Environmental Engineering Reference
In-Depth Information
1
9
100
Average excess pore water
pressure ratio, , percent
Average degree of consolidation
u, percent
Elapsed time subsequent to
loading years, months, days
3500
3000
2500
2000
u
u
o
7
6
5
4
3
90
10
Support line
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
50
Thickness of compressible stratum,
feet, one way drainage
1000
100
80
20
2
4
50
500
Coefficent of consolidation
0.20
5
40
30
20
FT
2
/day
4
C
v
400
300
Directions
To determine the average degree of consolidation
at a given time after instantaneous loading:
1. Pass a straight line between the coefficient of
consolidation C
v
(point 1) and the thickness of
compressible stratum having one-way
drainage (point 2) to establish (point 3) on the
support line.
2. From the given elapsed time after loading
(point 4) pass a straight line through point 3 to
obtain point 5. The desired value of the
average degree of consolidation (or average
excess pore water presssure ratio) in percent.
3. Proceed in a similar manner using known data
to establish unknown values, revising
sequence of operations as required.
Notes
1. Nomograph applies to one-way drainage of a
stratum.
2. If compressible stratum has two-way drainage
use one-half of stratum thickness.
3. Nomograph applies to cases of double
drainage where initial distribution of excess
pore water pressure is linear with depth or for
cases of single drainage where excess pore
water pressure is constant with depth.
1
70
30
10
2
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
200
60
40
10
5
50
50
5
4
3
2
100
1
40
60
30
70
50
40
30
0.02
20
80
10 90
5 5
0.01
20
FIGURE 3.84
Nomograph for consolidation with vertical drainage (1cm
2
/sec
93 ft
2
/day). (From NAVFAC, 1982.)
c
v
k
(1
e
)/
γ
w
a
v
k/
γ
w
m
v
(cm
2
/sec)
(3.69)
where
a
v
is the compressibility coefficient, or the ratio between the change in void ratio
and the change in vertical effective stress for the given increment, expressed as
a
v
(
e
o
e
1
/
p
1
p
o
) (cm
2
/g)
(3.70)
and
m
v
is the coefficient of volume change, or the ratio of the change in vertical strain to
the change in vertical stress, expressed as
m
v
∆
e
v
/
∆σ
v
a
v
/(1
e
o
) cm
2
/g
(3.71)
Settlement Analysis
Settlement from primary consolidation (
S
or
ρ
) is determined from the
e
-log
p
curve
(
Figure 3.78)
from the expression
S
(
∆
e
/1
e
o
)
H
(3.72)
or, if representative values for
C
c
have been obtained from a number of tests on similar
materials, from the expression
S
H
(
C
c
/l
e
o
) log(
p
o
∆
p
/
p
o
)
(3.73)
where
∆
p
is the average change in pressure resulting from the imposed stress (see
Section
3.5.1)
.
Secondary compression
can result in substantial compression in addition to primary
consolidation in very soft clays and organic soils. It can be estimated from the compression
