Bounding Cam Clay

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This command is used to construct a multi-dimensional bounding surface Cam Clay material object after Borja et al. (2001).

nDMaterial BoundingCamClay $matTag $massDensity $C $bulkMod $OCR $mu_o $alpha $lambda $h $m

$matTag	integer tag identifying material
$massDensity	mass density
$C	ellipsoidal axis ratio
$bulkMod	initial bulk modulus
$OCR	overconsolidation ratio
$mu_o	initial shear modulus
$alpha	pressure-dependency parameter (should be greater than or equal to zero)
$lambda	soil compressibility index for virgin loading
$h	hardening parameter
$m	hardening parameter

The material formulations for the BoundingCamClay object are "ThreeDimensional" and "PlaneStrain"

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Code Developed by Chris McGann & Pedro Arduino, at the University of Washington

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General Information

This nDMaterial object provides the bounding surface plasticity model of Borja et al. (2001) in which the bounding surface model is represented using modified Cam-Clay theory (Schofield and Wroth 1968). In addition to the standard capabilities of the Cam-Clay family of models (e.g., pressure dependence, hardening with plastic volumetric contraction, softening with plastic dilation, and coupled deviatoric and volumetric plastic deformation), the Borja et al. (2001) model has been enhanced to include an anisotropic bounding surface formulation that allows for consideration of hysteretic behaviour under cyclic loading. This bounding surface Cam-Clay model is coupled with a nonlinear hyperelastic model that considered pressure-dependency in the bulk and shear modulus. The full theory of this model is discussed in great detail in Borja et al. (2001).

Notes

• The ellipsoidal axis ratio parameter $C is defined such that the ellipsoidal surfaces are C times as wide in the deviatoric direction as they are along the hydrostatic axis. When $C = 1, the surfaces are spherical.

• The overconsolidation ratio (input parameter $OCR) defines the relationship between the loading surface and bounding surface. The radius of the bounding surface, R, is equal to the product of the OCR and the radius of the loading surface, r. When the soil is normally consolidated and $OCR = 1, the bounding and loading surfaces are coincident and virgin loading will occur.

References

Borja, R.I., Lin, C.-H., and Montans, F.J. (2001) 'Cam-Clay plasticity, Part IV: Implicit integration of anisotropic bounding surface model with nonlinear hyperelasticity and ellipsoidal loading function,' Computer Methods in Applied Mechanics and Engineering, 190(26), 3293-3323, doi: 10.1016/S0045-7825(00)00301-7.

Schofield, A. and Wroth, P. (1968) Critical State Soil Mechanics, McGraw Hill, New York.

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