Infinite Slope Calculator
A dry sand slope at 25° with φ = 32° has a factor of safety of 1.34004.
1.34003664958388
Full answer, then cut to fewer decimals (not rounded):
- 1.34003664958388
- 1.3400366495838
- 1.340036649583
- 1.34003664958
- 1.3400366495
- 1.340036649
- 1.34003664
- 1.3400366
- 1.340036
- 1.34003
- 1.3400
- 1.340
- 1.34
- 1.3
- Slope is
- stable but below the usual 1.5
Step-by-step solution
- FS = tan φ / tan β = 0.6248693519 ÷ 0.4663076582
- FS = 1.34003665
Infinite Slope Formula
FS = tan φ / tan β
seepage: (γ′/γsat) tan φ/tan β; c–φ: c/(γz cos²β tan β) + tan φ/tan β
Worked Example
A dry sand slope at 25° with φ = 32°:
- FS = tan φ / tan β = 0.6248693519 ÷ 0.4663076582
- FS = 1.34003665
GATE tip
The critical slope of dry sand is β = φ (FS = 1), the angle of repose.
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n = e/(1 + e), γd = Gγw/(1 + e), γsat = (G + e)γw/(1 + e), γ′ = γsat − γw
Example: A soil with G = 2.65, e = 0.7 and S = 80 %: Bulk unit weight γ = 18.5236 kN/m³.
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Shear Strength Calculator
τf = c + σ tan φ; σ₁ = σ₃ Nφ + 2c√Nφ
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Example: A soil with c = 10 kPa and φ = 30° under σ = 100 kPa: Shear strength τf = 67.735 kPa.
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Rankine Earth Pressure Calculator
σa = Ka(γz + q) − 2c√Ka, σp = Kp(γz + q) + 2c√Kp
Ka = tan²(45° − φ/2), Kp = tan²(45° + φ/2)
Example: A 6 m smooth vertical wall retaining dry sand with φ = 30° and γ = 18 kN/m³: Active thrust P = 108 kN/m.
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k = QL/(Aht); k = 2.303 (aL/At) log₁₀(h₁/h₂)
a standpipe area, A sample area, L sample length, h head, t time
Example: A constant-head test collecting 500 cm³ in 10 minutes through a 15 cm sample of 78.54 cm² under 40 cm head: Coefficient of permeability k = 0.00397886 cm/s.
Frequently asked questions
Why does seepage roughly halve the factor of safety?
With the water table at the surface, γ′/γsat ≈ 0.5, so FS drops to about half of the dry value.
Does the depth matter for a dry sand slope?
No. For a cohesionless soil FS = tan φ/tan β at every depth; depth matters only when c > 0.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Infinite Slope Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/infinite-slope-calculator/
IEEE
Scientific Converters, "Infinite Slope Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/infinite-slope-calculator/