Operations, Logistics & Engineering
Bjerrum Field Vane Shear Correction Factor (mu) Formula: Plasticity Index Clay Strength
Correct raw in-situ Field Vane Shear strength s_u,FV for strain-rate and anisotropy effects in high-plasticity soft clays using Laurits Bjerrum’s (1972/1973) mobilization factor mu = 1.7 - 0.54 * LOG10(PI) and s_u,design = mu * s_u,FV.
Why unfactored Field Vane Shear tests overestimate embankment stability in high-plasticity clays!
Investigating catastrophic embankment failures on soft marine and glacial clays that failed despite apparent Factors of Safety > 1.3–1.6 from in-situ Field Vane (FV) tests, Norwegian Geotechnical Institute director Laurits Bjerrum (1972/1973) discovered two systematic biases: standard vane rotation shears clay in ~1 minute (far faster than weeks-long embankment loading, inflating viscous undrained resistance in plastic clays!) and forces a vertical cylindrical shear surface despite strong clay anisotropy!
Back-analyzing full-scale failures against Atterberg Plasticity Index PI = LL - PL (%), Bjerrum established the empirical vane correction factor mu = MIN(1.0, 1.7 - 0.54 * LOG10(PI)) (capped at 1.0 for low-plasticity clays with PI <= 19.8%, per AASHTO/FHWA practice so strength is never artificially inflated above 1.0)! For a high-plasticity marine clay with LL = 85%, PL = 25% (PI = 60%) and raw vane s_u,FV = 42 kPa, mu = 1.7 - 0.54 * LOG10(60) = 0.740 (26% reduction!), yielding mobilized design s_u,design = 31.07 kPa!
| Clay Deposit & Atterberg Limits (LL - PL = PI) | Bjerrum Vane Factor mu (Capped <= 1.0) | Mobilized s_u,design for s_u,FV = 42 kPa |
|---|---|---|
| Lean Glacial Clay (LL = 32%, PL = 17% -> PI = 15%) | MIN(1.0, 1.065) = 1.000 (No Reduction) | 42.00 kPa |
| Soft Silty Clay (LL = 58%, PL = 23% -> PI = 35%) | 1.7 - 0.54 * LOG10(35) = 0.866 | 36.38 kPa |
| High-Plasticity Clay (LL = 85%, PL = 25% -> PI = 60%) | 1.7 - 0.54 * LOG10(60) = 0.740 | 31.07 kPa (-26% Rate Effect!) |
Bjerrum Field Vane Correction Factor mu = MIN(1, 1.7 - 0.54 * LOG10(LL - PL))
Computes Atterberg Plasticity Index PI = LL - PL from Liquid Limit B2 (%) and Plastic Limit B3 (%), then evaluates Bjerrum’s factor capped at 1.0.
=IF(OR(B2 <= B3, B3 <= 0, B4 <= 0), "Invalid Atterberg Limits or Vane Strength", ROUND(MIN(1, MAX(0.4, 1.7 - 0.54 * LOG10(B2 - B3))), 4))Mobilized Design Undrained Shear Strength s_u,design (kPa) = mu * s_u,FV
Multiplies raw in-situ field vane shear strength B4 (kPa) by Bjerrum’s correction factor mu.
=IF(OR(B2 <= B3, B3 <= 0, B4 <= 0), "Invalid Atterberg Limits or Vane Strength", ROUND(B4 * MIN(1, MAX(0.4, 1.7 - 0.54 * LOG10(B2 - B3))), 2))Try the example
Use the original values or change them to test your understanding.