Pillar Stability Factor Calculator
The stability factor (also called the pillar safety factor) is pillar strength divided by pillar stress.
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Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the cover depth to the pillar, the pillar width (Wp), the opening/room width (Wo) and the estimated pillar strength in MPa.
- Optionally enter the overburden unit weight (kN/m³) to compute in-situ vertical stress; leave it blank to use the default 0.027 MPa/m gradient.
- Read the stability factor (FoS), the assessment band, and the underlying pillar stress, vertical stress and extraction ratio, then open the steps panel to see the full working.
How it works
The stability factor (also called the pillar safety factor) is pillar strength divided by pillar stress. Pillar stress is estimated with the tributary-area method for square pillars: each pillar carries the full weight of the rock column above it plus the column above the adjacent openings, so σp = σv × (Wp + Wo)² ÷ Wp², where σv is the in-situ vertical stress. Vertical stress is taken as unit weight × depth ÷ 1000 (kN/m³ and m giving MPa), or from a default 0.027 MPa per metre gradient when unit weight is left blank.
A stability factor above about 1.5 is commonly targeted for long-term room-and-pillar stability, values between 1.0 and 1.5 are marginal, and below 1.0 the estimated stress exceeds strength. The tool also reports the extraction ratio, 1 − Wp² ÷ (Wp + Wo)², which is the fraction of ground mined out. The pillar strength you enter should come from an empirical strength formula (e.g. size-shape or Obert-Duvall type relations) calibrated to your rock — this calculator does not derive strength itself.
Worked example
6 m pillars at 200 m depth. A room-and-pillar operation has 6 m square pillars separated by 6 m wide openings, at 200 m cover depth in ground with an overburden unit weight of 25 kN/m³, and an estimated pillar strength of 25 MPa. Vertical stress = 25 × 200 ÷ 1000 = 5 MPa. Pillar stress = 5 × (6 + 6)² ÷ 6² = 5 × 4 = 20 MPa. Stability factor = 25 ÷ 20 = 1.25, with a 75% extraction ratio. That FoS of 1.25 is marginal — below the ~1.5 often targeted — so the design would be reviewed by a geotechnical engineer before mining.
Common mistakes
- Confusing pillar width Wp with opening width Wo. Wp is the solid pillar dimension and Wo is the void/room span between pillars; swapping them changes the tributary-area multiplier and the FoS.
- Mixing up unit weight and stress. Enter overburden unit weight in kN/m³ (rock is typically 24–27 kN/m³); the tool converts to MPa. Entering a stress value in the unit-weight field will overestimate vertical stress by ~1000×.
- Treating the tributary-area result as a design value. It assumes uniform square pillars, flat-lying ground and no abutment or barrier-pillar effects — real designs need site geotechnical analysis and numerical modelling.
Frequently asked questions
What stability factor is considered safe?
A factor of safety above roughly 1.5 is commonly targeted for long-term room-and-pillar stability, though the exact threshold depends on the empirical strength formula used, pillar recovery plans and site risk. Values of 1.0–1.5 are marginal and below 1.0 the estimated pillar stress exceeds its strength. Always confirm the required factor with your geotechnical design.
Does this calculator work out the pillar strength for me?
No. You enter the pillar strength (in MPa) from an appropriate empirical strength relation or lab-calibrated value. This tool computes the stress side (tributary-area) and divides strength by stress to give the stability factor. Different strength formulas can give very different numbers for the same pillar.
What is the tributary-area method?
It assumes each pillar supports the full weight of the rock column directly above it plus the columns above the surrounding openings, giving pillar stress = vertical stress × (Wp + Wo)² ÷ Wp² for square pillars on a regular grid. It is a first-pass estimate that ignores abutment loading, barrier pillars and irregular geometry.
Can I use it for rib or rectangular pillars?
This version models square pillars (Wp × Wp) with equal openings. Rectangular or rib pillars use a different tributary-area expression, so treat the result as indicative only and use a geotechnical model for non-square layouts.
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