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Water flow in saturated soil

- D A Cameron
- Civil Engineering Practice 1

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

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

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

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

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)

Hydraulic Gradient, i

Area of flow, A

Flow rate, q

Length of flow, l

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

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

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

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

1. Constant head permeameter

Water tank - moveable

A

B

C

D

soil

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?

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

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

2. Falling Head Permeameter

Level at time, t1

Tube of cross-sectional area 'a'

h1

To permeameter cell

Level of cell outflow

Falling head test

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

3. Field testing drawdown test

Pumping well

Water table

r2

r1

Impermeable boundary

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)

Solution

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

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

THE PROBLEM

Sand seam

RL 200 m

RL 193 m

canal

river

60 m

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

Hydraulic gradient, i 0.117

RL 200 m

RL 193 m

?h 7 m

l 60 m

Flow Lines shortest paths for water to exit

Phreatic surface

Equipotential lines

Flow tube

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

5 Flow Lines

Impervious boundary

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

Flownet Basics

- Water flow follows paths of maximum hydraulic

gradient, imax - flow lines and equipotentials must cross at 90,

since

Since ?q is the same, ratio of sides will be

constant for all the squares along the flow

tube

Equi- potential lines

Impervious boundary

Flow ?q

?hi

b

a

Common convention draw squares with a b

square, M, a x b

Discharge in flow direction, ?q per flow tube

Equipotentials

h3

h2

Flow lines

h1

Flownet Construction

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,

Flow Net Calculations

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

But only for squares!

Example if k 10-7 m/sec, what would be the

flow per day over a 100 m length of wall?

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

Example what is the hydraulic gradient in the

square C?

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

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

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)

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

(No Transcript)

Minimising the risk of erosion

- 1. Add more weight at exit points

permeable concrete mats?

Lengthen flow path?

1. Deeper cut-offs 2. Horizontal barriers 3.

Impermeable blanket on exit surface

Simple cut-offs (FESEEP)

Nf 5 Nd 10

Impermeable Clay Blanket

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

- 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

Finite Difference spreadsheet solutionand other

numerical approaches

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

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

9

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

Flow lines from finite difference program

(spreadsheet)

Equipotentials from finite difference program

(spreadsheet)

FESEEP University of Sydney

Mesh of foundation soil

FESEEP Output (University of Sydney)

flownet

increasing

pore pressures

(No Transcript)

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