SME
Soil Mechanics
Consolidation
Use this for “A 4 m clay layer (Cc = 0.3, e₀ = 0.9) is at σ′₀ = 80 kPa at its middle. A fill adds Δσ = 60 kPa there. How far does it settle?”
Diagram
S
=
Cc·
H
1 + e₀
×
log(
σ′₀ + Δσ
σ′₀
)
S
=
0.3
×
4
1.9
×
log(
140
80
)
=
0.1535
m
The dashed line is the surface after settling, drawn to the same scale as H.
This is an example. Type your own values to start a new problem.
S (m)
=
Cc
×
H (m)
÷
(1
+
e₀
)
×
log((
σ′₀ (kPa)
+
Δσ (kPa)
)
÷
σ′₀ (kPa)
)
Formulas
S
=
Cc
×
H
1 +
e₀
×
log(
σ′₀ + Δσ
σ′₀
)
0.1535
=
0.3
×
4
1 + 0.9
×
log(
80 + 60
80
)
Assumptions
•
Normally consolidated: σ′₀ is the most effective stress the clay has ever carried.
•
σ′₀ and Δσ are taken at the middle of the clay layer.
•
One-dimensional: the clay only shortens as water leaves its voids (primary consolidation).
Step-by-step
WE KNOW
H = 4 m, Cc = 0.3, e₀ = 0.9, σ′₀ = 80 kPa, Δσ = 60 kPa
FIND
settlement (S)
Step 1 · Find settlement (S)
Use S = Cc × H ÷ (1 + e₀) × log((σ′₀ + Δσ) ÷ σ′₀)
The
void
ratio
drops
by
Cc
for
each
tenfold
rise
in
σ′;
the
layer
shortens
by
that
over
1
+
e₀
.
S
=
0.3
×
4
1 + 0.9
×
log(
80 + 60
80
)
S
=
0.3
×
4
1 + 0.9
×
log(
140
80
)
S
=
0.3
×
4
1.9
×
log(1.75)
S
=
0.3
×
4
1.9
×
0.243
S
=
1.2
1.9
×
0.243
S
=
0.6316
×
0.243
S
=
0.1535
m
Check
Put the numbers back in. Both sides should match.
0.1535
=
0.3
×
4
1 + 0.9
×
log(
80 + 60
80
)
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Effective stress at a depth
Use this for “Dry sand 3 m thick (γ = 18 kN/m³) lies on clay with γₛₐₜ = 19 kN/m³, the water table on the clay. Find σ, u and σ′ at 5 m.”
Settlement of an overconsolidated clay
Use this for “The 4 m clay (Cc = 0.3, e₀ = 0.9, σ′₀ = 80 kPa) once carried σ′ₚ = 120 kPa; Cₛ = 0.05. How far does it settle under Δσ = 60 kPa?”
Time for a degree of consolidation
Use this for “A 4 m clay layer drains at its top and bottom, with cᵥ = 0.002 cm²/s. How long until it is 50% consolidated?”