FIGURE?
EAATH THRUST ON RETAINING WALL
CALCULATED BY RANKINE'S THEORY
A retaining wall 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 is vertical, and the surface of the backfill is
inclined at an angle of 15° with the horizontal. Applying Rankine's theory, calculate the
active earth pressure on the wall at a point 12 ft (3.7 m) below the top.
Calculation Procedure:
- Construct the Mohr's circle associated with the soil prism
Rankine's theory of earth pressure applies to a uniform mass of dry cohesionless soil.
This theory considers the state of stress at the instant of impending failure caused by a
slight yielding of the wall. Let h = vertical distance from soil surface to a given point, ft
(m); p = resultant pressure on a vertical plane at the given point, lb/ft
2
(kPa); <£ = ratio of
shearing stress to normal stress on given plane; 0 = angle of inclination of earth surface.
The quantity o may also be defined as the tangent of the angle between the resultant stress
on a plane and a line normal to this plane; it is accordingly termed the obliquity of the re-
sultant stress.
Consider the elemental soil prism abed in Fig. 8a, where faces ab and dc are parallel to
the surface of the backfill and faces be and ad are vertical. The resultant pressure pv on ab
is vertical, and/? is parallel to the surface. Thus, the resultant stresses on ab and be have
the same obliquity, namely, tan 6. (Stresses having equal obliquities are called conjugate
stresses.) Since failure impends, there is a particular plane for which the obliquity is tan
*.
In Fig. 86, construct Mohr's circle associated with this soil prism. Using a suitable
scale, draw line OD, making an angle Q with the base line, where OD represents pv. Draw
line OQ, making an angle <£ with the base line. Draw a circle that has its center C on the
base line, passes through D, and is tangent to OQ. Line OD' represents/?. Draw CM per-
pendicular to OD.
