Page 256 - Civil Engineering Formulas

190 CHAPTER EIGHT

LATERAL PRESSURE OF
COHESIONLESS SOILS

For walls that retain cohesionless soils and are free to move an appreciable
amount, the total thrust from the soil is

2
1 cos i 2 (cos i) (cos ) 2
P H cos i (8.15)
2
2
2 cos i 2 (cos i) (cos ) 2
When the surface behind the wall is level, the thrust is
1 2
P 2 H K A (8.16)
2
where K A tan 45 2 (8.17)

The thrust is applied at a point H/3 above the bottom of the wall, and the pressure
distribution is triangular, with the maximum pressure of 2P/H occurring at the
bottom of the wall.
For walls that retain cohesionless soils and are free to move only a slight
amount, the total thrust is 1.12P, where P is as given earlier. The thrust is
applied at the midpoint of the wall, and the pressure distribution is trapezoidal,
with the maximum pressure of 1.4P/H extending over the middle six-tenth of
the height of the wall.
For walls that retain cohesionless soils and are completely restrained (very
rare), the total thrust from the soil is

2
1 cos i 2 (cos i) (cos ) 2
2
P H cos i (8.18)
2
2 cos i 2 (cos i) (cos ) 2
When the surface behind the wall is level, the thrust is
1 2
P 2 H K P (8.19)
2
where K P tan 45 2 (8.20)

The thrust is applied at a point H/3 above the bottom of the wall, and the pres-
sure distribution is triangular, with the maximum pressure of 2P/H occurring
at the bottom of the wall.