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A hypoplastic model for clay and sand

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Abstract

The theory of hypoplasticity was developed initially for non-cohesive soils. However, sand and clay have many common properties; therefore arose the idea to extend the hypoplastic model to clay. The proposed model is able to describe the behaviour of cohesive soils with the incorporation of an appropriate structure tensor into the constitutive equation. This tensor is a stress-like internal parameter, also called back stress. This enables us to describe the behaviour of cohesive soils with the same material parameters for several states of consolidation and also to model barotropy and pycnotropy of sand. Numerical simulations of element tests are performed in order to check the performance of this hypoplastic model. Experimental data obtained with normally and overconsolidated clay and sand specimens with various densities are taken for comparison, and it is shown that the model is capable of describing the material behaviour of clay and sand. The determination of the material constants, the calibration method, is also presented in this paper.

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Notes

  1. This can be avoided with some modifications, which, however, cause other shortcomings, cf. [6].

  2. With T as the only state variable, cohesion can be modelled by replacing the stress tensor T by the modified stress T − k 1 with constant k [2].

  3. Note that anisotropic stress states can emerge (e.g. due to oedometric consolidation) from a hydrostatic initial S.

  4. The dilatancy angle β is defined as: tanβ is the slope of the curve in the volumetric strain versus axial strain diagram.

Abbreviations

T :

Stress tensor

T * :

Deviatoric part of stress tensor

D :

Stretching tensor

W :

Spin tensor

\(\hat{{{\mathbf{T}}}}\) :

Normalised stress tensor

\(\hat{{{\mathbf{T}}}}^{*}\) :

Normalised deviatoric stress tensor

\({\mathop{{\bf T}}\limits^{\circ}}\) :

Objective stress rate

S :

Structure tensor

S * :

Deviatoric part of structure tensor

p ref :

Reference stress

β:

Barotropy exponent

f b :

Barotropy factor

f b :

Factor of barotropy

f e :

Factor of pycnotropy

f d :

Factor of pycnotropy

a :

Parameter of limit condition

F :

Stress function according to Matsuoka/Nakai

e :

Void ratio

e c :

Critical void ratio

e d :

Minimum void ratio

e i :

Maximum void ratio

φ c :

Critical friction angle

OCR:

Overconsolidation ratio

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Acknowledgment

This paper is a partial research result of the first author which was financially supported by the Austrian Science Fund (FWF), Grant No. 14969, which is thankfully acknowledged, and supervised by the second author.

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  1. Unit of Geotechnical and Tunnel Engineering, Institute of Infrastructure, Technikerstr. 13, 6020, Innsbruck, Austria

    T. Weifner & D. Kolymbas

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  1. T. Weifner
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  2. D. Kolymbas
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Correspondence to T. Weifner.

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Weifner, T., Kolymbas, D. A hypoplastic model for clay and sand. Acta Geotech. 2, 103–112 (2007). https://doi.org/10.1007/s11440-007-0031-2

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