Bishop Simplified Slope Stability Calculator
Geotechnical slope stability: Determine the Factor of Safety ($FS$) against rotational circular failure using Bishop's Simplified Method of Slices and effective stress analysis.
Slope Geometry & Circular Arc
Vertical face height
e.g. 2H:1V = 26.6°, 1.5H:1V = 33.7°
Soil Shear Strength & Pore Water
Effective soil cohesion
Internal angle of shearing resistance
Total bulk unit weight
u / (γ · h) [0 = Dry, 0.45 = Steady seepage]
Bishop's Iterative Equilibrium Equation
Bishop's Simplified Method satisfies vertical force equilibrium and overall moment equilibrium for each slice:
$$FS = \frac{\sum \frac{c' b + (W - u b) \tan \phi'}{m_\alpha}}{\sum W \sin \alpha}$$
Where $m_\alpha = \cos \alpha \left(1 + \frac{\tan \alpha \tan \phi'}{FS}\right)$. Because $FS$ appears on both sides, the equation is solved iteratively until numerical convergence.
Stability Evaluation
Bishop Factor of Safety (FS)
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Ordinary / Fellenius FS
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Forces & Moments
Resisting Shear Force
--
Available shear capacity
Driving Gravitational Force
--
Sum of W · sin(α)
Geotechnical Classification
Slope Stability Status:
--
Pore Pressure Reduction Effect:
--
Standard Acceptance Criterion:
FS ≥ 1.30 (Temporary) / ≥ 1.50 (Permanent)
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