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