SME
Soil Mechanics
Soil classification
Use this for “A soil has Gₛ = 2.7, w = 18% and S = 0.9. Find its void ratio, porosity, dry unit weight and moist unit weight.”
Diagram
e
=
wGₛ
S
=
0.18
×
2.7
0.9
=
0.54:
voids
of
0.54
for
every
1
of
solids.
n
=
e
1 + e
=
0.351
of
the
volume
is
voids.
γd
=
Wₛ
V
=
26.5
1.54
=
17.2
kN/
m
3
;
γ
=
Wₛ + Ww
V
=
31.3
1.54
=
20.3
kN/
m
3
.
The block holds 1 m³ of solids (Vₛ = 1); a soil sample scales it.
This is an example. Type your own values to start a new problem.
S
×
e
=
w
%
×
Gₛ
γd (kN/m³)
=
Gₛ
×
9.81
kN/m³
÷
(1
+
e
)
γ (kN/m³)
=
γd (kN/m³)
×
(1
+
w
%)
The picture’s block holds 1 m³ of solids, so Wₛ = Gₛ × 9.81 kN and V = 1 + e; its γd = Wₛ ÷ V is the second line.
n
Porosity
calculated
Formulas
S
×
e
=
w
100
×
Gₛ
0.9
×
0.54
=
18
100
×
2.7
n
=
e
1 +
e
0.3506
=
0.54
1 + 0.54
γd
=
Gₛ
×
9.81
1 +
e
17.1994
=
2.7
×
9.81
1 + 0.54
γ
=
γd
×
(1
+
w
100
)
20.2952
=
17.1994
×
(1
+
18
100
)
Assumptions
•
Void ratio e is the volume of voids over the volume of solids; porosity n is voids over the whole.
•
Water content w is the weight of water over the weight of solids, written in %.
•
Degree of saturation S is the share of the voids filled with water, from 0 (dry) to 1.
•
γw = 9.81 kN/m³, and the air in the voids weighs nothing.
Step-by-step
WE KNOW
Gₛ = 2.7, w = 18%, S = 0.9
FIND
void ratio (e), porosity (n), dry unit weight (γd), moist unit weight (γ)
Step 1 · Find void ratio (e)
Use S × e = w ÷ 100 × Gₛ
Per
1
m³
of
solids
the
water
takes
wGₛ
m
3
,
and
that
fills
S
of
the
voids
e
.
e
=
w
100
×
Gₛ
S
e
=
18
100
×
2.7
0.9
e
=
0.18
×
2.7
0.9
e
=
0.486
0.9
e
=
0.54
Step 2 · Find porosity (n)
Use n = e ÷ (1 + e)
Per
1
m³
of
solids
the
voids
are
e
and
the
whole
is
1
+
e
.
n
=
0.54
1 + 0.54
n
=
0.54
1.54
n
=
0.3506
Step 3 · Find dry unit weight (γd)
Use γd = Gₛ × 9.81 ÷ (1 + e)
The
solids
weigh
Gₛγw
per
1
m³
of
solids,
spread
over
the
whole
1
+
e
.
γd
=
2.7
×
9.81
1 + 0.54
γd
=
2.7
×
9.81
1.54
γd
=
26.487
1.54
γd
=
17.1994
kN/
m
3
Step 4 · Find moist unit weight (γ)
Use γ = γd × (1 + w ÷ 100)
The
water
adds
w
times
the
weight
of
the
solids.
γ
=
17.1994
×
(1
+
18
100
)
γ
=
17.1994
×
(1
+
0.18)
γ
=
17.1994
×
1.18
γ
=
20.2952
kN/
m
3
Check
Put the numbers back in. Both sides should match.
0.9
×
0.54
=
18
100
×
2.7
✓
0.3506
=
0.54
1 + 0.54
✓
17.1994
=
2.7
×
9.81
1 + 0.54
✓
20.2952
=
17.1994
×
(1
+
18
100
)
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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