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Slope Stability — Simplified Bishop with Critical-Circle Search (U.S. units)

Overall stability of a simple homogeneous slope: the tool generates the slip circles, slices them, and searches for the minimum Bishop factor of safety; the Ordinary (Fellenius) value is shown on the same circle, and the result is compared with the AASHTO overall-stability resistance factor.

Geometry

Slope height H ft

Slope n (horizontal : 1 vertical)

Same soil below toe ft

Soil

c′ psf

φ′ deg

γ pcf

Pore-pressure ratio r_u

Resistance factor (AASHTO overall stability)

Default inputs reproduce the ACADS 1(a) benchmark (c′/γH = 0.015, φ′ 19.6°, 2:1 slope) in U.S. units.

Results

Minimum FS — Simplified Bishop—

FS — Ordinary (Fellenius), same circle—

Critical circle: centre, radius—

Required FS = 1/φ · min m_α—

MethodsSimplified Bishop (1955) and Ordinary / Fellenius (1936) method of slices; m_α < 0.2 flagged (Whitman & Bailey 1967). AASHTO LRFD overall stability resistance factors (Caltrans: 0.65 service ≈ FS 1.5; 0.9 extreme event).

VerifiedACADS 1(a) benchmark (Giam & Donald 1989): Bishop 0.987 (Slide2), 0.993 mean of 18 programs, referee 1.00 — this tool ≈ 0.985. Bishop = Fellenius identity at φ′ = 0 and slice-number convergence are tested.

Preliminary calculation tool. Final design requires the full text of the referenced standard (see the sources on this page) and review by a licensed PE.