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Basics of groundwater hydrology in geotechnical engineering
Part B
Prepared by Dr O. Hamzao hamzaat hotmaildot com_
_ _
Permeability Part B Dr O.Hamza
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Introduction
- -
Field determination of coefficient of permeability
ummary Example problems
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Introduction
y w
q=
where
s coe c en o permea y w
dimensions of velocity (length/time)
= = -----------------------Q Quantity of water
(Ref. Geotechnical on the Web)
In a saturated porous media, the rate of f low of water q (volume/time)
t Time
roug cross-sec ona area s oun o e propor ona o y rau c
gradient i
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Introduction
u e y w
Aquiferis a term used to designate a porous geological formation that:-
- permits water to move through it under ordinary field conditions
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Introduction
u e y w
The horizontal flow rate q is constant. For an,
Darcy's Law indicates that
q = A k i
= B t k i
or
Hydraulic gradient varies inversely with aquifer
Where flow occurs in a confined a uifer whose thickness varies entl with
thickness
position the flow can be treated as being essentially one-dimensional.
Permeability Part B Dr O.Hamza
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- -
Cylindrical flow: confined aquifer
Cylindrical flow: groundwater lowering Spherical flow
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Quasi-one-dimensional and radial flow
y w: e u e
Pum in a uifer
Confined aquifer
Steady-state pumping from a well which extends the full thickness of a
con ne aqu er s one o e one- mens ona pro em w c can e
analysed in cylindrical coordinates.
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Quasi-one-dimensional and radial flow
y w: e u e
Darcy's Law still applies, with hydraulic
gradient dh/dr and area A varying with radius: .
n s case pore pressure or ea var es on y w ra us r.
Permeability Part B Dr O.Hamza
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Quasi-one-dimensional and radial flow
y w: e u e
Integrating between the
borehole and at variable
s ance r:
where ro is the radius of the borehole and h0the constant head in the borehole.
Permeability Part B Dr O.Hamza
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Quasi-one-dimensional and radial flow
y w: u w e we
Pumping from a borehole can be used for
e era e groun wa er ower ng n or er o
facilitate excavation.
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Quasi-one-dimensional and radial flow
y w: e u e
Permeability Part B Dr O.Hamza
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Quasi-one-dimensional and radial flow
y w: u w e we
This is an example of quasi-one-
dimensional radial flow with flow thickness. .
Ori inal level of
Integrating between the borehole and
water table
The radius of influence
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Quasi-one-dimensional and radial flow
e w
Darcy's Law still applies, with hydraulic gradient dh/dr
and area A varying with radius: A=4r
head varies only
where r0 is the radius of the piezometer
and h0 the constant head in the piezometer
Variation of pore pressure around a point source or side (for example, a
.
p ezome er e ng use or - e erm na on o permea y s a one-
dimensional problem which can be analysed in spherical coordinates.
Permeability Part B Dr O.Hamza
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Determination of coefficient of permeability
a ora ory measuremen o e coe c en o permea y
Field measurement of the permeability
Empirical relations for the coefficient of permeability
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Determination of coefficient of permeability
e e u e e e e e y
Field measurement Laboratory measurement
Field or in-situ measurement of permeability avoids the difficulties involvedin obtaining and setting up undisturbed samples
Field or in-situ measurement of permeability provides information about bulk
permeability, rather than merely the permeability of a small and possibly
unrepresentative sample.
Is field measurement of permeability better than the lab
measurement?
Permeability Part B Dr O.Hamza
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Determination of coefficient of permeability
e e u e e e e e y
Well-Pumping test
Observational boreholes
In a well-pumping test, a number of observation boreholes at radii r1 and
r2 are monitored to measure the pressure heads.
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Determination of coefficient of permeability
e e u e e e e e y
Well-Pumping test
If the pumping causes a drawdown in an
unconfined (i.e. open surface) soil stratum
then the uasi-one dimensional flow e uation
is applied.
Integrating between the two test limits
and rearranging the equation:
(Assuming the pumping causes a drawdown in an
Observational boreholes. .
Permeability Part B Dr O.Hamza
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Determination of coefficient of permeability
e e u e e e e e y
Well-Pumping testIf the soil stratum is confined and of thickness tan rema ns sa ura e en
Confined stratum
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Determination of coefficient of permeability
e e e e e e y
Empirical relations
k = function of(other parameters)
the soil particles which can be simply described through void ratio e.
Several empirical equations for estimation of the coefficient of permeability
have been proposed in the past.
Permeability Part B Dr O.Hamza
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Determination of coefficient of permeability
e e e e e e y
For fairly uniform sand Hazen (1930)
ermea y o granu ar so s
proposed the following relation between the
coefficient of permeability k (m/s) and the
effective article size D in mm the
particle size than which 10% soil is finer):
where C is a constant a roximatel e ual to
10.=
0.01 (see the figure beside)
Hazzan equation and data relating coefficient of
permeability and effective grain size of granular soils
Hazzan equation and data relating coefficient of
permeability and effective grain size of granular soils
Permeability Part B Dr O.Hamza
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Determination of coefficient of permeability
e e e e e e y
ermea y o so c ays
amaras ng e, uang an rnev c ave sugges e a e
coefficient of permeability of clays can be given by the equation:
e1
eCk
+=
w ere
e is void ratio
C and n are constant to be determined experimentally
Consolidation of soft clay may involve a significant decrease in void ratio
and therefore of permeability.
Permeability Part B Dr O.Hamza
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Quizzes: quiz 3 to 6 * xamp e pro ems:
problem 3 and problem 4
* Note. uiz 1 and roblem 1 and 2 are covered in Part A of Permeability lecture
Permeability Part B Dr O.Hamza
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Working on Quizzes and Example problems
The sets of nested piezometers shown below penetrate a layered aquifer.
For one of the piezometers, indicate graphically the elevation head, pressure
head, and total head.
For both cases, indicate the direction of the vertical flow between the layers. or case , w a s a rea s c s ua on a m g resu n a se o ea s
such as this?
Note: The wells are drawn with some separation between them to allow you room to
label the heads. Assume, however, that they are truly nested, i.e., that they penetrate
the surface of the aquifer at the same location.
datumdatumdatum
Case 2Case 1Permeability Part B Dr O.Hamza
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Working on Quizzes and Example problems
o u on:
Flow
w
hz
h Flow
datumdatumdatum
Case 2Case 1
The situation in Case 2 might happen if the middle layer is being pumped
OR if the middle layer is a zone of incredibly high conductivity.
Permeability Part B Dr O.Hamza
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Working on Quizzes and Example problems
An inclined permeameter tube is filled with three layer of soil of different
permea es as s own n e gure.
(i) Formulate q in terms of the different dimensions and permeabilities for
each soil elemente erm ne e ea oss e ween eac so e emen assum ng
k1=k2=k3
(iii) Re-determine the head loss (h) between each soil element assuming
3k1=k2=2k3
(iv) Express the head at
, , ,
(with respect to the
datum)
heads versus
horizontal distance.
Permeability Part B Dr O.Hamza
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Working on Quizzes and Example problems
h
AkAkiq ==
32
221
11 ...qL
hAkq
L
hAkq ===
321
hhhh
qqqq
++=
===
Permeability Part B Dr O.Hamza
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Working on Quizzes and Example problems
321 qqqq ===
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Working on Quizzes and Example problems
321 qqqq ===
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Working on Quizzes and Example problems
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Working on Quizzes and Example problems
NOTE: It is coincident
a a ea s appears
in a straight line.
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Working on Quizzes and Example problems
u z
The site consists of an unconfined aquifer and a confined aquifer separated by a
-m c con n ng ayer. a er n e uncon ne aqu er s res , an wa er
in the confined aquifer is saline. Two nested piezometers have been drilled,
one penetrating the unconfined aquifer (P1), and one penetrating the confinedaqu er 2 .
Land surface elevation: 68.1 m Temperature of water in P1 and P2: 16 C
Depth to P1: 21.2 m Depth to P2: 38.6 m
Depth to water in the well at P1: 4.3 m Depth to water in the well at P2: 4.9 m
Unit weight of fresh water at 16 C: 9.99 kN/m3 Unit weight of water in P2: 10.21 kN/m3
Sketch a diagram (doesnt have to be to scale) showing the information
described above.
What is the total head (h1) for P1?
Determine the pressure head for P2 (hw2-saline), and the equivalent fresh-water
pressure head for P2 (hw2-frish) What is the total fresh-water head (h2-fresh) for P2?
Will you issue a permit to inject hazardous waste into the deep aquifer ? Why
or why not?
Permeability Part B Dr O.Hamza
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Working on Quizzes and Example problems
u z
4.3t
21.24.9
68.1 m
38.6 m
Datum
Permeability Part B Dr O.Hamza
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Working on Quizzes and Example problems
u z
Fresh water total head for P1 is 68.1 4.3 = 63.8 m
Saline pressure head for P2 is 38.6 4.9 = 33.7 m
- ,
uSaline = ufirsh
So Saline x 33.7 = frish x hw2-frish
solve for hw2-frish
: = Saline x 33.7 / frish
= 10.21 x 33.7 /9.99 = 34.4 m
= = =, 2- resh z2 w2- rish . . . .
Thus flow is in an UPWARD direction from the lower aquifer, and you should
. ,it will further increase the pressure head and increase the upward
gradient.)
Permeability Part B Dr O.Hamza
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Working on Quizzes and Example problems
u z
so pro e cons s s o ree ayers w proper es s own n e a e e ow.
Calculate the equivalent coefficients of permeability parallel and normal
to the stratum.
Layer Thickness (m) kx (parallel, m/s) kz (normal, m/s)
- -.
2 4 5x10-8 2.5x10-8
3 3 3x10-5 1.5x10-5
Answers:For the flow parallel to the layers: kx= 9.6x10^-6 m/s
For the flow normal to the layers: kz=6.1x10^-8 m/s
Permeability Part B Dr O.Hamza
W ki Q i d E l bl
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Working on Quizzes and Example problem
. e measuremen o e coe c en o permea y
A stratum of sandy soil overlies a horizontal bed of impermeable material;
the surface of which is also horizontal. In order to determine the in situ
permeability of the soil, a test well was driven to the bottom of the stratum.
Two observation boreholes were made at distances of 12.5m and 25mrespectively from the test well.
Water was pumped from the test well at the rate of 3x10-3 m3/s until the
boreholes were then found to be 4.25m and 6.5m above the impermeablebed.
Find the value, expressed in m3/day, of the Impermeable
coe c en o permea y o e san y so
Permeability Part B Dr O.Hamza
W ki Q i d E l bl
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Working on Quizzes and Example problem
. e measuremen o e coe c en o permea y
Key solution
This is a quasi-one dimensional
flow, from which we found that:
where:q (rate of flow) = 3x10-3 m3/s = 3x10-3 x 60 x
= .
r1= 12.5m and r2 = 25m
h1= 4.25m and h2= 6.5m
Impermeable
ln(r2/r1) = 0.693
Note ln is the logarithm to base e, also called the natural logarithm.
Permeability Part B Dr O.Hamza
Working on Quizzes and Example problems
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Working on Quizzes and Example problems
ro em . mp r ca re a ons o e coe c en o permea y
Void ratio 1.1 0.9
,
cm s 0.302 x 10- 0.12 x 10-
en=
proposed by Samarasinghe, Huang and Drnevich (1982) to estimate the
e1+
. .
Hint: form two equations with two unknowns C and n by substituting the
experimental values given in the table in the equation.
Permeability Part B Dr O.Hamza