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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.

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How to use this calculator

Enter Values

Range 0–90

Range 0–360

Range 0–90

Range 0–360

Range 0–90

Range 0–90

Enter your values and press Calculate to see results.

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

  1. Enter the slope face dip ψf and its dip direction αf (azimuth 0–360° clockwise from north).
  2. Enter the discontinuity dip ψp and dip direction αp, plus the available friction angle φ.
  3. 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.

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Cite this tool

Zerdly. (2026). Plane Failure Kinematic Screen. Retrieved from https://www.zerdly.com/tools/plane-failure-kinematic-screen/

Tip: Enter any known values to calculate the remaining results.

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