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Molecular structure of the clay minerals

VIEWS: 61 PAGES: 81

  • pg 1
									     Introduction to Soil Engineering

                              D. A. Cameron
                                   2007




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   1
                   Particle Interactions
                    Coarse soils v. Fine soils
                 [sand and gravel] v. [silt and clay]

                   STRENGTH DERIVED FROM

                   Friction, interlock v.
                           physico-chemical interaction



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   2
                 Fine - Grained Soils
                                  Cohesion
                           “Apparent” cohesion
                     “apparent” tensile strength,
                                  arising from

                        electrostatic forces
                   (are stronger, the finer the particle)

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   3
               • Clays form from weathering and
                 secondary sedimentary processes

               • Clays are usually mixed




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   4
      Properties of the clay minerals

                When mixed with a little water,
                clays become “plastic”
                   i.e. are able to be moulded

                SO, moisture affects clay soil
                engineering properties


DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   5
      Properties of the clay minerals
          •   Can absorb or lose water between the
              silicate sheets
               −   negative charge attracts H2O
          •   When water is absorbed, clays may
                                       Expand !
               − water in spaces between stacked layers
               − Montmorillonite most expandable
               − Kaolinite the least

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   6
          Illite v Montmorillonite
      Different forms of bonding between these minerals


             Illite - main component of shales and
                         other argillaceous rocks
                      - nett negative charge
               Montmorillonite
                       - greater nett negative charge




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   7
    Clay Minerals – capacity for water

         i) Kaolinite (China clay)
                   Water absorption, approximately 90%

         ii) Montmorillonite (Bentonite, Smectite)
                   Water absorption, approximately 300 - 700%

         iii) Illite
                   Intermediate water absorption


DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   8
                       In Summary
      1. The basic building blocks of clays are small
      2. Si, O, H and Al are the chief ingredients
      3. Different combinations of sheets form the
         basic micelles of clay minerals
      4. Clay mineral properties vary due to the
         nature of bonding of the sheets between
         micelles



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   9
      Engineering Soil Classification




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   10
                           The Soil Phases

        THEThe Soil SYSTEM
            SOIL System                          “PHASE” DIAGRAM

                                                               AIR


                                                            WATER



                                                             SOIL
                                                            SOLIDS



             Air pockets
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   11
         New Terms
         Density                                                      “rho”
         Unit weight                                                 “gamma”
           e.g. water = w = 1 t/m3 or 1 g/cc
                               w = 9.81 kN/m3




         Soil varies between                          15 - 21 kN/m3

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT             12
         Other densities
          1) Soil dry density, d
                                                            Mass of soil /
                                                            total volume

          2) Particle density, s

                                                                No air or
                                                                 water!

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT          13
   Introduction to soil terms, cont’d

             • Particle densities range
               between 2.6 and 2.7 t/m3

             • Moisture content, w

                  –   based on mass of water:mass
                      of solids (= dry soil)



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   14
          Moisture and Density




        where, w = water content (just a ratio, not %!)




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   15
               More soil terms………….
       4) Void Ratio, e




       5) Degree of saturation, SR




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   16
      VOID RATIO
                              V = Vs + Vw + Va

                 Ma, Va

                                                            Void volume,
                                       Mw, Vw                Vv = Vw + Va


                                        Ms, Vs               Solids




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT         17
                Soil “Consistency”

           a) DENSITY of granular soils
                “loose, dense, or very dense”


           b) STRENGTH of fine-grained soils
                “soft, firm, stiff or hard”




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   18
          Unified Soil Classification System
                        (USCS)

             Based on………...
             1) Particle size
                   - gravel, sand, silt, clay fractions
             2) Particle size distribution
                   - grading
             3) “Plasticity”



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   19
     Symbols of the USCS – coarse grained
      Class          Primary             Description                  Secondary
                     symbol                                            symbol
      Gravel            G                Well-graded                     W

                                        Poorly-graded                    P

                                       Excess of fines                 C or M

       Sand               S              Well-graded                     W

                                        Poorly-graded                    P

                                       Excess of fines                 C or M

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT               20
                  Defining Particle Sizes

          Grain
           size         0.002               0.2    2.36       20
          (mm)                      0.075      0.6      6.0        63   200

         Basic
          Soil                            F M C F M C
         Type
                  CLAY          SILT       SAND       GRAVEL COBBLES     BOULDERS

            Fine-grained                             Coarse-grained
                soil                                      soil




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT           21
                   Sieve Analysis - coarse soils
                                                 Uniform soil (SP)    Gravel (G)
                               100
        Percent finer by wt.


                                                          Sand (S)
                                            Silt (M)
                               50




                                0
                                    0.001     0.01       0.1     1      10    100
                                                                   Well graded (W) SM
                                                       Grain diameter (mm)
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT                 22
                     Particle Size
                  Distribution Terms
                                                        P - Poorly graded
                                                           (uniform sizes)



                                                        W - Well graded
                                                        Good mix of sizes



                                                        P - Poorly graded
                                                        Missing range of sizes


DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT          23
                  Fine-grained Soils
        • Too fine for sieving
        • Sedimentation and/or laser equipment?

            Even then, sizes say nothing about clay
            mineralogy and potential soil behaviour!

          Fine-grained soils are defined by
          how “plastic” they are



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   24
       Symbols for Fine Grained Soils
    Class Primary Characteristic                          A-line      Secondary
          symbol                                         position      symbol
    CLAY     C    Low plasticity                          above           L
                     LL < 35%
                              Med. plasticity              above          I
                               35 < LL < 50%
                              High plasticity              above         H
                                 LL > 50%
    SILT            M         Low plasticity               below         L
                                 LL < 50%
                              High plasticity              below         H
                                 LL > 50%
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT           25
     Consistency Limits of Fine Soils
             Defining water contents
             1. LIQUID PHASE
                       - fluid, low shear resistance
             2. PLASTIC PHASE
                       - easily moulded
             3. SOLID PHASE
                       - strong, resists deformation




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   26
                 ATTERBERG LIMITS

                                 Plastic Index or PI
                   solid                                              liquid

                                       The plastic
                                         zone

                           PL                                  LL


               0                Moisture content                          Max.
               %

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT              27
  CONSISTENCY LIMITS




     Change in
      Volume

                            Shrinkage
                              limit                      Soil
                                                        drying



                                           PL                         LL
                                   Moisture content (%)
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT        28
                   The Plasticity Chart


    PLASTIC
      INDEX
        (%)




                                                                      Example
                                   LIQUID LIMIT (%)
                                                                      LL = 75
                                                                      PL = 32
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT             29
                     Field Tests of the USCS
                          for fine-grained soils

              1. Dry strength
                   – relative strength of a dry ball of soil
                   – prepared at PL
              2. Toughness
                   – near PL when remoulded
              3. Dilatancy
                   – volume change upon shearing
                   – prepared at LL

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   30
       Interpretation of Field Tests

       • Dry strength is low for O and M soils of low
         plasticity
       • Dry strength increases with plasticity
       • Dry strength is greater for clay soils
       • Toughness increases with plasticity
       • Silts are dilatant but clays are not!
            – dilation = increase in volume (with shearing)


DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   31
        Classification of Mixed Soils

          1. Wet sieve on 0.075 mm sieve
                    > 50% retained? = “coarse”
          2. Sieve on 2.36 mm sieve
                   < 50% retained? = Sand
          3. Sieve for fines
                    < 5% = SP or SW (fines insignificant)
                    >12% = SC or SM (plasticity?)

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   32
                            SUMMARY
              Soil classification for engineering
                  purposes is based on:

              1. Fundamental particle sizes
                                 AND
              2. Particle size distributions
                                 OR
              3. Soil plasticity
                    (LL, PI, LS and/or field tests)

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   33
                             Soil Stresses

           ° Dead weight stresses
           ° Pore water pressures
                – steady state
                – no flow
                – water table

           ° Effective stress




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   34
                      VERTICAL STRESSES 
z = force from weight of prism above soil ÷ (area of
                                soil in x-y plane)
                                        = z
                             Soil
                             prism                               z
                    Unit area
   x
                                                            z

                         z                                           x
                                                    y
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT       35
          The dead weight stresses are
                                     termed


                   “TOTAL soil stresses”



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   36
                PORE WATER PRESSURES, 
              “u” in a soil mass with a water table,
              are due to the dead weight of water
                                    u =  w zw                                GL

            Saturated zone                                                z
                                u                          zw
      u
                                                            z

                                                    y                 x
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT            37
                  Concept of EFFECTIVE stress

                                [Terzaghi 1923]

       PWP reduces the stress felt by the soil in a
       saturated soil system (with no air voids)




                                    =  - u

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   38
                                                 Diameter of
                                                   tube, d

                                                     Height of
                                                   capillary rise,
                                                         hc




                      Height of rise = fn(d)
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   39
                  Dead weight soil stress
                   - total vertical stress
                     0m


                  = 16 kN/m3

                     5m                                    80 kPa


                  = 18 kN/m3

                      9m                        80            72      152
                                                                      kPa
                                                         v

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT         40
                  Dead weight soil stress
                 - effective vertical stress
                   0m

                = 16 kN/m3
                  2m                                32 kPa
                = 18 kN/m3
                  5m                                   86 kPa             29.4


                = 20 kN/m3

                    9m                         86       80
                                              166 kPa                 68.6 kPa
                                                 v                       u
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT              41
             Effective Stress Distribution
                     0m

                  = 16 kN/m3
                    2m                                      32 kPa
                  = 18 kN/m3
                    5m                                          56.6 kPa


                  = 20 kN/m3

                      9m
                                                      97.4 kPa
                                                   v = v - u

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT        42
                   Alternative approach
                effective unit weight,  =  -  w
                     0m

                  = 16 kN/m3
                     2m                                     32 kPa
                  = 8.2 kN/m3                                 32 + 24.6
                     5m
                                                                 = 56.6 kPa

                  = 10.2 kN/m3
                                                                      56.6 + 40.8
                      9m
                                                      97.4 kPa
                                                   v = v - u

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT            43
               COMPACTION OF SOIL
                               The Process

               • Expulsion of AIR
                  - air void volume, Va, reduced
                  - moisture content is unchanged or
                  constant




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   44
                      The Purpose of Compaction

                      increase                              decrease


            • STRENGTH                            • PERMEABILITY
            • STIFFNESS
            • DURABILITY




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT    45
                  Earthwork Applications

          Earth dams, Levee banks, Road subgrades,
          Pavement layers, Subdivisions, etc

       Water retaining structures – stability with low               permeability
       Roads - reduce pavement thickness by increasing strength
       Subdivisions - reduce footing stiffness by increasing
       foundation strength & stiffness




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT              46
                    Laboratory Soil Compaction

             Compaction of all soil materials, except clean
             gravels and sands



             - achieved by falling weight hammers of known mass
             and drop height

              under constant energy



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   47
                     AS1289 - Standard or Modified?


             (a) Standard Compaction
                   light compaction (low energy),



             (b) Modified Compaction
                   heavy compaction (high energy),
                   (thinner “lifts”)




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   48
                   Laboratory compaction testing
                            - relevance?
             How does the soil respond when compacted
               on site?


             So, the laboratory method, which best
               replicates the field compaction equipment
               on an earthworks job, must be chosen




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   49
                   The Compaction Curve

            For a particular soil and compactive effort ........

            “There is a unique relationship between the
              dry density that can be achieved and the
              moisture content of the soil”

            Warning: NA to clean sands and gravels




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   50
                   Removal of all air voids is impractical
                        -  d max at an air voids ratio, A  5%
                                         (A = Va / V )

             1.    w at  d max is termed the
                   OPTIMUM MOISTURE CONTENT (OMC)
             2.    < OMC, the soil is stiff and dry
                  ─     It’s difficult to re-orientate particles

             3.    > OMC, the soil is too deformable
                  ─     flows when compacted




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   51
           The Shape of the Compaction Curve
                                      A = 5%?
             Dry
             Density
                                                               Zero air
                d max                                         voids line



                            Soil too dry              Soil too wet and
                            and brittle               deformable

                                             OMC

                                                Moisture content
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT         52
               INFLUENCE OF SOIL TYPE ON COMPACTION
                               CURVE


          Dry     Sand with
          Density some fines
                                                           Zero air
                                                           voids line

             d max



                                                 Clay

           Constant compaction energy                      OMC          Moisture
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT     content
                                                                              53
                   Influence of Compaction
                           Energy
                            Modified
                            Compaction
            Dry
            Density




                                          Standard
                                          Compaction


                                                                      Moisture
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT
                                                                      content    54
                Influence of Compaction Energy

               The same effect is realised on earthworks
                 projects by:
               • Increasing the mass of compactors
               • Compacting in thinner lifts
               • Passing over each layer more
                     number of passes




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   55
                  Compaction and permeability


                                                 B
                         permeability
           Dry Density
                             or




                                                                C
                                        A

                                                      kmin

                                            Moisture content

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   56
                       Compaction Practice

              • Compacted in thin layers or “LIFTS”
                  (100 to 200 mm for fine grained soil)

              • Silts and Clays - need relatively long duration
                  loading
              • Sands and Gravels - vibration has greatest
                  effect




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   57
                 Specification of Compaction of
                    Clean Sands & Gravels

                      Maximum compaction when either
                                 bone dry or saturated

            Capillarity resists compaction
            Compaction defined in terms of maximum and
              minimum dry densities
                                    d max and d min



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   58
           Description of coarse-grained
                        soil


            Consistency              Loose          Med. dense        Very dense


            Density index
                  ID                15 to 35           35 to 65        85 to 100
                (%)




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT                59
                     Specification of Compaction
              AS3798 Guidelines on Earthworks for Commercial
                        and Residential Developments


                                 “Dry Density Ratio”, RD
               Ratio of desired dry density to the maximum
               achievable by the chosen laboratory method,
                     e.g. 95% (Standard Compaction)
                        or 98 % (Modified Compaction)




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   60
                          Notes on specification

                    Sometimes moisture contents for
                    compaction need to be tightly
                    specified…..
                              Why?
                    What if a soil on site is too wet for
                    compaction?



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   61
                                 SUMMARY
           1.    Granular soils specified by density index
           2.    Most soils specified by dry density ratio,R D
           3.    Compaction curve, d max and OMC
           4.    Not unique – depends on compactive effort
           5.    Field compaction curves
                     ─    Passes, lift thickness, equipment

           6.    Field tests for density
                     –    Penetration testing
                     –    Sand replacement
                     –    Nuclear density




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   62
       WATER SEEPAGE – water pressures

                Water flows from points of high to low
                              TOTAL head

         WATER HEADS
         [“head of water”] x [w] = water pressure, u


         Total head = [elevation head + pressure head]

         i.e                     h = hT = [he + hp]




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   63
                               Darcy’s 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)


DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   64
                     Hydraulic Gradient, i

                                                h

                                                                      Area of
                                                                      flow, A



 Flow rate,
       q
                                            Length of flow, l


DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT             65
                   Hydraulic Conductivity

    • Coefficient of permeability or just “permeability”

    • SATURATED soil permeability




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   66
         TYPICAL PERMEABILITIES

   Clean gravels                                          > 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




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT      67
                  Measuring Permeability
    [A] Laboratory                                 [A] Laboratory
    • Constant head test                             How good is the
    • Falling head test                              sample?
    • Other

    [B] Field                                       [B] Field
    • Pumping tests                                 Need to know soil
    • Borehole infiltration                         profile (incl. WT) &
                                                    boundary conditions
        tests

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT        68
     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



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   69
      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


DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   70
                        Drawdown test
      Needs
      1. a well-defined water table
      2. and confining boundary

      Must be able to
      1. pull down water table
      2. and create flow
            (phreatic line = uppermost flow line)



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   71
                                Flow Lines
           – shortest paths for water to exit

                                                Equipotential lines


                         hp1                                          h

           Flow
           tube                                                       hp2

                         h1e1                  l                     he2

                           Elevation head reference line
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT         72
                         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”

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   73
                              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



DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   74
                          Flownet Basics
                           Water flow follows paths
                           of maximum hydraulic
                           gradient, imax

                        flow lines and
                           equipotentials must
                           cross at 90




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   75
   Since q is the same, ratio of
   sides will be constant for all
   the squares along the flow
   tube

                                                               h


       5 Flow Lines

                                       M




Equi- potential lines
                                   Impervious boundary
DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   76
                       Flownet Construction




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   77
                    Flow Net Calculations

       Total flow for Nf “flow channels”, per unit width is:




                  But only for curvilinear “squares”!




DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   78
            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!

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   79
                  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

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   80
                                Key Points
              •   Heads in soil
              •   Darcy’s Law
              •   Coefficient of permeability
              •   Measurement of permeability
              •   Flownets
              •   Flownet rules
              •   Seepage from flownets
              •   Piping, boiling or erosion
              •   Critical hydraulic gradient

DIVISION OF INFORMATION TECHNOLOGY, ENGINEERING AND THE ENVIRONMENT   81

								
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