DHARM

SETTLEMENT ANALYSIS 413

Dense sand

9m gsat= 18.9 kN/m^3

3m Clay G = 2.70w = 40.5% LL = 54%

Hard rock 3.6 m

1.8 m

1.8 m

3.6 m

r

O

(a) Soil profile (b) Plan of footing
Fig. 11.14 Soil profile and plan of footing (Ex. 11.4)
The data area shown in Fig. 11.14.
The dimensions of the footing are more than one-third the depth at which the vertical
stress is to be computed. Therefore the load may be taken as being uniformly distributed.

q =

9000

36 36..×

= 694.4 kN/m^2

Since the stress below the centre of the footing is required, the area may be divided into
four squares and the load from each square may be treated as a point load, acting at the centre
of the square.

The radial distance of 0 from each point load,

r = 09 2. m

r

z

=

+

09 2

915

.

(.)

= 0.1212

Influence factor, KB = (/ ) (/ )

//{(. )}

32

1

32

(^21) 0 1212
2
52 2 52
ππ

• 
  

  F
  HG
  I
  KJ

  
  

  r +
  z
  = 0.460
  ∴σz = 4 ×
  0 460
  10 5
  9000
  (^24)
  .
  (.)
  × = 414/(10.5)^2 = 37.55 kN/m^2
  Void ratio for clay = wG = 0.405 × 2.70 = 1.094
  γsat for clay =
  ()
  ()
  .
  ..
  .
  Ge
  e w

  
  


• 
  


• 
  

  =
  F +
  HG
  I
  1 KJ
  2 70 1 094
  2 094
  γ × 9.81 = 17.56 kN/m^3
  γ′ for dense sand = 9.1 kN/m^3 γ′ for clay = 7.75 kN/m^3
  Overburden pressure at 10.5 m depth = (9 × 9.1 + 1.5 × 7.75) = 101.53 kN/m^2
  Cc = 0.009(54 – 10) = 0.396
  Consolidation settlement, Sc = 300 0 396
  2 094
  101 53 37 55
  (^10) 101 53
  ×+F
  HG
  I
  KJ
  .
  .
  log ..
  .
  cm ≈ 7.8 cm.