Civil Engineering Reference
In-Depth Information
and, substituting into Eq. (15.39),
H
2
2
u
b
σ
d
t
d
c
v
=
(15.43)
Then, from Eqs. (15.40) and (15.43) together with Eq. (15.10),
=
γ
w
H
2
u
b
d
H
d
t
k
(15.44)
The compression, consolidation and permeability parameters,
m
v
,
c
v
and
k
, can be
evaluated from any one-dimensional continuous loading test in terms of the curre
n
t
values of sample thickness
H
and the excess pore pressure at the undrained face
u
b
and the gradients d
σ
/d
t
and d
H
/d
t
. In a test in which the sample dimensions
and pore pressures are recorded at frequent intervals, values for the gradients may be
determined by a numerical procedure and the values for the soil parameters calculated
at equally frequent intervals.
σ
/d
H
,d
15.9 Summary
1. Consolidation occurs when excess pore pressures dissipate, usually at constant
total stress. This results in compression or swelling as the effective stresses change.
2. The basic equation of one-dimensional consolidation is
2
u
c
v
∂
=
∂
u
(15.9)
z
2
∂
∂
t
where the coefficient of consolidation is
c
v
k
/
m
v
γ
w
, which has the units of
square metres per year. Values of
c
v
can be determined from results of oedometer
tests.
=
3.
Solutions to Eq. (15.9) are represented by isochrones, which show the variation
of excess pore pressure with time throughout the consolidating layer. Simple
solutions for one-dimensional consolidation can be found, assuming that the
isochrones are parabolas.
4.
Standard solutions for consolidation settlements are given in terms of the degree
of consolidation and the time factor:
=
ρ
t
ρ
∞
U
t
(15.24)
c
v
t
H
2
T
v
=
(15.25)
Relationships between
U
t
and
T
v
depend on the distribution of the initial excess
pore pressures and the drainage geometry.
