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Lectures 6 and 7: Seepage
By
Dr. Amir Khan
Soil Mechanics 1 (ENG2001M)
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Learning outcomes:by the end of this session and the tutorial session, you should be able to:
1. Understand the seepage theory.
2. Determine the amount of seepage using graphical method
(Flow net).
3. Calculate the exist hydraulic gradient and factor of safety
against piping.
4. Evaluate different methods that can be implemented toprotect ground from seepage problems.
Permeability and seepage
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Text books:
The following books are recommended.
1. Craig. (2004). Soil Mechanics.
2. Barnes (2000). Soil Mechanics, Principles and Practice.
3. Smith and Smith (1998). Elements of Soil Mechanics.
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Seepage theory assumptions:
1. Soil is homogenous (same arrangement of particles)
2. Soil is isotropic with respect to K (if permeability coefficient is
same in every direction then soil is isotropic)
3. Soil is fully saturated
4. Darcys law is valid (continuality and steady state flow, same
particles come in and out there is no change in volume)
5. Flow is 2-D in x and z directions
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Underwater construction using cofferdams
Cofferdam is a watertight enclosure usually of steel sheet pile or concrete bored pile walls pumpeddry to permit construction work below the waterline, as when building bridges or repairing a ship.
The Main issues to consider when constructing a cofferdam are: What is the flow rate Q around the walls this will dictate pumping requirements.
What are the resulting pore pressures on the walls.
Will the seepage of water affect stability, i.e. will the ground between the walls fail.
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Permeability and seepageThe equation of continuityin two directions
No volume change, water incompressible
where vxis the velocity in the x direction and vz is
velocity in the z direction.
According to Darcys law:
The governing equation for steady-state flow of water through saturated soils in
two dimensions and is called Laplace equation
0
z
v
x
v zx
z
hKv
xhKv
z
x
02
2
2
2
z
h
x
h
with the total head h
decreasing in the
directions of vx and vz. Seepage through a soil element.
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Flow lines:
represent the flow direction of water between which
water can flow through a cross section
The path which a particle of water follows in its course
of seepage through a saturated soil mass is called a flow
line.
Equipotential lines:
As the water moves along the flow lines it experiences a
continuous loss of head. If we can obtain the head
causing flow at points along a flow line, then by joining
up points of equal potential we obtain a second set of
lines known as equipotential lines of equal energy or
equal total head.
Permeability and seepage
hKq
d
f
n
hh
hKnq
dn
fn
Khq
Flow direction
Flow lines
Equipotential lines
No. of flow channels
No. of drops
Tot. head differenceTot. discharge
Basis of constructing flow nets:
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Permeability and seepage
Common methods of flow net construction:
1. Graphical method by sketching flow net
2. Using numerical methods such as:
Finite element method
Boundary element method
Finite difference method
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Sketching a flow net
Specify a datum (usually downstream water level)
Specify boundary conditions
Sketch the first estimated flow lines
Draw trial equipotential lines forming curvilinear squares Continue by drawing other flow lines
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Permeability and seepage
Example of a flow net
For flow net aboveNd = 14 andNf = 4. These parameters for this particular examplegive a square flow net and a whole number of flow channels. This should be
formed by trial and error: a first attempt should be made and the positions of the flow
lines and equipotentials and even Nf and Nd should then be adjusted as necessary
until a satisfactory flow net is achieved.
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No. of flow paths (nf) = 4.2
(take ratio)
No. of drops (nd) = 12
h = 4.4 - 0.5 = 4.0 mh= 4.0/12 = 0.33 m
sq
q
dn
fnKhq
/3m5104.1
12
2.44510
Permeability and seepageWorked Example 1
Calculate the water pressure head at points P. assuming
K = 10-5m/s?
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Permeability and seepageWorked Example 1
At point P suppose 4m belowTotal head at point P:
Total head at any point = total head at the start (upstream) - n to the point x
where h = total head difference divided by total number of drops =
d h
h
2
44.5 4 2 4 2 3.33
12
Elevation head = - 4m
4
3.33 ( 4) 7.33
Pressure at point P:
x 7.33 x 9.81 = 71.91 kN/m
P P
P
P
d
p
t p p t p t P
P
p
P p w
n
h h
h Z h h h Z h h Z
Z m
h m
P h
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Critical hydraulic gradient (ic)
Critical hydraulic gradient can be obtained when:
Uplift pressure = Total weight of soil
w(h+L) = (w + sub) x L
sub is submerged unit weight of soil
Permeability and seepage
L
h
Constant head
Soil
Overflow
Datum
e
sG
w
sub
L
hci
1
1
If the hydraulic gradient were high enough the resultant body force would
be zero. The value of hydraulic gradient corresponding to zero resultant
body force is called the critical hydraulic gradient (ic). The soil will be in
quick condition i.e. reduced inter-granular pressure resulting in seepage
induced liquefaction.
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Critical hydraulic gradient:
If the hydraulic gradient of the flow
equals the critical hydraulic gradient,
it causes piping in silts and clays and
quicksand in sands
Permeability and seepage
L
h
Constant head
Soil
Overflow
Datum
e
sG
w
sub
L
hci
1
1
If , unstable condition, the soil particles tend to move.
if stable condition.cr
cr
i i
i i
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Permeability and seepage
Various methods that can be implemented to prevent occurring of soil piping
and quicksand are:
1. Compacting soils in the region vulnerable to soil piping. This leads to an
increased density of the soil resulting in an increase in the value of critical
hydraulic gradient.
2. Reducing the total head difference between the upstream and downstream.
3. Creating a filter layer at the downstream side of the structure to dissipatethe energy of flowing water.
4. Grouting the ground to create a plug. The weight of the plug should be
greater than the water pressure from underneath. Or creating a grouting
curtain underneath a dam.5. The use of sheet piling
