Engineering & geotechnics
Mohr Circle & Failure Envelope
Stress transformation and Mohr–Coulomb failure, interactively.
Draws the Mohr circle for any 2-D stress state, gives principal stresses, maximum shear and the stresses on any plane, checks it against a Mohr–Coulomb envelope, and fits c and φ from a series of triaxial tests.
Overview
Turn the plane-angle slider and watch the stress point travel around the circle. In triaxial mode, enter the confining and failure stresses of each specimen and the tool fits the envelope by least squares in p–q space.
What you enter · What you get
What you enter
- σx, σy, τxy or σ1, σ3
- Cohesion and friction angle
- Triaxial results (σ3, σ1 at failure)
What you get
- Principal stresses and directions
- Maximum shear stress
- Normal and shear stress on any plane
- Safety against Mohr–Coulomb failure
- Fitted c and φ
How it works in the field
Enter the stress state
Rotate the plane
Check failure
Method and equations
Stress transformation
Stresses on a plane rotated by θ.
σθ = (σx+σy)/2 + (σx−σy)/2 cos2θ + τxy sin2θ
Mohr–Coulomb
Failure when shear stress reaches the envelope.
τf = c + σ tanφ · sinφ = tanα, c = a / cosφ
Who uses it
Rock and soil mechanics studentsGeotechnical laboratoriesStructural geologists
Standards and references
- Mohr, O. (1882). Über die Darstellung des Spannungszustandes und des Deformationszustandes eines Körperelementes. Civilingenieur, 28, 113–156.
- Jaeger, J.C., Cook, N.G.W. & Zimmerman, R. (2007). Fundamentals of Rock Mechanics, 4th ed. Blackwell.
- Craig, R.F. & Knappett, J.A. (2012). Craig’s Soil Mechanics, 8th ed. Spon Press.
Results support professional judgement. They do not replace a licensed engineer’s or geologist’s sign-off.
At a glance
- Category
- Engineering & geotechnics
- Runs on
- Phone, tablet and desktop browser
- Export
- PNG figure, PDF report
- Access
- Subscribers
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