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Nonlinear modelling of soils
David Muir WoodUniversity of Bristol, UK
Workshop on Nonlinear modelling of geotechnical problems: from theory to practice
Johns Hopkins University, Maryland, 3-4 November 2005
Summary
1. Recent work on constitutive modelling
- hierarchical extensions of Mohr Coulomb, Cam clay
- multiaxial testing driving/informing modelling
2. Promotion of use of advanced numerical models in practice
Hierarchical extensions of Mohr Coulomb, Cam claybuild on familiar foundations
advantage in using well known models as basis – check implementation – acceptability
relatively straightforward to add extra features to a soil model
extra features imply additional soil parameters and additional calibration tests
seek adequate complexity in modelling – match complexity of model to availability of data and needs of application
Mohr-Coulomb model with strength dependent on state variable
influence of density
softening
dilatancy
simplicity
Mohr-Coulomb model with strength dependent on state variable
define state variable ψ
function of density and stress level
requires location of critical state line
mathematical definition not important
linear semi-logarithmic? (simple)
Mohr-Coulomb model with strength dependent on state variable
current available strength depends on current value of state variable ψ
ψ varies during test, stress history, etc
simple linear relationship?
(data collected by Been & Jefferies)
Mohr-Coulomb model with strength dependent on state variable
distortional hardening
monotonic increase of ratio of mobilised to available strength (η/ηp) with distortional strain εq
p
hyperbolic hardening law: simple
but available strength is not constant
Mohr-Coulomb model with strength dependent on state variable
flow rule links dilatancy with mobilised strength η
so density changes during shearing
linear relationship? (simple)
volume change accompanies shearing
hence change in state variable
hence change in available strength
model automatically homes in on critical state
softening emerges without being described mathematically
peak strength is moving target reached at infinite distortional strain – then identical with critical state strength
conventional drained triaxial compression tests
different initial density (state variable)
current peak strength
Severn-Trent sand
add kinematic hardening:
elastic region of high stiffness carried round with recent stress history
boundary of elastic region is the yield surface
use bounding surface plasticity:
plastic hardening stiffness depends on separation of the yield surface and bounding surface
kinematic hardening Mohr-Coulomb: strength dependent on state variable: hierarchical development
Severn-Trent sand
calibrated against triaxial test data for Hostun sand
effect of different density/stress level automatically described
(ignore practical problem of maintaining homogeneity within softening sample)
Gajo & Muir Wood, 1999
Severn-Trent sand
cyclic undrained test
Hostun sand
Stress response envelope for initilally isotropically compressed samples :
A
qz: kPa
Distortional strain: (%)
σz
σy
qx: kPa
σx
-250
-150
-50
50
150
250
-250 -150 -50 50 150 250
0.05%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
Stress response envelope for samples with stress histories AB:
A
qz: kPa
Distortional strain: (%)
σz
σy
qx: kPa
σx
B
-250
-150
-50
50
150
250
-250 -150 -50 50 150 250
0.05%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
Stress response envelope for samples with stress histories ABC:
A
qz: kPa
Distortional strain: (%)
σz
σyσx
qx: kPa
BC
-250
-150
-50
50
150
250
-250 -150 -50 50 150 250
0.05%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
multiaxial testing
distortional strain
0.05%: history recalled
1%: history ‘forgotten’Aisotropic compression
AB
radial shearing
ABC
two corners
Stress response envelopes: Hostun sand: small-medium strain
Modelling framework:kinematic elasto-plasticity
Target Surface
Loading Surface
A
Bounding surface
Sz/p
Sy/p Sx/p
learn from multiaxial experiments
defining hardening rule
exploring stress-dilatancy rule
importance of escaping from axial symmetry
Cam clay
elastic-hardening plastic model
volumetric hardening
associated flow – normality
kinematic hardening extension
yield locus carried around with stress state – 'bubble' –strongly influenced by recent history
stiffness falls as yield 'bubble' approaches bounding surface – controlled by distance b
when loading with 'bubble' in contact with bounding surface model is identical to Cam clay
kaolin
constant p' cycles
hysteresis
build up of volumetric strainexperiment simulation
volumetric strain
distortional strain
η
ηη
η
design model: yield surface has increased size as result of bonding
with plastic straining (or chemical weathering) yield surface shrinks to the yield surface, for remoulded, structureless material
extension of 'bubble' kinematic extension of Cam clay
all features of 'bubble' model retained
ratio of sizes of structure surface and reference surface gives indication of current degree of structure
natural soils often contain structure: bonding between particles: destroyed with mechanical or chemical damage…
…or developed with (geological) time
Norrköping clay – calibration tests
Rouainia & Muir Wood (2000)
Norrköping clay – undrained – isotropic overconsolidation
Rouainia & Muir Wood (2000)
simulation experimentBothkennar clay
results normalised by Hvorslev equivalent consolidation pressure p'e for structureless soil
Gajo & Muir Wood, 2001
Hierarchical extensions of Mohr Coulomb, Cam claybuild on familiar foundations
advantage in using well known models as basis – check implementation – acceptability
relatively straightforward to add extra features to a soil model
extra features imply additional soil parameters and additional calibration tests
seek adequate complexity in modelling – match complexity of model to availability of data and needs of application
Promotion of use of advanced numerical models in practice
• Education, education, education!• Keep it simple• Build on familiar foundations• Unification not disintegration• Develop respect
Education, education, education!
• has anything from the past 50 years of research in soil mechanics entered the undergraduate curriculum?
• is the answer to that challenge close to zero?• what about concepts of critical state soil mechanics (≠
Cam clay)?• is anything approaching even a simple complete soil
model introduced into a typical undergraduate degree programme?
• greater understanding and appreciation of soil models can only be obtained by wide appropriate introduction at least into graduate degree programmes
SBCSSM GM
Education, education, education!
• are these two books (Soil behaviour and critical state soil mechanics, (1990) CUP; Geotechnical modelling, (2004) Spon) helpful?
• defining a syllabus for educating engineers into the possibilities and problems of soil modelling
• also useful for continuing professional development courses for practising engineers – harder to convince them
• target the young!
Keep it simple• adequate complexity in geotechnical modelling• user of modelling should have some idea of
phenomena expected to be important• ensure that these phenomena are included in the
modelling• which aspects of soil response are first order or
second order for performance of a geotechnical system?
• experience?• careful parametric study
0.00
0.05
0.10
0.15
0.20
0.25
0 1 2 3 4 5 6Time (s)
Disp (m)
No Strengthening
Ground Anchors
Counterforts & Piles
displacement (m)
no strengthening
ground anchors
time (s) counterforts and pilesMair and Muir Wood (2001)
Mohr-Coulomb model (regulators)
Build on familiar foundations• engineers more likely to use models which are incrementally
different from ones with which they have some familiarity• (than models which adopt a completely different language)• certain models (with minor variations) generally available in
geotechnical numerical analysis programs (EPP Mohr Coulomb, Cam clay)
• some models can be readily developed from the teaching on soil strength – part of every undergraduate programme (EPP Mohr Coulomb)
• (undergraduate background for Cam clay less ubiquitous)• hence: develop hierarchical models from elastic-perfectly
plastic Mohr-Coulomb and Cam clay
Unification not disintegration
• separation in companies between structural and geotechnical divisions
• sparing in information in requests for parameters: control• plead guilty in universities too!• from first year of typical civil engineering degree: separate units
in structures, soil mechanics, hydraulics …• do we make enough effort to introduce unifying units requiring
combined appreciation of two or three of these subjects?• soil-structure interaction: obvious vehicle for
unification/integration• learn by doing• numerical analysis programs (black boxes?) not essential
thermal expansion of bridge deck
abutments move towards backfill
passive loading – governed by strength of backfill?
abutments can be flexible – vertical support for deck
integral bridge abutment – remove need for bearings between deck and supportsbut what are stresses on abutments?
numerical studies of actual prototype show that strength of backfill has noeffect on horizontal stresses on abutment!
relative stiffness of abutment and backfill is important
look at stress paths from numerical analysiselastic-perfectly plastic Mohr-Coulomb modeldominant effect: increase in mean stress with little change in shear stressnot heading towards failure
Develop respect• difficulties with numerical modelling (Potts,
2003):- because there is no standard numerical strategy for implementation of nonlinear models- because some constitutive models seem to be unable to give reasonable predictions- because, even for apparently simple problems, the results of numerical modelling can be very dependent on the decisions made by the user
Engineers increasingly "do things to a set routine rather than thinking for themselves".
What happened at NichollHighway was in part down to over-reliance by engineers on computerised soil analysis programs, he believes. These are "far more sophisticated than the people using them", Davies asserts. "What matters is how you put the data in to start with. You need to look at the overall problem." He maintains that use of inappropriate data in modelling soil behaviour skewed temporary works design in the wrong direction –steelwork was found to be under-strength.
PLAXIS analyses
same problem – different modellers
spread of predictions(Schweiger, 2003)
Develop respect
• restrict use to experts? (Potts…)• or educate students to explore, discover,
understand?• need for communication between computer
modellers and designers• education in respective languages• always support advanced modelling with back-of-
the-envelope estimates
Promotion of use of advanced numerical models in practice
• Education, education, education!• Keep it simple• Build on familiar foundations• Unification not disintegration• Develop respect