chapter 4 slope stability -...

40
CHAPTER 4 SLOPE STABILITY ANALYSYS Introduction: Slope Failures Types of Slope Causes of Failures Types of Failures Method of Analysis Slope stabilization Muhammad Azril Hezmi

Upload: ngotuong

Post on 14-Aug-2018

395 views

Category:

Documents


18 download

TRANSCRIPT

  • CHAPTER 4SLOPE STABILITY ANALYSYS

    Introduction: Slope Failures

    Types of Slope

    Causes of Failures

    Types of Failures

    Method of Analysis

    Slope stabilization

    Muhammad Azril Hezmi

  • Slope Failure

    is the movement of mass on slope

    (falls, slides, flows)

    Landslide: involves an extensive area, mild slope (

  • TYPES OF SLOPE

    Natural Slopes

    Long term process

    Short process

    Man-made Slopes

    Excavated Slopes

    Slopes of Embankment and Earth Dam

  • CAUSES OF SLOPE FAILURE

    Slope inclination

    Additional load or Fill height

    Excessive Pore water pressure

    Loss of shear strength due to

    Weathering

    Liquefaction

    Water (infiltration and seepage)

  • TYPES OF FAILURES

    Wedge Failure is the soil mass movement dueto external force. This type of failure usually occur on a weak plane or weak joint

    Circular Failure or non circular failure, Circular failure are associated with homogeneous soil conditions Non-circular slips are associated with non-homogeneous conditions

    Translational Failures occur where the form of failure is influenced by the presence of weak layer. The failure surface tends to be plane and roughly parallel to the slope surface

  • TYPES OF FAILURES

    Wedge Failure is the soil mass movement dueto external force. This type of failure usually occur on a weak plane or weak joint

  • TYPES OF FAILURES

    Circular Failure or non circular failure, the shape of failure plane maybe circular or non-circular.

    In general, circular slips are associated with homogeneous soil conditions while non-circular slips are

    associated with non-homogeneous conditions

  • TYPES OF FAILURES

    Translational Failures occur where the form of failure is influenced by the presence of weak layer. The failure surface tends to be plane and roughly parallel to the slope surface

  • Principle of Slope Stability

    Analysis

    Sliding will occur if the shear stress developed

    exceeds the corresponding shear resistance of the

    soil. In this case, failure is assumes at a certain

    plane

    W sin Rs

    Possible

    failure

    surface

    FS natural slope = 1.25 to 1.4

    FS man-made slope > 1.5

  • METHOD OF ANALYSISLIMIT EQUILIBRIUM METHODS

    Factor of safety is the shear strength at the time of failure f compared to the stress acting at that plane m.

    If FS = 1, then the slope is in critical condition.

    At the time of failure, the shear strength of the soil is fully mobilized along the failure plane. The shear strength is represented by the Mohr-Coulomb criteria:

    = cu (Total stress analysis)

    = c + tan (Effective stress analysis)

    1

    FS

    m

    f >=

  • Linear Methods: Relatively simple Infinite slope analysis Linear Failure Plane Analysis for the case of u = 0 (undrained condition) Wedge failure analysis

    Non- Linear Methods: Method of SlicesNecessary for irregular slope geometry, non-uniform soil condition, and seepagein soil.

    METHOD OF ANALYSIS

  • INFINITE SLOPE ANALYSIS

    1

    m z cos2

    z mzz

    W

    N or T or

    GWTT

    Flow net

    tan'tan'

    sincos2 satsat z

    cFS +=

  • INFINITE SLOPE ANALYSISThe shear strength along the failure plane

    The expression for , , and are

    = {(1-m) + m sat} z cos2 m = {(1-m) + m sat} z sin cos = m z w cos2

    ' tan ) - ( c' f +=

  • Substitute the above expressions to get F

    ( )m

    'tan-c'FS

    +=

    tan

    'tan

    '

    sincos z

    cFS

    sat2

    sat

    +=

    For special case where c =0, tan

    'tan

    'FS

    sat

    =

    For the case where water table is far below the failure plane (m = 0)

    tan

    'tan FS =

  • Note that when c = 0, then factor of safety is independent of the height of the slope. The slope will be stable as long as slope angle is less than the internal friction angle . If both cohesion and angle of internal friction angle is not zero, then the critical condition (FS = 1) will be achieved when

    tancos'c'

    zz2cr

    ==

    For a total stress analysis, the shear strength parameters cu and u are used with a zero value of m

  • FINITE SLOPE WITH LINEAR FAILURE PLANE

    H

    C B

    A

    W

    L

    h

    N =W cos T=W sin

    Rs

    W

    WLc

    W

    RFS s

    sin

    tancos

    sin

    +==

  • From the figure, line AC is the trial failure planeThe weight of soil (ABC) is:

    sin

    )(sinHL

    2

    1W

    =

    The force that will cause the failure is T = W sin

    and the resistance to sliding is given by Rs = cd L + W cos tand

    The factor of safety will be

    sinW

    tancosWLc

    sinW

    RFS s

    +==

  • Critical condition prevails when T = Rs.By substituting FS = 1, then

    for critical failure plane = ( + d)/2

    Substituting , we get

    And solving for H and replacing cd by c, then

    Where Hcr is the safe depth of cut and is the slope angle

    =

    ) - ( cos 1

    cos sin

    4c Hcr

    Critical Conditions

    ( )

    =d

    dd

    cossin

    )(sinsinH

    2

    1c

    ( )

    =d

    dd

    cossin

    cos1

    4

    Hc

  • Same principal valid for condition where a slope consists of two layers where the upper layer is assumed to slide along the interface between the two layers

    H D

    C

    B

    A

    W

    h

    T = Wsin N= Wcos

    Rs L

  • Circular slope failure

  • Defining a Failure surface for a toe circle

    1 211.3218.4326.5733.79

    4560

    252525262829

    353535353740

    Note: there other charts available as guidelines for finding the center of failure circle

  • zc

    R

    R B

    d

    W

    La

    Pw

    yc

    b. with tension crack

    A

    R

    R B

    d

    W

    La

    a. No tension crack

    Hydrostatic pressure in tension crack

    SLOPE WITH CIRCULAR FAILURE PLANE(homogeneous cohesive soils, fu = 0)

  • Slope in Homogeneous Cohesive soils, = 0 analysis

    FS

    c

    FS

    uf ==m

    au

    ams LFS

    cLR ==

    RLFS

    cdW a

    u=

    dW

    RLcFS au=

  • In the event of tension crack developing, then La is

    shortened and hydrostatic force will act normal to the crack

    if it is filled with water

    cw

    au

    yPdW

    R'LcFS

    +=

  • The use of Charts

    Taylors stability number

    Janbu stability charts

    Bischop and Morgenstein charts for effective stress analysis

    Morgensteins graphs for rapid drawdown

    Here we discuss the Taylors stability chart only

  • The Use of Charts, Taylors chart

    H nd H

  • METHOD OF SLICES

    In this method, the potential failure surface is assumed to be a circular arc with center O and radius r (see figure).The soil mass (ABCD) above the failure surface (AC) is divided by vertical planes into a series of slices of width b. The base of each slice is assumed to be a straight line. For any slice, the inclination of the base to the horizontal line is i and the height (measured at the centerline) is hi.

  • forces acting on a slice

    Wi

    1

    87

    6

    9

    54

    32

    Ei 1

    X i-1 Xi

    METHOD OF SLICES

    b

    h

    x

    R

  • As before,

    The factor of safety is defined as the ratio of the available

    shear strength to the shear stress acting on the plane

    The factor of safety is taken to be the same for each slice,

    implying that there must be support between slices

    (forces must act between slices)

    m

    f

    FS=

  • Forces acting on a slice are

    The total weight of the slice, W = bh The total normal force on the base: the effective

    normal force N = l and the boundary water force U = l. where u is the p.w.p. at the center of the base and l is the length of the base

    The shear force on the base, T = m l The total normal forces on the sides, E1 and E2

    The shear forces on the sides, X1 and X2

    Any external forces must be included in the analysis.

  • Assumptions must be made regarding the inter-slice forces E and X

    Taking moment about O, the sum of the moments of the shear forces T

    on the failure arc AC must be equal to the moment of the weight of

    the soil mass ABCD.

    = sin/)( WFlf

    ( )

    +=

    sin

    'tan''

    W

    NLcF

    a

    = sinRWTR

    =

    sinW

    lF

    f

    For analysis in terms of effective stress

    ( )

    +=

    sin

    'tan''

    W

    lcF or

    Where La is the arc length of AC

  • The Fellenius (Swedish) MethodFellenius assumed that the resultant of the inter-slice forces is zero, then

    N = W cos ul

    Hence the factor of safety in terms of effective stress is given by:

    The components W cos and W sin can be determined graphically while angle a can be calculated or measured

    For analysis in terms of total stress parameter or u = 0, then

    sinWF

    = au Lc

    ( )( )

    +=

    sin

    'tancos'

    W

    lWlcFm

  • The Bischop (Routine) MethodBischop assumed that the resultant of the inter-slice forces are horizontal i.e. X1 X2 = 0, then

    )'tanN'l(c'F

    1T +=

    Resolving forces in the vertical direction:

    sintanF

    N'sin

    F

    lc'cosulcosN'W ' +++=

    +

    =

    F

    luF

    lcW

    N

    sin'tancos

    cossin'

    ' By replacing l = b secaAnd after some rearrangementWe obtain:

  • ( ){ } ( )

    ++

    =

    FaubWbc

    aWFS

    /'tantan1

    sec'tan'

    sin

    1

    By replacing ru = u/h = u/(W/b) then:

    ( ){ } ( )

    ++

    =

    FarWbc

    aWFS u

    /'tantan1

    sec'tan1'

    sin

    1

    The Bischop (Routine) Method (contd)

  • Since F appear in both sides of the equation, then use trial and error.

    To simplify the calculation, the following chart could be used

    +=F

    ' tantan 1 cos m

    aa

    a

    The Bischop (Routine) Method (contd)

    ( ){ }

    +

    =a

    um

    rWbcaW

    FS1

    'tan1'sin

    1

    Then

  • To get FS from the equation,

    can use computer program or

    graph 1. Assume F right = 1, find m

    2. Find F left 3. Take the average of F

    right and F left 4. Use this average F,

    find m5. Find new F left6. Repeat steps 3 and 4

    until the difference between F right and F left is small enough (0.01)reroute to excell program for Bischop

  • COMMENT ON SLICES METHODS

    Due to repetitive nature of the calculations and the need

    to select the most critical failure surface, the method

    of slices in particularly suitable for solution by

    computer. More complex geometry and soil strata can

    be introduced.

    There are other methods of slices as shown in the following

    Table. These methods use different assumption on inter-

    slices forces.

  • Slices methods of analysis frequently used in practice.

    MethodForce

    equilibriumMoment

    equilibriumShape of slip surface

    Ordinary method of slices (Fellenius, 1927)

    Does not satisfy horizontal or vertical forces equilibrium

    Yes. Circular

    Bishops Modified (Bishop, 1955)

    Satisfy vertical force but not horizontal force equilibrium

    Yes. Circular only. Non circular may have numerical problems.

    Janbus simplified method(Janbu, 1956)

    Yes No Any shape. More frequent numerical problems than other methods

    Morgenstern and Price (Morgenstern and Price, 1965)

    Yes. Permits side forces to be varied

    Yes. Any shape.

    Spencers Method (Spencer, 1967)

    Yes. Side forces are assumed to be parallel

    Yes. Any shape.

  • ASSIGNMENT 1:

    SLOPE STABILITY ANALYSIS Pick a problem and the CD + manual

    Analyze the problem using SLOPE/W student version (in this case you can use Bischop, Janbu or GLE methods available for Student version).

    Find the slip surface that gives the lowest factor of safety (critical failure surface)

    Sketch of your slope in graph paper and trace the critical failure surface you obtained from SLOPE/W on your graph

    Use method of slices to calculate the factor of safety either using Bischop or Fellenius method (you may make use of Excell for your calculation).

  • ASSIGNMENT 1:

    SLOPE STABILITY ANALYSISDiscuss the results and write a report (Group). The report should include

    Introduction (the problem)

    Results of SLOPE/W output including contour of FS and the critical failure

    surface + analysis of 1 slice

    Results of your manual calculation (with the help of Excell program)

    Discussion and comparisons