The mitigation of fast mass movements entails a subtle interplay between field surveys, numerical modelling, and also experience. Hazard designers rely on a mix of ideal practices and, if available, historical facts together a critical prerequisite in establishing reproducible and also accurate peril zoning. Full-scale ar tests have actually been performed come reinforce the physical understanding of debris flows and also snow avalanches. Rockfall dynamics room - especially the quantification of power dissipation throughout the complex rock-ground communication - greatly unknown. The awareness of rock form dependence is growing, however presently, there exists small experimental basis on how rockfall danger scales through rock mass, size, and shape. Here, we existing a distinct data collection of induced single-block rockfall events comprising data native equant and wheel-shaped blocks through masses up to 2670 kg, quantifying the influence of rock shape and also mass on lateral spreading and longitudinal runout and also hence daunting common techniques in rockfall peril assessment.

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Two key factors in an exact quantification of rockfall risk are realistic approximates of the release conditions and also a sound evaluation of possible block propagation trajectories. Geologic, on-site, or remotely carried out studies define the location and spatial circulation of rock-face instabilities and, ideally, dominate the possible release scenarios in terms of volume, block mass, and shape as well as recurrence probability1,2,3,4,5,6. 3 dimensional, number rockfall tools room then applied to recognize propagation ranges to assess rockfall hazard7,8,9,10,11,12,13. Once the constitutive parameters administrate the rock-ground communication are collection for the corresponding model, the numerical simulations provide objective, spatially inclusive details on the relevant parameters of attention such together runout distances, run heights, and also kinetic energies as a duty of the digitised terrain. If the awareness that rock form dependence ~ above rockfall trajectory behaviour is fine established14, only the arrival of accessible computational method to incorporate facility shapes has triggered renewed attention in specific size and also shape therapy in rockfall risk assessments12,15,16,17,18,19,20,21,22,23 but equally its implications on number schemes11,12,13,24.

Establishing one experimental structure underpinning the non-smooth kinematics the rockfall activity presents the geohazard science and also engineering neighborhood with countless special challenges. The measurement methods used to catch the basically smooth propagation velocities that fluid-type natural hazards (see for example ref. 25 for debris operation or refs. 26,27 because that avalanches) can not be employed since they perform not have the spatial and also temporal resolution to record the sudden, short-duration affect phenomena administer rockfall motion. Several experimental studies that induced rockfall trajectories have actually been conducted9,28,29,30,31,31,32,33,34,35,36. Many of this studies emphasis on little numbers of rocks and/or rebounds, the is minimal falling distances. Current studies pave the means to a more complete and exhaustive experimental coverage of single-block experiments on a complete slope scale37,38 broadening experimental approaches for finish trajectory reconstructions comparable to previously pioneering studies30,34. These initial studies demonstrate the possibilities of brand-new experimental techniques, they still carry out not have the statistics basis, i.e., number of experiments, range of absent types, etc., come quantify power dissipation rates and also therefore calibrate modelling tools.

While the larger part of a rockfall movement is represented as a collection of tilt throws the follow ballistic trajectories through undisturbed rigid-body rotations, the facility rock-ground interaction leads to local and discrete energy transfer mechanisms. This provides the rockfall problem unique in natural hazards mitigation. Unlike other gravitationally driven dangers such as debris flows, or rock and snow avalanches, power dissipation mechanisms in the rockfall difficulty cannot it is in smoothed through modelling statistics averages of thousands of particle interactions v the soil and/or various other particles. Specific modelling the the rock-ground communication requires understanding the dynamic solution of the ground loaded by a single, spinning, and complex-shaped rigid body. Motion patterns such together sliding, slip-free roll (and combinations) boost the complexity and hence the an option of constitutive parameters administrate rebound and energy dissipation.

This study presents an unmatched dataset of induced single-block rockfall events. In regards to data volume, methodical sampling, and also consistent border conditions, the dimensions surpass existing rockfall datasets. Blend of external and in situ measure up methods39,40 enable exhaustive trajectory repair yielding info not just over the complete flight path including parameters of attention such together translational velocity vectors, angular velocities, ballistic run heights, and lengths but equally reveal insights in affect kinematics and also energy dissipation mechanisms. The gathered data can thus offer as a distinct calibration basis because that numerical rockfall models.

### The singing Sura experimental campaign

The presented Chant Sura experimental project (CSEC) consists of data collected over 12 separation, personal, instance days spread over the snow-free seasons of 2017–2019 at the chant Sura speculative site (46.74625∘N, 9.96720∘E) located on the Flüelapass, Switzerland (Fig.1). Check samples space perfectly symmetric, artificial test EOTA blocks, the norm absent of the European company for technical Assessment offered in standardised absent fence experimentation procedures in official European technological Approval Guidelines41. Greatly reinforced concrete blocks with weights of about 45, 200, 800, and 2670 kg—a subset of i beg your pardon are illustrated in Fig.1b—are cast and also repeatedly released from a hydraulic platform located at 2380 meter a.s.l. (see insets the Fig.1a). Initial problems vary just slightly in rock orientation ~ above the platform, positional deviations room negligible. The trajectory is initialised when the communication tilt permits the absent to slide off. Directional deviations of the individual trajectories are predominantly governed via geometrical configurations of the very first impacts. A previous little rock speculative campaign42 figured out equant and compact platy rocks as the worst-case scenario drivers. Thus, this two form variants that the EOTA rock room used, the equant EOTA111 with three the same axis lengths and the wheel-shaped EOTA221, where the wheel diameter is double as lengthy as the shortest axis.

Fig. 1: Aerial test site overview and also experimental impressions that helicopter-aided single-block rockfall experiments.

a Perspective outline of the rockfall test site Chant Sura situated on the Flüelapass, Switzerland, with its geographic location shown in the lower-left corner. A UAS-derived orthophoto is draped end the equivalent digital elevation version on height of a regular swisstopo map (Source: federal Office of Topography swisstopo). The relax platform is marked with a yellow pin. The ensemble of deposited rocks is indicated with red markers. The acceleration zone over the cliff, transition zone between cliff and scree line, and also runout zones/scree field are labelled. b reception of an EOTA\$$_221^2670kg\$$ by the ground crew in ~ the relax platform. c Slinging the a EOTA\$$_111^2670kg\$$ rock by a Kamov KA32 A12 ago to the release platform situated at 2380 m.a.s.l. d A subset that the supplied rocks all set for transportation: EOTA\$$_221^2670kg\$$ and EOTA\$$_111^2670,800,200kg\$$ native left to right. e steel reinforcement cage that a wheel-shaped EOTA\$$_221^200kg\$$ block come ensure maximal ruggedness and also lifetime.

The acceleration zone over the upper orange heat in Figs.2 and also 3 has actually soil qualities of dwarf shrubs while the change zone mirrors typical qualities of alpine meadow interspersed through rocks with a steep inclination in between 20–60 degrees. The flat runout is composed of a slightly dipping, unstable scree field. Two prominent spatial hallmarks are the virtually vertical cliff situated in the upper part of the slope and the scree line. Both space outlined with thicker present in Figs.1, 2, and also 3. The test rocks are equipped with sensor nodes moving with the absent in what is mathematically termed the Lagrangian reference structure to track parameters of interest in situ. The deployed StoneNode v1.1-343, a committed inertial measure up unit (IMU), mounted in the rock’s center of mass records accelerations up to 400 g and also angular velocities as much as 4000 ∘/s in ~ a data acquisition rate of 1 kHz. Because that a thorough presentation of the methodology consider37 and also the references therein. Rock transport is ensured via Airbus H125, H225, or Kamov KA32 A12 helicopters relying on the absent masses (see Fig.1c). The induced rockfall occasions are taped via exterior static, so-called Eulerian, measurements such together high-resolution videogrammetry because that optical projectile tracking. Camera constellations differ from single-camera setup up to static stereo-graphic videogrammetry via three spatially separated RED EPIC-W S35 Helium cameras record 8K video footage consists of a 25 frames per second image stream with picture resolution of 8192 × 4320 pixels. Most reliable high-speed synchronisation is achieved via a Tentacle Sync Lock-it collection enabling jitter-free frame-wise temporal pairing the the photo stream. High-accuracy differential GNSS handheld receivers such as the Trimble GeoXH and also Stonex S800 are supplied to measure endpoint and also scarring areas on the slope through an accuracy significantly below the degree of the deposited block.

Blue markers represent equant EOTA111 rocks differing from 45 kg (light blue) to 2670 kg (dark blue). Wheel-shaped EOTA221 deposition point out are displayed in magenta through masses indigenous 45 kg (light magenta) come 2670 kg (dark magenta). The corresponding centres the mass because that each rock category is suggested with a overcome circle in the exact same colour in addition to its an initial standard deviation ellipse.

Fig. 3: Complete set of 82 rebuilded rockfall trajectories of the CSEC and also their maximal jump heights.

Complete set of 82 reconstructed rockfall trajectories that the CSEC. The colour and size password of the deposition points is similar to Fig.2: Blue markers represent equant EOTA111 rocks varying from 45 kg (light blue) come 2670 kg (dark blue). Equivalently, the wheel-shaped EOTA221 deposition point out are represented with masses from 45 kg (light magenta) to 2670 kg (dark magenta). The translational kinematics are visualised with a velocity scaled, perceptually uniform, colouring48 the the trajectories. The inset corroborates the uniform kinematic behaviour throughout the shape and also weight great with comparable overall maximal run heights of every trajectory usually developing at the cliff jump (upper special grey line) together can likewise be derived from similar spatial velocity distribution of the trajectories.

For each experimental day, a high-resolution digital surface design (DSM) is produced pre- and post-experimentally via aerial remote sensing using various unmanned aerial equipment such together DJI Phantom 4 Pro, DJI Phantom 4 RTK, or the eBee+ equipped v 20–24 MP cameras. Trip planning is accomplished with the corresponding software tools to ensure precise navigation top top steep slopes and also sufficient image overlap, collection to 80% forward and also 60% next overlap. Flight altitude above ground level averages around 75 m and a mapping area that 0.2 km2 is covered. Roughly 500 photos were taken throughout each mapping job, yielding a really high suggest density that ~600 points/m2. To protect against systematic offsets in between pre- and also post-experiment flights, ground regulate points were spread for the absolute reference orientation and mapped utilizing a differential GNSS through tri-axial accuracies that 2–5 cm. The derived UAS imagery is processed making use of the latest AgiSoft PhotoScan pro v1.4.3-1.6.3, a advertising software generally used in the UAS community. The photogrammetric workflow ultimately provides a DSM resolution of 5 cm and also altitude unpredictabilities of ±3 cm, which permits the scaring mark detection in the matching differential DSM.

Figure2 reflects the complete collection of 183 deposition clues of the CSEC. Blue markers stand for equant EOTA111 rocks varying from 45 kg (light blue) to 2670 kg (dark blue). Wheel-shaped EOTA221 deposition point out are presented in magenta through masses indigenous 45 kg (light magenta) to 2670 kg (dark magenta). The respective centres of mass for each rock group are shown with a overcome circle in the same colour in addition to its an initial standard deviation ellipse for every the rocks reaching the runout zone.

### Four-dimensional trajectory reconstruction

In complete 82 absent trajectories were rebuilded in four-dimensional space—3 spatial coordinates and also time—visualised in Fig.3. Repair is perform in suitable case via equivalent temporal information around the influence and lift-off taken native the sensor streams linked with scarring places taken indigenous differential UAS surface ar models. The colour and size code of the deposition points room the exact same as in Fig.2, through blue mite representing the deposition point out of equant EOTA111 rocks varying through darker shades for heavier rocks. Equivalently, the deposition clues of wheel-shaped EOTA221 vary from light to dark magenta according to their weight class. The flight paths in Fig.3 room colour-coded by translational velocity, showcasing maximal velocities of roughly 30 m/s typically reached after the longest airborne free-fall step after the cliff. Every subsets consistently reach maximal velocities of 30 m/s in the cliff region. The translational kinematic behaviour is fairly uniform throughout the shape and also weight classes. Maximal run heights space 8.5 m for all EOTA111 blocks, if the EOTA221 samples function maximal run heights the 11.1/10.4/9.8 m because that the 200/800/2670 kg great plotted as an inset the Fig.3. Often, the rocks descend close to the ground, skimming the surface and also spinning rapidly, spanning the 250 m between release and deposition in less than 25 s. Maximal resultant angular velocities of 1000–5000 ∘/s (5.56π–27.78π rad/s) space measured. The insets highlight the comparison of angular velocities because that both shape classes. Throughout a usual descent, a rock rises its angular and also translational velocity throughout the acceleration/stabilisation phase. On this slope, this happens in the pre-cliff zone over the top thick grey heat in Fig.3. Here, wheel-shaped rocks often tend to stabilise about their largest moment that inertia—if no stopped immediately due come a landing ~ above their level side at short speed, check out uppermost deposition point out in Fig.2 and also hence have been skipping in the calculation of the deviational ellipses. Decreasing maximal rotational speeds with an enhanced moment the inertia in addition to the almost exclusive uni-axial rotations approximately the principal for wheel-shaped rocks room discernible both in the insets that Fig.3 as well as in Fig.4.

Fig. 4: Gyroscope data streams throughout all shape and weight classes and their derived benchmark measures, together as mean rotational relationship, wobbling frequencies, and also energy ratios.

a Gyroscope data streams for all measured absent shapes and masses. Grey lines separate the acceleration zone above the cliff, shift zone between cliff and scree, and also scree runout zones. Separation, personal, instance lines represent x-, y-, z-axis and its result angular velocities (thicker line). Diminish maximal rotational speeds through an increased moment the inertia along with the nearly exclusive uni-axial rotations about the major axis because that wheel-shaped rocks is visible, i.e. Practically perfect overlap in between the top axis and resulting axis except the acceleration phase. Here, various colour shades represent various rock axis. b review boxplot—median values with standard whisker coverage that 99.3% (2.7σ)—of the StoneNode gyroscope output from the entire Chant Sura experimental campaign with its mean rotational relationship as a feasible benchmark indicator for unobstructed slopes plotted in (c). d Wobbling frequency contents of to decrease rocks. e Rotational energy percentage that the presented operation in (a). Colour code for bc is tantamount to Fig.2: Blue markers stand for equant rocks differing from 45 kg (light blue) to 2670 kg (dark blue), Wheel-shaped rocks are presented in magenta with masses from 45 kg (light magenta) come 2670 kg (dark magenta).

Of interest for rockfall hazard assessment is that the total spreading edge of every trajectories is 38 degrees. The dispersing angle the the equant rocks reduces indigenous \$$\\phi _111^45kg=32^\\circ \$$ to \$$\\phi _111^200kg=23^\\circ \$$, \$$\\phi _111^800kg=27^\\circ \$$ as low as \$$\\phi _111^2670kg=13^\\circ \$$. Wheel-shaped rocks display screen inverse spreading behaviour with increasing spreading angle from \$$\\phi _221^200kg=30^\\circ \$$, \$$\\phi _221^800kg=32^\\circ \$$ to \$$\\phi _221^2670 kg=36^\\circ \$$. Moreover, the wheel-shaped rocks figured out the maximum spread out of the trajectories, if the equant shaped rocks show only marginal spreading. The dispersing angle shows up to it is in defined instantly after release; that is, countless of the wheel-shaped rocks followed straight trajectories when uprighted and also stable. This is a strong indication that the early wobble phase automatically after relax determines absent spreading. This fact can be exploited in rockfall hazard assessment.

### StoneNode data—Lagrangian methods gather inside information

The sometimes sensor failure in together a very dynamic environment is inevitable. The StoneNode sensor proved itself as extremely rugged equipment. Mechanical fail of the internal accelerometer cause data lose in five runs, a wrong compiler setup on the gyroscopic sensitivity programming cause 29 taped runs with endangered data quality. The key limitation for sensor data availability in the individual runs, was the variety of available sensors come equip all rocks, together they to be prototypically arisen during the very first part the the CSEC. The all at once sensor stream ease of access amounts to 66% because that accelerometer data and 63% for gyroscope data. Figure4a compares the gyroscope sensor calculation from both form classes throughout the investigated load categories. Clearly shows is the slope-specific bell curve evolution of angular velocity. The decreasing absolute resulting rotational speed with an enhanced moment that inertia as well as the nearly exclusive uni-axial rotations around the principal axis because that wheel-shaped rocks are primary features. To range the slope specificity because that a offered weight or shape class to a solitary measure the extrapolated approximated mean rotational speeds for various mass classes are shown in Fig.4c. If 10 kg rocks room expected to rotate up to 4000 ∘/s (11 Hz) the decreases to 130 ∘/s because that a 100 t block (0.36 Hz). The empirical power-law

$$\\bar\\omega _111=a_111\\cdot m^-0.37\\pm 0.06\\quad \\,\\mboxand\\,\\quad \\bar\\omega _211=a_221\\cdot m^-0.44\\pm 0.12$$

with the scaling parameters a111 = 9278 <∘ s−1kg0.37> a221 = 12480 <∘ s−1kg0.44> and mass m can carry out a calibration basis across the entire mass spectrum because that both shape classes because that this slope. Here, the shape specificity vanishes within the uncertainty, which corresponds to the uniform kinematic behaviour throughout shape classes. Equant rocks present tumbling behaviour, definition low frequency, huge amplitude oscillation in the minor axis extracted as its Fourier change spectra in Fig.4d. Wheel-shaped rocks on the other hand attribute a higher frequency, quicker wobbling about their young axis, rather insignificant with respect to the in its entirety rotational behaviour. Figure4e visualises the energy ratio advancement upon descent for the liked runs of Fig.4a. The maximal rotational energy ratio of 40% have the right to serve together the top limit estimation for energy threshold estimation for rockfall barriers.

The use of Lagrangian methods, i.e., in situ instrumentation, permits for comparably effortless extraction of crucial parameters as soon as the access of rugged sensor nodes spanning the required parameter varieties is given. Over all, equivalent angular velocities between simulation results and experiments is a seal of top quality for simulation password that relates come rigid-body approaches and also needs to calculate rock-ground interactions through its full geometrical and also kinematical complexity. The gift rotational magnitudes and also their empirical regulation may serve as a benchmark for calibration routines.

### The stiletto effect: area-dependent power dissipation

The 82 reconstructed trajectories consist of on typical of eighteen parabolic sections, and also a total of 1394 results can be analysed throughout all the weight and also shape classes for translational degrees of freedom, 656 impacts furthermore feature valid gyroscope information. The parabolic sections resulting from impact reconstruction always range from mentioned lift-off to subsequent affect location at the differential DSM. Every parameters of interest (POI) such together position, kinematic variables, StoneNode readings such together angular velocities and acting accelerations are extracted at any kind of given reconstruction suggest and permit to derive an additional variables such together translational and rotational energy. Impact analysis is composed of extract POI at the endpoint of one parabolic section and the lift-off POI that the succeeding parabolic section. Each impact corresponds therefore to a offered scar length from influence point to lift-off point. The full energy is specified as Ekin = Etrans + Erot and also reduced come Etrans in instance of gyroscope sensor failure. The mean soil-impact energy dissipation normalised every rock mass quantities to \$$\\Delta E_\\rmkin^kg=-0.042\\pm 0.005\$$ kJ/kg independent of absent shape and form. When furthermore normalising come the penetrating cross-section area as presented in Fig.5a, one empirical mass and area normalised energy dissipation power-law emerges

with b = −9 as depicted in the insets of Fig.5a. Figure5b depicts the pure mass and also cross-section normalised angular velocity readjust per impact. The deducted empirical power-law complies with a m−1.49±0.02 dependency because that cubic EOTA111 rocks, and m−1.2±0.1 for platy EOTA221 rocks, respectively, as shown in the insets the Fig.5b. The extrapolation and validity of those empirical fitting laws to smaller and larger masses and their site-specificity need to be proved in further studies. Future data sources can be additional experimental projects conducted under similar, controlled problems at different locations or the usage of publicly obtainable results of scientific literary works that follow a similar data collection technique given the temporal information in the trajectory data is available. Figure5d mirrors the shape-class-dependent angular velocity transforms upon 1361 analysed impacts across the various weight and also shape classes. Horizontal lines note the maximal rise or decrease in angular velocity featuring the expected inertia dependency.

Fig. 5: fixed and affect cross-section normalised energy dissipation and also angular velocity transforms for every analysed impacts.

a The stiletto impact in rockfall—mass and affect cross-section normalised power dissipation boxplot for the three larger weight classes. Insets current empirical power laws for both form categories through its 1σ-prediction bounds. b Impact-induced changes in pure angular velocity scaling through mass and surface area. Insets current empirical power regulations for both shape categories through its 1σ-prediction bounds. Both boxplots function median values v standard whisker coverage the 99.3 % (2.7σ). c Velocity dependence of load and affect cross-section normalised energy dissipation of 1394 analysed results for the three larger weight classes. The smaller sized the absent cross-section the an ext pronounced the effect—equivalently come a human being running in stiletto high heels as opposed to sneakers. The lines represent exponential fits come the different weight and also shape great in the general colour code and also serve as a overview to the eye. Upward facing triangles mark results in the acceleration zone, one in the shift zones, and also downward facing triangles in the runout zones. d Angular velocity transforms upon 656 analysed impacts across the various weight and also shape classes impact areas. Horizontal lines mark the maximal readjust in angular velocity per load class. Equivalent color code as in Fig.2 used.

Figure5c depicts the mass-normalised energy dissipation per affect with increasing influence velocities. The included lines represent exponential fits come the various weight and also shape class in the developed colour code and also serve together a overview to the eye. It confirms the intuition, the soil results of faster projectiles dissipate an ext energy as they generally penetrate further into the floor for identical soil problems than smaller rocks. This is fan to the fact, that the compressibility of the impacted soil is limited to a velocity-dependent maximal penetration depth44. This maximal penetration depth is dependent on floor composition and influence configuration, an interpretation larger and also faster rocks develop larger scars upon impact. The available travelling street for inert reversal therefore can reach an upper limit and scarring street remain lower for slow projectiles. Analogously to the high-pressure lots of a person walking in stiletto heels, smaller sized rocks dissipate significantly much more energy contrasted to larger ones fan to their smaller sized cross-section. This stiletto impact for rock-ground interactions scales with the travelling velocities together is shown in Fig.5c, similar to a to run person. It likewise remains shape-independent together the empirical fit lines group according to their weight classes. The presented data indicates that for particular load cases with tiny rocks, neighborhood peak energies may play a duty leading to the so-called \"bullet effect\", the perforation of a rockfall security mesh by an impact of a little block45, and with rocks bigger than 1 m3, the velocity dependency in energy dissipation requirements only consideration starting from around 25–30 m/s. The occasional impact with confident ΔEm&a deserve to be attributed to special rebound conditions—in state of affect geometry and also local influence conditions together for example on a downhill lean smooth rock confront in enhancement with a considerable potential energy intake when the impact happens top top steep terrain. A major uncertainty in the reconstruction arises indigenous impact/lift-off position placement and an outcome in reconstructed velocity unpredictabilities of ±0.5 ms−137. Figure5d plots the mass and area normalised absolute rotation adjust of every exploitable and its bespeak of magnitude move of rotation alters for the different mass classes.

The two vital physical difficulties that have to be solved to boost rockfall hazard assessment are: (1) determining just how rocks laterally disperse from a given release resource in herbal mountain terrain, and (2) expertise the ns of translational and also rotational kinetic energy throughout short-duration results with the ground. Power dissipation throughout the floor interaction defines rock speed, jump heights, and finally runout distance. Rockfall models must have the ability to correctly predict these worths for accurate hazard assessments.

Here, we current the results of a multi-year experimental campaign resulting in one unprecedented, comprehensive data list of single-block-induced rockfall experiments. The significantly higher lateral spread of wheel-shaped rocks is striking and also highly pertinent for risk assessments. When upright, the wheel-shaped rocks show up to follow directly trajectories on wide, open up slopes, unencumbered by young slope alters perpendicular to your direction of motion. Fluid-type gravitational movements, choose debris flows and also snow avalanches, would certainly react to these slopes, easily following the heat of steepest descent. The trajectories that wheel-shaped rocks resist this tendency, with the end effect that rocks can escape channels and terrain undulations, thereby boosting the broad of the peril zone.

We supplied the trajectories come quantify the change in rotational speed Δω and adjust in translational kinetic power ΔE during each soil interaction. We discovered that Δω111 ∝ 1/m0.83, Δω221 ∝ 1/m1.1, and ΔE ∝ 1/m0.70. If we let the absent mass m it is in approximated by a perfect ball of radius r, then m ∝ r3. We uncover approximately,

$$\\Delta \\omega _111\\propto \\frac1r^2.4\\,\\,,\\,\\,\\Delta \\omega _221\\propto \\frac1r^3.3\\,\\,\\,\\mboxand\\,\\,\\,\\Delta E\\propto \\frac1r^2$$

This is a much stronger radius dependence together the Δω ∝ 1/r behaviour of a stick-slip-rolling transformation of an ideal sphere projected follow me a unstable horizontal surface46. Frictional forces at the roll interface use a force and equivalent torque in ~ the rock’s centroid. Thus, the compilation of every the chant Sura dimensions indicates, that pressure tractions ~ above the rock’s surface manage both the rotational and translational changes in kinetic energy and also rock kinematics. Further evaluation might focus on disentangling increasing and decelerating behaviour and potentially identifying an optimal rock radius concerning energy buildup and dissipation during impacts.

This an outcome underscores when again the prominence of rock shape. In actual applications, for irregularly shame rocks, the radius r alters from influence to influence depending on the terrain slope and rock orientation; the traction force alters with the properties of the ground material. The difference between the measurements and also this ideal result should now be exploited come quantify traction forces for irregularly shame rocks impacting various ground types. The results presented here provide a thorough overview the the kinematic action of two distinctive rock shape classes approximately 1 m3 volume top top the test site Chant Sura. When translational kinematics current themselves uniform across all shape and also weight classes, solid shape dependence is found on the lateral spread and rotational axis stabilisation. Generalised, site-specific relationships for rotational and also energy dissipation behaviour room postulated and also may serve as calibration measures. Despite an extremely high level of detail in the data, solitary impact configurations are not resolvable down to their exact influence configuration and also location. Future sensor node advance coupling number of sensor nodes to a solved configuration can overcome the restoration limit given by error build-up through integration of solitary IMU nodes and carry out the missing information. The confirmation or adaptation that the proposed connection for different site configurations will certainly be of major interest for future work. Feasible necessary changes through topographic peculiarities such together couloirs or cliffs, the result of forests, and different lithology stay of importance. Future studies aim in the direction of rotational energy dissipation instrument upon effects in general and during rock-barrier interaction in flexible rockfall barriers in particular.

The main message of this work is thus to incorporate shape effects in state-of-the-art models offered for danger zoning13, defining hazard scenarios no only simply via block sizes but equally—if applicable—block shapes, the is incorporating a collection of site-specific, realistic rock shapes in risk assessments. As equivalent datasets are scarce to non-existent, the now publicly available CSEC dataset47 permits the geohazard ar to re-evaluate many of the currently models, which have actually been calibrated based on oversimplified assumptions and also data sources. It offer as second contribution to experimentally dissect rockfall propagation processes and also could offer as a structure ground because that more complex impact models because of its high number of recorded separation, personal, instance impacts. It permits detailed future sub-studies of different call models and energy dissipation mechanisms and the application of advanced machine learning algorithms as test ground because that suitably tuned neuronal networks for the investigation of inertial measurement unit sensor data. At last, the dataset can serve as a calibration landmark for any numerical model and hence leader to more accurate danger assessment and ultimately higher safety spare for cultures in rockfall vulnerable environments.

The hymn Sura Experimental project dataset created in this study has actually been deposited in the EnviDat repository under Caviezel, Andrin et al. (2020). Induced Rockfall Dataset #2 (Chant Sura speculative Campaign), Flüelapass, Grisons, Switzerland. EnviDat. Https://doi.org/10.16904/envidat.174.

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D’Amato, J., Guerin, A., Hantz, D., Rossetti, J.-P. & Jaboyedoff, M. In engineering Geology for society and territory (eds. Lollino, G et al.) vol. 2, 1919–1923. (Springer worldwide Publishing, 2015).

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Leine, R. I., Capobianco, G., Bartelt, P., Christen, M. & Caviezel, A. Stability of 6-dof rigid body motion: application to rockfall simulation. Multibody Syst. Dyn. 52, 431–455 (2021).

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Dewez, T., Kobayashi, H., Mathon, C. & Nachbaur, A. Programme arai2. Ofai, expérience de lâchers d eblocs en polynésie française pour calibrer les modèles de trajectographie en contexte volcanique tropical. Rapport final. 322 (2010).

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Niklaus, P. Et al. Stonenode: A low-power sensor an equipment for induced rockfall experiments. In IEEE Sensors Applications Symposium (SAS), 1–6 (2017).

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We say thanks to the municipality of Zernez, Switzerland, because that their consistent support and also permission to conduct experiments on the hymn Sura test site. Special thanks go come HeliBernina, Heliswiss international AG, and also Heli air AG for their repeated precision slinging work. We give thanks to Matthias Paintner and also Kevin Fierz for their support and guidance v the 8K videogrammetry.

### Affiliations

WSL Institute for Snow and also Avalanche study SLF, Davos, Switzerland

Andrin Caviezel, Adrian Ringenbach, Sophia E. Demmel, Claire E. Dinneen, Nora Krebs, Yves Bühler, Marc Christen, Guillaume Meyrat, Andreas Stoffel, Elisabeth Hafner, Lucie A. Eberhard, Daniel von Rickenbach, Kevin Simmler & Perry Bartelt

ETH Zurich, integrated Systems laboratory IIS, Zurich, Switzerland

Philipp Mayer, Pascal S. Niklaus, Thomas Birchler, Tim Aebi, Lukas Cavigelli, Michael Schaffner, Stefan Rickli, Christoph Schnetzler, Michele Magno & Luca Benini

### Contributions

A.C. Conceived the experiment. A.C., A.R., S.E.D., Y.B., M.C., G.M., A.S., E.H., L.A.E., D.v.R., K.S. And P.B. Lugged out the experiments. P.M., P.S.N., T.B., T.A., L.C., M.S., S.R., C.S. And M.M. Arisen StoneNode Sensors and also analysed sensor data. A.C., A.R., S.E.D., C.E.D. And N.K. Analysed the data. A.C and also P.B. Wrote the manuscript v discussions and also improvements from all authors. L.B. And also P.B. Oversaw the work.

### Corresponding author

Correspondence come Andrin Caviezel.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Caviezel, A., Ringenbach, A., Demmel, S.E. Et al. The relationship of rock form over mass—implications for rockfall risk assessments. Nat Commun 12, 5546 (2021). Https://doi.org/10.1038/s41467-021-25794-y