Workshop on Nonlinear modelling of geotechnical problems: from theory to practice Johns Hopkins University, Maryland, 3-4 November 2005

Nonlinear modelling of soils David Muir Wood University of Bristol, UK

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 clay build 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 εqp 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)

current peak strength

conventional drained triaxial compression tests different initial density (state variable) 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

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 envelopes: Hostun sand: small-medium strain Stress response envelope for samples with stress histories ABC:

Stress response envelope for samples with stress histories AB: σz

σz 250

250

150

150

Distortional strain: (%)

Distortional strain: (%) C

B

B

0.05% 0.2%

50

0.05% 0.2%

50

0.4% -250

ABC

-150

A

-50

qx: kPa 50

150

0.4%

0.6% -250 0.8%

250

-50

1.0%

qx: kPa -150

A

-50

50

σy

-150

two corners

σx

qz: kPa

-250

150

Distortional strain: (%)

AB qz: kPa

1.2%

radial shearing

distortional strain

0.05% 0.2%

50

0.4%

A -250

A

-150

-50

qx: kPa 50

150

250

-50

0.6% 0.8% 1.0% 1.2%

σx

σy

-150

isotropic compression -250

qz: kPa

0.8%

σy

multiaxial testing

σz 250

0.6% 1.0%

-150

-250

Stress response envelope for initilally isotropically compressed samples :

250

-50

1.2% σx

150

0.05%: history recalled 1%: history ‘forgotten’

Modelling framework: kinematic elasto-plasticity Sz/p

learn from multiaxial experiments Bounding surface

defining hardening rule A

Loading Surface Target Surface Sy/p

exploring stress-dilatancy rule importance of escaping from axial symmetry Sx/p

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

volumetric strain

η

kaolin

η

constant p' cycles hysteresis experiment

simulation

η η

distortional strain

build up of volumetric strain

natural soils often contain structure: bonding between particles: destroyed with mechanical or chemical damage… …or developed with (geological) time

ratio of sizes of structure surface and reference surface gives indication of current degree of structure

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

Norrköping clay – calibration tests

Rouainia & Muir Wood (2000)

Norrköping clay – undrained – isotropic overconsolidation Rouainia & Muir Wood (2000)

simulation

experiment

Bothkennar clay results normalised by Hvorslev equivalent consolidation pressure p'e for structureless soil

Gajo & Muir Wood, 2001

Hierarchical extensions of Mohr Coulomb, Cam clay build 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 3

0.25

Disp (m) displacement (m) 0.20

no strengthening No Strengthening

Mohr-Coulomb model (regulators) 0.15

0.10 Anchors groundGround anchors 0.05

Counterforts & Piles 0.00 0

Mair and Muir Wood (2001)

1

2

time (s)

3 Time (s) 4

5

counterforts and piles

6

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

integral bridge abutment – remove need for bearings between deck and supports but what are stresses on abutments?

thermal expansion of bridge deck abutments move towards backfill passive loading – governed by strength of backfill? abutments can be flexible – vertical support for deck

numerical studies of actual prototype show that strength of backfill has no effect on horizontal stresses on abutment! relative stiffness of abutment and backfill is important

look at stress paths from numerical analysis elastic-perfectly plastic Mohr-Coulomb model dominant effect: increase in mean stress with little change in shear stress not 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

What happened at Nicholl Highway 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. Engineers increasingly "do things to a set routine rather than thinking for themselves".

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-ofthe-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