Tributary Pillar Strength

Compare calibrated square-pillar empirical strength with tributary-area stress; coefficient assumes meter dimensions and stability certification is excluded.

Description

A tributary-area model concentrates overburden stress onto a square pillar footprint.

A tributary-area model concentrates overburden stress onto a square pillar footprint. An empirical width-height strength formula provides a supplied capacity estimate for comparison.

The tool returns empiricalPillarStrengthMpa (empirical pillar strength mpa); tributaryPillarStressMpa (tributary pillar stress mpa); capacityStressRatio (capacity stress ratio). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Tributary Pillar Strength

Use Tributary Pillar Strength when you already have pillarWidthM, pillarHeightM, roomWidthM, verticalStressMpa, strengthCoefficientMpa, widthExponent, heightExponent and want empiricalPillarStrengthMpa, tributaryPillarStressMpa, capacityStressRatio. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Tributary Pillar Strength and understand its results

Enter pillarWidthM, pillarHeightM, roomWidthM, verticalStressMpa, strengthCoefficientMpa, widthExponent, heightExponent using the field table below. Match the units, ordering and data boundaries described in the calculation.
Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
Read empiricalPillarStrengthMpa, tributaryPillarStressMpa, capacityStressRatio. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.

Input field	Meaning	Value type and bounds	Requirement
pillarWidthM	Pillar width m	number	Required
pillarHeightM	Pillar height m	number	Required
roomWidthM	Room width m	number	Required
verticalStressMpa	Vertical stress mpa	number	Required
strengthCoefficientMpa	Strength coefficient mpa	number	Required
widthExponent	Width exponent	number	Required
heightExponent	Height exponent	number	Required

Use positive pillar dimensions, stress and coefficient with nonnegative room width and exponents. Return strength, stress and their ratio.

strength = coefficient×width^widthExponent/height^heightExponent; stress = verticalStress×((width+room)/width)²

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "pillarWidthM": 10,
    "pillarHeightM": 5,
    "roomWidthM": 10,
    "verticalStressMpa": 2,
    "strengthCoefficientMpa": 5,
    "widthExponent": 0.5,
    "heightExponent": 0.5
  },
  "output": {
    "empiricalPillarStrengthMpa": 7.0710678118654755,
    "tributaryPillarStressMpa": 8,
    "capacityStressRatio": 0.8838834764831844
  }
}

Limitations and assumptions

The coefficient is calibrated for the metre-based dimension convention. Tributary loading and empirical strength do not establish pillar stability or design adequacy.

Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.

Alternative or Complementary methods

Room and Pillar Recovery: Estimate plan-area extraction for rectangular repeating cells and caller secondary pillar recovery; excludes seam losses and stability recommendations. Rock Bolt Spacing: Calculate square-grid tributary-load bolt-spacing screen; anchorage, wedges, corrosion and dynamics are not modeled or certified.

Methodological background: Pillar and Roof Span Design Guidelines for Underground Stone Mines.^[1]

References

Pillar and Roof Span Design Guidelines for Underground Stone Mines — NIOSH, Centers for Disease Control and Prevention

Similar or alternative tools

Room and Pillar Recovery
Estimate plan-area extraction for rectangular repeating cells and caller secondary pillar recovery; excludes seam losses and stability recommendations.
Rock Bolt Spacing
Calculate square-grid tributary-load bolt-spacing screen; anchorage, wedges, corrosion and dynamics are not modeled or certified.