Bearing Capacity and Shallow Foundations - Elements of Soil Mechanics - page 271

Solution:

(i) Safe bearing capacity
Self-weight of foundation, Wf = 0.5 × 24 × 1.8 = 21.6 f = 0.5 × 24 × 1.8 = 21.6 kN/m run
Weight of soil on top of foundation, W s = 0.25 × 20 × 1.8 = 9.0 kN/m run
Total weight of foundation + soil, W = 21.6 + 9.0 = 30.6 kN/m run

P e
P W

×
+

50 0 4
50

.

×
+

P

Eccentricity of bearing pressure e , = = = 0.25 m

30 6 .

Since e ≤ 6 , the total force acts within the middle third of the foundation.
Effective width of footing, B ′ = 1.8 − 2 × 0.25 = 1.3 m
From Table 9.1, for φ u = 0°, N c = 5.14, N q = 1.0, N γ = 0.
Footing is continuous, i.e. L → ∞ ; s c = 1.0.

1 0 4 0 75
1 3

.
.

=

d c = + . 1 23 .

q cN s d − γ z

u net c c c

Safe bearing capacity per metre run ( ) = + = γ z + γ z

3
30 5 14 1 0 1 23 20 0 75
3

3

× . × × . . − × .

= + × 20 0 75 .

73 2 . kPa

=

Safe bearing load = 73.2 × B ′ = 95.2 kN/m run
(ii) Eurocode 7 GEO limit state
1. Combination 1 (partial factor sets A1 + M1 + R1)
From Table 5.1: γ G; unfav = 1.35; γ Q = 1.5; γ cu = 1.0; γ Rv = 1.0.

c 30

1

u

Design material property c :

; =

= = 30 kPa

u d

γ

cu

Design actions:

Weight of foundation W W , = × γ = 30 6 1 35 . × . = 41 3 . kN m run /

d G unfav ;

Applied line load P , = × P γ = × 50 1 35 . = 67 5 . kN m run / d G unfav ;

Effect of design actions:

Total vertical force F , = 41 3 . + 67 5 . = 108 8 . kN m run / d

P e
P W

×
+

67 5 0 4
67 5

. ×

+

.

d P

Eccentricity e , = = = 0 248 . m

. 41 3 . d d

B

Since e ≤ 6 , the total force acts within the middle-third of the foundation.

Effective width of footing B , ′ = 1 8 2 0 248 . . 1 3 . m

− × =

Design resistance:
From before, N c = 5.14, N q = 1.0, N γ = 0, s c = 1.0.

Ultimate bearing capacity q , = γ

30 5 14 1 20 0 75 1 0
169 2

c N s + zN

u u d c c ; q

= × . × + × . × .

= . kPa