Calibration for the Service Limit States in AASHTO LRFD Bridge Design Specifications

Transcription

1 PROGRESS REPORT ON Calibration for the Service Limit States in AASHTO LRFD Bridge Design Specifications 2013 Louisiana Transportation Conference February 18, 2013 River Center Baton Rouge, Louisiana Presented By Wagdy G. Wassef, Ph.D. P.E. Modjeski and Masters, Inc. 1

2 PRESENTATION OUTLINE Research Teams, Objectives of SHRP2 R19B and NCHRP Summary of WIM Data Analysis WIM Data Analysis for Fatigue Limit State Example of the Calibration Process Applied to Service III Limit State 2

3 Research Team R19B 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., P.E. NCS Consultants: Naresh Samtani, Ph.D., P.E. TRB/SHRP Jerry DiMaggio Implementation Coordinator 3

4 Research Team NCHRP 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., P.E. Rutgers University Hani Nassif, Ph.D., P.E. TRB Dr. Waseem Dekelbab Senior Program Officer 4

5 SHRP2 R19B and NCHRP Both projects have same core team able to take advantage of synergy deals with only concrete SLS R19B Framework - deterioration General SLS Steel, foundations, bearings, joints Live Load Jointly with more done under SHRP R19B Fatigue Jointly 5

6 Review of Live Load Model Development Calibration requires knowing the statistical parameters of the loads Truck WIM data was obtained from the FHWA and NCHRP Project Total number of records about 60 million about 35 million used Some obviously bad data 6

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

8 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 8

9 Filtering by Limit State Vehicles Passing Filters #1 & #2 are used for calibration of all limit states except for fatigue and the limit state for permit vehicles. Vehicles filtered by Filter #2 are considered permit vehicles and will be reviewed and may be filtered further. Vehicles passing all three filters are used for the fatigue limit state. 9

10 Conclusion for Non-Fatigue SLS Not necessary to envelop all trucks SLS expected to be exceeded occasionally Scaled HL- 93 looks reasonable Site/region specific live load should be accommodated Some states with less weight enforcement may have to have additional consideration 10

11 Example of Live Load Parameters For general case (non-fatigue limit states/no permit vehicle): Parameters vary with span length, ADTT and period For example, for: 120 ft span, 1 year and 5000 ADTT, - Bias: COV: 0.09 Bias Table for ADTT

12 Fatigue Limit State WIM data passing through all filters was used for fatigue limit state For Fatigue I, the top 1-in vehicles are eliminated and only the heaviest remaining trucks are considered 12

13 Fatigue Limit State (cont d) For Fatigue II, all trucks are run on single and two-span simulated bridges (spans of 30, 60, 90, 120 and 200 are considered) With time and speed stamps on the WIM records, the trucks were run as a year long string including the effects of trucks trailing each other The results are cycles of stress (or moments) of different magnitudes 13

14 Fatigue Limit State (cont d) Miner s law is used to convert them to an equivalent number of cycles of the specifications fatigue truck The ratio of the equivalent number of cycles to the actual number of trucks gives the number of cycles per truck passage 14

15 Live Load for Fatigue II 6 NCHRP Data - Indiana Standard Normal Variable Station Ontario GVW [kips] Station Station Station Station 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

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

17 Fatigue II: Design Cycles Per Truck Current Span Length Longitudinal Members > 40 ft 40 ft Simple Span Girders Continuous Girders near interior support elsewhere Proposed Longitudinal Members Simple Span Girders 1.0 Continuous Girders near interior support n 1.5 elsewhere 1.0

18 Fatigue II: Improved Damage Ratios Simple Support mid-span Fatigue Damage Ratio (proposed) Arizona (SPS-1) Arizona (SPS-2) Arkansas (SPS-2) Colorado (SPS-2) Delaware (SPS-1) Illinois (SPS-6) Kansas (SPS-2) Louisiana (SPS-1) Maine (SPS-5) Maryland (SPS-5) Minnesota (SPS-5) Penn (SPS-6) Tennessee (SPS-6) Virginia (SPS-1) Wisconsin (SPS-1)

19 Fatigue II: Calculate COV and Mean Std Dev Continuous Spans Results Similar

20 Site Moments Normalized to Design Truck Fatigue Damage Ratio (proposed) for Fatigue II LS Span Mean Mean+1.5σ COV Simply Supported Mid-span Continuous Middle Sup. Continuous 0.4 L 30 ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft

21 Fatigue I Usually assumed that CAFL can be exceeded by 1/10,000 of the stress cycles 99.99% inclusion of normal random variables requires mean plus 3.8 standard deviations

22 Find Corresponding Point in WIM Data

23 Site Moments Normalized to Design Truck Simple Support - midspan "1/10000 Moment" / Design Truck Moment Arizona (SPS-1) Arizona (SPS-2) Arkansas (SPS-2) Colorado (SPS-2) Delaware (SPS-1) Illinois (SPS-6) Kansas (SPS-2) Louisiana (SPS-1) Maine (SPS-5) Maryland (SPS-5) Minnesota (SPS-5) Pennsylvania (SPS-6) Tennessee (SPS-6) Virginia (SPS-1) Wisconsin (SPS-1)

24 Same Process Continuous Spans Results similar

25 The Maximum Moment Range Ratio for Fatigue I LS Span Mean Mean+1.5 σ COV 30 ft ft Simple Supported 90 ft Mid-span 120 ft ft Continuous Middle Sup. Continuous 0.4 L 30 ft ft ft ft ft ft ft ft ft ft

26 Calibration of Service Limit States for Concrete Challenges: Limit states may be reversible or non-reversible No clear consequences for exceeding reversible limit states Exceeding service limit states, particularly reversible limit states, is not catastrophic Service limit states may be exceeded but no clear criteria for the frequency of exceedance 26

27 Calibration of Service III Limit State for Prestressed Concrete Beams Service III limit state is mainly related to the tension in prestressed concrete superstructures with the objective of crack control and to the principal tension in the webs of segmental concrete girders. Consequences of exceeding Service III Limit State are likely limited to crack opening. The crack closes after the truck passes. Can be exceeded frequently. Historical Changes to Bridge Design 27

28 Calibration of Service III Limit State for Prestressed Concrete Beams Beams may be designed using a certain criteria (say Max. Conc. Stress = 6 sqrt f c) and the reliability index is determined for different Performance Levels Performance Levels being considered: - Decompression - Calculated Maximum Tensile Stress - Maximum Crack Width 28

29 (Service III Limit State) Tension Tension Compression Compression Compression Compression Compression Compression Decompression Tension Tension Tension Tension (a) Initial (a) (a) Initial Initial State State State (b) Dead (b) (b) Dead Load Dead Load State Load State State (c) (c) (c) Decompression (d) (d) (d) Uncracked Section Section (e) Cracked (e) (e) Cracked Section Section ft < ft < ft ft < Allowable Tensile Tensile Tensile Stress Stress Stress ft > ft > ft ft > Allowable Tensile Tensile Tensile Stress Stress Stress Decompression Limit State Maximum Allowable Tensile Stress Limit State Maximum Allowable Crack Width Limit State with Specified Maximum Cracking Width

30 30 Target reliability indices in other specifications Irreversible Service Limit States Reliability Indices (Adapted from Table (C2)-EN1990) Reference Period Reliability Class (years) 1 50 RC

31 31 Target reliability indices in other specifications Target Reliability Indices (Adapted from Table E-2 of ISO ) Relative Costs of Consequences of Failure Safety Measures Small Some Moderate Great High 0 1.5(a) (b) Moderate (c) Low (a) For serviceability limit states, use β = 0 for reversible and β = 1.5 for irreversible limit states.

32 32 Reliability indices of existing structures Summary of Reliability Indices for Existing Bridges (30 I-Girders, 36 Spread Box Girder, and 31 Adjacent Box Girder) (1 Year of Return Period) ADTTs Performance Levels ADTT=1000 ADTT=2500 ADTT=5000 ADTT=10000 Decompression Maximum Tensile Stress Limit Maximum Crack Width 3 sqrt f'c sqrt f'c sqrt f'c in in in

33 Example of the Calibration Process 33

34 Calibration Process Original Bridge Database Load and Resistance Models Redesign with New Live Load Factor No Redesign with New Tandem Model, Dead Load or Resistance Factor No Check Reliability Index, β ave > β T Yes Check Uniformity Yes New Load & Resistance Factors 34

35 Simulated Bridges P/S Concrete beams with spans 30, 60, 90, 120, 140, 160, 180, 220 ft Girder spacing 6, 8, 10 and 12 ft. for beams up to 160 ft span, 6 & 9 ft for beams with 180 ft span and 9 ft for beams with 200 & 220 ft span. Total of 35 bridges Each bridge designed for the smallest AASHTO I-beams (longer spans different) 35

36 Reliability Indices for P/S Concrete Beams Step 1: Design According to Current Specs Decompression Max. Allowable Tension Max. Allowable Crack Width (0.016 in., 1 year return period) Reliability index of simulated bridges -Assuming ADTT Beams designed for 3 SQRT f c - Live Load factor = 0.8

37 Reliability Indices for P/S Concrete Beams Step 2: Design Using a Different Load Factor Decompression Max. Allowable Tension Max. Allowable Crack Width (0.016 in., 1 year return period) Reliability index of simulated bridges -Assuming ADTT Beams designed for 3 SQRT f c - Live Load factor = 1.0

38 Reliability Indices for P/S Concrete Beams Step 3: Design Using a Different Stress Limit Decompression Max. Allowable Tension Max. Allowable Crack Width (0.016 in., 1 year return period) Reliability index of simulated bridges -Assuming ADTT Beams designed for 6 SQRT f c - Live Load factor = 1.0

39 Summary Target reliability index can be achieved uniformly across various span lengths following the proposed calibration procedure. Several trial processes are needed to achieve a uniform target reliability index. To maintain current average reliability, the outcome of the calibration is expected to be a new live load factor and/or a different concrete tensile stress limit 39