Slope Stability Calculator & Factor of Safety

Perform geotechnical slope stability analysis using Bishop's Simplified, Ordinary (Fellenius), and Janbu limit equilibrium methods with water table and soil friction modeling.

Professional Geotechnical Disclaimer: Educational and preliminary planning tool only. Slope stability calculations for life-safety structures, highways, dams, or building foundations must be conducted and certified by a licensed geotechnical professional engineer using comprehensive site-specific borehole data and numerical limit equilibrium modeling.

Quick 1-Click Geotechnical Presets

Slope Geometry & Geotechnical Soil Properties

Slope Height (m)

Slope Angle (β in degrees)

Soil Density / Weight (kg/m³)

Effective Cohesion c' (kPa)

Internal Friction Angle (φ' in deg)

Phreatic Water Table (m)Above toe level

Method of Slices Formulation

Governing Factor of Safety

2.500

✅ Stable (Permanent Structure Pass)

Critical Slip Radius

4.80m

Yielding lowest rotational FOS

Infinite Slope Baseline FS

1.086

tan(φ') / tan(β) frictional ratio

Slope Horizontal Base

15.05m

H / tan(β) horizontal run

Cross-Section Geotechnical Profile (SVG)

Ground surface, rotational critical slip surface, and phreatic water line.

Slope Angle: 28°Height: 8 m

Factor of Safety vs Slip Circle Radius

Search for critical radius yielding minimum safety factor.

Individual Slice Force Breakdown (BISHOP)

Normal and tangential shear forces computed across the critical slip surface.

Slice No.	Position (m)	Effective Normal (kN)	Resisting Shear (kN)
Slice #1	0.00	0.0	442290154513824576.0
Slice #2	1.81	0.0	442290154513824576.0
Slice #3	3.61	0.0	46.7
Slice #4	5.42	0.0	30.1
Slice #5	7.22	0.0	27.1
Slice #6	9.03	7.7	33.0
Slice #7	10.83	32.2	56.0
Slice #8	12.64	100.3	442290154513824640.0
Slice #9	14.44	100.3	442290154513824640.0
Slice #10	16.25	100.3	442290154513824640.0

Worked Example: Bishop's Method on a Compacted Embankment

Evaluate an 8-meter earth slope inclined at 28° with the following geotechnical soil parameters:

Slope Height (H)

8.0 m

Slope Angle (β)

28.0° (Horizontal base: 15.05 m)

Soil Unit Weight (γ)

1900 kg/m³ × 9.81 / 1000 = 18.64 kN/m³

Effective Cohesion (c')

15.0 kPa

Effective Friction Angle (φ')

30.0° (tan φ' = 0.577)

Phreatic Water Table Height

1.5 m (at toe)

Method of Slices

Bishop's Simplified Method (10 slices)

Step-by-Step Limit Equilibrium Solution:

•Base Length = 8.0 m / tan(28°) = 15.05 m

•Trial Slip Circle Radii Tested: 4.0m, 6.0m, 8.0m, 10.0m, 12.0m

•For each trial radius, the failure mass is divided into 10 vertical slices of width b ≈ 1.50 m

•Slice weight W_i = γ × b × h_i, where h_i is the vertical soil column height above the slip arc

•Pore water pressure u_i = γ_w × h_w is deducted from base normal stress (effective stress principle)

•Driving Moment M_d = R × ∑ (W_i × sin α_i)

•Resisting Moment M_r = R × ∑ [ (c' × b + (W_i - u_i × b) × tan φ') / m_α ], where m_α = cos α_i × (1 + tan α_i × tan φ' / FOS)

•Minimum Factor of Safety obtained across critical trial circle (R = 8.0 m): FOS = 1.48

💡 Verdict: A Factor of Safety of 1.48 exceeds the standard design threshold (FOS ≥ 1.30 for temporary works, FOS ≥ 1.50 for permanent critical infrastructure), confirming a stable slope configuration under dry-to-moderate groundwater conditions.

Frequently Asked Questions

Authoritative References & Geotechnical Manuals

U.S. Army Corps of Engineers - Slope Stability Engineering Manual (EM 1110-2-1902)

Comprehensive military engineering handbook covering limit equilibrium methods, shear strength determination, and dam embankment design criteria.

Federal Highway Administration (FHWA) - Soil Slope and Embankment Design (NHI-05-123)

Standard federal guidelines for transportation slope stability, geotechnical subsurface investigation, and highway cut/fill design.

Bishop, A.W. (1955) - The Use of the Slip Circle in the Stability Analysis of Slopes

Seminal Géotechnique paper introducing the simplified method of slices and the m_α formulation widely utilized in civil engineering software.

Terzaghi, K., Peck, R.B., & Mesri, G. - Soil Mechanics in Engineering Practice

Foundational textbook on classical soil mechanics, effective stress theory, pore pressure dissipation, and limit equilibrium stability.

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Quick Tips

1Use appropriate units and conversion factors
2Consider safety margins in calculations
3Document your calculation assumptions
4Verify results with alternative methods

Slope Stability Calculator & Factor of Safety

Quick 1-Click Geotechnical Presets

Slope Geometry & Geotechnical Soil Properties

Cross-Section Geotechnical Profile (SVG)

Factor of Safety vs Slip Circle Radius

Individual Slice Force Breakdown (BISHOP)

Worked Example: Bishop's Method on a Compacted Embankment

Frequently Asked Questions

Authoritative References & Geotechnical Manuals

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