In passive state of cohesionless soil, minor stress is

Earth pressure theory:

When the soil is retained behind the retaining structures it will exert lateral pressure on the structure called earth pressure.

1. Active earth pressure in cohesionless soil

Since P_a is acting on minor principle plane,

Active earth pressure, ${\mathrm{P}}_{\mathrm{a}}={\mathrm{K}}_{\mathrm{a}}{\sigma }_{\mathrm{z}}-2\mathrm{C}\sqrt{K_a}$

Active earth pressure coefficient, $K_a=\frac{1-sin?}{1+sin?}={\tan }^2\left(45-\frac{?}{2}\right)$

2. Passive earth pressure cohesionless soil

Since P_p is acting on a major principle plane,

Passive earth pressure, ${\mathrm{P}}_{\mathrm{p}}={\mathrm{K}}_{\mathrm{p}}{\sigma }_{\mathrm{z}}+2\mathrm{C}\sqrt{K_p}$

Passive earth pressure coefficient, ${\mathrm{K}}_{\mathrm{P}}=\frac{1+\mathrm{s}\mathrm{i}\mathrm{n}?}{1-\mathrm{s}\mathrm{i}\mathrm{n}?}={\tan }^2\left(45+\frac{?}{2}\right)$

Where, μ = Poission ratio, σ_z = vertical stress, C = cohesion of soil, ? = Angle of internal friction,

σ₁ = Major stress and σ₂ = Minor stress