Blast Fragmentation K50 Calculator

Retrospective actual sampled fragment cumulative passing inverse 50percent endpoint interpolation, no extrapolation. Not Kuz–Ram charge-design prediction or explosive/site instructions.

Description

K50 is the size at which a supplied cumulative mass-passing curve reaches 50 percent.

K50 is the size at which a supplied cumulative mass-passing curve reaches 50 percent.^[1]

This tool interpolates recorded observations without estimating a future blast outcome.

When to use Blast Fragmentation K50 Calculator

This tool interpolates recorded observations without estimating a future blast outcome.

How to use Blast Fragmentation K50 Calculator and how it works

Prepare independently sampled fragment size knots, observed cumulative mass passing fractions, using the input definitions and matching units below.
Enter the required fields and run Blast Fragmentation K50 Calculator.
Read result.observedFragmentationSize using the units, signs and ordering explained below.
Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.

Input field	Meaning	Value type	Requirement
actualIndependentlySampledFragmentSizeKnots	Positive retrospective sampled sizes, aligned with the passing-fraction observations.	array of number	Required; other constraints below
actualObservedCumulativeMassPassingFractions	Strictly increasing cumulative passing fractions from 0 to 1, bracketing the requested percentile.	array of number	Required; other constraints below

Require aligned arrays of at least two positive sampled fragment sizes and cumulative passing fractions from 0 to 1. Passing fractions must strictly increase, with no plateau ambiguity. Invert using passing fractions as coordinates and sizes as responses, interpolating at 0.8 for K80 or 0.5 for K50. The criterion must lie in the inclusive observed range; exact knots are retained and extrapolation is rejected. Size ordering itself is not independently enforced by this branch, so a physically valid curve must be established externally.

observedKp=linearInterpolate(cumulativePassing,fragmentSize,p)

Apply the input ordering, units and branch conditions stated above.

Output field	Meaning	Value type
result	Object containing the calculated or selected fields below.	object
result.observedFragmentationSize	Interpolated observed K50 or K80 size in the supplied fragment-size unit.	number

json

{
  "input": {
    "actualIndependentlySampledFragmentSizeKnots": [
      1,
      2,
      3
    ],
    "actualObservedCumulativeMassPassingFractions": [
      0.2,
      0.5,
      0.8
    ]
  },
  "output": {
    "result": {
      "observedFragmentationSize": 2
    }
  }
}

Limitations and assumptions

The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.

All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.

Alternative or Complementary methods

Use Blast Fragmentation K80 Calculator for a complementary operation: K80 is the size at which a supplied cumulative mass-passing curve reaches 80 percent.

Use Blast Powder Factor Calculator for a complementary operation: A retrospective powder factor compares recorded consumed mass with independently surveyed broken-rock volume.

References

Blast Fragmentation K50 Calculator — tool.io

Similar or alternative tools

Blast Fragmentation K80 Calculator
K80 is the size at which a supplied cumulative mass-passing curve reaches 80 percent.
Blast Powder Factor Calculator
A retrospective powder factor compares recorded consumed mass with independently surveyed broken-rock volume.