SME
Soil Mechanics
Permeability and seepage
Use this for “A constant-head test on a sand sample 15 cm long and 80 cm² in area, under 60 cm of head, collects 450 cm³ in 300 s. Find k.”
Diagram
i
=
h
L
=
60
15
=
4.
Q = kAi = 1.5 cm³/s.
Water flows from high head to low (well 1 to well 2).
Heights
drawn
20
;
lengths
along
the
ground
to
scale.
This is an example. Type your own values to start a new problem.
Q (cm³/s)
=
V (cm³)
÷
t (s)
i
=
h (cm)
÷
L (cm)
Q (cm³/s)
=
k (cm/s)
×
i
×
A (cm²)
Formulas
Q
=
V
t
1.5
=
450
300
i
=
h
L
4
=
60
15
Q
=
k
×
i
×
A
1.5 = 0.004688 × 4 × 80
Assumptions
•
Steady laminar flow through a saturated sample, so Darcy’s law holds.
•
The head is held constant, so the gradient i stays fixed through the test.
•
Water near 20 °C; k is often corrected to 20 °C for the water’s viscosity.
Step-by-step
WE KNOW
L = 15 cm, A = 80 cm², h = 60 cm, V = 450 cm³, t = 300 s
FIND
flow rate (Q), hydraulic gradient (i), coefficient of permeability (k)
Step 1 · Find flow rate (Q)
Use Q = V ÷ t
The flow rate is the water collected per second.
Q
=
450
300
Q
=
1.5
cm³/s
Step 2 · Find hydraulic gradient (i)
Use i = h ÷ L
The head lost per centimetre of sample.
i
=
60
15
i
=
4
Step 3 · Find coefficient of permeability (k)
Use Q = k × i × A
Darcy’s
law:
the
flow
is
k
times
the
gradient
times
the
area;
divide
it
out.
k
=
Q
i
×
A
k
=
1.5
4 × 80
k
=
1.5
320
k
=
0.004688
cm/s
Check
Put the numbers back in. Both sides should match.
1.5
=
450
300
✓
4
=
60
15
✓
1.5 = 0.004688 × 4 × 80 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Falling-head test
Use this for “In a falling-head test on a silt 10 cm long and 40 cm² in area, the head in a 0.5 cm² standpipe falls from 100 cm to 50 cm in 600 s. Find k.”
Seepage from a flow net
Use this for “A flow net under a dam has 4 flow channels and 12 drops; k = 2 m/day, H = 6 m, the exit square 1.5 m. Find q and FS against piping (icr = 0.95).”