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  • REALISTIC DYNAMIC ANALYSIS OF REALISTIC DYNAMIC ANALYSIS OF JOINTED ROCK SLOPES USING DDAJOINTED ROCK SLOPES USING DDA

    Yossef H. HatzorDept. of Geological and Environmental Sciences, BGU

    Funded by National Park and Nature Authority, Israel

  • Geological and Seismological Setting

  • Seismicity along the Dead Sea Rift System

    4.0 < ML < 4.95.0 < ML < 5.96.0 < ML

  • Topographic Site Effect in Masada

    Spectral amplification of ground motions (Zaslavsky and Shapira, 2000)

    Station 1Station 2

    ..

    .Station 3

  • Typical Failure Modes

    King Herod Palace: combined sliding (East face) and toppling (West Face ) leading to deterioration of entire slope segments

    Snake Path Cliff: sliding, and block slumping, of large, removable key blocks + time dependentpropagation of tensile cracks

  • Rock Mechanics Considerations

  • Mechanical Properties of Intact Rock

    0

    60

    120

    180

    240

    300

    0 0.1 0.2 0.3 0.4 0.5Axial Strain (%)

    Axi

    al S

    tress

    (MP

    a)

    0

    60

    120

    180

    240

    300

    0 0.1 0.2 0.3 0.4 0.5Axial Strain (%)

    Axi

    al S

    tress

    (MP

    a)

    Uniaxial Compressive Strength of intact Dolomite c > 300 MPa;

    Elastic Modulus E = 43 GPa

    Poissons Ratio = 0.18

  • Shear Strength of Bedding Planes

    An example of a natural, filled, bedding planeIn Masada dolomites

    saw-cut = 28o residual = 23o

    Determination of residual friction angle using tilt testson saw cut, and groundsurfaces

  • Triaxial Tests of Inclined, Filled, Saw-Cut

    0

    5

    10

    15

    20

    25

    0 0.1 0.2 0.3 0.4 0.5 0.6

    Axial strain (%)

    Stre

    ss D

    iffer

    ence

    (MPa

    )

    )2.25.1

    6.3

    11.7

    13

    3 = 16.2 MPa

    8.9

    c = 0 MPa = 22.7o

    0

    5

    10

    15

    20

    25

    0 0.1 0.2 0.3 0.4 0.5 0.6

    Axial strain (%)

    Stre

    ss D

    iffer

    ence

    (MPa

    )

    )2.25.1

    6.3

    11.7

    13

    3 = 16.2 MPa

    8.9

    0

    5

    10

    15

    20

    25

    0 0.1 0.2 0.3 0.40

    5

    10

    15

    20

    25

    0 0.1 0.2 0.3 0.4 0.5 0.6

    Axial strain (%)

    Stre

    ss D

    iffer

    ence

    (MPa

    )

    )2.25.1

    6.3

    11.7

    13

    3 = 16.2 MPa

    8.9

    c = 0 MPa = 22.7o

    BB

  • Direct Shear Tests of Natural Bedding Planes

  • Direct Shear Tests for Rough Bedding Planes

    0 0.4 0.8 1.2 1.6Shear Displacement (mm)

    0

    0.4

    0.8

    1.2

    She

    ar S

    tress

    (MP

    a)

    Normal Stress 1.38 MPa

    1.2 MPa

    1.03 MPa0.86 MPa0.7 MPa0.52 MPa

    0.35 MPa

    0.17 MPa

    peak=41o residual= 23o

    0 5 10 15 20 25Normal Stress (MPa)

    0

    4

    8

    12

    Shea

    r Stre

    ss (M

    Pa)

    Direct Shear of Natural Bedding PlanesTriaxial Shear of Filled Saw-cut

  • Summary: Mechanical Properties of Rock Mass

    Strength of intact rock > Strength of intact rock > 300 MPa300 MPa

    Elastic modulus = Elastic modulus = 43 43 GPaGPa

    PoissonPoissons ratio = s ratio = 0.180.18

    Peak friction angle of bedding planes = Peak friction angle of bedding planes = 4141oo

    Residual friction angle of bedding planes = Residual friction angle of bedding planes = 2323oo

  • Measured keyblock Displacements

  • Block 2Block 1

  • LVDT based Joint Meter

    Joint Displacement Monitoring Devices

    Flat Jack

  • Block 3 the control block

  • Joint Meter Output - Block 3

    -1

    -0.9

    -0.8

    -0.7

    -0.6

    -0.5

    -0.4

    -0.3

    -0.2

    -0.1

    0

    14 / 1

    / 98

    18 / 1

    / 98

    23 / 1

    / 98

    27 / 1

    / 98

    31 / 1

    / 98

    4 / 2

    / 98

    8 / 2

    / 98

    12 / 2

    / 98

    16 / 2

    / 98

    21 / 2

    / 98

    25 / 2

    / 98

    1 / 3

    / 98

    5 / 3

    / 98

    9 / 3

    / 98

    13 / 3

    / 98

    18 / 3

    / 98

    22 / 3

    / 98

    28 / 3

    / 98

    02/04

    /9814

    / 4 / 9

    827

    / 4 / 9

    8 9

    / 5 / 9

    8 21

    / 5 / 9

    8 3

    / 6 / 9

    8 15

    / 6 / 9

    8 28

    / 6 / 9

    8

    Date

    Rel

    ativ

    e D

    ispl

    acem

    ent

    0

    50

    100

    150

    200

    250

    Flat

    jack

    Pre

    ssur

    e

    FJ 3

    JM 10

    JM 11

    JM = Joint Meter(LVDT) FJ = Flat Jack

    JM10

    JM11

    FJ3

  • Joint meter output - Blocks 1,2,3

    Gulf of Eilat Seismicity???April 7, 98: M=4.4

    April 10, 98: M = 4.3

    -1.6

    -1.4

    -1.2

    -1

    -0.8

    -0.6

    -0.4

    -0.2

    0

    0.2

    14 / 1

    / 98

    18 / 1

    / 98

    23 / 1

    / 98

    27 / 1

    / 98

    31 / 1

    / 98

    4 / 2

    / 98

    8 / 2

    / 98

    12 / 2

    / 98

    16 / 2

    / 98

    21 / 2

    / 98

    25 / 2

    / 98

    1 / 3

    / 98

    5 / 3

    / 98

    9 / 3

    / 98

    13 / 3

    / 98

    18 / 3

    / 98

    22 / 3

    / 98

    28 / 3

    / 98

    02/04

    /9814

    / 4 / 9

    827

    / 4 / 9

    8 9

    / 5 / 9

    8 21

    / 5 / 9

    8 3

    / 6 / 9

    8 15

    / 6 / 9

    8 28

    / 6 / 9

    8 12

    / 7 / 9

    8

    Date

    Rel

    ativ

    e D

    ispl

    acem

    ent

    Bedrock

    Block 1

    Block 3

    Block 2

  • Influence of climatic fluctuations Block 3

  • Summary: Joint Monitoring Program

    The monitored The monitored keyblockskeyblocks exhibit dynamic exhibit dynamic behaviorbehavior

    Periodic Periodic keyblockkeyblock displacements with amplitude displacements with amplitude of up to 1mm and period of 6 months of up to 1mm and period of 6 months most likely most likely climatically controlledclimatically controlled

    High High keyblockkeyblock sensitivity sensitivity most likely due to most likely due to limiting state of static equilibriumlimiting state of static equilibrium

  • Limit Equilibrium Analysis

  • Representative Keyblock in the East Face (Block 1)

    H = 15mV

    W

    U

    bA A

    J1J3

    J2

    A

    A

    Plan view of Block 1

    N

    5 m

    =2oo

    DDATUM, Zw = 0

  • Influence of Water Head in Tension Crack on Factor of Safety Against Sliding and Rotation Block 1

    availableavailable = 22.7= 22.7oo

  • True Geometry of Block 1

  • Elements of 3D Graphical Solution

    Static Solution Pseudo - Static Solution

  • Total Required Support Force (Ton) for Block 1

    0

    500

    1000

    1500

    2000

    2500

    3000

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7PEAK HORIZONTAL GROUND ACCELERATION (g)

    SU

    PPO

    RT

    FOR

    CE

    Dry Case

    Saturated Case

    FACTOR OF SAFETY = 1 . 5

  • Summary:Limit Equilibrium Analysis

    Fully three dimensional analysis is required when Fully three dimensional analysis is required when stability of individual, prismatic, stability of individual, prismatic, keyblockskeyblocks is of is of concern.concern.

    Dominant failure mode in east slope of mountain Dominant failure mode in east slope of mountain is block slidingis block sliding

    Relatively small water head will induce sliding of Relatively small water head will induce sliding of critical critical keyblockskeyblocks

  • Support Installation

    Support installation in progress Preparations for support installation

  • Horizontal Drilling

  • The Final Product in the Snake Path Cliff

  • Fully Dynamic DDA

  • Upper Terrace of King Herods Palace

  • Joint Trace Map Generation

  • Joint Spacing and Orientation North Palace

    0102030405060

    0.15

    2.78

    5.42

    8.05

    10.69 Mo

    re

    Joint Length (m)

    Freq

    uenc

    y

    N = 100Mean = 2.7m

    05

    10152025

    0.15 0.61 1.08 1.54

    Bed Spacing (m)

    Freq

    uenc

    y N = 59Mean = 60cm

    0

    10

    20

    30

    2.82 11.11 19.41 27.70 MoreJ2 Spacing (cm)

    Freq

    uenc

    y

    N = 80Mean = 14 cm

    0

    5

    10

    15

    3.00 10.93 18.87 26.80 More

    J3 Spacing (cm)

    Freq

    uenc

    y N = 69Mean = 16.8 cm

    J1 (bedding)

    J2

    J3

  • A Synthetic Joint Trace Map Model

  • A Photo-geological Discontinuity Trace Map

    - E - - W -

  • DC Realization of Digitized Photo-geological Map

    - W -- E -

  • Discontinuous Deformation Analysis (Shi, 1993)

    A Discrete Element Method (Completely Discontinuous)

    A Rigorous Contact Detection Algorithm

    Normal and Shear Springs at Contact Points Between Blocks

    No Tension / No Penetration Between Blocks

    Sliding Deformation Modeled Using Coulombs Law

    Solution for Displacement Obtained by Minimization of Total Potential Energy (as in FEM).

    Solution Progresses by a Time-Step Marching Scheme

    First Order Displacement Approximation

    Simply Deformable Blocks

  • DDA Validation

  • Block on an Incline:Gravitational Loading - Constant Acceleration

    (M

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