Big Dog Mining

Underground Pillar Design

What the pillars are carrying, what they can carry, and the ratio between the two — plus what you give up in recovery to get it.
Underground room-and-pillar layouts only — a regular array of pillars on one horizon. It is not a barrier pillar or panel design, it does not model abutment loading from an adjacent gob, it is not a numerical stress model, and it says nothing about the back between the pillars. Bolts hold the back up; this page is about what holds the mine up. A competent person signs the layout.

Step 1 — The layout

Pillar width against room span decides both the load and the recovery.

Units ?

Some formulas are valid in one system only. The page checks.

Pillar shape ?

Square grid, or long parallel ribs.

Pillar width ?

Short horizontal dimension.

m Pillar length ?

Equal to width if square.

Room span ?

The opening between pillars.

m Mining height ?

Floor to back. Also the pillar height.

Step 2 — Depth and stress

In-situ vertical stress is just the weight of what is above you.

Depth of cover ?

Surface to the mining horizon.

m Overburden rock ?

Fills in the density below.

Overburden density yours ?

Average over the whole cover.

t/m³

Step 3 — Pillar strength

Eight published formulas, and they do not agree. Pick deliberately.

Strength formula ?

Each was fitted to one district and material.

Cube strength σ_S ?

A cubical pillar, not a core sample. Far weaker than lab strength.

MPa Required factor of safety ?

The formulas give a MEAN strength. 1.0 means half fail.

Step 4 — What the pillars look like

A number is a prediction. This is an observation, and it outranks the number.

Observed pillar condition ?

What you can see underground. Compare it to the number.

The formulas were fitted to coal. The handbook is explicit that the statistical verification behind these constants concerns coal, and that there has been no similar verification for hard rock or even for softer minerals like trona, salt, oil shale or borates. Applying them outside coal is what the industry does, and it is still an extrapolation. The observed condition above is the check that costs nothing.

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pillar stress

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pillar strength

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factor of safety

Step	Value	Where it comes from

The layout, and what each pillar carries

Factor of safety against pillar width

The eight published strength formulas

Source	a	b	α	β	Fitted to

SME Mining Engineering Handbook, Table 13.1-1, p. 1329, after Zipf 2001. Two general forms are printed with it: σ_P = σ_S(a + b·W/H) (Eq. 13.1-12) and σ_P = K·W^α/H^β (Eq. 13.1-13). Obert-Duvall and Bieniawski follow the first; Salamon-Munro and Holland follow the second.

The daggers are not decoration. Three of the power-law formulas are printed “use with English units only” and one “use with metric units only”. A power law is not dimensionless, so running one in the wrong system does not scale — it gives a different answer with no sign that anything happened. This page refuses rather than converts.

A conflict worth knowing about. Rock Mechanics for Underground Mining p. 379 gives Salamon and Munro as α = −0.66, β = 0.46 — the same two numbers as the table above, with the letters swapped and a sign changed, because it writes the formula in a different form. Take α from one book and β from the other and the exponents land on the wrong variables. This page uses the SME convention throughout.

Rating a pillar by looking at it

Rating	Condition

SME Mining Engineering Handbook, p. 1331, after Carmack et al. 2001. Hourglassing is the shape a pillar takes when the walls have spalled away and the load has migrated to a smaller core, which is a late stage and not a warning.

Published pillar widths by depth and mining height

Depth of cover, m

SME Mining Engineering Handbook, p. 1028, adapted from Vandergrift et al. 2004. Read down for depth of cover and across for mining height; the cell is a pillar width in feet. Mining heights run 0.9 to 2.7 m, so this is a COAL table and it is here as a sanity check on the shape of an answer rather than as a design for a hard-rock heading. The blanks are blank on the printed page: not every depth and height combination is covered, and this page does not interpolate into them.

What this tool does not know. The tributary area method assumes vertical loading only, that each pillar carries the full column above its share of the area, and that the load is spread evenly across the pillar. The handbook notes that none of the last one is true: stress concentrates at the pillar corners. It knows nothing about horizontal stress, about an abutment load from an adjacent mined-out panel, about a pillar sitting on a weak floor, or about time — pillars that stand for a decade can fail in the eleventh year. It does not design barrier pillars, and it does not check the back. Every published value has been checked against the printed page.

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Terms of use and disclaimer

Estimating aid only. This calculator is an educational tool. It is not an engineering design and it is not a substitute for the judgment of a competent or qualified person.

No warranty. It is provided "as is", without warranty of any kind, express or implied, including any implied warranty of merchantability or fitness for a particular purpose. Equations and constants are cited to their published sources above, but transcription, implementation and the values you enter can all be wrong. Verify every result against the cited source and against your own site conditions before it informs a decision.

Not a statutory document. Nothing produced here is a ground control plan, ventilation plan, blast design, haul road design or hoist design. Those must be prepared, signed and approved under the regulations that apply to your operation. Compliance with MSHA, or with your own jurisdiction's mining regulations, is the operator's responsibility and remains so.

Assumption of risk. You use this tool entirely at your own risk. Mining is hazardous, and errors in ground support, ventilation, blasting or haulage can cause serious injury or death.

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