Numerical simulation of a soil model- model container-centrifuge shake table system University of California, Davis Mahadevan (Lanka) Ilankatharan Adviser:

Numerical simulation of a soil model-model container-centrifuge shake table system

University of California, Davis

Mahadevan (Lanka) Ilankatharan

Adviser: Professor Bruce Kutter

NEES 5th Annual Meeting

June 19-21, 2007 Snowbird, Utah

Main Points

Background and motivationScope of simulationsOutline of OpenSEES simulationsResultsSimulation archives in neescentralFuture work and concluding remarks

NEES Geotechnical Centrifuge at Davis

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.

SAND

50 g Centrifugal Force

Centrifuge shaker system

Actuator

Reaction Mass

Shaking table

Container

Structure

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 Material properties Constitutive model, or Integration scheme

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

Scope of OpenSEES Simulations:

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.

test specimenspecimen output

Shake table actuatorReaction mass

command from servo controller

shake table output

Experiment

Input: measured shake table output in experiment

specimen output

Simulation model1(BC1)

Input: command from servo controller

specimen output

shake table output

Simulation model2(BC2)

simulation1

experiment

specimen output

simulation2

experiment

specimen output

simulation2

experiment

shake table output

1) 2D Soil Shear beam Simulations:

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

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

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

Shear rods

Neoprene rings

Aluminum rings

Base plate

Modeling FSB02 Container:

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 0.788 m. Shear rods are modeled using elastic beam column element.

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)

2) Soil and container simulations:

Soil nodes are slaved with shear rod nodes in both horizontal and vertical directions

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

Plan view of vertical bearing supports

Rubber bearingsActuators

Reaction mass

Results:

Acceleration & time scale are in centrifuge model scale (“52g” increased gravity field)

time (sec)

Surf

ace

acc

ele

rati

on

(g)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

5

0

5

CentrifugeOpenSEES (soil 2D shear beam)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

5

0

5

CentrifugeOpenSEES (soil & container)

Input motion: Northridge (peak base acc=1.3g)

2D soil shear beam simulations

Soil & container simulations

AR

S

(g)

period (sec)1 10 3 0.01 0.10

5

10

15

20

25

30

CentrifugeOpenSEES (soil 2D shear beam)OpenSEES (soil & container)

ARS of surface motion

1 103

0.01 0.10

5

10

15

20

25

30

510 mm from bottom (surface motion)

1 103

0.01 0.10

5

10

15

20

25

30

288 mm from bottom (middle of container)

1 103

0.01 0.10

5

10

15

20

25

30

CentrifugeOpenSEES (soil 2D shear beam)OpenSEES (soil & container)

95 mm from bottom

Soil horizontal accelerations:

534mm

A

B

C

AR

S(

g)

Period (sec)

Sweep (peak base acc=1.3g)

1 10 3 0.01 0.10

5

10

15

20

25

30510 mm from bottom (surface motion)

1 10 3 0.01 0.10

5

10

15

20

25

30288 mm from bottom (middle of container)

1 10 3 0.01 0.10

5

10

15

20

25

30

CentrifugeOpenSEES (soil 2D shear beam)OpenSEES (soil & container)

95 mm from bottom

C

B

A

Soil vertical accelerations:

1 103

0.01 0.10

2

4

6

8

CentrifugeOpenSEES (soil and container)

487 mm from bottom - south end

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.751.5

1

0.5

0

0.5

1

1.5487 mm from bottom - North end

1 10 3 0.01 0.10

2

4

6

8487 mm from bottom - North end

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.751.5

1

0.5

0

0.5

1

1.5487 mm from bottom - south end

1 10 3 0.01 0.10

2

4

6

8487 mm from bottom - south end

Sweep (peak base acc=1.3g)

acc

(g)

Time(sec) Period (sec)

AR

S(

g)

acc

(g)

AR

S(

g)

3) Soil+container+shaker simulations:

k1k2

c2Finput Finput

connected to reaction mass

connected to container base

Excitation is applied through actuator elements

k1- stiffness to account for flow of oil in actuator.

k2, c2- stiffness and dashpot to account for compressibility of oil. Finput=k1*command displacement

(k1 k2)

Zero-length elements (vertical bearings) connect base of the container and reaction mass

Reaction mass

actuator elements

container base

Soil+container+shaker simulation results

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

4

2

0

2

4

Surface Motion

1 10 3 0.01 0.10

5

10

15

20

25

Surface Motion

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

4

2

0

2

4

Base Motion

1 10 3 0.01 0.10

5

10

15

20

25

Base Motion

Sweep (peak base acc=1.3g)

acc

(g)

acc

(g)

AR

S(

g)

AR

S(

g)

time(sec) period(sec)

1 103

0.01 0.10

5

10

15

20

25

CentrifugeOpenSEES (soil, container, and shaker)

Base Motion

25

0

ARS_cen_base

ARS_open_382_x

0.10.001 T

Sensitivity of estimated soil surface motion to reference maximum shear modulus of soil

1 10 3 0.01 0.10

10

20

30

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

1 10 3 0.01 0.10

10

20

30

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

1 10 3 0.01 0.10

10

20

30

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

2D soil shear beam soil+container soil+container+shaker

AR

S

(g)

period (sec)

1 10 3 0.01 0.10

10

20

30

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

1 10 3 0.01 0.10

10

20

30

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

1 10 3 0.01 0.10

10

20

30

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

-Sweep input (peak base acc=1.3g)

The above preliminary sensitivity analysis shows the sensitivity of soil surface motion depends on BC’s

Current/Future work: account for flexibility of reaction mass

include actuator-controller interaction

include centrifuge arm

Sensitivity analysis:

Comprehensive sensitivity studies to evaluate the effect of BC’s

SAND

Actuator

Reaction Mass

Shaking table

Bucket (I beam)

50 g Centrifugal Force

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

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.

Acknowledgements:

Dr. Dan Wilson, Lars Pedersen, and Peter Rojas (CGM UC Davis)

NEESit

Hyung-Suk Shin (University of Washington)

Prof. Scott Brandenberg (UCLA)

Thanks!

1 10 3 0.01 0.10

50

100

150

200

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

1 10 3 0.01 0.10

50

100

150

200

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

1 10 3 0.01 0.10

50

100

150

200

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

2D soil shear beam soil+container soil+container+shaker

AR

S

(g)

period (sec)

1 10 3 0.01 0.10

10

20

30

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

1 10 3 0.01 0.10

10

20

30

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

1 10 3 0.01 0.10

10

20

30

Base line casedecrease ref Gmax by 10%increase ref Gmax by 10%

-Sweep input (peak base acc=13g)

Sensitivity of estimated surface motion to reference maximum shear modulus of soil

0.1 0.15 0.2 0.25 0.3 0.35

15

10

5

0

5

10

15

487 mm from bottom - North end

1 103

0.01 0.10

20

40

60

80

100

487 mm from bottom - North end

0.1 0.15 0.2 0.25 0.3 0.35

15

10

5

0

5

10

15

487 mm from bottom - south end

1 103

0.01 0.10

20

40

60

80

100

487 mm from bottom - south end

acc

(g)

AR

S(

g)

Time(sec) Period (sec)1 10

30.01 0.1

0

2

4

6

8

CentrifugeOpenSEES (soil and container)

487 mm from bottom - south end

Sweep (peak base acc=13g)

Soil vertical accelerations:

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 =192852 kPa

Peak friction angle =37 degs

Peak shear strain (at p’=80 kPa) =0.1

Reference p’_r=80 kPa

Pressure depend coefficient, d=0.5 [ 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)

Numerical damping:

Newmark integration parameters (zero Newmark algorithmic damping)

Coefficient of stiffness proportional damping a0=0.0000385 (damping ratio, =a0/2*)

0 100 200 300 400 5000

1

2

3

4

5

6

7

Newmark damping (gamma=0.5, beta-0.25)Viscous damping (Stiffnees proportional damping)Total damping (gamma=0.5, beta=0.25, AND viscous dampin)

Newmark algorithimic damping and Viscous

Frequency (Hz)

Dam

ping

rat

io (

%)

1

2

1 2

f