Engineering & Fluid Mechanics
Skempton’s Pore-Pressure Parameters B & A Formula: Undrained Triaxial Soil Saturation & Shear
Verify triaxial specimen saturation (B >= 0.95) and diagnose contractive vs. dilative undrained shear behavior using Alec W. Skempton’s 1954 equation delta_u = B * [delta_sigma3 + A * (delta_sigma1 - delta_sigma3)].
How Alec Skempton’s 1954 B-check and A-parameter govern ASTM D4767 CU triaxial soil testing!
Alec Westley Skempton (1954, Géotechnique) decomposed undrained pore-water pressure change delta_u into two stages of a triaxial compression test: Stage 1 isotropic cell-pressure increment delta_sigma3 (where delta_sigma1 = delta_sigma3) gives Skempton’s saturation coefficient B = delta_u_iso / delta_sigma3 (reaching B >= 0.95–1.00 in fully saturated soft clays once back-pressure dissolves trapped air bubbles)!
During Stage 2 undrained deviatoric shearing (total increment delta_u_total across isotropic delta_sigma3 plus deviator stress delta_sigma_d = delta_sigma1 - delta_sigma3), solving delta_u_total = delta_u_iso + B * A * delta_sigma_d extracts Skempton’s shear pore-pressure parameter A = (delta_u_total - delta_u_iso) / (B * delta_sigma_d)! Normally consolidated clays contract positively (A ≈ +0.5 to +1.0, sensitive quick clays > +1.0), whereas heavily overconsolidated clays dilate and generate negative pore pressure (A < 0)! For delta_u_iso = 48.5 kPa under delta_sigma3 = 50 kPa, B = 0.9700; adding deviator stress delta_sigma_d = 120 kPa with delta_u_total = 82.0 kPa yields A = 0.2878 (rising to 0.5713 in softer clay where delta_u_total = 115.0 kPa)!
| Triaxial Test Response (d_sigma3 = 50 kPa, d_u_iso = 48.5 kPa) | Skempton Saturation B | Skempton Shear Parameter A | Geotechnical Clay State |
|---|---|---|---|
| d_sigma_d = 120 kPa, d_u_total = 82 kPa | 0.9700 (Saturated >= 0.95) | +0.2878 | Lightly Overconsolidated Clay |
| d_sigma_d = 120 kPa, d_u_total = 115 kPa | 0.9700 | +0.5713 | Normally Consolidated Contractive Clay |
| Invalid Isotropic Cell Increment <= 0 | Division by Zero | "Invalid Triaxial Stress Increments" | Positive Stress Guard |
Skempton Isotropic B-Value = delta_u_isotropic / delta_sigma_3
Evaluates triaxial saturation parameter B from isotropic pore-pressure response (B2, kPa) divided by cell-pressure step (B3, kPa).
=IF(OR(B2 <= 0, B3 <= 0, B2 > B3, B5 <= 0), "Invalid Triaxial Stress Increments", ROUND(B2 / B3, 4))Skempton Deviatoric Shear Parameter A = (delta_u_total - delta_u_iso) / (B * delta_sigma_d)
Extracts shear pore-pressure parameter A using B = B2 / B3, cumulative pore-pressure change B4, and deviator stress B5.
=IF(OR(B2 <= 0, B3 <= 0, B2 > B3, B5 <= 0), "Invalid Triaxial Stress Increments", ROUND((B4 - B2) / ((B2 / B3) * B5), 4))Try the example
Use the original values or change them to test your understanding.