(20 bjerrum lecture: oslo: november 2005) - … magic of sands david muir wood university of...

The magic of sandsDavid Muir Wood

University of Bristol, England

(20th Bjerrum Lecture: Oslo: November 2005)

HKIE Geotechnical Division: 6 November 2007

David Muir Wood

1949-1950 Folkestone

1950-1970 Beaconsfield

1967-1987 Cambridge

1975 Oslo

1978 Hong Kong

1986 Boulder

1987-1996 Glasgow

1995- Bristol

2000 Minneapolis

2003 Tokyo

The magic of sands

• Introduction: context: WAC Bennett Dam

• Particle-continuum duality

• Mohr-Coulomb model

• Elastic properties

• Critical states

• Severn-Trent sand

• Grading state index

• Conclusion

The magic of sands

• Introduction: context: WAC Bennett Dam• Particle-continuum duality



• Critical states



• Conclusion

WAC Bennett Dam

on Peace River, NE British Columbia

183m high, 2km long

reservoir 70x109m3; 2.73GW

completed 1968

WAC Bennett Dam

no incidents until 1996

sinkholes

1

2

sinkhole 1: June 1996

2.4m diameter at crest

6.7m deep hole

76m deep extremely

loose zone

114m variable zone

WAC Bennett Dam: sinkhole incident 1996

spillway flow 3000m3/s (> Canadian Niagara Falls)

fall in reservoir level: 2m in 7 weeks

MAXIMUM NORMAL RESERVOIR EL 672

675

650

625

600

575

550

525

500

475

EL

EV

AT

ION

(M

)

2.5

1 1

2

CL GROUT CURTAIN

GROUTING CULVERT

BEDROCK SURFACE

WAC Bennett Dam: cross section

zoned earthfill dam

blended 'till-like' core

well-graded transition and filter

high capacity drain

0

10

20

30

40

50

60

70

80

90

100

0.010.101.0010.00100.00Grain size (mm)

Perc

en

t P

assin

g

El 2215.0 El 2204.0El 2197.0 El 2184.5El 2181.8 El 2165.5El 2143.5 El 2125.5El 2105.5 El 2087.0El 2085.5 El 2084.0El 2082.3 El 2063.5El 2062.5 El 2043.5El 2025.5 El 2013.5El 2005.5 El 2002.0El 1985.5 El 1972.5El 1955.5 El 1952.5El 1933.5 El 1917.5El 1915.5 El 1904.5El 1894.5 El 1887.0El 1870.5 DH96-34 Avg.As-Built Avg.

#200#100#60#40#20#10#43/8"3/4"1 1/2"3"

GRAVEL

Coarse Medium Fine

SAND FINES

Silt

DH96-34 Gradations

Core material (Sinkhole 1)

as built

1996 gradings show loss of fines

2112 1995

2092 2012 1916

1965 1863 1790

2123 2067

18

00

1840

1880

1920

1960

2000

2040

2080

2120

2160

Canyon section: 2003 seepage model

silty transition material:

reduced permeability

pore pressures consistent with

permeability changes linked with fines

movement

WAC Bennett Dam: statement of problem

non-plastic material with changing granulometry and density

•what are consequences for mechanical response of dam?

•potential for future deformations?

need model of soil behaviour which can incorporate changes in density and grading of the soil

The magic of sands


• Particle-continuum duality• Mohr-Coulomb model


• Critical states



• Conclusion

paradox of sand:

blows in the wind

flows like a liquid

but supports loads like a solid

Particle-continuum duality

for analysis we need to treat soil as a continuum (stress, strain)

… but its properties emerge from its particulate nature

Leighton Buzzard sand (picture width 37 mm)

Particle-continuum duality

The magic of sands


• Particle continuum duality

• Mohr-Coulomb model• Elastic properties

• Critical states



• Conclusion

model = appropriate simplification of reality

modelling for working loads:

•serviceability limit states

•deformations of geotechnical systems

usually requires numerical analysis:

•for example, finite element, finite difference

Mohr-Coulomb model

equilibrium compatibility of deformations

stresses strains

stress:strain relationship

constitutive model

eg Mohr-Coulomb

constitutive model: central element of numerical modelling

linking change in stress with change in strain

generalised evolving incremental stiffness

Mohr-Coulomb model

Mohr-Coulomb familiar as strength/failure model

limiting stress ratio characterised by frictional strength φ' (ignore cohesion)

drives laboratory and in situ investigation of soil properties

Mohr-Coulomb model: failure

0

100

200

300

400

500

0 0.05 0.1 0.15 0.2

0

0.01

0.02

0.03

0.04

0 0.05 0.1 0.15 0.2

deviator

stress

shear strain

shear strain

volumetric

strain

Mohr-Coulomb model: parameter selection

loose Hostun sand

Benahmed, 2001

choice of stiffness, strength, dilatancy

pedagogic exercise

… as many answers as people!

compression +ve

The magic of sands




• Elastic properties• Critical states



• Conclusion

Elastic properties

stiffness does not imply elasticity (recoverable deformations)

fall of stiffness ⇒ plasticity (permanent changes on unloading)

… hence need for constitutive models

Quiou sand (LoPresti et al., 1997)

shear strain

shear stresslimit of elastic

response??

unloading

loading

perceptions of laboratory soil stiffness have changed as instrumentation for

measurement of deformations has improved

limit of elastic

response?then … paradox of low laboratory

stiffness – high in-

situ stiffness

now … consistency

of dynamic and static measurements

secant

stiffness

then

now

Elastic properties

bender element (s-waves)

extender element (p-waves)

+

–

+

+

–

+

laboratory geophysics: piezoceramic elements

v

h belt

h 90

V s(hv)

V s(hh)

V s(vh)b

V s(vh)

bender elements

on triaxial sample

deduction of elastic stiffness

elastic stiffness deduced from shear (or compression) wave velocity G = ρ vs

2

velocity = distance/time

arrival time? complex (attenuated) received signals –reflections, dispersion

the problem:

input signal: single sine pulse!!

output signal: complex

arrival time?

elastic properties: numerical simulation

FLAC-3D grid

reflection at boundaries

conversion of s-wave to p-wave energy

bender element

non-absorbing boundaries

experimental observation: note p-wave

arrival in s-wave trace

interpretation of numerical simulations

numerical simulation: objective

deduction of arrival time??

input signal: single sine pulse!!

compare theoretical p-wave and s-

wave arrival times


typical choices for arrival time from

inspection of received signal


no clear trends?

p-wave dominating with distance

cross-correlation

frequency domain

non-absorbing boundaries

distance from bender tip

vp/vs = 1.5

normalised shear wave

velocity

1.0

The magic of sands

• Introduction: context: Bennett Dam




• Critical states

• Severn-Trent sand• Grading state index

• Conclusion

Bristol

River Severn

Severn-Trent sand

Severn – river adjacent to Bristol

Trent – Alessandro Gajo, Italy

Trento

Hostun sand (Benahmed)

Severn-Trent sand

?

?

?

Mohr-Coulomb model: defects?

•incremental stiffness elastic or zero

•indefinite dilation/compression at failure

•strength chosen as soil constant

volumetric strain

constant strength

what is peak strength?

•property of the soil which

changes with stress level, density

•dependent quantity

Severn-Trent sand: strength

Been & Jefferies

state parameter ψ = volume distance

from critical state line

function of density and stress level

more useful than void ratio alone –indicating effect of density and stress'dense'

'loose'

ψ

critical state line

mean stress

specific volume


what is peak strength?

•property of the soil which changes

with stress level, density

data confirm link between strength

and state parameter ψ

Mohr-Coulomb model with current strength dependent on current stress level and density

Been & Jefferies

peak strength


'dense'

'loose'

ψ

mean stress

specific volume

state parameter ψ

Severn-Trent sand: dilatancy

Benahmed

volume strain

shear strain

dilatancy: volume change during

shearing

'dense' sand expands – negative state

parameter

'loose' sand contracts – positive state

parameter

dilatancy depends on density

dilatancy varies during test

link with state parameter (stress level

and density)

Severn-Trent sand: stiffness evolution

mobilised

strength φ'mob

shear strain

currently mobilised strength

currently available strength monotonic relationship

1ratio

available strength φ': varies with ψ

model complete

•monotonic travel towards current strength

•current strength depends on current density (state parameter)

•shearing leads to change in density (dilatancy): soil seeking

critical state

•change in density leads to change in strength

etc

predicted softening for dense sand as emergent property

Severn-Trent sand

drained triaxial compression tests

different initial density (state

parameter)

model automatically homes in on

critical state

peak strength is moving target

reached at infinite distortional strain –critical state

current peak

strength

Severn-Trent sand: simulations

increasing density

increasing density

calibrated against triaxial test data

for Hostun sand

undrained triaxial compression

effect of different initial density

automatically described

Gajo & Muir Wood, 1999

Severn-Trent sand: calibration

Mohr-Coulomb model with extra features

building on familiar foundations

•central role of state parameter

•feedback through dilatancy

•rich patterns of response simulated

mathematically elegant

economical in demand for soil parameters

Severn-Trent sand

The magic of sands





• Critical states


• Grading state index• Conclusion

occurrence of crushing

change in grading

irreversible

Chattahoochee River sand

Vesic & Clough, 1968

Grading state index

particle size distribution

1: before testing

2: after compression to 6.21MPa

3: after triaxial compression

21

3

0

20

40

60

80

100

100 1000Size, log d (µm)

% p

assin

g b

y v

olu

me Original PSD

20 MPa before shear

20 MPa axial strain = 0.3




Influence of axial strain:

(Cheng, 2004)numerical simulations – compression and shearing of assembly of agglomerates

gradings tend to self similar 'fractal' grading

continuous 'fractal' grading: every void space filled with progressively smaller particles

389 agglomerates

6.66 mm

Grading state index

Cheng

crushing

Maeda (2005)

crushing?

coordination number (number

of contacts) larger for larger particles

smaller particles tend to crush

Grading state index: crushing

Brazil cylinder test: tensile strength of

concrete

Grading state index IG: definition

definition of IG?

IG = area ABC/area ABD

0 < IG < 1

single size AB: IG = 0

fractal limit AD: IG = 1

0

0.2

0.4

0.6

0.8

1

0.0001 0.001 0.01 0.1 1

d/dmax: particle sizelogarithmic scale

fraction finer

d = dmax

current

grading

A

BC

D

(fractal) limiting grading

0

10

20

30

40

50

60

70

80

90

100

0.010.101.0010.00100.00Grain size (mm)

Perc

en

t P

as

sin

g

El 2215.0 El 2204.0El 2197.0 El 2184.5El 2181.8 El 2165.5El 2143.5 El 2125.5El 2105.5 El 2087.0El 2085.5 El 2084.0El 2082.3 El 2063.5El 2062.5 El 2043.5El 2025.5 El 2013.5El 2005.5 El 2002.0El 1985.5 El 1972.5El 1955.5 El 1952.5El 1933.5 El 1917.5El 1915.5 El 1904.5El 1894.5 El 1887.0El 1870.5 DH96-34 Avg.As-Built Avg.

#200#100#60#40#20#10#43/8"3/4"1 1/2"3"

DH96-34 Gradations

Chattahoochee River sand

grain crushing: IG increasing

WAC Bennett Dam core

fines removal: IG falling

Grading state index IG

•soil grading change: erosion/transport or crushing

•material changing (irreversibly) while being studied

•effect on mechanical behaviour?

0

50

100

0.001 0.01 0.1 1 10 100

Grading state index

particle size: logarithmic scale

% finer

fractal limiting gradings

residual granitic soil

glacial till

natural soils:

discovering fractal limiting gradings?

•material changing (irreversibly) while being studied

•modelling requirements:

�characterisation of evolving grading – additional grading state index

�evolution law for grading state index (mass conservation, transport, crushing criteria, etc)

�influence of grading state index on constitutive properties (for example, critical states)

•research in progress: add IG influence to existing model

Modelling grading change

Grading state index IG: influence

influence of grading state index on constitutive properties

•elastic properties – unchanged (first order)?

•friction/strength – unchanged (first order)?

•critical state line – expected to change!

evidence?

smaller particles tending to fill gaps

maximum and minimum void ratios ↓ as IG ↑

Grading state index IG: critical states

critical state line?

deduced from tests with

increasing stress levels

mean stress: log scale

specific

volume

IG increasing (irreversible)

changing material

onset of crushing

original material

crushing complete

critical state line –

before crushing: IG = 0

mean stress: log scale

reinterpretation:

critical state surface

limit of critical state lines –during crushing: 0 < IG < 1

critical state line –

crushing exhausted: IG = 1IG

specific volume

IG increasing: evolving

critical state line


0.7

0.9

1.1

1.3

1.5

1.7

1.9

2.1

2.3

2.5

2.7

1 10 100

Pressure, p' (MPa)

Vo

ids

rati

o, e

Dense

Loose

Loose, over-compressed

Final states of p' -constant tests:

Loose

Dense

Loose, over-compressed

simulations for assemblies of agglomerates

critical state line changes with crushing

fresh samples – pre-compressed samples

Cheng, 2005

389 agglomerates

6.66 mm

pre-compressed samples

fresh

samples


0.25

0.27

0.29

0.31

0.33

0.35

0.37

0.39

0.41

0.43

10 100 1000 10000

mean effective stress: kPa

vo

id r

ati

o

F = 34 %

F = 26 %

F = 19 %

csl_interpolation.xls

WAC Bennett Dam: interpretation of effect of fines content on location of critical state line (triaxial tests, artificial mixtures)

non-monotonic…!?

34% fines

19% fines26% fines


e

Grading state index

WAC Bennett Dam

Severn-Trent sand

transport of fines from core

void ratio ↑

grading state index ↓

critical state line ↓??

state parameter ↑

soil feels looser �

v

p’

e

Grading state index

WAC Bennett Dam

Severn-Trent sand

transport of fines from core

void ratio ↑

grading state index ↓

critical state line ↑??

state parameter ↓

soil feels denser ☺

v

p’

WAC Bennett Dam??

benefit of simple model that systematically incorporates changes in stress level and density and grading (making up

state of soil)

model has to be honed – subtle data requirements for

calibration

most testing has used artificially prepared mixtures

Grading state index

The magic of sands





• Critical states



• Conclusion

WAC Bennett Dam: Need for modelling able to include effects

of density, stress and evolving grading.

Mohr-Coulomb model: Use as basis for development of more

comprehensive models.

Severn-Trent sand: Mohr-Coulomb model with strength dependent on state parameter – softening as emergent

property.

Grading state index: How does the changing grading of a soil

affect its mechanical behaviour?

Conclusion

Nous nous sommes nourris de la magie des sables.

We are sustained by the magic of sands.

Antoine de St Exupéry: Terre des hommes (1939)

Thank you for your attention!

(20 bjerrum lecture: oslo: november 2005) - … magic of sands david muir wood university of...

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