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 azim@cu.edu.tr

or harald.krenn@strath.ac.uk

You can also visit the AMGISS website for further info:

http://www.civil.gla.ac.uk/amgiss