Foundation Settlement and Soil Compression - Elements of Soil Mechanics - page 351

Cell pressure = 35 kPa

σ ′ +

2

σ ′ σ − σ

1 3

′

1 3

Strain σ 1 − σ 3 u t = s =

2

0 0 0 0 35

1 10.4 0.4 5.2 39.8

2 20.7 4.8 10.3 40.5

3 29.0 9.7 14.5 39.8

4 33.2 13.2 16.6 38.4

5 35.8 16.6 17.9 36.3

6 37.3 17.9 18.6 35.7

6.8 37.8 19.3 18.9 34.6

Cell pressure = 70 kPa

0 0 0 0 70

1 20.7 4.1 10.3 76.2

2 42.7 12.8 21.3 78.5

3 54.4 22.1 27.2 75.1

4 63.4 30.4 31.7 71.3

5 66.1 34.8 33.0 68.2

6 71.7 37.9 35.8 67.9

7 75.8 40.7 37.9 67.2

The stress paths are shown in Fig. 11.20. From the K f line tan α ( = sin φ ) = tan 28.5° = 0.543.
⇒ K 0 = − 1 0 543 . = 0 457 .

Effective stresses at centre of layer before application of foundation load (initial)
′ =

σ 1 85 kPa

I

Clay is normally consolidated, therefore:

′ =

σ 3 0 457 85 . × = 38 8 . kPa I

85 + 38 8

2

. 85 38 8

2

− .

⇒ ′ = s = 61 9 . ; t = = 23 1 .

The coordinates s ′ and t are plotted on Fig. 11.20 to give the point A, the initial state
of stress in the soil.

Effective stress at centre of clay after application and consolidation of foundation load
(final)

′ = ′ +

σ σ ∆ σ = + 85 28 8 . = 113 8 . kPa 1 F 1 I 1

′ = ′ +

σ σ ∆ σ = 38 8 19 2 . + . = 58 0 . kPa 3 F 3 I 3

113 8 58
2

. + 113 8 58

2

. −

⇒ ′ = s = 85 9 . ; t = = 27 9 .