Foundation Settlement and Soil Compression - Elements of Soil Mechanics - page 344

Immediate settlement:

2

p ( 1 − υ ) Bf

s =

0

E m

2

116 4 . × − ( 1 0 5 . ) × 3 0 0 82 . × .

s 0 ( using Table 11 2 . )

=

60 000

= 3 6 . mm

Consolidation settlement:

Consider the base plan of the footing as 4 rectangles (1.5 m × 1.5 m) and use Fig 3.10
to establish increases in vertical stress at centres of layers beneath the footing. Deter-
mine the stress increments to depth of 2.0 B ( = 6.0 m) over 4 layers, each 1.5 m thick.
I σ is determined from Fadum's chart (Fig. 3.10) .

Stress increment at
centre of layer,
Δσ z (kPa)

z
(m) m = n = b/z Layer I σ 4 × I σ

1 0.75 2.0 0.237 0.948 = 0.948 × 136 = 128.9

2 2.25 0.67 0.118 0.472 64.2

3 3.75 0.4 0.06 0.24 32.6

4 5.25 0.29 0.035 0.14 19.0

Consolidation settlement s , = Σ m h v ∆ σ

2 6 19 0

1 z

= 0 04 1 5 . × × . ( 128 9 . + 64 2 . + 3 . + . )

= 14 7 . mm

. . .
The anticipated total settlement is therefore less than the permitted (25 mm) and thus
the serviceability limit state requirement is satisfied.

⇒ Total settlement = 3 6 14 7 + = 18 3 mm

11.7 Isotropic consolidation

Most soil samples tested in the triaxial apparatus (see Chapter 4 ) are isotropically consolidated, i.e. con-
solidated under an all-round hydrostatic pressure, before the commencement of the shearing part of the
test. It is appreciated that other forms of consolidation are possible, e.g. K 0 consolidation, but these forms
will not be considered here.
The form of the compression curve for an isotropically consolidated clay is shown in Fig. 11.13a . It
should be noted that the plot is in the form of a v-p ′ plot, the vertical axis being 0 : V and the horizontal
axis 0 : p ′ . The v-ln p ′ plot is shown in Fig. 11.13b and from this diagram we see that, if we are prepared
to ignore the slight differences between the expansion and the recompression curves, the semi-log plot
of the isotropic consolidation curve for most clays can be assumed to be made up from a set of straight
lines and to have the idealised form of Fig. 11.13c .
Any point on the line ABC represents normal consolidation whereas a point on the line BD, or indeed
any point below ABC, represents overconsolidation. As line DB represents the idealised condition that
the expansion and recompression curves coincide, it is probably best to give it a new name, and it is
therefore usually called the swelling line.