Civil Engineering Reference
In-Depth Information
where
ρ
i
=
ρi = immediate settlement
ρ
c
=
consolidation settlement.
In the consolidation test:
ρ
= ∆
1
m
σ
h
(1)
oed
v
where h
=
sample thickness.
Since there is no lateral strain in the consolidation,
Δ
σ
1
=
Δ
u. Hence:
ρ
oed
= ∆
v
m uh
or
H
=
∫
(2)
ρ
c
m udH
∆
v
oed
0
where H
=
thickness of consolidating layer.
In a saturated soil
Δ
u
=
Δ
σ
3
+
A(
Δ
σ
1
−
Δ
σ
3
). This may be expressed as:
∆
∆
σ
σ
3
∆
u
=
∆
σ
A
+
(
−
A
)
1
1
and, substituting for
Δ
u in Equation (2) we obtain a truer estimation of the consolidation settlement,
ρ
c
:
H
∆
∆
σ
σ
∫
3
ρ
=
m
∆
σ
A
+
(
1
−
A dH
)
(3)
c
v
1
0
1
Equation (3) can be expressed in terms of Equation (2), by introducing the correction factor
μ
:
ρ
=
µρ
=
ρ
c
c
oed
H
∫
=
µ
m
∆
1
σ
dH
v
0
where
H
∆
∆
∆
σ
σ
σ
∫
3
1
m
∆
σ
A
+
(
1
−
A dH
)
v
1
0
µ
=
H
∫
m
dH
v
1
0
If m
v
and A are assumed constant with depth the equation for
μ
reduces to:
µ
= + −
A
(
1
A
)
α
(4)
where
H
=
∫
∫
∆
σ
dH
3
α
0
H
∆
σ
dH
1
0
