Shear Box Test Strength Parameters Calculator
Derive the Mohr–Coulomb shear-strength parameters — cohesion c and friction angle φ — from two direct (small) shear-box test points. Geotechnical engineers and lab technicians use it to fit the failure envelope τf = c + σn·tan φ from measured normal and peak shear stresses.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the normal stress σn and peak shear stress τ for test 1 (kPa).
- Enter the normal stress σn and peak shear stress τ for test 2 (kPa) — the two normal stresses must differ.
- Read the friction angle φ (decimal degrees) and cohesion c (kPa).
How it works
In a direct shear-box test a soil specimen is sheared under a fixed normal stress and the peak shear stress at failure is recorded. Plotting (σn, τpeak) points defines the Mohr–Coulomb failure line τf = c + σn·tan φ. Two points fix that straight line: the slope is tan φ = (τ₂ − τ₁)/(σn₂ − σn₁), so φ = atan of that slope, and the intercept is c = τ₁ − σn₁·tan φ.
φ is reported in decimal degrees. A slightly negative fitted c is not a real tensile strength — it means the soil is effectively cohesionless (c ≈ 0), so the tool flags it. For a defensible envelope, test at least three normal stresses across the working range and regress the best-fit line; use effective stresses to obtain the drained parameters c′ and φ′.
Worked example
Two-point fit. Test 1: σn₁ = 100 kPa, τ₁ = 80 kPa. Test 2: σn₂ = 200 kPa, τ₂ = 140 kPa. tan φ = (140 − 80)/(200 − 100) = 0.60, so φ = atan(0.60) = 30.96°. c = 80 − 100 × 0.60 = 20 kPa.
Common mistakes
- Using only two points for design — always run three or more normal stresses and regress; two points can't reveal scatter or curvature.
- Reading a small negative intercept as real cohesion (or tension) — it means c ≈ 0 / cohesionless.
- Mixing total and effective stresses — decide up front whether you want (c, φ) total or (c′, φ′) drained, and keep the σn basis consistent.
Frequently asked questions
What does the shear box test measure?
The peak (and residual) shear resistance of a soil at a chosen normal stress, from which the Mohr–Coulomb strength parameters cohesion c and friction angle φ are derived.
How do I get c and φ from shear box results?
Plot peak shear stress against normal stress for each test. The best-fit line's slope gives tan φ and its intercept on the shear axis gives c. This tool does that from two points.
Why is my cohesion negative?
A negative fitted intercept usually reflects test scatter, not real tensile strength. Treat it as c ≈ 0 — the soil is effectively cohesionless (purely frictional).
Is φ in degrees or radians?
Degrees. The calculation is done with atan (which returns radians) and converted to decimal degrees for display.
Which standard covers the direct shear box test?
AS 1289.6.2.2 in Australia and ASTM D3080 internationally. Ring-shear testing is used for residual strength.
Related tools
- SPT N-Value to Relative Density Calculator
- Permeability from Falling Head Test Calculator
- Void Ratio Calculator
- Bulk Density Calculator
- Bearing Capacity (Terzaghi) Calculator
- Settlement (Consolidation) Calculator
Explore more in Geology, Geotechnical & Ground Engineering.
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.