Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 531

Wall

5m P

a1h

Pa 1

Pa1v

2.67 m

Pw Pah

49

Fig. 13.67 Horizontal thrust on wall from submerged fill

from Coulomb’s theory (Ex. 13.22)

Pa 1 =^1

2

1

2

γHK^22 .(..).a=×15 30 9 8− × × (^50132) kN/m = 9.06 kN/m
(since γ ′ = γsat – γw)
This is inclined at 20° with the horizontal.
∴ Its horizontal component, Pa 1 h = 9.06 × cos 20° = 8.50 kN/m
Water pressure, Pw =
1
2
1
2
γwH^22 =×981 5.kN/m× = 122.6 kN/m
Total horizontal thrust, Pah = PPaw 1 h+ = 8.5 + 122.6 = 131.1 kN/m.
This will act at (1/3) H or 2.67 m above the base of the wall, as shown in Fig. 13.67.
Example 13.23: A retaining wall 4.5 m high with a vertical back supports a horizontal fill
weighing 18.60 kN/m^3 and having φ = 32°, δ = 20°, and c = 0. Determine the total active thrust
on the wall by Culmann’s method. (S.V.U.—B.E. (R.R.).—Sep., 1978)
γ = 18.6 kN/m^3 φ = 32° c = 0 δ = 20° for the fill
Active thrust, Pa = FF′
≈ 51.5 kN/m. run
Check:
Ka from Coulomb’s formula =
cos
cos sin .sin
cos
2
2
32
20 1^5232
20
°
°+
°°
°
L
N
M
M
O
Q
P
P
= 0.2755
Pa =
1
2
1
2
γHK^22 a=× × ××18 6 4..5 0 2755 = 51.9 kN/m
The Culmann value agrees excellently with this value.