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  • Mat foundation on Ground

    ..

  • 2

    (Mat foundation

    or Raft foundation)

    2

  • 3

    (Mat foundation or Raft foundation)

  • 4

    (Mat foundation or Raft foundation)

  • 5

    4

    A-A

    A A

    B-B

    B B

    1. Flat plate 2. Flat plate thickened

    under column

  • 6

    4

    C-C

    C C

    D-D

    D D

    3. Beam and slab 4. Slab with basement

    walls as a part of the mat

  • 7

    1.

    ( )qqq ultnet =

    Meyerhof 1963

    disBNdisqNdiScNq qqqqccccult 21

    ++= (1)

    Bq

    1

    D

    D1

    (surcharge pressure) =

    (S.F.) safety factor = 2 cohesionless

    = 3 cohesive soil

    ../ FSqq neta =

    1

  • 8

    1.

    1 Meyerhof 1963

    0 5.14 1.0 0.0

    5 6.49 1.6 0.1

    10 8.34 2.5 0.4

    15 10.97 3.9 1.1

    20 14.83 6.4 2.9

    25 20.71 10.7 6.8

    26 22.25 11.8 8.0

    28 25.79 14.7 11.2

    cN qN N30 30.13 18.4 15.7

    32 35.47 23.2 22.0

    34 42.14 29.4 31.1

    36 50.55 37.7 44.4

    38 61.31 48.9 64.0

    40 75.25 64.1 93.6

    45 133.73 134.7 262.3

    50 266.50 318.5 871.7

    cN qN N

  • 9

  • 10

    1.

    0=

    > 10

    Factor Value For

    (Shape)

    (Depth)

    (Inclination)

    2

    LBK2.01s pc +=

    LBK1.01ss pq +==

    1ssq ==

    BDK2.01d pc +=

    BDK1.01dd pq +==

    1ddq == 2

    qc 901ii

    ==

    o

    o

    2

    1i

    = oo

    0i = 0>for

    Any

    > 10

    0=

    Any

    > 10

    0=

    Any

    ( )2/45tan2 +=pK

    H

    R V

  • 11

    2.

    3

    1. Conventional rigid method

    strip < 1.75/

    2. Approximate flexible method

    strip > 1.75/

    3. Discrete element method - Finite difference method

    - Finite element method (FEM)

    - Finite grid method (FGM)

    44 FF IEk

    =

    k = modulus of subgrade reaction

    EF = modulus of elasticity

    IF = moment of inertia

    PresenterPresentation Notes conventional rigid method Flexible method slide 47 slide 69

  • 12

    Q1

    Q 2R = Q1+Q2

    Q1 Q 2

    q

    q

  • 13

    3.

    (Conventional rigid method)

    1

    nQQQQQ ....321 +++=

    n

    Q1, Q2, Q3

    (5)

    L

    B

    Q9 Q10 Q11 Q12

    Q5 Q6 Q7 Q8

    Q1 Q2 Q3 Q4

    ey

    ex

    B7 B6 B5

    B3

    B2

    B1X

    Y

    x

    y

    A B C D

    J E

    FGHIx'

    y'

    B4

    PresenterPresentation Notes Q dimension B4 x y

  • 14

    2

    y

    y

    x

    xIxM

    IyM

    AQq ++= (6)

    Q A ( )LBA =

    xI x 3)12/1( BL

    yI 3)12/1( LB y

    xM yx eQM = x

    yM xy eQM = y

  • 15

    xe

    ye

    x ( )

    y ( )

    QxQ...xQxQxQx nn332211++++

    = (7)

    2Bxex = (8)

    QyQyQyQyQy nn ...332211++++

    = (9)

    2Lyey = (10)

    2

    L

    B

    Q9 Q10 Q11 Q12

    Q5 Q6 Q7 Q8

    Q1 Q2 Q3 Q4

    ey

    ex

    B7 B6 B5

    B3

    B2

    B1X

    Y

    x

    y

    A B C D

    J E

    FGHIx'

    y'

    B4

  • 16

    aqq

    3

    x y

    B1, B2, B3,...Bn

    4 (strip)

    L

    B

    Q9 Q10 Q11 Q12

    Q5 Q6 Q7 Q8

    Q1 Q2 Q3 Q4

    ey

    ex

    B7 B6 B5

    B3

    B2

    B1X

    Y

    x

    y

    A B C D

    J E

    FGHIx'

    y'

    B4

  • 17

    5

    dbfV cc 006.1 = (11)

    cV (kg)

    0.85

    d (cm)

  • 18

    5

    0b (cm)

    (d/2)

    (11) (Factored load)

    (d)

    ) ) )

  • 19

    6 (shear force diagram)

    (moment diagram)

    1 I

    F B1 B x

    2FI

    avqqq +=

    Iq Fq I F

    (12)

    B

    Q1

    Q2

    Q3

    Q4

    B1X

    FGHI

    y'

  • 20

    6 (shear force diagram)

    (moment diagram)

    BBqav 1

    =Q 4321 QQQQ +++ QBBqav 1

    avq

    =

    4

    ( )2

    43211 QQQQBBqloadAverage av ++++= (13)

    (14)

    =

    BBloadAverageqav

    1

  • 21

    6 (shear force diagram)

    (moment diagram)

    4321 QQQQloadAverageF+++

    = (15)

    321 ,, FQFQFQ 4FQ- factor F

    -

    -

    - x y

    avq

    PresenterPresentation Notes Unit length B

  • 22

    7

    2bdMR uu

    =

    bc

    u

    y

    cf

    Rff 75.0

    85.021185.0min

    =

    (16)

    bdAs =

    (17)

    (18)

    uM

    1 . (kg-m)

    0.90

    b 1 . (b = 100 cm)

  • 23

    cf (ksc)

    (ksc)yf

    min yf14

    min =

    yy

    cb ff

    f+

    =

    120,6120,685.0 1

    ( )

    >

    10

    Factor Value For

    (Shape)

    (Depth)

    (Inclination)

    2

    LBK2.01s pc +=

    LBK1.01ss pq +==

    1ssq ==

    BDK2.01d pc +=

    BDK1.01dd pq +==

    1ddq == 2

    qc 901ii

    ==

    o

    o

    2

    1i

    = oo

    0i = 0>for

    Any

    > 10

    0=

    Any

    > 10

    0=

    Any

    ( )2/45tan2 +=pK

    H

    R V

  • 28

    2

    BDK2.01d pc += 2.22

    5.112.01+= 014.1= ( 2)

    Dq = 635.19.0)175.1(6.06.1 =+= ton/m2 ( effective pressure

    ) 1ssq ==

    0=i( 2)

    1ddq ==

    ( 2)( 2)

    ++= disBN21disqNdiScNq qqqqccccult

    00.10.10.10.1635.1014.10.1154.114.55.3qult ++=

    686.22qult = ton/m2

    qqq ultnet =

    635.1686.22 =

    051.21qnet = ton/m2

    (safety factor = 3.0) 017.73/051.21qa == ton/m2

  • 29

    x,

    2

    193,448.282.22121BL

    121I 33x =

    =

    = 4m

    y, 259,262.228.28121LB

    121I 33y =

    =

    =

    4m

    x (7) = 0yM

    QxQxQxQxQx 1616332211 ..+++

    =

    ( )( ){ 32545986548227456.0x +++++++=

    ( )( )54821091819116354826.7 ++++++++

    ( )( )548213620011318154866.14 ++++++++( )( ) } 619,2/32545491549132506.21 ++++++++

    296.11x = m

    xe (8)

    2Bxex = 2

    2.22296.11 = 196.0= m

    L = 28.8 m

    B= 22.2 m

    X

    Y

    x

    y

  • 30

    y = 0xM (9) 2

    QyQ...yQyQyQy 166332211+++

    =

    { ( )( 3254548254823254)9.0y +++++++=( )( )549113620010918159869.9 ++++++++( )( )54911131819116354829.18 ++++++++( )( ) } 619,2/32505486548227459.27 ++++++++

    178.14y = m

    ye (10) 2Lyey = 2

    8.28178.14 = 222.0= m

    L = 28.8 m

    B= 22.2 m

    X

    Y

    ey= 0.222

    ex= 0.196

    meme

    y

    x222.0196.0

    ==

    x

    y

    PresenterPresentation NotesSlide Q Q allowable soil pressure Q 2619 Mx My Q slide Q

  • 31

    yx eQM = 42.581)222.0(2619 == ton-m

    xy eQM = 32.513196.02619 == ton-m

    y

    y

    x

    x

    IxM

    IyM

    AQq ++=

    259,2632.513

    193,4442.581

    8.282.222619 xyq ++

    =

    xyq 0195.00132.0096.4 +=

    (5)

    ton/m2

    ton/m2

    (service load)

  • 32

  • 33

    Point (ton/m2) x (m) 0.0195x y (m) -0.0132y q (ton/m2)

    A 4.096 -11.1 -0.216 14.4 -0.190 3.690

    B 4.096 -3.5 -0.068 14.4 -0.190 3.838

    C 4.096 3.5 0.068 14.4 -0.190 3.974

    D 4.096 11.1 0.216 14.4 -0.190 4.122

    E 4.096 11.1 0.216 -14.4 0.190 4.502

    F 4.096 3.5 0.068 -14.4 0.190 4.354

    G 4.096 -3.5 -0.068 -14.4 0.190 4.218

    H 4.096 -11.1 -0.216 -14.4 0.190 4.070

    1 4.096 -11.1 -0.216 4.5 -0.059 3.821

    2 4.096 11.1 0.216 4.5 -0.059 4.253

    3 4.096 -11.1 -0.216 -4.5 0.059 3.939

    4 4.096 11.1 0.216 -4.5 0.059 4.371

    4.096

    4.502

    AQ

    2 3

    PresenterPresentation Notes slide Slide -0.0199y -0.0199x 0.0296x 0.0296y

  • 34

    yx eQM = 18.881)222.0(3.3969 == ton-m

    xy eQM = 98.777196.03.3969 == ton-m

    y

    y

    x

    x

    IxM

    IyM

    AQq ++=

    259,2698.777

    193,44)18.881(

    8.282.223.3969 xyq ++

    =

    xyq 0296.00199.0208.6 +=

    (5)

    ton/m2

    ton/m2

    (ultimate load)

  • 35

    Point (ton/m2) x (m) 0.0296x y (m) -0.0199y q (ton/m2)

    A 6.208 -11.1 -0.329 14.4 -0.287 5.592

    B 6.208 -3.5 -0.104 14.4 -0.287 5.817

    C 6.208 3.5 0.104 14.4 -0.287 6.025

    D 6.208 11.1 0.329 14.4 -0.287 6.250

    E 6.208 11.1 0.329 -14.4 0.287 6.824

    F 6.208 3.5 0.104 -14.4 0.287 6.599

    G 6.208 -3.5 -0.104 -14.4 0.287 6.391

    H 6.208 -11.1 -0.329 -14.4 0.287 6.166

    1 6.208 -11.1 -0.329 4.5 -0.090 5.789

    2 6.208 11.1 0.329 4.5 -0.090 6.447

    3 6.208 -11.1 -0.329 -4.5 0.090 5.969

    4 6.208 11.1 0.329 -4.5 0.090 6.627

    6.208

    6.824

    AQ

    2 4

  • 36

    q 017.7=aq

    3

    = 4.502 ton/m2 <

    ***

    ****

    ton/m2 OK

    4 (strip)

    y 4 A-

    H, B-G, C-F D-E

    x 4

    EFGH, 3-4, 1-2 ABCD

    051.21=aq = 6.824 ton/m2 < ton/m2 OKq

    PresenterPresentation Notes pressure slide

  • 37

    5

    2

    2.219547.1914.1Q =+= ton ( ) ( ) d2240d602/d30602b0 +=++++=

    ACI dbfV cc 006.1 =

    200,219=QVc kg

    85.0=

    240=cf kg/cm2

    ( ) 200,219224024006.185.0 + dd

    ( ) 99.157032240 + dd

    078521202 =+ dd

    47d cm

    d/2

    d/2

    d/2

    b0=2(0.6+0.3+d/2)+(0.6+d)

    edge of mat

    0.6

    0.6

    0.60.6+0.3+d/2

    0.6+d

    DL=91 ton , LL= 54 ton

    2

    cm

  • 38

    5

    000,130=QVc kg

    ( ) 000,13021024006.185.0 + dd

    5.9313)210( + dd

    05.93132102 =+ dd

    6.37d cm

    H E

    130327.1544.1 =+=Q ton

    ( ) ( ) dddb +=+++++= 2102/30902/30600

    d/2

    d/2

    b0=(0.6+0.3+d/2)+(0.9+0.3+d/2)

    edge of mat

    edge of mat

    0.9 0.6

    0.6

    0.6+0.3+d/2

    0.9+0.3+d/2

    DL=54 ton , LL= 32 ton

    E,H

  • 39

    C-F 3-4

    2.5111367.12004.1 =+=Q

    5

    ton

    ( ) ddb 42406040 +=+=

    200,511= QVc

    ( ) 200,511424024006.185.0 + dd

    ( ) 5.366234240 + dd

    09.9155602 =+ dd

    3.70d cm

    d/2

    d/2

    d/2

    b0=4(0.6+d)

    d/2

    0.6+d

    0.6+d

    DL=200 ton , LL= 136 ton

    C-F 2-3

    80 . d = 80-7.5-2.5/2 = 71.25 cm > 70.3 cm

    DB 25 mm

  • 40

    6 (shear force diagram)

    (moment diagram)

    C-F

    factor (F)

    LBq 1av C-F 312.62599.6025.6

    =+

    =avq ton/m2

    50.272,18.280.7312.61 ==LBqav ton

    ( )( ) ( )( ) 20.212547.1864.1Q1 =+= ton

    ( )( ) ( )( ) 50.4451137.11814.1Q2 =+= ton

    ( )( ) ( )( ) 20.5111367.12004.1Q3 =+= ton

    ( )( ) ( )( ) 60.206547.1824.1Q4 =+= ton

    =+++= 50.375,160.20620.51150.44520.212Q ton 1,272.50 ton

  • 41

    q = 6.025

    q = 6.599

    7 m

  • 42

    ( )2

    QQQQLBqloadAverage 43211av ++++=

    6 (shear force diagram)

    (moment diagram)

    250.137550.1272 +

    =

    324,1=loadAverage ton

    LBloadAverageq

    1av = 567.68.287

    324,1=

    = ton/m2

    4321 QQQQloadAverageF+++

    = 963.050.375,1

    324,1==

    35.2042.212963.01 ==FQ ton

    02.4295.445963.02 ==FQ ton

    29.4922.511963.03 ==FQ ton

    96.1986.206963.04 ==FQ ton

  • 43

    0.16 m

    6 (shear force diagram)

    (moment diagram)

    avq

    Ix

    ARq Re+=

    R 62.324,196.19829.49202.42935.204 =+++ ton

    6.2018.280.7 ==A m2

    16.0=e m

    R

    9.2796.1989.1829.4929.902.4299.035.204)4.14(62.1324 +++=+ e

  • 44

    ( ) 352.659.934,13

    )4.14(16.062.324,16.20162.324,1

    1 =

    +=q ton/m2

    ( ) 790.659.934,13

    )4.14(16.062.324,16.20162.324,1

    2 =

    +=q ton/m2

    321 ,, FQFQFQ 4,FQ avq

    shear force diagram bending moment diagram

    Load diagram

    ( )( ) 59.934,138.287121 3 =

    =I m3

  • 45

    6 (shear force diagram)

    (moment diagram)

    Shear diagram

    (ton)

    Moment diagram

    (ton-m)

    6.790x7 =

  • 46

    6 (shear force diagram)

    (moment diagram)

    5 y

    (strip)

    (m)

    (ton/m2) (ton) (ton)Average load

    (ton) (ton/m2)

    Factor F

    A-H 4.1 5.879 694.19 666.20 680.20 5.761 1.021

    B-G 7.0 6.104 1230.57 1234.80 1232.69 6.115 0.998

    C-F 7.0 6.312 1272.50 1375.50 1324.00 6.567 0.963

    D-E 4.1 6.537 771.89 692.80 732.35 6.202 1.057

    3969.15 3969.30 3969.24

    avq LBqav 1 Q avq

  • 47

    6 y

    6 (shear force diagram)

    (moment diagram)

    1q

    2q

    (strip) A-H B-G C-F D-E

    Q1 (ton) 108.90 206.60 212.20 124.40

    Q2 (ton) 206.60 382.90 445.50 219.20

    Q3 (ton) 220.70 438.70 511.20 219.20

    Q4 (ton) 130.00 206.60 206.60 130.00

    FQ1 (ton) 111.19 206.19 204.35 131.49

    FQ2 (ton) 210.94 382.13 429.02 231.69

    FQ3 (ton) 225.33 437.82 492.29 231.69

    FQ4 (ton) 132.73 206.19 198.96 137.41

    e (m) 0.52 0.20 0.16 0.11

    A (m2) 118.08 201.60 201.60 118.08

    I (m4) 8161.69 13934.59 13934.59 8161.69

    5.136 5.858 6.352 6.059

    6.384 6.367 6.790 6.344

    Maximum positive moment (t-m/m) 14.69 44.64 74.54 9.89

    Maximum negative moment (t-m/m) 53.62 47.15 40.47 58.80

    Maximum Shear (ton)/m 28.73 32.72 38.04 28.81

  • 48

    6 (shear force diagram)

    (moment diagram)

    (strip)

    (m)

    (ton/m2) (ton) (ton)Average load

    (ton) (ton/m2)

    Factor F

    ABCD 5.4 5.921 709.81 652.10 680.96 5.680 1.044

    1-2 9.0 6.118 1222.38 1254.20 1238.29 6.198 0.987

    3-4 9.0 6.298 1258.34 1389.80 1324.07 6.627 0.953

    HGFE 5.4 6.495 778.62 673.20 725.91 6.055 1.078

    3969.15 3969.30 3969.23

    avq LBqav 1 Q avq

    7 x

  • 49

    6 (shear force diagram)

    (moment diagram) 8 strip x

    (strip) ABCD 1-2 3-4 HGFE

    Q1 (ton) 108.90 206.60 220.70 130.00

    Q2 (ton) 206.60 382.90 438.70 206.60

    Q3 (ton) 212.20 445.50 511.20 206.60

    Q4 (ton) 124.40 219.20 219.20 130.00

    FQ1 (ton) 113.69 203.91 210.33 140.14

    FQ2 (ton) 215.69 377.92 418.08 222.71

    FQ3 (ton) 221.54 439.71 487.17 222.71

    FQ4 (ton) 129.87 216.35 208.90 140.14

    e (m) 0.28 0.28 0.17 0.00

    A (m2) 119.88 199.80 199.80 119.88

    I (m4) 4923.47 8205.79 8205.79 4923.47

    5.249 5.727 6.324 6.054

    6.109 6.665 6.934 6.054

    Maximum positive moment/1 m (t-m/m) 6.77 20.55 35.29 1.09

    Maximum negative moment/1 m (t-m/m) 21.94 30.72 28.95 44.47

    Maximum Shear (ton)/m 21.40 25.47 28.78 22.33

    1q

    2q

  • 50

    7

    y

    +uM

    () = 74.54 ton-m/m ( CF)

    54.74= ton-m/m

    9.0= cmb 100= 2/240 cmkgfc =2/000,4 cmkgfy =

    0035.04000/14min ==

    , ,

    2bdM

    R uu

    = 31.1625.711009.0100000,154.742 =

    = kg/cm2

    0043.024085.031.16211

    000,424085.0

    85.021185.0 =

    =

    =

    c

    u

    y

    cf

    Rff

  • 51

    0197.0000,4120,6

    120,6000,424085.085.075.0

    120,6120,685.075.075.0 1

    =+

    =

    +

    =yy

    cb ff

    f

    )0043.0()0035.0(min

    mcmbdAs /94.2425.711000035.02===

    DB25 @ 0.15 . y

    mcmAs /72.3215.0/5.2422 ==

    OK

  • 53

    x

    7

    35.29 ton-m/m

    2bdMR uu

    = 30.875.681009.0100000,129.352 =

    = kg/cm2

    002.024085.030.8211

    000,424085.0

    85.021185.0 =

    =

    =

    c

    u

    y

    cf

    Rff

    9.0= cmb 100= 2/240 cmkgfc = 2/000,4 cmkgfy =

    0035.04000/14min ==

    , , ,

    cmd 75.685.225.71 ==

  • 54

    0197.0000,4120,6

    120,6000,424085.085.075.0

    120,6120,685.075.075.0 1

    =+

    =

    +

    =yy

    cb ff

    f

    )002.0()0035.0(min >

    ACI 0027.0002.033.133.1 === cal

    mcmbdAs /6.1875.681000027.02===

    DB25 @ 0.25 . x

    mcmAs /6.1925.0/5.2422 ==

    OK

    x

  • 55

    x

    7

    44.47 ton-m/m

    9.0= cmb 100= 2/240 cmkgfc =2/000,4 cmkgfy =

    0035.04000/14min ==

    , , ,

    2bdMR uu

    = 45.1075.681009.0100000,147.442 =

    = kg/cm2

    0027.024085.045.10211

    000,424085.0

    85.021185.0 =

    =

    =

    c

    u

    y

    cf

    Rff

    cmd 75.685.225.71 ==

  • 56

    0197.0000,4120,6

    120,6000,424085.085.075.0

    120,6120,685.075.075.0 1

    =+

    =

    +

    =yy

    cb ff

    f

    )0027.0()0035.0(min >

    mcmbdAs /06.2475.681000035.02===

    DB25 @ 0.20 . x

    mcmAs /5.2420.0/5.2422 ==

    OK

  • 57

    y, Vu = 38.04 Ton/m

    x, Vu = 28.78 Ton/m

    7.49000,1/25.7110024053.085.053.0 === bdfV cc Ton/m

    > Vu

    98.47000,1/75.6810024053.085.053.0 === bdfV cc Ton/m

    > Vu

  • 58

    Mat foundation on Ground (Mat foundationor Raft foundation) (Mat foundation or Raft foundation) (Mat foundation or Raft foundation) 4 Slide Number 61. 1. Slide Number 91. 2. Slide Number 123. (Conventional rigid method)Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Slide Number 47Slide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54Slide Number 55Slide Number 56Slide Number 57Slide Number 58


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