Rockfall Trajectories
Rockfall Trajectories runs falling blocks down a slope mesh. The blocks start where a layer of the mesh marks the sources, such as the probability of failure that Slope Stability maps. They fly, bounce and roll down the real surface. The result is a map of how often blocks reach each part of the slope, how much energy they carry there and how high they bounce.
Running it
- Mark the sources. Any value layer on the mesh will do: Probability of Failure or Kinematic Mode from Slope Stability, Key Block FoS from Key Blocks, or a layer you paint or calculate yourself.
- On the mesh's menu choose Attributes & Analysis → Rockfall Trajectories... and fill in the dialog. Open a report first to get the statistics in it.
| Field | Description |
|---|---|
| Blocks start where … is at least | The layer and the threshold. Every vertex at or above it can be a source. A layer whose name starts with Probability of Failure is chosen the first time. Default 0.5. |
| Source vertices, at most | The sources are spread evenly through the qualifying vertices, up to this many. Default 200. |
| Blocks from each | Each source releases this many blocks. Each block draws its own coefficients, so blocks from the same source follow different paths. Default 5. |
| Block volume (m³) | The block's mass at 2650 kg/m³. Mass scales the energy; it does not change the path. Default 1 m³. |
| Restitution Rn, Rt | The normal and tangential coefficients of restitution. Typical values are Rn 0.3–0.4 on rock and 0.2–0.3 on talus or soil, and Rt 0.8–0.9. Defaults 0.35 and 0.85. |
| Rolling friction (tan) | The rolling and sliding friction coefficient. Default 0.5. |
| Roughness (deg) | At each impact the surface normal is tilted at random by up to this. This stands in for roughness finer than the mesh. Default 5°. |
| Mesh wound inside out | Tick it when the mesh's faces point into the rock. Blocks start just off the surface along its normals, so a mesh wound the wrong way starts them inside the rock: every block then falls straight through and the report says they all left the mesh. Overhangs need no ticking; their normals point down out of the rock, as they should. |
Model units are taken as metres, with z up.
Results
- Rockfall Reach: the share of all the blocks that passed each vertex, from 0 to 1.
- Rockfall Energy: the largest kinetic energy, in kJ, of any block that passed it.
- Rockfall Bounce Height: the highest any block flew above the surface there, in m.
- The report: the number of blocks and the settings, how many came to rest and how many left the mesh, and the median, 90th and 95th percentiles and the maximum of the horizontal runout, the fall height, the peak energy and the bounce height.
- The messages panel: the 95th percentiles in one line.
A block passes a vertex when its path comes within about two triangle edges of it. Use the Energy and Bounce Height maps to size and place barriers or fences. Use Reach to set the extent of the hazard zone.
Each run is recorded in Analysis Runs, from where it can be run again. The random draws are fixed by the run's seed, so a re-run gives the same paths.
Method
Lumped mass. A block is a point with a mass (Pfeiffer & Bowen 1989; the lumped-mass model of Hoek's RocFall). It starts at rest just off the surface at its source vertex. It then follows three phases:
-
Flight. The block follows a parabola under gravity in time steps of 0.01 s until its path crosses a triangle of the mesh.
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Impact. The velocity is split along the surface normal, tilted at random by up to the roughness, and the tangent. It rebounds as
where Rn and Rt are drawn at every impact from normal distributions about their means (s.d. 0.04).
-
Rolling. A block that rebounds off the surface slower than 1 m/s rolls (slides) instead. It is driven by gravity down the slope and slowed by friction μ g cos θ, and it is re-seated on the surface at every step. It stops when it is slower than 0.15 m/s on a slope it can hold (tan θ ≤ μ). It flies again where the ground falls away from under it, over an edge.
A block is followed until it stops, leaves the mesh, or 120 s have passed.
Maps. Each path is sampled at every step. Every vertex within the mapping radius of a sample counts that block once, and keeps the largest speed and the highest flight above the last impact among the blocks that reached it.
Limitations
- The block is a point, so its shape, size, spin and break-up are not modelled. A rigid-body model is a later step.
- One set of coefficients covers the whole slope. Zoning Rn and Rt by surface material (rock, talus, soil, vegetation) is not supported yet.
- The mesh is the ground. Trees, fences and holes in the mesh are not in it; a block that reaches a hole leaves the mesh there.
- A block that grazes the underside of an overhang keeps flying; it can only roll on a surface beneath it.
References
- Pfeiffer, T. J., & Bowen, T. D. (1989). Computer simulation of rockfalls. Bulletin of the Association of Engineering Geologists, 26, 135–146.