l}:$ maximum distance between the source and the farthest block of deposits.

The measured reach angle of 22° shows strong agreement with the calculated reach angle of approximately 21°, derived from field evidence and considering maximum runout and height difference.

Figure 9. Explanation of runout model validation; (a) schematic section illustrating the terrain profile where the maximum runout was measured to calculate the reach angle. (b) stop points and cross-section location along the slope, the arrow with star indicates the geo-graphic North.

Figure 9. Explanation of runout model validation; (a) schematic section illustrating the terrain profile where the maximum runout was measured to calculate the reach angle. (b) stop points and cross-section location along the slope, the arrow with star indicates the geo-graphic North.

Importantly, both values fall within the 20–24° range, which aligns with literature data for rock avalanches in an Apennine context [49,50].

An important aspect of the simulations is the validation of the results. In this case we have used field and UAV images to compare between the observed deposits and the numerical results. Figure 10 shows the morphology of active processes and potential rockfall hazards. The Figure 10 shows a rock face with evident signs of fracturing and instability. This type of morphology is characteristic of areas with significant tectonic stress and a high risk of rockfalls. The Figure 10b shows extensive accumulation of debris blocks of considerable size related to both single falls and potential water-saturated debris flow under extreme conditions. On the overlying rock face, exposed fracture surfaces and precariously balanced rock blocks are evident. The Figure 10c shows inconsistent debris falls due to equally dangerous mass movement. The Figure 10d shows the largest blocks with low fracturing recorded in the area. These blocks demonstrate that the fragmentation effect is not uniform across the area and does not affect the entire unstable rock mass.

As shown in Figure 11, the field map comparison highlights a remarkable similarity between the shape of the observed slope deposits and the simulation results. This figure is based on extensive field data acquisition, which also involved UAV technology; some related schematics are presented in Figure 10.

The landslide simulations accurately replicate the spatial distribution of large blocks as observed in the field. A key finding is the absence of fragmentation, a phenomenon that is directly supported by field data. This behaviour is consistent with established fragmentation laws and principles of rockfall physics, where the smaller blocks are inherently more susceptible to disintegration due to repeated high-energy impacts with the rocky substrate and other moving debris during a landslide. Conversely, larger blocks, with their greater mass and inertia, are more resilient to such forces. These results validate the reliability of the models and support findings from other studies in this geographical area. This strong agreement across different data sources and methodologies improves our understanding of landslide dynamics and the factors that influence debris integrity [20,21,23].

4. Discussion

This work integrated the results obtained from the geomechanical analysis and rockfall simulation in an area characterized by a highly fractured aquifer and a geological setting prone to high instability. The aim of the study is to analyse how various factors, such as the rock mass quality, its interaction with water and/or the physical characteristics of rock blocks, affect both the stability and the behaviour of the rock mass. The runout dynamics are analysed, along with the influence of block size and properties on the distance travelled during the rockfall event [48]. However, this study presents some inherent limitations. The model does not allow for the definition of soil type, friction coefficient, or other parameters in the impact zone. Another limitation arises from the assumption that certain parameters remain constant throughout the model development [51,52]. The model is based on the characteristics of the slope at the time the data were collected and is not directly generalizable. Estimating the parameters for the model is particularly challenging in terms of both calculation and approach, and in some cases, it relies on sensitive parameter analyses as discussed in the existing literature on Rock-GIS [36,53]. Geomechanical investigations have revealed that the rock mass is of very poor quality and highly susceptible to instability. These findings are consistent with expectations given the prevailing geological conditions and the impact of prolonged weather exposure. The observed deterioration in geomechanical properties can be attributed to several factors. Notably, persistent tectonic stress has progressively weakened the rock mass, fostered the development of discontinuities and diminished its overall cohesion [54,55]. The simulation results are consistent with the existing literature on runout behaviour. They highlight the significant impact that the volume of intact blocks has on runout distance. Larger blocks have greater kinetic energy due to their increased mass. This increased energy enables them to overcome obstacles and resist dissipative forces that would otherwise slow them down. Consequently, the larger blocks follow longer trajectories and can travel much farther before coming to a complete stop. Both the shape and the internal structure of the blocks are key factors in determining landslide runout distance. Blocks with an irregular shape experience increased friction and resistance against the ground, which limits their travel distance. However, intact, larger blocks often undergo significant rolling during their movement. Driven by their weight and momentum, this rolling allows them to generate additional energy during the tumbling phase, thereby extending their runout distance. Therefore, the combined effects of the block’s size, the shape, and the dynamic energy exchanges throughout its movement, are fundamental to predicting how far it will travel down a slope during a rockfall. Simulation results demonstrate how different block sizes influence instability across various slope sectors [55,56]. Instability in the upper part of the slope has a negative impact on both the middle sector, characterised by a deep-seated rotational slide, and the end sector, which is susceptible to debris flows. Instability generates smaller blocks that can feed into the unstable cover layer. This influx of new material has the potential to increase local instability and modify water circulation. Conversely, larger blocks affect the overall instability conditions and can reactivate debris flow at the bottom, like the event that occurred on 21 March 2021. As with any modelling approach, this study also has inherent limitations that must be considered when interpreting the results. The first factor is related to the circulation of water and its specific impact on the runout [53]. There is a natural spring in the area that has a considerable impact on the slope stability. The high degree of the fracturing facilitates the infiltration and the circulation of the water, accelerating weathering and reducing the strength of rock joints. Additionally, the presence of a substantial detrital cover layer in the runout zone can alter water circulation, potentially leading to the formation of a suspended water table which can slow down or stop the movement of rocks, preventing them from travelling further along the slope [53]. This aspect was not considered in this work as it has not yet been implemented in the Rock-GIS tool. Integration would enable us to transition from a simulation primarily based on the mechanical properties of the rock mass to an approach that incorporates hydrogeological dynamics. A hydrological model could simulate water infiltration into fractures and joints and calculate the pressure variations that reduce shear strength along discontinuity surfaces, causing instability in the system. This would be a significant improvement, overcoming the limitations of the current study and enhancing the prediction of rockslides. Another important factor is that the analysis is based on a concentrated mass approach. While the concentrated mass method is computationally more efficient, it simplifies the complexity of interactions between rock blocks. In contrast, a comprehensive DEM (Discrete Element Method) approach simulates the movement and interactions of each individual block with its neighbours. While a DEM model provides greater spatial resolution and a more detailed understanding of collisions and friction, the present method incorporates many stochastic variables, providing a broader and more representative assessment of the natural variability of the phenomenon.

An important feature development of the work is the integration with artificial intelligence (AI) and neural networks. These represent an evolution in risk analysis methods, providing a more advanced approach that significantly improves the accuracy and effectiveness of the model, overcoming the limitations of traditional methods. Machine learning algorithms can process large amounts of data to identify patterns and correlations that often escape traditional models. Real-time data from sources such as ground sensors, inclinometers, GPS sensors, high-resolution satellite images and LiDAR scans can be fed into neural networks. These networks can analyse the data and learn from previous landslide events by recognising warning signs. In this context, AI acts as a powerful addition to the stochastic model. This would reduce initial uncertainty and make simulations more realistic, and this would offer a more accurate, dynamic risk assessment tool capable of adapting to frequently changing environmental conditions. However, it is important to highlight that the results of this study have clear practical implications for reducing the risk of landslides. Indeed, studying how uncertainties influence the evolution of debris allows to optimise the design of safety structures. In particular, the stochastic model enables more accurate prediction of the potential runout distance that debris can travel, thereby improving the positioning of defence works and the definition of safety zones.

5. Conclusions

This study focuses on fragmentation in landslide propagation and dynamics, paying particular attention to how variations in block size influence landslide volume, energy and runout. The analysis, supported by existing literature, reveals a key distinction: highly fragmented landslides, composed of smaller blocks, have limited propagation but can result in significant and hazardous accumulation on slopes. Conversely, less fragmented landslides, characterised by larger blocks, result in greater runout and contribute more to the landslide’s overall extent. The geomechanical surveys confirmed the preliminary observations and supported the actual geological settings. The Rock-GIS tool successfully reproduced the landslide characteristics and field observations detailed in Figure 10, with stochastic integration contributing to a realistic propagation pattern. Notably, the computed reach angle of 22° closely aligned with field observations and established literature models from comparable real-world scenarios. The correspondence between field observations and the simulation therefore underscores the reliability of the model in representing not only the trajectory of the blocks, but also their physical characteristics after transport, providing a valuable tool for predicting and managing geomorphological risks.

This research emphasises the vital role of rock fragmentation in accurately assessing risk in various rockfall scenarios. By refining numerical modelling techniques and incorporating stochastic variability, it is possible to rebuild a robust and exhaustive framework of the real phenomenon. The aim is to enhance landslide hazard assessment and mitigation planning, particularly in complex geological environments. In fact, the analysis of information from the simulations can aid in the development of numerical models aimed at identifying potential slip surfaces, estimating the volumes of other phenomena involved in complex dynamics, and studying specific, calibrated mitigation strategies.

In particular, the stochastic model enables more accurate prediction of the potential runout distance that debris can travel, thereby improving the positioning of defence works and the definition of safety zones. Furthermore, analysing the influence of fragmentation from dimensional and energetic perspectives enables the correct sizing of rockfall barriers, containment valleys and other protective structures. In conclusion, while the model simplifies certain dynamics compared to more complex techniques such as DEM, its capacity to incorporate the uncertainties of the phenomenon renders it a practical and valuable instrument for risk assessment and the development of effective mitigation strategies.