1. 1 NEESR Project Meeting 22/02/2008 Modeling of Bridge Piers with Shear-Flexural Interaction and Bridge System Response Prof. Jian Zhang Shi-Yu Xu Prof. Jian Zhang Shi-Yu Xu

2. 2 NEESR Project Meeting Prototype Bridges Structural Characteristics FHWA Design Example #4 Bridge #4 FHWA Design Example #8 Bridge #8 Mendocino Ave. Overcrossing Bridge Mendocino (1963) Span LengthThree-span continuous Five-span continuousUneven, four-span continuous Total Length320 ft long 500 ft long302 ft long Pier Type Two-column integral bent, monolithic at column top, pinned at base Two-column integral bent, monolithic at column top and base Single column variable height, monolithic at column top and base Abutment Type SeatStub abutment with diaphragmMonolithic Foundation Type Spread FootingPile Group Expansion Joints Expansion bearings & girder stops (shear keys) Expansion bearings & girder stops Force Resisting Mechanism [Longitudinal] intermediate bent columns & free longitudinal movement at abutments [Transverse] intermediate bent columns & abutments [Longitudinal] intermediate bent columns and abutment backfill [Transverse] intermediate bent columns and abutment backfill [Longitudinal] intermediate columns and abutment backfill [Transverse] intermediate columns and abutment backfill Plan Geometry 3 0° s kewed Straight Natural Period ～ 0.5 sec ～ 1.5 sec ～ 0.5 sec Design Method Old designNew designOld design Three box girder concrete bridges are selected as prototype bridges for preliminary analysis.

3. 3 NEESR Project Meeting Factors Affecting Bridge Response Site Conditions Soil-structure Interaction Earthquake Characteristics Ground Motion Selection Structure Properties Geometry (straight, skew or curved) Stiffness, ductility, energy dissipation

4. 4 NEESR Project Meeting k11k11 k44k44 k22k22 k 55 k33k33 k66k66 ksks kyky k θx kzkz Finite Element Bridge Models fixed k11k11 k44k44 k22k22 k 55 k33k33 k66k66 kzkz (a) Bridge #4 (b) Bridge #8 (c) Bridge Mendocino k11k11 k44k44 k22k22 k 55 k33k33 k66k66 kyky kxkx kzkz k θx XZ Y (d) Imaginary Bridge Mendocino with 30° skewed embankment & bent columns

5. 5 NEESR Project Meeting Summary of Modeling Parameters Interested IssueQuestion to AnswerModel Type Tested Bridges Bridge #4Bridge #8 Mendocino Effects of Input Ground Motion How are seismic demands related to ground motion intensity? Linear ●● Nonlinear ●● Effects of Vertical Acceleration How does vertical acceleration change the bridge seismic demand? Linear ●● Nonlinear ●● Effects of Nonlinearity How does nonlinear behavior in columns affect the seismic demand of the bridges? Linear v.s. Nonlinear ●● T/M ratio: Column type What type of column design (bent column v.s. single column design) yields higher T/M ratio? Bent ●●● Single ● T/M ratio: Skewness Will skewed bents and/or abutments cause higher T/M ratio? Straight ●● Skewed ●● T/M ratio: Stiffer column What is the effect of a stiffer (short) column in the bridge systems? One short column ● T/M ratio: Pinned design @ Column base Is pinned design at column bases advantageous in eliminating torsional demand on the columns? Pinned w/ SSI ●● Fixed w/ SSI ●● Fixed w/o SSI ● Effects of Axial- Shear- Flexural Interaction How the interaction between combined loadings affects the capacity of bridges? Nonlinear ABAQUS User Element under development

6. 6 NEESR Project Meeting Observations Effect of PGA  Linear Model : Response (A,D,SF,SM) increase almost linearly with PGA.  Non-linear Model : Response increase non-linearly with PGA. Effect of Non-linearity  Column forces (SF,SM) reduced by 5% ~ 60%.  Non-linearity effects is more significant in strong earthquakes than in small ones. Effect of Vertical Ground Motion  Only affect vertical response quantities.  Incorrect  Vertical responses increase almost linearly with maximum vertical PGA.  Tensile axial force is observed in columns during earthquakes.  For bent column bridges, tensile axial force is observed in columns in most of Bin 4 earthquakes; while axial force in the single column bridge seldom goes into tension side.

7. 7 NEESR Project Meeting Observations (continued) Effect of Column Type (Bent Column vs Single Column) on T/M ratio:  Bent column design greatly reduce the Torsion/Moment ratio in columns, if columns are the same in dimension and reinforcement.  For bridges with bents, reducing the lateral stiffness/capacity of columns will result in a higher T/M ratio.  If bending capacity of columns is met in one of the horizontal directions, torsion-moment interaction may become very significant. Effect of Skewness on T/M ratio:  Skewed bridges do NOT necessarily increase T/M ratio. (  ?) Effect of Stiffer Column on T/M ratio:  A relatively stiffer column in the bridges will introduce a higher level of asymmetry into the system and thus results in higher T/M ratios. Effect of Pinned Design at Column Base on T/M ratio:  Pinned design at column bases greatly eliminates torsional demand. Effect of Combined Actions  Investigate Shear-Flexural Interaction first.

8. 8 NEESR Project Meeting Model Verification – Specimen TP021 Input Displacement Cross Section Side View http://seismic.cv.titech.ac.jp/en/ Yoneda, Kawashima, and Shoji (2001) Displacement

9. 9 NEESR Project Meeting Experimental Program Overview Column with large aspect ratio are controlled by flexural behavior; Column with small aspect ratio are controlled by shear behavior; Aspect ratio ≒ 4 is about the ratio where moderate shear-flexural interaction can be observed. Height Diameter =

10. 10 NEESR Project Meeting Spring includes both flexural and shear deformation. Abaqus Comparison with Exp. Result – TP021

11. 11 NEESR Project Meeting Model Verification – Specimen TP031 & TP032

12. 12 NEESR Project Meeting Experimental Program Overview Height Diameter =

13. 13 NEESR Project Meeting Comparison with Exp. Result – TP031 & TP032 Ozcebe and Saatcioglu ’ s model (1989) works fine with these two specimens under either compressive or tensile axial force, despite the transverse reinforcement ratio of the columns is as high as 0.79%.

14. 14 NEESR Project Meeting Cyclic Loading: Abaqus UEL vs OpenSees OpenSees fails to capture: Strength deterioration due to cycles Pinching behavior UEL

15. 15 NEESR Project Meeting Validation of UEL + Rigid Column: Static Case UEL Deck UEL

16. 16 NEESR Project Meeting Dynamic Verification: UNR Test - Column 9F1 Column Loading Motions Column Details

17. 17 NEESR Project Meeting Column 9F1: Reinforcement & Test Setup

18. 18 NEESR Project Meeting Static Pushover Curve of Column 9F1

19. 19 NEESR Project Meeting Hysteretic Loop of Column 9F1: 0.33x

20. 20 NEESR Project Meeting Hysteretic Loop of Column 9F1: 0.66x

21. 21 NEESR Project Meeting Hysteretic Loop of Column 9F1: 1.00x

22. 22 NEESR Project Meeting Hysteretic Loop of Column 9F1: 1.50x

23. 23 NEESR Project Meeting Hysteretic Loop of Column 9F1: 2.00x

24. 24 NEESR Project Meeting Hysteretic Loop of Column 9F1: 2.50x

25. 25 NEESR Project Meeting Hysteretic Loop of Column 9F1: 3.00x

26. 26 NEESR Project Meeting Time Histories of Column 9F1: 3.50x

27. 27 NEESR Project Meeting Time Histories of Column 9F1: 4.00x

28. 28 NEESR Project Meeting Hysteretic Loop of Column 9F1: 0.33x

29. 29 NEESR Project Meeting Hysteretic Loop of Column 9F1: 0.66x

30. 30 NEESR Project Meeting Hysteretic Loop of Column 9F1: 1.00x

31. 31 NEESR Project Meeting Hysteretic Loop of Column 9F1: 1.50x

32. 32 NEESR Project Meeting Hysteretic Loop of Column 9F1: 2.00x

33. 33 NEESR Project Meeting Hysteretic Loop of Column 9F1: 2.50x

34. 34 NEESR Project Meeting Hysteretic Loop of Column 9F1: 3.00x

35. 35 NEESR Project Meeting Time Histories of Column 9F1: 3.50x

36. 36 NEESR Project Meeting Time Histories of Column 9F1: 4.00x

37. 37 NEESR Project Meeting Hysteretic Loop of Column 9F1: 0.33x ~0.66x

38. 38 NEESR Project Meeting Hysteretic Loop of Column 9F1: 1.00x ~1.50x

39. 39 NEESR Project Meeting Hysteretic Loop of Column 9F1: 2.00x~2.50x

40. 40 NEESR Project Meeting Hysteretic Loop of Column 9F1:3.00x ~3.50x

41. 41 NEESR Project Meeting Time Histories of Column 9F1: 4.00x

42. 42 NEESR Project Meeting Average Response Ratio of Bridge #8 UEL NL M-φ

43. 43 NEESR Project Meeting Average Response Ratio of Mendocino Bridge UEL NL M-φ

44. 44 NEESR Project Meeting 44 Verification of the nonlinear UEL spring  Almost done. Incorporating the nonlinear spring into 3D FE bridge models  Mendocino Bridge & Bridge #8. Effects of non-linear shear-flexural interaction on bridge responses  Cause and effect of the significant increase in moment need to be clarified. UEL to include Axial-Shear-Flexural Interaction Effects of axial load variation on bridge system responses Future Work: Update