SME
Construction Engineering · Problem type
Bank, loose and compacted volumes
Use this for “705 m³ of bank earth swells 25% when dug and shrinks 10% when compacted. What are the loose and compacted volumes, and how many 12 m³ truck loads is it?”
Chart
This is an example. Type your own values to start a new problem.
Vₗ (m³)
=
Vb (m³)
×
(1
+
s (%)
)
Vc (m³)
=
Vb (m³)
×
(1
−
sh (%)
)
N
=
Vₗ (m³)
q (m³)
s is the swell and sh the shrinkage, in %; q is one truck’s load and N the loads before rounding up.
LF
Load factor
calculated
n
Truck loads
worked out (not typed)
Formulas
Vₗ
=
Vb
×
(1
+
s
100
)
881.25
=
705
×
(1
+
25
100
)
Vc
=
Vb
×
(1
−
sh
100
)
634.5
=
705
×
(1
−
10
100
)
LF
=
1
1 +
s
÷ 100
0.8
=
1
1 + 25 ÷ 100
N
=
Vₗ
q
73.44
=
881.25
12
n
=
⌈
N
⌉
74 = ⌈73.44⌉
Assumptions
•
Swell and shrinkage are both measured against the bank (in-place) volume.
•
Trucks are filled by loose volume.
•
A fill specified compacted needs Vc ÷ (1 − sh ÷ 100) of bank earth.
Step-by-step
WE KNOW
Vb = 705 m³, s = 25%, sh = 10%, q = 12 m³
FIND
loose volume (Vₗ), compacted volume (Vc), load factor (LF), truck loads, before rounding (N), truck loads (n)
Step 1 · Find loose volume (Vₗ)
Use Vₗ = Vb × (1 + s ÷ 100)
Digging
loosens
the
earth:
it
swells
by
s
percent
of
its
bank
volume.
Vₗ
=
705
×
(1
+
25
100
)
Vₗ = 705 × (1 + 0.25)
Vₗ = 705 × 1.25
Vₗ = 881.25 m³
Step 2 · Find compacted volume (Vc)
Use Vc = Vb × (1 − sh ÷ 100)
Rolling packs the earth tighter than it lay in the ground: it shrinks by sh percent of its bank volume.
Vc
=
705
×
(1
−
10
100
)
Vc = 705 × (1 − 0.1)
Vc = 705 × 0.9
Vc = 634.5 m³
Step 3 · Find load factor (LF)
Use LF = 1 ÷ (1 + s ÷ 100)
The load factor turns loose volume back into bank volume: Vb = LF × Vₗ.
LF
=
1
1 + 25 ÷ 100
LF
=
1
1 + 0.25
LF
=
1
1.25
LF = 0.8
Step 4 · Find truck loads, before rounding (N)
Use N = Vₗ ÷ q
Each
truck
carries
q
of
loose
earth,
so
divide
the
loose
volume
by
it.
N
=
881.25
12
N
=
73.44
Step 5 · Find truck loads (n)
Use n = ⌈N⌉
A part load is still a trip: round up to whole loads.
n
=
⌈73.44⌉
n
=
74
Check
Put the numbers back in. Both sides should match.
881.25
=
705
×
(1
+
25
100
)
✓
634.5
=
705
×
(1
−
10
100
)
✓
0.8
=
1
1 + 25 ÷ 100
✓
73.44
=
881.25
12
✓
74 = ⌈73.44⌉ ✓
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