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Despite the fact that there are shear stresses also involved while considering deformations in soil why are the horizontal and vertical stresses on an element as shown in below figure considered as principle stresses while analyzing the active and passive earth pressures on retaining walls? In other words how does one conclude here in the first place that shear stresses on horizontal and vertical planes are zero when the soil mass is in active or passive stage?

enter image description here

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  • $\begingroup$ Because they come from the forces that need to be resolved. Barnes Wallis used those to good effect… $\endgroup$
    – Solar Mike
    Commented Sep 10, 2023 at 6:06
  • $\begingroup$ Can you elaborate ? $\endgroup$ Commented Sep 10, 2023 at 6:08
  • $\begingroup$ how doe one conclude here that there are no shear stresses on vertical and horizontal planes? $\endgroup$ Commented Sep 10, 2023 at 6:09
  • $\begingroup$ Why change the question? This is not a chat site. $\endgroup$
    – Solar Mike
    Commented Sep 10, 2023 at 6:27
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    $\begingroup$ Are the principal stresses in question in the retaining wall or in the soil held by it? The principal directions are correct for the soil. $\endgroup$ Commented Sep 10, 2023 at 7:47

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These are not principal stresses in the element. In my opinion this is simply a way of conveniently showing the stresses applied on the element, but not necessarily the principal ones (remember a triaxial test. Of course then the weakest plane on the element will be sloped). Showing stresses vertical and horizontal is convenient and can take us to solutions when solving the retaining wall.

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