Figure 1
Example:
1.
2.
3.
4.
gsand = 96 pcf
Soil sample was obtained from the clay layer
Conduct consolidation test [9 load increments ]
Plot e vs. log (p) (Figure 2)
Determine Compression Index (Cc ) & Swelling Index (Cs)
0.9
Sand
Void Ratio (e)
0.7
0.6
Soil Sample
eo = 0.795
Cc = 0.72
Cs = 0.1
In the lab and before
the consolidation test
the stresses on the
sample = 0.
During testing, the
geostatic stress is
gradually recovered
0.4
0.3
100
Determine
Po
16 ft
wc = 0.3
In the ground, the
sample was
subjected to
geostatic stresses.
0.5
5.
Clay
gclay = 110 pcf
4 ft
Dp1 Dp
2
0.8
In the lab the stresses are
added to the soil sample
3 ft
W.T.
1
In the lab and after removing
the soil sample from the ground,
the stresses on the soil sample = 0
Dp1
Dp
Stress
Dp7
Increments Dp
Dp9
G.S.
Po = 3.(96) + 4.(96-62.4) + 8.(110-62.4) = 803.2 lb/ft2
Cc
Cs
Dp9
Po 1000
Log (p)
10000
Figure 2
Tangent to point 1
Example:
6.
G.S.
gsand = 96 pcf
Using Casagrande’s Method to determine Pc
3 ft
W.T.
Sand
gclay = 110 pcf
Pc = 800 lb/ft2
4 ft
Clay
Po
16 ft
wc = 0.3
Overconsolidation Ratio
Pc
Po
1
=1
The soil is
Normally Consolidated
N.C. soil
0.9
Dp1
2
6
0.8
Void Ratio (e)
OCR =
Point of
maximum curvature
X
X
1
4
0.7
5
3
0.6
0.5
0.4
7
0.3
100
Po = Pc1000
Log (p)
10000
Casagrande’s Method to Determine Preconsolidation Pressure (Pc)
1
Normally Consolidated Soil
Point of
maximum curvature
1
0.9
2 Horizontal line
Void Ratio (e)
0.8
X
X
1
0.7
3
0.6
0.5
0.4
7
0.3
Po = Pc1000
100
Log (p)
Overconsolidation Ratio OCR =
Pc
Po
=1
The soil is Normally Consolidated (N.C.) soil
10000
2
Casagrande’s Method to Determine Pc
Overconsolidated Soil
Point of
maximum curvature
2 Horizontal line
X
X
Void Ratio (e)
1
3
7
Po
Overconsolidation Ratio OCR =
Pc
Po
The soil is oversonsolidated (O.C.) soil
>1
Pc
Log (p)
Building
qdesign
Example:
G.S.
gsand = 96 pcf
A 150’ x 100’ building will be constructed at the site.
The vertical stress due to the addition of the building
qdesign =1000 lb/ft2
W.T.
Sand
Clay
3 ft
4 ft
DP1
Po
Po
16 ft
The weight of the building Qdesign will be transferred
to the mid height of the clay layer
eo = wc . Gs = 0.3 x 2.65 = 0.795
1
Qdesign = 15,000,000 lb
The added stress at 15’ from
the ground surface is
0.9
Dp1
Dp =
15,000,000 lb
(150+15) x (100+15)
DP = 790.51 lb/ft2
Void Ratio (e)
0.8
0.7
0.6
0.5
DP + Po =
790.51 + 803 = 1593.51 lb/ft2
0.4
0.3
100
Po1000
Log (p)
10000
Building
Example:
qdesign
G.S.
DP + Po = 790.51 + 803 = 1593.51 lb/ft2
gsand = 96 pcf
Consolidation Settlement
DH =
DH =
Cc H
1 + eO
log (
W.T.
Sand
Po + DP
)
Po
0.72 x 16
1593.51
log (
)
1 + 0.795
803
DH = 1.9 ft
Clay
3 ft
4 ft
DP1
Po
Po
16 ft
eo = wc . Gs = 0.3 x 2.65 = 0.795
1
0.9
Dp1
Void Ratio (e)
0.8
DP1
0.7
0.6
0.5
0.4
0.3
100
Po1000
Po + DP
Log (p)
10000
Demolished
When the building was removed, the soil has become
an overconsolidated clay.
qdesign
G.S.
gsand = 96 pcf
The rebound has taken place through
swelling from pint 1 to point 2
W.T.
Sand
Clay
3 ft
4 ft
Po
Po
16 ft
eo = wc . Gs = 0.3 x 2.65 = 0.795
1
0.9
Dp1
Void Ratio (e)
0.8
DP1
0.7
2
0.6
1
0.5
0.4
0.3
100
Po1000
Po + DP
Log (p)
10000
Constructing a new building
Scenario #1
The soil now is overconsolidated Soil:
qdesign
G.S.
gsand = 96 pcf
Sand
The new building is heavier in weight
CS H
1 + eO
DH =
W.T.
Clay
3 ft
4 ft
DP2
Po
Po
16 ft
P
C CH
P + DP
log ( C ) +
log ( o
)
Po
PC
1 + eO
eo = wc . Gs = 0.3 x 2.65 = 0.795
1
eo = 0.61
0.9
DH =
0.1 x 16
1 + 0.61
log (
1593.51
803
+
0.72 x 16
log ( 2100
1 + 0.61
1593.51
)
DP2
0.8
Void Ratio (e)
Assume Po + Dp2 = 2100 psf
Dp1
DP1
0.7
0.6
CS
0.5
CC
)
0.4
=
0.3
100
Po1000
Pc
Log (p)
Po + DP
New Building
10000
Constructing a new building
Scenario # 2
The soil now is overconsolidated Soil:
qdesign
G.S.
gsand = 96 pcf
W.T.
Sand
Clay
The new building is lighter in weight
3 ft
4 ft
DP2
Po
Po
16 ft
eo = wc . Gs = 0.3 x 2.65 = 0.795
CS H
P + DP
log ( o
)
P0
1 + eO
DH =
1
0.9
eo = 0.61
=
log ( 1600
1593.51
)
Void Ratio (e)
0.1 x 16
1 + 0.61
DP2
0.8
Assume Po + Dp2 = 1600 psf
DH =
Dp1
DP1
0.7
0.6
CS
0.5
0.4
0.3
100
Po1000Po
+ DP
Log (p)
10000
New Building
Example of Semi-log Scale
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.1
1
10
100
1000