Shear tests; direct shear calculation

Laboratory shear strength tests: direct shear test, triaxial test (UU, CU, CD), unconfined compression test, and laboratory vane shear test.

Shear strength in the direct shear test

A soil specimen in a split box (commonly $60\times60$ mm) is loaded with a constant normal load $N$. The upper half is pushed horizontally until failure along the horizontal plane between the two halves. The horizontal force at failure is $T_f$ (read from the proving ring).

$$\sigma = \frac{N}{A}, \qquad \tau_f = \frac{T_f}{A}$$

where $A$ is the area of the specimen (corrected for the reduced contact area as the box moves, if required).

The test is repeated at three or more different normal stresses. The points $(\sigma, \tau_f)$ are plotted and a best-fit straight line is drawn. Its intercept on the $\tau$-axis is the cohesion $c$ and its slope is $\phi$:

$$\tau_f = c + \sigma\tan\phi$$

For sand, $c = 0$ and $\phi = \tan^{-1}(\tau_f/\sigma)$.