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

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.Karlsruher Institut für Technologie (KIT) (4220

The soilmodels.info project

The paper describes the soilmodel.info project to disseminate constitutive models among FE codes' users