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Behaviour of the Haarajoki test embankment constructed on soft clay
improved by vertical drainsAzim Yildiz
University of Cukurova, Turkey
Harald Krenn, Minna KarstunenUniversity of Strathclyde, UK
Outline of presentation
User defined soil model: SUser defined soil model: S--CLAY1S modelCLAY1S model
Haarajoki test embankment without vertical drainsHaarajoki test embankment without vertical drains
Modelling of vertical drainsModelling of vertical drains
Haarajoki test embankment with vertical drainsHaarajoki test embankment with vertical drains
ConclusionsConclusions
Structure of Natural Clays
Soil structure consists of:– fabric (anisotropy)– interparticle bonding
(sensitivity)
Due to plastic straining gradual degradation of bonding (destructuration) and changes in fabric
ln p'
vRe constitute d
soilNatural
soil
λi
1
λ
1
For a constant η stress path:
Modelling Plastic Anisotropy
1. Standard elasto-plastic framework (kinematic or translational hardening laws)• Nova (1985), Banerjee & Yousif (1986), Dafalias
(1986), Davies & Newson (1993), Whittle & Kavvadas (1994), Wheeler & al. (2003)
• Note: You cannot use invariants!
2. Multilaminate framework• Zienkiewicz & Pande (1977), Pande & Sharma (1983),
Pietruszczak & Pande (1987), Wiltafsky (2003), Neher et al. (2001, 2002), Mahin Roosta et al. (2004)
Modelling Destructuration
Concept of an intrinsic yield surface proposed by Gens & Nova (1993)– Lagioia & Nova (1995), Rouainia & Muir Wood
(2000), Kavvadas & Amorosi (2000), Gajo & Muir Wood (2001), Liu & Carter (2002), Karstunen et al. (2005)
q
p’ pm’ pmi’
M1
M 1
α 1
CSL
CSL
S-CLAY1S Model
q
p’ pm’ pmi’
M1
M1
α 1
CSL
CSL
p’σ’y
σ’x
σ’z
α
natural yield surface
intrinsic yield surface
mim 'p)x1('p +=Intrinsic yield surface (Gens & Nova 1993)
{ } { }[ ] { } { } [ ] 0'p'p'p23M'p'p
23F md
Td
2dd
Tdd =−⎥⎦
⎤⎢⎣⎡ αα−−α−σα−σ=
Definitions:
Deviatoric fabric tensor (in vector form)
Deviatoric stress vector
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
τττ−σ−σ−σ
=σ
zx
yz
xy
z
y
x
d
222
'p''p''p'
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
ααα−α−α−α
=α
zx
yz
xy
z
y
x
d
222
111
3'''
'p zyx σ+σ+σ= 1
3zyx =
α+α+α
Hardening laws:
κ−λε
=i
pvmi
mid'vp'dp
1) Size of the intrinsic yield surface
2) Rotation of the yield surface
⎥⎦
⎤⎢⎣
⎡εα−
ηβ+⟩ε⟨α−
ηµ=α p
ddpvdd d)
3(d)
43
(d
3) Degradation of bonding
( )⎥⎦
⎤⎢⎣
⎡ε+ε−= p
dpv dbdaxdx
S-CLAY1 and MCC
By setting x to zero and using an oedometric value (1D) for compressibility λ:
S-CLAY1 model (anisotropy only)
By setting, in addition, α and µ to zero:MCC model (isotropy only)
Additional State Variables and Soil Constants
Symbol Definition Method
α0Initial inclination of the yield curve
Estimated via φ’
β Proportion constant Estimated via φ’
µ Rate of rotation ≈ (10…20)/λK0
Ani
sotro
py
x0 Initial amount of bonding ≈ St -1
λiSlope of intrinsic compression line
Oedometer test on reconstituted soil
b Proportion constant For most clays 0.2-0.3
a Rate of destructuration Typically 8-11
Des
truct
urat
ion
The analysis of embankment on soft soil
During the construction of embankments(undrained behaviour)
– an increase in pore pressure.– the effective stress remains low
After construction (drained behaviour)– the excess pore pressures will dissipate– The consolidation settlements will start due to
drained behaviour.– The consolidation takes a long time to
complete because of the very low permeability,
– The effective stress will increase and soil can obtain the necessary shear strength to continue the consolidation.
timetc
σ
σ’
∆u
tc: construction time
σ = σ’-∆u
Vertical drains
• to reduce the length of the drainage paths
• to shorten consolidation time • to increase shear strength
Haarajoki Test Embankment
• Finnish National Road Administration organised an international competition to predict the behaviour of the Haarajoki Test Embankment.
• The embankment which is used as a noise barrier was constructed in 1997 after all participants of the competition submitted the results.
• Laboratory investigations have been carried out by Road Administration and the laboratory of Soil Mechanics and Foundation Engineering at the Helsinki University of Technology
• The embankment was monitored with settlement plates, piezometers, inclinometers, extensometers and total stress gauges.
Longitudinal section:
100m
Dry crust
Soft clay
SiltTill
2m
20m
2-3m2-3m
3m
Vertical drains
c/c 1m
35840 35880
Construction Schedule
0
0.5
1
1.5
2
2.5
3
3.5
0 7 14 21 28 35 42 49 56 63 70
Time (days)
Heig
ht (m
)
Total construction time: 14 dayseach layer: 2 days construction 1 day for consolidation.
Instrumentation installation
Measured Pore Pressures (35840)
Pore Water Pressure
60
80
100
120
140
160
180
200
0 50 100 150 200 250 300 350 400
Time
Act
ive
pore
pre
ssur
e, k
Pa
Depth=7.2mDepth=10.2mDepth=15.2m
Measured settlements (1997-2002)
0
100
200
300
400
500
600
700
800
900
1000
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Time (day)
Settl
emen
t (m
m)
Without PVD
With PVD
PVD: Prefabricated vertical drain
Initial conditions
0
2
4
6
8
10
12
14
16
18
20
22
0 40 80 120 160Vertical Stress, kN/m²
Dep
th, m
Initial vertical stress
Preconsolidation stress
σ’v : Pre-consolidation pressure
σ’v0 : : Initial vertical stress
Soil Parameters Initial State Parameters Additional Soil Constants
Name β µ λi a b
1 1.0 50 0.04 8 0.22 1.0 50 0.06 8 0.2
3a 0.7 20 0.38 8 0.23b 0.7 20 0.38 8 0.23c 0.7 20 0.38 8 0.24 0.6 20 0.27 8 0.25 0.6 20 0.19 8 0.26 0.6 20 0.33 8 0.27 0.7 20 0.3 8 0.28 1.0 20 0.13 8 0.29 1.0 20 0.03 8 0.2
Name depth [m] e0 POP α x0
[kN/m^2]1 0-1m 1.40 -76.5 0.58 42 1-2m 1.40 -60.0 0.58 4
3a 2-3m 2.90 -38.0 0.44 223b 3-4m 2.90 -34.0 0.44 223c 4-5m 2.90 -30.0 0.44 224 5-7m 2.80 -24.0 0.42 305 7-10m 2.30 -21.0 0.41 456 10-12m 2.20 -28.5 0.41 457 12-15m 2.20 -33.5 0.44 458 15-18m 2.00 -17.0 0.58 459 18-22.2m 2.00 -1.0 0.58 45
Conventional Soil ConstantsName γ κ ν ' λ Μ k_x k_y [kN/m^3] [m/d] [m/d]
1 17 0.006 0.35 0.12 1.50 1.30E-03 1.30E-032 17 0.009 0.35 0.21 1.50 1.30E-03 1.30E-03
3a 14 0.033 0.18 1.33 1.15 1.56E-04 1.30E-043b 14 0.033 0.18 1.33 1.15 1.56E-04 1.30E-043c 14 0.033 0.18 1.33 1.15 1.56E-04 1.30E-044 14 0.037 0.1 0.96 1.10 1.21E-04 8.60E-055 15 0.026 0.1 0.65 1.07 1.38E-04 6.90E-056 15 0.031 0.28 1.16 1.07 2.59E-04 1.30E-047 15 0.033 0.28 1.05 1.15 2.59E-04 1.30E-048 16 0.026 0.28 0.45 1.50 8.00E-04 1.12E-049 17 0.009 0.28 0.10 1.50 8.00E-03 8.00E-03
Plaxis simulations
• Two dimensional (2D) finite element code PLAXIS V8.
• The problem was analysed in a plane-strain conditions.
• The geometry of the test embankment was assumed symmetric
• The real construction schedule has been simulated in calculation.
• The initial stresses were calculated by using K0=(1-sinφ’) OCRsinφ’
(Mayne & Kulhawy 1982)
Soil permeability
• The changes of soil permeability during consolidation were taken into account according to the relationship (Taylor 1948)
∆e: change in void ratio,k : the soil permeability in the calculation stepk0 : the initial input value of the permeabilityck : the permeability change index
• It was assumed that ck=0.5e0 in the analyses (Tavenas et al. 1983).
k0 ce
kklog ∆
=⎟⎟⎠
⎞⎜⎜⎝
⎛
The analysis of area without vertical drains
(Cross-section 35840)
EMBANKMENT
DRY CRUST
SOFT CLAY
TILL/SILT
± 0.00
- 2.00
- 22.00
3.0m
8.0m
1/2
Time-settlement curve
Center Line (35840)
0
100
200
300
400
500
600
0 500 1000 1500 2000
Time (days)
Settl
emen
t (m
m)
ObservedMCCS-CLAY1S-CLAY1S
Pore pressures
Cross Section: 35840
50
70
90
110
130
150
170
190
0 50 100 150 200 250 300 350 400
Time (days)
Act
ive
Pore
pre
ssur
e (k
Pa)
ObserveredS-CLAY1SS-CLAY1MCC
15 m
10 m
7 m
Surface settlements
Cross section (35840)
-500
-400
-300
-200
-100
0
100
200
0 5 10 15 20 25 30 35 40
Time (days)
Settl
emen
t (m
m)
5.9.97
24.9.02
S-CLAY1S 5.9.97
S-CLAY1S 24.9.02
The analysis of improved area by vertical drains
(Cross-section 35880)8.0m
- 2.00
EMBANKMENT
DRY CRUST
SOFT CLAY
TILL/SILT
± 0.00
- 22.00
3.0m1/2
Drain properties in Haarajoki Test Embankment
• Vertical drains are 15m long
• They are installed in a square grid with 1m spacing
• Equivalent radius of drains is 0.034 m
• The radius of axsiymmetric unit cell = 0.565 m
• Discharge capacity, qw = 157 m3/year
Background theory of vertical drains
Barron (1948)Barron (1948) developed the solution of the horizontal developed the solution of the horizontal consolidation under ideal conditions using an consolidation under ideal conditions using an axisymmetric unit cell modelaxisymmetric unit cell model..
Radial drainage of a vertical drain
De
dw
kh
There are two important factors in the analysis of vertical drains.
smear effectwell resistance.
There are two important factors in the There are two important factors in the analysis of vertical drains. analysis of vertical drains.
smear effectsmear effectwell resistance.well resistance.
)T8exp(1U hh µ
−−=
Because of the installation of the drains soil around the drain (smear zone) is disturbed.
o The smear zone depends onthe method of drain installation the size and shape of mandrelthe soil structure
o Problems for the analysis:What is the diameter of the smear zone (ds) ?What is the permeability of soil in the smear zone (ks)
Recent investigations on a laboratory scaleds/dm = 4-5 (Indraratna and Redana, 1998) kh/ks = 2 (Bergado et al. 1993)
5 < kh/ks < 20 for field full-scale test (Bergado et al. 1993)
Smear effectSmear effect
Well resistanceWell resistance
The limited discharge capacity of drains can cause a serious delay in the consolidation process.
Modern drains have a high enough discharge capacity (qw>150 m3/year).
The effect of well resistance can be ignored in the design.
Hansbo (1981)Hansbo (1981) modified the equation of modified the equation of Barron (1948)Barron (1948) to to include include the effect of smear and well resistancethe effect of smear and well resistance
rs
rw
kskh
qw
)T8exp(1U hh µ
−−=
( )43nln −=µ (perfect drain)
l
43)sln(
kk
snln
s
−⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟
⎠⎞
⎜⎝⎛=µ (smear effect only)
R
w
h
s qkzzls
kk
sn )2(
43)ln(ln 2−+−⎟⎟
⎠
⎞⎜⎜⎝
⎛+⎟
⎠⎞
⎜⎝⎛= πµ
D
(smear effect and well resistance)
n = R/rw and s = rs/rw Axisymmetric Radial Flow
Finite element analysis of vertical drains
2-D FE analysis of embankments is conducted on the plane strain conditions whereas vertical drains are axisymmetric
2-D FE analysis of embankments is conducted on the plane strain conditions whereas vertical drains are axisymmetric
The Vertical drain system may be converted into equivalent The Vertical drain system may be converted into equivalent plane strain model by manipulating plane strain model by manipulating the drain spacing (B)the drain spacing (B) and/or and/or soil permeability (soil permeability (kkhh).).
Hird et al. (1992)Hird et al. (1992) developed an equivalent plane strain analysis developed an equivalent plane strain analysis considering a unit cell of the vertical drain based on considering a unit cell of the vertical drain based on Hansbo’sHansbo’stheory.theory.
The degree of consolidation in plane strain condition can be The degree of consolidation in plane strain condition can be expressed as follows:expressed as follows:
)T
8exp(1u
u1Up
ph
0
_
_
hp
_
µ−−=−=
u : the pore pressure at time t, uo : the initial pore pressureThp : the time factor in plane strainµpl : the parameter that includes the effect of smear and well resistance
Uhax = Uhpl
Average degree of consolidation for both axisymmetric and
equivalent plane strain conditions are made equal at each time
step and at a given stress level
Average degree of consolidation for both axisymmetric and
equivalent plane strain conditions are made equal at each time
step and at a given stress level
ax
2
hax
pl
2
hpl
Rtc
Btc
µ=
µax
hax
pl
hpl TTµ
=µ
or
( ) ( )21
s
h43sln
kknln
23
RB
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛+⎟
⎠⎞
⎜⎝⎛=
The spacing between the plane strain drains can be changed while keeping the permeability the same
The spacing between the plane strain drains can be changed while keeping the permeability the same
The permeability values in the plane strain analysis can be changed while keeping the spacing between the drains the same
The permeability values in the plane strain analysis can be changed while keeping the spacing between the drains the same⎥
⎦
⎤⎢⎣
⎡−⎟⎟
⎠
⎞⎜⎜⎝
⎛+⎟
⎠⎞
⎜⎝⎛
=
43)sln(
kk
snln3
k2k
s
ax
axpl
Permeability matching (B=R)
Geometry matching (kax=kpl)
Combined matching
( ) ⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛+⎟
⎠⎞
⎜⎝⎛
=
43sln
kk
snlnR3
kB2k
s
ax2
ax2
plThis method is a combination of permeability and geometry matching. B is preselected and then kpl is calculated to achieve matching.
This method is a combination of permeability and geometry matching. B is preselected and then kpl is calculated to achieve matching.
Geometry matching
Permeability matching
Combined matching
B 3.3 m kpl/kax 0.029 kpl/kax 0.361R 0.565 B 0.565 B 2.0rs 0.1 R 0.565 R 0.565k 20 rs 0.1 rs 0.1ks 1 kax 20 kax 20rw 0.033 ks 1 ks 1kh/ks 20 rw 0.033 rw 0.033ds/dm 2.0 kax/ks 20 kax/ks 20
ds/dm 2.0 ds/dm 2.0
Matching procedures for plane strain model
(a) Axisymmetric Radial Flow
rs
rw
R
D
l
kskh
bs
B
bw
2B
drain
Smear zone
(b) Plain strain
Unit cell analysis
Unit Cell Analysis
0
200
400
600
800
1000
1200
1400
0 100 200 300 400 500
Time (days)
Settl
emen
t (m
m)
Geometry matchingPermeability matchingcombined matchingAxisymmetric
Perfect drain
0
200
400
600
800
1000
1200
1400
0 1000 2000 3000 4000 5000 6000
Time (days)
Set
tlem
ent (
mm
)
axisymmetric analysisgeometry matchingpermeability matchingcombined matching
Smear effect (kh/ks=20 ds/dm=5)
Unit Cell Analysis (smear effect)
0
200
400
600
800
1000
1200
1400
0 1000 2000 3000 4000 5000 6000
Time (days)Se
ttlem
ent (
mm
)
k/ks=1
k/ks=2
k/ks=5k/ks=10
k/ks=20
0
200
400
600
800
1000
1200
1400
0 500 1000 1500 2000 2500 3000
Time (days)
Settl
emen
t (m
m)
ds/dm=1ds/dm=2ds/dm=3ds/sm=4ds/dm=5no smear
k/ks effect (ds/dm=5)
k=kh horizontal permeability in the undisturbed area
ds/dm effect (k/ks =10)
dm mandrel diameter
The simulation of Haarajoki Test embankment
Time – Settlement curves
0
100
200
300
400
500
600
700
800
900
1000
0 500 1000 1500 2000
Time (days)
Settl
emen
t (m
m)
ObservedMCCS-CLAY1S-CLAY1S
Comparison of the settlement behaviour of embankment
0100200300400500600700800900
1000
0 500 1000 1500 2000
Time (days)
Settl
emen
t (m
m)
Observed-NO PVDObserved-WITH PVDS-CLAY1S (WITH PVD)S-CLAY1S (NO PVD)
PVD: Prefabricated vertical drain
Excess pore pressures
-35
-30
-25
-20
-15
-10
-5
00 1000 2000 3000 4000 5000 6000 7000 8000
Time (days)
Exce
ss p
ore
pres
sure
(kN
/m2 ) No PVD
With PVD
Pore pressure distributionAfter
construction 6th layer
Vertical displacements After
construction 6th layer
Lateral displacementsAfter
construction 6th layer
Conclusions
S-CLAY1S simulations of Haarajoki test embankment on natural soil are in good agreement with observed settlements
It is important to account for anisotropy, bonding and degradation of bonds in boundary value problems where loading is dominant
Vertical drains can be modelled simply and successfully in plane strain simulations using a proper matching procedure
Smear effect must be taken into account in the analysis
Future Workfull 3D embankment simulations
enhance S-CLAY1S model to consider creep effects
Thank you for your attention!
For information email to [email protected]
You can also visit the AMGISS website for further info:
http://www.civil.gla.ac.uk/amgiss