Soil Mechanics TYS Exp 247

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Transcript of Soil Mechanics TYS Exp 247

  • Civil EngineeringSoil Mechanics

    & Foundation Engineering

    WORKBOOKWORKBOOKWORKBOOKWORKBOOKWORKBOOK

    2016

    Detailed Explanations ofTry Yourself Questions

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    Types and Properties of Soil1T1 : Solution

    Rh = 24.5 Rh = 24.5 + 0.5 = 25

    R = 24.5 2.50 = 22

    D = ( )

    where D is in mm, He is in cm and t is in min.For the present case, h = 0.008 104 kN-s/m2,

    He = 10.7 cm, G = 2.75 and w = 9.81 kN/m3; t = 30 min

    D = ( )

    =

    or D =

    =

    The percentage finer is given by

    N = ( )

    where Md = mass of dry soil = 50 g

    N = ( )

    =

    T2 : Solution

    We have

    Activity of clay A = ( )

    I

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    3Workbook

    =

    = = ...(i)

    Activity of clay B =( )

    ( )

    I

    =

    =

    Since activity of clay A is more than that of clay B, therefore clay A is more likely to undergo high volumechange so clay A has higher compressibility than that of B but permeability and rate of volume change aresmaller than that of clay B.

    T3 : Solution

    Given = 2.15 mg/m3

    (i) d =

    +

    =

    =

    +

    (ii) d =

    +

    1 + e =

    = = 1.38

    e = 1.38 1 = 0.38(iii) Se = wG

    S =

    =

    =

    S = 83.59%(iv)Air content, ac = (1 S)

    = 0.1641 = 16.41%

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    Classification of Soils2

    T1 : Solution

    Since more than 50% of the material is larger than 75 size, the soil is a coarse grained one.Since more than 50% of coarse fraction is passing sieve 2.032 mm, it is classified as a sand. (This will bethe same as percent passing 4.75 mm sieve)Since more than 12% of the material passes the 75 sieve, it must be SM or SC.Now, it can be seen that the plasticity index, Ip is (20 12) = 8% which is greater than 7%. Also, if thevalues of wL and Ip are plotted on the plasticity chart, the point falls above A-line.Hence, the soil is to be classified as SC.

    T2 : Solution

    Plastic index, Ip for soil S1 = wL wp = (38 18) = 20%Ip for soil S2 = wL wp = (60 20) = 40%

    Consistency index,

    Ic for soil S1 =( ) ( )

    = =

    I

    Ic for soil S2 =( )

    =

    The consistency index for soil S1 is negative, it will become a slurry on remoulding ; therefore, soil S2 islikely to be a better foundation material on remoulding.Flow index, If for soil S1 = 10

    If for soil S2 = 5

    Toughness index, IT for soil S1 =

    = =

    II

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    5Workbook

    IT for soil S2 =

    =

    Toughness index is greater for soil S2, it has a better strength at plastic limit.

    T3 : Solution

    (i)(i)(i)(i)(i) Soil A:Soil A:Soil A:Soil A:Soil A: Percent of soil between 4.75 mm and 0.075 mm = 92 14 = 78%. Hence the soil is sandy,with a symbol S.Plasticity index = 16 8 = 8 > 7. Hence it is clayey sand, SC.

    (ii)(ii)(ii)(ii)(ii) Soil B:Soil B:Soil B:Soil B:Soil B: Since more than half is passing 75 micron sieve, it is a fine grained soil.Also Ip = 58 14 = 44%.Plotting the point wL = 58% and Ip = 44%, we find that the soil is CH group. Hence soil B is clay ofhigh compressibility.

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    Soil Compaction3

    T1 : Solution

    t = 19 kN/m3w = 15%G = 2.7

    t =( )

    +

    +

    19 =( )

    +

    +e = 0.603

    Se = wG

    S =

    =

    Water content for full saturation

    w =

    = 0.223

    Additional water content required for full saturation= 22.33 15 = 7.33%

    T2 : Solution

    Air content, ac =

    =

    or, Va = 0.06 Vv,Hence Vw = 0.94 Vv

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    7Workbook

    Thus Va =

    =

    Volume of specimen, V =

    = l

    Now, V = Vs + Vw + Va2208.9 = Vs + Vw + 0.0638 Vw = Vs + 1.0638 Vw

    Writing volume in terms of mass,

    2208.9 =

    + Substituting Mw = 0.10 Ms,

    2208.9 =

    +

    or Ms = 4606.54 gm Mw = 460.65 gmMass of wet soil, M = Ms + Mw = 4606.54 + 460.65 = 5067.19

    Bulk density, =

    = = l

    Dry density, d =

    = =

    + +l

    and void ratio, e =

    = =

    T3 : Solution

    The embankment should be constructed by compacting the soil obtained from borrow pit the optimummoisture content and the corresponding maximum dry density. But the natural moisture content of theexisting soil is less than its OMC. Hence a certain amount of water is to be added to the soil before thecompaction.

    VbVv

    Vs

    wWs

    Ws

    Air

    Solid

    Air

    Solid Ws

    Borrow Pit From Embankment

    WaterWater wWs

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    8 Civil Engineering Soil Mechanics & Foundation Engineering

    For embankment:For embankment:For embankment:For embankment:For embankment: Data given, (d ) = 1.66 gm/ccOMC = w = 22.5%

    (d)max =

    =

    Ws = (1.66 100) = 166 tonnThe weight of water, Ww = wWs = (0.225 166) = 37.35 tonnFor borrow pit area:For borrow pit area:For borrow pit area:For borrow pit area:For borrow pit area:

    t = bulk density = 1.78 gm/cc = 1.78 t/m3w = 9 %

    Therefore, t = 1.78 =

    +

    Volume of borrow pit, Vb =

    +=

    Weight of water available from this soilWw = (Ws w) = (166 0.09) = 14.94. tonn.

    Therefore quantity of water to be added = (37.35 14.94) = 22.41 tonn.w = 1 gm/cc

    = 106 tonne/cc = (106 1000) tonne/lit. = 103 tonne/lit.

    Volume of water to be added = !"#$

    % & '!"#$

    = =

    T4 : Solution

    Data given : Volume of the mould =

    =

    =

    In the loosest state:In the loosest state:In the loosest state:In the loosest state:In the loosest state:

    Bulk density, t =

    =

    Min. Dry density (d)min. =

    = = + +

    In the densest state:In the densest state:In the densest state:In the densest state:In the densest state:

    Bulk density, =

    =

    (d)max =

    =

    +

    =

    In-situ density of the soil = 1.61 gm/ccw = 7%

    In-situ dry density, d =

    =

    +

    Relative density, RD =(

    (

    =

    =

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    Effective Stress, Capillarity andPermeability4

    T1 : Solution

    Let x be the depth of ground water table initially.

    Total upward water force on the sand stratum at the bottom of excavation

    = (6 x) wTotal downward force at the bottom of excavation

    = Weight of soil in saturated condition

    = sat (6 4.2)= (sub + w) 1.8

    When quicksand condition occurs, then total upward water force becomes equal to total downward forcei.e.

    (6 x) w = (sub + w) 1.8 (6 x) 10 = (11 + 10) 1.8

    x = 6

    x = 2.22 m

    Similarly, if the depth of displaced ground water table is y from the surface, then

    (6 y) w = (6 5) (sub + w) (6 y) 10 = 1 (11 + 10)

    y = 6 2.1

    y = 3.9 m

    Lowering of water table = y x

    = 3.9 2.2

    = 1.7 m

    6 m

    4.2 mx

    6 m5 m

    y

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    10 Civil Engineering Soil Mechanics & Foundation Engineering

    T2 : Solution

    Given

    Layer 1

    Layer 2

    Layer 3

    x

    x2

    4x

    k y

    k y

    k y

    1

    2

    3

    =

    = 2

    = 4

    kH =

    + +

    + +

    x x xx x x

    =

    + +=

    x x xx

    kV =

    + +

    + +

    x x xx x x

    =

    + +

    xx x x

    =

    xx

    =

    =

    =

    T3 : Solution

    k=

    = =

    Discharge velocity, v=

    = = =

    l

    Seepage velocity, vs=

    = =

    Again

    =

    ( )

    ( )

    + =

    +

    or, k2=( )

    ( )

    ( )

    ( )

    = =

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    Seepage Analysis5

    T1 : Solution

    x

    = 0

    Integrating both sides, we get

    x = C1 ...(i)

    Integrating againH = C1x + C2

    At x = 0, H = 5 5 = C2

    At x = 0,

    =

    xFrom eq. (i)

    C1 = 1 H = x + 5At x = 1.2 m H = 5 1.2 = 3.8 m

    T2 : Solution

    x=

    =

    D =

    = x

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    12 Civil Engineering Soil Mechanics & Foundation Engineering

    D = 30.4582 m

    S = + = + =

    q = kS

    k = = = x

    = 5.366 109 m/sq = 5.366 109 3.063 m3/s/m = 16.438 109 m3/s/m

    Total head = 14 m

    Total head at x =

    =

    Total head = Pressure head + elevation head

    11.67 =

    +

    x

    x

    = 5.67 m

    Px = 5.67 w = 56.7 kN/m2

    T3 : Solution

    From the Figure,Nf = No. of Flow channels = 5Nd = No. of Head drop = 16

    K = 0.015 cm/sec =

    )$'

    =

    H = 5 m

    q =

    )$'

    = =

    Total quantity of seepage loss per day = q Width = 20.25 55 = 1113.75 m3/dayThe avg. length of smallest flow element adjacent to the weir = 1.2 m.

    Exist Gradient, ie =

    = = = l l

    Critical Hydraulic Gradient, ic =

    = = + +

    Factor of safety against piping =

    = =

    ii

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    13Workbook

    T4 : Solution

    (i) Data Given k = 0.002 cm/sec

    =

    =

    Head available H = 4 0.5 = 3.5 mNf = No. of Flow channels = 7Nd = No. of potential drop = 12q = Quantity of seepage loss per unit width of sheet piles

    =

    )$'

    = =

    (ii) Initial piezometric head at the ground level on upstream side = 4 m

    Head drop between two equipotential lines

    =*

    +

    , =

    =

    No. of Head drop at the point A = 3

    Head loss at A = 3 ( 0.2917) = 0.875 m

    Residual head at A = (Initial head head loss) = (4 0.875) = 3.125 m

    Similarly the piezometric head at B, C and D are calculated below:

    Piezometric head at B = 4 5 0.2917 = 2.542 m

    at C = 4 10 0.2917 = 1.083 mat D = 4 10 0.2917 = 1.083 mThe point E lies in between the 5th and 6th flow lines.

    Hence the piezometric head at E should be obtained by linear Interpolation.

    Avg. no. of Head drop at E =

    + =

    Piezometric head at E = 4 ( 7.5 0.2917) = 1.812 m

    (iii) Avg. length of the smallest flow element near the downstream end = 1.1 m

    Exit gradient, ie =

    = = l

    (iv) The Critical Hydraulic Gradient

    ic =

    = = + +

    F.O.S. Against Piping =

    = = ii

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    Stress Distribution in Soils6

    T1 : Solution

    We know that, z = ( )

    !

    +

    Point P, r/z = 0 z =

    -+

    . /

    =

    +

    Point R, r/z = 5/6 z = ( )

    -+

    . /

    =

    +

    T2 : Solution

    We know that z = ( )

    "

    + x

    At point P, z = ( )

    +

    = 12.40 kN/m2

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    Compressibility andConsolidation7

    T1 : Solution

    # =

    = ( )# Where,

    = Effective stress at the level under consideration,

    For sample A

    2 m

    7.0 m

    = 18.3 kN/m3

    = 19.0 kN/m3

    4 m

    = (2 18.3) + (19 10) 2 = 54.6 kN/m2

    # = ( ) = = 46.4 kN/m2 At the centre of first layer effective stress before application of proposed fill

    = 2 18.3 + 3.5 (19 10) = 68.1 kN/m2

    = After placing the proposed fill = (8.5 20.3) = 172.55 kN/m2

    Final stress at centre = ( ) + = (68.1 + 172.55) = 240.65 kN/m2Pre consolidation stress at the point = ( ) + = 68.1 + 46.4

    = 114.5 kN/m2

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    16 Civil Engineering Soil Mechanics & Foundation Engineering

    Settlement of first layer

    H1 = ( )

    $

    $ $

    + + + +

    =

    %! %!

    +

    = (0.076 + 0.340) = 0.4160 m

    For sample B # = ( ) = 510 (2 18.3 + (19 10) 7 + 10 (19.0 10))= 320.4 kN/m2

    Preconsolidation stress = ( ) + = (320.4 + 2 18.3 + 9 7 + 9 10) = 510 kN/m2

    Final stress at the centre of clay of sample B

    = ( ) = (189.6 + 8.5 20.3) = 362.15 kN/m2

    If is evident that, preconsolidation stress is more than final stress at this level. Therefore onlypreconsolidation settlement will occur.

    H2 = ( )

    + +

    =

    %!

    =

    Total settlement H = (H1 +H2) = (0.416 + 0.225) = 0.641 m = 641 mm

    T2 : Solution

    Data Given 0 = 2 kg /cm2

    = 4 2 = 2 kg/cm2

    Cc = 0.009(wL 10) = 0.009(45 10) = 0.315

    we have Cc =

    %!

    +

    e =

    %!

    + =

    %!

    = 0.095 Final void ratio, ef = e0 e = (1.25 0.095) = 1.155(ii) Let H be the consolidation settlement of the clay layer

    = ( )

    +

    H = ( )

    =

    +

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    17Workbook

    (iii) In the pressure range of 2 to 4 kg/cm2

    mv =

    =

    + +

    = 0.021 cm2/kg k = 2.8 107 cm/sec

    w = 1 gm/cc = 103 kg/cc

    Cv = ( )

    =

    =

    For 50% consolidation T50 = ( )

    =

    t =

    %

    =

    t = 148120.3008 sec = 1.71 days

    T3 : Solution

    Raft

    9.2 t/m2 1.2 m2 m

    8 m

    6 m

    Sub layer - I

    Sub layer - II

    Sub layer - III

    Clay

    e G0 = 0.72, = 2.71

    w CL v = 42%, = 2.2 10 cm /sec3 2

    Sand

    = 1.90 t/m3d

    = 2.10 t/m3sat

    Impervious shale

    G.L.

    The clay layer is divided into three sub layers of thickness 2 m each.For the settlement of each layer

    We have H = ( )

    + + The computation of settlement for the first sub layer

    Cc = 0.009 (wL 10)Cc = 0.009 (42 10) = 0.288e0 = 0.72H0 = 2m = 200 cm

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    18 Civil Engineering Soil Mechanics & Foundation Engineering

    Depth of middle of the sub-layer-I below:

    GL =

    + =

    0 = Initial effective overburden stress at a depth of 9 mbelow G.L

    = (d h1 + sub h2+ clay h3)sat = 2.10 t/m3 ; w = 1.0 t/m3

    sub = (2.10 1.0) = 1.10 t/m3

    clay =

    + + = =

    + +

    0 = 1.9 2 + 1.10 6 + (2 1) 1 = 11.4 t/m2 = 1.14 kg/cm2

    Using 2 : 1 Dispersion Method

    q = 9.2 t/m2

    Z = (9 1.2) = 7.8 m

    21

    Z / 2 Z / 2L

    =

    & &+ +

    =

    = =

    + +

    H1 =

    + = +

    Similarily for second layer

    q = 9.2 t/m2

    Z = (11 1.2) = 9.8 m

    0 = (dh + sub h2 + clay h3) = ( 1.9 2 + 1.10 6 + 1 3) = 13.4 t/m2 = 1.34 kg/cm2

    =

    & &+ +

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    19Workbook

    =

    + += 2.48 t/m2 = 0.248 kg/cm2

    H2 =

    + = +

    Similarly for Third sub layer 0 = (d h1 + sub h2 + clay h3)= (1.9 2 + 1.1 6 + 1 5) = 15.4 t/m2 = 1.54 kg/cm2

    =

    & &+ +

    =

    + + + = 2.06 t/m2 = 0.206 kg/cm2

    h3 =

    + = +

    Probable settlement of the clay layerH = (H1 + H2 + H3) = (3.45 + 2.47 + 1.83) = 7.75 cm

    (ii) Degree of consolidation corressponding to a settlement of 5 cm

    U =

    =

    The corresponding time factor

    Tv = 1.781 0.933 log10 (100 64.52)

    Tv = 0.335

    As single drainage condition prevails at site

    t =( )

    ( )

    %

    = = 634 days

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    Shear Strength of Soils8

    T1 : Solution

    Undisturbed state

    f = c

    0 qu

    Initial Area of cross section of the sample,

    A0 =

    =

    Axial strain at failure, 0 =

    0 =

    =

    7.5 cm

    P = 116.3 kg

    3.75 cm

    Corrected area, Ac = ( ) ( )

    = =

    Normal stress at failure =

    -

    = =

    Unconfined compressive strength, qu = 9.27 kg/cm2

    and Cohesion, c =

    '

    = =

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    21Workbook

    (b) In Remoulded state :(b) In Remoulded state :(b) In Remoulded state :(b) In Remoulded state :(b) In Remoulded state :Axial deformation = 1.15 cm

    Axial strain, a =

    =

    7.5 cm

    P = 68.2 kg

    Corrected area, Ac = ( )

    = =

    unconfined compressive strength, qu =

    '

    = =

    and cohesion, c =

    '

    = =

    Sensitivity =0 1) 12) $

    0 !1%)) $

    =

    =

    As the value of sensitivity lies between 1 and 2, the soil is classified as a low sensitive soil.

    T2 : Solution

    Data Given H = 11.25 cm

    H

    D

    Vanes

    D = 7.5 cmIn undisturbed state, T = 417.5 kg.cmFor a cohesive soil = 0

    Therefore, for two way shearing, S = c =

    +

    S = c =

    +

    S = c = -

    =

    In the Remoulded state, T = 283.2 kg.cm

    S =

    = =

    Sensitivity (St) =

    =

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    T1 : Solution

    K0 = 1 sin = 1 sin 30 = 0.50At point B, = 2 17 = 34 kN/m2, u = 0

    p0 = K0 = 0.5 34 = 17 kN/m2

    At point C, = 2 17 + 19 2 = 72 kN/m2

    p0 = K0 = 0.5 72 = 36 kN/m2

    The pressure distribution diagram is shown below, the diagram has been divided into 3 parts, let P1, P2 andP3 be the total pressure due to these parts. Thus

    (1)

    (2) (3)

    17.0 kN/m2

    19.0 kN/m2

    P1 =

    = 17 kN

    P2 = 2 17 = 34 kN

    P3 =

    = 19 kN

    Total, P = P1 + P2 + P3 = 70 kNThe line of action of P is determined by taking moments about C.

    =

    + +

    = 1.32m (from base)

    T2 : Solution

    Sand silty layer

    pa =

    at Z = 0, pA =

    Lateral Earth Pressure andRetaining Walls9

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    23Workbook

    Ka =

    = +

    pA = = =

    pB = ( ) = ( ) =

    Hc = ( )

    = =

    (ii) Loose Sand Layer:

    Ka2=

    =

    +

    Equivalent surcharge q1 = 1h1 = 1.85 1.90 = 3.515 t/m2

    pB = Ka2q1 =

    =

    pC = (Ka2q1 + Ka22H2) =

    +

    = (1.172 + 0.573) = 1.745 t/m2

    (iii) For Dense sand layer:Equivalent surcharge

    q2 = (1.85 1.9 + 1.72 1) = 5.235 t/m2

    pC = (Ka3q2)

    Ka3=

    ( )( )

    =

    +

    pC = (0.2596 5.235) = 1.36 t/m2

    pD = (Ka3 q2 + Ka3 H3)= (1.36 + 0.2596 1.88 1.6) = 2.14 t/m2

    A

    B

    C

    D

    PA1.6 m

    1.0 m

    1.9 m

    Y P4

    1.36

    P20.573P3

    0.32

    P1

    1.54 m

    1.171.40

    1.36 0.75 t/m2

    P1 = ( )

    = Y1 =

    + =

    P2 =

    = Y2 =

    + =

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    24 Civil Engineering Soil Mechanics & Foundation Engineering

    P3 = ( )

    = Y3 =

    + =

    P4 = ! = Y4 =

    =

    P5 =

    = Y5 =

    =

    PA =

    !

    =

    = + + + + = ii

    ( =( )

    + + + +

    =

    + + + +

    ! = 1.21 m

    The point of application of PA = 4.30 tonne is located at 1.21 m above the base of the wall.

    T3 : Solution

    A

    B

    C

    2.5 m

    1.5 m

    1 = 17.6 kN/m = 15 kN/m

    3

    2c

    = 20 kN/mc 2

    = 19.2 kN/m3

    I

    II

    For Soil I pa =

    Ka =

    = +

    KP =

    =

    At Z = 0, pA = = 2 15 = 30 kN/m2

    pB = ( ) At Z = 2.5 m pB = (1 17.6 2.5 30) = 14.0 kN/m

    2

    H0 =

    = =

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    25Workbook

    For soil III

    Ka2 =

    = +

    Equivalent surcharge q = h = (17.6 2.5) = 44 kN/m2

    pb = ( ) = (1 44 2 20) = 4 kN/m2At point C pc = ( ) +

    = +

    = 44 + 28.8 40 = 32.8 kN/m2

    4 kN/m2

    b cd

    a

    A

    B

    C

    2.5 m

    1.5 m

    14 kN/m2

    f

    32.8 m kN/m2

    e

    30 kN/m2

    The total active thrust when crack has developed

    PA =

    + + = 33.165 kN/m

    T4 : Solution

    = 16 kN/m3, = 35, = 10, = 90 85 = 5, = 0

    Ka =

    + + +

    =

    +

    + +

    = 0.2877

    Pa =

    3 *

    = = 57.54 kN/m

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    Stability of Earth Slopes10

    T1 : Solution

    Data Given = 35, H = 15 m, = 15, c = 200 kN/m2, = 18 kN/m3, Sn = 0.06We know that Sn =

    #

    0.06 =

    cm = (0.06 18 15) = 16. 2 kN/m2

    Factor of safety w.r.t cohesion

    FC =

    #

    = =

    T2 : Solution

    X

    Y

    X

    Y

    Z

    b

    Z

    = 6

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    27Workbook

    Effective stress at point, = (sub Z cos2)Shear stress at at point, = satZ cos sinShear strength of the soil on YY

    f = ( ) ( ) + = Factor of safety, F =

    F =! $

    ! '

    &

    &

    =

    Data Given : = 16G = 2.70e = 0.72 = 35

    sub =

    +

    sub =

    =

    +

    sat = ( )

    + + = =

    + +

    F =

    $

    $

    =

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    T1 : Solution

    0.5 m

    1.5 m

    1.5 m

    WT (2)

    WT (1)

    G.LLet, qf be the ultimate bearing capacity for the given strip footingWhen water table is at the base of footing, then

    qf = 5.7 c + sat Df qf = 5.7 30 + 20 2 = 211 kN/m

    2

    When water table rises 0.5 m above the base, then

    " = ( )

    + + = 5.7 30 + 20 1.5 + (20 9.81) 0.5= 206.1 kN/m2

    Percentage reduction in

    qf =

    = =

    T2 : Solution

    Data given

    D = 1.2, t = 1.8 t/m3qu = 5.5 t/m

    2

    (i) By Terzaghis theory c =

    '

    = = qu = 1.3 cNc + DNq + 0.4 B N

    For cohesive soil, = 0, Nc = 5.7, Nq = 1.0, N = 0 qu = (1.3 2.75 5.7) + 1.8 1.2 1 + 0 = 22.54 t/m

    2

    qnu = (qu D) = 22.54 1.8 1.2 = 20.378 t/m2

    qs = '

    )*+

    + =

    + =

    Shallow Foundations11

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    29Workbook

    (ii) By Skemptons Theory

    =

    =

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    30 Civil Engineering Soil Mechanics & Foundation Engineering

    (0)XX = ( z1 + sub z2)= (1.8 1.0) + (1.8 1) (0.5 + 2.0) = 3.8 t/m2 = 0.38 kg/cm2

    using 2 : 1 dispersion method, stress increament at X X

    ()XX =

    +

    Assuming the footing to be loaded with 8.28 t/m2 and

    = 2.745 t/m2 = 0.2745 kg/cm2

    H =

    %!

    + +

    =

    + = +

    As the Estimated Settlement is greater than the maximum permissible limit of 7.5 cm. The allowablebearing capacity of the footing should be less then 10.98 t/m2

    ,,

    + + = 7.5

    + + = 7.5

    + = 1.3612

    = 0.1372 kg/cm2 = 1.372 t/m2

    =

    & & &

    = =

    + + + +

    1.372 =

    "

    q = (1.372 4) = 5.49 t/m2

    Hence a loading intensity of 5.49 t/m2 will result in a consolidation settlement of 7.5 cm. Therefore, therequired allowable bearing capacity of the footing = 5.49 t/m2

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    T1 : Solution

    Qg(u) = qp Ag + c(Pg D)= (9 100) (1.8 1.8) + 1 100 (4 1.8 10)

    or Qug = 10116 kNQu = qpAp + c(p D)

    = (9 100) /4 (0.3)2 + 0.6 100( 0.3) 10or Qu = 629.1 kN

    Qug = nQu= 9 629.1 = 5661.9 kN

    As the ultimate load for individual pile failure is less than the pile groupload, the safe load is given by

    Qn =

    -+

    =

    T2 : Solution

    From the Modified Hileys FormulaWe know that, the Ultimate load on pile

    Qu =( )

    +

    . . . (i)

    Where h = Efficiency of hammer = 75% = 0.75W = 2.0 tonneH = 91 cm

    Deep Foundations12

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    32 Civil Engineering Soil Mechanics & Foundation Engineering

    S = Avg. penetration under the last 5 blows = 10 mm = 1cmeP = 0.55 1.5 = 0.825 tonne

    W > eP

    b =

    + + = =

    + +

    In order to find out the value of Qu, assume as a first approximation,C = 2.5 cm

    Qu =

    = = + +

    Now using C1 =

    '

    "

    = =

    C2 =

    '

    "

    = =

    C3 =

    '

    "

    = =

    C = (C1 + C2 + C3) = 1.1885 < 2.5 cmLet Qu = 50 tonne

    C =

    =

    Qu =( )

    =

    +

    Let Qu = 55 tonne

    C =

    =

    Qu =

    !

    =

    +

    In the second iteration, the assumed and computed values of Qu are quite close. Hence the ultimate loadbearing capacity of the pile is 54 tonne Therefore, the safe bearing capacity

    Qs =

    !

    '

    )

    = =

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    33Workbook

    T3 : Solution

    0.75

    B = 2.5 m

    B

    Com

    pact

    fill

    Loos

    e fil

    l3

    m

    B = 3 0.75 + 0.25 = 2.5 mAssume m = 0.4(a) Pile acting individually(a) Pile acting individually(a) Pile acting individually(a) Pile acting individually(a) Pile acting individually

    Qun = n(mcpLf)= 16(0.4 18 0.25 3)= 271.4 kN ...(1)

    (b) Pile acting in a group(b) Pile acting in a group(b) Pile acting in a group(b) Pile acting in a group(b) Pile acting in a groupQug = c(4 B) Lf + Lf B2

    = 18 4 2.5 3 + 15 3(2.5)2

    = 540 + 281.3 = 821.3 kN ...(2) Greater of the above two = 821.3 kNHence negative skin friction = 821.3 kN

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    Soil Exploration and MachineFoundations13

    T1 : Solution

    The depth of the boundary between the two strata can be given by

    D =

    ! !"

    ! !

    + =

    + = 12.9 m