our approach
XPBD Cave-Flow Simulation (FS5)
See how Beck Engineering’s FS5 XPBD engine, coupled with advanced FEM models, simulates cave growth, ore flow and ground deformation with billion-particle precision.
Our Approach
Beck Engineering’s coupled FEM-XPBD workflow links two proven tools:
| Tool | What it does |
|---|---|
|
Finite Element Method
(FEM) |
Calculates how the host rock deforms as the
cave opens and draws. |
|
Extended Position-Based Dynamics (XPBD) |
Tracks every broken fragment, letting gravity,
cave geometry and contact forces control its
motion. |
Running both in tandem shows how the cave develops, how ore and waste mingle, and how ground movement evolves for a given draw schedule. Drawing on the extensive real-mine experience we’ve built through involvement in most of the world’s caving operations, we calibrated our simulations against field measurements — cave-back position, grade, seismicity and tunnel damage — achieving the industry’s closest match to observed cave behaviour.
A step beyond Cellular - Automata approaches
From 2010 through 2021 Beck Engineering also relied on Cellular Automata (CA) models. That decade of experience highlighted two core
limitations:
- Gravity is only approximated. CA tends to draw in straight, narrow columns, paying little attention to the evolving cave shape.
- Lateral spread is hard-wired. Horizontal draw width is usually injected via look-up tables, so complex, geometry-driven mixing never emerges.
XPBD resolves these issues:
- Gravity and cave geometry act together. The cave’s own shape governs where broken-rock (muck) flows.
- Emergent mixing, no tables. Drawpoint interactions, dilution trends and lateral dispersion arise naturally from contact physics.
- Speed with detail. Local-only contacts give DEM-level realism without DEM-level runtimes, so billion-particle studies are possible, and 100 Mparticle studies run overnight on a single workstation.
| Years | Core method | Particle capacity | Key advance |
|---|---|---|---|
|
2010 – 2021 |
Cellular Automata (CA) |
< 10 M |
Gravity simplified; lateral spread via look-up tables |
|
2021 – 2024 |
PBD – FS4 |
≤ 40 M |
2021 – 2024 PBD – FS4 ≤ 40 M Full gravity, geometry-aware flow |
|
2024 → |
XPBD – FS5 |
≤ 1 B (multi-GPU) |
More stable/realistic contacts, particle heterogeneity, billionparticle
scale |
Direct production insight
In our simulation, every particle carries ore grade, so the model outputs timebased forecasts for recovered tonnes, dilution and recovery—metrics essential for draw-strategy optimisation. Results focus on underground performance and can be combined with drill-and-blast or plant recovery models as needed.
Beck Engineering considers coupled FEM-XPBD the current best-practice toolset for cave flow studies worldwide.
About FS5
FS5 is the XPBD engine used in our studies. Purpose-built for caving, it:
- Scales to billions of particles via GPU acceleration and domain decomposition.
- Includes cohesion as well as friction, preventing the overly localised deformation typical of friction-only models.
- Handles heterogeneity—particle size, density and contact forces vary through the muckpile and evolve over time.
In laboratory and field comparisons (e.g., ), FS5 accurately reproduced draw-column flow and lateral dispersion without empirical rescaling. This direct similitude means one model spans from bench tests to full-scale mines, reducing calibration cycles and increasing predictive confidence.
Coupled with FEM, FS5 delivers a detailed yet computationally efficient picture of cave behaviour, enabling safer, more productive caving operations.
Cross section of particle flow in an example stope during extraction over 4 stages. Colours refer to normalised material grade.