Bishop parameter χ\chi from static equilibrium

For unsaturated soils, Terzaghi’s effective stress σ=σ$^{tot}$−u has been generalized by Bishop to the form σ$^{B}$=σ$^{tot}$−$\chi$u. Factor $\chi$, for example $\chi$(S)≈S, takes into account the degree of saturation S. However, σ$^{B}$ is unable to characterize strength and deformation of soil unless applied with suction. A new stress σ$^{E}$=σ$^{tot}$−$\chi$Eu with $\chi$$^{E}$(S,n) is proposed. It is likewise insufficient if applied without suction, but it has (at least) a clear physical meaning: σ$^{E}$ represents contact forces between grains in the static equilibrium in the same manner as the effective stress does in saturated soils. All grains must be entirely surrounded by free or capillary water

Removal of the membrane penetration error from triaxial data

Most triaxial tests are fraught with substantial membrane penetration errors. A simple correction procedure for data obtained from various tests is proposed. Correction formulas for the membrane penetration error have been derived for different types of tests including not perfectly saturated soils. In particular, a correction of the undrained cyclic stress paths is presented in detail. It is demonstrated that the correction for the membrane penetration error is indispensable for a realistic estimation of the cyclic resistance ratio in coarse- and mediumgrained liquefiable soils. A MATHEMATICA code for the correction of laboratory data is given. An analogous MATLAB code is available from the authors. Without the correction many results could lie far on the unsafe side. This is the case especially for the undrained cyclic loading

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

Residual deformations due to long-time cyclic loading with two dimensional strain loops

A cyclic loading with multidimensional strain loops in the soil may be caused by traffic loading, by wind and wave loading (e.g. offshore wind turbines) or by earthquake shaking. The present paper focuses on the accumulation of permanent deformations due to a high-cyclic loading, that means a loading with many cycles of small to intermediate strain amplitudes. Two different strategies for the consideration of multidimensional strain loops in a high-cycle accumulation model are presented. Experimental evidence for the first strategy is provided. However, it is suitable for convex strain loops only. The second strategy can handle also non-convex strain loops, but has not been confirmed experimentally yet. The paper discusses suitable experiments for such prove and documents some preliminary test series

Stress- and Strain-Controlled Undrained Cyclic Triaxial Tests on a Fine Sand for a High-Cycle Accumulation Model

The paper presents a discussion of the isotropic elastic stiffness E in the high-cycle accumulation (HCA) model proposed by Niemunis et al. (2005). The model may be used to predict permanent deformations or excess pore water pressures in non-cohesive soils due to cyclic loading. The stress-dependent bulk modulus K was determined from pairs of drained and undrained cyclic triaxial tests on a fine sand with constant stress amplitude and with similar initial conditions. K was found in good agreement with an earlier study on a medium coarse sand where a correction for membrane penetration effects had to be applied. Undrained cyclic triaxial tests with constant strain amplitude commenced at an anisotropic initial effective stress were performed for Poisson’s ratio ν. It is demonstrated that ν does not depend on amplitude, density and initial pressure. Its increase with the initial stress ratio may be disregarded for practical purposes

Characterization of the material response in the granular ratcheting

The existence of a very special ratcheting regime has recently been reported in a granular packing subjected to cyclic loading \cite{alonso04}. In this state, the system accumulates a small permanent deformation after each cycle. After a short transient regime, the value of this permanent strain accumulation becomes independent on the number of cycles. We show that a characterization of the material response in this peculiar state is possible in terms of three simple macroscopic variables. They are defined that, they can be easily measured both in the experiments and in the simulations. We have carried out a thorough investigation of the micro- and macro-mechanical factors affecting these variables, by means of Molecular Dynamics simulations of a polydisperse disk packing, as a simple model system for granular material. Biaxial test boundary conditions with a periodically cycling load were implemented. The effect on the plastic response of the confining pressure, the deviatoric stress and the number of cycles has been investigated. The stiffness of the contacts and friction has been shown to play an important role in the overall response of the system. Specially elucidating is the influence of the particular hysteretical behavior in the stress-strain space on the accumulation of permanent strain and the energy dissipation.Comment: 13 pages, 20 figures. Submitted to PR

A comparative study of different model families for the constitutive simulation of viscous clays

The simulation of the viscous behavior of some clays is of high importance in many geotechnical problems. The literature offers a vast amount of constitutive models able to simulate the rate dependence observed on these materials. Although most of thesemodels are calibrated to very similar experimental observations and share similar definitions ofmaterial parameters, some discrepancies of their response have been detected, which are related to their mathematical formulations. In this work, the causes of these discrepancies are carefully studied. To that end, four different model families are analyzed, namely, nonstationary flow surface (NSFS) models, viscoplasticity with overstress function (OVP), viscoplasticity with Norton\u27s power law (NVP), and visco-hypoplasticity (VHP). For the sake of a fair comparison, single constitutive models using the same set of material parameters, and following other requirements, are developed for each model family. Numerical implementations of the four resulting models are performed. Their response at different tests are carefully analyzed through simulation examples and direct examination of their constitutive equations. The set includes some basic tests at isotropic stress states and others as responses envelopes, undrained creep rupture, and an oedometer test with loading, unloading-reloading, creep, and relaxation. The article is concluded with some remarks about the observed discrepancies of these model families