Ground Support Interaction

Intersect piecewise-linear supplied ground/support curves within bounds; missing, multiple and coincident equilibria are errors, not stability certifications.

Description

A ground-support interaction diagram compares required ground pressure and provided support pressure at the same displacement.

A ground-support interaction diagram compares required ground pressure and provided support pressure at the same displacement. Their crossing is an equilibrium of the supplied curves.^[1]

The tool returns equilibriumDisplacementMm, equilibriumPressureMpa. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Ground Support Interaction

Use this for the following task: Intersect piecewise-linear supplied ground/support curves within bounds; missing, multiple and coincident equilibria are errors, not stability certifications. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Ground Support Interaction and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter displacementsMm, groundPressuresMpa, supportPressuresMpa according to the field table, then run the tool.
Read equilibriumDisplacementMm, equilibriumPressureMpa. Use the calculation below to interpret the selected mean or the model’s signs, units and comparison flags.
Review the supplied assumptions and calibration before comparing or reporting the result.

Input field	Meaning	Value type and bounds	Requirement
displacementsMm	Displacements mm	list of number	Required
groundPressuresMpa	Ground pressures mpa	list of number	Required
supportPressuresMpa	Support pressures mpa	list of number	Required

Require increasing nonnegative displacements and aligned nonnegative pressures. Find exact sampled roots and sign-changing segment roots, then interpolate pressure at the unique crossing.

equilibrium: groundPressure(u)−supportPressure(u)=0 using piecewise-linear interpolation

The symbols and boundary conditions refer to the supplied fields and the implementation described above.

Output field	Meaning	Value type
equilibriumDisplacementMm	Equilibrium displacement mm	number
equilibriumPressureMpa	Equilibrium pressure mpa	number

json

{
  "input": {
    "displacementsMm": [
      0,
      10,
      20
    ],
    "groundPressuresMpa": [
      2,
      1,
      0.5
    ],
    "supportPressuresMpa": [
      0,
      0.5,
      1
    ]
  },
  "output": {
    "equilibriumDisplacementMm": 15,
    "equilibriumPressureMpa": 0.75
  }
}

Limitations and assumptions

No crossing, multiple crossings and coincident intervals are rejected. The tool does not extrapolate, establish equilibrium stability or validate the geotechnical model.

Numerical inputs must be finite. Input-shape and calculation checks do not establish measurement quality or the validity of a supplied calibration.

Alternative or Complementary methods

Choose Ground Reaction Curve when you need its operation: Evaluate calibrated linear-unloading ground reaction with a residual floor; not an elastoplastic solution or an uncalibrated prediction. Choose Longwall Support Resistance for the complementary operation: Screen longwall resistance against supplied pressure×area factored load; canopy contact, dynamic roof behavior and hydraulic reliability are external.

Background reference: Pillar and Roof Span Design Guidelines for Underground Stone Mines.

References

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

Similar or alternative tools

Ground Reaction Curve
Evaluate calibrated linear-unloading ground reaction with a residual floor; not an elastoplastic solution or an uncalibrated prediction.
Longwall Support Resistance
Screen longwall resistance against supplied pressure×area factored load; canopy contact, dynamic roof behavior and hydraulic reliability are external.