Foundation Settlement and Soil Compression - Elements of Soil Mechanics - page 339

the total settlement of the foundation under its centre if the groundwater level occurs
at a depth of 5 m below the top of the layer.

Solution

The vertical pressure increment at the centre of the layer can be obtained by splitting
the plan area into four rectangles (Fig. 11.11a ) and using Fig. 3.10:
∆ σ 1

= 110 kPa

In order to obtain the E value for the soil, Δ σ 3 should now be evaluated so that the
deviator stress ( Δ σ 1 − Δ σ 3 ) can be obtained.
Alternatively the approximate method can be used:
65% of maximum deviator stress = 0.65 × 400 = 260 kPa
Strain at this value = 0.8% (from Fig. 11.11b )
Hence:

260 100
0 8

×

E = = 32 500 kPa = 32 5 . MPa

.

Immediate settlement

Using the rectangles of Fig. 11.11a and Fig. 11.2:

L
B

15
5

H
B

20
5

= = 3 0 . = = 4 0 .

Hence:

I p = 0 48 4 0 . × . = 1 92 .

( )

pB 1 − ν

2

I

p

ρ if =

E

200
32 500

= × × 5 0 75 1 92 0 8 . × . × . ( 0 8 . = rigidity facto r )

0 036 . m 36 mm

= =

Consolidation settlement

Initial effective overburden pressure = 18 5 10 9 81 5

136

. × − . ×

= kP a

Hence the range of pressure involved is from 136 to 246 kPa.
Using the e-p curve of Fig. 11.8a :

e = 0 6800 . ; e = 0 666 .

1 2

de
dp

0 680 0 666
110

. − . 0 014

110

.

a = = = = 0 000 127 . m /kN

2

a 0 000 127

1 680

.

m

v =

= = 7 6 10 . ×

− 5

m /kN

2

1 e .

+ 1

ρ c =

m dp H

= 7 6 110 20 10 . × × ×

− 5

= 0 167 . m = 167 mm

Total settlement = 36 + 167 = 203 mm
Some reduction could possibly be applied to the value of ρ c if the value of μ was known.