Civil, Structural & Geotechnical Engineering
Janbu Simplified Noncircular Slope Stability Formula: Correction Factor f_0 & FS_J
Analyze shallow translational and composite noncircular slip surfaces using Nilmar Janbu’s Simplified Method: compute empirical interslice shear correction f_0 = 1 + b_1 * ((d / L) - 1.4 * (d / L)^2) and corrected FS_J = f_0 * FS_0.
Why noncircular weak-seam slides require Janbu’s horizontal force equilibrium + f_0 correction!
When a landslide glides along a planar bedrock contact or thin weak clay seam rather than a circular arc, moment equilibrium around a single circle center no longer applies. Nilmar Janbu (1954, 1973) formulated horizontal force equilibrium across vertical slices (giving uncorrected factor FS_0 with zero interslice shear) and calibrated the empirical interslice-shear correction factor f_0 = 1 + b_1 * ((d / L) - 1.4 * (d / L)^2) (valid for depth-to-length ratios 0 < d / L <= 0.35)!
Here L is the straight chord length connecting toe to crest scarp, d is the maximum perpendicular depth of the slip surface below that chord, and soil-strength constant b_1 equals 0.31 for purely frictional (c = 0, phi > 0) sands, 0.69 for cohesive-frictional (c > 0, phi > 0) soils, and 1.00 for undrained cohesive (phi = 0, c > 0) clays — raising FS_0 by up to ~12% to match Janbu’s Generalized Method!
| Soil Strength Class | Janbu Constant b_1 | f_0 at d / L = 0.15 (d = 4.5 m, L = 30 m) | Corrected FS_J when FS_0 = 1.240 |
|---|---|---|---|
| Frictional Only (phi > 0, c = 0) | b_1 = 0.31 | 1.0367 | 1.286 |
| Cohesive-Frictional (c > 0, phi > 0) | b_1 = 0.69 | 1.0818 | 1.341 |
| Undrained Cohesive (phi = 0, c > 0) | b_1 = 1.00 | 1.1185 | 1.387 |
Janbu Empirical Interslice Shear Correction Factor f_0
Selects b_1 from soil regime B5 ("PHI", "C-PHI", or "C") and evaluates 1 + b_1 * ((d / L) - 1.4 * (d / L)^2) for 0 < d / L <= 0.35.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B3 / B4 > 0.35, AND(UPPER(TRIM(B5 & "")) <> "PHI", UPPER(TRIM(B5 & "")) <> "C-PHI", UPPER(TRIM(B5 & "")) <> "C")), "Invalid Janbu Geometry or Soil Class", ROUND(1 + IF(UPPER(TRIM(B5 & "")) = "C", 1, IF(UPPER(TRIM(B5 & "")) = "C-PHI", 0.69, 0.31)) * ((B3 / B4) - 1.4 * (B3 / B4) ^ 2), 4))Corrected Janbu Simplified Factor of Safety FS_J = f_0 * FS_0
Multiplies uncorrected horizontal-equilibrium factor FS_0 (B2) by f_0.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B3 / B4 > 0.35, AND(UPPER(TRIM(B5 & "")) <> "PHI", UPPER(TRIM(B5 & "")) <> "C-PHI", UPPER(TRIM(B5 & "")) <> "C")), "Invalid Janbu Geometry or Soil Class", ROUND(B2 * (1 + IF(UPPER(TRIM(B5 & "")) = "C", 1, IF(UPPER(TRIM(B5 & "")) = "C-PHI", 0.69, 0.31)) * ((B3 / B4) - 1.4 * (B3 / B4) ^ 2)), 3))Try the example
Use the original values or change them to test your understanding.