Pillar Factor of Safety

Strength over stress. The whole room-and-pillar exercise exists to produce this ratio, and it is worth being precise about what it does and does not mean.

It is not a probability. A factor of safety of 1.5 does not mean anything is 50% safe, and it does not mean the pillar will carry 50% more than it does today. It is a margin carried against the scatter in two empirical correlations — one for the strength, fitted on laboratory specimens and adjusted by judgement, and one for the stress, resting on a tributary assumption that ignores abutment arching. The honest way to read it is to ask how far the inputs would have to move before it reached 1.0. At FS = 1.5, the strength only has to be a third lower than assumed. A strength correlation good to ±30% eats that entirely.

The ranges usually quoted are 1.3 to 1.6 for short-term, actively worked openings that will be abandoned or backfilled within the mine life, and 1.6 to 2.5 for long-term stability — the upper end for anything that has to stand after closure, under a road, a river or a town. Above about 2.5 the design is conservative, and the question worth asking is what that costs in ore left in the ground. A factor of safety far above what the conditions and consequences justify is a real economic loss, not free insurance.

Three things this ratio cannot see, and each of them has closed a mine.

Time. Pillars in weak, weathered or moisture-sensitive rock lose strength over years as they spall and slab from the ribs inwards. Every increment of spalling reduces $W_p$, which reduces $W_p/h$, which reduces the strength, which accelerates the spalling. A factor of safety computed on the day of mining is the best that pillar will ever have.

Neighbours. Tributary area assumes every pillar in a regular panel carries its own share and no more. The moment one pillar fails, its load has to go somewhere, and it goes to the pillars around it — which were designed for their own share. Progressive pillar collapse across a panel is not a theoretical failure mode; it is fast, it is well documented, and it is why a panel of pillars at FS 1.3 is a different proposition from a single pillar at FS 1.3.

The roof. Pillars can be entirely adequate while the ground between them is not. Roof falls injure and kill far more people than pillar failures do, they are governed by span, bedding and bolting rather than by this ratio, and a comfortable pillar factor of safety says nothing whatever about them.

One procedural point that matters more than it sounds. Choose the factor of safety before doing the arithmetic, from the ground conditions, the design life and what sits above the workings — never afterwards, by looking at what the layout you already drew happens to give.