UCS as special case of UU test

In a UU triaxial test, a specimen is sheared without drainage and without prior consolidation under a cell pressure $\sigma_3$. The unconfined compression test is the same test with cell pressure equal to zero ($\sigma_3 = 0$).

For saturated clay, the undrained strength is independent of the confining pressure ($\phi_u = 0$). So a sample tested without any cell pressure gives a Mohr circle of the same diameter as one tested under a cell pressure; the circle is only shifted along the $\sigma$-axis:

$$q_u = \sigma_1 - 0 = \sigma_1 - \sigma_3 = 2c_u$$

Both tests also shear the sample quickly with no drainage (no change in water content). Hence the UCS test is a special case of the UU test with $\sigma_3 = 0$.