Plane Failure Kinematic Screen
Runs the Markland kinematic test for planar sliding on a single discontinuity in a rock slope. Enter the slope face and the discontinuity as dip and dip direction plus a friction angle, and it returns a pass or fail for each of the three sliding conditions and an overall feasibility verdict.
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 slope face dip ψf and its dip direction αf (azimuth 0–360° clockwise from north).
- Enter the discontinuity dip ψp and dip direction αp, plus the available friction angle φ.
- Read each criterion (daylights / frictional / direction) as Yes or No and the overall kinematic verdict.
How it works
Planar sliding is kinematically possible only when all three Markland conditions hold at once: the discontinuity must daylight in the face (ψp < ψf); its dip must exceed the friction angle (ψp > φ); and it must dip roughly out of the face, with the acute difference Δα between its dip direction and the face dip direction within about ±20°.
The acute difference wraps correctly around north: Δα = ((αp − αf) mod 360), reduced to 0–180° when it exceeds 180°. Passing all three means the mechanism is geometrically feasible and warrants a full limit-equilibrium check — it is not itself a factor of safety.
Worked example
60° face, joint dipping 35° nearly out of the face. For ψf = 60°, αf = 180°, ψp = 35°, αp = 190° and φ = 30°: Δα = 10°. Daylights (35 < 60) = Yes; frictional (35 > 30) = Yes; direction (10 ≤ 20°) = Yes. Verdict: Kinematically feasible.
Common mistakes
- Confusing strike with dip direction — enter the dip direction (the bearing the plane dips towards), not the strike.
- Treating a Yes verdict as proof of failure; it only means sliding is geometrically possible.
- Ignoring the lateral-limit condition — a joint that daylights and is steep enough still cannot slide planarly if it dips well oblique to the face.
Frequently asked questions
What is the Markland test?
A stereographic kinematic test that checks whether planar (and wedge) sliding is geometrically possible by comparing discontinuity orientation, slope orientation and friction angle.
Why the ±20° lateral limit?
Planar sliding requires release roughly parallel to the slope dip direction. The commonly adopted window is within about ±20° of the face dip direction; you can adjust it to your standard.
Does a 'feasible' result mean the slope will fail?
No. Kinematic feasibility means the geometry permits sliding. Whether it slides depends on the factor of safety from a limit-equilibrium analysis.
What friction angle should I use?
The effective friction angle of the discontinuity surface (basic or residual, allowing for roughness and infill), typically 25–40° for rock joints, from testing or established data.
Related tools
- Wedge Failure Kinematic Screen
- Toppling Kinematic Screen
- Kinematic Wedge Intersection Calculator
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Tip: Enter any known values to calculate the remaining results.
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