1. Konstantinos Agrafiotis
PROJECT PRESENTATION
Comparison of different types of modeling for seismic isolation devices Application to a typical bridge structure
Konstantinos Agrafiotis
Major Professor : Gary Dargush

2. Basic principles of seismic isolation Lead Rubber bearings
CONTENTS
Basic principles of seismic isolation
Lead Rubber bearings
Mechanical Characteristics of Lead Rubber Bearings
Important parameters for modeling LRB
Application of a LRB to a typical highway concrete bridge
Modeling LRB with bilinear spring
Modeling LRB with equivalent linear Keff and constant numerical damping
Friction Pendulum Bearings
Principles of Friction Pendulum bearings, and points under consideration.
A simple friction model.
Application of FPS to a typical bridge
Modeling FPS with bilinear spring elements (ABAQUS)
Modeling FPS with coupled velocity dependent friction properties and post-slip stiffness in the shear direction
Investigation on the importance of each parameter into modeling

3. Lead Rubber Bearing
Stiffness and damping

4. Comparison between the two models
2.5 sec

5. Friction Pendulum Bearings (FPS)
Articulated Slider
Spherical Concave Surface
“stopper”
Stainless steel

6. Function of Inverse Pendulum
Force-Displacement Diagram R R W
Κp= W /R μW
Fo=μW
W cosθ  W θ
W sinθ  W /R
μ W cosθ
 μ W

7. Consideration on modeling friction pendulum bearings (FPS)
Effect of temperature on the coefficient of friction (Constantinou et al 1999)
Effect of pressure on the coefficient of friction

8. Effect of velocity on the coefficient of friction
Constantinou et al. 1990

9. Methods of modeling Friction Pendulum Bearings
Equivalent linear model with viscous damping
Bilinear model using spring elements
Dynamic friction + Spring element for the modeling of restoring force
Gap element with friction properties
K=W/R

10. Simple Friction Preliminary Analysis
μ = 0,1
Fmax = µdNSdsign(db)

11. Simple Friction Preliminary Analysis

12. Simple Friction Preliminary Analysis

13. Simple Friction Preliminary Analysis

14. Simple Friction Preliminary Analysis

15. Simple FPS Preliminary Analysis
Friction properties (velocity dependent μ)

16. Application to the typical Highway Concrete Bridge
Finite Element Model
Beam elements
0.5m mesh on the deck and the piers
Different types of elements for modeling seismic isolation devices
Non linear behavior of piers based on the moment-curvature relation.
Fixed pier at base
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17. Friction Pendulum Bearings Analysis
For a FPS bearing a number of models are going to be tested in time history analyses:
FPS model as a linear spring
Modeling FPS with non linear element springs.
With a friction element, linear spring for the restoring force, velocity dependent coefficient of friction and coupling between the two horizontal direction.
The analyses that were conducted are aimed to show the importance of each one of parameters included in each model mention above:
The importance of velocity dependent coefficient of friction.
The importance of coupling between the two horizontal directions. (bidirectional or unidirectional modeling).
If modeling friction with bilinear springs gives close to friction model results.
The important of numerical damping in the direct integration methods used from the analyses.
Earthquake Histories used for the analysis
The MCEER west-coast ground motion were used. For the purposes of the conducted analyses 6 earthquake histories were selected from the bin of 2% probability of exceedance. The 6 earthquake histories were selected from the two first scenarios on the bases that they include considerable acceleration response for periods near 3 sec.

18. Scenario#1 (7.5 km, 6.6 Mw)

19. Scenario#1 (7.5 km, 6.6 Mw)

20. Scenario#2 (5.7 km, 6.8 Mw)

21. Scenario#2 (5.7 km, 6.8 Mw)

22. Friction-pendulum isolator with unidirectional bilinear spring (ABAQUS model)
A bilinear spring is applied in each global horizontal direction
A large initial stiffness is selected corresponding to 10-4 displacement for F=μw
The post-stiffness is equal to W/R.
W have been found from static analysis for each pier

23. Friction-pendulum isolator with unidirectional bilinear spring (ABAQUS model)

24. Friction-pendulum isolator with unidirectional bilinear spring (ABAQUS model)
Peak Ground Acceleration (PGA) g
Spectral Acceleration Sa (g)
Maximum relative displacement (m)
Scenario#1 Event#1
0.93
0.34
0.08
Scenario#1 Event#4
0.79
0.31
0.04
Scenario#1 Event#10
1.09
0.32
0.11
Scenario#2 Event#2
0.85
0.46
0.26
Scenario#2 Event#4
0.83
0.48
0.29
Scenario#2 Event#8
0.98
0.43

25. Park, Wen with A=1 and β=γ=0.5 ,otherwise
Biaxial friction-pendulum isolator with velocity depended coefficient of friction (SAP2000)
This friction model is based on the hysteretic behavior proposed by Wen (1976), and Park, Wen and Ang (1986), and recommended for base-isolation analysis by Nagarajaiah, Reinhorn and Constantinou (1991).
,if du1<0
Park, Wen with A=1 and β=γ=0.5
,otherwise
The frictional force-deformation relationship:

26. Full SAP2000 Model

27. Full SAP2000 Model

28. Comparison between the two models: ABAQUS vs SAP2000
Sources of differences between the two models
The SAP2000 model takes into account that the coefficient of friction depend on the velocity.
In the SAP2000 model the two directions are coupled.
At the ABAQUS model the friction is model with the use of a bilinear spring.
The SAP2000 model takes into account the variation of the axial load. In ABAQUS model axial load is presumed constant in the calculation of stiffness.
Finally there are many differences in the solution of the direct integration that the two programs are using.

29. Comparison between different models

30. Importance of Coefficient of Friction depend on Velocity

31. Importance of Coupling between the two orthogonal directions

32. Can FPS modeled with a bilinear spring ??

33. The importance of Numerical method used in the direct time history Integration
The integration method used in SAP2000 is Hilber-Hughes-Taylor alpha” (HHT) method :
Uses a single parameter called alpha, -1/3≤ α ≤ 0
For alpha = 0, the method is equivalent to the Newmark method with gamma = 0.5 and beta = 0.25 (highest accuracy)

34. Hysteretic Loops of different models

35. Maximum relative displacement of the bearing (m)
Comparison between different models
MODEL
Maximum relative displacement of the bearing (m)
ABAQUS
0.26
SAP FULL MODEL
0.39
SAP2000-Constant μ- with coupling
0.34
SAP2000-Constant μ- uncoupled
0.27
SAP2000-Bilinear Spring
(high numerical damping)
(no numerical damping)
0.46
(very small numerical damping)
0.23

36. Conclusions For Lead Rubber Bearings: For Friction Pendulum System:
Equivalent linear model with viscous damping is inappropriate for modeling LRB in dynamic analysis.
Vertical excitation role is negligible to the response of model with LRB as long as there is no uplift at the bearing.
For Friction Pendulum System:
Equivalent linear model with viscous damping is inappropriate for modeling FPS in dynamic analysis
The effect of vertical excitation to the friction properties of a simple model with no vertical damping is important.
Modeling of FPB with bilinear springs provides very good preliminaries results but more precise analysis should be pursue. The bilinear spring model can be used in order to model simple friction pendulum bearing (constant coefficient of friction, no coupling between the two directions) with considerable success.

37. Conclusions For Friction Pendulum System:
Velocity dependent coefficient of friction alter the response of structures and should be included in analysis.
Coupled plasticity in two direction provide more accurate results especially if the properties of the bearing and the excitation in two directions are significant different.
Simplified non-linear time history analyses that do not consider non-constant coefficient of friction, coupling between the two directions are not conservative. On contrast their results should be treated with caution.
The variation of the axial load should be included in analysis since the post yield stiffness depends on the axial load. Variation of axial load is small for bridge structure under consideration, but may be significant for other structures ( ex. Building structure).
The numerical method for the time history integration is of great importance and should be treated with extreme caution. More specifically the numerical damping introduced into the model should be investigated in every conducted analysis.

38. THANK YOU !
QUESTIONS