Basicsofgroundwaterhydrologyingeotechnicalengineeringpermeability Partb 100810060741 Phpapp01

7/25/2019 Basicsofgroundwaterhydrologyingeotechnicalengineeringpermeability Partb 100810060741 Phpapp01

1/38

Basics of groundwater hydrology in geotechnical engineering

Part B

Prepared by Dr O. Hamzao hamzaat hotmaildot com_

_ _

Permeability Part B Dr O.Hamza


2/38

Introduction

- -

Field determination of coefficient of permeability

ummary Example problems



3/38

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



4/38

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



5/38

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.



6/38

- -

Cylindrical flow: confined aquifer

Cylindrical flow: groundwater lowering Spherical flow



7/38

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.



8/38


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.



9/38


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.



10/38


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.



11/38


y w: e u e



12/38


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



13/38


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.



14/38

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



15/38


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?



16/38


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.



17/38


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. .



18/38


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



19/38


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.



20/38


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



21/38


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.



22/38


23/38

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



24/38

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


25/38


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.



26/38


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.



27/38


h

AkAkiq ==

32

221

11 ...qL

hAkq

L

hAkq ===

321

hhhh

qqqq

++=

===



28/38


321 qqqq ===


29/38


321 qqqq ===


30/38



31/38


NOTE: It is coincident

a a ea s appears

in a straight line.


32/38


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?



33/38


u z

4.3t

21.24.9

68.1 m

38.6 m

Datum



34/38


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.)



35/38


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


W ki Q i d E l bl


36/38

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


W ki Q i d E l bl


37/38

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.




38/38


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.


Documents

Basicsofgroundwaterhydrologyingeotechnicalengineeringpermeability Partb 100810060741 Phpapp01