EARTH THRUST ON RETAINING WALL
CALCULATED BY COULOMB'S THEORY
A retaining wall 20 ft (6.1 m) high supports sand weighing 100 lb/ft
3
(15.71 kN/m
3
) and
having an angle of internal friction of 34°. The back of the wall makes an angle of 8° with
the vertical; the surface of the backfill makes an angle of 9° with the horizontal. The angle
of friction between the sand and wall is 20°. Applying Coulomb's theory, calculate the to-
tal thrust of the earth on a 1-ft (30.5-cm) length of the wall.
Calculation Procedure:
- Determine the resultant pressure P of the wall
Refer to Fig. 9a. Coulomb's theory postulates that as the wall yields slightly, the soil
tends to rupture along some plane BC through the heel.
Let 8 denote the angle of friction between the soil and wall. As shown in Fig. 9b, the
wedge ABC is held in equilibrium by three forces: the weight W of the wedge, the result-
ant pressure R of the soil beyond the plane of failure, and the resultant pressure P of the
wall, which is equal and opposite to the thrust exerted by the each on the wall. The forces
R and P have the directions indicated in Fig. 9b. By selecting a trial wedge and computing
its weight, the value of P may be found by drawing the force polygon. The problem is to
identify the wedge that yields the maximum value of P.
In Fig. 90, perform this construction: Draw a line through B at an angle <£ with the hor-
izontal, intersecting the surface at D. Draw line AE, making an angle 8+ 4> with the back
of the wall; this line makes an angle /3 - 8 with BD. Through an arbitrary point C on the
surface, draw CF parallel to AE. Triangle BCF is similar to the triangle of forces in Fig.
9b. Then P = Wu/x, where W = w(area ABQ. - Set dP/dx = O and state Rebhann's theorem
This theorem states: The wedge that exerts the maximum thrust on the wall is that for
which triangle ABC and BCF have equal areas.
(a) Location of plane of failure (b) Free-body diagram
of sliding wedge
FIGURE 9