Pillar Strength Calculations
Work through one calculation stage at a time. The live summary stays visible while advanced comparisons, exports, and reference notes stay collapsed until needed.
These calculations are simplified empirical and tributary-area estimates and should not be used blindly for final design.
Outputs are screening-level only. Final design requires site-specific geology, stress analysis, calibration, monitoring data, and professional engineering judgment.
Guided workflow
Open a step, make the decision, then continue. Closed steps keep a short summary so the page stays readable.
wp for square pillars; a or W for rectangular formulas.
Linked to width for square pillars.
Mining height used in width-to-height and strength equations.
Width-to-height ratio
2.00 (squat)
wo for square tributary-area stress.
Using the same opening width in both directions.
Plan-view geometry
Shaded area is the tributary cell; the white rectangle is the pillar. Diagram is schematic, not to exact drawing scale.
Mode
unit-weight
Depth
300 m
Vertical stress
8.10 MPa
Formula
Pzz = gamma Z
Pillar stress
24.81 MPa
Extraction
67.3%
Pillar area
64.00 m2
Tributary area
196.00 m2
Equation
Salamon and Munro (1967)
Status
Implemented
Strength
7.51 MPa
Rock context
Coal / soft rock
FS
0.30
Strength
7.51 MPa
Stress
24.81 MPa
Warnings
0
Advanced AnalysisEquation comparison and width sensitivity are available when needed.
Compare equations
Select implemented equations to compare with the same geometry, overburden, and equation input values.
Equation comparison
| Equation | Strength | FS |
|---|---|---|
| Salamon and Munro | 7.51 MPa | 0.30 |
| Hedley and Grant | 179.00 MPa | 7.22 |
| Lunder and Pakalnis | 49.05 MPa | 1.98 |
Width sensitivity
Screens how pillar width changes affect stress, recovery, strength, and FS while other inputs stay fixed.
| Width change | Width (m) | Stress (MPa) | Extraction | Strength (MPa) | FS |
|---|---|---|---|---|---|
| -20% | 6.40 | 30.41 | 73.4% | 6.77 | 0.22 |
| -10% | 7.20 | 27.22 | 70.2% | 7.15 | 0.26 |
| 0% | 8.00 | 24.81 | 67.3% | 7.51 | 0.30 |
| 10% | 8.80 | 22.91 | 64.6% | 7.84 | 0.34 |
| 20% | 9.60 | 21.39 | 62.1% | 8.16 | 0.38 |
Assumptions and LimitationsReference notes are kept separate from the main calculation flow.
Do not use pillar strength equations blindly.
Choose equations that reflect the rock type, geometry, specimen basis, and calibration context.
- Tributary-area loading assumes simplified equal load sharing.
- Pillars are assumed loaded approximately parallel to their vertical axis.
- Equal load sharing may not be valid near abutments, faults, or excavated edges.
- Empirical equations are calibration-dependent.
- Geology, joints, scale effects, blasting damage, time effects, and irregular geometry matter.
- Rib and irregular pillars need additional geometry and stress logic.
Full Summary and ExportsDetailed values and report export tools.
- Pillar shape
- square
- Selected equation
- Salamon and Munro (1967)
- Equation status
- Implemented
- Rock workflow
- Coal / soft rock
- Pillar width (m)
- 8
- Pillar length (m)
- 8
- Pillar height (m)
- 4
- Opening X (m)
- 6
- Opening Y (m)
- 6
- Depth (m)
- 300
- Vertical stress (MPa)
- 8.10
- Pillar area (m2)
- 64.00
- Tributary area (m2)
- 196.00
- Pillar stress (MPa)
- 24.81
- Extraction ratio (%)
- 67.3
- Pillar strength (MPa)
- 7.51
- Factor of safety
- 0.30
- Warnings / notes
- None
- Share link
- Unavailable