CREEP School 1

Transcription

CREEP School 1

CREEP School 1 – Creep in Soft Soils
September 10-11, 2012
Trondheim, Norway
Course Handouts
This material may not be published, reproduced, rewritten, or redistributed without
permission. CREEP is funded by the People Programme (Marie Curie Actions) of the
European Union's Seventh Framework Programme FP7/2007-2013/ under REA
grant agreement n° PIAP-GA-2011-286397.
Monday, 10.09.12
Time
Topic
10:00 - 10:15 Welcome - CREEP project
Lecturer
Benz
10:15 - 11:15
Experimental observations and 1D empirical models for creep in soft soils (1) Den Haan
11:15 - 12:00
12:00 - 13:15
13:15 - 14:00
14:15 - 15:00
15:00 - 15:15
15:15 - 16:45
16:45 - 18:00
Experimental observations and 1D empirical models for creep in soft soils (2)
Break
Viscoplasticity - Posible creep formulations - Soft Soil Creep in 3D
Surcharging effects and 1D isotache behaviour
Break
Performance of different creep models in comparison
Performance of different creep models in comparison - Exercise
Tuesday,
T
esda 11.09.12
11 09 12
Time
Topic
8:15 - 9:00
Anisotropy and destructuration - Experimental observations
9:00 - 9:45
Anisotropy and destructuration - Aspects of modelling
9:45 - 10:00
Break
10:00 - 11:00 Some creep models that incorporate anisotropy and destructuration
11:00 - 12:00 Exercise: Test fill - Parameter determination from Oedometer test
12:00 - 13:15 Break
13:15 - 14:45 Exercise: Test fill - Numerical analysis with different models
14:45 - 15:00 Break
15:00 - 15:45 Creep in various geomaterials C
Creep
and
d smallll strain
t i stiffness
tiff
Discussions
15:45 - 16:00 Closure
Den Haan
Benz
Den Haan
Jostad
Jostad
Lecturer
Karstunen
Karstunen
Grimstad
Grimstad
Grimstad
Benz
8 september 2012
Time scales in creep compression
(and a few more additional slides)
Trondheim CREEP course
E.J. den Haan
10-11.09.2012
primary
compression 
u
secondary
log t
slope
c
The well-known eps - log t graph gradually attains a straight tail with slope c. But
primary has usually already passed before this. Why isn’t the creep tail straight
straight after primary?
1
8 september 2012
R
pe
slo
c
1/
t
tr
primary
secondary
u
log t
tr
compression 
By reducing time t with a
constant time shift t_r the
whole secondary curve can
be straightened. Obviously
the soil is obeying another
time: its in its own time
zone. This is the intrinsic
time. Or Bjerrum's
equivalent time, but it has
turned out to be a
fundamental concept hence
'intrinsic‘, following
Schiffman.
slope
c
intrinsic time isobar for acting 'v
intrinsic time  = t - tr
 = cst + c log (t-tr)
d/dt = c/(t-tr)
Resistance concept H. Lundgren - N. Janbu
R = dt/d = 1/c (t-tr)
tr now smaller than 0
primary
tr
pe
slo
c
1/
u
log t
compression 
tr
c
R
secondary
e
op
sl
Negative time shift can
occur. Your time is smaller
than the soil's intrinsic time.
This occurs when you apply
a small load and reset your
clock. Nothing much
happens in terms of primary
compression, and
secondary continues as
before. Only now you've
reset your time to smaller
values. On the log t scale
this distorts the shape of the
creep curve.
intrinsic time isobar for acting 'v
intrinsic time  = t - tr
 = cst + c log (t-tr)
d/dt = c/(t-tr)
t
Resistance concept H. Lundgren - N. Janbu
R = dt/d = 1/c (t-tr)
2
8 september 2012
primary
secondary
ttransfer
log t
compression 
u
tr = ttransfer
slope
c
The negative time-shift is well illustrated by resetting the time when a project is
transferred from contractor to client. The secondary slope has already been reached and
the soil has found it’s intrinsic eps – log t creep tail. Putting t_client = 0 at t = t_transfer,
the curve is pulled back to negative infinity, and then gradually curves back to the
intrinsic creep tail. The time difference remains t_r = t_transfer.
The Scandinavian resistance concept is often applied to
1D stiffness M, and in the nc region an offset linear
relation with sigma is often found. This resemble the time
shift in the creep resistance, and is the structural bond
strength
thesis den Haan 1994
Resistance concept applied to stiffness
M
 = cst + b log (-s)
M = d/d = 1/b (-s)
pe
slo
s
b
1/

3
8 september 2012
log v
log 

v 
slope b
slope c


creep isobars (v cst)
creep isochrones
creep isotaches: dvp/dt = c/
Creep isobars and Creep isochrones
(isotaches) cover the whole eps – sigma –
intrinsic time or creep rate of strain space.
log 
v0
log v

v 
slope b
slope c


creep isobars (v cst)
creep isochrones
creep isotaches: dvp/dt = c/
Creep is synonomous with visco-plastic. In addition there are elastic
strains which are uniquely related to change of effective vertical stress.
Total strains are the sum of vp and el strains. These are used in a Darcy
type consolidation calculation. In each time increment, both strain types
occur
4
8 september 2012
specific volume – an alternative for strain
(v = 1 kPa, v1)
30
30
v1
v1
1.37
y = 1.04x
v1 = 1.336 exp(9.26 b )
25
25
Sliedrecht
Sliedrecht
11.7

v0 v0
lnv
b
ln v
11.7
16.7
20
20
16.7
0.605
b = 0.0622(v1 - 1.54)
(remoulded clay - eq. 15,
Den Haan 1992)
15
15
10
10
5
5
1
0
0
0.0
0.1
0.2
b
0.3
0.4
0
5
10
15
vo
Plot deformation as ln v (with v = specific volume), and it turns out that normally
consolidated states plot on a unique line for a given soil. v_1 and b are interrelated, and for
remoulded clays and natural organic Dutch clays, the relationship is unique.
This depiction gives extra information which should not be ignored. Many modellers
however work only with epsilon
5
8 september 2012
2
'V [kN/m ]
1
3.3
10
100
1000
2.9
0.4
b16d 1 achter
b15d 1 sloot
b10d 3 achter
b22d 4 achter
2.7
ln (v)
20ab
33a
55b
112da
0.2
 natural
e0 =
20ab b16d 1 achter 14.2
33a b15d 1 sloot 14.5
55b b10d 3 achter 19.4
112da b22d 4 achter 21.3
3.1
0
2.5
2.3
2.1
0.6
1.9
0.8
1.7
1.5
1
1
10
100
1000
2
'V [kN/m ]
1.2
using v allows identification of similar soil at different density
0.5
30
b [-]
b/c
0.4
25
b = 0.326 (t /w)
-2.11
20
0.3
15
0.2
10
Sliedrecht
5
boring 11.7
boring 16.7
0.1
0
0.9
0
1.0
1.1
1.2
1.3
1.4
t / w
1.5
1.6
1.7
1.8
0.9
1.1
1.3
1.5
 nat /  w
1.7
1.9
correlations, organic clay
6
Compression and Creep
CIE4367
E.J. den Haan
Compression and Creep: History
Terzaghi 1918 – 1925 (Istanbul)
permeability, stiffness, consolidation of clay
- k depends on voids ratio
- effective stress principle
(but earlier also Fillunger 1915)
- flow of water analogous to flow of heat
(Forchheimer)
- k determined from hydro-dynamic phase
1925 Erdbaumechanik
2012
T
1.E-04
0
1.E-03
1.E-02
1.E-01
1.E+01
0
solution to Terzaghi's consolidation equation:
0.1

0.1
2
0.2
U = 1 - 2M x exp(-M T)
M=/2, 3/2, 5/2, ..
0.3
U = Z/Zmax = 1 - uav/
0.2
0.3
T = t cv / L2
0.4
U
1.E+00
0.4
0.5
0.5
0.6
U-logT
first term
1/6th power
U-sqrt T
sqrt
approach
wortelbenadering
0.7
0.8
best approximation
(relatively unknown):
U = {4T/}
U 6
0.6
T3
T 3  0.5
0.7
0.8
0.9
0.9
1
1
0
0.5
1
1.5
T/4=0.886
T
Terzaghi’s consolidation:
- 1d
- saturated
- homogeneous
- incompressible water and grains
- compressibility of grain skeleton a constant
- permeability a constant
- small strain
Here:
- natural strain
- compressibility of grain skeleton: elasto-viscoplastic
- permeability: f(e)
- consolidation equation large strain
2
2.5
3
3.5
U
NATURAL
STRAIN
Natuurlijke rek
gewone
rek
linear
strain
C=h/ho (Cauchy)
Almansi
Almansi rek = h/h = h/(h-h)
e0
ho
Green
...
Green
h
natuurlijke
rek(Hencky,
(Hencky, eerder
Röntgen):
Natural
strain
earlier
Röntgen)
h
H
 =


ho
dh
h
1
e
h
1
dh
C
h = -ln(h/ho) = -ln((ho-h)/ho) = -ln(1- )
ho
v = soortelijk
specific volume
volume
hoogte
height
v = 1 + e => H = -ln v/v0
H
C
h=0

rek
strain
"zakking
groterexceeds
dan laagdikte"
settlement
initial layer thickness!!
Not only no settlement larger than layer thickness, but also better fits to
H - ln v for most soils without brittle, cemented structure, especially
for soft soils.
v' kPa
1
10
100
1000
0
0.2
0.4

C
rek
0.6
0.8

1
1.2
1.4
Veen Zegveldpolder
H
10000
Terzaghi’s consolidation:
- 1d
- saturated
- homogeneous
- incompressible water and grains
- compressibility of grain skeleton a constant
- permeability a constant
- small strain
Here:
- natural strain
- compressibility of grain skeleton: elasto-viscoplastic
- permeability: f(e)
- consolidation equation large strain
Elasto-viscoplastic behaviour - history:
- “creep”
- Buisman pre 1936: direct and secular
- North America pre 1936: primary and secondary
(Gray 1936, Mesri from 1970’s)
- Koppejan 1948: time lines model
- Bjerrum 1967: conceptual isotache model
- Leroueil 1985: first isotache model + Darcy
- Mesri ~1985: EOP principle + secondary + Darcy
- Delft abc model 1994: isotache + Darcy + large strain
- Mesri / Leroueil ‘roadshow’: EOP versus isotache concept
time [sec.]
10
100
1000
10000
100000
0.0
10000000
10 kPa
22 kPa
‫فين الخث‬
торф
tørv
Torf
turve
τύρφη
‫כבול‬
पीट
tőzeg
gambut
泥炭
turba
veen
0.2
0.4
natural strain [-]
1000000
0.6
0.8
1.0
1.2
34 kPa
68 kPa
134 kPa
270 kPa
600 kPa
1200 kPa
Zegveldpolder peat 25D
2400 kPa
time in step [sec.]
10
100
0.0
1000
10000
100000
1000000
10 kPa
22 kPa
34 kPa
0.2
68 kPa
natural strain [-]
0.4
134 kPa
0.6
270 kPa
0.8
600 kPa
1.0
1200 kPa
1.2
2400 kPa
time in step [sec.]
10
100
0.2
1000
10000
100000
34kPa
00
1000000
tp
primary secondary
ural strain [ ]
0.4
68kPa
Mesri:
strain at tp independent
of layer thickness.
End of Primary EOP concept
13134
4kPakPa
0.6
270kPa
Creep models based on time
Creep models based on visco-plasticity
 H  a log( p /  v0 )  b log( v /  p )  c log(t / t0 )
v0
1
p
a
logv

H
1
 dH
b
 sH
c

e.g. Maxwell element
 v
Elastic (direct)
compression
Visco-plastic (secular)
compression
t0
10t0
100t0
Buisman & Koppejan: divergence
t0 : 1 day (rest of the world)
: Mesri: tp
 H   dH   sH
 H  dH  sH
time in step [sec.]
10
100
1000
10000
0.0
100000
1000000
10 kPa
22 kPa
34 kPa
0.2
68 kPa
natural strain [-]
0.4
134 kPa
0.6
270 kPa
0.8
600 kPa
1.0
1200 kPa
1.2
2400 kPa
1e-4 1/s
1e-4.5 1/s
1e-5 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
1e-7 1/s
time in step [sec.]
10
100
0.0
1000
10000
100000
1000000
10 kPa
22 kPa
34 kPa
0.2
68 kPa
natural strain [-]
0.4
134 kPa
0.6
270 kPa
0.8
600 kPa
1.0
1200 kPa
1.2
2400 kPa
1e-4 1/s
1e-4.5 1/s
1e-5 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
1e-7 1/s
time in step [sec.]
10
100
1000
10000
100000
0.0
10 kPa
22 kPa
34 kPa
0.2
68 kPa
0.4
natural strain [-]
1000000
134 kPa
0.6
270 kPa
0.8
600 kPa
1.0
1200 kPa
1.2
1
2400 kPa
10
100
1000
10000
effective vertical stress [kPa]
1e-4 1/s
1e-4.5 1/s
1e-5 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
1e-7 1/s
time in step [sec.]
10
100
1000
10000
100000
1000000
0.0
0.2
natural strain [-]
0.4
0.6
0.8
1.0
1.2
1
10
100
1000
10000
1e-4 1/s
1e-4.5 1/s
1e-5 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
1e-7 1/s
time in step [sec.]
10
100
1000
10000
100000
1000000
0.0
0.2
natural strain [-]
0.4
0.6
0.8
1.0
1.2
1
10
100
1000
10000
1e-4 1/s
1e-4.5 1/s
1e-5 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
1e-7 1/s
time in step [sec.]
10
100
1000
10000
100000
1000000
0.0
0.2
natural strain [-]
0.4
0.6
0.8
1.0
1.2
1
10
100
1000
10000
1e-4 1/s
1e-4.5 1/s
1e-5 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
1e-7 1/s
time in step [sec.]
10
100
1000
10000
100000
1000000
0.0
0.2
natural strain [-]
0.4
0.6
0.8
1.0
1.2
1
10
100
1000
10000
1e-4 1/s
1e-4.5 1/s
1e-5 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
1e-7 1/s
time in step [sec.]
10
100
1000
10000
100000
1000000
0.0
0.2
natural strain [-]
0.4
0.6
0.8
1.0
1.2
1
10
100
1000
10000
1e-4 1/s
1e-4.5 1/s
1e-5 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
1e-7 1/s
time in step [sec.]
10
100
1000
10000
100000
1000000
0.0
0.2
natural strain [-]
0.4
0.6
0.8
1.0
1.2
1
10
100
1000
10000
1e-4 1/s
1e-4.5 1/s
1e-5 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
1e-7 1/s
time in step [sec.]
10
100
1000
10000
100000
1000000
0.0
0.2
natural strain [-]
0.4
0.6
0.8
1.0
1.2
1
10
100
1000
10000
1e-4 1/s
1e-4.5 1/s
1e-5 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
1e-7 1/s
time in step [sec.]
10
100
1000
10000
100000
1000000
0.0
0.2
 v   v and   creep
distorted o.c. isotaches
natural strain [-]
0.4
creep isotaches
0.6
0.8
b
1.0
ln(10)
1.2
1
vertical spacing c = ln(d/dt)
10
100
1000
10000
1e-4 1/s
1e-4.5 1/s
1e-5 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
1e-7 1/s
tijd na in
begin
stap[sec]
[sec.]
time
step
10
100
1000
10000
100000
1000000
0.0
natural
strain
natuurlijke
rek [-][-]
0.2
0.4
24 uur
0.6
0.8
1.0
1.2
Zegveldpolder veen 25D
1
10
100
stress [kPa]
spanning [kPa]
1000
10000
1e-4 1/s
1e-7 1/s
1e-4.5 1/s
1e-7.5 1/s
1e-5 1/s
1e-8 1/s
1e-5.5 1/s
1e-6 1/s
1e-6.5 1/s
tijd inindestep
stap [days]
[dagen]
time
0.01
0.0
0.10
1.00
10.00
0.1
natuurlijke
rek [-]
[-]
natural
strain
0.2
0.3
0.4
0.5
0.6
Oostvaardersplassenklei (gehomogeniseerd)
0.7
1
10
100
1000
10000
spanning[kPa]
[kPa]
stress
Elastic-Viscoplastic model equations
Maxwell element
Secular strain (visco-plastic component)
 H  b ln( v /  p )  c ln(sH,ref / sH )
v0
sH  sH,ref ( v /  p )b / c exp( H / c)
Lines of equal rate of creep strain:
isotaches
p
1
a
lnv
1
 dH
b
 sH
Direct strain (elastic component)
 dH  a ln( v /  vo )
dH  a v /  v
Summation
 H  dH  sH
 H   dH   sH

H
c

 H
s ,ref
 v
  
ln ’v
onderbouwing
   0  c ln 0  ln    c ln 0 

 0
0H
t0
H
t

    0   0 
exp



c


 

   0 
exp
d  0 dt
 c 

t
   0 
 exp c d   0 dt


0
t0
0
  
-tr
    0  0
t  t 0   1  t  t 0   0  
exp

c 1/
0
0
 c 

 t  tr 
  

   0  c ln   c ln

t t 
 0
 0
r 
  t  tr 
 

  c ln
 0

 t  tr
   0  c ln
 t0  tr
c


 0 
  c ln


  

  t  tr
time shift
Intrinsic time
Time registration
time shift makes good the difference between the intrinsic time and
the value of t resulting from the chosen time zero.
shape of secondary phase curve depends on sign of tr
ln ’v
t’0
0
t’’0
ln(t), ln()
c
0,t0
H
• H - ln is linear, not H – ln(t)
• 0 < t0 (tr > 0) for large v
• 0 > t0 (tr < 0) for small v
log t
creep tail:
1
   i  c log t
  c /(t - tr )
   i  c log
ln(10)

c
Integrate
The intrinsic creep time
is
  t  tr 
c

   i  c log(t  t r )
For each arbitrary choice of time zero in a settlement calculation,
tr gives the difference between t and : tr = t - 
Finite strain consolidation + isotache compression
q= -


   ue 


k
    w 
v   v o   ue

=- o
k
v  z  v  z   w
datum
z



d=
v
vo
dz

dz
d
u e 
=
(  - p - u s ) ( p =  v )
z z
initial state
 - w

(  - u s )= s
z
vo
q= -
Fig. 3. Coordinates of an element of soil
in the initial and deformed states.
 s -  w vo   k

v z  v
w
 1 vo   k vo p 
+


  w v z  v z 
v
v
 H = dH +  sH
v
v
deformed state
mass conservation
finite strain consolidation
d p p   s -  w vo   k  1 vo   vo  p  c 
equation for
=  +
 k
- 
dt a 
v z  v   w v z  v z   
elasto-viscoplastic solid
w
q= -
 H = -
Note: MSettle now superseded by D-Settlement
80
60
load in kPa
40
20
time in seconds
2
4
settlement in mm
model effects, demonstrated by Consef
Consef: consolidation and secular effect. Solves
finite strain consolidation equation including
a visco-plastic term
d v  v   s   w vo   k  1 vo   vo  v  c 
 
k
 
 
dt
a   w v z  v   w v z  v z   
elastic
Darcy, self weight
Darcy, proper
for single, double draining layer, and single load
slope a
ref=1d
=104d
vp
Ko - C.R.S. oedometer
load cell
v top
backpressured
triaxial cell
piston
Ko-ring with
insulation
strain gauges
sample
platen and
drainage filter
soil sample
h
Ko ring
load cell
v bottom
excess pore
pressure
v' kPa
1
10
100
1000
1
0.0
0.9
0.1
0.8
0.2
0.7
0.6
0.5
0.4
Ko
H
 [-]
0.3

0.5
0.4
0.3
0.6

Ko - C.R.S. oedometer test 710402 46A 152/.011-066
0.7
Sliedrecht Gorcum Licht clay wet = 1.29 t/m
3

0.2
0.1
0
0.8
v' kPa
1
ko
10
0.0
100
1000
710402 46A 152/.011-066
0.1
 = -Ck log (k/ko)
]
0.2
0.3
0.4
0.5
slope Ck
0.6
1.E-11
logv'
logk
1.E-10
1.E-09
1.E-08
k [m/s]
1.E-07
1.E-06
v' kPa
1
10
100
1000
1
0.0
0.9
0.1
0.8
Ko,nc
slope a
0.2
0.7
0.6
Ko

0.4
0.5
0.5
Ko
H
 [-]
0.3
0.4
0.3
0.6
Ko - C.R.S. oedometer test 710402 46A 152/.011-066
0.7
Sliedrecht Gorcum Licht clay wet = 1.29 t/m
slope b
3


0.2
0.1
0
0.8
creep parameter c from relaxation phase
 b  vR
 
 1 
 v   vR
t
 
 c  vR
vR'
102
v' in kPa
97
c / b
92
87
relaxation
82
77
Ko - C.R.S. oedometer test 710402 46A Sliedrecht Gorcum Licht clay wet = 1.29 t/m3
72
0
2
4
6
8
relaxation time in hours
10
12
14
Imai 1989
The Hypothesis A vs.
Hypothesis B controversy
EOP vs. Isotache models?
Exercise:
Use Consef to show that the isotache model
can yield both Hypothesis A and Hypothesis B
type behaviour
CREEP – School1
Trondheim, September 10th 2012
Viscoplasticity - Posible creep formulations Soft Soil Creep in 3D
Thomas Benz
With thanks to Valentina Berengo, Martino Leoni & Pieter A. Vermeer
Table of contents
Part 1 Possible approaches to creep modeling
Part 2 Possible creep formulations
Part 3 Soft Soil Creep 3D as an example
Part 1
Possible approaches to creep modeling
Part 1: Possible approaches to creep modeling
RHEOLOGICAL MODELS
Uniaxial condition
condition, aiming to
conceptual understanding
1D EMPIRICAL MODELS
Data fitting of experimental data
Data-fitting
Specific boundary conditions
GENERAL STRESS-STRAIN-TIME MODELS
Mostly 3D models in incremental form
Liingaard et al. (2004) Characterization of Models for Time-Dependent Behavior of Soils
Part 1: Possible approaches to creep modeling – Rheological models
Basic components (solid mechanics)
Constitutive models can be built by combining these basic elements, e.g.:
((Maxwell model))
Part 1: Possible approaches to creep modeling
RHEOLOGICAL MODELS
Uniaxial condition
1D EMPIRICAL MODELS
Data-fitting
Part 1: Possible approaches to creep modeling – Empirical models
Well known creep rate concepts:
Norton (1929):
ε 
Prandtl (1928):
ε 
Soderberg (1936):
ε 
1

1

1

(σ  σ o )α
 sinh (ασ  ασ o )
for 
 ( exp (ασ  ασ o )  1)
for 
 = reference time, may be temperature dependnet
Bj
Bjerrum
(1967)
t
Cα = SECONDARY COMPRESSION INDEX
t eoc
Void ra
atio e
e = e e o c - C α lo g
eeoc
1
Cα
teoc
log t
eeoc = void ratio at end of consolidation
teoc = time at end of consolidation
Garlanger (1972):
e  eeoc - C α log
τ + t
τ
with:
τ = extra parameter
t’ = t - teoc
Bj
Bjerrum
(1967)
e
OCR 
NC-Line
Cs
CS
1
σo
σp
σo
σp
= SWELLING INDEX
log 
AN OVERCONSOLIDATED STATE CAN BE REACHED BOTH BY CREEP
AND UNLOADING
Šuklje (1957): Isotache model
Unique relationship between e, log and e
e
e  a1
e  a2
e  a3
log 
Further example: Den Haan (1994)
Incomplete list of 1D empirical models
Sing and Mitchell (1968) – 3 parameter, constant stress, primary loading, ...
Lacerda and Houston relaxation model - Relaxation, undrained, ...
Prevost relaxation model (1976) – Triaxial,
Triaxial undrained
Strain rate approach:
Sukjle (1957)
Leroueil et al. (1985)
Viad and Campanella (1977)
Vermeer, Stolle & Bonnier (1998)
Vermeer & Neher, (1999)
Vermeer, Leoni, Karstunen & Neher (2006)
Part 1: Possible approaches to creep modeling – General models
RHEOLOGICAL MODELS
Uniaxial condition
1D EMPIRICAL MODELS
Data-fitting
Part 1: Possible approaches to creep modeling – General models
1 O
1.
Overstress concept (Malvern,
(M l
19
1951;
1 P
Perzyna, 1963)
“Overstress models”
2. Nonstationary Flow Surface theory (NSFS) (Sekiguchi & Ohta,1977);
Nova, 1982)
3. Others
Note:
General 3D creep models typically belong to the class of viscoplastic
models. Differences and similarities to elastoplastic models see next
section. The word "viscosity" is derived from the Latin "viscum",
meaning
i mistletoe.
i tl t
A viscous
i
glue
l called
ll d bi
birdlime
dli
was made
d ffrom
mistletoe berries and was used for lime-twigs to catch birds
[http://www.etymonline.com].
Part 2
Elastoplasticity - Viscoplasticity
Part 2: Elastoplasticty – Viscoplasticity
Elastoplasticity
Viscoplasticity – Possibility 1: Overstress concept
• No viscous strain inside the yield surface
• No
N consistency
i t
condition
diti
• Non-associated flow rule possible
• Creep strain rate is function of overstress
Viscoplasticity – Possibility 2: NSFS
Define yield function as function of:
• Stress
• Internal variables
variables, including viscoplastic strains
• Time  = (t)
and
d th
then enforce
f
consistency
i t
condition
diti so that:
th t
• No viscous strain inside the yield surface
• Consistency
C
i t
condition
diti enforced
f
d
• Non-associated flow rule possible
• Creep strain rate is function of overstress
Viscoplasticity – Comparison
Viscoplasticity – Comparison
Viscoplasticity – Other possibilities exist, too.
Example: Soft Soil Creep 3D
e

e e  e c   

p 


p
 p eq

 pp



 

q2
peq  p  2
M p
q
NCL
σi
peq
p´
pp
Part 3
Soft Soil Creep 3D
Part 3: Soft Soil Creep 3D
e
1+e
e
1
1

Cc
Cs

1
1
Cα
1
log V′
 = Cc / ln10
= modified
difi d compression
i iindex
d
  2Cs / ln10
= modified swelling index
 = Cα / ln10
= modified creep index
ln p′
log t
( 1 = 2 = 3 )
CREEP MODEL FOR ISOTROPIC LOADING
p 
1  p
e  e e  e c   


p
τ  pp



 

p 
 = Cc / ln10
l 10
= modified
f
compression index
  2Cs / ln10
= modified swelling index
 = Cα / ln10
= modified creep index
1
3
 1   2   3 
The preconsolidation pressure pp is continuously updated by using:
 e c
p p   p p 
 -


a T 

(Model derivation)
Assume:
 v   v e,eop   v p,eop   v creep   *ln
p ' pc,eop
 t'
p'
 ( *  *) ln
  *ln c
p '0
p ' pc 0
c
Hardening rule:
  creep 
dp ' pc
p ' pc  p ' pc 0 exp  v
 and thus d  v creep    *  *
  *  * 
p ' pc


A creep model based on Bjerrum’s
’ idea ((e.g. above hardening rule):
)
 v   ve   v creep   *ln
p ' pc
p'
 ( *  *) ln
p '0
p ' pc 0
Equate the first and third equation above:
 v   *ln
p ' pc,eop
p ' pc
 t'
p'
p'
 ( *  *) ln
  *ln c
  *ln
 ( *  *) ln
c
p '0
p ' pc 0
p '0
p ' pc 0
 *ln
p ' pc
c  t '
 ( *  *) ln
c
p ' pc,eop
(1)
(Model derivation)
Assume p ' pc  p ' and t '    t EOP then:
 *ln
 c    t EOP
p'
 ( *  *) ln
c
p ' pc,eop
Furthermore if  c  t EOP   then:
( * *)
 *
 
p'


 c  p ' pc,eop 
 p ' pc,eop 
c   

p' 

thus
( * *)
*

   OCReopp
Finally, develop model formulation from:
v  v e  v creep   *
(1)
(2)
dp '
*

p ' c  t '
d  v  d  v e, eop  d  v creep   *
dp '  * 
d


p '  c 
( * *)
 *
dp '  *  p '
d v   *



p '   p ' pc 
( * *)
p ' pc, eop   *
p ' pc



dp '  *  1 
*



p '   OCR 
( * *))
*
ELLIPSES OF MODIFIED CAM CLAY ARE CONTOURS FOR
CONSTANT RATE OF VOLUMETRIC CREEP STRAIN
q
e c = a
e c<< a
NCL
σi
p´
p
peq
peq  pequivalent  p 
q2
M 2 p
pp
NCL : peq = p p


(2)
Summary 3D formulation
 p eq
ε i  ε  ε  C  σ j  Λ 
e
i
c
i
e
ij
C eij 
1 μ  p eq
Λ 

d τ  p p

σ i
1
E
 1

 ν

 ν
 ν

 ν

1 
ν
1
ν
q



 

 q p 
d  1 

 M 
E  3(1  2  )
p p  p p0
σi
ε ic
peq
NCL
2
p
κ
 ec0  ec 
exp 

 λκ 
p e q  p  
q2
M 2p 
p´
pp
ν  Poisson's
P i
' ratio
i
κ   κ/(1
/(  e0 )
Model parameters:  ,  ,  ,  , M  = 1 day)
μ   μ/(1
/(1  e0 )
Initial conditions:
 1o ,  2 o ,  3 o , p p o , e o
M d l prediction
Model
di ti iin undrained
d i d ttriaxial
i i l ttests
t
(σ1  σ3 )/ 2
q/2
•
•
FAST SHEARING
•
•
Cu FAST
SLOW
Cu SLOW
p´
ε1  ε3
E t
Extension
i for
f anisotropy
i t
(see
(
Minna
Mi
Karstunen)
K t
)
ε i  ε  ε  C  σ j  Λ 
e
i
c
i
e
ij
peq
σ i
1 μ  peq
Λ

d τ  pp




 

1 q 2  α 2 p 2
d  1 
p 2 M 2  α 2
q
p eq  p  
NCL
peq
pp
q  αp 
M α
2
 e c
p p  - p p 
 -
2
2
1
p

 a T 

p´
  3q


 q

q
α    
 α  ε cv   
 α  ε dc 

 3p'

  4p'

Model parameters:
Initial conditions:
 ,  ,  ,  , M, a,  , 
 1o ,  2 o ,  3 o ,  o , p p o , e o , To
Although
g the p
physical
y
nature of the creep
pp
phenomenon is still unclear,, several 1D
constitutive laws have been proposed based on experimental observations, e.g.
Bjerrum (1967): an overconsolidated state can be reached by creep and
unloading
Sukljie (1956): isotache model
These early researches were the basis of the development of more general
constitutive laws, mainly within the framework of visco-elasto-plasticity. An
example is Soft Soil Creep 3D.
Soft
S
ft Soil
S il Creep
C
3D iis nott an overstress
t
model,
d l and
d also
l cannott be
b fformulated
l t d as
a NSFS model (no elastic nucleus).
References (1/2)
Creep in soft soils
Bjerrum, L. 1967. Engineering geology of norwegian normally-consolidated marine clays as related to settlements of
buildings. Géotechnique, 17: 81-118.
Boudali, M. 1995. Comportement tridimensionnel et visqueux des argiles naturelles. PhD Thesis, Université Laval,
Québec.
Claesson, P. 2006. Creep around the preconsolidation pressure – a laboratory and field study. In CREBS Workshop.
Edited by N.G.I. Oslo.
Garlanger, J.E. 1972. The consolidation of soils exhibiting creep under constant effective stress. Géotechnique, 22:
71-78.
Janbu, N. 1969. The resistance concept applied to deformations of soils. In 7th ICSMFE. Mexico City, Vol.1.
Leroueil, S. 1987. Tenth Canadian Geotechnical Colloquium: Recent developments in consolidation of natural clays.
Canadian Geotechnical Journal, 25: 85-107.
Leroueil, S. 2006. The isotache approach. Where are we 50 years after its development by Professor Šukljie?
Simonini, P. and Berengo, V. 2006. Private communication
Constitutive modelling of creep
Den Haan, E.J. 1996. A compression model for non-brittle soft clays and peat. Géotechnique, 46: 1-16.
Liingaard, M., Augustesen, A., and Lade, P.V. 2004. Characterization of Models for Time-Dependent Behavior of Soils.
International Journal of Geomechanics: 157-177.
157 177
Malvern, L.E. 1951. The propagation of longitudinal waves of plastic deformation in a bar of metal exhibiting a strain
rate effect. Journal of Applied Mechanics, 18: 203-208.
References (2/2)
Nova,, R. 1982. A viscoplastic
p
constitutive model for normally
y consolidated clays.
y In IUTAM Conference on
Deformation and Failure of Granular Materials. Delft, pp. 287-295.
Perzyna, P. 1966. Fundamental problems in viscoplasticity, New York.
Sekiguchi, H., and Ohta, H. 1977. Induced anisotropy and time dependency in clays. In 9th ICSMFE. Tokyo, pp. 229-238.
Š
Šukljie,
L. 1957. The analysis of the consolidation process by the isotaches method. In 4thh ICSMFE, Vol.1, pp. 200-206.
Yin, J.-H. 1999. Nonlinear creep of soils in oedometer tests. Géotechnique, 49(2): 699-707.
Yin, J.-H., and Graham, J. 1999. Elastic viscoplastic modelling of the time dependent stress-strain behaviour of soils.
Isotropic (Soft Soil Creep model) creep model:
Stolle, D.F.E., Bonnier, P.G., and Vermeer, P.A. 1997. A soft soil model and experiences with two integration schemes.
In NUMOG VI. Edited by Pietruszczak S. and Pande G.N. Montreal. 2-4 July 1997. Balkema, Rotterdam.
Vermeer, P.A., and Neher, H.P. 1999. A soft soil model that accounts for creep. In Int.Symp. "Beyond 2000 in
Computational Geotechnics". Edited by R.B.J. Brinkgreve. Amsterdam. Balkema, Rotterdam, pp. 249-261.
Vermeer, P.A., Stolle, D.F.E., and Bonnier, P.G. 1998. From the classical theory of secondary compression to modern
creep analysis.
l i In
I Computer
C
t M
Methods
th d and
d Advances
Ad
in
i Geomechanics.
G
h i
Edit d b
Edited
by Yuan.
Y
B
Balkema,
lk
R
Rotterdam.
tt d
Anisotropic creep model:
Vermeer, P.A., Leoni, M., Karstunen, M., and Neher, H.P. 2006. Modelling and numerical simulation of creep in soft
soils. In ICMSSE. Vancouver, p. Proceedings in print.
Wheeler, S.J., Näätänen, A., Karstunen, M., and Lojander, M. 2003. An anisotropic elastoplastic model for soft clays.
Surcharging and Isotache models
Trondheim Creep Course
E.J. den Haan
10-11.09.2012
Unloading <> Service-life settlement
In NL, “restzetting” or service-life settlement is much more important
than settlement during construction.
Very often, surcharging and vertical prefab drains are used to expedite
creep during construction.
More effective:
- larger surcharge
- longer duration of surcharge
- closer spacing pvd’s
Compression models must deal with effects of unloading
Imposed criteria on service-life settlement
Extreme: HSL railway max. 3cm/100y
Tramway: max. 5cm/2y then 10cm/10y
Trunkroad: 15cm/30y
Polder urbanisation landfills: 10-50cm/30y
settlement rate, city of Rotterdam (Frits van Tol):
old quarters: 1cm/y
some new quarters: 2-3cm/y
Preloading inevitable => unload/reload behaviour
Mesri’s Definitions wrt Surcharge
Termen
final
surcharge
“OCR” = vs/vf
Rs = OCR - 1
extra surcharge
negative creep
“creep recovery”
Dr. Eric Farrell:
“Period of Grace”
end of primary swelling
Definitions, Mesri
renewed creep
“recompression”
Views on post-unloading behaviour – Deltares
colleagues and clients (2005)
A (isotaches): 9
B: 3
C: 2 and a nr. of clients
D (Koppejan): 7
belasting
II
I
III
log t
I
II
A
B
z
D
C
Jamiolkowski, Ladd, Wolski 1971, 1983
case B
Road crossing peat bog, Canada
Samson & La Rochelle, 1972 Case B
Samson, 1985
C reduced relative to n.c. value
C increases to n.c.-value
C increases to n.c.-value
Case1970
B?
Johnson 1970
Johnson
Johnson 1970
isotache concept!
 = C log [ 1 +  t / tsc ]
Austria Case C
Case A MSettle isotache model applied to
embankment in highway N11 (SSB project)
9
Fig. 1
8
7
zanddikte [m]
6
5
4
as built, N11 terpkop 15950-Z-HB-A
3
schematisatie Boskalis
2
installatie verticale drains
1
0
0
50
100
150
200
250
tijd [d]
300
350
400
450
500
200
Fig. 2
1 basissom
2 geen voorbelasting
3 geen ontlasting
gem. wateroverspanning 1
totale spanning op halve laagdikte [kN/m2]
150
1
100
3
2
50
0
0
100
200
300
400
500
600
-50
tijd in dagen
2
v' [kN/m]
tijdindagen
1.E+00
0.0
1.E+01
1.E+02
1.E+03
1.E+04
100
0.00
Fig. 3
0.5
-0.05
-0.10
1.0
1.5
rek [-]
1basisgeval
2geenvoorbelasting
3geenontlasting
-0.15
-0.20
1
2.0
-0.25
2
3
isotachen1(10x)1e5d
2.5
-0.30
200
F ig . 2
1 b as isso m
2 g ee n v o o rb ela stin g
3 g ee n o n tla stin g
g em . w ate ro v e rsp a n n in g 1
150
totale spanning op halve laagdikte [kN/m2]
zetting [m]
10
1.E+05
1
100
3
Isotache calculation
of post-unloading
deformations.
Probably too optimisitic
2
50
0
0
100
200
300
-5 0
tijd in d ag en
400
500
600
6
-0.015
Fig. 12
5
-0.005
1.E-01
0.000
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
4
tijd na ontlasten [d]
3
0.005
0.010
1 basissom
1b kleinere voorbelasting smaller preload
1c kortere voorbelasting
shorter preload
meting zakbaak 15950-Z-HB-A, terpkop N11 measured
zanddikte sand thickness
0.015
0.020
zanddikte [m]
rek na ontlasten [-]
-0.010
2
1
0
0.025
Initial swelling well-predicted. But much shorter ‘period of grace’. Creep already
returning after 15d. Could be 2D effect.
Note increase of load after 30 days. But swelling increases concommitantly!
No sensible model could account for that. But such is ‘practice’.
Klapwijk Pijnacker – Test embankments Boskalis
2.5m on extensive fill of 4m
With close drain spacing, to all intents and purposes, Case C
Gemiddelde zandhoogte proefterp
7000
Gemiddelde zakkingen Pijnacker
0
6000
-400
zakking [mm]
hoogte [mm]
5000
4000
3000
2000
-800
voorspelde zetting voor
spuitvak na 0.5 a 1.5 jaar
-1200
-1600
1000
-2000
0
0
0
100
200
300
400
tijd [dag]
500
600
100
200
700
terp, 2 m hoh
300
400
500
600
tijd [dag]
terp, 0.5 m hoh
terp, 1 m hoh
spuitvak, 2 m hoh
700
Characteristics post-unloading behaviour in-situ
swelling
after undefined period, renewed creep
beter drainage, more preload => longer swelling period
Confusing data. We’re no-where close to resolving post-unloading
deformation behaviour. Will CREEP help?
Oedometer post-unload behaviour
Small strains during oedometer post-unloading
and strong temperatue effects on creep rate. Pumping?
6.500
1E-03
6.550
1E-04
1E-05
abs(-dv/dt)
1E-06
1E-07
6/4 n~40
1E-08
6/4 n=20
6/4 n=6
1E-09
hele dagen na ontlasten
1E-10
1E-11
reduction from 100 kPav to 64 kPa
smoothed with n points
red dots full days after unloading
Book 1940 Keverling Buisman
Case D
reduced creep?
6.600
Long duration unload test peat Bergambacht
Case D reduced creep?
0.0
15 kPa
30 kPa
60 kPa
0.1
linear strain
80 kPa
120 kPa
0.2
80 kPa
eps - log(t)
0.3
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+09
time [sec]
long duration unloading, organic clay,
N11 – Alphen a/d Rijn (concluded 2009)
t: log scale
Case B or C
reduced creep!
natural strain
80 kPa
0.4
depth 5.2 m-g.l.
bulk density 1.30 t/m3
w0 158%
LOI 14.2%
v0 5.12
duration of unloading 596 days
excellent T-control
105 kPa
Expected characteristics in oedometer
Systematische oedometerstudie
OCR : swelling  swelling duration  C,new 
ts’ : ontlastgedrag
swelling  swelling duration  C,new 
softer clay: swelling  swelling duration  C,new 

Kamao 1995 Chiba peat
swell : Ip , OCR 
longer preloading => less swelling!!
swelling period : OCR 
swelling period  preload duration !! (useful rule of thumb)
Cnew  : soil softness , OCR 
Cnew  : ts’ , OCR 
Method Mesri – nomograms from oedometer tests
Method Mesri
- tl/tpr dubius
- tpr how to find?
- amount of swelling?
Method Mesri
Isotaches and Post-unload behaviour
60 min
1 day
dHH/dt sec-1
d dt　1/s
1.E-01
1.E-04
1.E-07
1.E-10
7 days
0.20
40kPa
80 kPa
60 kPa
H
H
0.25
60 kPa
OCR=1.3
tp=60min
tp=1day
tp=7day
80kPa
0.30
Kamao: Renewed creep on unique (steeper) isobar independent of duration of
preloading
Isotaches <> Post-unload behaviour
renewed creep: hopeful.
but not very important
swelling: (period of grace)
• elastic
• negative creep
difficult but important
drainage capacity => layer thickness-effect
Postulated Principle of behaviour (den Haan)
- AB Creep after monotonic loading follows virgin isotaches
- AC Relaxatie eg. in middle of thick layer
- AD Elastic swelling eg. at draining boundaries
- After swelling first negative creep
- Renewed creep after neg. creep following Kamao’s steeper isobar
- Renewed creep after relaxatie following virgin isotaches
- Reloading after swelling followin distorted isotaches
Competing view – Di Benedetto & Tatsuoka
Final creep state in the EVP model of Di Benedetto
and Tatsuoka
J.H. Yin has a similar final creep state
Creep downwards above reference curve
Creep upwards (negative) below reference curve
Isobars virgin and renewed compression don’t line up
d/dt [sec-1]
1E-02
0.35
1E-03
1E-04
1E-05
1E-06
1E-07
1E-08
1E-09
1E-10
1E-11
8.5
0.40
0.45
0.50
7.5
0.55
7
0.60
0.65
0.70
100 kN/m2
specific volume v 
 natural strain 
8
68 kN/m2 isobar
(extrapolated)
heave after unloading
from 100 kN/m2
to 68 kN/m2
6.5
100 kN/m2 isobar
"resettlement" at 68 kN/m2 following heave
Deltares model and Deltares test results

1
6m/3m thick
0.9
Rate Reduction Ratio R
0.8
6m/4m clay
6m/4m thick
0.7
6m/3m
0.6
6m/4m
4m/2.7m
0.5
4m/2m
0.4
0.3
0.2
0.1
0
1
1.2
1.4
1.6
1.8
2
OCR
 for thicker sample !
 =1 in-situ??
2.2
Comparison
p
of different
creep models
Hans Petter Jostad
Discipline leader in numerical modeling at NGI
Adjunct Professor at NTNU
1st CREEP Course, Trondheim, Norway,
10-11th September 2012
Keyy q
questions
What is the definition of creep?
Do we have creep deformations at the same time as we
have deformations due to pore pressure/stress
changes?
When does creep start?
What controls the (volumetric) creep deformation?
Motivation
How to calculate long term settlements in soft clay?
Primary and secondary compression phases?
Coupled consolidation and creep?
de  e  d '  e 
 e dT   e d i 
  




dt   '  t dt  t  '  T dt    i dt 
stress induced creep (temperature) (chemical)
tp
t
 e  d'  e  
 e  
e   
   dt     dt

'  t dt  t   ' 
t   ' 
0 
t p 
Primary (consolidation)
Secondary (creep)
Bjerrum's delayed compression concept
Main challenges
g
Problem
Due to significant different time scale in field and laboratory
conditions, the deformation in the field must be described
(extrapolated) by a creep model based on input from laboratory
tests.
Verification/calibration of creep models
Back-analyses of measured field data
Generally large number of uncertainties
Back-analyses
y
of idealised model tests (e.g.
( g oedometer tests with
different specimen heights)
Extrapolation is still necessary
Long term laboratory tests
Extrapolation is still necessary
Key questions related to long term settlements
Extrapolation of laboratory data; rate?
Extrapolation of laboratory data; time?
Long time oedometer tests
Time (min)
1.E+03
1
E+03
0.0
1 day
1 E+04
1.E+04
1 E+05
1.E+05
1 E+06
1.E+06
400 days
0.5
 crreep
1.0
1.5
p'/po'=1.2
2.0
p'/po'=1.5
p
p
2.5
p'/po'=1.75
p/'po'=1.6
3.0
p'/po'=2.3
3.5
KRYKON, r=150
Behaviour around pc' (destructuration)?
Effect of varying load history?
Effective stress kPa
-5 %
0
100
200
300
400
500
600
several years
KRYKON, r=300
4.0
0.6
700
1.0
p' / po'
1.5
2.0
3.0
0%
2
Strain
5%
0 , R0
4
10 %
400 days
v (%)
6
15 %
10 yr
-1
-1
0.1 yr
20 %
0.001 yr-1
25 %
R = 0.1
R=1
R = 10
R = 100
Time resistance (years)
400 days
8
24 hrs
Test 1
10
R = 1000
12
Test 2
Test 4
400 days
400 days
Sample
p disturbance
Effective stress (kPa)
0
2
4
6
8
10
12
14
16
18
20
22
24
100
8
1000
Block
Tangent modulus (MPa)
T
Strain (%)
10
Block
54 mm
54 m m
6
4
2
0
0
100
200
300
400
500
(
)
Effective stress (kPa)
Is soil disturbance the reason for
good agreements between standard
consolidation
lid i
analyses
l
((without
ih
creep))
and field observation?
Moc = a · Mpc
a = 5 -> 15
CREBS
• 3 Workshops on CREep Behaviour of Soft clay)
• NGI (Oslo, Norway, January 2006)
• Univ.
Univ Stuttgart (Pisa
(Pisa, Italy
Italy, September 2007)
• Univ. Chalmers (Gothenburg, Sweden, July 2009)
Establish a common basis of understanding
g long
g term
compaction in soft soil
- analyse a set of well defined hypothetical cases
Example calculations
• C
Comparison off results obtained by different
ff
calculation
programs (for a set of well defined cases)
• Comparison of material models
• Interpretation of laboratory tests (model dependent)
• Recommendations of laboratory tests and field
investigation
• Not a competition!
Hypothetical
yp
cases
1. NC-behaviour (OCR=1)
(
)
2. NC-behaviour with apparent pre-consolidation
3 Varying time history (pre
3.
(pre-loaded
loaded several years)
4. Layered soil profile (different permeability)
5. Stress distribution with depth (some shear strain)
The real case: Oslo Railroad Customs Building
- 50 years with measurements (may include additionally 30 years)
Soil Investigation
Soil profile from e.g. CPTU and location of depth to bedrock (or a stiff
layers)
In-situ pore pressure measurements (piezometers)
Soil samples from different depths
Standard index tests
Oedometer tests
- constant strain rate (CRS) tests with unloading/reloading loops.
- x days creep test (and/or CRS tests with different rates)
- additional permeability tests?
- incremental loading (IL) tests (specification: Dq/q=1?, duration=24
hours or EOP,
EOP pore pressure measurements
measurements, long term creep
phases, etc)
Hypothetical cases
q = 50 kPa (light) and 90 kPa (heavy)
GWT
drainage
 10 MPa
10
MP
'' = 10 kN/
kN/m3
' = 10 kN/m3
OCR = 1.4 (10 000 years old)
e0 = 1.17 (po'=143 kPa)
kv = 0.02 m/year
Open and closed bottom
Hsand = 10
0m
Hclay = 30 m
Main assumption
1
1.
Fully saturated clay (incompressible pore water)
2.
1D Condition
a. 1D pore water flow with defined drainage conditions
b. Negligible horizontal strains (oedometer condition)
3.
g in stress levels and initial void
Uniform material ((onlyy changes
ratio) within the soil layers
4.
Assumed perfect oedometer test data (no effect of sample
disturbance?)
Oedometer results – standard IL test
20 mm sample with drainage at top and bottom
Test 693 (load step 280 kPa creep phase)
Odometer test 693
(24 hours results)
time (min.)
Effective vertical stress (kPa)
0
500
1000
0.1
1500
0.00
0,0
2,0
5.8 days creep phase
0.50
6,0
8,0
10 0
10,0
12,0
14,0
16 0
16,0
18,0
20,0
eo = 1.17 (p0' = 143 kPa)
y
Results after 1 day
Vertical sttrain (%)
Vertical strain (%)
4,0
1.00
1.50
2.00
2.50
3.00
3.50
4.00
1
10
100
1000
10000
Oedometer test data
Test no. 693, po' = 143 kPa
Ti
Time
(min.)
( i )
0.1
1.0
10.0
100.0
1000.0
10000.0
0.00
1.00
Increme
ental strain (%
%)
2.00
3.00
0-10 kPa
10-20 kPa
4.00
20-40 kPa
40-80 kPa
5.00
80-130 kPa
130-180 kPa
6.00
180-280 kPa
280-320 kPa
7.00
320-640 kPa
640-1280 kPa
8.00
Hypothetical cases
q = 50 kPa and 90 kPa
GWT
drainage
vo'+
+q
10 MPa
'' = 10 kN/
kN/m3
Hsand = 10
0m
' = 10 kN/m3
OCR = 1.4
vo'
e0 = 1.17 (po'=143 kPa)
kv = 0.02 m/year
vc'
Open
p
and closed bottom
Hclay = 30 m
6 Participants
p
•
University of Stuttgart
•
•
Dr. Martino Leoni and Professor Pieter Vermeer
University of Strathclyde (and Ecole Central de Nantes)
•
•
Dr. Zhen-Yu Yin and Professor Minna Karstuen
University of BRISTOL
•
•
Dr. David Nash
Chalmers University of Technology (Gothenburg)
•
•
Mats Olsson and Professor Claes Alén
Swedish Geotechnical Institute (SGI)
•
•
g
and Rolf Larsson
Per-Evert Bengtsson
Norwegian Geotechnical Institute (NGI)
•
Professor II Hans Petter Jostad
Models
•
Plaxis (FE) with Soft Soil Creep and Anisotropic Creep (3D)
•
•
Plaxis (FE) with EVP SCLAY-1S (3D)
•
•
EVP, structure, stress dependent creep parameter
Embankco (FD) with an isotache model (1D)
•
•
EVP, rotated
EVP
t t d modified
difi d CC,
CC over-stress
t
formulation,
f
l ti
structure,
t t
two
t
creep parameters
Briscon (FD) with a general isotache model (1D)
•
•
EVP MCC,
EVP,
MCC rotated modified CC
CC, no structure,
structure one creep parameter
EPVP, structure and threshold value for creep
G S i (FE) with
GeoSuite
i h two slightly
li h l diff
different isotache
i
h models
d l (1D)
•
EPVP, structure by stress dependent creep
Comparison based on Janbu’s resistance
concept
 v‘
vc‘
vo‘
1
teqv
Mt
constant v‘
Ro
increasing
time
1
reference strain
at a reference time

t

R
Mt = f(v’)
d v
1 d v ' 1


dt M t dt
R
R = f(v’, e or )
Janbu’s time resistance
R = Ro + r (t - to)
teqv
1 R 1 t
ln   ln 
r  Ro  r  to 
 creep 
R  Ro e
e

1
constant v‘
r  creep 
1
R  rteqv 
R
teqv
tref
*
*  *
*
OCR 
N ( OCRs 1)
 1
1
1
* 
r
t
R

R
Time resistance (y
(years))
50
100
150
1%
0
Sttrain (%)
2%
3%
4%
 
1
R
0 = 1.2 %
R0 = 0
0.3
3 year
r = 150
1
R
Creep strain rate ( 1 / year)
0
0%
10
R  R0 e r (  0 )
1
0.1
0
5%
0.01
0%
6%
2%
4%
Strain
3D formulation
ijvp     F 
f d
 ij




 pmd
  
 1   1
s
 pm   
   F    exp  N  
6%
Interpretation – reference strain (24 hours)
Odometer
Od
t ttestt 693
(24 hours results)
0
500
1000
1500
0,0
2,0
4,0
Vertical strain ((%)
V
 y '  152 kPa
Disturbed, Moc = 1.5 · m · pc’
6,0
Cc
 0.167
1 eo
Virgin loading
loading, MNC = 14 · (
( v’ – pr)
8,0
10,0
Unloading, Mu = 5 · m · pc’
12,0
Cs
 0.021
1
1
 eo
14,0
,
16,0
18,0
20,0
Interpretation - creep phase (NC-regime)
t (min)
2000
4000
6000
8000
R = Ro + r (t-to)
10000
0,0
5
0,5
4
1,0
,
1,5
2,0
2,5
3,0
3,5
4,0
R (yea
ars)
Verrtical strain increment (%)
0
r
3
1
2
1
0
0
2000
4000
time (min)
6000
8000
Interpretation - creep phase (NC-regime)
(
g
)
 creep 
t 
C
log 
1 e
 to 
t 
 creep   * ln 
 to 
Interpretation - creep phase (OC-regime)
100/r
r = 300
Anisotropic elasto
elasto-viscoplastic
viscoplastic model
(EVP-SCLAY1S)
User-defined model in Plaxis 2D
Overstress principle (Perzyana)
Elasto-plastic model,
model S-CLAY1S (Karstuen et al.)
al )
Average strain rate during each step (Crank-Nicolson rule)
ijvp     F 




f d
 ij
 pmd
  
 1   1
s
 pm   
   F    exp  N  
 creep 1
1
 
t
R rs teq
EVP-SCLAY1S - interpretation
* 

1  eo
 0.162 /(1  1.215)  0.073
Comparison of stress-strain-time curves
Reference strain at 24 hrs at top of clay layer
Reference strain (24 hrs) at bottom of clay layer
120
140
160
180
200
400
00
0.0
0 00
0.00
0.5
0.50
Vertical sstrain (%)
100
1.0
Krykon
1.5
SCC/ACM
20
2.0
Briscon
2.5
EVP‐SCLAY1S
3.0
Embankco
Chalmers
3.5
Briscon
2.50
EVP‐SCLAY1S
3.00
Embankco
Chalmers
Time dependent strain at bottom of clay layer
20
40
60
Time (years)
80
0
100
1.5
EVP‐SCLAY1S
2.0
Embankco
2.5
Chalmers
3.0
3.5
60
80
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.0
4.5
4.5
Results – Case 1
40
0.5
SCC/ACM
Briscon
20
00
0.0
Krykon
500
4 00
4.00
0
1.0
480
SSC/ACM
2 00
2.00
Time (years)
0.5
460
Krykon
1.50
Time dependent strain at top of clay layer
0.0
440
1.00
3.50
40
4.0
420
Krykon
SCC/ACM
Briscon
EVP‐SCLAY1S
Embankco
Chalmers
q = 50 kPa
100
Results – Case 1
Generation of pore pressure due to creep?
Results – Case 2
u
 0?
t
t
Results (strain after 50 yr)
Case 2 (q = 50 kPa,Open bottom)
Strain [%]
0
1
2
3
4
5
6
0
5
10
Briscon 3
Depth [m]
15
Briscon 3-d1
Briscon 3-d2
20
Embancko
Krykon
25
Chalmers
30
SSC/ACM
EVP-SCLAY1S
35
40
Results – Case 5
Li ht building
Light
b ildi
Heavy building
Oslo Railroad Customs Building
Measured Results
Time (years)
0
10
20
30
40
0
0.1
0.2
Settlements (m)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Light builing
Heavy builing
50
Recommendations of laboratory tests
IL tests are well suited to provide data on creep
parameters and the location of the RTL
CRS tests is recommended to define the shape of one
p
y around the yyield stress
isotache specially
How should we define creep behaviour before pc?
Conclusions
• Large differences in settlements for well defined idealized examples
• The main reason is uncertainties in the creep behaviour before the
yield stress (apparent pre-consolidation pressure)
• The differences may have been even larger due to uncertainties in
the pre-consolidation pressure (if not given!)
• The programs and material models seems to work well (except
EMBANCKO?)
• Difficult
ff
to check the results obtained with the general 3D models
(especially EVP-SCLAY1)
• Diffi
Difficult
lt to
t compare models
d l due
d tto different
diff
t sets
t off input
i
t parameter
t
even when they are based on the same framework
Anisotropy and destructuration
Anisotropy
and destructuration
Experimental observations
p
Prof. Minna Karstunen
Chalmers University of Technology
Chalmers University of Technology & University of Strathclyde
Acknowledgements
•
Co‐workers (past and current):
•
Current sponsors:
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
Prof. Simon Wheeler (GU)
Prof. Pieter Vermeer (USTUTT/Deltares)
Prof Helmut Schweiger (Tu Graz)
Prof. Helmut Schweiger (Tu Graz)
Dr Martino Leoni (Wechselwirkung Studio Italiano, previously USTUTT)
Dr Zhenyu Yin (Shanghai Jiaotong University, previously USTRAT)
Dr Rachid Zentar (Ecole des Mines Douai, France, previously GU)
Dr Christoph Wiltafsky (Garber, Dalmatiner & Partner ZT‐OG, Austria, previously GU)
Dr Urs Vogler (FutureShip GmbH, Germany, previously USTRAT)
Dr Harald Krenn (Zublin Austria previously GU/USTRAT)
Dr Harald Krenn (Zublin, Austria, previously GU/USTRAT)
Dr Jorge Castro (University of Cantabria, Spain, previously USTRAT)
Dr Mohammad Rezania (University of Portsmouth, formerly USTRAT)
Dr Patrick Becker (USTRAT)
Dr Daniela Kamrat‐Pietraszewska (previously USTRAT)
Dr Nallathamby Sivasithamparam (USTRAT/PLAXIS)
Dr Ronald Brinkgreve (Plaxis bv/TUD)
Dr Paul Bonnier (Plaxis bv)
Ms Anu Näätänen (HUT)
Mr Matti Lojander (HUT)
Ms Mirva Koskinen (AU)
Mr Igor Mataic (AU)
GEO‐INSTALL “Modelling Installation Effects in Geotechnical Engineering” IAPP project funded by the EC/FP7 2009‐
2014
CREEP “Creep
CREEP Creep of Geomaterials of Geomaterials ” IAPP project funded by the EC/FP7 2012
IAPP project funded by the EC/FP7 2012‐2016
2016
Experimental work funded by the Academy of Finland (Grant 128459 “Modelling progressive failure of embankments and slopes”) Outline
• Motivation
• Origin and structure of natural clays
• Anisotropy Anisotropy
•
•
•
•
Basic concept and definitions
Anisotropy of strength
Anisotropy of initial yield
Changes in anisotropy
• Destructuration
• Experimental evidence (1D, 2D)
• Implications for rate‐dependent behaviour
• Conclusions
• Key references
World Population Distribution
World Population Distribution
Formation of soft clays
Formation of soft clays
• Composition and mineralogy of clay minerals
Origin of clays by rock weathering and soil
• Origin of clays by rock weathering and soil formation
• Erosion, sedimentation
E i
di
i
q
g
g
g
• Subsequent loading due to geological processes
• Geochemical alterations (leaching etc.)
G h i l lt ti
(l hi
t )
Str ct re of Nat ral Cla s
Structure of Natural Clays
e.g. Craig (1974): (a) dispersed; (b) flocculated; (c) bookhouse; (d) turbostratic (e) natural clay with silt particles
SEM images of clay structures
SEM images of clay structures
Source : http://www‐odp.tamu.edu/publications/190196SR/212/212_f5.htm
Sensitive clay (quick clays)
Sensitive clay (quick clays)
Crawford 1967
http://www.landslideblog.org/2010/05/possible‐flowslide‐not‐sinkhole‐in‐st.html
Types of clays
Types of clays
•
•
•
•
Natural clays
Natural
clays
Remoulded clays
Reconstituted clays
Compacted clays
Compacted clays
15 kPa
Piston with openings for
escaping water
Perspex cylinder
Filter p
paper
p
Recons-
Porous stones tituted
clay
sample
Filter paper
Piston with openings for
escaping
i water
Leroueil & Vaughan (1990)
• Soil structure consists of:
– fabric ((anisotropy
py)
– interparticle bonding
(sensitivity)
• D
Due to
t plastic
l ti straining
t i i
– gradual degradation of bonding (destructuration)
– changes in fabric (
h
i f b i (anisotropy)
• All these phenomena are rate‐dependent
rate dependent
Anisotropy
• Material is anisotropic if its properties are p
direction dependent
• Clayey soils generally anisotropic:
– Composition (clay platelets)
C
iti ( l
l t l t)
– Deposition (preferred orientation of particles)
– Previous stress history (K0 consolidation, groundwater changes, geochemical changes)
K0 consolidation
Anisotropy in macroscale
Anisotropy in macroscale
Laminated clays from Lake Malawi
After Casagrande & Carillo (1944)
After Casagrande & Carillo (1944)
• Inherent anisotropy ‘physical characteristic inherent to material and entirely independent of applied stress’
• Induced anisotropy py
‘due exclusively to the strains associated with applied stress’
• Initial anisotropy Combination of both applies to soil in situ
Combination of both –
applies to soil in situ
Geotechnical problems
• Highly non‐linear response with a range of strain levels
• Anisotropic stress changes, involving rotation of the direction of major principal stress 1
of the direction of major principal stress 
between 0°‐90°
Hight & Higgins (1994)
• Changes in the relative magnitude of the intermediate principal stress 
p
p
2
2
3
1
3
b takes values between 0 → 1
Hight & Higgins (1994)
Experimental investigation
Experimental investigation
Standard equipment:
Standard triaxial test b=0
0 or b
or b=1
1
• Standard triaxial test b
• Direct shear and simple shear allow continuous changes in b, but no control
i
h
i b b
l
Special equipment
• Hollow cylinder apparatus
Hollow cylinder apparatus
Hollow cylinder apparatus
No longer element test but a
element test but a BVP
Zdravkovic & Potts (2000)
(
)
Effect of sample disturbance
Vertical samples of Bothkennar clay
Vertical samples of Bothkennar clay
=1.4
c=34.6°
e°
=1.1
McGinty (2006)
Horizontal samples of Bothkennar clay
Horizontal samples of Bothkennar clay
McGinty (2006)
y(
)
Hong Kong Marine Deposit
cu= 93 kPa
cu= 30 kPa
Hong Kong Marine Deposit (data from Zhou et al. (2006))
Hong Kong Marine Deposit
Influence of
anisotropy
1D Compression of “ideal”
1D Compression of ideal clay
clay


1 day

lnt
Each day:
CC = compression index
l ’
lnp’
  constant  
CS = swelling index
C = creep index
Anisotropy of yielding
Anisotropy of yielding
S CLAY1
S‐CLAY1
Yield curve for simplified conditions of triaxial test


f  q  p  M 2   2  pm  p p  0
2
Dafalias (1986), Korhonen & Lojander (1987)
80
1
Wi i
Winnipeg
clay
l
241 kPa
310 kPa
380 kPa
0.5
q/
q, kP a
M = 0.67
0 67
0.25
40
M = 0.84
20
0
0
0.25
Marjamäki clay
Depth 5.5-6.1 m
60
vc ',
kkPa
0.75
191 kPa
0.5
0.75
0
1
0
p'/ v c ', kPa
-0.25
20
40
60
-20
90
80
p', kPa
90
Mexico City clay
Depth 1.7 m
Bothkennar clay
Depth 5.3 - 6.3 m
M = 1.4
M=1.75
60
q, kPa
q, kPa
60
30
’ = 18‐43 degrees
30
yield points
from p'-v
yield points
undrained
failure
from q-s
Wheeler et al. (2003)
0
0
0
30
60
0
90
30
p', kPa
60
90
p', kPa
-30
-30
Strain‐Rate Dependency
Critical state line M = 1.5

20
q (kPaa)
1
Corresponding to
in-situ 'v0
Corresponding
to in-situ 'v0
10
Murro clay
Intact
Remoulded
0
(a)
1

Vanttila clay
Experiment
0
0
-20
Critical state line M = 1.35
20
q (kPa)
40
20
40
60
80
0
Corresponding to 'pi
p' (kPa)
p
10
20
-10
(b)
p' (kPa)
30
40
Pseudo‐isotropic loading of Otaniemi clay
50
Test series B
1=0.11
e d
q , kP a
2
25
q
c
 = 0.11
0
0
25
a
a: CAE2550
b: CAE2561
c: CAD2422
d. CAD2423
e: CAD2422
-25
b
K0
50
75
p', kPa
p’
Wheeler et al. 2003
Loading with different stress ratios
Loading with different stress ratios
20
40
60
p', kPa
-10 0
-30
0
20
40
-20
60
80
p', kPa
CAD2264
0.30
30
=0

=0.25
20
0
0
20
-20
40
60
80
p', kPa
-25
25
25
50
75
p', kPa
p
0
-25
60 80
p', kPa
25
10
-10 0
20
50
CAD227 & CAD2464
0.90
=0.90

=0.34
25
0
40
60
p', kPa
CAD2280
0.42
42
=0

=0.33
25
0
25
50
75
p', kPa
0
25
50
75
p', kPa
-25
25
50
CAD2463
=1.00
=0.44
0
0
40
CAE2496
=-0.35
0 11
=-0.11
-30
0
CAD2260
=1.08
=0.46
25
q, kPa
0
q, kPa
CAD2251 & CAD2530
=0.60
25
=0.38
20
-25
50
50
0
50
-40
-40
40
0
-20
q, kPa
0
20
30
-40
40
q, kPa
CAD2276
0.25
=0.25

=0.15
20
q, kPa
40
60
p', kPa
-30
40
q, kPa
20
CAE2586
=-0.40
0 06
=-0.06
q, kPa
-10 0
10
40
q, kPa
10
CAE2544
=-0.59
0 15
=-0.15
q, kPa
30
CAE2513
=-0.66
0 11
=-0.11
q, kPa
q, kPa
30
0
0
50
75
p', kPa
25
50
75
p', kPa
p
-25
Wheeler et al. 2003
E
Experimental evidence
i
t l id
1

0.8
06
0.6
/M=0
0.5
0.4
1
0.2
M
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1
0.5
-0.4
-0.6
-0.8
0.8
1

-0.2
Otaniemi clay
Natural POKO clay
Reconstituted POKO clay
Natural Murro clay
Reconstituted Murro clay
-1
Determination of yield points
Ideal sample with K0= 0.83
Koskinen et al. (2003)
Ideal sample with K0= 0.83
Koskinen et al.(2003)
a)
0
0.00
10
p' (kPa)
20
30
40
b)
20
-20
0.00
p'y=12.1 kPa
0.04
0.04
 v 0.08
 v 0.08
0.12
0.12
0.16
c)
1
q (kPa)
-10
10
-5
5
0
p'y=11.6 kPa
Otaniemi clay
CAE 2544
0.53
53
=-0
0.16
0
p' (kPa)
10
20
30
40
d)
-20
-0.04
-0.04
-0.03
-0.03
-0.02
1
-0.01
-15
q (kPa)
-10
-5
0
CAE 2544
S-CLAY1
S
CLAY1
-0.02
-0.01
0.00
0.00
p'y=12.4 kPa
0.01
-15
15
p'y=11.9 kPa
0.01
Koskinen et al. (2003)
Tests on Natural Clay Samples
M=1.6
=0.63
pp'm=34.5 kPa
a) Murro clay
40
30
30
20
20
10
M=1.2
=0.46
pp'm=49
49 kPa
50
40
q (kP
Pa)
q (kP
Pa)
50
b) POKO clay
10
0
0
0
10
20
30
40
50
60
70
0
-10
10
20
30
40
50
60
70
-10
-20
20
-20
20
p' (kPa)
p' (kPa)
c) Otaniemi clay
d) Vanttila clay
M=1.3
=0.50
p''m=19.5
19 5 kP
kPa
20
M=1.35
=0.52
p'm=18.5
=18 5 kPa
20
10
q (kPaa)
q (kPaa)
10
0
0
0
10
20
30
-10
0
10
20
30
-10
p' (kPa)
p' (kPa)
Tests on Reconstituted Clays
Yield points
M=1 6
M=1.6

max
Max. stress
during 0
loading
40
30
q (kPa)
20
10
p'm=35.5 kPa
0
-10
0
10
20
30
40
50
60
b) POKO clay
30
20
70
-20
-30
-30
Yield points
M=1.3

Max.
max stress
during 0
loading
30
0
10
20
30
40
50
60
70
p' (kPa)
Yield points
d) Vanttila clay
M=1 35
M=1.35

Max.
max stress
during 0
loading
40
30
20
p'm=26.0 kPa
0
0
10
20
30
40
50
60
70
p' (kPa)
q (kPa)
20
10
-10
p'm=42.0 kPa
0
-20
40
q (kPa)
10
-10
p' (kPa)
c) Otaniem i clay
Yield points
M=1
M
1.2
2

Max. stress
max
during 0
loading
40
q (kPa)
a) Murro clay
10
p'm=26.0 kPa
0
-10
-20
20
-20
-30
-30
0
10
20
30
40
50
60
70
p' (kPa)
Karstunen & Koskinen (2008)
After Leroueil & Vaughan (1990)
The Grande Baleine clay (Locat & Lefebre
1982)
Mexico City Clay (Mesri et al. 1975)
1D Compression of natural and 1D
Compression of natural and
reconstituted clays
y
'pi = 6 kPa
2.4
4
'p = 45 kPa
0 37 kPa
kP
''pi = 0.37
Vanttila clay
3.2
1.6
e
e
2
Reconstituted
Intact
Remoulded
2.4
Reconstituted
Murro clay
1.2
1.6
Intact
Remoulded
0.8
1
(a)
kPa
''p = 29 kP
10
100
'v (kPa)
Karstunen & Yin (2010)
0.8
1000
01
0.1
(d)
1
10
100
'v (kPa)
Yin & al
al. (2011)
1000
10000
1D Compression of natural and 1D
Compression of natural and
reconstituted clays
y
0.1
0.04
Intact
Remoulded
0.03
IIntact
Remoulded
Vanttila clay
0.08
Murro clay
C e
C e
0 06
0.06
0.02
0.04
0.01
0.02
0
1
10
100
'v (kPa)
(b)
0
1000
1
10
100
'v (kPa)
(e)
1000
Yin & al
al. (2011)
Constant q/p’ tests
Vanttila
V
ttil clay
l
St>30
POKO clay
St=12
1.2
1.4
1.0
1.2

0.8
  
  
0.6
0.4
0.2
0.0
-1.0
i

-0.5
0.0
0.5
q/p’

i
1.0

10
1.0
0.8
06
0.6
0.4
0.2
0.0
-1.0
i

-0.5
0.0

q/p’
0.5
1.0
10000


f  q  p  M 2   2  pm  p p  0
2
Dafalias (1987), Korhonen & Lojander (1987)
Effect of destructuration on Effect
of destr ct ration on
undrained creep
p
10
-2
Vanttila clay
d a/d
dt (%/s)
10
(c)
Tertiary creep
With destructuration
-4
Without destructuration
Secondary creep
10
10
-6
6
CAUCR1 q=14.4 kPa
CAUCR2 q=17
q 17.3
3 kPa
CAUCR3 q=20.0 kPa Primary creep
EVP-SCLAY1S
EVP-SCLAY1
(c)
-8
10
1
10
2
10
3
10
Time (s)
4
10
5
10
6
Data from Yin & al. (2011)
C l i
Conclusions
• N
Natural soft clays are complex materials, structured l f l
l
i l
d
and time‐dependent • Initial anisotropy & changes is anisotropy
I iti l i t
& h
i
i t
• Bonding and destructuration
• Results
Results rely on high quality sampling and testing
rely on high quality sampling and testing
• Anisotropy affects both yielding and mobilised strength and changes with plastic straining
strength and changes with plastic straining
• Salinity of the sedimentation environment affects the slope of NCL
slope of NCL
• At the onset of yielding, significant compression and (creep) that reduces as destructuration progresses
(creep) that reduces as destructuration progresses
• All plastic strains contribute to destructuration Some Key References:
•
•
•
•
•
•
•
•
•
•
•
•
•
A. CASAGRANDE & N. CARILLO (1944). Shear Failure of Anisotropic Materials. Proc. Boston Soc. of Civil Eng. Vol. 31, pp. 74 – 87
D.W. HIGHT & K.G. HIGGINS (1994). An approach to the prediction of ground movement in engineering practice: background and applications. Pre‐failure deformation of geomaterials, IS‐
Sapporo, Japan. Vol. 2, pp. 909‐945.
M KARSTUNEN & Z ‐Y YIN (2010) Modelling time‐dependent behaviour of Murro test
M. KARSTUNEN & Z.‐Y. YIN (2010). Modelling time‐dependent behaviour of Murro test embankment. Géotechnique 60(10): 735‐749. M. KARSTUNEN & M. KOSKINEN (2008). Plastic anisotropy of soft reconstituted clays. Canadian Geotechnical Journal 45: 314‐328.
M. KARSTUNEN, C., WILTAFSKY, H., KRENN, F., SCHARINGER & H.F. SCHWEIGER (2006). Modelling the stress‐strain behaviour of an embankment on soft clay with different constitutive models. International Journal of Numerical and Analytical Methods in Geomechanics 30(10): 953‐982
M. KARSTUNEN, H., KRENN, S.J., WHEELER, S.J., M. KOSKINEN & R. ZENTAR (2005). The effect of anisotropy and destructuration on the behaviour of Murro test embankment. ASCE International ( )
Journal of Geomechanics 5(2): 87‐97.
M. KOSKINEN, M. KARSTUNEN & M. LOJANDER (2003). Yielding of “ideal” and natural anisotropic clays. Proc. Int. Workshop on Geotechnics of Soft Soils‐ Theory and Practice, 17‐19 September 2003, Noordwijkerhout, The Netherlands. pp. 197‐204.
K. McGinty (2006) The stress‐strain behaviour of Bothkennar clay. PhD thesis. University of Glasgow
S. LEROUEIL & P.R. VAUGHAN (1990). The general and congruent effects of structure in natural soils &
(
) h
l d
ff
f
l l
and weak rocks. Géotechnique 1990 Vol. 40 No. 3 pp. 467‐488
S.J. WHEELER, A. NÄÄTÄNEN, M. KARSTUNEN & M. LOJANDER (2003). An anisotropic elasto‐plastic model for natural soft clays. Canadian Geotechnical Journal 40(2). pp. 403‐418. Z ‐YY. YIN, M. KARSTUNEN, C.S. CHANG, M. KOSKINEN & M. LOJANDER (2011). Time
Z.
YIN M KARSTUNEN C S CHANG M KOSKINEN & M LOJANDER (2011) Time‐dependent
dependent behaviour of soft sensitive clay. ASCE International Journal of Geotechnical and Geoenvironmental Engineering 137(11):1103‐1113. L. ZDRAVKOVIC & D.M. POTTS (2000). Advances in modelling soil anisotropy, Workshop on Constitutive Modelling of Granular Materials, Springer Verlag, Berlin pp. 491‐521.
C Zh
C. Zhou, J.H. Yin, J.G. Zhu & C.M. Cheng (2005). Elastic anisotropic viscoplastic modelling of the J H Yi J G Zh & C M Ch
(2005) El i
i
i i
l i
d lli
f h
strain‐rate‐dependent stress‐strain behaviour of K0‐consolidated natural marine clays in triaxial shear tests. ASCE International Journal of Geomechanics 5 (3): 218‐232
Anisotropy and destructuration
Anisotropy
and destructuration
Aspects of modelling
p
g
Prof. Minna Karstunen
Chalmers University of Technology & University of Strathclyde
E il i
Email: [email protected]
k t
@ h l
Acknowledgements
•
Co‐workers (past and current):
•
Current sponsors:
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
Prof. Simon Wheeler (GU)
Prof. Pieter Vermeer (USTUTT/Deltares)
Prof Helmut Schweiger (Tu Graz)
Prof. Helmut Schweiger (Tu
Dr Martino Leoni (Wechselwirkung Studio Italiano, previously USTUTT)
Dr Zhenyu Yin (Shanghai Jiaotong University, previously USTRAT)
Dr Rachid Zentar (Ecole des Mines Douai, France, previously GU)
Dr Christoph Wiltafsky (Garber, Dalmatiner & Partner ZT‐OG, Austria, previously GU)
Dr Urs Vogler (FutureShip GmbH, Germany, previously USTRAT)
Dr Harald Krenn (Zublin Austria previously GU/USTRAT)
Dr Harald Krenn (Zublin, Austria, previously GU/USTRAT)
Dr Jorge Castro (University of Cantabria, Spain, previously USTRAT)
Dr Mohammad Rezania (University of Portsmouth, formerly USTRAT)
Dr Patrick Becker (USTRAT)
Dr Daniela Kamrat‐Pietraszewska (previously USTRAT)
Dr Nallathamby Sivasithamparam (USTRAT/PLAXIS)
Dr Paul Bonnier (Plaxis bv)
Ms Anu Näätänen (HUT)
Mr Matti Lojander (HUT)
Ms Mirva Koskinen (AU)
Mr Igor Mataic (AU)
GEO‐INSTALL “Modelling Installation Effects in Geotechnical Engineering” IAPP project funded by the EC/FP7 2009‐
2014
CREEP “Creep
CREEP Creep of Geomaterials of Geomaterials ” IAPP project funded by the EC/FP7 2012
IAPP project funded by the EC/FP7 2012‐2016
2016
Experimental work funded by the Academy of Finland (Grant 128459 “Modelling progressive failure of embankments and slopes”) Outline
• Modelling elastic anisotropy
• Modelling large strain anisotropy
M d lli l
t i
i t
• Introduction to various approaches
• Elasto
Elasto‐plastic
plastic models
models
• Microstructural models
• Modelling large strain anisotropy with elasto‐
plastic approach
plastic approach
•
•
•
•
Modelling destructuration
Example: simple model S‐CLAY1S
Example: simple model S
CLAY1S
Conclusions
Key references
Key references
Real problem
Idealized
(conceptual
model)
Idealizedproblem
problem
(conceptual
model)
R
Relevant
p
phenomen
a
Mathematical
M th
ti l
Model (PDE)
Results
m a.s.l.
440
400
North portal
(Lleida)
360
320
280
411+100
412+000
Quaternary
Colluvion
Solution
S
Analytical Numerical
Middle Eocene
4
Early Eocene
Limestone
Claystone & Siltstone
Marl
Anhydritic-Gypsiferous Claystone
• Soil structure consists of:
– fabric (
fabric (anisotropy)
– interparticle bonding
(
(sensitivity)
y)
• D
Due to
t plastic
l ti straining
t i i
– gradual degradation of bonding (destructuration)
– changes in fabric (
h
i f b i (anisotropy)
• All these phenomena are rate‐dependent
rate dependent
Constitutive modelling
Elastic Anisotropy
Elastic Anisotropy
Isotropic
p elasticityy in 3D
 y
 yz
 zy
y
z
 yx
 xy
 xz  zx
 x
 xy 
 z
x
1
( ' x v' ' y v' ' z )
E'
1
 y  ( ' y v' ' x v' ' z )
E'
1
 z  ( ' z v' ' x v' ' y )
E'
x 
 yz 
 zx 
 xy
G'
 yz
G'
 zx
G'
Cross‐isotropic
p elasticityy ((around yy‐axis))
Sampling direction
h
v
 yz
 zy
y
z
x
 y
 yx
x 
 xy
 xz  zx
 z
General 3D elasticity would require the specification of 21 ifi ti
f 21
elastic constants!
 'x
Eh '
y  
 x
z 
 xy 
 yz 
 zx 

vhh '
v '
 ' y  vh  ' z
Ev '
Ev '
' v '
vhh '
 ' x  y  hh  ' z
Ev '
Ev ' Ev '
vvh '
v '
'
 ' x  hh  ' y  z
Eh '
Ev '
Eh '
 xy
Gvh '
 yz
Gvh '
 zx
Ghh '
Needs 5 elastic constants!
Large Strain Anisotropy
Large Strain Anisotropy
Modelling large strain anisotropy
d lli l
i
i
1 Standard elasto‐plastic framework
1.
Standard elasto plastic framework
•
Nova (1985), Banerjee & Yousif (1986), Dafalias
(1986) D i & N
(1986), Davies & Newson
(1993) Whittl &
(1993), Whittle & Kavvadas (1994), Wheeler & al. (2003)
2. Micromechanical models
K0 consolidation
Standard elasto‐plastic framework
• Because the directions of the principal y
stresses and the fabric do not necessarily coincide, cannot use purely stress/strain invariants
 Deviator stress tensor
 Fabric tensor
b
Example of definitions:
Deviatoric stress vector
Deviatoric fabric tensor (in vector form)
'x p'
' p'
 y 
 ' z  p ' 
d  

2

xy


 2 yz 


 2 zx 
p' 
' x   ' y   ' z
3
 x 1 
  1 
 y 
 z 1 
d  

2

xy


 2 yz 


 2 zx 
x  y  z
3
1
• Because the directions of the principal y
stresses and the fabric do not necessarily coincide, cannot use purely stress/strain invariants
 Deviator stress tensor
 Fabric tensor
b
Only in a special when looking at vertical samples being loaded in a triaxial cell can use triaxial invariant combined with a scalar  related to the inclination of the yield surface in p’‐q – plane
• Elastic law
Inclined initial yield surface (dependant on
• Inclined initial yield surface (dependant on initial state) F(’, , ) = 0
• (Volumetric hardening) law relating to the size (V l
i h d i )l
l i
h i
of the yield surface p0’ = f(vp)‐ same as MCC
• Kinematic or translational hardening laws (often called rotational hardening) – evolution (often called rotational hardening) –
evolution
of anisotropy (additional soil constants)
– Soil constants with a physical meaning, but not always easy to derive
S il
t t ith h i l
i b t t l
t d i
• Flow rule
Flow rule
– Associated or non‐associated? Depends on the combinations of the yield surface formulation and the
combinations of the yield surface formulation and the hardening law
– Controls the prediction of K
Controls the prediction of K0 and strain path (and hence and strain path (and hence
ultimately the undrained shear strength)
0.0
0.1
0.2
0.3
v
0.05
d
0.15
0.25
• Failure condition
’3
’1=’

 2= 
’3
’2
’1
Potts & Zdravkovic (1999)
• Failure condition
Need modified definition of Lode angle (Sivasithamparam 2012)
Modelling large strain anisotropy
d lli l
i
i
2
2. Micromechanical models
Micromechanical models
i.
Multilaminate framework
•
Zienkiewicz & Pande (1977), Pande & Sharma (1983), Pietruszczak & Pande (1987), Karstunen (1998), Wiltafsky (2003), Neher et al. (2001, 2002), Mahin Roosta et al. (2004)
ii. Microplane models
•
(
),
g
(
),
g
Bazant (1995), Chang & Liao (1990), Chang & Gao (1995), Chang & Hicher (2005), Yin et al. (2009)
Multilaminate model
Multilaminate model
Multilaminate model
Multilaminate model
• No global equivalent for yield surface, so yielding, K
No global equivalent for yield surface so yielding K0
prediction and mobilized undrained strength need to be checked through simulations at global level
• Computational costs is high
Microplane models
• Considers clay as a collection of clusters
Sliding and compressing
Sliding and compressing the clusters along their contact planes
E l ti
Evolution of the state f th t t
variables at each contact plane
•
•
• Assumptions need to be made for contact number and mean cluster size
• Inter‐cluster properties (shear sliding, dilation and normal compression) not directly measurable
l
i ) t di tl
bl
• Extra computational costs
Modelling destructuration
Modelling Destructuration
• Concept of an intrinsic yield surface proposed b G
by Gens & Nova (1993)
&N
(1993)
– Lagioia & Nova (1995), Rouainia & Muir Wood (2000), Kavvadas & Amorosi (2000), Gajo & Muir Wood (2001), Liu & Carter (2002), Karstunen et al. (2005)
CSL
q
1
M
1
pmi’
1
CSL
M
pm’
p’

• Initial amount of bonding
CSL
q
1
M
1
pmi’
1
CSL
M
pm’
p’

– Relates
Relates the size of natural yield the size of natural yield
curve to the intrinsic yield curve
– Additional state variable ddi i
l
i bl
(scalar)
– Approaches to zero
pp
• Hardening law for destruction of bonding
– Gens & Nova (1993) assume all plastic strains contribute
– Slightly different forms Slightly different forms
proposed by various authors
Gens & Nova (1993)
Gens & Nova (1993)
Simple model: S‐CLAY1S
Simple model: S
CLAY1S
Constitutive models
• Anisotropy
– S‐CLAY1 (see Wheeler et al. 2003, Karstunen & Koskinen 2008)
’y
• Bonding & destructuration

p’
– Adding intrinsic yield surface (Gens & N
Nova, 1993) resulted in S‐CLAY1S 1993)
l d i S CLAY1S
(Karstunen et al. 2005)
• Time‐dependence & creep
– Anisotropic
Anisotropic creep model ACM & ACM‐S creep model ACM & ACM S
(Leoni et al. 2008, Kamrat‐Pietraszewska 2011)
– n‐SAC (Grimstad et al. 2010)
– EVP‐SCLAY1S (Karstunen & Yin 2010)
EVP‐SCLAY1S (Karstunen & Yin 2010)
– Ani‐Creep (Yin at al. 2011)
’’x
’z
E
Experimental evidence
i
t l id
1

0.8
06
0.6
/M=0
0.5
0.4
1
0.2
M
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.5
1

-0.2
Otaniemi clay
-0.4
Natural POKO clay
-0.6
Reconstituted POKO clay
Natural Murro clay
-0.8
-1
S CLAY1
S‐CLAY1 model (Wheeler et al . 2003)
d l (Wh l
t l 2003)
0
’y

20
40
60
p’
80
80
60
40
20
’x
0
0
’z
20
40
60
80
F


3
d  p'  d T  d  p'  d   M 2  3  d T  d p'm p'p'  0
2
2


Dafalias (1986), Korhonen & Lojander (1987), Wheeler (1996), Wheeler et al. (2003)
Simplified case: vertical sample in triaxial space 
f  q   p    M
2
2

2
 p 
m
 p p   0
Dafalias ((1987),
) Korhonen & Lojander
j
f  ( q  (1987)
p' ) 2  (  2   2 )( p'm  p' ) p'  0
Definitions:
Deviatoric stress vector
Deviatoric fabric tensor (in vector form)
'x p'
' p'
 y 
 ' z  p ' 
d  

2

xy


 2 yz 


 2 zx 
p' 
' x   ' y   ' z
3
 x 1 
  1 
 y 
 z 1 
d  

2

xy


 2 yz 


 2 zx 
x  y  z
3
1
Fabric Tensor for K0 consolidated soil
 x 1 
  1 
 y 
  1 
d   z

 2 xy 
 2 yz 


 2 zx 
 1

 3 ( x   y ) 
 2

  ( x   y ) 

 3
1


d 
 3 ( x   y ) 


0


0




0


 xy   yz   zx  0
x  z
 
 3 
 2 


 3 
 d    
 3
 0 


 0 
 0 


 1

 3 (3 x  3) 
 2

 (3 x  3)
 3

 d   1 (3  3) 
x
 3



0


0




0


x  y  z
3
1
2 
3
 d T  d 
2
Need to be careful with axes notation!
Fabric Tensor for K0 consolidated soil
Hardening Laws:
1) Size of the yield surface
vp'm d vp
dp'm 
 

2) Rotation of the yield surface

 3

d  d   (   d ) d vp   d (   d )d dp 
3
 4

Yield points
M=1 6
M=1.6

max
Max. stress
during 0
loading
40
30
q (kPa)
20
10
p'm=35.5 kPa
0
-10
0
10
20
30
40
50
60
b) POKO clay
30
20
70
-20
-30
-30
Yield points
M=1.3

Max.
max stress
during 0
loading
30
0
10
20
30
40
50
60
70
p' (kPa)
Yield points
d) Vanttila clay
M=1 35
M=1.35

Max.
max stress
during 0
loading
40
30
20
p'm=26.0 kPa
0
0
10
20
30
40
50
60
70
p' (kPa)
q (kPa)
20
10
-10
p'm=42.0 kPa
0
-20
40
q (kPa)
10
-10
p' (kPa)
c) Otaniem i clay
Yield points
M=1
M
1.2
2

Max. stress
max
during 0
loading
40
q (kPa)
a) Murro clay
10
p'm=26.0 kPa
0
-10
-20
20
-20
-30
-30
0
10
20
30
40
50
60
70
p' (kPa)
d
p'
Simulations with S-CLAY1
S CLAY1
1.5
2.5
3.5
4.5
5.5
0.0
-0.05
0 05
ln p'
-50
0
50
100
150
q (kPa)
0.05
0.1
d
v
0.15
0.2
0.3
-0.05
0.25
0.0
0.1
0.2
0.3
CAD 3216R
6 9-7 6 m
6.9-7.6
0=0.98, 1=-0.62, 2=0.60
v
0.05
d
0.15
CAE 3216R
S-CLAY1
S
CLAY1
MCC
0.25
Karstunen
& Koskinen
(2004)
For full validation
For full validation, see Karstunen & Koskinen (2008), Can. Geotech. J.
see Karstunen
& Koskinen (2008) Can Geotech J
S‐CLAY1S Model
S‐CLAY1S Model
(Karstunen et al. 2005)
q

’y
“intrinsic” yield
curve
CSL
1
pp’
M
Natural yield curve
1
pmi’
’x
’z
pm’

p’
1
CSL
p 'm  (1   ) p 'mi
Intrinsic yield surface
F

M

3
d  p'  d T d  p'  d   M 2  3  d T  d p'm p'p'  0
2
2


Hardening Laws:
Hardening Laws:
1) Size
Si off th
the iintrinsic
t i i yield
i ld surface
f
vp'mi d vp
dp 'mi 
i  
2) Degradation of bonding


dx    d vp   d d dp 


 

3) Rotation of the yield surface

 3
p
p
d  d   (   d ) d v   d (   d )d d 
3
 4

M=1.6
=0.63
pp'm=34.5 kPa
a) Murro clay
40
30
30
20
20
10
M=1.2
=0.46
pp'm=49
49 kPa
50
40
q (kP
Pa)
q (kP
Pa)
50
b) POKO clay
0
10
0
0
10
20
30
40
50
60
70
0
-10
10
20
30
40
50
60
70
-10
-20
20
-20
20
p' (kPa)
p' (kPa)
c) Otaniemi clay
d) Vanttila clay
M=1.3
=0.50
p''m=19.5
19 5 kP
kPa
20
M=1.35
=0.52
p'm=18.5
=18 5 kPa
20
10
q (kPaa)
q (kPaa)
10
0
0
0
10
20
-10
30
0
10
20
-10
p' (kPa)
p' (kPa)
30
d
p'
Si l ti
Simulations with S‐CLAY1 and S‐CLAY1S
ith S CLAY1 d S CLAY1S
POKO clay 1=0.95, 
POKO clay, 
=0 95 2=0.06
=0 06
a)
1.5
v
2.5
3.5
d
b)
ln p'
4.5
5.5
0.0
6.5
0.1
0.2
c)
0.3
0.4
0.0
0.0
0.00
0.1
0.1
0.05
0.2
0.2
0.10
0.3
v
0.3
d
0.4
0.20
0.5
0.5
0.25
0.6
0.6
0.30
0.7
0.35
S CLAY1
S-CLAY1
CAD 2751
20
40
0.15
0.4
0.7
q
0
S-CLAY1S
Creep models for natural clays
Creep models for natural clays
60
80
100
Rate‐dependent models
EVP-SCLAY1S
q
Dynamic loading surface
1
q
M
psm’
Dynamic loading surface
1
1
pmi’
pdm’


psm’
pmi’
p’
pdm’
Normal consolidation
surface
1
p’
peq’ pp’
pmi’
Intrinsic surface

 pmd  f d
r 
 pm   ij
ijvp   
Grimstad et al. (2010),
Yin et al. (2011)
c
vol

 * 1 


  OCR * 

Leoni et al. (2008), Kamrat‐Pietraszewska (2011)
EVP‐SCLAY1S
Influence of
anisotropy

p’
Current stress surface
Intrinsic surface
 pmd
   f
 1   1 d

p
 m     ij
M
1

Static loading surface
ijvp   exp  N  
q
1
Intrinsic yield surface

M

Static yield surface

ACM/ACM-S
AniCreep/n-SAC
Influence of
destructuration
EVP‐SCLAY1S
Influence of
destructuration
Influence of
anisotropy
Influence of
anisotropy
EVP‐SCLAY1S
10
-2
(c)
Tertiary creep
d a/d
dt (%/s)
10
With destructuration
-4
Without destructuration
Secondary creep
10
10
-6
6
CAUCR1 q=14.4 kPa
CAUCR2 q=17
q 17.3
3 kPa
CAUCR3 q=20.0 kPa Primary creep
EVP-SCLAY1S
EVP-SCLAY1
(c)
-8
Vanttila clay
y
10
1
10
2
10
3
10
Time (s)
4
10
5
10
6
C l i
Conclusions
• Of
Of the various approaches exist for modelling large h
i
h
i f
d lli l
strain anisotropy elasto‐plastic approach computationally most efficient but requires
computationally most efficient, but requires additional state variable (fabric tensor) and additional soil constants
additional soil constants
• Largely a consensus on how to model the effect of bonding and destructuration
bonding and destructuration
• S‐CLAY1S model is a simple model which incorporates both anisotropy and destructuration
incorporates both anisotropy and destructuration
• Combining these effects to rate‐formulations rather straight‐forward,
straight
forward, but challenges remain as selection but challenges remain as selection
of creep formulation not trivial
Some key references:
Some key references:
•
•
•
•
•
•
•
•
•
•
•
•
A. Gens & R. Nova (1993). Conceptual bases for a constitutive model for bonded soils and weak rocks.” Proceedings of International Symposium on Hard Soils ‐ Soft Rocks, Athens, 485–494.
G. GRIMSTAD, S.A. DEGADO, S. NORDAL & M. KARSTUNEN (2010). Modelling creep and rate effects in structured anisotropic soft clays. Acta Geotechnica 5: 69–81. Z.‐Y. YIN, C.S. CHANG, M. KARSTUNEN & P.‐Y. HICHER (2010). An anisotropic elastic viscoplastic
model for soft clays. International Journal of Solids and Structures 47(5): 665‐677. Z ‐Y YIN C S CHANG P ‐Y HICHER & M. KARSTUNEN
Z.‐Y. YIN, C. S. CHANG, P.‐Y. HICHER
& M KARSTUNEN (2009). Micromechanical analysis of kinematic (2009) Micromechanical analysis of kinematic
hardening in natural clay. Int. J. Plasticity 25(8):1413‐1435. M. KARSTUNEN & M. KOSKINEN (2008). Plastic anisotropy of soft reconstituted clays. Canadian Geotechnical Journal 45: 314‐328.
M. KARSTUNEN & Z.‐Y. YIN (2010). Modelling time‐dependent behaviour of Murro test embankment. Géotechnique 60(10): 735‐749. M. LEONI, M. KARSTUNEN & P. VERMEER (2008). Anisotropic creep model for soft soils. Géotechnique 58 (3): 215‐226. M. KARSTUNEN, C., WILTAFSKY, H., KRENN, F., SCHARINGER & H.F. SCHWEIGER (2006). Modelling the stress‐strain behaviour of an embankment on soft clay with different constitutive models
stress‐strain behaviour of an embankment on soft clay with different constitutive models. International Journal of Numerical and Analytical Methods in Geomechanics 30(10): 953‐982
M. KARSTUNEN, H., KRENN, S.J., WHEELER, S.J., M. KOSKINEN & R. ZENTAR (2005). The effect of anisotropy and destructuration on the behaviour of Murro test embankment. ASCE International Journal of Geomechanics 5(2): 87‐97. D. POTTS, D. & L. ZDRAVKOVIC (1999). Finite element analysis in geotechnical engineering‐
(
)
l
l
h
l
Theory. h
Thomas Telford,1999.
S.J. WHEELER, A. NÄÄTÄNEN, M. KARSTUNEN & M. LOJANDER (2003). An anisotropic elasto‐plastic model for natural soft clays. Canadian Geotechnical Journal 40(2). pp. 403‐418
Z ‐YY. YIN, M. KARSTUNEN, C.S. CHANG, M. KOSKINEN & M. LOJANDER (2011). Time
Z.
YIN M KARSTUNEN C S CHANG M KOSKINEN & M LOJANDER (2011) Time‐dependent
dependent behaviour of soft sensitive clay. ASCE International Journal of Geotechnical and Geoenvironmental Engineering 137(11):1103‐1113. Some creep models that
i
incorporate
t anisotropy
i t
and
d
destructuration
Assoc. Prof. Gustav Grimstad (HiOA)
Fundamental aspects of soft clay behavior
— Creep
— Anisotropy
A i t
— Strength
— Stiffness
— Yield stress
— Structure and destructuration
— Unloading/reloading cycles – small strain
— Degradation during cyclic loading
— ALL ARE LINKED!
“1D” Creep – (24h) incremental oedometer
t t
test
— Advantages:
— Gives first estimate of creep/consolidation parameters and the
“vertical” pre-consolidation stress directly
— Disadvantages
— Time consuming compared to CRS tests
— Only average settlement parameters for large stress
increments
— Ideally back calculation with mathematical model is needed
(FEA)
Current Norwegian engineering practice
— Using low OCR (if material has not been subjected to
preloading an OCR of 1
1.0?
0? is often used)
— Ignoring creep
— Adding creep after consolidation?(Hyp.
consolidation?(Hyp A!)
— Advanced: Janbu´s time resistance concept
— What about the selected pre
pre-consolidation
consolidation stress?
IMPORTANT!!!
— What about sample quality?
Sample quality
Compression curves for Väsby clay at a depth of 4.0 – 4.3 m (after Leroueil and Kabbaj, 1987)
j,
)
DeGroot et. al. (2005)
Janbu´s time resistance concept
— Increment in time
divided by the increment
in strain (Cause/Effect)
(Cause/Effect).
R = ∂t/∂ε
1D equation
ddt
 t   rs   t     Rref  rs  t
d  vvp
”Pure creep”
rs
Rref
tref
1
rs  tref  Rref when tref
t
l ( refeq = peq), t
ln(p
) t=τ
d
1
1 t

  vvp  ln
dt
rs  t
rs 
vp
v
tp
l ( refeq), (t = t)
ln(p
) (t t)
1
ζ
ln(τ)/rs
eq
ref
vp
v
dp
d

p
  vvp    ln 
 p


eq
ref
p
d
1

dt
Rref
vp
v
eq
ref
eq
 p

 p eq
 ref
eq



rs 




Δεvvp
ln(t)/rs
*  p 


  pref eq 
eq
 *  *
*
εv
vvp 
1
1

rs   Rref
vvp 
1
rs  t
prefeq is important for creep rate! Initial value is the pre consolidation stress!
value is the pre‐consolidation stress!
“Alternative approaches” to Janbu for 1D
— Yin and Graham (equivalent time approach) – Adopted
from Bjerrum
— Leroueil
— Den Haan (ABC model)
— etc.
ALL ARE THE SAME?
Ignoring creep?
Illustration of dependence of OCR on the corresponding reference time ().
A case of SSC and SS model giving the same final settlement
final settlement. The effect of the μ*/(λ*-κ*) ratio on OCR (creep rate)
H
H0
*
 *  *

1
rs  
age = 10000 yrs
OCR = 1.3
OCR
age
λ* decreasing with stress
ln(σ’)
0.010
1.163
6.79E+08 years
0.015
1.254
1.08E+05 years
0 020
0.020
1 353
1.353
1 36E+03 years
1.36E+03 years
0.025
1.459
98.9 years
0.030
1.574
17.2 years
0.035
1.697
4.93 years
0.040
1.830
1.93 years
0.050
2.129
0.518 years
0.070
2.880
0.113 years
H
H0
H
H0
σv0’
σvc’24h
ln(σ’))
ln(σ
μ* decreasing with time
ln(σ’)
“Recommended” range (PLAXIS manual) ~0.04 ‐ 0.07
Same μ*
μ
Same λ*
Anisotropy
— First:
— Undrained Triaxial Compression versus Undrained Triaxial
Extension and Direct Simple Shear (Bjerrum 1973)
— Second:
— Preconsolidation stress from Oedometer test versus isotropic
consolidation test (Feng 1991)
— Third:
— “Stress/strain induced anisotropy” – Changes in macroscopic
yield surface (Wheeler 2003)
Undrained shear strength
— Used as basis
for the NGIADP model
0.5
0.4
cr/ v00'
0.3
0.2
0.1
0
90
60
30
0
 [ o]
30
60
90
Pre-consolidation stress and ”cap” yield
surface
f
— Experiments from
literature on finding
cap surface – yield
points in p’ – q space
Stress/strain induced anisotropi
— Wheeler
et al.
Destructuration
2500
Eberg clay, 6.47 m
Eberg clay, 6.13 m
2000
1.8
1.6
1.4
12
1.2
2.0
0.8
0.6
0.4
1500
rs
Vooid ratio [-]
22
2.2
2.0
1000
Undisturbed sample
In situ state
Reconstituted at wL
Predicted ICL
SCL
1
10
100
'v[kPa]
500
0
1000
0
200
400
600
v'
800
1000
1200
Christensen (1985)
10000
Burland (1990)
Creep - Yield surface becomes reference
surface
f
1.2
d /dt = constant - ACM
d /dt = constant - new formulation
1
— Option 1 – extending by volume
strain (ACM)
— Option 2 – extending by plastic
multiplier directly
08
0.8
0.6
eq
q/pref
0.4
0.2
0
-0.2
02
-0.4
-0.6
0
0.2
0.4
0.6
eq
p'/pref
0.8
1
1.2
Anisotropy and creep –
Th n-SAC
The
SAC model
d l
— A non-associated creep model for structured
anisotropic clay
— Non-associated because:
— prediction of the strain behavior under various stress paths
paths,
based on experimental evidence from e.g. Feng (1991)
3
T
σ d  p ' β d  σ d  p ' β d 

p eq  p ' 2
 2 3 T 
 M  βd βd  p '
2


3
T
σ d  p ' α d  σ d  p ' α d  eq
2
 pQ  0
Q  p '
3 T 

2
 M f  αd αd  p '
2


where p’ = mean stress; σd=deviatoric
stress vector; βd = deviatoric rotational
vector; M = Lode angle dependent peak of the reference curve of in p’‐q space
where Mf is the Lode angle dependent citical state line in p’‐q
p q space; α
p ; d is the deviatoric rotational vector. Modelling of destructuration
State variables inc. x
Models with anisotropy and destructuration
— Option 1
— ACM ->
> ACM
ACM-S
S (Leoni 2008
2008, Kamrat-Pietraszewska
Kamrat Pietraszewska 2011)
— Extension of SSC (Stolle et al. 1999) (PLAXIS current model)
— Option
p
2
— EVP-SCLAY1S (Karstunen and Yin 2010)
— Ani-Creep (Yin et al. 2011)
— n-SAC (Grimstad et al. 2010)
— n-SAC –using creep limit and option 2:


1
p eq
 
 

rsi   1  x   pmi ' 
rsi  i


tmax
 mK 0 NC
How to use/Parameters for analyses
• Two models ‐
d l SSC and n‐SAC
SSC d S C
• Three analysis cases ‐ SSC1, SSC2 and n‐SAC
Model
SSC1
SSC2
n‐SAC
ν
0.15
0.15
0.15
K0NC
0.54
0.54
0.5
Eref / pref
200
200
200
{Eoedref}i / pref
9.5
6.0
13.0
rsmin
‐
‐
200
rsi
267
233
625
kv = kh = 5e‐5 m/day; γ’ = 10 kN/m3, K0 = 0.54, OCR = 1.36
ω
‐
‐
0.3
φp
‐
‐
25°
φcs
35°
35°
35°
Oedometer simulations
400
R = Δt/Δε (d
days)
350
300
250
200
SSC1
150
SSC2
100
n‐SAC
50
0
4
5
6
7
8
Time [days]
14000
Eoed = Δσ/Δε [kP
Pa]
12000
10000
Two way drainage
8000
SSC1
6000
SSC2
4000
n‐SAC
2000
0
0
200
400
600
800
1000
V i l
Vertical stress, σ
[kP ]
[kPa]
Example: settlement problem
SSC1
n SAC
n‐SAC
Uy [m]
0
SSC1 - Point A
-0.3
SSC2 - Point A
-0.6
n-SAC - Point A
-0.9
-1.2
-1.5
1
10
100
1e3
Time [day]
1e4
1e5
1e6
Profiles
Horizontal displacements [m]
0.05
0.10
0.15
0.00
0
‐5
‐5
‐10
‐10
‐15
‐15
Dep
pth [m]
0
‐20
0.20
0.40
0.60
0.80
‐20
‐25
SSC1
‐25
SSC1
‐30
SSC2
‐30
SSC2
n‐SAC
n‐SAC
‐35
‐35
‐40
‐40
Mesh dependency due to softening
Time [days]
[ y]
0
0.5
1
1.5
2
2.5
3
0
‐0.1
‐0.2
Vertical displacement [m
m]
Dep
pth [m]
0.00
Vertical displacements [m]
Application of load, fine mesh
Undrained creep phase, fine mesh
Application of Load, coarse mesh
Undrained creep phase, coarse mesh
‐0.3
‐0.4
‐0.5
‐0.6
‐0.7
‐0.8
‐0.9
60 kPa
Shadings of “structure”
Effect of stiffness
30
25
 xyy ' [kPa]
20
High Eref
Low Eref
15
10
 v0' = 105 kPa
d/dt = 1/(3E5 s)
5
0
DSS
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
xy *2
”stiff” ”soft” 25.7 days. Looks more like perfectly plastic behavior!
Conclusions
— Creep/rate and anisotropy are important if we want to
fully understand soil behavior
behavior.
— Sample quality is crucial and deserves more attention
as it forms the basis for numerical modeling.
modeling
— With increased sample quality and testing procedure,
the soil models also needs to be improved
— The “huge gap” between state-of-the-art and state-ofp
must be closed or at least narrowed
the-practice
down!
Laboratory study of creep
— Creep can be studied in all types of soil tests as it manifests
itself along with all soil behavior
— Incremental oedometer test – the standard
— Loads typically applied incrementally with sequence 12.5 kPa,
25 kPa, 50 kPa, 100 kPa, 200 kPa, 400 kPa, 700 kPa and
1200 kPa
— Time between load increments is 24 hr
— Deformation under each load increment is measured
2 oedometer
Schematic drawing of the 20 cm
h
d
f h
d
cell (www.ngi.no )
ll (
)
Exercise - Oedometer
1. Open geometry from file oedo.P2D
2 Input material properties – n-SAC (not the “default”?)
2.
default ?) or SSC
1.
3.
4.
5.
6
6.
Optional: run “SoilTest”, play around with triax etc.
Go to calculation
Mark all calculate
Run oedometer
O t t and
Output
d curves
1.
2.
Make curve with time deformation – Export to excel and calculate
stress- strain and time – strain curves and resistance curves (excel
sheet oed.xlsx can be used)
Curve with p’-q
Exercise – Test fill
— See handout
Exercise on settlement of the Väsby test fill with SSC and n-SAC
Grimstad1, G. and Degago2, S. A. Brief description of the Väsby test fills (Extracted from Chang (1981) SGI report No 13, Larsson (1986) SGI report No 29, Larsson and Mattsson (2003) SGI report No 63.) The Väsby test fills were designed and constructed by the Swedish Geotechnical Institute (SGI) and are located 30 km north of Stockholm. The test fills were constructed in order to assess the suitability of a site for construction of an airport. The test fills have been monitored with extensive instrumentations installed before and after the fills were constructed. The instrumentations consist of surface and sub‐surface settlement gages and piezometers. Three fills have been constructed, with and without vertical drains, from 1945 to 1948. Of the three test fills constructed the one considered in this exercise is without drains (denoted the undrained fill), constructed in October‐November 1947 and is simply hereafter referred to as the Väsby test fill. The Väsby test fill is still under monitoring and with the latest extensive field measurements were conducted in May‐June 2002. The Väsby test fill was constructed with 2.5 meter high fill of gravel with a density of 16.5 kN/m3. The fill had bottom dimensions of 30 x 30 m and slopes of 1:1.5. Time for construction was 25 days and no change in load other than natural variations has been made after that. The net increase in vertical stress directly under the fill was calculated to originally be around 41 kPa. 1
HiOA 2
SVV Figure 1: Soil profile at the Väsby test fill area (Chang , 1981) The Väsby test fill site consists of soft sediments of glacial and post‐glacial origin. The soft soil layer under the fill is 14 m thick. A generalized characterization of the soil profile in the natural ground in the test fill area is shown in Figure 1. The ground water table outside the loaded area is hydrostatic with a ground water level of about 0.8 m below the surface with little seasonal variations of ± 0.2 m measured throughout the year. Due to excessive settlements in the order of 2 meters the original surface soil and some of the fill is today below the groundwater level. This implies that the load has actually been reduced over time related to increased buoyancy (2m higher GW level – relatively speaking – reducing the load by 20 kPa.), see Figure 2. An updated mesh Plaxis simulation is proposed in this exercise to automatically take this into account (wit an updated mesh analysis you do not need to unload manually, just leave the load on). 50 kPa
100 kPa
Vertical stress
0m
“Load” reduction due to settlements
5m
“Final” load
Immediately after loading:v0’ + v
10 m
Initial stress v0’
15 m
Depth
Figure 2: Initial effective stresses and additional total stresses under fill (Rolf Larson 1986, SGI report no 29) Laboratory test data for interpretation of soil parameters The following selection of laboratory data is provided to let you try to evaluate the proposed soil parameters for the 13 m thick bottom clay layer. Most of the tests shown are from samples taken at about 4 meter depth. You may not get exactly the same parameters, but this will give you an idea on how they, in principle, may be determined. Oedometer test results on samples taken by the Swedish standard piston sampler are reproduced in Figure 3. One of the results are compared to a test on a block sample, see Figure 4. Consider the tests on samples at 4 or 4.3 meter depth and use the parameters for the entire 13 meter thick lower soil layer. Try to determine the * and * parameters from these tests: See the Wed 01 lecture. Figure 4: Oedometer test results on Swedish piston tube sampler (Chang, 1981). Initial effective stress:
22 – 24 kPa Over‐
consolidation 35 – 40 kPa ? Figure 4: Block samples Oedometer tests Väsby clay, End of Primary Tests (not 24 hour tests), (Kabbaj, Tavenas and Leroueil 1988, Geotechnique vol 38 No 1) Please note that the piston tube sampler indicates an OCR = 1,1 or less while the block sample gives higher OCR closer to 1.5 or even 1.7(?) Figure 5: Deformation with time in an oedometer test. Chang (1987), SGI report No 13 Try to evaluate a secondary compression index * from Figure 5 above. You may also consider the */* ‐ ratio found in the tests on the piston sampled soil samples and apply this ratio to estimate * based on the * from the block sample test. (I could not find the deformation versus time curves in the literature for the block sample tests.) Figure 6: Determination of permeability coefficients. (SGI report No. 63) Please note that the permeability changes as the soil is compressed under the fill. We may use an average value in this exercise or try to find a k0 and a ck for a changing permeability used in “Advanced parameters”: log(k/k0) = e/ck PLAXIS analyses of the Väsby test fill The Väsby test fill is analyzed using PLAXIS. Important considerations and idealizations made for the analysis of the fill are highlighted below. Geometry An axisymmetric model shall be used. The 2.5 meter high, 30 by 30 meters square fill is to be represented by a circular fill of 34 m diameter:. Details of the geometry are given below. The geometry is provided in *.P2D file. 13.25 m 4
5
0
8
x
Dry crust GWL 2.5 m Gravel fill y
1 m 6
1
3
17 m 13 m Väsby clay 7
2
Figure 7: Layout of the axisymmetric FE model: Material settings and input parameters Average soil parameters are used. For a more refined analysis the clay should be divided in many layers. Table 1: Material properties of the Gravel fill
Parameter Material model Material type Unit weight above phreatic level Unit weight above phreatic level Permeability in vertical direction (constant) Permeability in horizontal direction (constant) Young’s modulus (constant) Poisson’s ratio Name Model Type unsat unsat ky
kx
Eref
 Value Linear Elastic Drained 16.5 16.5 1.0 1.0 10000 0.0 Unit ‐ ‐ kN/m3
kN/m3
m/day
m/day
kN/m2
‐ Table 2: Material properties of the Dry crust
Parameter Material model Material type Unit weight above phreatic level Unit weight above phreatic level Permeability in vertical direction (constant) Permeability in horizontal direction (constant) Modified swelling index Modified compression index Modified creep index Pre‐over burden pressure Cohesion Friction angle Dilatancy angle Earth pressure coefficient at rest Name Model Type unsat unsat ky
kx



POP
c


K0NC Value Soft Soil Creep Undrained 14.0 14.0 5.5×10‐05 5.5×10‐05 0.025 0.2 0.012 40 5.0 30.0 0.0 0.65 Unit Value Soft Soil Creep Undrained 15.0 15.0 4.0×10‐05 4.0×10‐05 0.030 0.357 0.021 1.6 0 33.5 0.0 0.6 Unit ‐ ‐ kN/m3
kN/m3
m/day
m/day
‐ ‐ ‐ kPa kN/m2
o
o
‐
Table 3: Possible material properties of the Väsby clay - SSC
Parameter Material model Material type Unit weight above phreatic level Unit weight above phreatic level Permeability in vertical direction (constant) Permeability in horizontal direction (constant) Modified swelling index Modified compression index Modified creep index Over Consolidation Ratio Cohesion Friction angle Dilatancy angle Earth pressure coefficient at rest Name Model Type unsat unsat ky
kx




OCR
c


K0NC ‐ ‐ kN/m3
kN/m3
m/day
m/day
‐ ‐ ‐ ‐ kN/m2
o
o
‐ Initial conditions Initial pore pressure conditions The Ground water level is set to 1 m below the surface. And a closed consolidation boundary is specified only at the line of symmetry (at the left end of the model). The bottom boundary is free for drainage. 4
Phreatic level 5
y
0
x
6
General
8
1
3
Closed consolidation boundary 7
Figure 8: Initiating pore water conditions and flow boundaries Initial stress condition The initial stresses are set after giving the POP and OCR values of the soil layers. When an OCR value is given, PLAXIS automatically changes the K0 value. However, the K0 value needs to be changed back to its initial value of K0. (Remark: PLAXIS considers OCR to come from unloading and adjusts its K0 value. However, in creep analysis, the OCR that results from creep does not induce a significant change to K0.) When initiating, the initial stresses, remember to switch off the gravel fill! 2
Calculation Three phases are defined. They are named as Apply Gravel fill, Settlement analysis – 1 and Settlement analysis – 2 (See Figure 9) Advanced feature for Large deformation analyses Figure 9: Calculation phases First phase (Apply Gravel fill) ‐ On the parameters tab specify the Time interval under Stage construction as 25 days ‐ Activate the gravel fill (by clicking on the define button and updating it finally) ‐ Calculation type = Consolidation analysis ‐ Loading input = Staged construction ‐ Click on the advanced tab found below Calculation type (see Figure 9). Then on the Advanced General Settings check the Updated mesh and Updated water pressures options ( Figure 10) ‐ On the Parameters tab click on Manual setting and Define the Manual settings. Tolerated Error = 0.001 (Remark: The updated mesh analysis is necessary in cases where deformations are expected to be significant. More and interesting discussion on this option can be found in PLAXIS user’s manual) Second phase (Settlement analysis ‐1) ‐ On the parameters tab specify the Time interval under Stage construction as 375 days ‐ Calculation type = Consolidation analysis ‐ Loading input = Staged construction ‐ Do Large Deformation analysis (see Figure 10) ‐
On the Parameters tab click on Manual setting and Define the Manual settings. Tolerated Error = 0.001 Third phase (Settlement analysis ‐2) ‐ On the parameters tab specify the Time interval under Stage construction as 2.1 E4 days ‐ Calculation type = Consolidation analysis ‐ Loading input = Staged construction ‐ Do Large Deformation analysis (see Figure 10) ‐ On the Parameters tab click on Manual setting and Define the Manual settings. Tolerated Error = 0.01, Maximum iterations = 50, Desired minimum = 2, Desired minimum = 50 and First time step = 200 . This should give constant time steps with 200 days in between each of the calculation steps. (Remark: The need to use the Manual iteration scheme (Figure 11) is to control the output data. It is possible to use the Standard setting but the time steps could be large after the initial part of the consolidation. So what is done is to do the analysis with automatic time stepping until 400 days (25 + 375 days), then to run the analysis at a given time step of 400 days. In this way, the output data after the first 400 days, will be given with constant interval. Analysis Before running the the calculations, points needs to be selected for Curves At Väsby test fill, settlement have been monitored, below the centerline of the embankment, at a depth of 0 m (surface), 2.5 m, 5.0 m and 7.3 m. Excess pore pressure a have also been monitored, , below the centerline of the embankment, at a depth of 2.6 m, 6.4 m and 9.1 m. Post processing Measurements of actual time‐ settlement behavior and pore pressures can be found on the following pages. If time allows then compare your results to the measurements. 1. Open output 2. Make relevant curves What about the far field settlements? Excess pore pressure [kPa]
0
5
10
15
20
25
30
35
0
2
Depth [m]
4
6
8
Measured - 1968
10
Measured - 1979
Measured - 2002
12
Measured - 2002
Measured - 2002
14

CREEP School 1

Transcription

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