SlideShare una empresa de Scribd logo
1 de 38
Descargar para leer sin conexión
Basics of groundwater hydrology in geotechnical engineering




                               Part B

                   Prepared by Dr O. Hamza
                         o_hamza at hotmail dot com



                        Lecture reference: OH GA03 B
                                           OH_GA03_B


Permeability – Part B                                         Dr O.Hamza
Content


  •   Introduction
  •   Quasi-one-dimensional
      Quasi one dimensional and radial flow
  •   Field determination of coefficient of permeability
  •   Summary
      S mmar
  •   Example problems




Permeability – Part B                                      Dr O.Hamza
Introduction

 Darcy’s law



       q = Aki


where
k i coefficient of permeability with
  is   ffi i t f          bilit ith
                                                    (Ref. Geotechnical on the Web)
dimensions of velocity (length/time)
                   Q      Quantity of water
q is flow rate =        = -----------------------
                   t         Time

 In a saturated porous media, the rate of flow of water q (volume/time)
 through cross-sectional area ‘A’ is found to be proportional to hydraulic
 th     h           ti  l         i f    dt b           ti   lt h d     li
 gradient ‘ i ’
Permeability – Part B                                                           Dr O.Hamza
Introduction

 Aquifer and Darcy’s law




   Aquifer is a term used to designate a porous geological formation that:
   - contains water at full saturation
   - permits water to move through it under ordinary field conditions
Permeability – Part B                                                    Dr O.Hamza
Introduction

 Aquifer and Darcy’s law


    The horizontal flow rate q is constant. For an
    aquifer of width B and varying thickness tt,
    Darcy's Law indicates that
        q=Aki
         =Btki

   or


   Hydraulic gradient varies inversely with aquifer
   thickness

   Where flow occu s in a co
      e e o occurs         confined aqu e whose t c ess varies ge t y with
                                  ed aquifer   ose thickness a es gently t
   position the flow can be treated as being essentially one-dimensional.

Permeability – Part B                                                Dr O.Hamza
Quasi-one-dimensional
     Quasi one dimensional and radial flow
     •   Cylindrical flow: confined aquifer
     •   Cylindrical flow: groundwater lowering
     •   Spherical flow




Permeability – Part B                             Dr O.Hamza
Quasi-one-dimensional and radial flow

 Cylindrical flow: confined aquifer


                        Pumping aquifer



                           Confined aquifer




  Steady-state pumping from a well which extends the full thickness of a
  confined aquifer is one of the one dimensional problem which can be
                                 one-dimensional
  analysed in cylindrical coordinates.
Permeability – Part B                                                      Dr O.Hamza
Quasi-one-dimensional and radial flow

 Cylindrical flow: confined aquifer




Darcy's Law still applies, with hydraulic
gradient dh/dr and area A varying with radius:
A = 2πr.t
    2 rt


  In this case pore pressure or head varies only with radius r
                                                             r.

Permeability – Part B                                             Dr O.Hamza
Quasi-one-dimensional and radial flow

 Cylindrical flow: confined aquifer




Integrating between the
borehole and at variable
distance r:
di t




where ro is the radius of the borehole and h0
the constant head in the borehole.


Permeability – Part B                           Dr O.Hamza
Quasi-one-dimensional and radial flow

 Cylindrical flow: groundwater lowering




  Pumping from a borehole can be used for
  deliberate groundwater lowering in order to
  facilitate excavation.
Permeability – Part B                           Dr O.Hamza
Quasi-one-dimensional and radial flow

 Cylindrical flow: confined aquifer




Permeability – Part B                   Dr O.Hamza
Quasi-one-dimensional and radial flow

 Cylindrical flow: groundwater lowering

 This is an example of quasi-one-
 dimensional radial flow with flow thickness
 t=h Then A=2πr h and
 t=h.       A=2πr.h                            Groundwater lowering

                                                               Original level of
                                                               water table

Integrating between the borehole and
at variable distance r:                                                Drawdown



                                                        The radius of influence




Permeability – Part B                                                  Dr O.Hamza
Quasi-one-dimensional and radial flow

 Spherical flow

Darcy's Law still applies, with hydraulic gradient dh/dr
and area A varying with radius: A=4πr²




     where r0 is the radius of the piezometer
     and h0 the constant head in the piezometer               head varies only
                                                              with radius r
                                                                          r.

  Variation of pore pressure around a point source or side (for example, a
  piezometer being used for in situ determination of permeability) is a one
                             in-situ                                    one-
  dimensional problem which can be analysed in spherical coordinates.
Permeability – Part B                                                      Dr O.Hamza
Determination of coefficient of permeability
  •   Laboratory measurement of the coefficient of permeability
      L b    t                  t f th      ffi i t f         bilit
  •   Field measurement of the permeability
  •   Empirical relations for the coefficient of permeability




Permeability – Part B                                                 Dr O.Hamza
Determination of coefficient of permeability

 Field measurement of the permeability

       Field measurement                    Laboratory measurement




  • Field or in-situ measurement of permeability avoids the difficulties involved
  in 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
                                    y
 measurement?

Permeability – Part B                                                       Dr O.Hamza
Determination of coefficient of permeability

 Field measurement of the permeability

                          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.

Permeability – Part B                                                    Dr O.Hamza
Determination of coefficient of permeability

 Field measurement of the permeability

If the pumping causes a drawdown in an
unconfined (i.e. open surface) soil stratum         Well-Pumping test
then the quasi one dimensional flow equation
         quasi-one
is applied.

Integrating between the two test limits
and rearranging the equation:


                                                    Impermeable


(Assuming the pumping causes a drawdown in an
unconfined (i.e. open surface) soil stratum then)
                                                         Observational b h l
                                                         Ob     ti   l boreholes




Permeability – Part B                                                  Dr O.Hamza
Determination of coefficient of permeability

 Field measurement of the permeability


If the soil stratum is confined and of thickness t   Well-Pumping test
and remains saturated th
    d       i     t t d then




                                                         Confined stratum




Permeability – Part B                                                 Dr O.Hamza
Determination of coefficient of permeability

 Empirical relations for the coefficient of permeability



                        Empirical relations
                          p

                k = function of (other parameters)

 Permeability of all soils is strongly influenced by the density of packing of
 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
Determination of coefficient of permeability

 Empirical relations for the coefficient of permeability

  Permeability of granular soils
  P     bilit f        l     il
  For fairly uniform sand Hazen (1930)
  proposed the following relation between the
  coefficient of permeability k (m/s) and the
  effective particle size D10 (in mm) (the
  particle size than which 10% soil is finer):


    k = C D10
        C.D 2
 where C is a constant approximately equal to
                         pp        y q
 0.01 (see the figure beside)


                                                 Hazzan equation and data relating coefficient of
                                                 permeability and effective grain size of granular soils



Permeability – Part B                                                                    Dr O.Hamza
Determination of coefficient of permeability

 Empirical relations for the coefficient of permeability

  Permeability of soft clays
  P     bilit f ft l

  Samarasinghe, H
  S         i h Huang and D  d Drnevich (1982) h
                                      i h        have suggested th t th
                                                             t d that the
  coefficient of permeability of clays can be given by the equation:

        en
   k=C
       1+ e
   where
     h
   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
Summary

• All soils are permeable materials, water being free to flow through the
interconnected pores between the solid particles.
• Water in saturated soil will flow in response to hydraulic g
                                          p         y        gradient and occurs
towards the lower total head.
• Flow rate is proportional to the hydraulic gradient and can be affected by the
geometry of the pores.
                pores
• The hydraulic gradient may be associated with natural flow or induced by
loading the soil (i.e. due to excavation or construction).
• Coefficient of permeability may be determined from laboratory experiments or
from in situe measurements
• Pore water pressure u at any point of the soil is computed from the definition
of the hydraulic head, u = γw(h-hz)      (where h is total head and hz is
elevation head).




Permeability – Part B                                                       Dr O.Hamza
Quizzes and example problems


      Work on:

      • Quizzes: quiz 3 to 6 *
      • Example problems: *
                        problem 3 and problem 4


        * Note. quiz 1 and problem 1 and 2 are covered in Part A of
        Permeability lecture




Permeability – Part B                                                 Dr O.Hamza
Working on Quizzes and Example problems

 Quiz 3

 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.
 • F case 2, what is a realistic situation th t might result i a set of h d
   For      2 h ti          li ti it ti that i ht            lt in  t f heads
 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.




                                                   datum


                Case 1                                          Case 2
Permeability – Part B                                                             Dr O.Hamza
Working on Quizzes and Example problems

 Quiz 3

 Solution:
 S l ti




           hw
   h                                Flow                                     Flow
             hz
                                             datum


                  Case 1                                 Case 2


  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
Working on Quizzes and Example problems

 Quiz 4
An inclined permeameter tube is filled with three layer of soil of different
      permeabilities as shown in the figure
                                     figure.
(i) Formulate q in terms of the different dimensions and permeabilities for
      each soil element
(ii) D t
      Determine th h d l
             i the head loss (Δh) b t
                                    between each soil element assuming
                                                h il l        t         i
      k1=k2=k3
(iii) Re-determine the head loss (Δh) between each soil element assuming
      3k1=k2=2k3

(iv) Express the head at
     points A, B, C, and D
            A B C
     (with respect to the
     datum)
(v) Plot the various
     heads versus
     horizontal distance.



Permeability – Part B                                                      Dr O.Hamza
Working on Quizzes and Example problems

 Quiz 4

(i) Flow rate q in each soil element is equal:
             Δh
q = Aki = Ak
             L
         Δh           Δh 2
q1 = Ak1 1 q 2 = Ak 2                 q 3 = ...
          L1          L2
q = q1 = q 2 = q 3
Δh = Δh1 + Δh 2 + Δh 3




Permeability – Part B                             Dr O.Hamza
Working on Quizzes and Example problems

Quiz 4

(ii) Flow rate q in each soil element is equal:


    q = q1 = q 2 = q 3
Working on Quizzes and Example problems

Quiz 4

(iii) Flow rate q in each soil element is equal:


    q = q1 = q 2 = q 3
Working on Quizzes and Example problems

Quiz 4

(iv) Heads
Working on Quizzes and Example problems

     Quiz 4

    (v) Plotting




NOTE: It is coincident
that ll heads
th t all h d appears
in a straight line.
Working on Quizzes and Example problems

    Quiz 5
The site consists of an unconfined aquifer and a confined aquifer separated by a
   5-m thick
   5 thi k confining layer. Water in the unconfined aquifer i f h and water
                 fi i l        W t i th          fi d     if is fresh, d     t
   in the confined aquifer is saline. Two nested piezometers have been drilled,
   one penetrating the unconfined aquifer (P1), and one penetrating the confined
   aquifer (P2)
              ).
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 (doesn’t 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)
                              w2 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
Working on Quizzes and Example problems

 Quiz 5




                 4.3t
                               4.9
         21.2

                                      38.6 m
                                               68.1 m




       Datum




Permeability – Part B                              Dr O.Hamza
Working on Quizzes and Example problems

 Quiz 5

 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
 For the equivalent fresh-water pressure head, pressure must be equal:
                       fresh water              head
              uSaline = ufirsh
 So γSaline x 33.7 = γfrish x hw2-frish
 solve for hw2-frish: = γSaline x 33.7 / γfrish
                     = 10.21 x 33.7 /9.99 = 34.4 m
 so,
 so h2-fresh = hz2 + hw2-frish = (68 1 – 38 6 ) + 34.4 = 63 9 m
        f                  f      (68.1 38.6      34 4 63.9

 Thus flow is in an UPWARD direction from the lower aquifer, and you should
    not issue the permit (In addition if you inject waste into the lower aquifer
                     permit.    addition,
    it will further increase the pressure head and increase the upward
    gradient.)



Permeability – Part B                                                     Dr O.Hamza
Working on Quizzes and Example problems

 Quiz 6

 A soil profile consists of th
     il    fil      i t f three l
                                layers with properties shown i th t bl b l
                                        ith       ti    h    in the table below.
    Calculate the equivalent coefficients of permeability parallel and normal
    to the stratum.


  Layer       Thickness (m)    kx (parallel, m/s)     kz (normal, m/s)
  1           3                2x10-6
                                    6                 1.0x10 6
                                                      1 0x10-6
  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
Working on Quizzes and Example problem

 Problem 3 Field measurement of the coefficient of permeability
         3.

 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 25m
 respectively from the test well.
 Water was pumped from the test well at the rate of 3x10-3 m3/s until the
 water level became steady. The heights of the water in the two observation
 boreholes were then found to be 4.25m and 6.5m above the impermeable
 bed.




Find the value, expressed in m3/day, of the            Impermeable
coefficient of permeability of the sandy soil
   ffi i t f         bilit f th       d    il

Permeability – Part B                                                       Dr O.Hamza
Working on Quizzes and Example problem

 Problem 3 Field measurement of the coefficient of permeability
         3.
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
60 x 24 = 259 2 m3/day
           259.2
                                                        Impermeable
r1= 12.5m and r2 = 25m
h1= 4.25m and h2= 6.5m
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

 Problem 4 E i i l relations of th coefficient of permeability
         4. Empirical l ti    f the   ffi i t f         bilit


  For a clay soil, the following are given:
             soil

                   Void ratio    1.1              0.9
                   k (cm/s)
                     ( /)        0 302 x 10-7
                                 0.302      7     0 12 x 10-7
                                                  0.12      7



                                                   en
  Use the following empirical relation:       k=C
                                                  1+ e
  proposed by Samarasinghe, Huang and Drnevich (1982) to estimate the
  coefficient of permeability of the clay at a void ratio of 1 2
                                                             1.2.




  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

Más contenido relacionado

La actualidad más candente

Lecture 8 consolidation and compressibility
Lecture 8  consolidation and compressibilityLecture 8  consolidation and compressibility
Lecture 8 consolidation and compressibilityDr.Abdulmannan Orabi
 
Bearing capacity of shallow foundations by abhishek sharma
Bearing capacity of shallow foundations by abhishek sharma Bearing capacity of shallow foundations by abhishek sharma
Bearing capacity of shallow foundations by abhishek sharma ABHISHEK SHARMA
 
Chapter 4. Bearing Capacity of Soil.pdf
Chapter 4. Bearing Capacity of Soil.pdfChapter 4. Bearing Capacity of Soil.pdf
Chapter 4. Bearing Capacity of Soil.pdfgashutube
 
Consolidation of Soil
Consolidation of SoilConsolidation of Soil
Consolidation of SoilArbaz Kazi
 
Lecture 11 Shear Strength of Soil CE240
Lecture 11 Shear Strength of Soil CE240Lecture 11 Shear Strength of Soil CE240
Lecture 11 Shear Strength of Soil CE240Wajahat Ullah
 
Infiltration presentation by zulfiqar UET Lhr
Infiltration presentation by zulfiqar UET LhrInfiltration presentation by zulfiqar UET Lhr
Infiltration presentation by zulfiqar UET LhrZulfiqar Ali
 
Swelling correlations
Swelling correlationsSwelling correlations
Swelling correlationsAli Rehman
 
Lecture 07 permeability and seepage (11-dec-2021)
Lecture 07 permeability and seepage (11-dec-2021)Lecture 07 permeability and seepage (11-dec-2021)
Lecture 07 permeability and seepage (11-dec-2021)HusiShah
 
Class 5 Permeability Test ( Geotechnical Engineering )
Class 5   Permeability Test ( Geotechnical Engineering )Class 5   Permeability Test ( Geotechnical Engineering )
Class 5 Permeability Test ( Geotechnical Engineering )Hossam Shafiq I
 
Consolidation settlement
Consolidation settlementConsolidation settlement
Consolidation settlementParth Joshi
 
SOIL PERMEABILITY PPT
SOIL PERMEABILITY PPTSOIL PERMEABILITY PPT
SOIL PERMEABILITY PPTJISMI JACOB
 
Permeability of Soils & Seepage Analysis
Permeability of Soils & Seepage AnalysisPermeability of Soils & Seepage Analysis
Permeability of Soils & Seepage Analysiswasim shaikh
 
shear strength of soil
shear strength of soilshear strength of soil
shear strength of soilAamir Ali
 
Experimental conceptualisation of the Flow Net system construction inside the...
Experimental conceptualisation of the Flow Net system construction inside the...Experimental conceptualisation of the Flow Net system construction inside the...
Experimental conceptualisation of the Flow Net system construction inside the...Dr.Costas Sachpazis
 
Geotechnical Engineering-I [Lec #27: Flow Nets]
Geotechnical Engineering-I [Lec #27: Flow Nets]Geotechnical Engineering-I [Lec #27: Flow Nets]
Geotechnical Engineering-I [Lec #27: Flow Nets]Muhammad Irfan
 

La actualidad más candente (20)

Permeability
PermeabilityPermeability
Permeability
 
Darcy's law
Darcy's lawDarcy's law
Darcy's law
 
Lecture 8 consolidation and compressibility
Lecture 8  consolidation and compressibilityLecture 8  consolidation and compressibility
Lecture 8 consolidation and compressibility
 
Bearing capacity of shallow foundations by abhishek sharma
Bearing capacity of shallow foundations by abhishek sharma Bearing capacity of shallow foundations by abhishek sharma
Bearing capacity of shallow foundations by abhishek sharma
 
Chapter 4. Bearing Capacity of Soil.pdf
Chapter 4. Bearing Capacity of Soil.pdfChapter 4. Bearing Capacity of Soil.pdf
Chapter 4. Bearing Capacity of Soil.pdf
 
Consolidation of Soil
Consolidation of SoilConsolidation of Soil
Consolidation of Soil
 
Lecture 11 Shear Strength of Soil CE240
Lecture 11 Shear Strength of Soil CE240Lecture 11 Shear Strength of Soil CE240
Lecture 11 Shear Strength of Soil CE240
 
Soil Compaction
Soil CompactionSoil Compaction
Soil Compaction
 
Infiltration presentation by zulfiqar UET Lhr
Infiltration presentation by zulfiqar UET LhrInfiltration presentation by zulfiqar UET Lhr
Infiltration presentation by zulfiqar UET Lhr
 
Swelling correlations
Swelling correlationsSwelling correlations
Swelling correlations
 
Lecture 07 permeability and seepage (11-dec-2021)
Lecture 07 permeability and seepage (11-dec-2021)Lecture 07 permeability and seepage (11-dec-2021)
Lecture 07 permeability and seepage (11-dec-2021)
 
Class 5 Permeability Test ( Geotechnical Engineering )
Class 5   Permeability Test ( Geotechnical Engineering )Class 5   Permeability Test ( Geotechnical Engineering )
Class 5 Permeability Test ( Geotechnical Engineering )
 
Consolidation settlement
Consolidation settlementConsolidation settlement
Consolidation settlement
 
SOIL PERMEABILITY PPT
SOIL PERMEABILITY PPTSOIL PERMEABILITY PPT
SOIL PERMEABILITY PPT
 
Consolidation
ConsolidationConsolidation
Consolidation
 
Permeability of Soils & Seepage Analysis
Permeability of Soils & Seepage AnalysisPermeability of Soils & Seepage Analysis
Permeability of Soils & Seepage Analysis
 
shear strength of soil
shear strength of soilshear strength of soil
shear strength of soil
 
Experimental conceptualisation of the Flow Net system construction inside the...
Experimental conceptualisation of the Flow Net system construction inside the...Experimental conceptualisation of the Flow Net system construction inside the...
Experimental conceptualisation of the Flow Net system construction inside the...
 
Geotechnical Engineering-I [Lec #27: Flow Nets]
Geotechnical Engineering-I [Lec #27: Flow Nets]Geotechnical Engineering-I [Lec #27: Flow Nets]
Geotechnical Engineering-I [Lec #27: Flow Nets]
 
Earth pressure
Earth pressureEarth pressure
Earth pressure
 

Similar a Basics of groundwater hydrology in geotechnical engineering: Permeability - Part B

Basics of groundwater hydrology in geotechnical engineering: Permeability - ...
Basics of groundwater hydrology in geotechnical engineering: Permeability -  ...Basics of groundwater hydrology in geotechnical engineering: Permeability -  ...
Basics of groundwater hydrology in geotechnical engineering: Permeability - ...ohamza
 
Unlined Canal design
Unlined Canal designUnlined Canal design
Unlined Canal designPreetAwesome
 
Q921 re1 lec5 v1
Q921 re1 lec5 v1Q921 re1 lec5 v1
Q921 re1 lec5 v1AFATous
 
Q913 re1 w2 lec 6
Q913 re1 w2 lec 6Q913 re1 w2 lec 6
Q913 re1 w2 lec 6AFATous
 
Engineering properties of soil
Engineering properties of soilEngineering properties of soil
Engineering properties of soilRakesh Reddy
 
Irrigation engineering
Irrigation engineeringIrrigation engineering
Irrigation engineeringNagma Modi
 
RTe-bookCh5Hydraulics.ppt
RTe-bookCh5Hydraulics.pptRTe-bookCh5Hydraulics.ppt
RTe-bookCh5Hydraulics.pptfirdaus daoesy
 
A Note on the Beavers and Joseph Condition for Flow over a Forchheimer Porous...
A Note on the Beavers and Joseph Condition for Flow over a Forchheimer Porous...A Note on the Beavers and Joseph Condition for Flow over a Forchheimer Porous...
A Note on the Beavers and Joseph Condition for Flow over a Forchheimer Porous...IJRESJOURNAL
 
Q913 re1 w2 lec 5
Q913 re1 w2 lec 5Q913 re1 w2 lec 5
Q913 re1 w2 lec 5AFATous
 
Groundwater movement Hydraulics, Darcy's law
Groundwater movement Hydraulics, Darcy's lawGroundwater movement Hydraulics, Darcy's law
Groundwater movement Hydraulics, Darcy's lawNaresh Kumar
 
UNIT 1 UNIFORM FLOW.pptx
UNIT 1 UNIFORM FLOW.pptxUNIT 1 UNIFORM FLOW.pptx
UNIT 1 UNIFORM FLOW.pptxreenarana28
 
Boundary Layer Displacement Thickness & Momentum Thickness
Boundary Layer Displacement Thickness & Momentum ThicknessBoundary Layer Displacement Thickness & Momentum Thickness
Boundary Layer Displacement Thickness & Momentum ThicknessHaroon Rashid
 

Similar a Basics of groundwater hydrology in geotechnical engineering: Permeability - Part B (20)

Basics of groundwater hydrology in geotechnical engineering: Permeability - ...
Basics of groundwater hydrology in geotechnical engineering: Permeability -  ...Basics of groundwater hydrology in geotechnical engineering: Permeability -  ...
Basics of groundwater hydrology in geotechnical engineering: Permeability - ...
 
laminar and Turbulent flow
laminar and Turbulent flowlaminar and Turbulent flow
laminar and Turbulent flow
 
Unlined Canal design
Unlined Canal designUnlined Canal design
Unlined Canal design
 
Q921 re1 lec5 v1
Q921 re1 lec5 v1Q921 re1 lec5 v1
Q921 re1 lec5 v1
 
Q913 re1 w2 lec 6
Q913 re1 w2 lec 6Q913 re1 w2 lec 6
Q913 re1 w2 lec 6
 
Vertical Drain
Vertical Drain Vertical Drain
Vertical Drain
 
Engineering properties of soil
Engineering properties of soilEngineering properties of soil
Engineering properties of soil
 
Irrigation engineering
Irrigation engineeringIrrigation engineering
Irrigation engineering
 
RTe-bookCh5Hydraulics.ppt
RTe-bookCh5Hydraulics.pptRTe-bookCh5Hydraulics.ppt
RTe-bookCh5Hydraulics.ppt
 
A Note on the Beavers and Joseph Condition for Flow over a Forchheimer Porous...
A Note on the Beavers and Joseph Condition for Flow over a Forchheimer Porous...A Note on the Beavers and Joseph Condition for Flow over a Forchheimer Porous...
A Note on the Beavers and Joseph Condition for Flow over a Forchheimer Porous...
 
Sm Chapter V
Sm Chapter VSm Chapter V
Sm Chapter V
 
Catchment.pdf
Catchment.pdfCatchment.pdf
Catchment.pdf
 
Q913 re1 w2 lec 5
Q913 re1 w2 lec 5Q913 re1 w2 lec 5
Q913 re1 w2 lec 5
 
SOIL PERMEABILITY.pdf
SOIL PERMEABILITY.pdfSOIL PERMEABILITY.pdf
SOIL PERMEABILITY.pdf
 
Chapter 04
Chapter 04Chapter 04
Chapter 04
 
Groundwater movement Hydraulics, Darcy's law
Groundwater movement Hydraulics, Darcy's lawGroundwater movement Hydraulics, Darcy's law
Groundwater movement Hydraulics, Darcy's law
 
UNIT 1 UNIFORM FLOW.pptx
UNIT 1 UNIFORM FLOW.pptxUNIT 1 UNIFORM FLOW.pptx
UNIT 1 UNIFORM FLOW.pptx
 
Boundary Layer Displacement Thickness & Momentum Thickness
Boundary Layer Displacement Thickness & Momentum ThicknessBoundary Layer Displacement Thickness & Momentum Thickness
Boundary Layer Displacement Thickness & Momentum Thickness
 
3.uniform flow.pptx
3.uniform flow.pptx3.uniform flow.pptx
3.uniform flow.pptx
 
Lecture 1.pptx
Lecture 1.pptxLecture 1.pptx
Lecture 1.pptx
 

Basics of groundwater hydrology in geotechnical engineering: Permeability - Part B

  • 1. Basics of groundwater hydrology in geotechnical engineering Part B Prepared by Dr O. Hamza o_hamza at hotmail dot com Lecture reference: OH GA03 B OH_GA03_B Permeability – Part B Dr O.Hamza
  • 2. Content • Introduction • Quasi-one-dimensional Quasi one dimensional and radial flow • Field determination of coefficient of permeability • Summary S mmar • Example problems Permeability – Part B Dr O.Hamza
  • 3. Introduction Darcy’s law q = Aki where k i coefficient of permeability with is ffi i t f bilit ith (Ref. Geotechnical on the Web) dimensions of velocity (length/time) Q Quantity of water q is flow rate = = ----------------------- t Time In a saturated porous media, the rate of flow of water q (volume/time) through cross-sectional area ‘A’ is found to be proportional to hydraulic th h ti l i f dt b ti lt h d li gradient ‘ i ’ Permeability – Part B Dr O.Hamza
  • 4. Introduction Aquifer and Darcy’s law Aquifer is a term used to designate a porous geological formation that: - contains water at full saturation - permits water to move through it under ordinary field conditions Permeability – Part B Dr O.Hamza
  • 5. Introduction Aquifer and Darcy’s law The horizontal flow rate q is constant. For an aquifer of width B and varying thickness tt, Darcy's Law indicates that q=Aki =Btki or Hydraulic gradient varies inversely with aquifer thickness Where flow occu s in a co e e o occurs confined aqu e whose t c ess varies ge t y with ed aquifer ose thickness a es gently t position the flow can be treated as being essentially one-dimensional. Permeability – Part B Dr O.Hamza
  • 6. Quasi-one-dimensional Quasi one dimensional and radial flow • Cylindrical flow: confined aquifer • Cylindrical flow: groundwater lowering • Spherical flow Permeability – Part B Dr O.Hamza
  • 7. Quasi-one-dimensional and radial flow Cylindrical flow: confined aquifer Pumping aquifer Confined aquifer Steady-state pumping from a well which extends the full thickness of a confined aquifer is one of the one dimensional problem which can be one-dimensional analysed in cylindrical coordinates. Permeability – Part B Dr O.Hamza
  • 8. Quasi-one-dimensional and radial flow Cylindrical flow: confined aquifer Darcy's Law still applies, with hydraulic gradient dh/dr and area A varying with radius: A = 2πr.t 2 rt In this case pore pressure or head varies only with radius r r. Permeability – Part B Dr O.Hamza
  • 9. Quasi-one-dimensional and radial flow Cylindrical flow: confined aquifer Integrating between the borehole and at variable distance r: di t where ro is the radius of the borehole and h0 the constant head in the borehole. Permeability – Part B Dr O.Hamza
  • 10. Quasi-one-dimensional and radial flow Cylindrical flow: groundwater lowering Pumping from a borehole can be used for deliberate groundwater lowering in order to facilitate excavation. Permeability – Part B Dr O.Hamza
  • 11. Quasi-one-dimensional and radial flow Cylindrical flow: confined aquifer Permeability – Part B Dr O.Hamza
  • 12. Quasi-one-dimensional and radial flow Cylindrical flow: groundwater lowering This is an example of quasi-one- dimensional radial flow with flow thickness t=h Then A=2πr h and t=h. A=2πr.h Groundwater lowering Original level of water table Integrating between the borehole and at variable distance r: Drawdown The radius of influence Permeability – Part B Dr O.Hamza
  • 13. Quasi-one-dimensional and radial flow Spherical flow Darcy's Law still applies, with hydraulic gradient dh/dr and area A varying with radius: A=4πr² where r0 is the radius of the piezometer and h0 the constant head in the piezometer head varies only with radius r r. Variation of pore pressure around a point source or side (for example, a piezometer being used for in situ determination of permeability) is a one in-situ one- dimensional problem which can be analysed in spherical coordinates. Permeability – Part B Dr O.Hamza
  • 14. Determination of coefficient of permeability • Laboratory measurement of the coefficient of permeability L b t t f th ffi i t f bilit • Field measurement of the permeability • Empirical relations for the coefficient of permeability Permeability – Part B Dr O.Hamza
  • 15. Determination of coefficient of permeability Field measurement of the permeability Field measurement Laboratory measurement • Field or in-situ measurement of permeability avoids the difficulties involved in 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 y measurement? Permeability – Part B Dr O.Hamza
  • 16. Determination of coefficient of permeability Field measurement of the permeability 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. Permeability – Part B Dr O.Hamza
  • 17. Determination of coefficient of permeability Field measurement of the permeability If the pumping causes a drawdown in an unconfined (i.e. open surface) soil stratum Well-Pumping test then the quasi one dimensional flow equation quasi-one is applied. Integrating between the two test limits and rearranging the equation: Impermeable (Assuming the pumping causes a drawdown in an unconfined (i.e. open surface) soil stratum then) Observational b h l Ob ti l boreholes Permeability – Part B Dr O.Hamza
  • 18. Determination of coefficient of permeability Field measurement of the permeability If the soil stratum is confined and of thickness t Well-Pumping test and remains saturated th d i t t d then Confined stratum Permeability – Part B Dr O.Hamza
  • 19. Determination of coefficient of permeability Empirical relations for the coefficient of permeability Empirical relations p k = function of (other parameters) Permeability of all soils is strongly influenced by the density of packing of 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
  • 20. Determination of coefficient of permeability Empirical relations for the coefficient of permeability Permeability of granular soils P bilit f l il For fairly uniform sand Hazen (1930) proposed the following relation between the coefficient of permeability k (m/s) and the effective particle size D10 (in mm) (the particle size than which 10% soil is finer): k = C D10 C.D 2 where C is a constant approximately equal to pp y q 0.01 (see the figure beside) Hazzan equation and data relating coefficient of permeability and effective grain size of granular soils Permeability – Part B Dr O.Hamza
  • 21. Determination of coefficient of permeability Empirical relations for the coefficient of permeability Permeability of soft clays P bilit f ft l Samarasinghe, H S i h Huang and D d Drnevich (1982) h i h have suggested th t th t d that the coefficient of permeability of clays can be given by the equation: en k=C 1+ e where h 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
  • 22. Summary • All soils are permeable materials, water being free to flow through the interconnected pores between the solid particles. • Water in saturated soil will flow in response to hydraulic g p y gradient and occurs towards the lower total head. • Flow rate is proportional to the hydraulic gradient and can be affected by the geometry of the pores. pores • The hydraulic gradient may be associated with natural flow or induced by loading the soil (i.e. due to excavation or construction). • Coefficient of permeability may be determined from laboratory experiments or from in situe measurements • Pore water pressure u at any point of the soil is computed from the definition of the hydraulic head, u = γw(h-hz) (where h is total head and hz is elevation head). Permeability – Part B Dr O.Hamza
  • 23. Quizzes and example problems Work on: • Quizzes: quiz 3 to 6 * • Example problems: * problem 3 and problem 4 * Note. quiz 1 and problem 1 and 2 are covered in Part A of Permeability lecture Permeability – Part B Dr O.Hamza
  • 24. Working on Quizzes and Example problems Quiz 3 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. • F case 2, what is a realistic situation th t might result i a set of h d For 2 h ti li ti it ti that i ht lt in t f heads 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. datum Case 1 Case 2 Permeability – Part B Dr O.Hamza
  • 25. Working on Quizzes and Example problems Quiz 3 Solution: S l ti hw h Flow Flow hz datum Case 1 Case 2 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
  • 26. Working on Quizzes and Example problems Quiz 4 An inclined permeameter tube is filled with three layer of soil of different permeabilities as shown in the figure figure. (i) Formulate q in terms of the different dimensions and permeabilities for each soil element (ii) D t Determine th h d l i the head loss (Δh) b t between each soil element assuming h il l t i k1=k2=k3 (iii) Re-determine the head loss (Δh) between each soil element assuming 3k1=k2=2k3 (iv) Express the head at points A, B, C, and D A B C (with respect to the datum) (v) Plot the various heads versus horizontal distance. Permeability – Part B Dr O.Hamza
  • 27. Working on Quizzes and Example problems Quiz 4 (i) Flow rate q in each soil element is equal: Δh q = Aki = Ak L Δh Δh 2 q1 = Ak1 1 q 2 = Ak 2 q 3 = ... L1 L2 q = q1 = q 2 = q 3 Δh = Δh1 + Δh 2 + Δh 3 Permeability – Part B Dr O.Hamza
  • 28. Working on Quizzes and Example problems Quiz 4 (ii) Flow rate q in each soil element is equal: q = q1 = q 2 = q 3
  • 29. Working on Quizzes and Example problems Quiz 4 (iii) Flow rate q in each soil element is equal: q = q1 = q 2 = q 3
  • 30. Working on Quizzes and Example problems Quiz 4 (iv) Heads
  • 31. Working on Quizzes and Example problems Quiz 4 (v) Plotting NOTE: It is coincident that ll heads th t all h d appears in a straight line.
  • 32. Working on Quizzes and Example problems Quiz 5 The site consists of an unconfined aquifer and a confined aquifer separated by a 5-m thick 5 thi k confining layer. Water in the unconfined aquifer i f h and water fi i l W t i th fi d if is fresh, d t in the confined aquifer is saline. Two nested piezometers have been drilled, one penetrating the unconfined aquifer (P1), and one penetrating the confined aquifer (P2) ). 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 (doesn’t 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) w2 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
  • 33. Working on Quizzes and Example problems Quiz 5 4.3t 4.9 21.2 38.6 m 68.1 m Datum Permeability – Part B Dr O.Hamza
  • 34. Working on Quizzes and Example problems Quiz 5 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 For the equivalent fresh-water pressure head, pressure must be equal: fresh water head uSaline = ufirsh So γSaline x 33.7 = γfrish x hw2-frish solve for hw2-frish: = γSaline x 33.7 / γfrish = 10.21 x 33.7 /9.99 = 34.4 m so, so h2-fresh = hz2 + hw2-frish = (68 1 – 38 6 ) + 34.4 = 63 9 m f f (68.1 38.6 34 4 63.9 Thus flow is in an UPWARD direction from the lower aquifer, and you should not issue the permit (In addition if you inject waste into the lower aquifer permit. addition, it will further increase the pressure head and increase the upward gradient.) Permeability – Part B Dr O.Hamza
  • 35. Working on Quizzes and Example problems Quiz 6 A soil profile consists of th il fil i t f three l layers with properties shown i th t bl b l ith ti h in the table below. Calculate the equivalent coefficients of permeability parallel and normal to the stratum. Layer Thickness (m) kx (parallel, m/s) kz (normal, m/s) 1 3 2x10-6 6 1.0x10 6 1 0x10-6 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
  • 36. Working on Quizzes and Example problem Problem 3 Field measurement of the coefficient of permeability 3. 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 25m respectively from the test well. Water was pumped from the test well at the rate of 3x10-3 m3/s until the water level became steady. The heights of the water in the two observation boreholes were then found to be 4.25m and 6.5m above the impermeable bed. Find the value, expressed in m3/day, of the Impermeable coefficient of permeability of the sandy soil ffi i t f bilit f th d il Permeability – Part B Dr O.Hamza
  • 37. Working on Quizzes and Example problem Problem 3 Field measurement of the coefficient of permeability 3. 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 60 x 24 = 259 2 m3/day 259.2 Impermeable r1= 12.5m and r2 = 25m h1= 4.25m and h2= 6.5m ln(r2/r1) = 0.693 Note ‘ln’ is the logarithm to base e, also called the natural logarithm. Permeability – Part B Dr O.Hamza
  • 38. Working on Quizzes and Example problems Problem 4 E i i l relations of th coefficient of permeability 4. Empirical l ti f the ffi i t f bilit For a clay soil, the following are given: soil Void ratio 1.1 0.9 k (cm/s) ( /) 0 302 x 10-7 0.302 7 0 12 x 10-7 0.12 7 en Use the following empirical relation: k=C 1+ e proposed by Samarasinghe, Huang and Drnevich (1982) to estimate the coefficient of permeability of the clay at a void ratio of 1 2 1.2. 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