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Constitutive Models for Agricultural Soils
Published in Jie Shen, Radhey Lal Kushwaha, Soil-Machine Interactions, 2017
Two-dimensional cases are of two classes: plane stress and plane strain. Suppose that we investigate stresses on an infinitesimal rectangular element in the x-y plane, as shown in Fig. 3.2. Plane stress means that there are no forces out of the plane, that is, σzz, σxz, and σyz equal to zero; Plane strain means that no displacements occur out of the plane, that is, stresses σxz, σyz and strain εzz equal zero, but stress σzz does not vanish. Even though σzz is non-zero in plane strain cases, the condition εzz = 0 may be used to determine σzz based upon σzz, σyy and some other material parameters. Hence, we can process σzz separately and equation (3.1) shrinks into: () σ=[σxxσxyσxyσyy]
Basic geotechnical concepts
Published in Robin Chowdhury, Phil Flentje, Gautam Bhattacharya, Geotechnical Slope Analysis, 2009
Robin Chowdhury, Phil Flentje, Gautam Bhattacharya
In usual triaxial compression tests, two principal stresses (minor and intermediate) are equal. In extension tests, the major and intermediate principal stresses are equal. Apart from usual triaxial apparatus, tests may be carried out in plane strain compression apparatus so that strain is not allowed in one of the directions. These tests have been successfully carried out at many research centres in UK, USA and elsewhere. In these tests the intermediate principal stress has a magnitude which is determined by the soil properties and is not equal to either the major or the minor principal stress. Plane strain compression tests are better than triaxial compression tests in simulating deformation conditions in the field. The deformation of long soil structures, such as embankments, slopes, earth dams and retaining walls, is considered to approximate to plane strain. In all such cases, the strain in the direction of length or the axis is regarded as negligible or zero.
Plasticity theory for granular materials
Published in I. Vardoulakis, J. Sulem, Bifurcation Analysis in Geomechanics, 1995
In many geo-engineering applications ‘long’ structures are studied (e.g. embankments, earth dams, tunnels, etc.) which suggests investigating the material behavior under plane-strain conditions. Accordingly, the behavior of the granular material in plane-strain deformations is of certain interest, and the following sections will focus on this subject. Ideally, for the analysis of plane-strain problems one should use data from plane-strain tests as well. However, such data are usually not readily available, and the behavior of the considered material under plane-strain conditions must be inferred theoretically from provided triaxial test data. In the previous sections we saw that we may have to select between competing models, e.g. the M.-C./D.-P. model (M.-C. yield surface and D.-P. plastic potential surface), and the M.-C./M.-C. model. The M.-C./M.-C. model is more attractive from the engineering application point of view, since in this case the concepts of friction and dilatancy are the same for all values of the intermediate principal stress and we do not have to distinguish, for example, between friction angle in compression, in extension and plane strain. In other words, within the M.-C./M.-C. model ϕm and ψm depend only on the initial porosity, and the accumulated plastic strain gp, and not on the value of the intermediate principal stress σ3.
Stability analysis of crown pillar under the zone of relaxation around sub-level open stopes using numerical modelling
Published in Geomatics, Natural Hazards and Risk, 2023
Vishal Babu Guggari, Hemant Kumar, Gnananandh Budi
The plane strain condition assumes that the deformation occurs only in two dimensions and that there is no deformation in the third dimension. As a result, all FE models are analysed considering plane strain conditions with non-linear material behaviour.