1. Mahadevan (Lanka) Ilankatharan Adviser: Professor Bruce Kutter
Numerical simulation of a soil model-model container-centrifuge shake table system
Mahadevan (Lanka) Ilankatharan
Adviser: Professor Bruce Kutter
University of California, Davis
I am Lanka Ilankatharan, a graduate student at UC Davis, working with Prof. Bruce Kutter. My title of the ppt is Numerical simulation of a soil model-container-centrifuge shake table system.
NEES 5th Annual Meeting
June 19-21, 2007 Snowbird, Utah

2. Main Points Background and motivation Scope of simulations
Outline of OpenSEES simulations
Results
Simulation archives in neescentral
Future work and concluding remarks
The outline of my today's presentation is
Background & Motivation of research
Scope of outline of OpenSEES simulations
Some results
Simulations archives in neescentral
Future work and concluding remarks

3. NEES Geotechnical Centrifuge at Davis
This is the picture of 9m radius NEES geotechnical centrifuge at Davis.
Increased gravity field in centrifuge environment allows proper modeling of stress dependent behavior of soil under static and dynamic loading conditions.
Picture shows a centrifuge bucket, shaking table, and a container.
I’ll be talking about the simulations on this centrifuge-shake table-container-soil model system

4. Motivation:
Account for soil-container-shaker-bucket-centrifuge interaction on numerical models.
Centrifuge shaker-system includes soil model, container, shaking table and their reaction mass.
Dynamic properties of different components interact with model during shaking.
Interaction of soil model and centrifuge system might attenuate or amplify the discrepancies in response of numerical modeling and physical modeling.
The relative error between a numerical and physical simulation depends on how the boundary conditions and interaction among different components in the physical model are included in the numerical model. S A N D
50 g Centrifugal Force
Centrifuge shaker system
Actuator
Reaction Mass
Shaking table
Container
Structure
This picture shows a centrifuge shaker system
It includes soil model, container, shake table, and reaction mass
Dynamic properties of components interact with model during shaking
This interaction might attenuate of amplify the discrepancies of in response of numerical modeling and physical modeling
The relative error between a numerical and physical simulation depends on how the BC’c and interaction among different components of physical model are included in the simulation

5. Scope of OpenSEES Simulations:
How do we judge the quality of a comparison between experiment and simulation?
What is the goal of comparison between a simulation and experiment?
Material properties
Constitutive model
Integration scheme
How sensitive is the comparison to
Constitutive model, or
How does the sensitivity depend on boundary conditions in experiment or simulation?
input motion specification (location, time history)
Interaction between test apparatus and test specimen
A basic question “How do we judge the quality of a comparison between experiment and simulation?” (Does the simulation work or not?)
To answer above question we need to find answers to following questions
What is the goal of a comparison?
- To evaluate uncertain material properties
- To validate a constitutive model, or solution algorithm
How sensitive is the comparison to
- material properties, constitutive model, or integration scheme
How does the sensitivity depend on BC’s ?
We hypothesize that the sensitivity depends on how we model the boundary conditions in both the experiment and the simulation. Without understanding this, it is difficult to judge the quality of a comparison between experiment and simulation.

6. Experiment Simulation Simulation model2(BC2) model1(BC1) test specimen
output
test specimen
Shake table
actuator
Reaction mass
command from servo controller
shake table output
Experiment
Input: command from servo controller
specimen output
shake table output
Simulation
model2(BC2)
Input: measured shake table output in experiment
specimen output
Simulation
model1(BC1)
This cartoon illustrate an example of experiment BC’s and simulation BC’s in two different simulation models
Different components in are shown and input is specified at the actuator from servo controller. There are two outputs (shake table, and specimen)
Simulation model1 models the test specimen, input (measured shake table output from experiment) is specified at the base and the specimen out put is measured
Simulation model2 considers similar BC’s of experiment. Input is specified at the actuator from servo controller and out put measured at the shake table and specimen
The graphs show comparison between experiment and simulation
To judge the quality of these comparisons we need answer, How these comparisons are sensitive to BC’s ?
simulation1
experiment
specimen output
simulation2
experiment
shake table output
simulation2
experiment
specimen output

7. 1) 2D Soil Shear beam Simulations:
Slave Horizontal & Vertical DOF’s
Input motion
Horizontal & Vertical DOF’s of bottom nodes are constrained & input motion: measured base motion from experiment (Uniform excitation command)
80% density dry-dense sand
Only soil is modeled here using shear beam BC (same H and V DOFs at both ends)
2D plane strain model
Bottom nodes are fixed in H and V direction
Input is specified at bottom nodes in H direction
2D Plane strain model
Soil: 4-Node quad element and PDMY (Pressure Dependent Multi Yield) material
Soil density increased by 30% to account for container mass

8. Properties of flexible shear beam (FSB) container
inside dimensions
length=1.65m
width=0.788m
depth=0.584m
5 Metal rings (Bottom ring- steel, others aluminum)
5 Neoprene rings of 0.5 inches thickness
Shear rods at the end of container to provide complementary shear stress
Neoprene rings
Aluminum rings
Base plate
Shear rods
A flexible shear beam container is included in the next step of analysis
The above picture shows a flexible shear beam, the main components are labeled
Neoprene rings, sandwiched in between metal rings, allow the container to deform with soil during dynamic shaking
Vertical shear rod at the end of container to provide complementary shear stress

9. Modeling FSB02 Container:
Middle nodes of North and South ends are connected using truss elements (axial stiffness, k=AE/L, A- Cross sectional area of rings at East & West sides)
Container metal rings, neoprene rubber rings, and base plate were modeled as elastic nD material.
Mass and stiffness properties of 2D FE container match the mass and stiffness of the real container when the thickness of the plane strain FE domain is set to m.
Shear rods are modeled using elastic beam column element.
This slide explains the modeling procedure of FSB container

10. 2) Soil and container simulations:
Soil nodes are slaved with shear rod nodes in both horizontal and vertical directions
Plan view of vertical bearing supports
Rubber bearings
Actuators
Reaction mass
Vertical bearing supports on the bass of the container are modeled using zero-length elastic springs
Uniform excitation at bottom of container using horizontal acceleration measured from experiment
The effect of container is included in these suite of analysis
Soil nodes are slaved with shear rod nodes in both H and V direction

11. Results:
time (sec)
Surface acceleration (g)
Input motion: Northridge (peak base acc=1.3g)
2D soil shear beam simulations
Soil & container simulations
ARS (g)
period (sec)
Shows time histories and ARS of surface motion in experiment and simulations to a scaled version of input motion from 1994 Northridge earthquake
acc and time scales are in centrifuge model scale (prototype acc=model acc/50, and prototype time=model time*50)
ARS of motion from experiment shows peak at sec(0.234 sec prototype) and sec (0.62 sec)
Simulation results are different in two different BC’s. Inclusion of container improves the comparison at fundamental mode (0.62sec).
Acceleration & time scale are in centrifuge model scale (“52g” increased gravity field)

12. Soil horizontal accelerations:
ARS(g)
Period (sec)
Sweep (peak base acc=1.3g) C B A
534mm A B C
The results show soil site response (in terms of horizontal accs)
ARS of horizontal accs in 3 different locations (bottom, middle, and top)
Closer to bottom simulation results in two different BC’s are similar to experiment output
When move upward results are different in different BC’s.
Also shows interaction of model container with soil model during shaking
Better results when we include container

13. Soil vertical accelerations:
Sweep (peak base acc=1.3g)
acc(g)
Time(sec)
Period (sec)
ARS(g)
Shows time histories and ARS of vertical accs at both end of container
Vertical accs from experiment shows rocking of the container.
Vertical bearings on the base of the container are included in this analysis.
This allows better modeling of rocking behavior pf container during shaking (Results are reasonably predicted with OpenSEES model, expect a jump at 0.004sec)

14. 3) Soil+container+shaker simulations:
Zero-length elements (vertical bearings) connect base of the container and reaction mass
container base
Reaction mass
actuator elements k1 k2 c2
Finput
connected to reaction mass
connected to container base
Excitation is applied through actuator elements
This corresponding 3rd BC.
The effect of shaker (actuator flexibility) included in these series of analysis.
Excitation is applied through actuator elements (Force input)
The schematic of simple model of actuator elements is shown here
Stiffness to account the compressibility of oil is calculated
Then, k1>> k2, k1 =10k2 (assumption)
Start with command displacement=displacement of container base (from double integration of H acc )
Then tune command displacement to get comparable results at the base of the container
k1- stiffness to account for flow of oil in actuator.
k2, c2- stiffness and dashpot to account for compressibility of oil.
(k1
k2)
Finput=k1*command displacement

15. Soil+container+shaker simulation results
Sweep (peak base acc=1.3g)
acc(g)
ARS(g)
time(sec)
period(sec)
Shows simulation results from soil, container, and shaker simulations.
Bottom graphs presents base response, and top graphs show soil surface response
The initial results are promising, better simulation of experiment.
The effect of actuator-controller interaction, reaction mass flexibility need to be included

16. Sensitivity of estimated soil surface motion to reference maximum shear modulus of soil
-Sweep input (peak base acc=1.3g)
2D soil shear beam
soil+container
soil+container+shaker
ARS (g)
period (sec)
Show results from a preliminary sensitivity analysis. Present the effect of reference shear modulus on soil surface motion at 3 different BC’s.
Reference shear of 80% density Nevada sand is calculated based on Vs=65.4(p”)^0.25 (Arulnathan et al, 2000)- Base line case
Then Gmax is changed by +/- 10% from base line case
The results are not sensitive to change in shear modulus when we include the effect of shaker.
Sensitivities are different in different BC’s
The above preliminary sensitivity analysis shows the sensitivity of soil surface motion depends on BC’s

17. Current/Future work: Sensitivity analysis:
account for flexibility of reaction mass
include actuator-controller interaction
include centrifuge arm S A N D
Actuator
Reaction Mass
Shaking table
Bucket (I beam)
50 g Centrifugal Force
Details of current and future work
Sensitivity analysis:
Comprehensive sensitivity studies to evaluate the effect of BC’s

18. Experiment & simulation data archives in NEEScentral
A most completely documented centrifuge test data set from MIL test series is available in NEEScentral
Numerical models will be documented and archived in NEEScentral so that the models are available to others through the NEEScentral archive
Details about the data archives

19. Concluding Remarks:
Sensitivity of simulation results to material properties depends on boundary conditions. Therefore it is important to accurately model boundary conditions.
A numerical model is developed using OpenSEES to represent the dynamics of soil model-model container-shaking table-centrifuge system.
Mass & flexibility of container, shear rods, vertical bearing supports to incorporate rocking of container, actuator flexibility, flexibility of reaction mass, etc.
Comprehensive sensitivity studies will be performed to evaluate the effect of BC’s on the sensitivity of computational modeling results to uncertain soil properties.
Computational models and results will be documented and archived in NEES data repository (NEEScentral) with the existing centrifuge test data archives. So others can use our OpenSEES models of container/shaker for other NEES projects.

20. Acknowledgements:
Dr. Dan Wilson, Lars Pedersen, and Peter Rojas (CGM UC Davis)
NEESit
Hyung-Suk Shin (University of Washington)
Prof. Scott Brandenberg (UCLA)

21. Thanks!

23. Sensitivity of estimated surface motion to reference maximum shear modulus of soil
-Sweep input (peak base acc=13g)
2D soil shear beam
soil+container
soil+container+shaker
ARS (g)
period (sec)

24. Soil vertical accelerations:
acc(g)
ARS(g)
Time(sec)
Period (sec)
Sweep (peak base acc=13g)
Soil vertical accelerations:

25. Soil (PDMY) input parameters:
Soil density=1.66 ton/m3
Reference Gmax (at p’=80kPa), Gmax_r=64284 kPa (Arulnathan et al 2000, Vs=65.8(p’)0.25 for 80% density Nevada sand)
Reference Bulk Modulus (at p’=80kPa), K_r = kPa
Peak friction angle =37 degs
Peak shear strain (at p’=80 kPa) =0.1
Reference p’_r=80 kPa
Pressure depend coefficient, d= [ Gmax=Gmax_r(p’/p’_r)0.5 , K=K_r(p’/p’_r)0.5 ]
Phase transformation angle, PTang=27 degs
Parameters defining the rate of shear induced volume change (Medium dense sand (65%-85%)-PDMY user manual);
- contrac=0.05
- dilat1=0.6
- dilat2=3
Parameters defining controlling the liquefaction-induced perfectly plastic shear strain accumulation(liquefac1, liquefac2, and liquefac3; liquefac1=0 deactivate this mechanism)

26. Numerical damping:
Newmark integration parameters (g=0.5, b=0.25; zero Newmark algorithmic damping)
Coefficient of stiffness proportional damping a0= (damping ratio, z=a0/2*w)