Stability of rock blocks - .Influence of water on slope stability EPFL -LMR Sliding stability of

download Stability of rock blocks - .Influence of water on slope stability EPFL -LMR Sliding stability of

If you can't read please download the document

  • date post

    16-Sep-2018
  • Category

    Documents

  • view

    212
  • download

    0

Embed Size (px)

Transcript of Stability of rock blocks - .Influence of water on slope stability EPFL -LMR Sliding stability of

  • 1

    COLE POLYTECHNIQUEFDRALE DE LAUSANNE

    L M RRock mechanics

    LABORATOIRE DEMCANIQUE DES ROCHES

    V. Labiouse, J. Abbruzzese

    Stability of rock blocks

    EPFL - LMR

    Stability of rock blocks

    1. Stability of one block

    2. Stability of a column

    3. Stability of two blocks

    4. Stability of several blocks (fauchage)

    5. Influence of water on slope stability

    EPFL - LMR

    Sliding stability of a block

    W cos

    W sin

    W = N/A = W cos /A

    b h

    res = tan + c*

    sol = T/A = W sin /A

    EPFL - LMR

    W cos

    W sin

    W

    b h

    W sin /A < (W cos /A) tan + c* sol < res = tan + c*

    Stable if

    Sliding stability of a block

  • 2

    EPFL - LMR

    Safety Factor with respect to sliding :

    solsol

    ress

    ctanF

    +=

    =

    W

    b h

    +

    =

    sinWAc

    tantanFs

    +=

    sinAW

    ctancosAW

    Fs

    Sliding stability of a block

    EPFL - LMR

    >

    <

    =

    Sliding

    Stable

    Stability limit

    Sliding of a block on a smooth plane (c* = 0)

    EPFL - LMR

    SlidingStable

    tan

    b/h

    > <

    tan

    Sliding of a block on a smooth plane (c* = 0)

    EPFL - LMR

    W cos

    W sin

    W

    Mdestabilizing,0 = W sin . h/2 b

    h

    Toppling stability of a block

    Toppling instability occurs if the direction line of the weight vector Wintersects the slope surface beyond the base of the column.

    destab,0 < stab,0Stable if

    0

    Mstabilizing,0 = W cos . b/2

    tan < b/h

  • 3

    EPFL - LMR

    W cos

    W sin

    W

    b

    h

    Safety Factor with respect to toppling :

    ==

    tanhb

    MM

    F0,dstab

    0,stabs

    Toppling stability of a blockEPFL - LMR

    b/h < tan

    b/h > tan b/h = tan

    Toppling

    Stable

    Stability limit

    b

    h

    Toppling stability of a block

    EPFL - LMR

    Toppling

    Stable

    tan

    b/h

    b/h < tan

    b/h > tan

    b / h= t

    an

    Toppling stability of a blockEPFL - LMR

    Sliding and toppling stability of a block on a smooth plane (c* = 0)

    Sliding

    Stable

    tan

    tan

    b/h

    b / h= t

    an

    Slidingand

    Toppling

    Toppling

  • 4

    EPFL - LMR

    Safety Factor with respect to sliding :

    A

    +

    =

    sinWAc

    tantanFs

    res = tan + c*

    WCG

    Sliding stability of a columnEPFL - LMR

    ==

    tanhb

    MMF

    CG

    CG

    dstab

    stabsCG

    bCG

    hCG

    Toppling instability occurs if the direction line of the weight vector Wintersects the slope surface beyond the base of the column.

    Toppling stability of a column

    Safety Factor with respect to toppling :

    EPFL - LMR

    Sliding and toppling stability ofrock columns

    EPFL - LMR

    Stability of two blocks

    Toppling of the two blocks

    Toppling and sliding

    Stability of the two blocks

  • 5

    EPFL - LMR

    The fauchage phenomenon

    Toppling in layered or

    fractured rocks

    characterized by a

    system steeply dipping

    into the slope EPFL - LMR

    b

    huu = w h cos

    Pressure distributions for allowed seepage

    0

    Hypotheses:1. Hydrostatic along the

    rear fracture2. Flow with constant

    gradient in the basaldiscontinuity

    u0 = 0

    V

    UV = w h2 cos U = w h b cos

    EPFL - LMR

    W cos

    W

    b

    h

    res = tan + c* V

    U

    W sin

    = N/Asol = T/A

    Sliding stability for allowed seepage

    0N = W cos - UT = W sin + V

    Stable if sol < res

    Stability highly endangered

    EPFL - LMR

    W cos

    W

    b

    h

    V

    U

    W sin

    Toppling stability for allowed seepage

    0

    Mdestabilizing,0 = W sin . h/2 + V. h/3 + U. 2b/3

    destab,0 < stab,0Stable if

    Mstabilizing,0 = W cos . b/2

    Stability highly endangered

  • 6

    EPFL - LMR

    Pressure distributions if no outflow possible

    b

    h

    V

    U

    u0

    u = w h cos

    Hypotheses:1. Hydrostatic along the

    rear fracture2. No outflow at the toe of

    the basal discontinuity

    u0 = w (h cos + b sin )

    V = w h2 cos U = w b (2h cos + b sin )

    COLE POLYTECHNIQUEFDRALE DE LAUSANNE

    L M RRock mechanics

    LABORATOIRE DEMCANIQUE DES ROCHES

    V. Labiouse, J. Abbruzzese

    Plane slide

    EPFL - LMR

    Stability of a plane slide

    1. Kinematical conditions

    2. Sliding along a plane

    3. Sliding along a plane, with a rear tension crack

    4. Stabilising measures

    Control of water

    Pre-tense anchors (active)

    Grouted bar bolts (passive)

    EPFL - LMR

    Plane slide on the D526 roadconnecting Mens and Clelles (Isre France)

    http://www.irma-grenoble.com/

  • 7

    EPFL - LMR

    Plane slide in layered rocksin Sylans (France)

    EPFL - LMR

    When is a sliding mechanism possible ?

    Yes No

    NoNoautomatic detection of potential sliding planes, based on the use

    of DTM25.

    examplefor plane sliding

    EPFL - LMR

    Slide on a single plane joint: dry slope

    Factor of safety:max. shear strengthapplied shear stressFS =

    - applied shear stress:sol = (T/A) = W/A sin

    A = L x 1 (m)= (N/A) = W/A cos = (T/A) = W/A sin c*= 0

    =

    =tantan

    sinWtancosWFS

    - max. shear strength:res = tan + c*

    = (N/A) tan

    W cos W

    W sin

    L

    EPFL - LMR

    U

    Hw

    Slide on a single plane joint: role of water

    U = resultant of the pore water pressure distribution, as a function of the hydraulic conditions

    ( )

    =

    sinWtanUcosWFS

    res = ( - u) tan res =[ (Wcos-U)/ ] tan

    The maximum shear strength on the failure surface is reduced

    W cos W

    W sin

    L

  • 8

    EPFL - LMR

    Slide on a single joint (with tension crack)

    Seepage allowedActions due to water presence:

    1. Hydrostatic pressure in the tension crack;

    2. Seepage through the joint at the base.

    at the toe of the tension crack:u = w hw

    L

    V

    UW cos

    W

    W sin u

    hw

    2ww h2

    1V = Lh21U ww=

    EPFL - LMR

    Slide on a single joint (with tension crack)

    Seepage allowedstability against sliding

    : = W cos U V sin : = W sin + V cos

    ( )+

    +=

    cosVsinWA*ctansinVUcosWFS

    Shear strength reduced and applied forces increasedstability highly endangered.

    L

    V

    UW cos

    W

    W sin u

    hw

    EPFL - LMR

    Slide on a single joint (with tension crack)

    No outflow possible (at 0)Actions due to water presence:

    1. Hydrostatic pressure inthe tension crack;

    2. No water flow; Hydrostatic pressure in the failure plane.

    at the toe 0 of the basal plane:u = w (hw+ L sin)

    L

    V

    UW cos

    W

    W sin u

    hw

    0

    2ww h2

    1V = ( )2

    sinLh2LU ww +=

    EPFL - LMR

    1. Surface drainage(cut-off ditch)

    2. Pumping from wells3. Gravity drainage of

    the rear tension crack4. Gravity drainage of

    the basal plane5. Drainage gallery and

    radial drains

    Methods to control water in jointed rock slopes

    1.2.

    3.

    4.

  • 9

    EPFL - LMR

    Support methods: active measures

    Pre-tension active anchors

    Free length

    Spiral winding cables or rodsGrouted zone

    Fixed anchor length

    EPFL - LMR

    : = Wcos - U - Vsin + Pa sin( + ) : = Wsin + Vcos - Pa cos( + )

    V

    UW cos

    W

    W sin

    Pa

    Pa cos( + )

    Pa sin( + )

    Support methods: active measures

    EPFL - LMR

    V

    UW cos

    W

    W sin

    Pa

    Pa cos( + )

    Pa sin( + )

    Support methods: active measures

    ( )( )( )++

    ++=

    cosPcosVsinWtansinPsinVUcosWFS

    a

    a

    The pre-tension of anchors both increases N and

    decreases T, thus improving the stability of the slope.

    EPFL - LMR

    Support methods: passive measures

    Grouted boltsGrouting all along the bars length

    Thread bar Grouted zone

    Passive anchors increasethe rock mass cohesion(Bjurstrm, 1974):

    f

    ca

    aa S

    SC

    =

    Sa = area of bars transversal sectionS = area of the surface reinforced by boltsa = shear strength of the bar (a 0.6 f)c = rocks compressive strengthf = yielding stress of the bars material (steel)

    ! Take care that there is also tension in the bolts in addition to bending and shear stresses

  • 10

    EPFL - LMR

    Support methods: passive measures

    : = Wcos - U - Vsin : = Wsin + Vcos

    V

    UW cos

    W

    W sin T

    ScS*ctanNFS a ++=

    ! either c*S or caS(do not add contributions)

    EPFL - LMR

    Support methods: passive measures

    TS*ctanNFS +=

    ( )+

    +=

    cosVsinWSCtansinVUcosWFS a

    V

    UW cos

    W

    W sin

    COLE POLYTECHNIQUEFDRALE DE LAUSANNE

    L M RRock mechanics

    LABORATOIRE DEMCANIQUE DES ROCHES

    V. Labiouse, J. Abbruzzese

    Wedge slide

    EPFL - LMR

    Wedge slide above the road of Cogne (Italy)

    http://www.crealp.ch/

    Wedge sliding on

    two intersecting

    discontinuities

  • 11

    EPFL - LMR

    Wedge sliding stability

    Vertical plane Transverse section to i direction

    Sliding failure of a rock wedge on the S1 and S2planes, which define an intersection line