BULACAN STATE UNIVERSITY
GEOTECHNICAL ENGINEERING MODULE 8
COLLEGE OF ENGINEERING
CIVIL ENGINEERING DEPARTMENT
PREPARED BY: ENGR. MARPEE S. GABUAT
CHAPTER 8: FLOW NETS
Rate of Seepage through Foundation
Flow Line
1. For isotropic soils
A line along which a water particle will travel
from upstream to the down stream side in the
permeable soil medium
𝑄=
𝐾𝐻𝑁𝑓
𝑁𝑑
Seepage through an Earth Dam on an Impervious
Dam
1.
, rate of seepage from a flow net
Equipotential Line
A line which the potential head at all points are
equal.
𝑄=
𝐾𝐻𝑁𝑓
𝑁𝑑
Flow Net
Nf = 3
A combination of a number of flow lines and
equipotential lines.
Nd = 11
Kx = Kz = K (coefficient of permeability)
, rate of seepage from a flow net
2.
Nf = 5 (number of flow channels)
Characteristics of Flow Net
Nd = 8 (number of potential drops)
1. The equipotential lines intersect the flow lines
at right angles.
2. The flow elements formed are approximate
squares.
2. For non-isotropic soils
𝑄=
√𝐾𝑥 𝐾𝑧 𝐾𝐻𝑁𝑓
, rate of seepage from a flow net
𝑁𝑑
Where Kx ≠ Kz
𝐾 = √𝐾𝑥 𝐾𝑧
𝑄=
𝐾(ℎ1 2 −ℎ2 2 )
, rate of seepage from a flow net
2𝐿
BULACAN STATE UNIVERSITY
GEOTECHNICAL ENGINEERING MODULE 8
COLLEGE OF ENGINEERING
CIVIL ENGINEERING DEPARTMENT
PREPARED BY: ENGR. MARPEE S. GABUAT
PROBLEM SOLVING
3.
Problem No. 1
Compute the seepage flow under the foundation
of the dam shown.
K = 0.002 m/s
(Ans. 0.0143 m3/s/m)
𝑄 = 𝐾𝐿𝑡𝑎𝑛𝜃𝑠𝑖𝑛𝜃, rate of seepage from a flow net
𝐿=
𝑑
𝑑2
𝐻2
√ 2 − 2 ,
cos 𝜃 𝑐𝑜𝑠 𝜃
𝑠𝑖𝑛 𝜃
Problem No. 3
Seepage through the foundation
Problem No. 2
Calculate the seepage loss per length of the sheet
pile (at right angle to the cross section shown). K
= 6.5 x 10-6 m/s.
𝑄=
𝐾𝐻𝑁𝑓
𝑁𝑑
Nf = 4
Nd = 9
(Ans. 1.3975x10-5 m3/s/m)
, rate of seepage from a flow net
The sheet pile is driven in the Cebu South
reclamation area and the area to one side is
pumped down as shown in the flow net. The
permeability of the sand is 0.001 m/sec. Below the
elevation 20 m is an impermeable rock layer.
Determine the flow per unit length and the
pressure at point A at elevation 22m.
(Ans. 1.5x10-3 m3/s/m, 53.9550 kPa)
BULACAN STATE UNIVERSITY
GEOTECHNICAL ENGINEERING MODULE 8
COLLEGE OF ENGINEERING
CIVIL ENGINEERING DEPARTMENT
PREPARED BY: ENGR. MARPEE S. GABUAT
Problem No. 6
An earth dam on a previous but strong earth
foundation has the cross section shown. The core
of the dam is sealed from the joined rock
foundation with a thin layer of gunite or splush
grout.
Problem No. 5
From the given base of the weir shown and the
given equipotential lines, compute the following:
Problem No. 4
Two sheet piles are driven to support a sewer
excavation in a medium sand having a void ratio
of 0.5 and specific gravity of 2.60. The interior of
the excavation is dewatered to the bottom
elevation of 118m. If the permeability of the sand
k = 0.001 m/s, calculate the total in flow of water
into the foundation for a 30m length of the
excavation.
(Ans. 0.0800 m3/s)
1. The uplift pressure at A. (Ans. 112.8150 kPa)
2. The uplift pressure at B. (Ans. 34.3350 kPa)
3. The uplift force per unit length measured along
the axis of the weir. (Ans. 882.9000 kN)
1. Calculate the seepage through the dam. (Ans.
0.0350 m3/day/m)
2. Calculate the seepage through the foundation.
(Ans. 3.3750 m3/day/m)
3. Compute the total seepage. (Ans. 3.4100
m3/day/m)
4. What minimum permeability is required in
drain B to prevent saturation from rising into
the random fill zone. (Ans. 136.4000 m/day)