Against a strong wall midterm the backfill attains pressure at rest. On the other hand, for cohesionless backfills it may be acceptable to think the friction angle at the interface is close to the inner friction angle. One way of seeing it for a pressure caused for an area load is to interpret that the stresses at such interface would be those there caused by the area load in an elastic halfspace, that is, by the integration of the effects of elements of area load in different points of interest in the wall through the Bpussinesq equation.
I have the case of the infinite strip load at a distance such way in Mathcad Collaboratory, which has only values varying along the depth in the interface.
Unfortunately I have not it for the finite rectangle in which also would vary along the length of the wall, but to make a sheet to such purpose wouldn't be as difficult starting from the formulation of the stresses for a point load or modifying other sheets.
By the way note that as interesting is then to determine the tangential loads in the wall, that help in stabilization and give the inclination of the resultant in a particular element.
Now a formulation in card OCE 5
Numerator= b x c x s x k
Divisor=
((a+b) x tan ((fi/4)+(pi/2)) - a x tan (fi)) x (a + c))
Unitary push= Numerator / Divisor
a shortest distance in plan of load to wall
b dimension of load perpendicular to wall
c dimension of load parallel to wall
s uniform load per unit surface
k active pressure coefficient
fi angle of inner friction
pi 3.1416
This unitary load affects to the region
in plan
spreading 1 along the wall to 2 along the normal to the wall
(i.e. spreads at 26.66 deg from closest vertices to wall)
in section
from the closest point in the load, draw a line at fi with the horizontal downwards and towards the wall.
The region above gets excluded from loading.
from the farther point to the wall, draw a line at
(fi/4)+(pi/2) with the horizontal downwards and towards the wall.
The region below gets excluded from loading.
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