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Stresses acting on an infinitesimal soil element are shown in the figure (with $\sigma_{z} > \sigma_{x}$). The major and minor principal stresses are $\sigma_{1}$ and $\sigma_{3},$ respectively. Considering the compressive stresses as positive, which one of the following expressions correctly represents the angle between the major principal stress plane and the horizontal plane?

 

  1. $\tan^{-1} \left( \frac{\tau_{zx}} {\sigma_{1} – \sigma_{x}} \right)$
  2. $\tan^{-1} \left( \frac{\tau_{zx}} {\sigma_{3} – \sigma_{x}} \right)$
  3. $\tan^{-1} \left( \frac{\tau_{zx}} {\sigma_{1} + \sigma_{x}} \right)$
  4. $\tan^{-1} \left( \frac{\tau_{zx}} {\sigma_{1} + \sigma_{3}} \right)$
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