Tension Crack Depth Calculator
Estimates the critical depth and location of the vertical tension crack that forms in the upper bench of a rock slope prone to plane failure, using the Hoek & Bray geometry for a horizontal upper slope surface. Rock-slope and mining geotechnical engineers use it to define the top of a potential sliding block.
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 height H (m), the slope face angle ψf (°) and the failure-plane dip ψp (°), all as dip angles from horizontal.
- Make sure the face is steeper than the plane (ψf > ψp) so the plane daylights — otherwise the tool returns an error.
- Read the critical crack depth zc, the ratio zc/H, and the distance bc behind the crest.
How it works
For a plane-failure block with a horizontal upper surface, Hoek & Bray showed the tension-crack depth that minimises stability is zc = H·(1 − √(cotψf·tanψp)). Geometry then fixes the crack location a distance bc = H·(√(cotψf·cotψp) − cotψf) behind the crest.
The crack marks the rear release surface of the sliding wedge; a water-filled crack adds a horizontal thrust and uplift that lower the factor of safety. This tool gives the geometry only — feed zc and bc into a full limit-equilibrium plane-failure calculation.
Worked example
100 m slope, 50° face, 30° joint. With H = 100 m, ψf = 50° and ψp = 30°: √(cotψf·tanψp) = 0.696, so zc = 100×(1 − 0.696) = 30.4 m (zc/H = 0.30). The crack sits bc = 100×(1.206 − 0.839) = 36.6 m behind the crest.
Common mistakes
- Entering a face angle flatter than the plane (ψf < ψp): the plane cannot daylight and there is no plane-failure tension crack.
- Confusing the failure-plane dip ψp with the joint's apparent dip in section; use the true dip in the sliding direction.
- Assuming the crack is always at the crest — its critical position is a real distance bc back on the bench.
Frequently asked questions
What is a tension crack in slope stability?
A near-vertical crack that opens in the ground surface behind the crest as the slope starts to move. It forms the rear boundary of the sliding block and, if it fills with water, adds driving force.
Which formula does this use?
The Hoek & Bray result for a plane failure with a horizontal upper slope: zc = H·(1 − √(cotψf·tanψp)) and bc = H·(√(cotψf·cotψp) − cotψf) behind the crest.
Why does the plane need to daylight (ψf > ψp)?
A plane failure can only slide if the discontinuity is exposed on the face, which requires the face to be steeper than the plane. If ψf ≤ ψp the block is kinematically locked.
Does a water-filled tension crack change the result?
The crack depth geometry is unchanged, but water in the crack adds hydrostatic thrust plus uplift on the failure plane, both reducing the factor of safety. Include those in the full analysis.
Related tools
- Saturated Slope FoS Calculator
- Drainage Effect on FoS Estimator
- Plane Failure Kinematic Screen
- Factor of Safety Calculator
- Bench Face Height Calculator
- Overall Slope Angle Calculator
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Tip: Enter any known values to calculate the remaining results.
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