SME
Soil Mechanics · Problem type
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).”
Diagram
i
=
Δh
l
=
0.5
1.5
=
0.3333.
Water flows from high head to low (well 1 to well 2).
Heights
drawn
2
;
lengths
along
the
ground
to
scale.
This is an example. Type your own values to start a new problem.
q (m³/day per m)
=
k (m/day)
×
H (m)
×
Nf
÷
Nd
i
=
Δh (m)
÷
l (m)
FS
=
icr
÷
i
Nf counts the flow net’s flow channels and Nd its equipotential drops; l is the side of the last square, where the water comes out.
Formulas
q
=
k
×
H
×
Nf
Nd
4
=
2
×
6
×
4
12
Δh
=
H
Nd
0.5
=
6
12
i
=
Δh
l
0.3333
=
0.5
1.5
FS
=
icr
i
2.85
=
0.95
0.3333
Assumptions
•
Each element is a curvilinear square: every channel carries equal flow; every drop loses H ÷ Nd.
•
Isotropic soil (one k in every direction) and steady flow.
•
icr = γ′ ÷ γw, about 1 for most sands; FS of 3 to 4 is the usual target.
Step-by-step
WE KNOW
k = 2 m/day, H = 6 m, Nf = 4, Nd = 12, l = 1.5 m, icr = 0.95
FIND
seepage (q), head lost per drop (Δh), exit gradient (i), factor of safety against piping (FS)
Step 1 · Find seepage (q)
Use q = k × H × Nf ÷ Nd
Each
channel
carries
k
times
the
head
lost
per
drop,
H
Nd
;
add
up
the
Nf
channels.
q
=
2
×
6
×
4
12
q
=
12
×
4
12
q
=
48
12
q
=
4
m³/day
per
m
Step 2 · Find head lost per drop (Δh)
Use Δh = H ÷ Nd
Every equipotential drop loses the same share of the head.
Δh
=
6
12
Δh = 0.5 m
Step 3 · Find exit gradient (i)
Use i = Δh ÷ l
The
head
lost
in
the
last
drop
over
the
exit
square’s
length
l
.
i
=
0.5
1.5
i
=
0.3333
Step 4 · Find factor of safety against piping (FS)
Use FS = icr ÷ i
How many times the exit gradient would have to grow to lift the sand grains (piping).
FS
=
0.95
0.3333
FS = 2.85
Note
FS = 2.85 is below the usual 3 to 4: lengthen the flow path (a deeper sheet pile or a longer apron).
Check
Put the numbers back in. Both sides should match.
4
=
2
×
6
×
4
12
✓
0.5
=
6
12
✓
0.3333
=
0.5
1.5
✓
2.85
=
0.95
0.3333
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.