The critical vertical depth Hc of free standing soil can be upto active earth pressure, is given by _______

Where ‘c’ is cohesion, ‘γ’ is the density of the soil, ‘h’ is the depth of filling and ‘ϕ’ is the angle of internal friction.

1
\({{\rm{H}}_{\rm{c}}}{\rm{\;}} = {\rm{\;}}\frac{{{\rm{\gamma h}}}}{2}{\tan ^2}\left( {45 - \frac{\phi }{2}} \right)\)
2
\({{\rm{H}}_{\rm{c}}}{\rm{\;}} = {\rm{\;}}\frac{{{\rm{\gamma }}{{\rm{h}}^2}}}{2}{\tan ^2}\left( {45 - \phi } \right)\)
3
\({{\rm{H}}_{\rm{c}}}{\rm{\;}} = {\rm{\;}}\frac{{4{\rm{c}}}}{{{\rm{\gamma }}\tan \left( {45 - \frac{\phi }{2}} \right)}}\)
4
\({{\rm{H}}_{\rm{c}}}{\rm{\;}} = {\rm{\;}}\frac{{4{\rm{c}}}}{{{\rm{\gamma }}\tan \left( {45 + \frac{\phi }{2}} \right)}}\)

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