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Seismic Simulation of Bridge Systems Under Multi-directional Motions

Seismic Simulation of Bridge Systems Under Multi-directional Motions. Jian Zhang Assistant Professor Yuchuan Tang and Shi-Yu Xu Graduate Student Researcher Department of Civil and Environment Engineering University of California, Los Angeles. UCLA Progress & Scope of Work.

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Seismic Simulation of Bridge Systems Under Multi-directional Motions

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  1. Seismic Simulation of Bridge Systems Under Multi-directional Motions Jian Zhang Assistant Professor Yuchuan Tang and Shi-Yu Xu Graduate Student Researcher Department of Civil and Environment Engineering University of California, Los Angeles

  2. UCLA Progress & Scope of Work • Selected 4 ground motion suites that incorporate the site-dependent probabilistic hazard analysis and ground motion disaggregation analysis. • Selected 2 bridge prototypes that are distinctive in terms of structural characteristics and dynamic properties. • Conducted linear and nonlinear time history analysis of prototype bridges subjected to multi-directional ground shakings and evaluate the effect of vertical motions on seismic demand. • Implement nonlinear structural and foundation elements to realistically capture the response under multi-directional ground shakings.

  3. Ground Motion Selection • Selection Procedure • Select the Los Angeles Bulk Mail Building (LABMB) site used by PEER Building Benchmark project for prototype bridges (NEHRP Class D) • Conduct site-specific Probabilistic Seismic Hazard Analysis (PSHA) using HAZ software to evaluate the probability of exceeding a given intensity measure within a given time period • Multiple Hazard Levels: 2% in 50 Years and 50% in 50 Years • Structural Period of Interest: T=0.5s (Bridge #4) and T=1.5s (Bridge #8) • Conduct dis-aggregation analysis to select ground motion records that reasonably represent possible future realizations of ground shaking for the appropriate ground intensity measure level • Maginitude (M), Distance (r) and Epsilon (ε) • Fault Type, Directivity and Site Condition

  4. Uniform Hazard Curves Uniform Hazard at LABMB Site

  5. Ground Motion Record Selection Criteria • Magnitude (M) and Site-Source Distance Range (r) • Epsilon (ε) • The physical interpretation of ε is the offset between the value of the record’s intensity measure and the expected value from an attenuation relationship. • Parameter ε is model dependent. Attenuation relationship by Abrahamson and Silva (1997) is used to quantify ε. • Positive ε (“peak record”) motions lead to reduced seismic demand as building softens. • Negative ε (“valley record”) motions lead to larger seismic demand as building softens. • Scaling Factor • Scaling is needed to enforce a consistent value of target intensity measure • Scaling factor is obtained from the geometric mean of a single recording and applied equally to all components of the recorded motions

  6. 8.0-8.5 7.0-7.5 6.0-6.5 5.0-5.5 Seismic Hazard Disaggregation (T=0.5s) Hazard Level: 50% in 50 Years (Targeted PGA=0.47g) Hazard Level: 2% in 50 Years (Targeted PGA=1.24g) 0.2 2.00E-01 1.80E-01 0.18 1.60E-01 0.16 1.40E-01 0.14 1.20E-01 0.12 Relative Contribution 1.00E-01 0.1 8.00E-02 0.08 6.00E-02 0.06 4.00E-02 0.04 2.00E-02 8.0-8.5 0.02 7.5-8.0 7.0-7.5 0.00E+00 6.5-7.0 0 Magnitude 6.0-6.5 0-10 10-20 5.5-6.0 Magnitude 20-30 30-40 40-50 5.0-5.5 50-60 60-70 70-80 80-90 90-100 100-1000 Distance Distance • For most hazard levels, the intensity measure is dominated by two clusters of magnitude-distance combinations: • Cluster A: Small r and small M • Cluster B: large r and large M

  7. 2.00E-01 2.00E-01 1.80E-01 1.80E-01 1.60E-01 1.60E-01 1.40E-01 1.40E-01 1.20E-01 1.20E-01 1.00E-01 1.00E-01 8.00E-02 8.00E-02 6.00E-02 6.00E-02 4.00E-02 4.00E-02 2.00E-02 2.00E-02 8.0-8.5 8.0-8.5 7.0-7.5 7.0-7.5 0.00E+00 0.00E+00 Magnitude Magnitude 6.0-6.5 6.0-6.5 5.0-5.5 5.0-5.5 Distance Distance Seismic Hazard Disaggregation (T=1.5s) Hazard Level: 50% in 50 Years (Targeted PGA=0.22g) Hazard Level: 2% in 50 Years (Targeted PGA=0.61g) • For most hazard levels, the intensity measure is dominated by two clusters of magnitude-distance combinations: • Cluster A: Small r and small M • Cluster B: large r and large M

  8. Selected Earthquake Motions • Hazard Level: 2% in 50 Years; Dissaggregation Period: 0.5s

  9. Selected Earthquake Motions • Hazard Level: 50% in 50 Years; Dissaggregation Period: 0.5s

  10. Hazard Level: 50% in 50 Yrs Hazard Level: 2% in 50 Yrs Acceleration Spectra of Motions Selected for T=0.5s A=1.24g A=0.47g

  11. Selected Earthquake Motions • Hazard Level: 2% in 50 Years; Dissaggregation Period: 1.5s

  12. Selected Earthquake Motions • Hazard Level: 50% in 50 Years; Dissaggregation Period: 1.5s

  13. Acceleration Spectra of Motions Selected for T=1.5s Hazard Level: 50% in 50 Yrs A=0.61g A=0.22g Hazard Level: 2% in 50 Yrs

  14. Prototype Bridges • Two box girder concrete bridges (FHWA Bridge #4 and 8) are selected as prototype bridges for analysis

  15. Bridge #4 – Structural Details

  16. 48” 34 #11 bars Bridge #4 – Pier Details Moment-Curvature Curve Pier Cross Section

  17. Bridge #4 – Surface Foundation Details Equivalent Radii : R = (4*L*B/π)^0.5 = 7.9 ft Half of footing plan dimension : L = B = 7 ft Spring and dashpot coefficients based on elastic half-space model by Meek & Wolf (1993) • K11= 1.50E9 N/m =1.03E5 kips/ft, C11= 1.56E7 N.s/m • K22= 1.50E9 N/m = 1.03E5 kips/ft, C22= 1.56E7 N.s/m • K33= 1.38E9 N/m = 9.44E4 kips/ft, C33= 2.46E7 N.s/m • K44= 9.66E9 N*m/rad = 7.12E6 kip*ft/rad C44= 1.08E7 N*m*s/rad • K55= 9.66E9 N*m/rad = 7.12E6 kip*ft/rad C55= 1.08E7 N*m*s/rad • K66= 1.56E10 N*m/rad = 1.15E7 kip*ft/rad C66= 1.45E7 N*m*s/rad

  18. Bridge #4 – Dashpot of Surface Foundation Cross area : A = 2L*2B = 18.209 m^2 Thickness : D = 3.5ft = 1.067 m Soil density : ρ = 1.835 Mg/m^3 Shear wave velocity : Cs = 360 m/sec ; Cp=2*Cs (Soil Type II, SPT N=50) Poisson’s ratio : ν = 0.35

  19. Bridge #4 – Abutment Modeling (Bin4)

  20. Bridge #4 – Natural Frequencies and Modes Mode #1, T=0.81s Mode #4, T=0.32s Mode #2, T=0.51s Mode #5, T=0.22s Mode #3, T=0.40s Mode #6, T=0.21s

  21. Bridge #4 – Max. response vs. PGA (Linear, 3EQ case) Max Acceleration (g) Max Section Force (N) PGA along x, y, and z directions PGA along x, y, and z directions Max Relative Displacement (m) Max Section Moment (N-m) PGA along x, y, and z directions PGA along x, y, and z directions

  22. Bridge #4 – Response Ratio vs. PGA Ratio Linear(3EQ/2EQ) Max Acceleration Ratio Max Section Force Ratio Vertical to Horizontal PGA Ratios Vertical to Horizontal PGA Ratios Max Displacement Ratio Max Section Moment Ratio Vertical to Horizontal PGA Ratios Vertical to Horizontal PGA Ratios

  23. Bridge #4 – Max. response vs. PGA (non-Linear, 3EQ case) Max Acceleration (g) Max Section Force (N) PGA along x, y, and z directions PGA along x, y, and z directions Max Relative Displacement (m) Max Section Moment (N-m) PGA along x, y, and z directions PGA along x, y, and z directions

  24. Bridge #4 – Response Ratio vs. PGA Ratio Non-Linear(3EQ/2EQ) Max Acceleration Ratio Max Section Force Ratio Vertical to Horizontal PGA Ratios Vertical to Horizontal PGA Ratios Max Displacement Ratio Max Section Moment Ratio Vertical to Horizontal PGA Ratios Vertical to Horizontal PGA Ratios

  25. Non-LinearLinear Bridge #4 – Response Ratio vs. PGA Max Acceleration Ratio Max Section Force Ratio PGA along x, y, and z directions PGA along x, y, and z directions Max Displacement Ratio Max Section Moment Ratio PGA along x, y, and z directions PGA along x, y, and z directions

  26. Bridge #4 – Section Moment-Curvature Curve

  27. Bridge #4 – Column Pushover Curve

  28. With HingeW/O Hinge Bridge #4 – Response Ratio vs. PGA (Linear) Max Acceleration Ratio Max Section Force Ratio PGA along x, y, and z directions PGA along x, y, and z directions Max Displacement Ratio Max Section Moment Ratio PGA along x, y, and z directions PGA along x, y, and z directions

  29. With HingeW/O Hinge Bridge #4 – Response Ratio vs. PGA (non-Linear) Max Acceleration Ratio Max Section Force Ratio PGA along x, y, and z directions PGA along x, y, and z directions Max Displacement Ratio Max Section Moment Ratio PGA along x, y, and z directions PGA along x, y, and z directions

  30. Bridge #8 – Structural Details

  31. 48” 20 #10 bars Bridge #8 – Pier Details Pier Cross Section

  32. x 22’-0” z 46’-0” Bridge #8 - Pile Foundation Details CIP concrete pile with steel casing Pile diameter: d=2 ft; Pile cross section area(including transformed area of steel casin): A=673 in2 Spacing between piles: Sx = Sy = 8 ft Spring and dashpot coefficients based on model by Makris and Gazetas (1993) • Kx= 1.1497e+009 N/m =7.8869E4 kips/ft, Cx= 3.5792e+007 N.s/m = 2.4553E3 kips.s/ft, • Ky= 3.1174e+009 N/m = 2.1385E5 kips/ft, Cy= 1.0927e+008 N.s/m = 7.4959E3 kips.s/ft, • Kz= 1.1510e+009 N/m = 7.8959E4 kips/ft, Cz= 3.0441e+007 N.s/m = 2.0883E3 kips.s/ft.

  33. Bridge #8 – Natural Frequencies and Modes Mode #4, T=0.68s Mode #1, T=1.62s Mode #2, T=1.38s Mode #5, T=0.45s Mode #6, T=0.29s Mode #3, T=1.05s

  34. Structural Response of Bridge #8 Displacement Demand Force Demand Tension At bottom node of Column in Bent#3 Column in Bent#3 At top node of Column in Bent#1 Column in Bent#1 Column in Bent#1 At bottom node of Column in Bent#1 1986 N. Palm Springs Earthquake

  35. Bridge #8 – Max. response vs. PGA (Linear, 3EQ case) Max Acceleration (g) Max Section Force (N) Pga-x,y,z PGA along x, y, and z directions PGA along x, y, and z directions Max Relative Displacement (m) Max Section Moment (N-m) PGA along x, y, and z directions PGA along x, y, and z directions

  36. Bridge #8 – Response Ratio vs. PGA Ratio Linear(3EQ/2EQ) Max Acceleration Ratio Max Section Force Ratio Vertical to Horizontal PGA Ratios Vertical to Horizontal PGA Ratios Max Displacement Ratio Max Section Moment Ratio Vertical to Horizontal PGA Ratios Vertical to Horizontal PGA Ratios

  37. Bridge #8 – Max. response vs. PGA Non-Linear(3EQ case) Max Acceleration (g) Max Section Force (N) PGA along x, y, and z directions PGA along x, y, and z directions Max Relative Displacement (m) Max Section Moment (N-m) PGA along x, y, and z directions PGA along x, y, and z directions

  38. Bridge #8 – Response Ratio vs. PGA Ratio Non-Linear(3EQ/2EQ) Max Acceleration Ratio Max Section Force Ratio Vertical to Horizontal PGA Ratios Vertical to Horizontal PGA Ratios Max Displacement Ratio Max Section Moment Ratio Vertical to Horizontal PGA Ratios Vertical to Horizontal PGA Ratios

  39. Non-LinearLinear Bridge #8 – Response Ratio vs. PGA Max Acceleration Ratio Max Section Force Ratio PGA along x, y, and z directions PGA along x, y, and z directions Max Displacement Ratio Max Section Moment Ratio PGA along x, y, and z directions PGA along x, y, and z directions

  40. Bridge #8 – Section Moment-Curvature Curve

  41. Bridge #4 – Bending vs Torsional Moment Ratio

  42. Bridge #4 – Bending vs Torsional Moment Ratio

  43. Bridge #8 – Bending vs Torsional Moment Ratio

  44. Bridge #8 – Bending vs Torsional Moment Ratio

  45. Bridge #4 – Bending vs Torsional Moment Ratio

  46. Bridge #4 – Bending vs Torsional Moment Ratio

  47. Preliminary Conclusions • Vertical Motion Effects • Only affect vertical response. • Vertical response ratio increase as vertical to horizontal PGA ratio increases, except for max section moment. • Vertical responses increase almost linearly with max vertical PGA. • Non-linear Flexural Behavior Effects • Not significant in transverse direction. • Max longitudinal response ratio decreases as PGA increases, which means the non-linearity effects is more significant in strong earthquakes than in small ones.

  48. Future Research Plan • Perform high quality pretest simulations of test specimens with realistic loading and boundary conditions • Provide guidance for tests conducted at UIUC • Optimize number and parameters of test specimens • Identify realistic loading and boundary conditions • Integrate various analytical models into the framework of UI-Simcor for pseudo-dynamic hybrid testing

  49. UCLA Contribution: Post-test Model Development • Use test results to develop accurate shear-flexure interaction and axial-shear-flexure models for beam-column elements • Improve existing models with better shear-flexure interaction representation • Investigate the effect of shear-axial-flexure interaction in the presence of high vertical motion • Parametric analytical studies to develop design equations and procedures • Parametric assessment and improvement of code shear equations

  50. UCLA Contribution: Post-test System Analysis • Perform system analysis of bridge systems using the improved component models of columns • Derive probabilistic fragility relationships for RC bridges including axial-shear-flexure interaction • Develop recommendations for bridge column design to account for reduced shear capacity due to combined loading conditions

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