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
e_{i} and e_{d}. 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.
p>
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.