Subsidence Strain
Differentiate u(x)=c·s′(x) for caller downward-positive Gaussian subsidence; positive tensile/negative compressive strain depends on supplied c.
Description
Horizontal strain in this subsidence model is proportional to the curvature of a Gaussian trough.
Horizontal strain in this subsidence model is proportional to the curvature of a Gaussian trough. Its sign changes at one trough scale from the center.
The tool returns horizontalStrains (horizontal strains). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Subsidence Strain
Use Subsidence Strain when you already have positionsM, maximumSubsidenceM, troughScaleM, horizontalDisplacementCoefficientM and want horizontalStrains. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Subsidence Strain and understand its results
- Enter positionsM, maximumSubsidenceM, troughScaleM, horizontalDisplacementCoefficientM 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 horizontalStrains. 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 |
|---|---|---|---|
| positionsM | Positions m | list of number | Required |
| maximumSubsidenceM | Maximum subsidence m | number | Required |
| troughScaleM | Trough scale m | number | Required |
| horizontalDisplacementCoefficientM | Horizontal displacement coefficient m | number | Required |
Use positive scale, nonnegative subsidence and displacement coefficient in m, and nonempty positions in m.
strain(x) = coefficient×Smax/scale²×exp(−z²/2)×(z²−1); z=x/scale The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"positionsM": [
-10,
0,
10
],
"maximumSubsidenceM": 1,
"troughScaleM": 10,
"horizontalDisplacementCoefficientM": 2
},
"output": {
"horizontalStrains": [
0,
-0.02,
0
]
}
}Limitations and assumptions
The coefficient and Gaussian profile are supplied assumptions. The result is not a calibrated damage prediction or full geomechanical analysis.
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
Subsidence Tilt: Evaluate spatial derivative of supplied downward-positive Gaussian trough; distinct from horizontal strain and excludes building response. Subsidence Trough Width: Estimate geometric influence envelope from panel width, depth and caller angle from vertical; does not infer geology or Gaussian trough scale.
Methodological background: Mine Slope and Subsidence Monitoring Partnership.1
References
-
Mine Slope and Subsidence Monitoring Partnership — NIOSH, Centers for Disease Control and Prevention
Similar or alternative tools
- Subsidence Tilt
Evaluate spatial derivative of supplied downward-positive Gaussian trough; distinct from horizontal strain and excludes building response.
- Subsidence Trough Width
Estimate geometric influence envelope from panel width, depth and caller angle from vertical; does not infer geology or Gaussian trough scale.