Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 527

γ = 18 kN/m^3 H = 10 m. φ = 30° δ = 20° β = 20° α = 90°

ψ = α – δ = 90° – 20° = 70°

φ + δ = 30° + 20° = 50°

C

A b= 20°

(+)

= 50°

fd

10 m

Wall

60°

B

E

f= 30°

d c

b

10° D

f= 70°

Repture line

G

fad=( – )

= 70°

a

Fig. 13.62 Coulomb’s analytical approach (Ex. 13.17)

(^) AB = H = 10 m a =
10
70
60 9 216
sin
.sin.
°
°= m
d =
10
sin 70 °

. sin 50° (from ∆ABE) = 8.152 m

b =

10

10

110

sin

.sin

°

°(from ∆ABD) = 54.115 m

c = bd=×8152 54 115.. m = 21.003 m

x =

ab

()bc

..

+.

=

9 216 54 115×

75118 m = 6.639 m

Pa =

1

2

1

2

γψx^22 .sin =× × 18 ( .6 639) sin 70 °kN / m. run

= 373 kN/m. run
Example 13.18: A retaining wall, 3.6 m high, supports a dry cohesionless backfill with a plane
ground surface sloping upwards at a surcharge angle of 10° from the top of the wall. The back
of the wall is inclined to the vertical at a positive batter angle of 9°. The unit weight of the
backfill is 18.9 kN/m^3 and φ = 30°. Assuming wall friction angle of 12°, determine the total
active thrust by Rebhann’s method.

H = 3.6 m φ = 30° δ = 12° β = 10° α = 81° γ = 18.9 kN/m^3

ψ = α – δ = 69° Pa =

1

2

1

2

γψx^22 sin =× ×18 9 2 40.. ×sin 69 °

= 51 kN/m. run