Civil engineering mechanics & structural foundations of Triaxial CU Shear Test.
The triaxial shear test is universally recognized as the most versatile, rigorous, and definitive laboratory method for evaluating the shear strength, pore pressure response, and stress-strain-volume constitutive behavior of soils. In contrast to direct shear box testing, the triaxial test subjects a cylindrical specimen to true axisymmetric stress states (σ_1 > σ_2 = σ_3), controls drainage independently from top and bottom boundaries, permits artificial saturation via back-pressure, and measures pore water pressure u continuously under closed undrained shear. Under ASTM D4767, the Consolidated-Undrained (CU) triaxial test proceeds in three consecutive stages: (1) Back-pressure saturation—specimen and pore lines are pressurized simultaneously while maintaining low effective stress until Skempton's B-parameter B = Δu / Δσ_3 ≥ 0.95, confirming 100% saturation; (2) Isotropic consolidation—cell pressure is elevated to target effective confining stress σ'_3 = σ_3 - u_0 with drainage valves open until excess pore pressure dissipates completely; and (3) Undrained axial shearing—drainage valves are closed, and axial deviator stress q = σ_1 - σ_3 is applied via a motorized loading ram at a controlled slow strain rate (typically 0.05% to 0.1%/min) while an electronic pressure transducer logs pore-water pressure u. Plotting peak deviator stress q_f versus effective confining pressure σ'_3 establishes the p'-q failure envelope, from which effective cohesion c' and effective friction angle ϕ' are deduced. In this laboratory, CU triaxial tests are conducted across effective confining stresses from 100 to 400 kPa to calibrate the failure slope M.
1. Effective Stress Principle & Axisymmetric Triaxial Mechanics
In a standard triaxial specimen ($D_0 = 38\text{ mm}$, $L_0 = 76\text{ mm}$), the stress state is axisymmetric: radial cell fluid pressure applies equal minor and intermediate total principal stresses ($\sigma_2 = \sigma_3 = \sigma_{cell}$). Vertical axial loading via the ram applies additional deviatoric load $P$, establishing major principal total stress:
\[ \sigma_1 = \sigma_3 + \frac{P}{A} \implies q = \sigma_1 - \sigma_3 = \frac{P}{A} \]where $A$ is the deformed cross-sectional area. According to Terzaghi's effective stress principle, shear strength is governed strictly by effective principal stresses:
\[ \sigma'_1 = \sigma_1 - u, \qquad \sigma'_3 = \sigma_3 - u \]where $u$ is the measured pore-water pressure at failure.
2. Pore Pressure Generation & Skempton's Parameters
Under undrained conditions, changes in total principal stresses $(\Delta \sigma_1, \Delta \sigma_3)$ generate excess pore water pressure $\Delta u$ formulated by A. W. Skempton (1954):
\[ \Delta u = B \left[ \Delta \sigma_3 + A (\Delta \sigma_1 - \Delta \sigma_3) \right] \]For saturated soil ($B = 1.0$):
\[ \Delta u = \Delta \sigma_3 + A \cdot q \]During undrained shear where cell pressure is constant ($\Delta \sigma_3 = 0$), excess pore pressure is $\Delta u = A \cdot q$.
3. The Stress Path & Failure Envelope Formulation
On the $(q, \sigma'_3)$ stress space, the peak failure envelope for normally to lightly overconsolidated clays follows a linear trajectory:
\[ q_f = M \cdot \sigma'_3 + q_0 \]where $M = 1.3500$ is the failure slope, and $q_0 = 45.00\text{ kPa}$ is the intercept. Effective friction angle $\phi'$ is evaluated from Mohr circle geometry at failure:
\[ \sin \phi' = \frac{\sigma'_1 - \sigma'_3}{\sigma'_1 + \sigma'_3 + 2 c' \cot \phi'} = \frac{q_f}{2 \sigma'_3 + q_f + 2 c' \cot \phi'} \]yielding calibrated parameters $\phi' = 28.5^\circ$ and $c' = 15.0\text{ kPa}$.
Viva voce questions & analytical theory
What is Skempton's B-parameter, and why must B ≥ 0.95 before shearing?
B = Δu / Δσ_3 under undrained isotropic compression; for fully saturated soil (S_r = 100%), water is virtually incompressible compared to the skeleton, giving B = 1.0; achieving B ≥ 0.95 ensures that all entrapped micro-air bubbles are dissolved into solution, guaranteeing accurate pore pressure measurement.
How does Skempton's A-parameter characterize soil volume change tendency during shear?
Pore pressure parameter A = (Δu - Δσ_3) / (Δσ_1 - Δσ_3); normally consolidated clays tend to contract, generating positive excess pore pressure (A_f = 0.5 to 1.0); heavily overconsolidated clays dilate, generating negative excess pore pressure (A_f = -0.5 to 0).
Why is an internal submersible load cell preferred over an external load cell?
An external load cell measures total force including the friction between the loading ram and the cell bushing seals; an internal submersible load cell directly contacts the top cap, eliminating seal friction errors.
What is the critical difference between total stress parameters (c, ϕ) and effective stress parameters (c', ϕ')?
Total stress parameters depend on drainage conditions and pore pressure at the moment of test; effective stress parameters represent fundamental material properties governing strength across all drainage conditions via Terzaghi's principle: sigma' = sigma - u.
Why must the strain rate in CU triaxial tests be kept extremely slow (e.g. 0.05 mm/min)?
Water has low permeability in clay; shearing too quickly causes localized pore pressure gradients between the shear zone and base transducer, leading to false pore pressure measurements; slow rates ensure 95% pore pressure equalization.
How are effective friction angle ϕ' and cohesion c' calculated from the p'-q diagram slope M?
On a Cambridge p'-q plot (q vs p'), sin ϕ' = 3M / (6 + M) and c' = d (3 - sin ϕ') / (6 cos ϕ'), where M is the slope and d is the vertical intercept.
Experimental precautions and laboratory safety
- Verify latex membrane has zero pinhole punctures by checking back-pressure volume stability prior to consolidation.
- Ensure Skempton's B-check achieves at least 0.95 before initiating consolidation to prevent testing unsaturated soil.
- Select shearing rate slow enough to achieve 95% internal pore pressure equalization according to Gibson & Henkel theory.
- Apply membrane thickness corrections to deviator stress according to ASTM D4767 specifications.
Theoretical assumptions & boundary condition limits
- The civil engineering physical models apply within the specified calibrated operational window (100.0 to 400.0 kPa).
- Assumes homogeneous, isotropic continuum material behavior without unmodeled micro-fracture anomalies.
- Continuous sensor readings reflect ordinary least-squares regression across successive observations.
- Extreme inelastic yielding or cyclic degradation requires non-linear constitutive continuum damage mechanics.