Vogler Krenn w(h)Ydoc05

8/12/2019 Vogler Krenn w(h)Ydoc05

http://slidepdf.com/reader/full/vogler-krenn-whydoc05 1/27

Numerical Modelling ofDeep Mixed Columns

Harald Krenn

University of Strathclyde

Urs Vogler

University of Glasgow



Outline of Presentation

- Deep mixed columns under embankment fill

- Numerical modelling deep mixed columns

- Results of numerical study

- Enhanced numerical 2D model – volume averaging technique

- Future work



Columns under embankment fil l

– Improve stability – Reduce settlements

– Reduce the time

for settlements

– Reduce vibrations

c

Embankment

Column

c



Deep mixed columns



2D Numerical Modelling

2D model – PLAXIS 2D v8.2 finite element

code

– Axisymmetric unit cell

– Radii of the unit celldependent on the c/c –

spacing

Restriction: – Not a true geometric

representation

π

c R =



3D Numerical Modelling

3D model

– PLAXIS 3D beta version – True unit cell

– All calculation phases

fully drained

Restrictions: – Idealisation of columns in

square/triangular grid

under the centreline of an

embankment

Column

Soil

Soil

Column

Embankment

fill



Volume averaging technique

Columns and soil Composite system

Idea: model 3D column behaviour within 2D calculations



Idealised Soil Profile

Vanttila clay (Finland)

– Dry crust (0-1m depth)• over-consolidated (POP

30kPa)

• Limited lab data available

– WT at 1 m depth – Soft Vanttila clay (1-12 m

depth)

• Lightly over-consolidated(POP 10 kPa)

• Plenty of lab dataavailable



S-CLAY1S Model

q

p’ pm’ pmi’

M

1

M1

α1

CSL

CSL

p’σ’y

σ’x

σ’z

α

mim ' p)x1(' p +=Intrinsic yield surface (Gens & Nova 1993)

{ } { }[ ] { } { } [ ] 0' p' p' p2

3

M' p' p2

3

F md

T

d

2

d d

T

d d =−⎥⎦

⎤

⎢⎣

⎡

αα−−α−σα−σ=



Soil Parameters

Soil Depth e0 POP [kPa] α x

Dry crust 0 - 1 1.7 30 0.63 90

Vanttila clay 1 - 11 3.2 10 0.46 20

Soil γ[kN/m3]

κ ν’ λ M kx= ky

[m/day]

Dry crust 13.8 0.029 0.2 0.25 1.6 -

Vanttila clay 13.8 0.032 0.2 0.88 1.2 6.9E-5

Soil β µ λi a b

Dry crust 1.07 15 0.07 11 0.2

Vanttila clay 0.76 40 0.27 11 0.2



Deep-Stabilised Columns

Drained and undrainedtriaxial tests – Stiffness is highly non-

linear and dependent onconfining pressure

Hardening Soil model

020

40

60

80

100

120

140

160

180

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

Axial strain, 1, %

q [

k P a ]

CADC C29

HS-model

E50ref Eoed

ref Eur ref ν’ur M c’ ϕ’ γ’

[kPa] [kPa] [kPa] - - kPa [ ° ] [kN/m3]

12000 12000 27000 0.35 0.8 27 36 15

Reference stress for stiffness, pref =100kPa



Predicted Settlements

c/c - spacing [m]

0.8 1.0 1.2 1.4 1.6

D i s p l a c e m e

n t s [ m ]

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

2D MCC

2D S-CLAY1

2D S-CLAY1S

3D S-CLAY1 Preliminary



Vertical Stress Distributions

1 m c/c 1.2 m c/c 1.4 m c/c

d 'v [kN/m²]

-250-200-150-100-500

D e p t h [ m ]

-12

-10

-8

-6

-4

-2

0

d 'v [kN/m²]

-250-200-150-100-500

d 'v [kN/m²]

-250-200-150-100-500

Soil

ColumnSoil SoilColumn

Column

2D MCC

2D S-CLAY12D S-CLAY1S

3D S-CLAY1 Preliminary



Principal Stress Directions



Conclusions (numerical study)

• Anisotropy and destructuration have a

– minor effect on the predicted verticalstresses

– greater effect on the predicted settlements

• Hardening soil model gives a realistic stress-strain relationship for deep-stabilized columns

2D - unit cell

3D model versus 2D - unit cell• Preliminary simulation “less settlements”





Aim: model 3D column behaviour within 2D calculations- Obtain overall response of system

- Save computational costs

- Feed model with known behaviour of constituents

(soil and column)





- Assumptions for volume averaging technique- Determination of equivalent constitutive material matrix

- Solution strategy

- Example

- Further work



Assumptions- Perfect bonding between in-situ soil and columns

- Volume ratio of the columns is not negligible

- Columns have a regular pattern

( ) soil soil soil εDσ && =

′

( ) columncolumncolumnεDσ && =′

J.-S. Lee, 1993:

Finite Element Analysis of Structured Media



Assumptions

( ) eqeqeqεDσ && =

′

( ) soil soil soil εDσ && =

′

( ) columncolumncolumnεDσ && =′

- Equilibrium and kinematics satisfied between constituents

- Analysis with equivalent stress/strain relationship

- Separate yield function for soil and column

J.-S. Lee, 1993:

Finite Element Analysis of Structured Media



Equilibrium and KinematicsLocal equilibrium conditions:

column

yz

soil

yz

eq

yz

column

xy

soil

xy

eq

xy

column

z

soil

z

eq

z

columnxsoilxeq x

τ=τ=τ

τ=τ=τ

σ=σ=σσ=σ=σ

&&&

&&&

&&&

&&& xy

z

Acolumn A soil

Kinematic conditions (bonding):

column

zx

soil

zx

eq

zx

column

y

soil

y

eq

y

γ=γ=γ

ε=ε=ε

&&&

&&&



Averaging Rules

column

column

soil

soil

eq

column

column

soil

soil

eq

εεε

σσσ

&&&

&&&

µ+µ=

µ+µ=

Volume fraction of soil / column:

A

A

;A

A columncolumn

soilsoil =µ=µ



Determination of D

eq

By combining the constitutive equations

with the kinematic and equilibrium conditions:

column

1columncolumn

soil

1

soil

soil

eq SDSDD µ+µ=

columnsoil

soil

column,soil

1 ,,f DDS µ=

With the material matrixes S1soil and S1

column :



Solution Strategy-Calculate equivalent material matrix

Deeq or Dep

eq

-Calculate strain increment

δBε

PK δ

&&

&&

=

= −

eq

1

eqcolumncolumneq soil soil

εSεεSε

&&&&11 ==

-Calculate stress increments

( ) ( ) columncolumncolumn soil soil soil

εD

σεD

σ &&&&

=

′

=

′

-Trial stresses

( ) ( ) ( ) ( ) ( ) ( )

′+

′=

′′+

′=

′−−

columnn

columnn

column soil n

soil n

soil σσσσσσ && 11



Solution Strategy-Check yielding

00 ≤≤ columncolumn soil soil F F σσ

-Return mapping soil/column-Adjust stress components if necessary

column

yz

soil

yz

column

yz

column

xy

soil

xy

column

xy

column

z

soil

z

column

z

column

x

soil

x

column

x

d d

d d

τ τ τ τ τ τ

σ σ σ σ σ σ

−=−=

−=−=

( ) ( ) ( )′+′

=′

− column

ncolumn

ncolumn d σσσ 1

-Recheck column yielding

0≤columncolumn F σ

-Calculate stress in equivalent material

column

column

soil

soil

eq

σσσ &&&

µ µ +=



First ExampleSingle integration point program – triaxial loading

Soil: Mohr-Coulomb model, linear elastic – ideal plastic

Columns: Linear elastic columns with 50% area ratioEcolumn = 2 Esoil

-0.018

-0.016

-0.014

-0.012

-0.01

-0.008

-0.006

-0.004

-0.002

0

-400-300-200-1000 2

2

equivalent

soil

column

Sig_soil(1)

Sig_column(1)



Future Work

full 3D simulations of embankments on deep mixed columns

use of advanced constitutive models for soil and columns

for homogenisation technique (S-CLAY1S, …)

implementation of averaging technique as constitutive model into

2D finite element code (Plaxis)

comparison of volume averaging method with full 3D simulations



Thank you very much for your attention

Vogler Krenn w(h)Ydoc05

Documents