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    Installation Effects in Geotechnical Engineering Hicks et al. (eds) 2013 Taylor & Francis Group, London, ISBN 978-1-138-00041-4

    large deformation analysis of cone penetration testing in undrained clay

    l. BeuthDeltares, Delft, The Netherlands

    P.a. VermeerDeltares, Delft, The Netherlands University of Stuttgart, Germany

    aBstract: cone penetration testing is a widely-used in-situ test for soil profiling as well as estimating soil properties of strength and stiffness. In this paper, the relationship between the undrained shear strength of clay and the measured cone tip resistance is investigated through numerical analysis. such analyses serve to refine and establish correlations between cone penetration testing measurements and soil properties; thus enabling more reliable predictions of soil properties. the presented analyses are performed by means of a Material Point Method that has been developed specifically for the analysis of quasi-static geotechnical problems involving large deformations of soil. Both, the load-type dependency of the shear strength of undrained clay as well as the influence of the anisotropic fabric of natural clay on the undrained shear strength are taken into account through a new material model, the anisotropic Undrained clay model. results indicate that the deformation mechanism relevant for cone penetration in undrained normally-consolidated clay differs significantly from predictions based on the tresca model, but resulting cone factors appear to be useful.

    deformation processes imposed by the cone on the surrounding soil. Because the cone is pushed into the ground with a constant rate of penetra-tion of 2 cm/s, inertia and damping effects can be neglected. thus, the considered problem full-fills the requirements of quasi-static analysis. the method used in this study, the quasi-static Material Point Method (MPM), has been developed specifi-cally for the analysis of such problems.

    furthermore, the non-linear stress-strain rela-tionship of undrained clay must be considered. When using the well-known elastic-plastic tresca material model for such analyses, su is specified as the cohesion parameter of the model. such com-putations assume an undrained shear strength that is independent of the loading path. Generally, an undrained shear strength obtained from simple shear tests is used as a kind of average for such simplifed analyses.

    although the widely-used Mohr-coulomb model does predict a higher undrained shear strength for triaxial compression than for triaxial extension, it overpredicts the magnitudes of both undrained shear strengths, at least for normally-consolidated clays. In order to reproduce the mag-nitudes of undrained shear strengths for triaxial

    1 IntroDUctIon

    the undrained shear strength of soil, su, represents no unique soil parameter, but largely depends on the type of loading. for normally-consolidated clays, the undrained shear strength found for tri-axial compression is for instance much larger than the strength found for triaxial extension. simple shear tests render an undrained shear strength that lies in between the strength values obtained for triaxial compression and extension. this has to be taken into consideration when using this param-eter in geotechnical analyses. When deriving an undrained shear strength from cone penetration measurements of tip resistance, qc, it is important to know which undrained shear strengths domi-nate the failure mechanism found during cone penetration testing.

    In this paper, results of numerical analyses of cone penetration testing (cPt) in normally-con-solidated undrained clay are presented to provide new insight into the mechanical processes that occur during a cone penetration test.

    an accurate computation of the stress field that evolves in the vicinity of the penetrating cone requires one to take into account the complex large

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    compression and extension more accurately, a model based on critical state soil mechanics such as the well-known Modified cam clay model might be used. this model takes into account the shear-induced volume change of drained clay (schofield & Wroth 1968). Indeed, for normally-consolidated clay as considered in this paper, this model correctly predicts lower undrained shear strengths for triaxial compression and extension than the Mohr-coulomb model.

    Due to the deposition process of clay, natural clay generally shows a different strength in hori-zontal directions than in the vertical direction. In order to further increase the accuracy of cPt analyses, this anisotropic strength of clay must also be taken into consideration. therefore, the aniso-tropic Undrained clay (aUc) model is used in the presented analyses.

    It implements the theory of critical state soil mechanics and also considers the strength anisot-ropy of natural clay (Vermeer et al. 2010; Beuth 2012). It is largely based on the s-claY1 model developed by (Wheeler et al. 2003) but consid-ers neither density and rotational hardening nor softening.

    to the authors knowledge, usage of a quasi-static MPM in combination with the aUc model for cPt analysis exceeds the accuracy of numerical studies reported so far in literature, such as (Van den Berg 1994) and (lu et al. 2004).

    In the following section, the used numeri-cal method will be introduced briefly. a detailed description of it would exceed the scope of this paper. for further information, the reader is there-fore referred to (Beuth et al. 2007; Vermeer et al. 2009; Beuth et al. 2011) and (Beuth 2012). the con-stitutive modelling of undrained clay is treated in section 3. subsequently, the geometry and discreti-sation of the performed numerical analyses are pre-sented in section 4. In section 5, results obtained for the analysis with the aUc model are compared to results for the tresca model. the paper ends with an outlook on possible future work.

    2 QUasI-statIc MatErIal PoInt MEthoD

    the quasi-static MPM can be considered as an extension of the classical Updated lagrangian finite Element Method (Ul-fEM). With the Ul-fEM, a solid body is discretised by finite elements that follow the deformations of the solid body. In case of large deformations of the solid body, the finite element grid might eventually experi-ence severe distortions which lead to numerical inaccuracies and can even render the calculation impossible.

    the Material Point Method discretises a solid body by means of a cloud of material points that move through a fixed finite element grid. thereby, the material points capture the arbitrary large deformations of the solid body without the occur-rence of severe deformations of the finite elements. Material and state parameters of the solid body as well as applied loads are stored in material points whereas the mesh does not store any permanent information.

    With the MPM, the underlying finite element grid is used as with the Ul-fEM to solve the sys-tem of equilibrium equations for an applied load increment on the basis of those finite elements that contain material points at the considered loading step. once displacement increments are mapped from nodes to material points, once strain incre-ments are computed at the locations of material points, the mesh is usually reset into its original state. It might be changed arbitrarily.

    obviously, the finite element grid used with the MPM must cover not only the solid in its initial con-figuration as with the Ul-fEM but the entire region of space into which the solid is expected to move.

    It should be emphasised, that in contrast to mesh-less lagrangian methods such as the Dis-crete Element Method, the material points repre-sent subregions of a solid body and not individual particles such as sand grains. the mass and volume of subregions is memorised with material points, but changes in the shape are not traced.

    With one exception (Guilkey & Weiss 2003), existing implementations of the MPM are dynamic codes that employ an explicit time integration scheme (sulsky et al. 1994; Wi eckowski et al. 1999; coetzee et al. 2005). Using these codes for the analysis of quasi-static problems is computation-ally inefficient as explicit integration requires very small time steps. the quasi-static MPM makes use of an implicit integration scheme and thus circum-vents the limitation on step size of dynamic codes.

    In recent years, the quasi-static MPM has been validated with numerous geotechnical benchmark problems. furthermore, it has been extended by a contact formulation for modelling reduced frictional or adhesive contact between structure and soil based on interface elements (Vermeer et al. 2009).

    3 constItUtIVE MoDEllInG

    3.1 Modelling of undrained elasticity

    the total mean stress rate of the undrained soil is split into the effective mean stress rate, p , and the change of excess pore pressures, pw, through con-sideration of strain compatibility between the two materials

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    pK

    np Kw = =

    watervol voland

    (1)

    where Kwater is the bulk modulus of water, n is the porosity and K is the bulk modulus of the soil skeleton. the term Kwater/n can be written as

    Kn

    v vv v

    Kuu

    water = ( )

    ( ) + ( ) 3

    1 2 1

    (2)

    where vu is an undrained Poisson ratio and v the effective Poisson ratio of the soil skeleton. Incompressibility of the soil implies vu being close to 0.5. In this paper, it is taken to be 0.49 for the computation with the tresca model and 0.495 for the computation with the aUc model. the effective Poisson ratio is assumed to be v = 0.25 and the Youngs modulus is E = 6 MPa. this yields K = 4 MPa and Kwater/n = 110 MPa for vu = 0.49 and 235 MPa for vu = 0.495. It should be noted that elastic behaviour (inside the yield surface) is assumed to be isotropic a