Ground Reaction Curve

Evaluate calibrated linear-unloading ground reaction with a residual floor; not an elastoplastic solution or an uncalibrated prediction.

Description

A calibrated ground-reaction curve can model declining required support pressure as displacement grows.

A calibrated ground-reaction curve can model declining required support pressure as displacement grows. A residual floor prevents the linear unloading model from declining indefinitely.^[1]

The tool returns requiredSupportPressuresMpa, residualTransitionDisplacementMm. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Ground Reaction Curve

Use this for the following task: Evaluate calibrated linear-unloading ground reaction with a residual floor; not an elastoplastic solution or an uncalibrated prediction. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Ground Reaction Curve and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter displacementsMm, initialPressureMpa, unloadingStiffnessMpaPerMm, residualPressureMpa according to the field table, then run the tool.
Read requiredSupportPressuresMpa, residualTransitionDisplacementMm. 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
initialPressureMpa	Initial pressure mpa	number	Required
unloadingStiffnessMpaPerMm	Unloading stiffness mpa per mm	number	Required
residualPressureMpa	Residual pressure mpa	number	Required

Use increasing nonnegative displacements, positive initial pressure and stiffness, and a residual pressure from zero through the initial pressure. Return pressures and the floor-transition displacement.

pressure(u) = max(residualPressure,initialPressure−stiffness×u)

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

Output field	Meaning	Value type
requiredSupportPressuresMpa	Required support pressures mpa	list of number
residualTransitionDisplacementMm	Residual transition displacement mm	number

json

{
  "input": {
    "displacementsMm": [
      0,
      10,
      20
    ],
    "initialPressureMpa": 2,
    "unloadingStiffnessMpaPerMm": 0.1,
    "residualPressureMpa": 0.5
  },
  "output": {
    "requiredSupportPressuresMpa": [
      2,
      1,
      0.5
    ],
    "residualTransitionDisplacementMm": 15
  }
}

Limitations and assumptions

This supplied linear model is not a constitutive elastoplastic solution. Parameters must be calibrated for the intended ground and excavation conditions.

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 Support Interaction when you need its operation: Intersect piecewise-linear supplied ground/support curves within bounds; missing, multiple and coincident equilibria are errors, not stability certifications. 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 Support Interaction
Intersect piecewise-linear supplied ground/support curves within bounds; missing, multiple and coincident equilibria are errors, not stability certifications.
Longwall Support Resistance
Screen longwall resistance against supplied pressure×area factored load; canopy contact, dynamic roof behavior and hydraulic reliability are external.