Chapter 6 Seismic Design of Bridges. Kazuhiko Kawashima Tokyo Institute of Technology

Transcription

1 Chapter 6 Seismic Design of Bridges Kazuhiko Kawashima okyo Institute of echnology

2 Seismic Design Loading environment (dead, live, wind, earthquake etc) Performance criteria for gravity (deflection, stresses) and environmental loads (damage, displacement, collapse) Geometric (space) requirements ime available for construction Soil condition Cost..

3 Process of Seismic Design Functional Requirements Site Evaluation Design to Static Loads Evaluate Seismic Performance Goals by Equivalent Static Analysis Evaluate Seismic Performance Goals by Dynamic Response Analysis Evaluate Design Detailings

4 Requirements in Seismic Design Load Resistance Factor Design (LRFD ) γ D φ ave C ave Capacity Capacity Factor Demand Load Factor γ γ... φ γ n Dave φ1 φ2 n C ave A limit states format is currently based on performancebased design

5 Variation of Demand and Capacity Probability Demand Capacity Low frequent but high consequence events Demand or Capacity

6 Seismic Design Process with Emphasis on Japanese Seismic Design

7 Japanese Codes for Design of Highway Bridges Japan Road Association Design Specifications of Highway Bridges Part I Common Part Part II Steel Bridges Part III Concrete Bridges Part IV Foundations Part V Seismic Design he code applies to highway bridges with a center span no longer than 200m

8 Number of Pages related to Seismic Design of Highway Bridges in Japan Most bridges which collapse during 1995 Kobe earthquake were designed according to this code Number of Pages 1923 Kanto EQ 1925 Seismic Design Started 1964 Code for Steel Bridges 1995 Kobe EQ Year

9 1971Code and the Latest Code (2002)

10 Part V Seismic Design, Design Specifications of Highway Bridges, Japan Road Association 1. General 2. Principles of seismic design 3. Loads considered in seismic design 4. Design ground motions 5. Evaluation of seismic performance 6. Performance evaluation by static analysis 7. Performance evaluation by dynamic analysis 8. Effect of unstable soils 9. Menshin design (Seismic Isolation)

11 Part V Seismic Design, Design Specifications of Highway Bridges, Japan Road Association (continued) 10. Strength & Ductility of RC piers 11. Demand & capacity of steel piers 12. Demand & capacity of foundations 13. Demand & capacity of abutment foundations on liquefiable ground 14. Demand & capacity of superstructures 15. Seismic design of bearings 16. Unseating prevention devices

12 Seismic Performance Goals

13 Seismic Performance Criteria James Roberts (1999), Previous Caltran s Chief Engineer How do you want the structure to perform in an earthquake? How much danger can you accept? What are the reasonable alternate routes?

14 Ground Motion Japan Road Association Ordinary Bridges Important Bridges Function Evaluation GMs Functional Functional Safety Evaluation GMs ype-i (Kanto) ype-ii (Kobe) Prevent critical damage Retain limited damage AC and Caltrans (1999) Ground Motions Service Level Ordinary Important Damage Level Ordinary Important Function Evaluation Immediate Immediate Reparable damage Minimum damage Safety Evaluation Limited Immediate Significant damage Repairable damage

15 Seismic Performance Goals SEAOC Vision 2000 Earthquake Probability Frequent Fully Operation al Performance Objective Operation al Life Safety Near Collapse Occasiona l Rare Very Rare

16 Definition of Limit States Limit State Fully Operational Operational Life safety Near Collapse Collapse Description of Damage No damage, continuous service Most operations and functions can resume immediately. Repair is required to restore some non-essential services. Damage is light. Structure is safe for immediate occupancy. Essential operations are protected. Damage is moderate. Selected building systems, features or contents may be protected from damage. Life safety of generally protected. Structure is damaged but remains stable. Falling hazards remain secure. Repair possible. Structural collapse is prevented. Nonstructural elements may fall. Repair generally not be possible. Complete structural collapse

17 Probability of Occurrence of Seismic Ground Motions { } D D t y Y P y Y P 1, ( 1 1 ), ( = > = > Probability of occurrence of a ground motion with its intensity larger than within a life time of a structure y D Y Return Period = Averaged Recurrence Interval 1), ( 1 ) ( = > = t y Y P y R D R D y y Y P = > ) ( ), ( Probability of not being exceeded D R D D y y Y P y Y P = > = < ) ( 1 1 ), ( 1 ), (

18 An Exmple of Definition of Probability of Occurrence of Earthquakes Classification of Earthquakes Frequent Recurrent Interval 43 years Probability of Occurrence 70% in 50 years Occasional 72 years 50% in 50 years Rare 475 years 10% in 50 years Very Rare 970 years 10% in 100 years

19 Recommended Maximum ransient & Permanent Drift Vision 2000, SEAOC Limit State Fully Operational Operational Life Safety Near Collapse Collapse Maximum ransient Drift (%) > 2.5 Maximum Permanent Drift (%) Negligible Negligible > 2.5

20 Seismic Design Force

21 Seismic Design Force Seismic design force should be determined based on the seismic environment (seismicity, fault length and rupture, etc) around the construction sites Seismic hazard map in terms of PGA is frequently used to scale the seismic design force. Response accelerations are widely used to provide the seismic design force of bridges. Multiplying it to mass, lateral force can be directly evaluated.

22 Seismic Design Force (continued) Standard response spectra are generally modified to take account of regional seismicity as S A (, ξ ) = c S (, ξ ) design z A s tan dard Importance of structures are sometimes reflected to evaluate the design seismic force. here are two groups in this treatment as Larger design seismic force is considered for a structure with higher importance Since seismic force which applies to a structure does not change depending on the importance of the structure, the importance is considered in the evaluation of the capacity

23 < = ) ( / ) ( ) ( /3 1 S S S k k S D Z F Function Evaluation (6.1) < = ) ( / ) ( ) 0 ( /3 4 S S S k k S D Z SI Safety Evaluation ype I GM (6.2) < < < = ) ( / ) ( ) (0 6 5/ /3 7 S S S k k S d Z SII ype II GM (6.3) Japan Road Association (1996 &2002)

24 Design Specifications of Highway Bridges, Japan Road Association ξ = 0.05 Function Evaluation GM Safety Evaluation GM Response Accleration S F (g) Ground I Ground II Ground III Natural Period (s) Response Accleration S (g) Ground I Ground II ype I Ground III Ground I Ground II ype II Ground III Natural Period (s)

25 Seismic Design Force + = s k s k k k a k k S C D C C D C B D B D B g GC I ) ( β β β β EC code Elastic response accelerations for the referenced return period depending on soil condition (6.44) 0.9 & , 1.0, 0.7

26 Seismic Loads (continued) Eurocode 8 Part Bridges 1994 k I k GC k D a g k GC a g Response Acceleration (g) Period (s) 5 B C D

27 ransit New Zealand Bridge Manual (1995) S = k k k S i Z I GC µ ( ) =1 µ

28 AASHOO 1.2 ag kgc S = 2. 5a 2/3 g 1.0, 1.2, 1.5, 2.0 Given as a contour for R =475 years

29 AC-32 & Caltrans (1999) Deterministic & probabilistic evaluation R =1,000-2,000 years Response Acceleration (g) Stiff Site (Soil Profile E) M=8+/ Period (s) Soft Site (Soil Profile C) M=8+/ Period (s)

30 Comparison of Design Response Accelerations AASHOO (1995) AC (1996) & Caltrans (1999) Eurcode 8 (1994) JRA (1996 & 2002) ransit NZ (1995) a g =0.8g Soil profile II, III & IV a g =0.8g at stiff site a g =0.4g at soft site M=7.25+/-0.25 M=8.0+/-0.25 Soil profile C, D. & E k I =1.3 k I =1.0 k I =1.3 a g =0.7g k I =1.2 Determine the largest elastic design response accelerations with damping ratio of 0.05 assuming the largest factor prescribed in each code

31 Comparison of Design Response Accelerations (continued) 2.5 Stiff Soil Sites 2.5 New Zealand EC8 ype I Japan ype II M= Caltrans M= AASHO Soft Soil Sites Seismic Coefficient Period (sec) Period (sec)

32 Deterministic or Probabilistic? Deterministic ground motions which occurred in okyo during the 1923 Kanto EQ and in Kobe during the 1995 Kobe EQ is used with modification of regional

33 2009 M7.2, M7.3, Max. magnitude which could happen due to hidden faults inside Japan

34 M 7.3 II m/s 2 ) II I Ground motions generated by a MJ7.3 is the same level with the ground motions during the 1995 Kobe earthquake.

35 Probabilistic response acceleration levels (m/s 2 ) Assume longer Is this possible level for seismic design? Assume shorter & M Near-field GM by M8 M7 event Near-field GM by M7 event No part of structural members are determined by seismic effect.

36

37 EC M J 7.2 M J 8

38 Seismic Zoning Map widely accepted in Japan since his minimum value was very important to mitigate damage

39 Evaluation of Demand

40 Evaluation of Demand Force based seismic design * * ξ Nonlinear dynamic response analysis Static analysis D ave = m S A ( R * ξ * Response modification factor, ) 2µ r 1 R = µ r...empirical values

41 Japanese practice to consider damping ratio in the evaluation of elastic load Since µ r is not known at the first stage of the design, the response modification factor is evaluated as R = 2µ a 1 Design displacement ductility factor Q µ r (< ) µ a γ D φ ave C ave

42 Where do we consider the damping characteristics of the bridge in the static design?

43 How should we incorporate the damping ratio of the bridge in the static seismic design? Dynamic Analysis * * ξ Static Analysis * ξ * m S, ) D A ( *,0.05) = R Ground Accelerations Response Acceleration Dynamic Response Analysis Damping Ratios Static Analysis Compute Demands Compute Demands

44 How can we estimate the damping ratio of bridges? Empirical relation on the damping ratio vs. fundamental natural period of bridges his is based on force excitation tests on bridges supported by various types of foundations ξ = 0.02

45 ξ c Why is the damping ratio inversely proportional to the fundamental natural period? ξmφkm kmφkm ξ = m φkm kmφkm ξ D 0.05 m 0.05 ξ cp 0.15 Radiational energy dissipation ξ f >> 0. 3

46 How should we incorporate the damping ratio of the bridge in the static seismic design? Damping ratio of the bridge should be incorporated in the evaluation of response accelerations used in the static analysis Not ( *, ξ * S ( * A,0.05) but SA ) where SA ( * ξ *, ) * A c D = S (,0.05) * 1.5 c D ( ξ ) = * 40ξ + 1 * 0. ξ = 02 * ( ξ * )

47 How should we incorporate the damping ratio of the bridge in the static seismic design? ( *, ξ * * * SA ) = S A(,0.05) c D ( ξ ) * 1.5 = S A (,0.05) *

48 How should we incorporate the damping ratio of the bridge in the static seismic design? * ξ * 0. ξ = 02 * c D ( ξ = ) = c D * S A S(,0.05) S eq ( ) * ξ = 0. 4s

49 Safety Evaluation Ground Motion ype II GM < = S S S c S s s s Z essii 6 4/ /3 7 / 0 < < < = ) ( / ) ( ) (0 6 5/ /3 7 S S S c c S D Z SII Japanese practice to take the damping ratio of bridge into account in the static design force Dynamic response analysis ) S A (,0.05 Static analysis ),0.02/ ( S A

50 Japanese practice to take the damping ratio of bridge into account in the static design force Dynamic response analysis S A (,0.05) Static analysis S A,0.02/ ( ) Response Accleration S (g) Ground I Ground II ype I Ground III Ground I Ground II ype II Ground III Natural Period (s) Response Accleration S S (g) Ground I Ground II ype I Ground III Ground I Ground II ype II Ground III Natural Period (s) (b) R A l i f E i l

51 Features of the Japanese Practice in the Evaluation of Design Seismic Forces Explicit wo Level Design Forces are used Near field GMs and Middle field GMs resulted from M 8 EQs are used for the safety evaluation GMs Importance is accounted for not in the evaluation of design ground motions but in the evaluation of design ductility factors A damping force vs. natural period relation is included in the design seismic forces for static analysis

52 Evaluation of Capacity

53 Evaluation of Capacities Deck Bearings Columns/Piers Foundations Stability of foundations Surrounding ground

54 Evaluation of Capacities (continued) Reinforced concrete columns/piers 1) Assume a section based on the requirement for static loads 2) Evaluate tie reinforcement ratio ρ s 3) Evaluate stress vs. strain relation of confined concrete and reinforcing bars 4) Evaluate strength and ductility of columns using the fiber element analysis

55 Appropriate Idealization of Hysteresis of Confined Concrete and Reinforcing Bars Confined Concrete ε cc Rebars E des E s E s2 0.8σ cc σ cc Core concrete Cover concrete

56 Evaluate the Yield & Ultimate Curvature Bars E s2 Moment Ultimate (ype-i GM) Ultimate (ype-ii GM) E s Yield Initial Yield Curvature φ u φ u ε cc Ultimate Strain of Confined Concrete ype-i GMs E des Concrete 0.8σ cc σ cc ε cu = ε ε cc cc f cc / E des ype-ii GMs

57 Evaluate the Yield & Ultimate Lateral Displacement Lateral Force Ultimate displacement for ype-i GMs L p h L p 2 d y Yield d u Lateral Displacement Ultimate displacement Lp d u = d y + ( φu φy)( h ) L 2 Design displacement du da = d y + α d du y Ultimate displacement for ype-ii GMs p

58 Design displacement du d y da = d y + α Design displacement ductility factor da du d y µ a = = 1+ d αd y Lateral Force d a y ype-ii GM ype- I GM ype-ii GM d u Ultimate Importa nt bridge Standar d Bridges Lateral Displacement Lateral Force d a ype-i GM Ultimate d u Lateral Displacement

59 Failure Mode of RC Columns (continued) Flexural failure Lateral Force P u Capacity Lateral Displacement Shear failure after flexural failure Shear failure Lateral Force P u Lateral Force P u Lateral Displacement Lateral Displacement

60 Design Strength & Ductility Capacities P a P = P u s0 flexural failure + shear failure after flexural damage shear failure µ a = du d y 1 + flexural failure α d y 1 shear failure after flexural damage + shear failure (6.26)

61 Sizing of Structures γ D φ ave C ave Where, D ave = m S A ( R * ξ *, ) R = 2µ a 1

62 Consideration for the Repairability after an Earthquake Residual Displacement ilting after the 1995 Kobe EQ hey were demolished and rebuilt because of difficulty to repair

63 Requirement for the Check of Residual Displacement of Columns A wide range of residual displacement occurs for the same ductility demand Function & Safety Repairbility

64 Requirement for the Check of Residual Displacement of Columns d r dr d Ra H Design (allowable) residual displacement d Ra 100 H 1 =

65 Determination of residual displacement Residual displacement ratio response spectra S = RDR u u r r,max r = Maximum possible residual displacement u ) r, max = ( µ 1)(1 r u y k k 2 1 u r,max u = S ( µ 1)(1 r) u r RDR y For reinforced concrete columns S RDR = 0.6 r = 0

66 Residual Displacement Significance of Bridges with Fewer Static Indeterminacy than Buildings Plastic Hinges

67 Features of Japanese Practice in the Evaluation of Design Ductility Capacity Compute design ductility factor for every columns using the fiber element analysis. In the fiber element analysis, stress vs. strain relations of confined concrete and bars are explicitly considered. Characteristics of ground motions (loading hysteresis & number of repeated loadings) is accounted in the evaluation of the ultimate displacement, therefore the ultimate displacement depends on the ground motions (ype I & II ground motions).

68 Importance of bridges is accounted for not in the evaluation of design ground motions but in the evaluation of design ductility factor o account for repairability, residual displacement that would occur after an earthquake is checked

69 Displacement based Seismic Design

70 Displacement-based Seismic Design Column Displacement Effective stiffness Equivalent damping vs. ductility Design displacement response spectrum Priestley et al, Seismic Design & Retrofit of Bridges, John Wiley

71 Displacement-based Seismic Design (continued) It is interesting because Displacement which is important in design is always accounted in the displacement design However, the following points need further clarification Damping ratio which has a large scattering is directly included in the process of main design calculation Determination of the stiffness of a bridge from a design displacement involves a large error because k 2