Geotechnical Engineering

DHARM

508 GEOTECHNICAL ENGINEERING

∴ x = (Wx 1 + Pav.x 2 + Pah.z 1 – Ppv.b – Pph.z 2 )/N =

Σ

Σ

M

V

...(Eq. 13.71)

*e = (~/)xb^2 ...(Eq. 13.72)
Here ΣM = Algebraic sum of the moments of all the actuating forces, other than that of
reaction N.
ΣV = Algebraic sum of all the vertical forces, other than T.
This simply means that the resultant of W, Pa, and Pp must be just equal and opposite to
the resultant of N and T, and must have the same line of action, for equilibrium of the wall.

The problem becomes essentially one of trial; the necessary width of the base usually
falls between 30% and 60% of the height of the wall.

The criteria for a satisfactory design of a gravity retaining wall may be enunciated as
follows:

(a) The base width of the wall must be such that the maximum pressure exerted on the
foundation soil does not exceed the safe bearing capacity of the soil.

(b) Tension should not develop anywhere in the wall.
(c) The wall must be safe against sliding; that is, the factor of safety against sliding
should be adequate.

(d) The wall must be safe against overturning ; that is, the factor of safety against
overturning should be adequate.

For any trial value of the base width these criteria are investigated as follows:
(a) The pressure exerted by the force N on the base of the wall is a combination of direct
and bending stresses owing to the eccentricity of this force with respect to the centroid of the
rectangular area b × 1 on which it acts. Assuming linear variation of pressure, the intensities
of pressure at the toe and the heel are given by:

σmax =

N

b

e

b

F 1 + 6

HG

I

KJ

...(Eq. 13.73)

σmin =

N

b

e

b

F 1 − 6

HG

I

KJ ...(Eq. 13.74)

respectively.

Three different cases arise depending upon the value of e : –e <

be b

66

,,= and e > b

6

.

These correspond to the situations where the resultant force (or N) strikes the base within the

‘middle-third’ of the base, at the outer third-point of the base, and out of the middle-third of

the base, respectively. The corresponding pressure diagrams for the base are shown in Fig. 13.51.

*If x > b/2, the maximum normal pressure occurs at the toe; and, if x < b/2, the maximum value

occurs at the heel.