Many examples of rockfall simulation software provide great flexibility to the user at the expense of a hardly achievable parameter unification. With sensitive site-dependent parameters that are hardly generalizable from the literature and case studies, the user must properly calibrate simulations for the desired site by performing back-calculation analyses. Thus, rockfall trajectory reconstruction methods are needed. For that purpose, a computer-assisted videogrammetric 3D trajectory reconstruction method (CAVR) built on earlier approaches is proposed. Rockfall impacts are visually identified and timed from video footage and are manually transposed on detailed high-resolution 3D terrain models that act as the spatial reference. This shift in reference removes the dependency on steady and precisely positioned cameras, ensuring that the CAVR method can be used for reconstructing trajectories from witnessed previous records with nonoptimal video footage. For validation, the method is applied to reconstruct some trajectories from a rockfall experiment performed by the WSL Institute for Snow and Avalanche Research SLF. The results are compared to previous ones from the SLF and share many similarities. Indeed, the translational energies, bounce heights, rotational energies, and impact positions against a flexible barrier compare well with those from the SLF. The comparison shows that the presented cost-effective and flexible CAVR method can reproduce proper 3D rockfall trajectories from experiments or real rockfall events.
Many examples of rockfall simulation software provide great flexibility to the user at the expense of a hardly achievable parameter unification, as highlighted by Berger and Dorren (2006), Berger et al. (2011), Volkwein et al. (2011), Jarsve (2018), Garcia (2019), Bourrier et al. (2021), and Noël et al. (2021). Even when using the same rebound model, though it may be implemented in a different piece of software, the results using the same parameters may vary, as shown previously in Noël et al. (2021) when comparing CRSP 4 (Pfeiffer and Bowen, 1989; Jones et al., 2000) with RocFall 8 (Stevens, 1998; Rocscience Inc., 2022). The settings of the rebound model parameters are often specific to the model, rockfall software, and version used. Thus, it is difficult to transpose them from experimental results, such as the apparent coefficient of restitution from impact experiments. Indeed, even if rebound model parameters are classically called “coefficients of
restitution” (e.g.,
Therefore, it is often emphasized that proper calibration is important for simulations of the desired site, which is done by performing back calculation analyses on similar sites and on-site rockfall experiments (Jones et al., 2000; Labiouse, 2004; Berger and Dorren, 2006; Berger et al., 2011; Volkwein et al., 2011; Valagussa et al., 2015; Bourrier et al., 2021; Noël et al., 2021). For that purpose, it is necessary to evaluate the main trajectory paths of the rockfalls; their runouts; how the velocities, bouncing heights, and energies evolve along these paths and after each impact; and how the rocks deviate laterally. This raises the need for cost-effective and flexible 3D trajectory reconstruction methods to help gather and share the data needed for a site-specific calibration of rockfall simulations. Additionally, the gathered data could later be used for the improvement and development of more objective rockfall simulation methods that are less dependent on the inconvenient and expensive need to perform back analyses.
As illustrated by Volkwein and Klette (2014) and Caviezel et al. (2019),
different methods exist for reconstructing rockfall trajectories. Some
reconstructed parts of the trajectories in 2D as seen from above (e.g.,
Volkwein and Klette, 2014; Volkwein et al., 2018), and others did so using 2D vertical
profiles (e.g., Glover et al., 2012; Wyllie, 2014; Spadari et al., 2012;
Bourrier et al., 2012). Few reconstructed the trajectories in 3D space
and documented their lateral deviations (e.g., Dorren et al., 2005; Dorren
and Berger, 2006; Dewez et al., 2010; Hibert et al., 2017; Caviezel et al.,
2019; Bourrier et al., 2021). Of these, Dorren et al. (2005) and Dorren and
Berger (2006) used range finders with a tiltmeter and a compass to measure
the position of each impact, requiring time-consuming and potentially
exposed fieldwork to obtain the valuable field data. Dewez et al. (2010)
also reconstructed trajectories in 3D, but this time the rock positions
were remotely estimated from video footage using the cameras as references.
For that, their method required precisely synchronized and undistorted video
pairs captured with a wide field of view (FOV) of
This time-consuming manual process can be partly automated based on the method proposed by Caviezel et al. (2019), increasing the objectivity of the reconstruction process. This is done by producing dense 3D point clouds by photogrammetry from each synchronized undistorted frame of steady video footage captured from different viewpoints. The 3D points corresponding to the visible side of the artificial rocks facing the cameras are then extracted based on their contrasting artificial painted colors compared to the background. The center of mass of the rocks is estimated from the convex hulls formed by meshing the extracted 3D points.
Compared to Dewez et al. (2010), this automation process can introduce an erroneous shift in the reconstructed center of mass toward the cameras if the 3D points of the occluded backsides of the rocks not visible to the cameras are missing. However, this can be worked around by fitting 3D models of the controlled rock shapes onto their partial photogrammetric reconstruction. Additionally, ultra-high resolution (e.g., 8K UHD in Caviezel et al., 2019) and sharp contrasting of the falling rocks with their backgrounds are needed for feature recognition to compensate for the relatively wide FOV needed for framing the whole site from each fixed viewpoint. Due to recording data rate constraints, ultra-high resolutions and raw footage can limit the recording frame rate depending on the acquisition equipment (e.g., 25 fps in Caviezel et al., 2019), thus reducing the time resolution and related precision. Consequently, the method requires relatively high-end camera bodies coupled with proper sharp lenses and powerful computers for processing the associated data, producing thousands of frame-by-frame dense 3D point clouds and aligning them.
Despite being partly automated, the time-consuming processing complexifies the iterative visual validation that the reconstructed trajectories match with reality and fine-tuning processes following the first reconstructions. As a result, numerous reconstructed impacts with an energy balance above 1.00 involving an apparent gain in kinetic energy can be obtained with this method, sometimes with an increase for both the translational and angular velocities after impact, as shown in Caviezel et al. (2019, 2021). These abnormal impacts can be explained by energy transfers from the height differences between the beginning and the end of the impacts with long rock–ground interactions (Caviezel et al., 2019, 2021). As shown later in the paper, this may also be attributed to timing and positioning imprecisions, especially for impacts with short rock–ground interactions.
In this work, an alternative cost-effective and flexible computer-assisted videogrammetric 3D trajectory reconstruction method (CAVR) is proposed. It can be used in addition to the aforementioned approaches, as it brings complementary information when the video footage is not optimal, automatic tracking is not possible, or abnormal apparent kinetic energy gain is observed at impact. The improved method is built from the concepts of the previous methods, and it was preliminarily tested in Noël et al. (2017, 2018). It involves computer-assisted manual tracking of rocks and a high frame rate (e.g., 120 fps) for a precise time resolution, as in Dewez et al. (2010). The time-consuming tracking of the free-falling phases is, however, avoided, as this phase can be accurately and efficiently reconstructed from ballistic equations, as in Volkwein et al. (2011), Wyllie (2014), Glover (2015), and Gerber (2019) and similar to the method used in Bourrier et al. (2012) and Hibert et al. (2017).
As in Caviezel et al. (2019), the proposed CAVR method relies on the use of 3D models to estimate the position of the rocks. However, instead of generating thousands of frame-by-frame 3D photogrammetric models of the rocks, the proposed method uses one detailed textured 3D terrain model for the spatial reference coupled to the efficient 3D point cloud impact detection algorithm by Noël et al. (2021). The algorithm is used to locate (with proper offset) the center of mass of the rocks above the ground at impact. Contrary to the tracking methods of Dewez et al. (2010) and Caviezel et al. (2019), the cameras can be zoomed to narrow FOVs and be moved or panned to track the rocks, since the 3D detailed terrain model acts as the spatial reference instead of the cameras. This produces detailed close-up footage of the rocks and the surrounding terrain features that facilitate the visual identification of the impact points with the ground. Lens distortion is less problematic as it equally shifts the captured rocks with their surrounding terrain that acts as reference. It also increases the flexibility of the method, as different video footage can be used as input. Additionally, it reduces its cost by avoiding the need for high-end cameras and related processing equipment. The computer-assisted reconstruction process is semiautomatic, and the user obtains a real-time update of the 3D reconstructed free-falling parabolas forming the trajectory at the center of mass of the rock projectile that is properly offset from the ground. The impact point on the ground can be updated in real time following the mouse cursor on the screen. This incorporates the important visual validation of the reconstructed trajectories and iterative fine-tuning processes directly as part of the reconstruction process. This ensures the reconstruction of dissipative impacts (without apparent gain of kinetic energy) for impacts with short rock–ground interactions, as detailed later in this paper.
The proposed CAVR method relies on two inputs: the impact positions and their related time. The impacts are visually identified and timed from the high-frame-rate video footage, and they are manually transposed on a detailed corresponding 3D terrain model to obtain the 3D coordinates of their positions. In this paper, the common ballistic equations used for reconstructing the trajectories from these two inputs are first given with the other equations related to the different reconstructed values. Following this, since the video footage is a central piece for the method, especially if there is no impact mark on the ground to act as a guide, the details about the acquisition of the video footage and the related precision and accuracy are meticulously described. This is followed by short subsections concerning the 3D terrain model, the rock block geometric characteristics, and the validation of the reconstructed trajectories. A developed computer tool incorporating the described concepts to assist and homogenize the reconstruction process is then described. Finally, a comparison of methods is presented and discussed.
List of variables for the rockfall ballistics.
Rockfall trajectories can be reconstructed from the impact positions and the associated times. This section details the ballistic equations required for the reconstruction of the 3D trajectories, related angles, velocities, kinetic apparent coefficient of restitution, momentum, and energies.
Impact configurations for the reconstructed parabolas. Note how the offset of the impacts minimizes the common issues associated with the exaggerated parabola's lengths of impacts simplified to single points.
The airborne 3D rockfall trajectory segments are a sequence of oblique
throws, and their parabolic nature has been described previously by Galileo Galilei
(Drake and MacLachlan, 1975). The position, translational velocity, and
acceleration of a rock during its ballistic (free-falling) phase is defined
by Eqs. (1), (2), and (3) as follows:
Geometric configuration at impact of the reconstructed
translational velocity vectors and the related angles (see Table 1 for the
variable's descriptions). Note that such angles are measured based on the
normal vector to the terrain (
Apparent coefficients of restitution can be calculated for each impact from
the components of the obtained velocities (Fig. 2). They also correspond to
the ratio of momentum preserved by the rock projectile after each impact.
One should not use them directly as parameters for rockfall simulations
since they generally do not correspond to the parameters used in the rebound
models as mentioned in introduction and described in Noël et al. (2021).
The total, tangential, and normal apparent kinematic coefficients of
restitution are given by Eqs. (10), (11), and (12), respectively, as follows:
The rock's total deviation due to the impact is given by Eq. (17) as
follows:
As defined with the previous equations, it is possible to reconstruct rockfall trajectories with their velocity in between recorded impacts with a short rock–ground interaction period. The impact time and position are visually evaluated from video footage of rockfall events. The impact positions are then transposed onto a detailed 3D high-resolution terrain model used as the spatial reference to retrieve their precise coordinates. Such coordinates on the ground need to be offset to the center of mass of the rocks, requiring the acquisition of the rock block geometry. Finally, the reconstructed trajectories must be visually validated, ensuring that they are aligned with the falling rocks. Such steps and inputs are detailed in this section.
Because the detailed 3D terrain model is the spatial reference for the position of the impact, the reconstruction method is not constrained to the use of a special type of video footage or steady cameras with fixed viewpoints or lenses without distortion. Thus, it is well suited for reconstructing trajectories from previously witnessed records to help gather the data needed for site-specific calibration of sensitive rockfall simulations. Good video footage for this method is any footage where the position of the impacts can be visually located and timed. Therefore, “zoomed” footage with a narrow field of view (FOV), a manual panning to track the falling rocks, a high captured frame rate, and a high resolution adapted to the “sharpness” given by the acutance and resolving power of the lens is ideal for obtaining the most precision out of the method. The precision and the related acquisition setup concepts are detailed in the following subsections.
Conceptualization of the spatial accuracy from projecting the
picking accuracy to the terrain. The picking accuracy is degraded to
The optimal video footage for this method is any footage where a series of
successive impacts can be visually located and timed. The sharper and more
detailed the image around the impact point is, the easier it is to precisely
visually locate and time it. The resolving power of a camera system or of a
lens attached to the camera body can be measured with the modulation
transfer function (MTF). This optical performance measurement is often
expressed as the number of alternating black and white line pairs (lp) that
can be resolved on 1 mm of a camera sensor or film at a given
contrast (Rowlands, 2020). The more lines that are captured, the finer the
details that can be captured are. The more detailed the images captured are, the
more accurate and precise they are for transposing the impact positions when
picking their position on the detailed terrain model. The circular area of
the picking accuracy (
For an impact close to the center of the video frame, the simplified
projection of the circular area perpendicular to the camera viewpoint
generates a right circular cone with an aperture (
Examples of spatial accuracies from the projection of
Concerning the sharpness associated with the level of detail of the footage,
counterintuitively, lower-resolution footage with a narrow FOV can be better
than ultra-high resolution for this method. Sharp and detailed
ultra-high-resolution footage (e.g., at 8K UHD resolution,
Abacus showing the lens-resolvable line pairs given
by the modulation transfer function (MTF) for the corresponding video
resolution at maximum resolving capacity for different common sensor sizes
and perpendicular distant object diameters equivalent to four line pairs that
can be resolved through lenses of different fields of view (FOVs) given by
their 35 mm equivalent focal lengths. The equivalent focal lengths of the
Canon at 400 and Zeiss 55 mm lenses used on cameras with Super 35/
Combining the previous concept of the lens sensor resolving power with the precision and accuracy concepts of the previous section, the on-sensor resolving power can be transposed to a perpendicular distant object to predict the level of detail that can be captured in the center of the frame for a desired contrast (Fig. 5). As shown, the amount of captured detail at a lower resolution (e.g., at HD or FHD) with a narrower FOV can be very similar or even better than if captured at an ultra-high resolution with a wider FOV (Fig. 5). In the following paragraphs, the previous data captured at the Chant Sura rockfall test site with a wider FOV and steady cameras (Caviezel et al., 2020), referred to with the acronym “SLF 2020”, are compared to newer footage captured with a narrower FOV and manual tracking allowed by the CAVR method as acquisition examples (Fig. 5).
The WSL Institute for Snow and Avalanche Research SLF performed novel rockfall experiments with instrumented rocks at the Chant Sura test site (Fig. 6) that involved a 5 m tall by 60 m long 2000 kJ ROCCO flexible barrier from Geobrugg (Caviezel et al., 2019, 2020, 2021; Sanchez and Caviezel, 2020). They opened their experiment to the public with Geobrugg at the GEO summit 2019 conference and publicly shared part of the acquired data in Caviezel et al. (2020). The transparency of such an action toward open science should be emphasized. The accessible data can be very helpful to the geohazard community when assessing the sensitivity of current rockfall simulation software and for finding the right simulation parameters to be used for similar sites.
Simple camera setup based on the presented acquisition concepts
for the CAVR method tested here at the Chant Sura rockfall test site during
the 13 September 2019 SLF experiment. The white rectangle shows the
close-up area of the site used in Fig. 7 to compare the SLF RED video
footage to the FHD footage from this simple camera setup. The Samsung NX1
camera body from 2014 could deliver 4K UHD footage (6.5K full sensor readout
downscaled to 4K), but the lens from 1998 used here does not have the
resolving power for the resolution on the
Comparison of the FHD
In parallel to the common acquisition setup previously used by the SLF at
that site (Caviezel et al., 2019), the alternative CAVR camera setup
following the previously described concepts was deployed from one viewpoint
for the rockfall experiment performed on 13 September 2019 (some
footage is publicly available in Caviezel et al., 2020). The simple and
affordable alternative setup consists of a camera capturing at FHD
resolution, 119.88 fps, and a fast shutter speed, coupled to a zoom telephoto
lens used at 400 mm (
The CAVR narrower FOV FHD footage is compared to the SLF 2020 older 8K UHD high-end RED video footage from the SLF (Caviezel et al., 2020) in Fig. 7 for rocks sharing similar trajectories. The resolution of the CAVR narrower FOV footage is also downscaled to HD in Fig. 7c to compare with the SLF 2020 footage at 4K UHD downscaled from the 8K UHD visible in Fig. 7b. Even with a resolution reduced by half from FHD, it is possible to see that the sharpness of the CAVR narrower FOV footage at HD surpasses the SLF 2020 high-end RED footage. Indeed, the CAVR narrower FOV footage (Fig. 7a) resolves smaller distant objects, as foreseen in the abacus (Fig. 5) and confirmed by the sharper edges and the visible details around the bright outcrops. The CAVR narrower FOV footage following the previously described concepts shows more details and sharpness thanks to the narrow FOV used, despite having been captured with a 5-year-old camera body coupled with a 20-year-old telephoto lens at the time of performing the experiment.
The limitations by the lens, as previously observed on the older SLF 2020 footage, are likely to occur on super 35/APS-C sensors, even with the extremely sharp Zeiss Otus 55 mm f/1.4 used in Caviezel et al. (2019). Reducing the aperture could help (Fig. 5), as no lens is perfect when wide open, especially in the corners. This is especially true when the camera is kept still with the rocks moving across the frame and potentially reaching the corners. However, with the CAVR reconstruction method, one can pan to track the rock projectiles to keep them close to the center of the frame where lenses are most of the time at their best, allowing a wider aperture to be used without degrading the sharpness in the center. A wider aperture comes with a shorter exposure period from a faster shutter speed or a lower ISO sensitivity, reducing the motion blur or the noise level of the captured footage. With the panning motion, a narrower FOV can be used while tracking the moving rock, as with the FHD camera setup shown in Fig. 6. A camera body with a fast sensor read should be used to reduce the rolling shutter skew distortion with such a configuration.
Therefore, as conceptualized in Figs. 3 and 5 and shown in Fig. 7, more detail around the impact points can be obtained at lower resolution if the panning motion and the narrow FOV are combined for tracking the rocks. This in turn allows a higher constant frame rate and a faster shutter speed to be used, as often required for tracking the angular velocities and for timing the impacts. Lower-resolution file handling and playback are also simplified because the footage can be played fluently and edited efficiently on most common computers to add, for example, an overlaying time code and electronic image stabilization. Additionally, blurry footage can still be sufficient for timing impacts if they can be located from the impact marks left on the terrain. As the 3D detailed terrain model is the spatial reference for the impact positions and not the cameras, this CAVR method is flexible enough for use with the many types of video footage available. Thus, it is well suited for reconstructing 3D trajectories from nonoptimal previous records to help gather data needed for site-specific calibration of sensitive rockfall simulations. Consequently, valuable rockfall data, such as the data gathered by the SLF (Caviezel et al., 2021), could also be acquired with an affordable camera setup and from previously witnessed rockfall events.
A corresponding detailed 3D model of the terrain is needed to extract the coordinates of the impacts for reconstructing the trajectories. As covered in Noël et al. (2021), it can be acquired in many ways, e.g., by structure from motion photogrammetry (SfM) or by a airborne, mobile, or terrestrial laser scanner (ALS, TLS). The SfM method is preferable because it is often exempt of occluded part and properly captures the terrain roughness as perceived by the rocks (Noël et al., 2021). It can also texture the 3D model from the acquired pictures, which is very helpful to visually locate the impacts and extract their position coordinates when no indentation mark or scar is visible. Other methods can be textured from projected photos and orthophotos or from the return signal's intensity. Vegetation is often not a problem for freshly affected sites, since large rockfall events usually remove part of it. Artifacts and bushes might be present, however, and should be avoided when evaluating the impact position and the local terrain orientation. They can be highlighted by artificial shading methods, such as the eye dome lighting method (EDL) (Boucheny, 2009) or the ambient occlusion method (PCV) (Duguet and Girardeau-Montaut, 2004; Tarini et al., 2006). Local geomorphological features and impact marks are also highlighted with these shading methods (Fig. 8). These methods can also be combined with coloring methods based on the local terrain orientation (e.g., the Coltop method by Jaboyedoff et al., 2007, which is also implemented with a slightly different color distribution in the CloudCompare open-source software; Girardeau-Montaut, 2006). A comparison of two terrain models, from before and after the rockfall event(s), can also help highlight the impact marks if such models are available, as shown by Caviezel et al. (2019).
The same 3D scene with different rendering settings for the 3D terrain model. The EDL shading filter can be very useful for highlighting artifacts and impact marks. The scenes are rendered in a custom tool developed to help assist the reconstruction process, as described in Sect. 4. The trajectory under reconstruction shown in red with dotted white normal vectors from each impact mark visible on the ground corresponds to the block with the longest runout from the 2015 Mel de la Niva rockfall event (Noël et al., 2022; Lu et al., 2018). It transitions from longer free-falling phases to a “rolling–bouncing” phase.
It is then necessary to evaluate the rock block geometry to properly offset
the impact positions to the center of mass. It can be tempting to simply use
the impact positions without the offsets, but the resulting trajectories
would not have the right lengths, which is highlighted by Volkwein et al. (2011) as shown in Fig. 1, and incorrectly reconstructed velocities would be
obtained (see Appendix B for information about how the change in impact-to-impact distance
can affect the results). The rock geometry can be evaluated from on-field
measurements, with 3D models acquired by SfM, or by mobile and TLS methods.
The mass can be determined from the volume (
If the video frame rate is sufficient, the angular velocity can be estimated by counting the number of rock rotations completed over the free-falling period between the impacts. The main axis that the rock rotates around should be noted. The angular momentum and kinetic energy can then be estimated by selecting the corresponding moment of inertia. As this is time consuming, the method can be combined with the approaches from Volkwein and Klette (2014) and Caviezel et al. (2019) to retrieve the angular velocity from inboard gyroscopes.
It is recommended to visually validate if the reconstructed trajectory matches what is seen from the video footage. For this purpose, the trajectory can be loaded into 3D visualization software together with the terrain model. They can then be analyzed visually by placing the viewpoint from the same position as the cameras used to capture the event with perspective and a similar field of view. Properly reconstructed trajectories should be aligned with the rocks from the video footage. In other words, they should align with the same background elements on the terrain model (e.g., characteristic ground textures, bushes, or rocks on the ground) as those momentarily occluded by the falling rocks in the video footage when the rocks pass in front of them. This approach is later used to compare the older reconstructed trajectories from the SLF (Caviezel et al., 2020) with newer trajectories using the CAVR reconstruction method.
The total apparent kinematic coefficient of restitution (COR
To facilitate and homogenize the reconstruction process, we develop a tool with a graphical user interface (GUI) that incorporates the previously mentioned concepts of the reconstruction method. The 3D detailed terrain model can be visualized with a perspective from two viewpoints simultaneously (Fig. 9). The field of view can be adjusted to match the video footage. The pre-rendered terrain from the chosen viewpoints can be shown with only its textured RGB colors, only the EDL shader, or a combination of the two to facilitate the localization of the impact point and the eventual scars (Fig. 8). The terrain can be explored by panning around the camera point of view on either one of the two viewing windows, reproducing the panning motion from the video footage to track the rock projectiles. The other window then pans automatically to follow the same part of the terrain tracked in the center.
From there, a trajectory and impact number to be edited must be selected.
The frame number at which the impact occurs in the main video file can be
set. The impact time is then calculated from the constant frame rate set for
the video file (e.g., the 13th impact being reconstructed in Fig. 9 has
an impact time related to the beginning of the cropped video file of
It is possible to define an impact position on the ground either by directly pointing at the terrain model with the mouse cursor or by entering the coordinates manually. The normal to the terrain is then updated automatically in real time using the efficient impact detection algorithm that works on a detailed 3D terrain model while considering the rock size (Noël et al., 2021). The normal is shown as a white line perpendicular to the terrain in the footprint of the rock and follows the mouse cursor if the position is defined with it. The trajectory is then updated in real time and is properly perpendicularly offset to the terrain from the mouse cursor. The impact time can also be slightly adjusted by scrolling while picking the impact point with the mouse to see the effect on the reconstructed parabolas in real-time.
Graphical user interface for assisting the reconstruction process, shown here during the reconstruction of the trajectory of the eighth rockfall run performed by the SLF at the Chant Sura test site on 13 September 2019 (Caviezel et al., 2020; Sanchez and Caviezel, 2020). A trajectory being reconstructed is shown in red in the two viewing windows, with the impact points and normal vectors for the automatic offset shown in white. The on-ground impact position can be entered manually (minus a global shift translation to bring the coordinates close to a local origin) or set by clicking directly on the 3D terrain model. The reconstructed trajectory is updated in real time following the mouse cursor.
This emphasis on the real-time updating of the reconstructed trajectories is important because the validation and fine-tuning processes then become part of the reconstruction process. The goal for this process is, after all, to reconstruct data that match with what is observed as much as possible despite sometimes having to struggle with some unknowns or nonoptimal video footage. Therefore, having the flexibility to instantly see the reconstructed result when hesitating between two frames for the impact time or when hesitating regarding the impact location by a few centimeters to decimeters truly helps find the best parameters to make the trajectory match what is seen on the video footage. Of course, the quality of the reconstructed trajectories depends on the quality of the input footage and the 3D terrain model. Therefore, if it is impossible to see part of a trajectory and its bounding impacts on the footage or the terrain, this part should simply be discarded or kept for qualitative purposes only.
To further ease the reconstruction and validation process, some
reconstructed properties of the impacts are shown in two graphs (COR
In this section, the presented trajectory reconstruction method (CAVR) is challenged by being compared to the results of an existing peer-reviewed method. A comparison of the produced results can provide a validation that the presented method produces valid results. The concept of this comparison is as follows: if the rockfall trajectories are properly reconstructed, they should align with the real rock positions from the video footage. The reconstructed trajectories and energies should also correspond with those from the existing reconstruction method. Such a comparison would show that the presented flexible rockfall reconstruction method reproduces proper 3D trajectories from real rockfall events or experiments.
For this exercise, the CAVR method is used with the presented computer assisting tool to reconstruct the nine trajectories from the SLF rockfall experiment performed on 13 September 2019 at the Chant Sura site (Sanchez and Caviezel, 2020). The reconstruction is quickly performed in approximately 1 d for the purpose of this comparison, and with the nonoptimal configuration of using only one viewpoint. The 119.88 fps FHD video footage with a narrower FOV using the camera setup previously described (Fig. 6) is used for the reconstruction (footage available for the sixth and seventh rockfall runs in Caviezel et al., 2020).
The detailed digital terrain model (DTM) used as a spatial reference for the reconstruction corresponds to the model from before the experiment performed that day. The DTM is generated by the SLF with structure from motion photogrammetry using precisely geolocated pictures acquired with a DJI Phantom 4 RTK. For the reconstruction with the CAVR method, the terrain model is textured based on the orthophoto after the experiment using the publicly available terrain models and orthophotos from the SLF in Caviezel et al. (2020).
With one camera input per rock publicly available for that site at the time
of writing, it is not possible to independently reproduce the method of
Caviezel et al. (2019), which relies on video stereo pairs.
Therefore, the method comparison focuses on comparing the reconstructed
trajectories from the CAVR method with the rocks visible on the stacked
aligned FHD video frames. Nevertheless, the older 3D reconstructed
trajectories from the SLF (Caviezel et al., 2020) based on Caviezel et al. (2019) can be visually compared side-by-side with the newer trajectories
based on the CAVR method. The newer reconstructed trajectories, however,
differ by being offset to the center of mass of the rocks instead of being
reconstructed directly from the contact points on the ground, as illustrated
in Fig. 1. This side-by-side height difference affects the reconstructed
bounce heights by approximately half of
The intercepting reconstructed impacts at the 2000 kJ flexible ROCCO barrier from Geobrugg in Sanchez and Caviezel (2020) are used to refine the comparison with the reconstructed energies and bounce heights. Apart from the fact that the intercepted rocks were all stopped by the flexible barrier, the related information is here kept succinct, as the authors do not want to impinge on future publications focusing on the behavior of the flexible barrier. The reader is referred to Sanchez and Caviezel (2020) for more information about the novel experimental setup with the flexible barrier.
The reconstructed translational velocities and related energies, parabola
lengths, and vaulted shapes from the two side-by-side 3D reconstructed
trajectories (
Unlike in Caviezel et al. (2019, 2021), only dissipative impact processes
are obtained with the CAVR approach. Indeed, no apparent gain of kinetic
energy at impact that would be manifested by COR
Side-by-side comparison of the reconstructed translational
velocities, positions, translational energies, and bounce heights of the
reconstructed trajectories with the CAVR method compared to the older
trajectories from the SLF (Caviezel et al., 2020). The
The bounce heights from the center of mass of the rocks with the CAVR method
are always above the terrain surface and have values that rarely fall under
one radius of the rocks (
Most energy peaks from the typical sawtooth rockfall energy profiles align
and reach similar values between the two methods. This shows that the
presented flexible rockfall reconstruction method can reproduce proper 3D
trajectories from real rockfall events or experiments. Focusing on the few
abnormal local differences, the reconstructed translational energy values
mostly differ for
The reconstructed trajectory segments of the few abnormal energy mismatches
previously highlighted are detailed in Fig. 11. For proper trajectory
reconstruction, the impact position and timing must be chosen precisely by
deciding on the right free-falling period (see Appendix B about the
positioning and timing precision). The timed dashed pattern should follow
the appearance of each new stacked frame if the timing of the chosen period
is correct. The chosen bounding impact position for the beginning and the
end of the three free-falling reconstructed parabolas should also align with
the yellow frames with thicker added black contours corresponding to the
observed rock positions at the start and the end of each period. With the
timing and position of the bounding points of the parabola matching the
observations, the reconstructed parabolas from the CAVR method in Fig. 11a,
c, and e align well visually with the observed positions of the
free-falling rocks. Therefore, the resulting reconstructed translational
velocity and energy values are close to reality. Sharp detailed video
footage with a high frame rate for a precise time resolution following the
presented acquisition concepts, combined with the computer-assisted tool,
helps in the identification of the right free-falling period and the accurate transposition of the impact positions. In the 3D space, the
Conversely, choosing bounding impact positions further apart or free-falling
periods shorter than the observed would artificially boost the reconstructed
translational velocities as longer travel distances must be connected in
shorter periods. This can explain the three abnormal higher mismatching
reconstructed translational energies of the older reconstructed trajectories
from the SLF shown in Fig. 10e and f and detailed in Fig. 11b, d, and f. Such timing and positioning imprecision can also
contribute to some of the apparent gain in kinetic energy at impact
manifested by COR
Detailed portion of the three abnormally mismatching
reconstructed trajectory segments previously highlighted in Fig. 10e and f. The reconstructed trajectories repeatedly change colors every
For the intercepting impacts at the 2000 kJ flexible ROCCO barrier from Geobrugg, the reconstructed trajectories overlaid with the CAVR method on the stacked video frame using the same viewpoint in Fig. 12 show a good match with the artificial reinforced rocks. The automatically calculated white vectors normal to the terrain are used to obtain a proper offset at the center of mass of the rocks from the impact point chosen on the detailed 3D terrain model. With a proper offset and precise timing from 119.88 fps, which is 10 times more frames than those shown in the figures (Figs. 7, 10, 11 and 12), the reconstructed parabolas of the trajectories have heights matching the positions of the real rocks. Thus, the reconstructed velocities are close to reality. Slight visual misalignments are present in rare occasions, within a margin of approximately half of a radius of the related rocks in that case. For example, the 840 kg equant rock at the fifth contact point in line with the posts from the left appears slightly too far to the left or the impact with the ground preceding the impact with the fence of the outermost right trajectory is slightly too high. Therefore, these impacts could be refined further, especially if improved by using video footage from other viewing angles.
Reconstructed trajectories using the CAVR method overlaid on the stacked video frames of the different rockfall runs from the SLF experiment performed on 13 September 2019. For every 10 frames, only a single frame is shown for each trajectory from the 119.88 fps footage captured with the FHD camera setup shown in Fig. 6. All of these rocks that are intercepted by the flexible ROCCO barrier from Geobrugg are stopped (Sanchez and Caviezel, 2020). The reconstructed energies in line with the posts from both methods are put side by side.
Despite the slight visual misalignments, the impact positions and heights in
line with the posts match the impact fields and points from the nine sectors in
Sanchez and Caviezel (2020). The red points numbered from 1 to 7 from left
to right in Fig. 12 correspond to rockfall runs 1.3, 1.9, 1.4, 1.5, 1.2, 1.8,
and 1.1, respectively, in Sanchez and Caviezel (2020). The rotational
energies with the CAVR method are equal to or slightly above the older
values from the SLF. The differences between the two methods are relatively
low, with an average of
The differences are greater with the translational energy from the two
trajectory reconstruction methods. For the smaller rocks (approximately 800 kg), they are
With the publicly shared data, it is possible to use the CAVR method for the comparison of the nonoptimal single viewpoint configuration, highlighting the flexibility of the method to handle the variable available footage. It is demonstrated that the reconstructed trajectories align relatively well with the real timed rock positions from the stacked video frames. The velocities and energies also compare well with those from the older reconstructed trajectories of the SLF from the side-by-side comparison. The bounce heights, rotational energies, and impact positions against the flexible barrier also compare well with those from the SLF. Therefore, the comparison shows that the presented reconstruction method can reproduce proper 3D rockfall trajectories from experiments or real events, despite some discrepancies observed with the older reconstructed translational energies from the SLF. All methods can be improved, and the CAVR method is no exception. Therefore, opening access to the valuable input data as previously done by the SLF allows for the independent review of the data, the combination of different approaches, and the development of innovative solutions. The contribution enables transparent and open rockfall science to be very helpful for the geohazard community when assessing the sensitivity of current rockfall simulation software and for finding the right simulation parameters to be used for similar sites. This will hopefully also facilitate the development of more objective rockfall simulation models that are less dependent on inconvenient and expensive back analyses.
As has been shown in this paper, the implications of the CAVR reconstruction method can be
numerous. The reconstructed trajectories and associated information provided
can serve three main purposes. (1) The first purpose is facilitating the
calibration of rockfall simulations from back analysis. (2) The second
purpose is allowing a better understanding of the rockfall and impact
dynamics. (3) The last purpose is helping in the development of new
simulation rebound models. The presented flexible and cost-efficient
reconstruction method offers many benefits over automatic tracking methods
or frame-by-frame photogrammetry of video footage, especially for
reconstructing part of the trajectories of past rockfall events where video
footage is not optimal. Indeed, it works with nonoptimal video footage,
including the following issues:
blurry footage, unstable footage from a handheld camera, low-resolution footage, loss of sight of the rock for some frames, low contrast of the falling rock with the background, acquired from only one point of view.
Furthermore, the relatively light file handling helps by saving time and resources. Indeed, most current computer hardware can easily handle FHD footage. Scrolling through video timelines is not interrupted by frame drops, even at a high bitrate, and does not require a powerful graphics processing unit (GPU). Common affordable camera equipment can capture footage at an FHD resolution and should be combined with a bright telephoto lens with good resolving power and acutance at that resolution for the aperture range that is used. The provided abacus can be used to help plan video and photo acquisitions for similar experiments that rely on remote imagery. It can also be used in other situations to ensure that the inputs for photographic monitoring, photogrammetric models, or gigapixel panoramic images have the desired level of detail.
Moreover, the CAVR method can work with large rockfall volumes and high energy values unlikely to be experimented with artificially. The exposure to hazardous slopes is reduced since there is no need to measure the impact positions with GNSS. It does not require time-consuming installation of rock inboard sensors, and thus it is not sensitive to high angular velocity changes or acceleration at impact that could saturate the sensors. Additionally, it is not affected by sensor drift due to the accumulation of measurement errors. As a drawback of not using inboard sensors, it does not provide the fine details, such as the accelerations and changes in angular velocity that occur during the short contacts with the ground. The single-point impact information is rather generalized to the form of impulses but with detailed evolution of the free-falling phases, which provides data that fulfill the first purpose of facilitating the calibration of rockfall simulations from the back analysis and the two other main purposes to a certain extent. Instrumented rocks provide complementary valuable information depending on what is needed. Therefore, methods should be combined based on the desired advantages when needed.
The computer-assisted trajectory reconstruction with live visual validation
of the output parabola and COR
Concerning the understanding of rockfalls and impact dynamics, as well as helping the development of new simulation rebound models, the computer-assisted method reconstructs trajectories using an impact detection algorithm that ensures that the geometrical impact configuration is properly measured. The way the terrain is perceived by the rocks relative to their sizes is measured in the same way as how a rebound model can be applied for simulations. In that sense, further developments will consist of using this reconstruction method to acquire data from a previously witnessed large rockfall event and from a collaborative rockfall experiment, which will be analyzed in detail and combined with the reconstructed data from this paper.
For simplicity, the CAVR method, its ballistic equations, and comparison
results given as examples in this paper neglect the resistance due to air
drag. The method could, however, estimate the drag force (
Because the acceleration is not constant anymore, new position and velocity
equations could be found by integrating Eq. (A2) over time. Using the
Newton–Cotes trapezoidal rule with small time step increments (e.g.,
To illustrate the differences induced by air drag, an arbitrary
unlikely or unrealistic extreme bounce of a hockey-puck-sized ellipsoid rock
over an impact-to-impact distance (
For more realistic and applicable examples evaluating the differences induced
by air drag, the longest parabola and a following smaller parabola of the
reconstructed
Unlikely or unrealistic extreme bounce of a hockey-puck-sized rock
over an impact-to-impact distance (
Chosen parabolas to evaluate the significance of air drag on the
reconstructed results and the positioning and timing precision in Appendix B. Note that
The 2D vertical profile of the longest parabola of
The 2D vertical profile of the smaller parabola of
The ranges of obtained differences when considering drag vs. without drag
for reconstructing the trajectory segments of the two chosen parabolas are
shown in Fig. A2 and are detailed for the 2670 kg wheel- or disk-shaped rock of the
The obtained differences are lower than
As shown, neglecting the effect of the air resistance has little influence on the obtained results most of the time. Still, the effect of air drag might be significant in the case of reconstructing the trajectories of small free-falling rock fragments over long distances at high velocities. In that case, the method can be improved, for example, by implementing the air drag from Eqs. (A1) and (A2).
When the impact position cannot be resolved from visible impact marks on the
detailed terrain model and when the impact timing cannot be resolved from
rock inboard sensors or proximal geophones, both must be determined visually
from the video footage. Sharp and detailed video footage is of great help in
that case. When multiple cameras are used, they can be synchronized visually
from fast-changing objects, like the face of the rotating rock quickly
passing from being exposed to sunlight to shadow, or from the quick
projection of small fragments. Whatever timing method is used, the error in
the estimation of the free-falling period (
The obtained differences when comparing the reconstructed values at
different impact-to-impact distances relative to their references are
shown in Fig. B1a and b. Those related to different
Its incident parabola becomes more vaulted and with lower velocities, as shown by the increase in the incident and returned angles and decrease in corresponding velocities due to the shortened impact-to-impact distance or prolonged period.
Its returned parabola behaves in the opposite way due to its extended
impact-to-impact distance or shortened period. In such circumstances, a shift of 0.5 m in an impact bounded by two similar
parabolas would overestimate its COR
Fortunately, an erroneous position or time shift induces opposite changes in the vaults of the incident and returned parabolas, which can be noticed if they are pronounced enough during the visual validation and fine-tuning of the results. The impact can then be fine-tuned to balance the bounding parabolas until they match with the observations. This highlights the advantage of the computer-assisted reconstruction where the reconstructed parabolas updated in real-time can be quickly validated without time-consuming intermediate steps.
Differences induced by erroneous positioning or timing shifts for
the two reference parabolas of the
The video footage, 3D detailed high-resolution terrain models, and older reconstructed trajectories are available via
The 3D reconstructed trajectories for the side-by-side comparison are available as in the Supplement. As previously mentioned, they can be refined further.
The reconstruction tool can be customized for different rockfall test sites and camera setups and can be freely obtained upon request to the first author.
The impact detection algorithm applicable to 3D rockfall simulations from
Noël et al. (2021) can be freely obtained via
The supplement related to this article is available online at:
FN, MJ, AC, CH, FB, and JPM conceptualized the research. FN and AC oversaw the data curation. FN and MJ did the formal analysis. FN and AC contributed to the investigation. FN, MJ, and AC developed the methodology. FN, MJ, and AC oversaw the project administration. FN, MJ, and AC provided the resources. FN developed the software. MJ and AC supervised the experiment and the research. FN, MJ, AC, CH, FB, and JPM validated the reconstruction approach. FN designed and produced the figures. FN wrote the original draft. FN, MJ, AC, CH, FB, and JPM reviewed and edited the original draft.
The contact author has declared that none of the authors has any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors acknowledge American Journal Experts (AJE) for editing the English of the manuscript. A special thanks goes to the SLF and Geobrugg for the collaboration and access to the Chant Sura test site during the rockfall experiment on 13 September 2019. We thank Synnøve Flugekvam Nordang for her help with the reconstruction of the trajectories with the presented CAVR method and with the design of the figures. Finally, the authors would like to acknowledge the reviewers of the present paper.
This paper was edited by Wolfgang Schwanghart and reviewed by two anonymous referees.