Zerdly

Toppling Kinematic Screen

Applies the Goodman–Bray kinematic conditions for flexural toppling of steeply dipping rock layers. Enter the slope face, the layer orientation and a friction angle, and it returns a Yes/No for the inter-layer slip and into-slope conditions plus an overall feasibility verdict.

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How to use this calculator

Enter Values

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 dip direction αf.
  2. Enter the layer (discontinuity) dip ψd and dip direction αd, plus the friction angle φ.
  3. Read the inter-layer slip and into-slope criteria and the overall toppling verdict.

How it works

Flexural toppling develops when steeply dipping layers rotate forward out of a slope. The inter-layer slip condition requires (90 − ψd) ≤ (ψf − φ) — the normal to the layers dips flatter than a line at φ from the face. The orientation condition requires the layers to dip steeply into the slope, within about ±10° of (αf + 180°).

The into-slope check uses the acute wrap difference between the layer dip direction αd and the anti-face direction (αf + 180°). When both conditions pass, flexural toppling is kinematically feasible. The screen assumes closely spaced, continuous, near-parallel discontinuities and a planar face.

Worked example

Layers dipping 70° into a 60° face. For ψf = 60°, αf = 90°, ψd = 70°, αd = 270° and φ = 30°: inter-layer slip needs (90 − 70) = 20° ≤ (60 − 30) = 30° = Yes. The anti-face direction is 270°, so Δα = 0° ≤ 10° = Yes. Verdict: Kinematically feasible.

Common mistakes

  • Entering the layer dip direction as the same bearing as the face — for toppling the layers must dip into the slope (αf + 180°).
  • Forgetting the slip condition uses (90 − ψd): shallow-dipping layers rarely satisfy it.
  • Reading a feasible result as a stability verdict rather than a geometric possibility needing further analysis.

Frequently asked questions

What is flexural toppling?

A failure mode where steeply dipping, closely spaced rock layers bend and rotate forward out of the slope like a row of books. The Goodman–Bray conditions test whether it is kinematically possible.

Why does the slip condition use (90 − ψd) ≤ (ψf − φ)?

Inter-layer slip develops only if the normal to the layers is inclined more than the friction angle from the face. Rearranged for the layer dip, that is (90 − ψd) ≤ (ψf − φ).

How close to opposite must the layers dip?

Within roughly ±10° of directly into the face (αf + 180°). You can adjust the tolerance to your project standard.

Does this cover block toppling?

No. This screen is for flexural toppling and gives a kinematic yes/no only. Block and block-flexure toppling need a dedicated analysis.

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