Geotechnical Engineering

DHARM

520 GEOTECHNICAL ENGINEERING

47.8

18.6

3m 18.6 kN/m^2

Pa

2.89 m

Wall

9m

g= 21 kN/m^3

f= 33°

g= 27 kN/m^3

f= 33°

(a) (b)

Fig. 13.56 Lateral pressure due to stratified backfill (Ex. 13.8)

∴ Ka =

133

133

−°

+°

sin

sin

= 0.295, for both the strata of the backfill.

Active pressure at 3 m depth
Ka. σv = 0.295 (21 × 3) = 18.6 kN/m^3
Active pressure at the base of the wall
Ka. σv = 0.295 (21 × 3 + 27 × 6) = 66.4 kN/m^2
The variation of pressure is linear, with a break in the slope at 3 m depth, as shown in
Fig. 13.56 (b). The total active thrust per metre run, Pa, is given by the area of the pressure
distribution diagram.

∴ Pa =

1

2

3186 6186^1

2

××..+× + ×× 6478. = 283 kN

The height, above the base, of the point of application of this thrust is obtained by tak-
ing moments about the base

z =

(... )27 9 7 111 6 3 143 4 2

283

×+ ×+ ×m

= 2.89 m

Example 13.9: A retaining wall, 7.5 m high, retains a cohsionless backfill. The top 3 m of the fill
has a unit weight of 18 kN/m^3 and φ = 30° and the rest has unit weight of 24 kN/m^3 and φ = 20°.
Determine the pressure distribution on the wall.

18.6

3m^18

Pa

Wall

g= 18 kN/m^3

f= 30°

g= 24 kN/m^3

4.5 m f= 20°

26.46 52.92

79.38 kN/m^2

Z = 2.244 m

(a)

(b)

Fig. 13.57 Stratified backfill with different Ka-values for different layers (Ex. 13.9)