DESIGN SPECIFICATION AS N EXAMPLE OF PROBABILISTIC-BASED SPECIFICATIONS

Transcription

1 THE DEVELOPMENT OF AASHTO LRFD BRIDGE DESIGN SPECIFICATION AS N EXAMPLE OF PROBABILISTIC-BASED SPECIFICATIONS State University of New York at Buffalo November 7, 2011 Presented By Wagdy G. Wassef, P.E., Ph.D. Modjeski and Masters, Inc.

2 A Brief History 1931 First printed version of AASHO Standard Specifications for Highway Bridges and Incidental Structures 1970 s AASHO becomes AASHTO (1990 s AREA becomes AREMA) Early 1970 s AASHTO adopts LFD Late 1970 s OMTC starts work on limit-states based OHBDC 1986 AASHTO explores need to change

3 Design Code Objectives Technically state-of-the-art specification. Comprehensive as possible. Readable and easy to use. Keep specification-type wording do not develop a textbook. Encourage a multi-disciplinary approach to bridge design.

4 Major Changes A new philosophy of safety - LRFD The identification of four limit states The relationship of the chosen reliability level, the load and resistance factors, and load models through h the process of calibration new load factors new resistance factors

5 LRFD - Basic Design Concept

6 Some Algebra Q R 2 Q 2 R -Q) (R + = 2 Q 2 R + Q - R = x 1 R = = + = Q + R i i 2 Q 2 R 2 2 i i + + Q x = 2 Q 2 R + + Q

7 Load and Resistance Factor Design Ση i γ i Q i R n = R r in which: i = D R I 0.95 for loads for max = 1/( I D R ) 10f 1.0 for loads for min where: i = load factor: a statistically based multiplier on force effects = resistance factor: a statistically based multiplier applied to nominal resistance

8 LRFD (Continued) i = load modifier D = a factor relating to ductility R = a factor relating to redundancy I = a factor relating to importance Q i = nominal force effect: a deformation stress, or stress resultant R n = nominal resistance R r = factored resistance: R n

9 Reliability Calcs Done for M and V Simulated Bridges Based on Real Ones 25 non-composite steel girder bridge simulations with spans of 30,60,90,120,and 200 ft, and spacings of 4,6,8,10,and 12 ft. Composite steel girder bridges having the same parameters identified above. P/C I-beam bridges with the same parameters identified above. R/C T-beam bridges with spans of 30,60,90,and 120 ft, with spacing as above.

10 Reliability of Std Spec vs. LRFD 175 Data Points

11 Major Changes Revised calculation of load distribution S S K g g = L Lt s Circa 1990

12 Major Changes (Continued) Combine plain, reinforced and prestressed concrete. Modified compression field/strut and tie. Limit state-based provisions for foundation design. Expanded coverage on hydraulics and scour. The introduction of the isotropic deck design. Expanded coverage on bridge rails. Inclusion of large portions of the AASHTO/FHWA Specification for ship collision.

13 Major Changes (Continued) Changes to the earthquake provisions to eliminate the seismic performance category concept by making the method of analysis a function of the importance of the structure. Guidance on the design of segmental concrete bridges from Guide Spec. The development of a parallel commentary. New Live Load Model HL93 Continuation of a long story

14 1923 AREA Specification 10-Ton 15-Ton 20-Ton 4k 6k 8k 14' 16k 24k 32k 5.5' VERY CLOSE!!

15 Conference Specification 6k 24k 14' 30' 6k 14' 24k 30' 8k 14' 32k 30' 6k 14' 24k 30' 6k 14' 24k 15-Ton 15-Ton 20-Ton 15-Ton 15-Ton 18,000 lb for Moment 26,000 lb for Shear 640 lb/ft

16 1944 HS 20 Design Truck Added

17 Live Load Continued to be Debated Late 60 s H40, HS25 and HS30 discussed 1969 SCOBS states unanimous opposition to increasing weight of design truck wasteful obsolescence of existing bridges 1978 HS25 proposed again 1979 HS25 again commentary need for heavier design load seems unavoidable HS25 best present solution 5% cost penalty Motion soundly defeated

18 E l i L d B d TRB Exclusion Loads Based on TRB Special Report 225, 1990

19 EXCL/HS20 Truck or Lane or 2 25 kips 4 ft ( m)

20 Selected Notional Design Load HL-93

21 EXCL/HL 93 Circa 1992

22 NCHRP Project Schedule First Draft general coverage Second Draft workable Third Draft pretty close Fourth Draft ADOPTED!! 12,000 comments Reviewed by hundreds Printed and available

23 Upgrades and Changes to 1990 Technology 1996 foundation data reinserted. New wall provisions ongoing upgrade upgraded to ASBI LFRD Segmental Guide Specs. MCF shear in concrete simplified and clarified several times major update in Load distribution application limits expanded several time in 1990 s due to requests to liberalize. More commentary added.

24 Upgrades and Changes 2004 major change in steel girder design in anticipation of 2005 seamless integration of curved steel bridges ending three decade quest

25 Upgrades and Changes (Continued) 2005 P/C loses updated 2006 complete replacement of Section 10 Foundation Design 2006 more concrete shear options 2007 big year Streamline MCF for concrete shear design 1,000 year EQ maps and collateral changes Seismic Guide Spec - displacement based Pile construction update Coastal bridge Guide Spec

26 Where Do We Go From Here?

27 Where Do We Go From Here? The original AASHTO LRFD live load study was based on load measurements made in the 1970 s in Ontario. How this relates to today s loads?

28 Where Do We Go From Here? The specifications was calibrated for the strength th limit it state t where the definition iti of failure is relatively simple: if the factored loads exceed the factored resistance, failure, i.e. severe distress or collapse, will take place. What about service limit state and what is failure under service limit states?

29 Where Do We Go From Here? Two Current Projects of Special Note: SHRP R19 B - Bridge for Service Life Beyond 100 Years: Service Limit State Design (SLS) NCHRP 12-83, Calibration of Service Limit State for Concrete

30 R19B Research Team Modjeski and Masters, Inc.: John Kulicki, Ph.D., P.E. Wagdy Wassef, Ph.D., P.E. University of Delaware: Dennis Mertz, Ph.D., P.E. University of Nebraska: Andy Nowak, Ph.D. NCS Consultants: Naresh Samtani, Ph.D., P.E. NCHRP Research Team Same except that NCS Consultants are replaced with Rutgers University: Hani Nasif, Ph.D., P.E.

31 Current General SLS s Live load deflections Bearings-movements and service forces Settlement of foundations and walls

32 Current Steel SLS s Permanent deformations in compact steel components Fatigue of structural steel, steel reinforcement and concrete (through its own limit state) Slip of slip-critical bolted connections

33 Current Concrete SLS s Load induced Stresses in prestressed concrete under service loads Crack control reinforcement Non-Load induced Shrinkage and temperature reinforcement Splitting reinforcement

34 Desired Attributes Is an SLS meaningful? Can it be calibrated? Does it really relate to service---or something else? Can (should) aging and deterioration be incorporated? Can it reflect interventions?

35 General Topics Special challenges for SLS development Survey of owners Use of WIM data Calibration process

36 General Topics (cont d) Improvements to current SLS Crack control in reinforced concrete Tension in P/S beams Load induced fatigue in steel and concrete Use of Weigh-In-Motion Data

37 Current Status Vetted WIM data SLS Live Load live load model Finite Life fatigue load model Infinite Life fatigue load model Preliminary Betas for Service III (Tension in P/s beams) Work on deflections Work on compiling info on joints and bearings

38 Service and Fatigue LL has been a challenge Truck WIM was obtained from the FHWA and NCHRP Project T t l b f d b t 60 illi Total number of records about 60 million about 35 million used

39 Initial Filtering Criteria For Non-Fatigue SLS (FHWA Unless Noted) Excluded Vehicles Individual axle weight > 70kips - GVW < 10 7 >Total length >200 ft First axle spacing <5 ft Individual axle spacing < 3.4ft 10 > Speed > 100 mph GVW +/- the sum of the axle weights by more than 7%. FHWA Classes 3 14

40 Additional Filtering Filter #1 Questionable Records 1 - Truck length > 120 ft 2 sum of axle spacing > length of truck. 3 - any axle < 2 Kips 4 - GVW +/- sum of the axle weights by more than 10% 5 - GVW < 12 Kips Filter #2 Presumed Permit Trucks 6 - Total # of axles < 3 AND GVW >50 kips 7 - Steering axle > 35 k 8 individual axle weight > 45 kips Filter #3 Traditional Fatigue Population 9 - Vehicles with GVW <20 Kips

41 Filtering By Limit State Vehicles Passing Filters #1 & #2 will be used for calibration of all limit it states t except for Fatigue, the limit state for permit vehicles and possibly Strength th II. Vehicles filtered by Filter #2 will be considered Permit vehicles and will be reviewed and may be filtered further. Vehicles passing all three filters will be used for the fatigue limit state

42 5 14 sites Representing 1 year 4 of traffic at most sites 3 The maximum 2 recorded GVW is kips 0 Mean values range -1 from 20 to 65 kips -2 WIM Data - FHWA Standard d Normal Va ariable -3-4 Arizona(SPS-1) Arizona(SPS-2) Arkansas(SPS-2) Colorado(SPS-2) Illinois(SPS-6) Indiana(SPS-6) Kansas(SPS-2) Louisiana(SPS-1) Maine(SPS-5) Minnesota(SPS-5) New Mexico(SPS-1) NewMexico(SPS-5) Tennessee(SPS-6) Virginia(SPS-1) Wisconsin(SPS-1) Delaware(SPS-1) Maryland(SPS-5) Ontario GVW [kips]

43 Analysis of the WIM Data Live load effect maximum moment and shear Simple spans with span lengths of 30, 60, 90, 120 and 200 ft Trucks causing moments or shears < 0.15 (HL93) were removed

44 Removal of the Heavy Vehicles for SLS Filter trucks causing moments or shears more than 1.35(HL93 live load effect) were removed Number of trucks before filtering 1,551,454 Number of trucks after filtering 1,550,914 Number of removed trucks 540 Percent of removed trucks 0.03% Standard Norm mal Variable New York 8382 Span 90ft No Trucks Removed 0.03% Trucks Removed Truck Moment / HL93 Moment

45 Multiple Presence Cases Simultaneous occurrence of trucks on the bridge: Filter based on time of a record and a speed of the truck T1 Headway Distance max 200 ft T1 Headway Distance max 200 ft Distance from the first axle of first truck to the first axle of the second truck maximum 200 ft T2 T2 Two cases of the simultaneous occurrence

46 Correlation Criteria Both trucks have the same number of axles GVW of the trucks is within +/- 5% All corresponding spacings between axles are within +/- 10%

47 Adjacent Lanes - Florida Florida I10 Time record accuracy 1 second Number of Trucks : 1,654,004 Number of Fully Correlated Trucks: 2,518 Max GVW = 102 kips Frequenc cy Gross Vehicle Weight - Trucks in Adjacent Lanes

48 Adjacent Lanes Florida 2,518 of 1,654, Normal Varia able Standard Florida I Correlated Trucks - Side by Side Florida I10 - All Trucks Gross Vehicle Weight

49 One Lane Florida 4,190 of 1,654, le Standard Normal Variab Florida I Correlated Trucks In One Lane Florida I10 - All Trucks Gross Vehicle Weight

50 Conclusions for Multiple Presence Vehicles representing the extreme tails of the CDF s need not be considered d to occur simultaneously l in multiple lanes. For the SLS, only a single-lane lane liveload model need be considered.

51 Statistics of Non-fatigue SLS Live Load Based on 95% limit: ADTT = I,000, Project Bias on HL 93 = 1.4 ADTT = 5,000, Project Bias on HL 93 = 1.45 COV = 12% Based on 100 years: Project Bias varies with time interval which will be reflected in calibrated load factor Not strongly influenced by span length

52 Typical Results For SLS Live Load Model 1.60 Span 60 ft Bias ADTT 250 ADTT 1000 ADTT 2500 ADTT 5000 ADTT years Days

53 Conclusion For Non-fatigue SLS Not necessary to envelop all trucks SLS expected to be exceeded occasionally Some states with less weight enforcement may have to have additional considerations (site/region specific live load) HL-93 adaptable as national notional SLS live load model

54 Non-Fatigue SLS LL Model Mean, Bias and project LL model at mean plus 1.5 standard deviations tabulated with and without DLA for parameters: 5 ADTTs = 250, 1,000, 2500, 5000 and 10, Time periods = 1 day, 2 weeks, 1 month, 2 months, 6 months, 1 year, 5 years, 50 years, 75 years and 100 years 6 Spans = 30 ft, 60ft, 90ft,120ft, 200 ft & 300ft With and w/o DLA

55 Fatigue SLS LL Model

56 Live Load For Fatigue II (finite fatigue life) 6 NCHRP Data - Indiana 4 Standard Normal Variable Station Station Station Station Station Ontario GVW [kips] Miner s law yields one effective moment per span Miner s law yields one effective moment per span Rainflow counting yields cycles per truck Variety of spans and locations yields Mean, bias and COV

57 Examples Using FHWA WIM Data n 3 * 3 M p m eq i i i 1 M eff [kip-ft] for 3 sites 30 ft (-184)* 60 ft (-360)* 90 ft (-530)* 120 ft (-762)* 200 ft (-1342)* * Values in parentheses= current AASHTO fatigue moment 15 sites processed so far

58 Example Using FHWA WIM Data 3 sites M M eq / Fat Trk Fatigue II Load Factors for 3 sites 30 ft 60 ft 90 ft 120 ft 200 ft So far looks good now add cycles per So far looks good, now add cycles per Passage and compare to current

59 Cycles Per Passage C y c l e s 4.00 Arizona (SPS 1) 3.50 Arizona (SPS 2) Arkansas (SPS 2) 3.00 Colorado (SPS 2) 2.50 Dl Delaware (SPS 1) Illinois (SPS 6) % damage increase Kansas (SPS 2) 1.50 Current Louisiana (SPS 1) Maine (SPS 5) 1.00 Maryland (SPS 5) Continuous Bridges Virginia (SPS 1) Wisconsin (SPS 1) 0.00 Middle Support Span length

60 Rainflow Cycles - n rc Continuous Spans 30 ft 60 ft 90 ft 120 ft 200 ft

61 Damage Factor Compared to Current M M Fat Trk 3 eq n rc / n AASHTO Current = ft 60 ft 90 ft 120 ft 200 ft High = 0.87 or 116% of current

62 MM Independent Check of UNL UNL running all filtered trucks at a site using the time stamps Traffic simulation Not individual trucks one at a time Test axle train evaluated by UNL and MM 8 hypothetical trucks 49axles 963 ft 843,000 lbs

63 MM Independent Check of UNL MM Cobbled together existing pieces: Variation of program MM used in early 1990 s truck study that resulted in HL93 Loading modified to calculate moment time histories Used rainflow counting algorithm based on ASTM E previously developed to process instrumentation data for repair of in-service bridge to calculate cycles per truck; and Miner s Law to calculate late Meq.

64 MM Independent Check of UNL Results: Only a few issues negotiated t Final results damage factors same for simple span, very close for Neg moment at pier of continuous. Sometimes intermediate results varied seemed to depend maximum magnitude of small cycles (noise) that t was ignored---like data smoothing Common sense check MM found that equivalent single cycle damage factor for the 8 truck train could be used as a comparison check worked well.

65 Does This Increase Make Sense? 2,500, ,000,000 1,500,000 1,000, , Number of Truck Combinations Year

66 Does This Increase Make Sense? nt Change Perce 140.0% 120.0% 100.0% 80.0% 60.0% 40.0% 0% 20.0% 0.0% 20.0% Truck Weight

67 Does This Increase Make Sense?

68 Current Status of LL Studies Fatigue II Being calibrated now Concrete and steel Fatigue I model being finalized Other SLS Design model will be HL93 factored per calibration LL was handed off to NCHRP team for concrete SLS calibration - working SHRP team is following with deflections and foundations

69 Concrete-Related Limit States LRFD Description article Control of cracking by distribution of reinforcement Reinforcement requirements for concrete deck designed using empirical method Stresses check at service III limitit state tt after losses fully ll prestressed components Proposed SLS Service I A: Crack control of R/C Service I B: Crack control of R/C concrete deck designed using empirical method Service III A: Decompression Service III B: Un cracked section (max tensile stress) Service III C: Cracked section (specified crack width)

70 Reliability Indices of Existing P/S Conc. Bridges Service III Limit State

71 Reliability Indices of Existing P/S Conc. Bid Bridges Relialbity Ind dex βave= Span Length (ft.) Decompression Relialbity Ind dex βave= Span Length (ft.) Max. Allowable Tension Relialbity Index βave= Span Length (ft.) Max. Allowable Crack Width (0.016 in., 1 year return period) Reliability index of existing bridges Assuming ADTT 5000

72 Reliability Indices of Existing P/S Conc. Bid Bridges Reliability index (return Period 1 year) ADTT Maximum Maximum Decompression Allowable Tensile Allowable Crack Stress Width Proposed Target Beta 0.0* In any one year period the limit state will be exceeded in: 500 of 1000 bridges for reliability index of of 1000 bridges for reliability index of 2.0

73 Reliability Indices of Bridges Designed to Current Specifications Relialbity Ind dex βave= Span Length (ft.) Decompression Relialbity Ind dex βave= Span Length (ft.) Max. Allowable Tension Relialbity Index βave= Span Length (ft.) Max. Allowable Crack Width (0.016 in., 1 year return period) Same existing bridges except No. of strands determined using current specifications Reliability Index Assuming ADTT 5000

74 Reliability Indices of Bridges Designed to Current Specifications Performance Level ADTT Maximum Maximum Decompression Allowable Tensile Allowable Crack Stress Width In any one year period the limit state will be exceeded in: 660 of 1000 bridges for reliability index of of 1000 bridges for reliability index of 1.90

75 Parametric Study of Reliability Index Three cases were considered: Bridges designed with various spacing, span lengths, and section types Bridges designed with different span lengths and section types but same girder spacing Bridges designed with different span lengths and girder spacing but same section types.

76 Parametric Study of Reliability Index Relialbity Index Index Relialbity Span Length (ft.) Existing Bridges Redesigned Bridges Span Length (ft.) Various girder spacing, section types, and span lengths. ADTT = 5000 Max allowed crack width

77 Conclusions Related to SLS for Concrete Structurest Different limit states may require different target reliability index to maintain current performance

78 Bluewater Bridge #2 First LRFD Major Bridge Opened 1997