Strain accumulation in sand due to cyclic loading: drained triaxial tests

Our aim is the prediction of the accumulation of strain and/or stress under cyclic loading with many (thousands to millions) cycles and relatively small amplitudes. A high-cycle constitutive model is used for this purpose. Its formulas are based on numerous cyclic tests. This paper describes drained tests with triaxial compression and uniaxial stress cycles. The influence of the strain amplitude, the average stress, the density, the cyclic preloading history and the grain size distribution on the direction and the intensity of strain accumulation is discussed.     

On hyperelasticity for clays

Under purely elastic conditions a constitutive model for clays should be conservative. This can be achieved by using a hyperelastic stress–strain relation derived from an elastic potential. To circumvent problems connected with formulation of a suitable potential a simple concept of back-stress elasticity is proposed. Several elastic models are critically reviewed, two of which had been originally incorrectly classified as hyperelastic. A novel elastic potential which can be used to generate various hyperelastic models is proposed. Its salient feature is that the resulting stiffness is a homogeneous function of order 1 with respect to stress. An example of Mathematica calculation with tensorial differentiation is enclosed (Wolfram S. Mathematica. A system for doing mathematics by computer. Addison-Wesley Publishing, 1988). ©     

Pure cross-anisotropy for geotechnical elastic potentials

The pure cross-anisotropy is understood as a special scaling of strain (or stress). The scaled tensor is used as an argument in the elastic stiffness (or compliance). Such anisotropy can be overlaid on the top of any elastic stiffness, in particular on one obtained from an elastic potential with its own stress-induced anisotropy. This superposition does not violate the Second Law. The method can be also applied to other functions like plastic potentials or yield surfaces, wherever some cross-anisotropy is desired. The pure cross-anisotropy is described by the sedimentation vector and at most two constants. Scaling with more than two purely anisotropic constants is shown impossible. The formulation was compared with experiments and alternative approaches. Static and dynamic calibration of the pure anisotropy is also discussed. Graphic representation of stiffness with the popular response envelopes requires some enhancement for anisotropy. Several examples are presented. All derivations and examples were accomplished using the algebra program Mathematica.

     

Separation of time scales in the HCA model for sand

Separation of time scales is used in a high cycle accumulation (HCA) model for sand. An important difficulty of the model is the limited applicability of the Miner’s rule to multiaxial cyclic loadings applied simultaneously or in a combination with monotonic loading. Another problem is the lack of simplified objective HCA formulas for geotechnical settlement problems. Possible solutions of these problems are discussed.     

Anisotropic visco-hypoplasticity

Apart from time-driven creep or relaxation, most viscoplastic models (without plastic and viscous strain separation) generate no or a very limited accumulation of strain or stress due to cyclic loading. Such pseudo-relaxation (or pseudo-creep) is either absent or dwindles too fast with increasing OCR. For example, the accumulation of the pore water pressure and eventual liquefaction due to cyclic loading cannot be adequately reproduced. The proposed combination of a viscous model and a hypoplastic model can circumvent this problem. The novel visco-hypoplasticity model presented in the paper is based on an anisotropic preconsolidation surface. It can distinguish between the undrained strength upon triaxial vertical loading and horizontal loading. The strain-induced anisotropy is described using a second-order structure tensor. The implicit time integration with the consistent Jacobian matrix is presented. For the tensorial manipulation including numerous Fréchet derivatives, a special package has been developed within the algebra program MATHEMATICA (registered trade mark of Wolfram Research Inc.). The results can be conveniently coded using a special FORTRAN 90 module for tensorial operations. Simulations of element tests from biaxial apparatus and FE calculations are also shown.     

Shear banding in geomaterials under extensional plane strain conditions: Physical and analytical model

The shear band (SB) spacing phenomenon in geomaterials is addressed in this paper under plane strain extensional conditions. On the basis of sand box observations, a method is proposed for the prediction of the spacing between shear bands based on the so-called “bookshelf” deformation mechanism. The proposed method is based on the assumption that the material is softening inside the shear bands whereas outside the SB it undergoes elastic unloading. The underlying assumption for the prediction of SB spacing is that the material reaches the lowest possible energy rate. An analytical expression for the determination of the shear band spacing is presented taking into account the plane strain extensional deformation of the specimen. The friction due to the normal off-plane shear acting on the boundaries is then taken into account.     

Paraelasticity

A 3D hysteretic, fully reversible constitutive model with rate-independent damping and with variable secant stiffness is proposed. A reversible dilatancy–contractancy effect is an optional feature as described in the companion paper (Niemunis et al. in Acta Geotech, 2011). The present paper describes the basic aspects of the model only. A strain path reversal is defined, and a treatment of the past reversals using a stack structure is proposed.     

An averaging procedure for layered materials

In order to model thin‐layered soils a special averaging procedure is proposed. It works with very few restrictions imposed on the constitutive equations used for individual materials. General considerations are followed by an example from open pit mining industry. Geometrical non‐linearity is considered. The proposed method is not necessarily restricted to the problems of soil mechanics. It could also be applied on composite materials. Copyright © 2000 John Wiley & Sons, Ltd.     

Pure elastic stiffness of sand represented by response envelopes derived from cyclic triaxial tests with local strain measurements

Acta Geotechnica - The elastic stiffness of a fine sand at small to moderate strains ( $$\varepsilon \le 2 \times 10^{-4}$$ ) has been studied based on cyclic triaxial tests on cube-shaped samples...