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Geotechnical Analysis Tool

Janbu Slope Stability

Simplified method of slices for non-circular slip surface analysis (Janbu 1973). Satisfies horizontal and vertical force equilibrium. Includes Berger-Fellenius f0 correction.

Janbu Simplified Method -- Core Equations (Janbu 1973)

FS = f0 * [ Sum{ (c'*b + (W + Q - u*b)*tan(phi')) / (cos(a)*m_a) } ] / [ Sum{ (W + Q)*sin(a) } ]

m_a = cos(a) * [ 1 + tan(a)*tan(phi') / FS ]
f0 = 1 + A * (d/L - 1.4*(d/L)^2) -- Berger & Fellenius (1980)
A = 0.50 (c-phi soil) | 0.69 (purely cohesive) | 0.31 (purely frictional)
d = max depth of slip surface below chord; L = chord length; a = base inclination angle

Global Parameters

Applied across all slices

Unit Weight of Water -- gw (kN/m3)

Lateral Force at Toe -- Ea (kN)

Lateral Force at Head -- Eb (kN)

Pore Pressure Input Mode Direct u (kPa) -- enter per slice Water table h (m) -- u = gw*(h - y) Pore pressure ratio ru -- u = ru*g*H

Slice Input Data

b = horizontal width | z = ground elev | y = slip surface elev

Slope Stability Results

Janbu simplified + Berger-Fellenius f0 correction

Factor of Safety (uncorrected)

--

Before f0 correction

Corrected FS (x f0)

--

Recommended design value

Stability Status

--

FS >= 1.5 stable | 1.2-1.5 marginal | < 1.2 unstable

f0 Correction Factor

--

Berger & Fellenius 1980

Iterations to Converge

--

Tolerance: 0.0001

Sum Driving Force (kN)

--

Sum (W+Q)*sin(alpha)

Slope Profile and Slip Surface

Mohr-Coulomb: Failure Envelope vs Slice States

Detailed Results by Slice

Slice	b (m) Width	H (m) Height	W (kN) Weight	alpha (deg) Base Angle	u (kPa) Pore Press	m_alpha Factor	N' (kN) Eff Normal	c'*b (kN) Cohesion	Resisting (kN)	Driving (kN)

Janbu Simplified -- Important Notes:
(1) This method satisfies only horizontal and vertical force equilibrium; it does NOT satisfy moment equilibrium. This typically gives FS values 5-15% conservative compared to rigorous methods (Spencer, Morgenstern-Price) for c-phi soils.
(2) The f0 correction (Berger and Fellenius 1980) partially compensates for neglected interslice shear forces. Use the corrected FS (x f0) for design decisions.
(3) Base angle alpha is computed by central-difference of adjacent slip surface elevations. Accurate geometry input is essential for reliable results.
(4) For steeply inclined slice bases, m_alpha may approach zero -- examine individual slice data carefully.
(5) Always verify critical slopes with a rigorous method (Spencer, Morgenstern-Price) before final design.

Data Management

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References and Further Reading

• Janbu, N. (1973). Slope stability computations. In Hirschfeld, R. C. and Poulos, S. J. (eds.), Embankment Dam Engineering -- Casagrande Volume, pp. 47-86. John Wiley and Sons, New York. [Original derivation of the simplified and generalised Janbu methods.]
• Berger, B. and Fellenius, B. H. (1980). Correction factors for simplified Janbu method. Internal report, Swedish Geotechnical Institute. [Source of the f0 correction: f0 = 1 + A*(d/L - 1.4*(d/L)^2).]
• Duncan, J. M. and Wright, S. G. (2005). Soil Strength and Slope Stability. John Wiley and Sons, Hoboken, New Jersey. ISBN 978-0-471-69163-1. [Comprehensive treatment; Chapter 6 covers the Janbu simplified method in detail.]
• Fredlund, D. G. and Krahn, J. (1977). Comparison of slope stability methods of analysis. Canadian Geotechnical Journal, 14(3), 429-439. [Classic comparison of Janbu simplified vs. Bishop, Spencer, Morgenstern-Price; demonstrates the 5-15% error range.]
• Nash, D. F. T. (1987). A comparative review of limit equilibrium methods of stability analysis. In Anderson, M. G. and Richards, K. S. (eds.), Slope Stability, Chapter 11. John Wiley and Sons, Chichester.
• Morgenstern, N. R. and Price, V. E. (1965). The analysis of the stability of general slip surfaces. Geotechnique, 15(1), 79-93. [Rigorous method recommended for verification of critical slopes analysed with Janbu simplified.]
• IS 7894 (1975). Code of Practice for Stability Analysis of Earth Dams. Bureau of Indian Standards, New Delhi. [Indian standard covering accepted limit equilibrium methods for embankment and dam slope analysis.]
• USBR (2011). Design Standards No. 13 -- Embankment Dams, Chapter 7: Slope Stability. U.S. Bureau of Reclamation, Denver, Colorado. [Minimum FS criteria: 1.5 long-term static, 1.3 rapid drawdown, 1.0 seismic.]

Implementation: Janbu (1973) simplified method with f0 correction per Berger and Fellenius (1980). Base angle alpha by central-difference of slip surface elevations. Pore pressure modes: direct u | water table h | pore pressure ratio ru. Convergence tolerance: 0.0001 on FS | max 200 iterations.