Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 533

t′ t′: Tangent to the modified Culmann line, parallel to φ-line.
α = 75° φ = 36° δ = 18° β = 10° γ = 15 kN/m^3
Active thrust, Pa, on the wall per metre run = Vector F′G′ = 360 kN.
Example 13.25: A retaining wall 4.5 m high with vertical back supports a backfill with hori-
zontal surface. The unit weight of the fill is 18 kN/m^3 and the angle of internal friction is 36°.
The angle of wall friction may be taken as 18°. A footing running parallel to the retaining wall
and carrying a load of 18 kN/m is to be constructed. Find the safe distance of the footing from
the face of the wall so that there is no increase in lateral pressure on the wall due to the load
of the footing. tt: tangent to the Culmann-curve without line load, parallel to the φ-line.
The safe distance beyond which the line load does not increase the lateral pressure is
3.5 m in this case.
The Culmann-curve without the line load is drawn as usual. Now the modified Culmann-
curve, with the line load included at C 1 , C 2 , C 3 ..., the borders of each of the wedges such as
ABC 1 , ABC 2 , ABC 3 , ..., is drawn. A tangent tt to the Culmann-curve without the line load is
drawn parallel to φ-line to meet the modified curve with line load in F′. BF′ is joined and
produced to meet the surface in C, which gives the critical position of the line load, beyond
which location, it does not affect the lateral pressure.

A

3.5 m

f

B y72°

36°

1

1 ¢

2

2 ¢

3

3¢

4 ¢

4

F

Culmann curve

without line load

5

5 ¢

6

6 ¢

F¢

Culmann curve

with line load

C 1 C 2 C 3 CC 4 C 5 D(C ) 6

q

H=

4.5 m

Wall

K

Fig. 13.70 Location of critical position of line load Culmann’s method (Ex. 13.25)

Example 13.26: A masonry retaining wall is 1.5 m wide at the top, 3.5 m wide at the base and 6

m high. It is trapezoidal in section and has a vertical face on the earth side. The backfill is level

with top. The unit weight of the fill is 16 kN/m^3 for the top 3 m and 23 kN/m^3 for the rest of the

depth. The unit weight of masonary is 23 kN/m^3. Determine the total lateral pressure on the

wall per metre run and the maximum and minimum pressure intensities of normal pressure at

the base. Assume φ = 30° for both grades of soil. (S.V.U.—Four-year B.Tech.—July, 1984)