August 2011 c ZACE Services Ltd - ??Modi ed Cam-Clay (MCC) c ZACE Services Ltd August 2011 1/62...

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Transcript of August 2011 c ZACE Services Ltd - ??Modi ed Cam-Clay (MCC) c ZACE Services Ltd August 2011 1/62...

  • Advanced model for soft soils.Modified Cam-Clay (MCC)

    cZACE Services Ltd

    August 2011

    1 / 62

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  • MCC: Yield surface

    F (,pc) = q2 + M2c r

    2() p (p pc) = 0

    -1

    -2-3

    rc

    rt

    = /6

    = +/6

    Tensile meridian

    Compression meridian

    = 0

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    The yield surface has a form of an ellipse in the p q plane. It is closedin all directions for stress paths that are generated in isotropic oroedometric compression, direct shear or triaxial laboratory tests. Due tothis one may easily reproduce most of the basic phenomena andnonlinearities in soil behavior but with limitation to monotonic loads.The size of the yield surface is not fixed in 1 2 3 space and it ischaracerized by a parameter called preconsolidation pressure pc . Thispressure increases once soil densifies for all stress paths that are goingoutside the surface but below the critical state (wet side) line inclined atangle 1 : M. For stress paths that remain on the critical state line (atlimit state) there is no volumetric plastic strain produced hence soil doesnot densify nor dilates. On the other hand for overconsolidated soilsstress paths may hit the yield surface above the critical state line (dryside) and therefore dilative plastic strains are produced and yield surfacemay shrink. In the deviatoric plane (the intersection perpendicular to thep axis) the shape of the MCC surface is not circular as in the originalmodel but it exhibits so called strength anisotrophy (like classicalMohr-Coulomb criterion). This effect is crucial in correct predictions ofbearing capacities and safety factors. This strength anisotrophy ismanaged through function r(..) following the formula proposed by vanEkeelen. So the model is an elasto-plastic one with an associative plasticflow rule and a hardening/softening mechanism.

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  • MCC: Isotropic compression test and pc

    evolution law

    e

    1

    1

    Virgin consolidation line

    Swelling line

    p(t=0) ln(p)ln(pco)

    dpc

    = 1 + eo

    pc

    dpkk

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    The role of the hardening law is to describe (in incrementalmanner) the relation between the hardening parameter pc andplastic volumetric strain. In order to identify this relation one hasto perform an isotropic compression test and to plot the result ine-ln(p) axes. By doing this we can observe that the virgin loadingand unloading paths, for soft cohesive soils, become stright lines.This allows us to identify the hardening law. For small strains wecan assume that de = (1 + eo) dv (compressive strains arenegative). So we can imagine that starting from a certain point onvirgin loading path let say p(to) e1 we perform a stress cycle byan increment of p continuing the virgin loading and then weperform unloading with same increment p. The virgin andunloading branches can be described by the formulae = eo ln(p) , e = eo ln(p). So let us compute

    increments of de and de (de = p

    dp, de = p

    dp. Their

    difference will exactly be the plastic change of the void ratio hence

    dep = de de = ( ) 1p

    dp. The last step is to say that in

    isotropic compression p = pc and the hardening law is identified. 6 / 62

  • MCC: Setting material properties

    Material properties: , , , Mc , k

    Initial state : pco

    , OCR

    Restrictions:

    0 < < Mc > 0

    0.5 < k 1 and such that ( =k

    1n 1

    k1n + 1

    ) 0.7925

    minimum value of pco> 0 and OCR 1.00

    eo 00 0.49999

    Remarks:

    0 may yield convergence problem

    k=1 (as in the original version of the model will always significantlyoverestimate ultimate limit load or safety factors; hence using default setting forthe k parameter is advised

    the parameter can be estimated as = 0.36 (LL 0.09) with liquid limitdenoted by LL (Schoefield and Wroth 1968

    MC can be estimated based on value of the residual friction angle as

    MC =6sin()

    3 sin()7 / 62

    The and parameters can be identified based on isotropiccompression test but also on oedometric test as well. In both testsslopes and are the same.

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  • MCC: Setting the initial effective stresses 0

    Input files:mcc-slope-initstate1init-state-mohr-coulomb-siggiven

    The MCC model, contrary to CAP model, requires aninitial guess for the initial effective stress state to be setby the user

    In the initial state computation hardening is deactivatedand MCC behaves as classical elasto-plastic model withdeviatoric flow rule

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    Notice that once the unloading branch, that we assume does notproduce any plastic strains, is linear in e-ln(p) axes the soil stiffnessmust depend on the effective stresses. The bulk modulus is

    expressed as K =1 + eo

    p. So every computation with that

    model (also HSs) will require to set up the initial guess forthe initial effective stress no matter whether the initial statedriver is active or not.

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  • MCC: Setting 0

    hy=-h

    x= -Koh

    Clay deposits Natural slopes

    How can we guess the initial stresses in that case?

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    Setting the initial effective stresses can be made exclusively at theFE level through the Initial conditions/Initial stresses.

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  • MCC: Setting 0

    12

    3 4

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    To define the initial stresses in quadrilateral regions (covering ourFE mesh) we can set all stress components at each vertexseparately or we can use a simplied method where we fix thevertical stress at the top and we define the in situ Ko coefficientand soil unit weight that will produce correct o . Note that byrunning the Initial State driver and assuming Ko coefficient locallyat the material level we do not need to be very precise when weguess the initial in situ stress state. The driver will corect itanyway.

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  • MCC: Setting 0

    1

    2

    3 4

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    The previous comment applies to the case of inclined part of theslope.

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  • MCC: Setting 0

    Let us compare results obtained for cohesionless soil using standardM-C model and MCC

    First we run standard M-C model with (Ko = 0.5 defined atthe material level

    Then we run MCC with the initial guess for the initial stresses

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  • MCC: Setting 0: Results for x

    1 MCC

    2 M-C

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    MCC: Setting 0: Results for x

    1 MCC

    2 M-C

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  • MCC: Setting 0: Results for y

    1 MCC

    2 M-C

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    MCC: Setting 0: Results for y

    1 MCC

    2 M-C

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  • MCC: Setting 0: Results for xy

    1 MCC

    2 M-C

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    MCC: Setting 0: Results for xy

    1 MCC

    2 M-C

    24 / 62

  • MCC: Setting initial preconsolidation pressure pco

    pco

    , like o is not a material parameter but rather an initialstate parameter and it is a function of x,y,z coordinates

    Once the initial stress state is defined we can set pco

    by usingthe definition of the overconsolidation ratio OCR (OCR > 1)

    The OCR=1 condition is equivalent to the state of normalconsolidation and OCR > 1 corresponds to the state ofoverconsolidation

    If the Initial state driver is activated then the resulting in situstress state o is taken to set the initial pco , otherwise userprescribed o is used

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    The initial pc parameter is not a material parameter but rather aninitial state one like the in situ stresses. The most common way todefine the initial preconsolidation stress is to set up the OCR valuethat can be estimated based on CPTU test (refer to our report onHSs model to find more information or try to use parameterestimation for HSs model to reuse part of the data).

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  • MCC: Setting initial preconsolidation pressure pco

    Let us assume that we know the initial stress state o

    q

    p

    1M

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    This plot shows the result of the Initial State driver at a givenGauss point in a given finite element. As we can see in the initialstate computation the MCC ellipse is deactivated and model workslike a standard Mohr-Coulomb but with a nonlinear elasticstiffness. This way all stress points must stay below the criticalstate line (CSL).

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  • MCC: Setting initial preconsolidation pressure pco

    From the equation of the yield surface for given MC and kparameters we can compute pc1 such that F (o, pc1 = 0)

    q

    p

    1M

    pc1

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    At the final stage of the Initial State driver we know the in situeffective stresses o at each point in the mesh. The first step is toposition the MCC ellipse such that the stress point remains on theyield surface. This corresponds to the state of normal conslidation(OCR=1). This step is done internally in the code.

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  • MCC: Setting initial preconsolidation pressure pco

    Compute: pc2 = OCR pc1

    The initial pco is set to: pco = max (pcomin, pc2)

    q

    p

    1M

    pc2

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    The second step corresponds to final size adjustement of the MCCellipse based on assumed OCR value and computed initial stresses.From now on the initial ellipse size is adjusted.

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  • MCC: using with Stability driver

    In the case of stability analysis the SF factor scales directlythe critical slope MC while hardening is disabled.

    Stability analysis is run enforcing the nonassociated purelydeviatoric flow rule

    In this method it may happen that the current safety factorcan be smaller than 1.0 (due to overconsolidation effect).

    For that reason it is recommended to start safetyanalysis with the initial safety factor smaller than 1