Seismic Design of Bridges

Transcription

1 Seismic Design of Bridges Anat Ruangrassamee, Ph.D. Center of Excellence in Earthquake Engineering and Vibration Department of Civil Engineering Chulalongkorn Universit 1. Design philosoph Course Outline 2. Design response spectra and design procedures 3. Modeling of bridges 4. Design of RC columns 5. Foundation stabilit and design of foundations 6. Design of movement joints 1

2 Chapter 1: Design Philosoph 1. Lessons learned from past earthquakes Those who ignore the lessons of histor are doomed to repeat its mistakes. From Seismic Design and Retrofit of Bridges b Priestle et al. (1996) 2. Performance criteria How do ou want the structure to perform in an earthquake? How much danger can ou accept? Roberts, J. (1999) Lessons Learned from Past Earthquakes column failure pounding bearing failure unseating foundation failure soil liquefaction 2

3 Lessons Learned: Liquefaction Large settlements of ground near crane girders on piles. Kobe 1995 Photo from EASY Niigata, Japan earthquake, June 16, 1964 Photo from NISEE Pull-out of piles (Mexico, 1985) Photo from EASY Lessons Learned: Foundation Failure Cracked pile and extension of nominal vertical reinforcing. (Kobe, 1995) Photo from NISEE Pile staed in place while soil oscillated, leaving imprint in soil about 30cm. Photo from NISEE 3

4 Lessons Learned: Flexural Failure of Column Hanshin Expresswa, Kobe 1995 Photo from NISEE Lessons Learned: Shear Failure of Column Railwa bridge, Kobe 1995 Photo from EASY 4

5 Lessons Learned: Splice Failure of Column Hanshin Expresswa, Kobe 1995 Photo from NISEE Lessons Learned: Splice Failure of Column Different tpe of column failure with man failed splices Hanshin Expresswa, Kobe 1995 Photo from NISEE 5

6 Lessons Learned: Shear Failure of Cap Beam Railwa bridge, Sannomia, Kobe, 1995 Photo from EASY Lessons Learned: Bearing Failures Kobe 1995 Photo from EASY Nishinomia Bridge Kobe 1995 Photo from NISEE 6

7 Lessons Learned: Pounding Interstate-5 at Santa Clara River. Joint was open about 1/2 inch. Northridge EQ 1994 Photo from NISEE Steel deck girder hit into the abutment and locall buckled. The abutment failed in shear. Kobe 1995 Photo from EASY Lessons Learned: Unseating Kobe 1995 Photo from NISEE 7

8 General Philosoph of Seismic Design It is accepted worldwide that the design should accomplish the following objectives: 1. Prevent nonstructural damage in minor earthquake ground shakings, which ma occur frequentl during the service life of the structure. 2. Prevent structural damage and minimize nonstructural damage during moderate earthquake ground shakings, which ma occasionall occur. 3. Avoid collapse or serious damage during severe earthquake ground shakings, which ma rarel occur. Frequent Occasional Rare Ver Rare Performance Design Objectives Seismic Performance Design Objective Matrix (SEAOC Vision 2000, 1995) Earthquake Performance Level Earthquake Design Level How do ou want the structure to perform in an earthquake? How much danger can ou accept? Roberts, J. (1999) Full Operational Operational Basic objective Essential/hazardous objective Safet critical objective Life Safet Near Collapse Unacceptable performance 8

9 Seismic Design Codes Japan Road Association: Design Specifications of Highwa Bridges Part V Seismic Design, 2002 (JRA) AASHTO: Standard Specifications for Highwa Bridges, 1996 (AASHTO) Applied Technolog Council: Improved Seismic Design Criteria for California Bridges Provisional Recommendations (ATC-32), 1996 (ATC-32) Transit New Zealand: Bridge Manual, 1995 (TNZ) CEN: Eurocode 8 - Design Provisions for Earthquake Resistance of Structures, 1994 (EC8) Performance Criteria: JRA Ground Motion Ordinar Bridge Important Bridge GM with high possibilit of occurrence (Level-1 GM) Functional (1) Functional (1) GM with low possibilit of occurrence (Level-2 GM) Tpe-I GM (Kanto EQ) Tpe-II GM (Kobe EQ) Prevent critical damage (3) Retain limited damage (2) 9

10 Performance Criteria: ATC-32 Ground Motion Level of Post-EQ Service Level of Damage Ordinar Bridges Important Bridge Ordinar Bridges Important Bridge Functional-Evaluation GM Immediate Immediate Reparable Minimum Safet-Evaluation GM Limited Immediate Significant Reparable 1. Design philosoph Course Outline 2. Design response spectra and design procedures 3. Modeling of bridges 4. Design of RC columns 5. Foundation stabilit and design of foundations 6. Design of bearings and movement joints 7. Capacit design of bridges 10

11 Chapter 2: Design Response Spectra and Design Procedures 1. Elastic and inelastic response spectra 2. Force reduction factor - Equal-energ approximation - Equal-displacement approximation 3. Design response spectra (review of various design codes) 4. Design procedures 5. Load combination Elastic Response Spectra Bridge m k c Natural period T = 2π m k Damping ratio ξ = 2 c k m Building Displacement Natural period 11

12 Acceleration (m/s 2 ) Example of Elastic Response Spectra JMA Kobe record (Measured at the JMA Kobe Observator in the 1995 Kobe earthquake) Time (s) Displacement Response Spectrum (m) Acceleration Response Spectrum (m/s 2 ) Natural Period (s) Natural Period (s) Visualization of Elastic Response Spectra BiSpec 12

13 Nonlinear Inelastic Behavior Dead load Lateral load Idealized behavior (elastoplastic) Actual behavior Lateral load Lateral displacement Lateral displacement Yielding displacement of idealized behavior Photos from Dr. Jun-ichi Sakai (TIT) Actual ielding displacement Definition of Ke Parameters of Elastoplastic Sstem Consider an elastic sstem and an elastoplastic sstem subjected to an earthquake. The following figure show the envelop curve. Lateral load uo = maximum displacement of an elastic sstem f o fo = maximum force of an elastic sstem u = ielding displacement of an elastoplastic sstem f um = maximum displacement of an elastoplastic sstem f = ielding force of an elastoplastic sstem u uo um Lateral displacement um fo ductilit factor ( μ ) = Force reduction factor ( R) = u f 13

14 Constant-Ductilit Response Spectrum For design purposes, it is desired to determine the ield strength of the sstem for a certain design ductilit factor. It can be accomplished b resorting to a constant-ductilit response spectrum. The conventional elastic response spectrum can be considered as a constant-ductilit response spectrum with a ductilit factor of 1. How should we present the response spectrum? stiffness mass pseudo-acceleration A f = ku = m u = m u = ma = w g natural angular frequenc weight 2 2 Yield strength ( ω ) ( ω ) A g Ductilit factor Natural period How to Construct Constant-Ductilit Response Spectrum? 1. Define a ground motion. 2. Fix a mass and a damping ratio (tpicall 0.05). 3. Set a natural period T. 4. Determine response of a linear sstem. f o f o f u o 5. Set a target ductilit factor μ t 6. Determine response of an elastoplastic sstem with f < fo assumed 7. Compute a response ductilit um factor μ r = u 8. If μr μt > tolerance 0, repeat Step 6 b changing f until μr μt tolerance. Then keep u and f 9. Repeat Step 5 for a different target ductilit factor. 10. Repeat Step 3 for a different natural period. 11. Plot a constant-ductilit response spectrum. 2 A ω u = g g μ t u u o um T 14

15 Visualization of Constant-Ductilit Response Spectrum BiSpec Force Reduction Factor A g Force Reduction Factor R A g 1 Elastic response spectra μ =1 Ductilit factor Inelastic response spectra Ductilit factor μ =1 T μ = 1 T Instead of directl computing an inelastic response spectrum, we can use an elastic response spectrum (due to its simplicit) with a force reduction factor (dependent on a natural period and a ductilit factor). A ( μ, T) = f f ( μ, T) = A ( μ = 1, T ) R( μ, T) ( μ = 1, T ) R( μ, T) T 15

16 Force Reduction Factor JMA Kobe record Normalized Strength (f /w = A /g) Inelastic Response Spectrum μ=1 μ=3 μ=5 μ=7 Elastic Response Spectrum Natural Period (s) Force Reduction Factor Force Reduction Factor Natural Period (s) Generalized Force Reduction Factor Kawashima and Watanabe (2003) considered 70 free-field ground motion records. Proposed empirical model vs. mean force reduction factor 16

17 Approximation of Force Reduction Factor: Equal-Displacement Approximation It is assumed that the maximum displacement of an inelastic sstem is equal to the maximum displacement of an elastic sstem. This assumption is considered applicable to long-period structures. This assumption is used in US and NZ. Lateral load uo = maximum displacement of an elastic sstem f o fo = maximum force of an elastic sstem u = ielding displacement of an elastoplastic sstem f um = maximum displacement of an elastoplastic sstem Lateral f = ielding force of an elastoplastic sstem displacement u u m = u u Ductilit factor ( μ) = u o m fo uo u μ u m Force reduction factor ( R) = = = = = μ f u u u R = μ Approximation of Force Reduction Factor: Equal-Energ Approximation It is assumed that the strain energ of an inelastic sstem is equal to the strain energ of an elastic sstem. This assumption is used in Japan. Lateral load f o f u uo um equal Lateral displacement u = maximum displacement of an elastic sstem f u u f o o m = maximum force of an elastic sstem = ielding displacement of an elastoplastic sstem = maximum displacement of an elastoplastic sstem = ielding force of an elastoplastic sstem Formulation: = 1 f ( um uo) = ( uo u)( fo f) 2 17

18 Approximation of Force Reduction Factor: Equal-Energ Approximation 1 f( um uo) = ( uo u)( fo f) 2 1 u f( μu uo) = ( fo f)( fo f) 2 f fu o 1 u f ( μu ) = ( fo f)( fo f) f 2 f fo 1 u fu ( μ ) = ( fo f)( fo f) f 2 f fo 1 1 μ = 2 ( fo f )( fo f ) f 2 f fo 1 f ( o f 1)( o μ = 1) f 2 f f 1 μ R= ( R 1)( R 1) 2 2μ 2R= R 2 2R + 1 R = 2μ 1 Lateral load f o f u uo um equal Lateral displacement R = 2μ 1 Comparison of Force Reduction Factors and Soft Soil (Kawashima and Watanabe (2003) Not conservative at short periods Taking account of the considerable scattering of the force reduction factors depending on the ground motions, it is conservative to assume the equal energ assumption instead of the equal displacement assumption for the evaluation of the force reduction factors 18

19 Function-Evaluation (Level-1) Design Response Spectra: JRA S = c c S z D 0 damping modification factor zone factor Standard Acceleration Response Spectrum S 0 (gal) Soil I Soil II Soil III Natural Period (s) Design Response Spectra: JRA Safet-Evaluation (Level-2) Tpe-I ground motion SI = czcdsi 0 Tpe-II ground motion S = c c S II z D II 0 Represent the 1923 Kanto EQ Represent the 1995 Kobe EQ Standard Acceleration Response Spectrum S I0 (gal) Soil I Soil II Soil III Natural Period (s) Standard Acceleration Response Spectrum S II 0 (gal) Soil I Soil II Soil III Natural Period (s) 19

20 Design Response Spectra: JRA Damping modification factor c D Damping Modification Factor c D Damping Ratio h Standard response spectra are presented for the 5% damping ratio. Design Response Spectra: JRA Zone factor c z c z = 1.0 c z = 0.85 c z =

21 Design Response Spectra: JRA Lateral strength capacit P S I or II g R W weight response modification factor A response modification factor (force-reduction factor) is determined based on the equal-energ approximation. Lateral load f o R = 2μ 1 equal a f u uo um Lateral displacement design ductilit factor Design Response Spectra: AASHTO Elastic seismic response coefficient C s site coefficient (= 1.0, 1.2, 1.5, 2.0) 1.2AS = 2.5A 2/3 ground acceleration (g) T period C sm / A 21

22 Design Response Spectra: AASHTO Ground acceleration (called acceleration coefficient ) in % of g Note: 1. The return period is approximatel 475 ears. 2. Acceleration >0.8g in a part of California and Alaska Design Response Spectra: AASHTO Response modification factor (R-factor) Substructure R Wall-tpe pier RC pile bents vertical piles onl one or more batter piles Single columns Steel or composite steel and concrete pile bents vertical piles onl one or more batter piles Multiple column bents

23 Design Response Spectra: ATC-32 Elastic acceleration response spectrum on a rock site Elastic response spectrum = ARS peak rock acceleration (g) site modification factor Design Response Spectra: ATC-32 Response modification factor (Z-factor) Important bridges must be designed as full ductilit structures. 23

24 Design Response Spectra: TNZ Seismic coefficient (V/W) = C μ Z R S p > 0.05 risk factor basic seismic coefficient zone factor structural performance factor Basic acceleration coefficient C μ for stiff soil Basic acceleration coefficient C μ for soft soil Design Response Spectra: TNZ 24

25 Design Response Spectra: TNZ Zone factor Z Z = Design Response Spectra: TNZ Risk factor R Structural performance factor S p Importance Categor R Site Subsoil Categor S p Bridges carring more than 2500 vpd Bridges carring or crossing motorwas and railwas 1.3 Rock or ver stiff sites Intermediate soil sites Bridges carring between 250 and 2500 vpd 1.15 Flexible or deep soil sites 0.67 Bridges carring less than 250 vpd Non permanent bridges 1.0 The return periods of design earthquakes are about 900, 650, and 450 ears for bridges with risk factors of 1.3, 1.15, and 1.0, respectivel. This factor accounts for damping arising from radiation and inelastic behavior in the foundation. 25

26 Design Response Spectra: EC8 spectral acceleration amplification factor (=2.5) T 1 + ( k D β0 1) ; 0 T T B ground acceleration (g) TB kd β0 ; TB T TC S = ki ks ag TC kd β0 ; TC T 3 T important factor (=1.3, 1.0, 0.7) 2 TC 3 kd β0 ; 3 T site modification factor 3 T (=1.0, 1.0, 0.9) damping modification factor Values of T B and T C Damping modification factor Soil Classification A B C T B (s) T C (s) k D 0.07 = h damping ratio Design Response Spectra: EC8 Response modification factor (q-factor) Substructure Seismic Behavior RC columns slender (H/L > 3.5) short (H/L=1) Abutment Limited Ductile Ductile

27 Comparison of Design Response Spectra Codes Factors Zone factor Importance factor Site modification factor Damping modification factor Response modification factor JRA (2002) c z = 1.0, 0.85, categories - For computing ductilit R-factor -3 tpes - Response spectra c D = h R = 2μ a 1 AASHTO (1996) Specif ground acceleration -2 categories - For computing R-factor -4 tpes - S = 1.0, 1.2, 1,5, 2.0 No -R-factor -From table ATC-32 (1996) Specif ground acceleration - 2 categories - For computing Z-factor -6 tpes - Response spectra No - Z-factor - From chart TNZ (1995) Z = categories - R = 1.3, 1.15, tpes - Response spectra -S p = 0.9, 0.8, 0.67 No Use inelastic response spectra ( R = μ ) EC8 (1994) Specif ground acceleration - 3 categories -k I = 1.3, 1.0, tpes -k S = 1.0, 1.0, 0.9 k D 0.07 = h -q-factor -From table Design Response Spectra of Thailand The contour map of PGA was proposed b Professor Panitan Lukkunaprasit. Maximum ground acceleration is about 0.15 g. During the lack of acceleration data, basic response spectra specified in AASHTO or EC8 should be cautiousl use. Design response spectra 27

28 Start Design for ordinar loads Design Procedure: JRA Determine stiffness, period, seismic coefficient, lateral force Yes (dimension, no. of piles) Change configuration? No (reinforcement) out out Check foundation stabilit Check cap beam, column, foundation Determine stiffness, period, seismic coefficient Check column for lateral strength capacit and residual displacement Check foundation stabilit Check foundation Design bearing Design movement joint Seismic Coefficient Method Ductilit Design Method (If liquefaction occurs) out End Load Combination Code Load Combination JRA D+PS+CR+SH+E+HP+B+EQ AASHTO D+E+B+SF+EQ TNZ EC8 1.00{kD+1.35(E+HP+B)+SG+ST+EQ+0.33TP} 1.35(D+E+HP+B+SG+0.33EQ+1.1CN) (k=1.3 or 0.8, whichever is more severe, to allow for vertical acceleration) D+PS+EQ+ψL (ψ=0 for bridges with normal traffic, ψ=0.2 for bridges with heav traffic, ψ=0.3 for railwa bridges) 28