Walk into any room-and-pillar coal mine and the first thing you notice, once your eyes adjust to the cap lamp, is the pillars. Big blocks of coal, left standing in neat rows, holding up millions of tonnes of rock above your head. They look boring. They are anything but.
Every pillar is a decision someone made: how big to leave it, how far apart to place it, and how much good coal to sacrifice so that the roof stays where it is. Get that decision right and the mine runs for decades. Get it wrong and you get anything from cracked ribs and spalling coal to a full-scale collapse that can spread across a panel. That is why pillar design sits at the heart of underground mine planning.
This post walks through how pillars are designed, the factors that matter, the common formulas, and a worked example so the numbers feel real.
What exactly does a pillar do?
When you excavate a roadway or a room, the load that used to be carried by the removed rock does not disappear. It shifts onto whatever is left standing. In a room-and-pillar layout, that means the pillars carry the weight of the overburden, along with some load transferred from the roof and floor strata around them.
A pillar has to do three jobs at once:
- Carry the vertical load of the overlying strata without crushing.
- Keep the roof from sagging or breaking in the openings next to it, so roads stay safe for people and machines.
- Stay stable over the life of the working. In some mines that is a few months, in others it must be permanent.
The basic idea behind pillar design
Strip away the complexity and pillar design comes down to one comparison: how much load will the pillar carry, and how much load can it actually take? The ratio between the two is the factor of safety.
Factor of Safety (FoS) = Pillar Strength ÷ Pillar Stress
If the FoS is below 1, the pillar is overloaded on paper and will probably fail. Designers usually aim well above 1 because rock is variable, data is never perfect, and the cost of being wrong is high. For coal pillars, values around 1.5 to 2 are commonly used as a starting point, and the exact requirement depends on the mine, the depth, the intended life of the pillar and the local regulations. Always check the statutory rules that apply to your coalfield.
Key factors that shape pillar design
1. Geotechnical assessment
Everything starts with knowing the ground. That means measuring the strength of the coal and the rock around it, how they deform under load, and what the in-situ stress field looks like. Boreholes, core logging, laboratory tests on samples and sometimes in-situ stress measurements all feed into this. Skimp here and every calculation after it is built on guesswork.
2. Rock mass classification
Rock is rarely a clean, uniform block. It has joints, faults, bedding planes, slickensides and weak bands. Classification systems turn all that mess into numbers that engineers can compare. Rock type, rock quality, spacing and condition of discontinuities, and the presence of water are all taken into account. The result helps decide which design approach suits the site, and whether an empirical formula from another mine can be trusted here at all.
3. Stability analysis
Once the ground is understood, stability analysis checks whether a proposed pillar will survive. Three broad approaches are used:
- Empirical formulas built from databases of pillars that stood and pillars that failed.
- Analytical methods such as tributary area theory for estimating load.
- Numerical modelling (finite element, boundary element, finite difference) for complex geometry, multiple seams or unusual geology.
In practice, experienced engineers use more than one and see whether the answers agree.
4. Mining method
The method decides the layout before you ever draw a pillar. In bord and pillar development, pillars are meant to be left or later split and extracted. In longwall mining, the large panels are separated by chain pillars whose job is to protect the gate roads from abutment stress. In block caving or stoping operations, pillars may be left between stopes, or crown and sill pillars are kept to protect infrastructure. Same word, very different roles.
5. Stress distribution
Vertical stress usually comes mainly from the weight of the overburden, and it grows with depth. Horizontal stress can be just as important in some basins, especially in deeper mines or tectonically active areas. On top of that you get mining-induced stress: the abutment load around a working face, side abutments next to goaf areas, and stress concentrations at pillar corners. A pillar that looks perfectly safe under virgin stress can be in trouble once an adjacent panel is extracted.
6. Pillar dimensions
This is where the engineering meets the economics. The key dimensions are the pillar width, length and height. One idea matters more than any other: the width-to-height ratio (w/h). A tall, thin pillar is weak and tends to fail by splitting or buckling. A short, squat pillar is much stronger because the confinement in its core builds up. This is why, for a given seam height, making a pillar wider increases its strength faster than its area alone would suggest.
Design aims to find the smallest pillar that still gives an acceptable factor of safety, so you are not leaving coal behind for no reason.
7. Pillar spacing
Spacing is tied closely to the load each pillar has to carry. Put pillars closer together and each one carries less, but you leave more coal in the ground and recovery falls. Spread them out and recovery goes up, but each pillar carries more load and the roof spans get wider. Roof span matters too. Roof bolting, strata type and the immediate roof thickness all limit how wide an opening can safely be.
8. Monitoring and evaluation
No design survives contact with the real ground unchanged. Once pillars are formed, you watch them. Convergence stations, stress cells, borehole extensometers, tell-tales and simple visual inspections for rib spalling or roof cracking all tell you whether the pillar behaves the way the design predicted. If it does not, the design gets adjusted, whether that means extra support, smaller extraction, or a revised layout in the next panel.
Estimating the load: tributary area theory
The simplest way to estimate the stress on a pillar is tributary area theory. It assumes the pillars are all the same size, laid out on a regular grid, in a flat seam that is wide enough that every pillar carries its share of the full overburden weight.
For square pillars of width w with openings (roadway width) of B, the average vertical stress on a pillar is:
σv = γ × H × ((w + B) ÷ w)²
Here γ is the unit weight of the overburden (about 0.025 MPa per metre of depth is a common figure), H is the depth below surface, and (w + B) is the centre-to-centre distance of the pillars.
Notice what is hiding in that formula: the extraction ratio. The more you extract, the bigger the bracket gets, and the more stress each pillar has to take. It is also a limited tool. It ignores the stiffness of the roof and floor, edge effects near the panel boundary, and any pillar size variation. It is a first estimate, not the final word.
Estimating the strength: common formulas
Pillar strength is harder than pillar load. Over the years researchers have proposed many formulas. A few of the best known are below. Treat the ones based on a specific coalfield as valid only for that kind of coal and similar conditions.
| Formula | Expression | Notes |
|---|---|---|
| Obert-Duvall | σp = σ1 (0.778 + 0.222 w/h) | σ1 is the strength of a small cube or the unit strength of the material. Widely quoted and easy to use. |
| Bieniawski | σp = σ1 (0.64 + 0.36 w/h) | Based on in-situ tests on large coal specimens in South Africa. |
| Salamon-Munro | σp = 7.176 × w0.46 ÷ h0.66 (MPa) | Derived from a database of South African coal pillar failures. Pillar dimensions in metres. |
| Sheorey | σp = 0.27 σc h-0.36 + (H ÷ 160) × (w/h − 1) | Developed for Indian coalfields. σc is the uniaxial compressive strength of the coal, H is depth in metres. |
Please verify the constants against the original papers before using any of these formulas in an actual design.
A worked example
Numbers always make this clearer, so here is a simple case. Say we are planning a bord and pillar panel with the following data:
- Depth of cover, H = 200 m
- Seam height, h = 3 m
- Square pillars, width w = 25 m
- Roadway width, B = 5 m (so the centre-to-centre distance is 30 m)
- Unit weight of overburden, γ = 0.025 MPa/m
Step 1: Virgin vertical stress.
γ × H = 0.025 × 200 = 5.0 MPa
Step 2: Pillar stress using tributary area theory.
σv = 5.0 × (30 ÷ 25)² = 5.0 × 1.44 = 7.2 MPa
Step 3: Pillar strength using Salamon-Munro (for illustration).
σp = 7.176 × 250.46 ÷ 30.66
250.46 ≈ 4.40 and 30.66 ≈ 2.07, so σp ≈ 7.176 × 4.40 ÷ 2.07 ≈ 15.3 MPa
Step 4: Factor of safety.
FoS = 15.3 ÷ 7.2 ≈ 2.1
Step 5: Extraction ratio.
1 − (25 ÷ 30)² ≈ 0.31, so roughly 31% of the coal is taken in development.
A factor of safety of about 2.1 is comfortable for a case like this. Now look at what happens if you try to push recovery up. Narrow the pillar to 15 m with the same 5 m roadways and the stress jumps (the bracket becomes (20/15)² ≈ 1.78, giving 8.9 MPa) while the strength drops, and your factor of safety falls fast. That is the trade-off in a nutshell. This example uses an empirical formula from one coalfield, so in a real design you would calibrate against local experience and cross-check with other methods.
Common mistakes to avoid
- Using a formula outside its range. A formula developed for South African coal at shallow depth is not automatically valid for a deep, soft-floor Indian seam.
- Ignoring the floor and roof. A strong pillar sitting on a weak clay floor can punch into it, and the design fails even though the coal itself was strong enough.
- Forgetting about time. Coal pillars slowly weather and degrade, especially with water. Designs for long-life pillars need extra margin.
- Treating every pillar the same. Pillars near the edge of a panel, near faults or under thicker cover carry different loads.
- Skipping monitoring. Design is a prediction, and the mine is the test.
Frequently asked questions
Why are pillars left in a mine at all?
They hold up the roof. Without them, the overlying strata would collapse into the openings. Leaving pillars is the price of working safely underground.
What is a good factor of safety for a coal pillar?
It depends on the depth, the pillar's intended life and the local regulations. Many designs target somewhere around 1.5 to 2 or higher, but you should always follow the statutory requirements and site experience.
Does a wider pillar always mean a safer pillar?
Mostly yes, because a higher width-to-height ratio gives a stronger pillar. But wider pillars mean lower recovery, so the design is always a balance between safety and economics.
Can pillars be extracted later?
Yes, in many coal mines the pillars formed during development are later extracted in a controlled way (depillaring), usually with additional support, stowing or caving. That is a separate design problem with its own risks.
Final thoughts
Pillar design is one of those jobs where the maths is the easy part. The hard part is judgement: knowing which data you trust, which formula fits your ground, and how much margin you can afford to leave. It is a complex process and it should be carried out by qualified mining engineers who understand the specific conditions of the mine. Use the methods in this post to understand the logic, not to replace proper site-specific design.
If you found this useful, share it with a classmate or colleague, and drop your questions in the comments. I would be happy to cover depillaring, longwall chain pillars or numerical modelling in a follow-up.
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