Retaining & slopes · Slope stability

Planar failure with tension crack (Hoek & Bray) calculator

Factor of safety of a planar slide with a water-filled tension crack, uplift on the plane and optional horizontal seismic coefficient.

Standard: Hoek & Bray plane failure

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Diagram for the worked example

Plane length (H − z)/sin ψp = (20-6)/SIN(RADIANS(35)) = 24.408 m
Weight 0.5γH²[(1 − (z/H)²)cot ψp − cot ψf] = 0.5*26*20^2*((1-(6/20)^2)/TAN(RADIANS(35))-1/TAN(RADIANS(60))) = 3755.8 kN/m
Uplift 0.5γw zw A = 0.5*9.81*3*24.408 = 359.17 kN/m
Crack water force 0.5γw zw² = 0.5*9.81*3^2 = 44.145 kN/m
FS = (25*24.408+(3755.8*(COS(RADIANS(35))-0*SIN(RADIANS(35)))-359.17-44.145*SIN(RADIANS(35)))*TAN(RADIANS(35)))/(3755.8*(SIN(RADIANS(35))+0*COS(RADIANS(35)))+44.145*COS(RADIANS(35))) = 1.1392

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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.