à¸à¸²à¸£à¸§à¸´à¹€à¸„ราะห à¹à¸¥à¸° ... foundation on Ground ... Discrete element method - Finite difference method - Finite element

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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.