Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulation

The stability properties of a freely rotating rigid body are governed by the intermediate axis theorem, i.e., rotation around the major and minor principal axes is stable whereas rotation around the intermediate axis is unstable. The stability of the principal axes is of importance for the prediction of rockfall. Current numerical schemes for 3D rockfall simulation, however, are not able to correctly represent these stability properties. In this paper an extended intermediate axis theorem is presented, which not only involves the angular momentum equations but also the orientation of the body, and we prove the theorem using Lyapunov’s direct method. Based on the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints. In particular, we show how this scheme is incorporated in an existing 3D rockfall simulation code. Simulations results reveal that the stability properties of rotating rocks play an essential role in the run-out length and lateral spreading of rocks.

Impact-Detection Algorithm That Uses Point Clouds as Topographic Inputs for 3D Rockfall Simulations

Numerous 3D rockfall simulation models use coarse gridded digital terrain model (DTM raster) as their topography input. Artificial surface roughness is often added to overcome the loss of details that occurs during the gridding process. Together with the use of sensitive energy damping parameters, they provide great freedom to the user at the expense of the objectivity of the method. To quantify and limit the range of such artificial values, we developed an impact-detection algorithm that can be used to extract the perceived surface roughness from detailed terrain samples in relation to the size of the impacting rocks. The algorithm can also be combined with a rebound model to perform rockfall simulations directly on detailed 3D point clouds. The abilities of the algorithm are demonstrated by objectively extracting different perceived surface roughnesses from detailed terrain samples and by simulating rockfalls on detailed terrain models as proof of concept. The results produced are also compared to that of rockfall simulation software CRSP 4, RocFall 8 and Rockyfor3D 5.2.15 as validation. Although differences were observed, the validation shows that the algorithm can produce similar results. With the presented approach not being limited to coarse terrain models, the need for adding artificial terrain roughness or for adjusting sensitive damping parameters on a per-site basis is reduced, thereby limiting the related biases and subjectivity.

Rockfall hazard in the Imja Glacial Lake, eastern Nepal

In Nepal, rockfall related studies are rarely conducted and are limited to the landslide study along with few case studies on rockfall events. Rockfall problems in Nepal are more frequent in the Higher Himalayan region than Midland and Lesser Himalayan regions. In the glaciated valley and glacial lakes, rockfall and associated tsunami like huge wave are a recently initiated research. In this context, a glacial lake of the Himalaya, named as Imja Glacial Lake situated in eastern Nepal has been selected to understand the rockfall problems and their possible consequences. The lake was formed at the end part of the Imja glacier. The northern valley slope of Imja Glacier Lake, i.e. southern slope of the Island Peak has serious problem of rockfall into the lake. Rockfall simulation was performed during this research with field data. Three different Plots were defined for simulation of rockfall. Among them, Plot III seems to be the most hazardous since the detached boulders on the higher elevation can enter into the lake with the maximum velocity of 40 m/s with pre-impact energy more than 3500 kJ. This can develop a surge in the lake water that can break moraine dam. This leads to a serious threat to the downstream communities. Moreover, this research confirms that the rockfall hazard in the higher mountain region of Nepal is critical to creating flash floods due to tsunamis like surge in the lake water and breaching of the dam.

A New Methodology for Mapping Past Rockfall Events: From Mobile Crowdsourcing to Rockfall Simulation Validation

Rockfalls are one of the most common natural hazards in mountainous areas that pose high risk to people and their activities. Rockfall risk assessment is commonly performed with the use of models that can simulate the potential rockfall source, propagation and runout areas. The quality of the models can be improved by collecting data on past rockfall events. Mobile crowdsourcing is becoming a common approach for collecting field data by using smartphones, the main advantages of which are the use of a harmonised protocol, and the possibility of creating large datasets due to the simultaneous use by multiple users. This paper presents a new methodology for collecting past rockfall events with a mobile application, where the locations and attributes of rockfall source areas and rockfall deposits are collected, and the data are stored in an online database which can be accessed via the WebGIS platform. The methodology also presents an approach for calculating an actual source location based on viewshed analysis which greatly reduces the problem of field mapping of inaccessible source areas. Additionally, we present a rockfall database in the Alpine Space that has been created by the presented methodology, and an application of collected data for the calibration and validation of two rockfall models (CONEFALL and Rockyfor3D).

Identifying past rockfall trajectories and runout distances from detailed 3D terrain model: The case of the Mel de la Niva mountain, Switzerland.

<p>When planning for the implantation of transport infrastructures or buildings, it is necessary to identify the land zones that can be reached by rockfalls. These zones should then be avoided if possible, or stabilisation and risk mitigation measures must be considered. 3D preliminary rockfall simulations can be used to help finding the areas where inspections should be prioritised. Using orthophotos, a detailed shaded representation of the terrain and field work, geologists can then note the position of the deposited blocks and sources from past events, among other things. Collecting this information can however be complex, and the blocks can sometimes be mistaken for glacial deposits.</p><p>To increase the accuracy of this inspection task, the land can be analysed using a 3D detailed terrain model with artificial colors based on its aspect orientation and slope steepness and artificial shadows based on the ambient occlusion and eye dome lighting methods. Scars left by past rockfall events are then highlighted and some trajectories can be reconstituted. This method can help isolating identified rockfall deposited boulders from erratic blocks and help finding where is the source from. It can also draw attention to the location where a block has settled by showing parts of its trajectory. A relative aging can also be attributed based on the sharpness of the scar edges, with older events appearing smoother or partly erased. This can help estimating the activity of the site when no other information is known.</p><p>We applied this method to the Mel de la Niva site in Switzerland while analysing the two main rockfalls from the 2015 event. The 3D model used was created from SfM photogrammetry using pictures acquired on the field by manually flying a DJI Phantom 4 drone over the terrain. The method allowed to identify 1 rockfall that followed the main 2015 event and 7 rockfalls that preceded it, which is quite interesting. Indeed, if activity is observed on a site, inspection of the source cliff should be done to try to identify if a larger event is about to occur.</p><p>These identified rockfalls trajectories were validated using a time series of available orthophotos from SWISSIMAGE. Two paths were present before the oldest photo from 1983. Three appear on the 1999 photo. They then happened in between the previous photo from 1995 and the 1999 one. One happened in between the 1999 and 2005 photos. One happened in between the 2010 and 2013 photos and one in between the 2016 and 2017 photos.</p><p>The 8 identified trajectories combined with the 2 from 2015 also have an interesting shape. They tend to not directly follow the steepest path of the terrain. This behavior seems to be frequent, especially when the blocks are disk-shaped, and it has also been observed and partly quantified from the rockfall experiment we presented here last year (2019). Data from the Mel de la Niva site has been added to our rockfall database and it will used for the calibration and further developments of our rockfall simulation model.</p>

Simulation of fragmental rockfalls detected using terrestrial laser scans from rock slopes in south-central British Columbia, Canada

Rockfall presents an ongoing challenge to the safe operation of transportation infrastructure, creating hazardous conditions which can result in damage to roads and railways, as well as loss of life. Rockfall risk assessment frameworks often involve the determination of rockfall runout in an attempt to understand the likelihood that rockfall debris will reach an element at risk. Rockfall modelling programs which simulate the trajectory of rockfall material are one method commonly used to assess potential runout. This study aims to demonstrate the effectiveness of a rockfall simulation prototype which uses the Unity 3D game engine. The technique is capable of simulating rockfall events comprised of many mobile fragments, a limitation of many industry standard rockfall modelling programs. Five fragmental rockfalls were simulated using the technique, with slope and rockfall geometries constructed from high-resolution terrestrial laser scans. Simulated change detection was produced for each of the events and compared to the actual change detection results for each rockfall as a basis for testing model performance. In each case the simulated change detection results aligned well with the actual observed change in terms of location and magnitude. An example of how the technique could be used to support the design of rockfall catchment ditches is shown. Suggestions are made for future development of the simulation technique with a focus on better informing simulated rockfall fragment size and the timing of fragmentation.

Simulation of Fragmental Rockfalls Detected Using Terrestrial Laser Scans from Rock Slopes in South-Central British Columbia, Canada

Rockfall presents an ongoing challenge to the safe operation of transportation infrastructure, creating hazardous conditions which can result in damage to roads and railways, as well as loss of life. Rockfall risk assessment frameworks often involve the determination of rockfall runout in an attempt to understand the likelihood that rockfall debris will reach an element at risk. Rockfall modelling programs which simulate the trajectory of rockfall material are one method commonly used to assess potential runout. This study aims to demonstrate the effectiveness of a rockfall simulation prototype which uses the Unity3D game engine. The technique is capable of simulating rockfall events comprised of many mobile fragments, a common limitation of available rockfall modelling programs. Five fragmental rockfalls were simulated using the technique, with slope and rockfall geometries constructed from high-resolution terrestrial laser scans. Simulated change detection was produced for each of the events and compared to the actual change detection results for each rockfall as a basis for testing model performance. In each case the simulated change detection results aligned well with the actual observed change in terms of location and magnitude. An example of how the technique could be used to support the design of rockfall catchment ditches is shown. Suggestions are made for future development of the simulation technique with a focus on better informing simulated rockfall fragment size and the timing of fragmentation.