Water flow in saturated soil

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Water flow in saturated soil

• D A Cameron
• Civil Engineering Practice 1

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SEEPAGE water pressures

• Water flows from points of high
  to low TOTAL head
• WATER HEADS
• height of water x ?w water pressure, u
• Total head elevation head pressure head
• i.e h hT he hp
• Kinetic head is ignored in soils

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Head of Water

• Pressure head height water rises to in a
  standpipe above the point

No loss of head, h, in soil mass, so no flow -
Steady State
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Confined Aquifer

• A water bearing layer, overlain and underlain by
  far less permeable soils.

Water level in aquifer
Clay, silt - no free water
x
Sand aquifer
Clay, silt
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Steady flow in soils Laminar flow

• Assumptions to theory
• Uniform soil, homogeneous isotropic
• Continuous soil media
• Small seepage flow (non turbulent flow)
• Darcys Law of 1850 a Frenchman

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Darcys Law

• q kiA
•  
• where q rate of flow (m3/s)
• i hydraulic gradient
• A area normal to flow direction (m2)
• k coefficient of permeability (m/s)

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Hydraulic Gradient, i
Area of flow, A
Flow rate, q
Length of flow, l
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Hydraulic Conductivity

• Coefficient of permeability or just
  permeability
• SATURATED soil permeability

Hazens formula, for clean, almost uniform sands
m/sec if particle size in mm
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TYPICAL PERMEABILITIES

• Clean gravels gt 10-1
  m/s
• Clean sands, sand-gravel 10-4 to 10-2 m/s
• Fine sands, silts 10-7 to 10-4
  m/s
• Intact clays, clay-silts 10-10 to 10-7
  m/s

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Measuring Permeability

• A Laboratory
• Constant head test
• Falling head test
• Other

A Laboratory How good is the sample?
B Field Need to know soil profile (incl. WT)
boundary conditions

• B Field
• Pumping tests
• Borehole infiltration
• tests

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Lab Test 1 Constant head test

• Cylinder of saturated coarse grained soil
• Water fed under constant head
• elevated water tank with overflow
• Rate of outflow measured
• Repeat the above after raising the water tank

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1. Constant head permeameter
Water tank - moveable
A
B
C
D
soil
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Constant head test

• Suitable for clean sands and fine gravels
• EXAMPLE
• If the sample area is 4500 mm2,
• the vertical distance between the 2 standpipe
  points is 100 mm,
• ?h is 75 mm
• Outflow is 1 litre every minute
• What is the coefficient of permeability?

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Solution

• 1000 cm3/min
• OR q 16.7 cm3/sec 16.7x10-6 m3/sec
• i 75/100 0.75
• k q/(iA)
• (16.7x10-6)/(0.75x4500x10-6) m/sec
• k 5 x 10-3 m/sec
• Typical permeability of a clean sand or gravel

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Test 2 Falling head permeameter

• For fine sands, silts, maybe clays
• Rate of water penetration into cylindrical sample
  from loss of head in feeder tube
• Must ensure
• no evaporation
• sufficient water passes through
• A slow procedure

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2. Falling Head Permeameter
Level at time, t1
Tube of cross-sectional area 'a'
h1
To permeameter cell
Level of cell outflow
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Falling head test

• Soil sample length, L, area, A
• Flow in the tube flow in the soil
• tube has area a

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3. Field testing drawdown test
Pumping well
Water table
r2
r1
Impermeable boundary
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Drawdown test

• Needs
• a well-defined water table and
• a confining boundary
• Must be able to
• pull down water table and
• create flow
• (phreatic line uppermost flow line)

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Solution

• Axi-symmetric problem
• By integration of Darcys Law,

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TUTORIAL PROBLEMS

• A canal and a river run parallel, an average of
  60 m apart. The elevation of water in the canal
  is 200 m and the river 193 m. A stratum of sand
  intersects both the river and canal below the
  water levels
• The sand is 1.5 m thick and is sandwiched between
  strata of impervious clay
• Compute the seepage loss from the canal in m3/s
  per km length of the canal, given the
  permeability of the sand is 0.65 mm/s

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THE PROBLEM
Sand seam
RL 200 m
RL 193 m
canal
river
60 m
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SOLUTION

• q kiA
• k 0.65 mm/s 0.65 x 10-3 m/s
• ?h 7 m
• q 0.65 x 10-3 x 0.117 x 1.5 m2/m length
• q 0.114 x 10-3 m3/sec /m length
• q 0.114 m3/sec/km length

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Hydraulic gradient, i 0.117
RL 200 m
RL 193 m
?h 7 m
l 60 m
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Flow Lines shortest paths for water to exit
Phreatic surface
Equipotential lines
Flow tube
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The Flow Net - FLOW LINES
Run ? parallel to impervious boundaries
(impermeable walls or cut-offs) and the
phreatic surface The Phreatic surface is the
top flow line 2 consecutive flow lines constitute
a flow tube
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5 Flow Lines
Impervious boundary
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The Flow Net - EQUIPOTENTIALS

• Are lines of equal total head
• The total head loss between consecutive
  equipotentials is constant
• Equipotentials can be derived from boundary
  conditions and flow lines

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Flownet Basics

• Water flow follows paths of maximum hydraulic
  gradient, imax
• flow lines and equipotentials must cross at 90,
  since

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Since ?q is the same, ratio of sides will be
constant for all the squares along the flow
tube
Equi- potential lines
Impervious boundary
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Flow ?q
?hi
b
a
Common convention draw squares with a b
square, M, a x b
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Discharge in flow direction, ?q per flow tube
Equipotentials
h3
h2
Flow lines
h1
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Flownet Construction
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Flow Net Calculations

• Nd equal potential drops along length of flow?
  Then the head loss from one line to another is
• ?h1-2 ?(?h) ?h / Nd
• From Darcys Law, flow rate in a flow tube,

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Flow Net Calculations

• BUT a b
• AND total flow for Nf flow channels,
• per unit width is  

But only for squares!
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Example if k 10-7 m/sec, what would be the
flow per day over a 100 m length of wall?
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Calculations

• Answer
• 10-7(5/14)45 x 100 m length
• 0.000161 m3/sec
• 13.9 m3/day

• Nf 5
• Nd 14
• ?h 45 m
• k 10-7 m/sec

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Example what is the hydraulic gradient in the
square C?
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Calculations
Answer 1.1 and therefore dangerous!
?h / Nd 45/14 3.2 m head per
drop Average length of flow is about 3 m
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Critical hydraulic gradient, ic

• The value of i for which the effective stress in
  the saturated system becomes ZERO!
• Consequences
• no stress to hold granular soils together
• ? soil may flow ?
• boiling or piping EROSION

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Seepage Condition upward flow of water

• ?satz total stress
• ?u due to seepage,
• i(z)(?w)
• (represents proportion of ?h occurring over
  length AB)
• ?? ? - u
• (?satz) (?wz i(z)?w)
• ?? ??z i(z)?w

B
z
A
?? 0, when ??z i(z)?w OR i
(??/ ?w)
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Likelihood of Erosion
GRANULAR SOILS chiefly! When the effective stress
becomes zero, no stress is carried by the soil
grains Note when flow is downwards, the
effective stress is increased! So the erosion
problem and ensuing instability is most likely
for upward flow, i.e. water exit points through
the foundations of dams and cut-off walls
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Minimising the risk of erosion

• 1. Add more weight at exit points

permeable concrete mats?
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Lengthen flow path?
1. Deeper cut-offs 2. Horizontal barriers 3.
Impermeable blanket on exit surface
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Simple cut-offs (FESEEP)
Nf 5 Nd 10
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Impermeable Clay Blanket
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Summary Key Points

• Heads in soil
• Darcys Law
• Coefficient of permeability
• Measurement of permeability
• Flownets
• Flownet rules
• Seepage from flownets
• Piping, boiling or erosion
• Critical hydraulic gradient

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• Exercises
• a) Draw a flow net for seepage under a vertical
  sheet pile wall penetrating 10 m into a uniform
  stratum of sand 20 m thick.
• b) If the water level on one side of the wall is
  11 m above the sand and on the other side 1.5 m
  above the sand, compute the quantity of seepage
  per unit width of wall. k 3 ? 10-5 m/s
• What is the factor of safety against developing
  the quick condition on the outflow side of the
  wall? ?sat 21 kN/m3

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Finite Difference spreadsheet solutionand other
numerical approaches

• Authors
• Mahes Rajakaruna (ex UniSA)
• University of Sydney (FESEEP)

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ROWCO
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
L
Soil level
1
100
104
2
100
104
3
100
104
Cell H5
4
100
104
5
100
104
6
100
104
7
100
104
8
100
104
Interior cell value (H4I5H6G5)/4
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100
104
104
104
104
104
104
104
10
100
11
100
Impermeable boundary
12
100
13
100
14
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
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Flow lines from finite difference program
(spreadsheet)
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Equipotentials from finite difference program
(spreadsheet)
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FESEEP University of Sydney
Mesh of foundation soil
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FESEEP Output (University of Sydney)
flownet
increasing
pore pressures
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