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Geotechnical modelling and critical state soil mechanics

Naples, May 2007

David Muir WoodUniversity of Bristol

13. Designer models addition of e!tra features

"#M 2, 3, $M, #eo%&

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Designer models addition of e!tra features

1.'inemati( yielding

2. )am (lay3. Mo*r+)oulom

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s*earstress

mean

stress

elasti( +

stiff

plasti( -

less stiffs*earstress

s*earstrain

(lassi(al elasti(+plasti( modelling of soil

for e!ample, )am (lay "1/3, 1/&

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stress

yield

strain

typi(al a(tual response

voidratio

verti(al stress

"log s(ale&pre(onsolidation

pressure

(lassi(al identifi(ation of yield

from stressstrain response

geometri(al (onstru(tion for

estimation of pre(onsolidation

pressure

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-150

-100

-50

0

50

100

150

200

0 100 200 300 400

Cam clay?

p': kPa

q: kPa

%ig 3 nisotropi( yield lo(us for one+dimensional stress *istory

"after l+aaa, 1.4&

)am (lay providing inspiration

sear(* for 5)am (lay li6e yield lo(i

eg 6aolin "l+aaa, 14&

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yield lo(i for natural (lays

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

p/vc

q/

vc

Rang de le!"e

#el$a%&

(nn(peg

)& *l+an

,ynd!%&

/a%&emy

(olle(ted y #ra*am et al "1&

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typi(al e!perimental oservation

stiffness falls steadily 8it* monotoni( straining

is t*ere an elasti( region

s*ear stiffness degradation data for 9uiou sand from resonant

(olumn and torsional s*ear tests "after :o;resti et al, 17&

l(m(& $ ela%&(c

e%pn%e??

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*o8 do 8e o

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-20

-10

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60

>1 yield lo(us

>2 yield lo(us

>3 yield lo(us

q: kPa

p': kPa

yielding of Bot*6ennar

(lay

oundaries dedu(ed

from inspe(tion of

stressstrain response

>1 appro!imately(entred on in situ

stress state

>3 refle(ts natural

stru(ture - damagedy anyirre(overale

strain + evanes(ent

after ?mit* et al "12&

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6aolin revisited

isotropi( (onsolidation *istories

-50

0

50

100

150

200

0 50 100 150 200 250 300 350 400 450

mean e$$ec&("e %&e%% p': kPa

de"(a& %&e%% q: kPa

a.

data from l+aaa "17&

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6aolin revisited

one+dimensional (onsolidation *istories

data from l+aaa "17&

-50

0

50

100

150

200

0 50 100 150 200 250 300 350 400

mean e$$ec&("e %&e%% p': kPa

de"(a& %&e%% q: kPa +.

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q

6;aq

6;a

q

6;a

q

6;a

p'6;a p'6;a

p'6;ap'6;a

plasti( strain in(rements appro!imate normality to 6inemati( yield lo(i

6aolinl+aaa, 17

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e"(a&(c %&e%% e%pn%e en"elpe%

qz:kPa

qx:kPa

x y

z

270

)+300

)+330 )+0 )+30

)+/0

)+.0

)+120

)+1@0)+10)+210

)+240

+2@0

+1@0

+@0

@0

1@0

2@0

+2@0 +1@0 +@0 @0 1@0 2@0

Stress response envelope for initilally isotropically compressed

qz: kPa

z

y

qx: kPa

x+1@0

+@0

@0

1@0

2@0

+2@0 +1@0 +@0 @0 1@0 2@0

d(%&&(nal %&e%% p+e %e&&e%cn%&an& mean %&e%%c%% an(%&py?

3" 3

d 0.057 0.27 0.47 0.67 0.87 17 1.2

9 9y

9;

9 9y

9;

*: (%&p(c cmpe%%(n

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B)30

qz:kPa

qx:kPa

x y

z

B)/0

B)0

B)120 B)1@0

B)10

B)210

B)240

B)270B)300

B)300

B

B)330

)

B)3/0

+2@0

+1@0

+@0

@0

1@0

2@0

+2@0 +1@0 +@0 @0 1@0 2@0

B30

z

yx

qx:kPa

qz:kPa

B/0

B0

B120

B1@0

B10

B210

B240

B270

B

B300B330

B3/0

+2@0

+1@0

+@0

@0

1@0

2@0

+2@0 +1@0 +@0 @0 1@0 2@0

d(%&&(nal p+(ng

cn%&an& mean %&e%%

nn-mn&n(c %&e%% pa&%

%&e%% p+e %e&&e%

*#C = p+e

*# = p+e

9;

9

9

9y

9y

9;

)adek7 2006

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Stress response envelope for samples *ith stress histories AB:

qz: kPa

Di

z

y

qx: kPa

x

B

+1@0

+@0

@0

1@0

2@0

@0 +1@0 +@0 @0 1@0 2@0

Stress response envelope for samples *ith stress histories ABC:

qz: kPa

Distortional strain "A&

z

yx

qx: kPa

B)

+1@0

+@0

@0

1@0

2@0

+2@0 +1@0 +@0 @0 1@0 2@0

0.0@A

0.2A

0.4A

0./A

0.A

1.0A

1.2A

d(%&&(nal %&a(n

0.05: (%&y ecalled

1: (%&y >$g&&en

ad(al %ea(ng

*#&@ cne%

*#C

)&e%% e%pn%e en"elpe%:

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qz: kPa

z

x y

q

B)

a

,(

+@0

@0

1@0

+1@0 +@0 @0 1@0

rosette

rosette B

rosette )

cmpa(%n $ 0.05 %&a(n

e%pn%e en"elpe% $

(%&(e%*7*#7*#C

%&e%% e%pn%e en"elpe%

%mallAmed(!m %&a(n %&($$ne%%

k(nema&(c aden(ng

cen&e a% (nd(ca& $ c!en&

$a+(c

but strain too large

)adek7 2006

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Designer models addition of e!tra features1. 'inemati( yielding

2. )am (lay3. Mo*r+)oulom

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)am (lay

elasti(+*ardening plasti( model

volumetri( *ardening

asso(iated flo8 - normality

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)am (lay

response in drained tria!ial(ompression tests 8it*

(onstantp'

asymptoti( approa(* to

(riti(al stateeffe(t of over(onsolidation

ratio

s*arp division et8een

elasti( and plasti( response

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(ompare response of soil on nonmonotoni( loading

8it* (apaility of single yield surfa(e model

e!tension to simple models

using 6inemati( *ardening

and ounding surfa(e plasti(ity

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(ompare response of soil on nonmonotoni(loading 8it* (apaility of single yield surfa(e

model

elasti(+*ardening plasti( model e!pe(ts elasti(

e*aviour on reversal, sudden drop in stiffness atyield

soils typi(ally s*o8 *ystereti( e*aviour on

unload+reload (y(les, steady (*ange in

in(remental stiffness

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6inemati( *ardening e!tension

yield lo(us (arried around 8it* stress state - ule -

strongly influen(ed y re(ent *istory

stiffness falls as yield ule approa(*es ounding surfa(e- (ontrolled y distan(e b

8*en loading 8it* ule in (onta(t 8it* ounding surfa(e

model is identi(al to )am (lay

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assume relative siCeR of ule

assume rule for translation of ule

assume interpolation rule lin6ing plasti( stiffness 8it* b

ot*er8ise identi(al to )am (lay

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6aolin

(onstantp'(y(les

*ysteresis

uild up of

volumetri( straine!periment simulation

volumetri( strain

distortional strain

E

E

E

E

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migration of ule during (onstantp'unloading

after one+dimensional normal (ompression

*ardening of ule and ounding surfa(e

q

6;a

p'6;a

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e!periment simulation

(onstant q(y(les after one+dimensional normal (ompression

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add furt*er effe(ts in a similarly *ierar(*i(al 8ay

(ementation and stru(ture e!tension to ule model

natural soils often (ontain stru(ture onding et8een parti(lesdestroyed 8it* me(*ani(al or (*emi(al damage

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design model in 8*i(* yield surfa(e *as in(reased siCe as a result of

t*e onding

8it* plasti( straining "or (*emi(al 8eat*ering& t*e yield surfa(e

gradually s*rin6s to t*e yield surfa(e, for remoulded, stru(turelessmaterial

e!tension of ule 6inemati( e!tension of )am (lay

all features of ule model retained

ratio of siCes of stru(ture surfa(e and

referen(e surfa(e gives indi(ation of(urrent degree of stru(ture

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add measure of stru(ture or onding single s(alar parameter r

ounding surfa(e no8 (alled stru(ture surfa(e siCe r times larger

t*an a referen(e surfa(e

stru(ture lost 8*enever plasti( strains o((ur

damage la8

damage plasti( strain in(rement FGdp(omines plasti( volumetri(

and plasti( distortional strain in(rements

- additional parameter to (ontrol t*eir relative importan(e

stru(ture progressively disappears

r 1 as plasti( deformation in(reases

( ) p

d1r

6

r =

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logi(al stru(tureless soil is one 8*i(* *as een so me(*ani(ally

pummelled t*at it *as no remaining onds et8een parti(les

parti(ular forms of laoratory testing "tria!ial testing, for e!ample&

may not e ale to provide suffi(ient damage

evolution la8 and definition of damage strain may need to in(lude

some more sutle referen(e to t*e nature of t*e strain pat*

s*earing 8it* rotation of prin(ipal a!es is li6ely to e espe(ially

damaging

feasile to introdu(e ot*er evolution la8s 8*i(* relate (*ange

"in(rease or de(rease& of s(alar measure of stru(ture r to (*emi(alenvironment or time or temperature effe(ts

)am (lay (an e regained y setting r H 1,R H 1

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*ierar(*i(al e!tension of ule

model to in(lude effe(ts of stru(ture

ot*er evolution la8s relate (*ange

"in(rease or de(rease& of s(alar

measure of stru(ture r to (*emi(alenvironment or time or temperature

effe(ts

)am (lay (an e regained y setting r H 1,R H 1

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Norr6Iping (lay - (aliration tests

Jouainia K Muir Wood "2000&

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Norr6Iping (lay - parametri( variation


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Norr6Iping (lay - undrained - isotropi(

(onsolidation


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Norr6Iping (lay - undrained - anisotropi( (onsolidation


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Norr6Iping (lay - undrained - isotropi( over(onsolidation


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simulation e!periment

Bot*6ennar (lay

results normalised y Lvorslev euivalent

(onsolidation pressurep'eforstructurelesssoil

#a

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Lierar(*i(al e!tensions of )am (lay

it is relatively straig*tfor8ard to add e!tra features to a soil

model

advantage in using 8ell 6no8n model as asis - (*e(6implementation - a((eptaility

e!tra features imply additional soil parameters and

additional (aliration tests

see6 adeuate (omple!ity in modelling - mat(* (omple!ity

of model to availaility of data and needs of appli(ation

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Designer models addition of e!tra features1. 'inemati( yielding

2. )am (lay

3. Mo*r+)oulom

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standard elasti(+perfe(tly

plasti( Mo*r+)oulom model

non+asso(iated plasti( flo8

simpli(ity

s*arp stiffness (*anges

tangent stiffness eit*er

elasti(or Cero

(ontinuing volume (*ange

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standard elasti(+perfe(tly plasti(Mo*r+)oulom model

availale in all numeri(al analysis

programs

su

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elasti(+*ardening plasti( Mo*r+)oulom model

non+asso(iated flo8 steady fall in stiffness (ontinuing volume (*ange

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is post+pea6 softening important

design a model to in(lude softening

Mo*r+)oulom family

post+pea6 softening to (riti(al state

t*ree regimes of response

adaptation of *ardening Mo*r+)oulom model

for E O Epresponse is elasti( E O Ep, EyH EpFGpH 0

after pea6, linear fall in yield stress ratio 8it* strain

0 O GpO b "distortional *ardening la8&

eventual perfe(tly plasti( (riti(al state Gpb, EyH M

non+asso(iated flo8 rule as efore

M

p

p

yp =

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(onventional tria!ial drained (ompression test

elasti(

post+pea6 softening

(riti(al state

tria!ial undrained (ompression test

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tria!ial undrained (ompression test

+

=

p

ppp

p

i

M12

M211

,'

pp

effe(tive stress pat*

elasti( "isotropi( Fp H 0&

post+pea6 softening

(riti(al state

limited model

(on(entration on single aspe(t

of response

M * ) l d l it* t t* d d t t t i l

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Mo*r+)oulom model 8it* strengt* dependent on state variale

?evern+rent sand

influen(e of density

softening

dilatan(y

simplicity

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+!(ld n /-C!lm+ mdel

de%c(+e B!ney $m (n(&(al

ela%&(c e%pn%e & !l&(ma&e

c(&(cal %&a&e

(ncl!de nnl(nea(&y7 peak

%&eng& and %$&en(ng

simplicity?

adequate complexity?

)e"en-en& %and

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#een D Ee$$e(e%

%&a&e paame&e F "l!me d(%&ance

$m c(&(cal %&a&e l(ne

$!nc&(n $ den%(&y and%&e%% le"elme !%e$!l &an "(d a&( alne G

(nd(ca&(ng e$$ec& $ den%(&y and%&e%%'den%e'

'l%e'

F

c(&(cal %&a&e l(ne

mean %&e%%

%pec($(c"l!me

)e"en-en& %and: %&eng&

) d

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@a& (% peak %&eng&?

da&a cn$(m l(nk +e&@een

%&eng& and %&a&e paame&e F

/-C!lm+ mdel @(&

current%&eng& dependen& n

current%&a&e paame&e

#een D Ee$$e(e%

peak

%&eng&


'den%e'

'l%e'

F

mean %&e%%

c(&(cal %&a&e l(ne

%pec($(c"l!me

%&a&e paame&e F

) & d & &

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@a& (% peak %&eng&?

ppe&y $ &e %(l @(c

cange% @(& %&e%% le"el7

den%(&y

da&a cn$(m l(nk +e&@een%&eng& and %&a&e paame&e F

/-C!lm+ mdel @(&

current%&eng& dependen& n

current%&a&e paame&e

#een D Ee$$e(e%

peak

%&eng&


'den%e'

'l%e'

F

mean %&e%%

%pec($(c"l!me

%&a&e paame&e F

)e"en en& %and: d(la&ancy

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)e"en-en& %and: d(la&ancy

#enamed

d(la&ancy: "l!me cange d!(ng

%ea(ng

'den%e' %and epand%

'l%e' %and cn&ac&%

d(la&ancy depend% n den%(&y

d(la&ancy "a(e% d!(ng &e%&

@a& d @e mean +y'den%e'and'l%e'?

"l!me

%&a(n

%ea %&a(n

)e"en en& %and: d(la&ancy

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da&a cn$(m l(nk +e&@een d(la&ancy and %&a&e paame&e F

($ %(l (% nota& c(&(cal %&a&e @en (& (% +e(ng %eaed HF 0I:

&en "l!me cange% cc! &@ad% &e c(&(cal %&a&e: d(la&ancy

'l%e': F 0: cn&ac&(n

'den%e': F J 0: d(la&(n

'l%e''den%e'

%&a&e paame&e F

#een D Ee$$e(e%

d(la&ancy

'den%e'

'l%e'

F

c(&(cal %&a&e l(ne

mean %&e%%

%pec($(c

"l!me

)e"en-en& %and: d(la&ancy

Mo*r )oulom model 8it* strengt* dependent on state variale

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moilisedstrengt* mo

s*ear strain

currentlymoilised strengt*

currentlyavailale strengt*

monotoni(relations*ip

1ratio

availablestrengt*

varies 8it* state parameter

distortional *ardening

monotoni( in(rease of ratio of moilised

to availale strengt* "E=Ep& 8it*

distortional strain Gp

*yperoli( *ardening la8 simple

Mo*r+)oulom model 8it* strengt* dependent on state variale

(onventional drained tria!ial (ompression tests(urrent pea6 strengt*

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volume (*ange a((ompanies s*earing

*en(e (*ange in state variale

*en(e (*ange in availablestrengt*

model automati(ally *omes in on (riti(alstate

softening emerges8it*out eing

des(ried mat*emati(ally

pea6 strengt* is moving target rea(*ed at

infinite distortional strain - t*en identi(al

8it* (riti(al state strengt*

(onventional drained tria!ial (ompression tests

different initial density "state variale&

p g

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(*ara(terisation of variation of tangent stiffness

soil response perfe(tly plasti( model

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nonlinearity and reversed plasti(ity oserved 8*en dire(tion

of loading is reversed

elasti(+*ardening plasti( model e*aviour purely elasti( for

stress ratios lo8er t*an t*e previous ma!imum stress ratio

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?evern+rent sand

add 6inemati( *ardening

elasti( region of *ig* stiffness (arried round 8it* re(ent stress *istoryoundary of elasti( region is the yield surfa(e

use ounding surfa(e plasti(ity

plasti( *ardening stiffness depends on separation of t*e yield surfa(eand ounding surfa(e

6inemati( *ardening Mo*r+)oulom strengt* dependent on state

variale hierarchical development

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?evern+rent sand

(alirated against tria!ial test data for

Lostun sand

effe(t of different density=stress level

automati(ally des(ried

ignore pra(ti(al prolem of maintaining*omogeneity 8it*in softening sample

#a

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use model to simulate (y(li( undrained loading leading toeventual liuefa(tion

model fails after 2@ (y(les

a(tual soil "Lostun sand& fails after (y(les

numer of (y(les to liuefa(tion is not a parti(ularly reliale

parameter to use for model (aliration

ovious signifi(ant differen(e et8een samples 8*i(* liuefy in

one or t8o (y(les and t*ose 8*i(* survive for many (y(les

characterof (y(li( pore pressure uild+up reprodu(ed in model

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messages

possile to develop elegant models 8*i(* reprodu(e

desirale me(*ani(al (*ara(teristi(s

espe(ially effe(ts of density and stress level

mat*emati(al (omple!ity not essential

uild up from 8ell 6no8n model - Mo*r+)oulom

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Documents

Naples 200713