Civil Engineering Reference
In-Depth Information
value about 0.85. Determine approximate values for the excess pore pressures that will
exist within the embankment 3 months after further construction is commenced. c
v
for
the soil
=
0.558 m
2
/month.
Solution:
Check the r value with
Δ
z taken as equal to 1.52 m.
For
Δ
z
=
1.52 m, t
=
1.0 month:
0 558 1
1 52
.
( .
×
=
r
=
0 241
.
)
2
This value of r is satisfactory and has been used in the solution (if r had been greater
than 0.5 then
Δ
t and
Δ
z would have had to be varied until r was less than 0.5).
A 1.52 m deposit of the soil
il
will induce an excess pressure, throughout the whole
embankment, of
1 52 19 2
× × =
B kPa
. This pressure value must be added to the
value at each grid point for each time increment. The pore pressure increase is in fact
applied gradually over a month, but for a numerical solution we must assume that it is
applied in a series of steps, i.e. 24.8 kPa at t
=
1 month, at t
=
2 months, and at t
=
3
months. From t
=
0 to t
=
1 no increment is assumed to be added and the initial pore
pressures will have dissipated further before they are increased.
The numerical iteration is shown in Fig.
12.15b
.
.
.
24 8
.
12.14 Numerical solutions for two- and three-dimensional consolidation
12.14.1 Two-dimensional consolidation
The differential equation for two-dimensional consolidation has already been given:
∂
∂
2
u
x
+
∂
∂
u
y
2
=
∂
u
t
c
v
2
2
∂
Part of a consolidation grid is shown in Fig.
12.16a
; from the previous discussion of the finite difference
equation we can write:
Fig. 12.16
Schematic form of the finite difference equation (two dimensional).
