A wall carrying a sloping backfill is shown in Fig.1. Consider an element subjected to a stress Ïƒ_{v} in the vertical direction and Ïƒ_{x} in the direction parallel to the backfill. As these stresses in one plane are parallel to the direction of another plane, these stresses are conjugate stresses and the planes are the conjugate planes. The equivalent vertical stress acting parallel to the surface of backfill is given by:

Ïƒ_{ve} = Ïƒ_{v}cosi ———- (1)

Ïƒ_{ve} = Î³zcosi

The Mohr Circle, which represents this case of inclined backfill is shown in the Fig 1.

Referring to the figure, the coefficient of active earth pressure can be written as:

We can also write:

CD = OC sini

OD = OC cosi

Because PC = R

R = OC sin É¸

By substitution these values in the expression for K_{a} we get;

Therefore, P_{a} = K_{a}Î³z cosi = K_{A}Î³z

Where,

and is known as the coefficient of active earth pressure.

If, Î±_{1} and Î±_{2} are the inclination of failure planes with horizontal as shown in figure 3

Ï´_{f1} = Î±_{1} + Ï´_{1}

Î±_{1} = Ï´_{f1} – Ï´_{1}

Î¨ = i + 2Ï´_{1}

But,

Hence,

And Similarly,

Where, CD normal to OA

and