Discussion
The maximum shear stress (τmax ) for a soil mass is equal to :
Answer: B
The maximum shear stress is \((\sigma_{1} - \sigma_{3})/2\).
On Mohr's circle the major and minor principal stresses \(\sigma_1\) and \(\sigma_3\) mark the two ends of a diameter. The greatest shear stress is the radius of the circle, acting on planes at 45° to the principal planes:
\[ \tau_{max} = \frac{\sigma_1 - \sigma_3}{2} \]
\((\sigma_1 + \sigma_3)/2\) is the centre of the circle, the normal stress on the plane of maximum shear. \((\sigma_3 - \sigma_1)/2\) has the right size but is negative, and the product of the stresses has the wrong units.
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