The study area is located close to the village of Villanova di Accumoli, in the Accumoli municipality, central Italy (Fig. 1a). In the area, the main vulnerable element subject to rockfalls was a portion of the SP18 road connecting Villanova di Accumoli to the San Giovanni village (Fig. 1a).

The area consisted of a rocky hillslope from which rockfalls detached, reaching the SP18 road (Fig. 1a). Visual interpretation of stereoscopic black and white aerial photographs taken in 1954 at 1:33 000 scale revealed that the cliff from where the rockfall originated is part of a partially dismantled scarp of a deep-seated, disrupted rockslide (Fig. 1b). Additional visual interpretation of stereoscopic colour aerial photographs taken in 1977 at 1:13 000 scale revealed that the main landslide rocky escarpment is characterized by two areas that underwent progressive retreat, forming three cone-shaped, convex, sparsely vegetated talus deposits (Fig. 1b). The analysis of the two sets of aerial photographs revealed that in the central part of the escarpment the talus deposit was mined and partly removed between 1954 and 1977 (Fig. 1b). Outside of the talus deposits, the landslide scarp shows an average slope of around 40^∘, it is mainly bare and bedrock crops out. At the base of the slope, the top of the landslide deposit is covered partially by talus that supports a dense deciduous wood.

In the study area, a regional thrust brings the carbonatic units of the Umbria-Marche stratigraphic sequence over the Laga Formation (Cacciuni et al., 1995). The boulders that hit the SP18, and the majority of the boulders found on the talus slope above the SP18 road, belong to the Maiolica Fm., a layered and highly fractured mudstone, upper Jurassic to lower Cretaceous in age.

In the following, we describe the two rockfall source areas, shown as “site 1” (S1) and “site 2” (S2) in Fig. 1a, c, recognized during the field survey.

Site 1 (S1 in Fig. 1c, d) is a 30 m high cliff in fractured limestone 110 m NE from the road. The talus downhill of the cliff has an average slope of about 31^∘. It was partly exploited in the 1950s, and in the quarry area, the average slope is 40^∘. Moving from the source area to the road, the slope shows a decreasing inclination. For a distance of 50 m uphill of the road, a system of scarps, counter scarps and rough and ruined embankments parallel to the SP18 was developed to protect the road during the quarry activities that removed a large part of the original talus. The quarry protection system is now completely wooded. Field observations revealed that the boulders detached from S1, moved primarily along ballistic trajectories (“ree fall”) as suggested by the impact points found on the ground and the scars left on the tree trunks. At impact points on bedrock and talus, the fallen blocks broke up in pieces, the larger of which 0.25–0.30 m³ in volume, were found on the nearly flat area uphill of the road. Analysis of the scars left by the falling blocks on the trees revealed that the rockfall trajectories did not exceed an elevation above the local terrain of about 1.5 m. Based on the boulders found in the field, the area enclosing the trajectories of the rockfalls detached from S1 is estimated in about 4000 m². The pre-failure morphology of the S1 source area was estimated heuristically, by visual interpretation of the orthophotos, which then allowed to estimate the volume of the detached mass (about 7 m³) from the DEM, where the height of the unstable wedge was measured. Based on the evidence of the fracturing of the remaining unstable rock mass (i.e. orthophotos and field observations), it is possible to hypothesize that the initial detached rock mass consisted of a few large boulders that then further fragmented. The rocky material detaching from S1 did not reach the SP18, but stopped on the talus deposit and on the quarry protection system. Visual analysis of the photographs taken by the RPAS (Fig. 1d) allowed identification of several unstable rock blocks present in the vicinity of S1. Such rock blocks were partially separated from the bedrock by open fractures, which could be further enlarged due to intense rainfall and by frost and thaw cycles, not infrequent in the area from late autumn to early spring. The overall volume of the unstable blocks was estimated in the range of 30–50 m³ by combining a GIS measure of the area recognized on the orthophoto (10 m²) and field observation together with 3-D measures obtained from the DEM, for which the height of the unstable rock blocks was estimated to range between 3 and 5 m.

Site 2 (S2 in Fig. 1c) is located along a slope covered by a talus deposit, with a mean slope angle of about 32^∘. From S2, a 1 m³ boulder detached and reached the SP18 road (Fig. 1c, e). The analysis of the boulder impact points on the road (Fig. 1e) and its final position allowed us to reconstruct the boulder trajectory, from 70 to 90 m uphill of the road, where we were able to identify the most likely source area (Fig. 1a, c). Along the hillslope of S2, six boulders of similar size were found on the talus deposit. It is possible that the seismic shocks worsened the stability conditions of the boulders, increasing the rockfall hazard along the road.

Analysis of the distribution of the rockfall impact points and of the tree scars suggested that the height of the trajectory of the 1 m³ boulder never exceeded 1 m above the ground. The boulder did not break along its path and stopped 15 m downslope of the SP18.

From the 1938 cells identified as source areas (light blue polygons in Fig. 3a), STONE was run 100 times, one for each modified DEM (see Sect. 3.4), simulating a total of 193 800 rockfall trajectories per simulation (i.e. 100 launches per source cell). The raster map in Fig. 3a shows, for each cell, the mode of the number of trajectories obtained in the 100 simulations, whereas the plot in Fig. 3b shows the values obtained along the SP18 track. Figure 3c shows, for the pixel along the road, the number of simulations in which the trajectory count is greater than 0.

Figure 3(a) The map shows the mode of count of trajectories of 100 STONE simulations (see text for explanation). Black circles indicate the location of large boulders observed during the field survey at their farthest distance from the source areas (light blue polygons). For each pixel along the road track, (b) shows the values of the map (a) and (c) shows the number of STONE simulations in which trajectory count is greater than 0. The star indicates the position of the impact point along the SP18; blue symbols show the end points of the road track.

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Considering the map in Fig. 3a, the trajectories affect an area of 56 032 cells (m²), with the count values ranging between 1 and 652. Furthermore, a total of 32 800 pixels assume a value greater than 1.

Inspection of Fig. 3b–c reveals that the tract of the road downhill of S2 is the most hazardous and that the location of the impact point matches the area where the STONE output assumes the highest values of both the number of trajectories (Fig. 3b) and the hit frequency (Fig. 3c). The portion of the SP18 closest to the source site S1 was not hit by the rockfalls during the seismic sequence. This is confirmed by the STONE simulations, which reveal a total of 957 pixels affected by possible trajectories with a mode value of 1 within the road or downhill of it. The 957 pixels represent 0.49 % of the total number of the simulated trajectories and 0.6 % of the trajectories simulated uphill from this tract of the road (152 300). Such figures can be considered negligible. The plot in Fig. 3c also confirms that in most of the simulations, the trajectories did not reach this tract of the SP18. Contrary, the portion of the SP18 downhill from S2, and which was hit by the rockfall during the seismic sequence, is correctly predicted by the model as subject to rockfall hazard. In detail, the model output identifies a total of 12 123 trajectories crossing the road, accounting for 6.2 % of the total number of simulated trajectories and 29.2 % of those simulated uphill from this portion of the road track. Furthermore, local values reaching 204 trajectories were identified downhill from S2.

Finally, at the pixel scale, we computed the coefficient of variation (CV $=\mathit{\sigma }/\mathit{\mu }$) of the number of trajectories computed in the 100 simulations. CV is a measure of the variability in a sample normalized by the average value of the distribution. The distribution of the CV values shows a standard deviation of 0.17 and a mean of 0.20, which indicates that the model can be considered stable despite the errors introduced by the GNSS RTK topographic measurements.

The workflow described in this paper for the assessment of the road exposure to rockfall hazard was carried out during a seismic emergency phase to support the Italian National Department of Civil Protection in the decision whether or not to safely reopen the SP18 road to traffic. The diffuse presence of trees in the study area would have required an ALS survey to collect ground elevation data under the tree canopy. However, since the seismic emergency framework imposed a strict time constraint, a lidar acquisition was ruled out since it would have required a long planning, preparation, and post-processing time compared to other techniques. Among the existing photogrammetric acquisition approaches, use of RPAS photogrammetry has a number of advantages in terms of feasibility, planning and management easiness, and good-quality data acquisition, which also make it one of the most widespread and used approaches in the private professional sector. From the methodological point of view, the application described in this study can be considered a procedure, applicable during emergencies, for the acquisition of all the required elements that can support the implementation of numerical models for rockfall hazard and risk assessment at a relatively low cost. For areas up to a few tens of square kilometres, the use of RPASs is the cheapest and fastest method for the acquisition of orthophotos and DSMs but, conversely , vegetation hampers the quality of the resulting DEMs, which is fundamental to obtaining reliable numerical rockfall simulations. To overcome this limitation, integration of aerial imagery with GNSS RTK points measured in the field is mandatory for accurate mapping applications, especially when the accuracy required as input by the numerical model is not very high. The availability of ultra-high-resolution images can be very useful for the delineation of rockfall source areas, one of the inputs required by numerical modelling.

The results of STONE are influenced by the values of the tangential and normal restitution and dynamical friction coefficient, which are assigned based on the characterization of the land cover, in most cases accomplished by geomorphological mapping (Fig. 1b). In this case, the detailed geomorphological mapping was carried out based on a rigid set of rules and criteria that make it repeatable and less subjective (Santangelo et al., 2015a, b; Fiorucci et al., 2018). To prove the influence of the detail of the geomorphological mapping on the results, we run STONE assigning the parameters by generalizing the initial geomorphological map, considering the entire scarp of the rockslide as a talus, instead of distinguishing the three smaller talus deposits in the same slope. Results showed that assigning the parameters based on a generalized version of the geomorphological map results in trajectories that do not reproduce the location of the boulders observed in the field. This is consistent with the relatively larger value of the friction coefficient ascribed to talus than landslide scarp (Guzzetti et al., 2004). Such evidence shows that the quality of the geomorphological mapping (Guzzetti et al., 2012) has a relevant effect on model results. The rockfall simulation prepared by STONE confirmed that the portion of the SP18 road affected by the rockfall is rather limited (Fig. 3c). During the emergency phase, this information was provided to the National Department of Civil Protection to support the decision about the road reopening conditions. It was advised that the road could be safely reopened to the traffic, provided that (i) protection measures were installed above the SP18 road where the model indicated the exposure of the road to rockfall trajectories and (ii) that the rockfall barriers installed should take into account the size of the boulders recognized in the field.

Modelling results show that outside the most hazardous part of the SP18 (Fig. 3), only a few locations are potentially affected by rockfalls. Here, the pixels that could potentially be reached by rockfalls along the road show count values of 1. It is worth noting that, over 100 trajectory simulations for each source pixel, a count value of 1 suggests a probability of occurrence that is equal to $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{2}}$. It actually corresponds to probability values much smaller since most frequently a single pixel can be crossed by trajectories starting from different (even not so close) locations. In the case of the tract of the road threatened by the site S1, the 957 trajectories that could reach the road represented 0.6 % of the total number of simulated trajectories (152 300). This estimate was obtained by counting the number of pixels used as source area located uphill of the road in S1 and the total number of trajectories that reached the road in the mode map (Fig. 3a). Such a method represents a semi-quantitative estimate. Like other rockfall modelling software, STONE outputs a frequency map, whereas the evaluation of the probability of rockfall still represents an open problem due to the presence of the pixels where modelled trajectories overlap with others modelled from other source areas. Hence, a rigorous probabilistic estimation would require that each trajectory should be modelled keeping track of the source area. Possible future development of STONE or similar rockfall models should be able to define a probability value, which would allow better comparison of the rockfall hazard conditions in different areas.

STONE does not take into account the vegetation effect, although, in this case, the presence of a thick wooded area at the foot of the slope acts as a natural rockfall attenuator between the source areas and the road. As already pointed out by Guzzetti et al. (2004), despite the rockfall modelling being aimed at describing possible rockfall scenarios given the current state of the places, it appears poorly precautionary to consider the barrier effect of the trees in the final assessment. Future wildfires could leave the road unprotected, causing an increase in the overall rockfall hazard.

A non-negligible point of discussion consists in the caveats that should be taken into account when using model outputs that contain sources of uncertainty at some step of the procedure to support decision-making. In this case, for instance, a DSM at 20 cm GSD, which is inhomogeneous across the study area due to the presence of the tree canopy, was acquired. The entire DSM was resampled at 1 m GSD, which is the minimum working resolution of the model STONE and a reasonable resolution able to capture micro-morphological features and portray the general morphology reconstructed under the tree canopy by the GNSS RTK survey. Despite the average GNSS point density being one point per 100 m², the acquisition was planned to best represent the ground morphology, which is characterized by a series of two scarps and counter-escarpments probably built during the quarry exploitation. In our case, it was not possible to obtain a better acquisition because of the following practical limitations: (i) the GNSS signal under the tree canopy was unstable; hence almost every measure had to be repeated several times to obtain the minimum required accuracy of 1 m, and (ii) the GPRS signal was also poor, causing several interruptions in the RTK connection. For these reasons, when acquiring such data in the field, it is advised to collect as many data points as possible. Moreover, in places where the environmental conditions are unfavourable, acquisition should be performed to catch the most representative morphological features.

The overall cost of the materials (i.e. the RPAS, software licenses, GNSS receiver) used in our test case totalled about EUR 23 000, which is considerably less than lidar acquisition at a comparable resolution. The entire procedure was carried out in 4 working days (estimated to be about 15 working days for one person), including the initial survey, the RPAS and the GNSS acquisitions, the photogrammetric processing and the DSM filtering, and the integration of the RPAS DSM and the GNSS data points. The application of the presented procedure based on a RPAS acquisition has an overall cost that is lower compared to the same procedure involving an ALS survey.

Data are available at https://doi.org/10.17605/OSF.IO/VKGW8 (Santangelo et al., 2019).

MS contributed to the field survey and the geomorphological mapping, acquired the GNSS RTK data, analysed the results, and wrote the text. MA ran the model STONE and contributed to writing the paper. MB acquired and processed the RPAS data. MC contributed to the geomorphological mapping and reviewed the text. DG acquired and processed the RPAS data, analysed the results, and contributed to writing the text. FG contributed to the field survey and reviewed the text. IM acquired the GNSS RTK data, analysed the results, and contributed to writing the text. PR reviewed the text.

The authors declare that they have no conflict of interest.

In this work, use of copyright, brand, trade names, and logos is for descriptive and identification purposes only, and does not imply endorsement from the authors, or their institutions.