TASK Quarterly   Scientific Bulletin of the Centre of Informatics - Tricity Academic Supercomputer & networK   ISSN 1428-6394

    3/2000 "Modelling of the Behaviour of Granular Bodies with a Hypoplastic Constitutive Low"


    Contents:

    • G.Gudehus, A Comprehensive Constitutive Equation for Granular Materials - abstract
    • D.Kolymbas, Introduction to Hypoplasticity (GeoMath1) - abstract
    • E.Bauer, Modelling of the Pressure and Density Sensitive Behaviour of Sand within the Framework of Hypoplasticity - abstract
    • I.Herle, Granulometric Limits of Hypoplastic Models - abstract
    • A.Niemunis, K.Nübel and Ch.Karcher, The Consistency Conditions for Density Limits of Hypoplastic Constitutive Law - abstract
    • V.A.Osinov and R.Cudmani, Expansion of a Cylindrical Cavity in Sand - abstract
    • P.Kudella, Evaluation of Liquefaction Potential for Loose Minefill Slopes - abstract
    • P.Kudella and P.-M.Mayer, Calculation of Soil Displacements due to Retaining Wall Construction - abstract
    • E.Bauer and W.Huang, The Evolution of Strain Localisation in a Hypoplastic Cosserat Material under Shearing - abstract
    • J.Tejchman, Numerical Studies on Patterning of Shear Zone in Granular Bodies - abstract
    • J.Wehr and J.Tejchman, FE- Modelling of Behaviour of Granular Anchors in Rock and Soils - abstract


    Abstracts:

  • G.Gudehus, A Comprehensive Constitutive Equation for Granular Materials
  • A constitutive equation is proposed for describing changes of states of granular materials, which are sufficiently characterised by the void ratio and the stress tensor. It may be considered as an extension of the Critical State concept. It is based on recently published hypoplastic equations and covers a wide range of densities, pressures and deformations. A factorial decomposition allows a rather easy separation and determination of material parameters. Two factors depend on a relative void ratio so that it remains within lower and upper bounds. The bounding void ratios decrease monotonously from maximal values to zero with increasing pressure. The same reduction of the void ratio is proposed for an isotropic compression starting from a suspension. Thus a granulate hardness is defined, and a stiffness factor can be determined. Four material parameters can be estimated from classification tests and determined from the asymptotic behaviour in element tests. Four further parameters are determined by calibration; they are rather constant for wide groups of materials. Strength and stiffness values can be derived and used for the analysis of deformations, stability, and flow. The viscous behaviour is modelled by a rate dependent factor with one further parameter. Limitations and possible extensions of this comprehensive approach are also outlined.

  • D.Kolymbas, Introduction to Hypoplasticity (GeoMath1)
  • Rational mechanics offers a tool to objectively describe the mechanical behaviour of granular materials by means of non-linear tensorial functions. This new framework is called hypoplasticity and is characterized by the simplicity of the mathematical formulations. The stress dependency of incremental stiffness, yield, loading-unloading hysteresis and dilatancy-contractancy are included. One of the features of hypoplasticity is that yield is a natural outcome of the theory and needs not be calibrated a priori. Also loss of uniqueness and localization of deformation are realistically predicted by hypoplasticity.

  • E.Bauer, Modelling of the Pressure and Density Sensitive Behaviour of Sand within the Framework of Hypoplasticity
  • In this paper a hypoplastic model proposed by Gudehus and Bauer is presented which is apt to describe the mechanical behaviour of loose and dense sand within a wide range of pressures and densities using a single set of constants. State changes are assumed to depend on the current void ratio, the Cauchy stress tensor and the stretching tensor. The constitutive equation is of the rate type and based on non-linear tensor-valued functions. By including a pressure dependent relative density the hypoplastic model describes the influence of pressure and density on the incremental stiffness, the peak friction angle and on the void ratio in a stationary state. The performance of the hypoplastic models is discussed and the results of numerical simulations are compared with experiments.

  • I.Herle, Granulometric Limits of Hypoplastic Models
  • Several successful applications of the hypoplastic models would not be possible without a reliable and simple calibration procedure of the model parameters. The procedure utilizing standard properties of grain assemblies is well-suited for sands and is briefly outlined here. However, there are limits for the application of this approach for other soils. This is demonstrated for a coarse-grained limestone rockfill and a fined-grained loess. Whereas the parameter determination of the limestone rockfill is mainly limited by the available laboratory equipment, the calibration procedure must be significantly modified for the loess soil. Finally, a serious problem concerning the application of the hypoplastic model for soils with low friction angles is discussed. It is shown that in this case the ratio of incremental stiffness moduli in triaxial and isotropic compression is unrealistically low.

  • A.Niemunis, K.Nübel and Ch.Karcher, The Consistency Conditions for Density Limits of Hypoplastic Constitutive Law
  • The so-called phase diagram of grain skeletons illustrates the range of possible void ratios between the pressure dependent bounds ei and ed. It can be shown that in the framework of the actual hypoplastic model these bounds can be surpassed by particular deformation paths. This inconsistency is particularly acute in recently proposed FE-calculations with density fluctuations. Here we propose a modification to render the formulation consistent.

  • V.A.Osinov and R.Cudmani, Expansion of a Cylindrical Cavity in Sand
  • The paper presents numerical solution to the problem of the symmetri quasi-static large-strain expansion of a cylindrical cavity in sand. The boundary value problem is solved with the use of a constitutive equation of hypoplasticity calibrated for a particular sand. As the radius of the cavity increases, the stresses and the density on the cavity surface asymptotically approach limit values which correspond to a so-called critical state of the sand. The limit values depend on the initial stresses and the initial density. The solutions are compared with experimental results for the same sand available in the literature. A comparison is also made with numerical solutions obtained by other authors.

  • P.Kudella, Evaluation of Liquefaction Potential for Loose Minefill Slopes
  • Uncompacted embankments of certain fine sands exhibit a spontaneous liquefaction potential, which cannot be evaluated basing on undrained shear strength alone. A novel procedure for stability analysis has been developed, basing on Hill's stability criterion and a hypoplastic constitutive law. With given relative densities, assumed initial stress states and variations of perturbation directions, stability or instability of slope sections can be assessed. Catastrophic landslides observed in the past could thus be explained.
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  • P.Kudella and P.M.Mayer, Calculation of Soil Displacements due to Retaining Wall Construction
  • With regard to serviceability state deformations, diaphragm walls and slurry walls cause considerable soil deformations during trench construction. 3-dimensional finite element analyses are able to quantify these deformations. They are compared to measurements and to the results of simplified 2-dimensional models. The dependence of soil stiffness on the actual state can be accounted for by using a hypoplastic constitutive law. Trench geometry and construction sequence are considered as factors of influence. It is shown, how the wall construction process can be modelled at the beginning of an overall 2-dimensional deformation analysis using prescribed initial deformation or stress fields.

  • E.Bauer and W.Huang, The Evolution of Strain Localisation in a Hypoplastic Cosserat Material under Shearing
  • Numerical studies of the evolution of strain localisation and polar effects within a plane layer of a granular material under monotonic shearing are presented. Herein a micro-polar approach is formulated within the framework of a hypoplastic Cosserat continuum to describe the essential properties of a dry and cohesionless granular material like sand. The constitutive model is based on incremental non-linear tensor-valued functions and captures the influence of the pressure, the void ratio, the mean grain diameter and the rotation resistance of the grains on the evolution of the stresses and couple stresses. The Cosserat boundary conditions are suitable to model the rotation resistance at the interface between the granular layer and the surfaces adjoining the boundaries of the granular body. The numerical investigations show that the location, thickness and evolution of strain localisation within the shear layer are strongly influenced by the boundary conditions and the initial state quantities.

  • J.Tejchman, Numerical Studies on Patterning of Shear Zone in Granular Bodies
  • The paper deals with numerical investigations on the patterning of shear zones in granular bodies. The behaviour of dry sand during plane strain compression tests was numerically modelled with a finite element method using a hypoplastic constitutive relation within a polar (Cosserat) continuum. The constitutive relation was obtained through an extension of a non-polar one by polar quantities, viz. rotations, curvatures, couple stresses using the mean grain diameter as a characteristic length. This relation can reproduce the essential features of granular bodies during shear localisation. The material constants can be easily determined from element test results and can be estimated from granulometric properties. The attention is laid on the influence of boundary conditions and the distribution of imperfections in the granular specimen on the formation of patterns of shear zones.

  • J.Wehr and J.Tejchman, FE- Modelling of Behaviour of Granular Anchors in Rock and Soils
  • The paper is concerned with granular anchors in rock and soils. Model tests and numerical calculations were performed. The effect of different parameters on the behaviour of anchors was investigated: anchor length, anchor diameter, initial density and mean grain diameter of the granular material, anchor roughness and stiffness of the borehole wall. The experiments were modelled with a finite element method and a polar hypoplastic constitutive relation. The relation can capture the salient properties of granular materials during shearing. A satisfactory agreement between experiments and numerical calculations was obtained. Advantages and limitations of granular anchors in rock and soils were outlined.