What is the Langefors-Kihlstrom burden formula?

The formula estimates the maximum burden B (m) a charge can break: B = (d/33)·√(ρe·S_rel/(ρr·f)), where d is hole diameter (mm), ρe is explosive density (g/cm³), ρr is rock density (t/m³), S_rel is relative weight strength of the explosive vs ANFO (%), and f is a fixation factor (typically 1 for a bench). This calculator uses the simplified practical form commonly applied in quarry practice.

What is the modified Ash method?

The Ash (1963) method gives geometry ratios relative to burden: spacing S = 1.25·B (for single-row shots), stemming T = 0.7·B, and subdrill J = 0.3·B. These ratios produce good fragmentation in moderately hard, massive rock. They are adjusted for very soft or very hard, jointed rock.

What is powder factor?

Powder factor (PF) is the mass of explosive used to break one unit volume (or tonne) of rock. A higher PF means more explosive per rock volume, which typically yields finer fragmentation but higher cost. Typical open-pit values range from 0.1 to 0.5 kg/t depending on rock hardness.

What explosive types are included?

The calculator covers ANFO (relative weight strength 100%), Heavy ANFO blend 70/30 (115%), emulsion (125%), TNT (equivalent reference, 100% ANFO-equivalent), and ANFO/emulsion blend 50/50 (112%). These are industry-standard typical values; actual RWS depends on the specific product and blend ratio.

How accurate are the results?

The Langefors-Kihlstrom and Ash formulas give first-estimate parameters for initial blast design. Final designs require geotechnical characterisation (rock mass classification, joint orientation, UCS), trial blasts, and vibration/flyrock assessment. Never use calculator outputs as the sole basis for live blasting without site engineering review.

Can I use imperial units?

Yes. Switch to Imperial mode to enter hole diameter in inches, bench height in feet, rock density in lb/ft³, and explosive density in lb/ft³. Burden, spacing, stemming, subdrill, and hole depth are returned in feet; powder factor is in lb/ton.

Bench Blast Design Calculator

Name: Bench Blast Design Calculator
Availability: InStock
Author: Nham Vu

Enter rock density, explosive density, bench height, and hole diameter to compute burden, spacing, stemming, subdrill depth, total hole depth, and powder factor using Langefors-Kihlstrom and modified Ash formulas.

Blast Design Inputs

Units:

Hole Diameter (mm)

Typical open-pit range: 100 – 350 mm (4 – 14 in).

Bench Height (m)

Typical range: 5 – 20 m (16 – 65 ft).

Rock Density (t/m³)

Limestone 2.3–2.7, granite 2.6–2.8, basalt 2.8–3.1 t/m³.

Explosive Type

Explosive Density Override (g/cm³) (optional)

Leave blank to use the value from explosive type above.

Relative Weight Strength Override (% vs ANFO) (optional)

ANFO = 100%. Leave blank to use the value from explosive type.

Sample Scenarios

Enter parameters and click Calculate Blast Parameters.

Burden, spacing, stemming, subdrill, hole depth, and powder factor will appear here.

Burden (B)

—

Spacing (S)

—

Powder Factor

—

kg/t

Blast Geometry Parameters

Burden (B) Langefors-Kihlstrom

—

Spacing (S) S = 1.25 × B (Ash)

—

Stemming Length (T) T = 0.7 × B

—

Subdrill Depth (J) J = 0.3 × B

—

Total Hole Depth (L) L = H + J

—

Charge Length (Lc) Lc = L − T

—

Explosive Load & Ratio Checks

Explosive mass per hole —

Rock volume per hole (B × S × H) —

Rock mass per hole —

Powder factor (by mass) —

S/B ratio —

H/B ratio —

Blast Hole Cross-Section (schematic)

Stemming Explosive charge Subdrill

Formula Reference

B = (d / 33) × √(ρe × RWS / (ρr × 100)) [Langefors-Kihlstrom, SI]

S = 1.25 × B [Ash ratio]

T = 0.70 × B [stemming]

J = 0.30 × B [subdrill]

L = H + J [total hole depth]

Lc = L − T [charge length]

PF = m_exp / (ρr × B × S × H) [kg/t]

d = hole diameter (mm), ρe = explosive density (g/cm³), ρr = rock density (t/m³), RWS = relative weight strength (%).

Summary

How it works

Enter hole diameter (mm or inches), bench height (m or ft), rock density (t/m³ or lb/ft³), and explosive density (g/cm³ or lb/ft³).
Select the unit system (SI or Imperial) and the explosive type for relative weight strength.
The tool applies the Langefors-Kihlstrom formula to compute the critical burden B.
Spacing (S = 1.25·B), stemming (T = 0.7·B), and subdrill (J = 0.3·B) follow from B via modified Ash ratios.
Total hole depth is L = bench height + subdrill.
Powder factor is computed as explosive mass per unit volume of rock broken.

Use cases

Preliminary blast pattern design for open-pit quarrying or mining.
Comparing explosive types and densities for a given rock mass.
Estimating powder factor and explosive consumption for cost planning.
Checking burden-to-spacing ratios against rule-of-thumb limits.
Student coursework and exam preparation in rock blasting or mine planning.
Sensitivity analysis — how hole diameter change affects burden and drill cost.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu