Numerical Modelling of Deep Mixed Columns Harald Krenn University of Strathclyde Urs Vogler University of Glasgow
Numerical Modelling of Deep Mixed Columns
Harald KrennUniversity of Strathclyde
Urs VoglerUniversity 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 fill
– 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 cell
dependent on the c/c –spacing
Restriction:– Not a true geometric
representation
πcR =
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 data
available
S-CLAY1S Model
q
p’ pm’ pmi’
M1
M1
α 1
CSL
CSL
p’σ’y
σ’x
σ’z
α
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=
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 undrained triaxial tests– Stiffness is highly non-
linear and dependent on confining pressure
Hardening Soil model
020406080
100120140160180
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
Axial strain, ε 1, %
q [k
Pa]
CADC C29HS-model
E50ref Eoed
ref Eurref 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
Dis
plac
emen
ts [m
]
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
2D MCC2D S-CLAY12D S-CLAY1S3D S-CLAY1 Preliminary
Vertical Stress Distributions
1 m c/c 1.2 m c/c 1.4 m c/c
dσ'v [kN/m²]
-250-200-150-100-500
Dep
th [m
]
-12
-10
-8
-6
-4
-2
0
dσ'v [kN/m²]
-250-200-150-100-500
dσ'v [kN/m²]
-250-200-150-100-500
Soil
ColumnSoil SoilColumnColumn
2D MCC 2D S-CLAY1 2D S-CLAY1S 3D S-CLAY1 Preliminary
Principal Stress Directions
Conclusions (numerical study)
• Anisotropy and destructuration have a – minor effect on the predicted vertical
stresses– 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”
Volume averaging technique
Columns and soil Composite system
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)
Volume averaging technique
Columns and soil Composite system
- 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
( ) soilsoilsoil εDσ && =′
( ) columncolumncolumn εDσ && =′
J.-S. Lee, 1993:Finite Element Analysis of Structured Media
Assumptions
( ) eqeqeq εDσ && =′
( ) soilsoilsoil εDσ && =′
( ) columncolumncolumn εDσ && =′
- 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:
columnyz
soilyz
eqyz
columnxy
soilxy
eqxy
columnz
soilz
eqz
columnx
soilx
eqx
τ=τ=τ
τ=τ=τ
σ=σ=σ
σ=σ=σ
&&&
&&&
&&&
&&&x
yz
AcolumnAsoil
Kinematic conditions (bonding):
columnzx
soilzx
eqzx
columny
soily
eqy
γ=γ=γ
ε=ε=ε
&&&
&&&
Averaging Rules
columncolumn
soilsoil
eq
columncolumn
soilsoil
eq
εεε
σσσ&&&
&&&
µ+µ=
µ+µ=
Volume fraction of soil / column:
AA;
AA column
columnsoil
soil =µ=µ
Determination of Deq
By combining the constitutive equations with the kinematic and equilibrium conditions:
column1columncolumn
soil1
soilsoil
eq SDSDD µ+µ=
( )columnsoilsoil
column,soil1 ,,f DDS µ=
With the material matrixes S1soil and S1
column :
Solution Strategy-Calculate equivalent material matrix
Deeq or Dep
eq
-Calculate strain increment
δBεPKδ&&
&&
=
= −
eq
1
eqcolumncolumneqsoilsoil εSεεSε &&&& 11 ==
-Calculate stress increments
( ) ( ) columncolumncolumnsoilsoilsoil εDσεDσ &&&& =′
=′
-Trial stresses
( ) ( ) ( ) ( ) ( ) ( )′+′
=′′
+′
=′
−−column
ncolumn
ncolumnsoil
nsoil
nsoil σσσσσσ && 11
Solution Strategy-Check yielding
( ) ( ) 00 ≤≤ columncolumnsoilsoil FF σσ-Return mapping soil/column-Adjust stress components if necessary
columnyz
soilyz
columnyz
columnxy
soilxy
columnxy
columnz
soilz
columnz
columnx
soilx
columnx
dddd
ττττττ
σσσσσσ
−=−=
−=−=
( ) ( ) ( )′+′
=′
−column
ncolumn
ncolumn d σσσ 1
-Recheck column yielding
( ) 0≤columncolumnF σ-Calculate stress in equivalent material
columncolumn
soilsoil
eq σσσ &&& µµ +=
First ExampleSingle integration point program – triaxial loadingSoil: Mohr-Coulomb model, linear elastic – ideal plasticColumns: 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
σ2
ε 2
equivalentsoilcolumnSig_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 into2D finite element code (Plaxis)
comparison of volume averaging method with full 3D simulations
Thank you very much for your attention