Seepage: Camarines Norte State College

Republic of the Philippines
CAMARINES NORTE STATE COLLEGE

F. Pimentel Avenue, Brgy. 2, Daet, Camarines Norte – 4600, Philippines
College of Engineering
CE7a/b – Geotechnical EngineeringSumm
1 (Soil Mechanics) (Lecture & Laboratory)
Second Semester, AY 2019-2020
Finals
Chapter 8 – Seepage
There are instances where water flows through soil in multiple directions and it is non-uniform over the entire
area perpendicular to the flow. For this case, a flow net is used to calculate the flow of water through the soil. Flow nets
are based from Laplace’s equation of continuity that govern the steady flow condition for a given point in the soil mass.
Flow Nets and Seepage Calculation

A flow net is composed of two orthogonal families of curves called the flow line and the equipotential line. The
flow line is the line travelled by a water particle from the upstream side to the downstream side of the permeable
medium. On the other hand, an equipotential line is a line along which all points have an equal potential head. If
piezometers are placed along this line, the water level will rise to the same elevation.
Flow Line and Equipotential Line
Flow Net
Page 1 of 3
Finals
A flow channel is a strip between two adjacent flow lines. A potential drop is the drop in piezometric level
between two adjacent equipotential line. Construction of flow nets takes several trials. One must remember that:
1. Equipotential lines intersect the flow lines at right angles.

2. The flow elements formed are approximate squares.
An example of a completed flow net is given in the preceding page. At the figure, N f is the number of flow
channels and Nd is the number of potential drops. The following conditions also apply:
1. The upstream and The upstream and downstream surfaces of the permeable layer (lines ab and
de) are equipotential lines.
2. Because ab and de are equipotential lines, all the flow lines intersect them at right angles.
3. The boundary of the impervious layer—that is, line fg—is a flow line, and so is the surface of the
impervious sheet pile, line acd.
4. The equipotential lines intersect acd and fg at right angles.
Letting H=head difference between the upstream and the downstream side, the total rate of flow, q through all
the channels per unit length is given by:
𝑯 𝑵𝒇
𝒒=𝒌
𝑵𝒅
Square elements are not always necessary. One can draw a rectangular mesh for a flow channel as long as
all the width-to-length ratios for all rectangles are the same. The formula for this case is:
𝑯 𝑵𝒇
𝒒=𝒌 𝒏
𝑵𝒅
Example Problem:
A flow net for flow around a single row of

sheet piles in a permeable soil layer is shown. Given
that kx = kz = k = 5 x 10-3 cm/sec, determine
a. How high (above the ground surface) will

the water rise if piezometers are placed at
points a, b, c, and d?
b. What is the rate of seepage through flow
channel II per unit length (perpendicular to
the section shown)?
Solution:
a. From the figure Nf = 3 , Nd = 6, H= 5m – 1.67m = 3.33m.

3.33m
Headloss for each drop = = 0.555m
5
At point A, the water at the piezometer will rise at an elevation of:

5m – (1)0.555m = 4.445m above ground surface
As for points b, c, and d:
b = 5m - (2) 0.555m = 3.89 m above the ground surface
c = 5m - (5) 0.555m = 2.225 m above the ground surface
d = 5m - (5) 0.555m = 2.225 m above the ground surface
Page 2 of 3
Finals
b. k = 5x10−3 cm/ sec = 5x10−5 m/sec

H 3.33m
Δq = k = 5x10−5 m/sec( )
Nd 6
𝚫𝐪 = 𝟐. 𝟕𝟕𝟓 𝐱 𝟏𝟎−𝟓 𝐦𝟑 /𝐬𝐞𝐜
Flow Nets in Anisotropic Soil
The preceding discussion is applicable when the soil is assumed to be isotropic. However, because the soil
grains are not perfectly spherical, one must also study the flow nets for anisotropic soil. In anisotropic soils, k x ≠ kz. The
following procedure can be used in constructing the flow net for an anisotropic soil.
1. Adopt a vertical scale (that is, z axis) for drawing the cross section.
𝑘𝑥
2. Adopt a horizontal scale (that is, x axis) such that horizontal scale = √ x vertical scale.
𝑘𝑥
3. With scales adopted as in Steps 1 and 2, plot the vertical section through the permeable layer parallel to the
direction of flow.
4. Draw the flow net for the permeable layer on the section obtained from Step 3, with flow lines intersecting
equipotential lines at right angles and the elements as approximate squares.
The rate of seepage is given by:
𝒌 𝒛 𝑯 𝑵𝒇
𝒒= √ ( )
𝒌𝒙 𝑵𝒅
Example Problem:
A section of a dam is given in the figure (a). If k z = 5.67 ft/day

and kx = 11.34ft/day, draw the flow net and calculate the seepage
loss of the sam in ft3/day per ft.
Solution:
ft
5.67day
Horizontal Scale = √ ft (vertical scale)
11.34
day
1
Horizontal scale = (vertical scale)
√2
Replotting the dam section, and drawing the flow net (see
figure (b)), the rate of seepage is given by:
ft ft 2.5
𝑞 = √(5.67 ) (11.34 ) (20ft) ( )
day day 8
𝟓𝟎. 𝟏𝟐𝐟𝐭 𝟑
𝐪= 𝐩𝐞𝐫 𝐟𝐭
𝐝𝐚𝐲
Page 3 of 3

Seepage: Camarines Norte State College

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Republic of the Philippines

CAMARINES NORTE STATE COLLEGE

Flow Nets and Seepage Calculation

Flow Line and Equipotential Line

1. Equipotential lines intersect the flow lines at right angles.

A flow net for flow around a single row of

a. How high (above the ground surface) will

a. From the figure Nf = 3 , Nd = 6, H= 5m – 1.67m = 3.33m.

At point A, the water at the piezometer will rise at an elevation of:

b. k = 5x10−3 cm/ sec = 5x10−5 m/sec

Flow Nets in Anisotropic Soil

The rate of seepage is given by:

A section of a dam is given in the figure (a). If k z = 5.67 ft/day

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