Numerical Simulation of the Response of Sandy Soils Treated with PV-drains Antonios Vytiniotis, Andrew J. Whittle & Eduardo Kausel MIT Department of Civil & Environmental Engineering Progress Report for NEESR GC Workshop February 5 th 2009
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Numerical Simulation of the Response of Sandy Soils Treated with PV-drains
Antonios Vytiniotis, Andrew J. Whittle & Eduardo Kausel
MIT Department of Civil & Environmental Engineering
Progress Report for NEESR GC Workshop
February 5th 2009
Outline
� Planned activities for 2008
[NEESGC meeting January 2008]� Treating of PV-drains
� Implementing an element for PV-drains
� Use a non-linear model to simulate response
� Implementing a soil model
� Progress during 2008� Progress during 2008
� PV Drain elements in OpenSees
� Evaluation using Centrifuge Model Data
� Research Plans for 2009
PV-Drains
•Installation •Centrifuge Model
•Outflow during shaking
Storage Capacity Effect
ClayGW Level
Storage Capacity
Bedrock
Sand
Applied acceleration
Analytical Solutions
� Radial Dissipation of Excess Pore Pressure:
� Excess Pore Pressure Accumulation:
Unit Cell
� Key References� Seed & Booker: Perfect drains
� Onoue et al. Effect of well resistance
� Pestana et al.: FEQDRAIN (includes storage effect)
Validation : Importance of Drain Resistance[ Gravel drains: Onoue et al., 1987]
� Predictions of
Seed & Booker
� Read ru
� Much lower than
measured datameasured data
� Measured ru fit
modified theory
(well resistance)
Onoue, 1987
2-D (Plane-Strain) Modeling Approximation
PV Drain
Equivalent
plane strain PV
Drain
Match the degree of consolidation (average diffusion) within soil
Doesn’t match the pore pressures at all points
Hird et al., 1992
For infinite permeability drains inside a uniform soil:
kax : true soil permeability,
kpl : equivalent soil permeability in a plane stain analysis
n :drain spacing ratio
kax kpl
Equivalence between radial and plane strain drainage around a pre-fabricated drain
Normalized Excess Pore Pressure Ratio around a
perfect PV drain
ABAQUS results0.7
0.8
0.9
1
No
rmali
zed
Excess P
ore
P
ressu
re R
ati
o
Great match using Hird
et al equation!!!0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.0 0.2 0.4 0.6 0.8 1.0
No
rmali
zed
Excess
Pre
ssu
re R
ati
o
R/Ro or x/Ro
Axisymmetric, t=1s
Plane Strain, t=1s
Axisymmetric, t=0.1s
Plane Strain, t=0.1s
x,R0
R
PV-Drains: Hydraulics
� Darcy Weisbach Equation� λ, dimensionless flow coefficient
� L, length of pipe
� D, diameter of pipe
� ρ, mass density of fluid
� V , average velocity of the flow
PV-Drain Elements: Laminar flow
PV-Drain Elements: Turbulent flow
PV-Drains: Opensees Implementation
� Laminar flow:� element Pipelin2 element Pipelin2 element Pipelin2 element Pipelin2 eleideleideleideleid node1 node2 Material Area node1 node2 Material Area node1 node2 Material Area node1 node2 Material Area CCCCllll γγγγwwww
� Turbulent Flow� Turbulent Flow� element Pipe4 element Pipe4 element Pipe4 element Pipe4 eleideleideleideleid node1 node2 Material Area Cnode1 node2 Material Area Cnode1 node2 Material Area Cnode1 node2 Material Area Ctttt γγγγw w w w ddddcccc
PV-Drains: Scale Modeling Issues (I)
� Scaling of flow:
� QP = QM ·N2
� Scaling of Drain Flow Properties:
� Laminar flow
� ClP = Cl
M ·N3
� Turbulent flow
� CtP = Ct
M ·N5/2
PV-Drains: Scale Modeling Issues (II)
� Scaling of Reynolds number
� For the same pore fluid:
� ReP = ReM ·N
� For different pore fluid (diffusion scaled)
� ReP = ReM ·N2
� Problem Statement:
“What is the model scale diameter of a PV-drain (where flow is laminar) that corresponds to a selected prototype scale diameter (where flow is turbulent)?”
PV-Drains: Scale Modeling Issues (III)
Flow Rate, Q
Pressure
QmaxLaminar Drains
Fully Turbulent
Drains
Pressure Gradient, iimax
The model scale diameter that minimizes
differences between model scale laminar and
prototype scale turbulent flow is:
PV-Drains Validation: Centrifuge Model
Kamai et al, 2008
PV-Drains Validation: Centrifuge Model
Yolo Loam
PV drains
Applied acceleration
Loose Sand
Dense Sand
Loose Sand
Dense Sand
1650mm
24.75m
437mm
6.56m
PV-Drains Validation: Centrifuge Model
� Shaking sequence
PV-Drains Validation: Base Case Scenario
Drains
Periodic
Boundary
Conditions
No-tension
connection
Yolo Loam*
Applied acceleration
Loose Sand**, kax
*pressure independent multiyield model, QUAD Elements
Nodal mass
** pressure dependent multiyield model, QUADUP Elements
Dense Sand**, kax
Loose Sand**, kpl
Dense Sand**, kpl
#1 #2 #3 #4 #5 #6 #7 437 mm6.56 m
1650 mm24.75 m
PV-Drains Validation: Final Deformed Shape
� Numerical simulations indicate the
effectiveness of PV-Drains!!
PV-Drains Validation:PV-drain outflow
0 2 4 6 8 10 12 14-2
0
2
4x 10
-3
Time (s)
Flo
w R
ate
(m
3/s
)a. Flow coming out of drain No2 vs Time
6x 10
-3 b. Volume of water coming out of drain No2 vs Time
Laminar limit (model scale)
Solution
Laminar limit (prototype scale)
0 2 4 6 8 10 12 140
2
4
6
Time (s)
Vo
lum
e (
m3)
0 2 4 6 8 10 12 14-2
0
2
4x 10
-3
Time (s)
Dis
pla
ce
me
nt
(m)
c. Vertical displacement on top of drain No2
Indirect
Direct
0
10
20
Treated side Untreated side
50
60
Po
re P
res
su
re, p
(k
Pa
)
A
B
D
E
PV-Drains Validation:
Pore Pressures, amax=0.07g
30
40
Po
re P
res
su
re, p
(k
Pa
)
0 5 10 15 20 25 30
50
60
70
80
Time, t (s)0 5 10 15 20 25 30
Time, t (s)
Experiment
Simulation
C F
-2
-1
0
1
2Treated side Untreated side
1
2
Ho
rizo
nta
l A
cc
ele
rati
on
, αα αα
(m
/s2)
A
B
D
E
PV-Drains Validation: Horizontal Accelerations, amax=0.07g
-2
-1
0
1
Ho
rizo
nta
l A
cc
ele
rati
on
,
0 2 4 6 8 10 12
-1
0
1
Time, t (s)0 2 4 6 8 10 12
Time, t (s)
Experiment
Simulation
B
C
E
F
-0.2
-0.1
0
0.1
0.2Treated side Untreated side
0.1
0.2
Ho
rizo
nta
l, u
(m
)
C
B
F
E
PV-Drains Validation: Surface Horizontal Displacements, amax=0.07g
-0.2
-0.1
0
0.1
Ho
rizo
nta
l, u
(m
)
0 2 4 6 8 10 12
-0.1
0
0.1
Time, t (s)0 2 4 6 8 10 12
Time, t (s)
Experiment
Simulation
B
A
E
D
Predicted Net Lateral Movements, amax=0.07g
0
0.02
0.04
Treated side Untreated side
0
0.02
0.04
0.06
Ve
rtic
al S
ett
lem
en
t, u
y (
m)
C
B
F
E
PV-Drains Validation:
Surface Settlements, amax=0.07g
0.08
Ve
rtic
al S
ett
lem
en
t, u
0 2 4 6 8 10 12
0
0.05
0.1
Time, t (s)0 2 4 6 8 10 12
Time, t (s)
Experiment
Simulation
A D
PV-Drains: Validation Observations
� Excess Pore Pressures� Reasonable agreement at mid layer
� Underestimate at top of sand
� Horizontal Accelerations� Good agreement on treated side
� No deamplification in untreated sand
No ‘prediction’ of liquefaction event� No ‘prediction’ of liquefaction event
� Horizontal Displacements� Reasonable magnitudes
� No slippage between sand and loam
� Vertical Displacements (surface)� Mismatched across model
� Effect of variable g field (centrifuge) and/or slope failure mechanism?
PV-Drains: Summary
� Implementation of new PV Drain Elements
� Laminar & fully turbulent flow regimes
� Capability to evaluate mass balance in
controlled experiments (centrifuge)
� Established new understanding for scale
modeling of PV drainsmodeling of PV drains
� Include drain storage effect
� Evaluation using centrifuge model data
� SSK01, March 2007 (Kamai, et al., 2008a)
� Performance close to perfect drain case
� Field performance
� Long term performance?
� Effect of clogging, sedimentation & biofouling?
Constitutive Models� Current application
� Multi-yield surface plasticity (Elgamal & Yang, 2001-2002)� Advantages:
� Available in Opensees� Parameters previously selected: Nevada sand, Yolo Loam
� Disadvantages:� Re-calibration of parameters for each density� Limited predictive capability (cyclic mobility)
� Future applications� Future applications� Bounding surface plasticity models (UC Davis & NTUA groups)
� Family of models (many sub-versions!) � Dafalias, Manzari, Papadimitriou, Andrianopoulos (2004-2008)
� More predictive capability� Unique set of material input parameters (void ratio as state variable)
� Implementation in Opensees� V1: Dafalias-Manzari implemented
� Opensees wrapper: Jeremic – currently being evaluated� V2: Papadimitriou-Andianopoulos implemented in Flac
� To be ported to Opensees
Project Side Deliverables
� Publications
� Vytiniotis SM Thesis, February 2009
� Draft paper to be submitted on PV drain
implementation (Spring 2009)
� Opensees documentation: PV-drain elements� Opensees documentation: PV-drain elements
Research Goals 2009
� Upgrade analyses with better constitutive
model
� Evaluate predictive capabilities of UCD-NTUA
models
� Effect on predicted performance
Equivalent properties of improved soil � Equivalent properties of improved soil
mass
� Free-field properties for SSI research
� Application Colloidal Silica treatment
� Background studies completed
� Importance of gel compressibility?
� Immobilized pore space
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