Calibration for the Service Limit States in AASHTO LRFD ... of the... · in AASHTO LRFD Bridge Design Specifications ... prestressed concrete superstructures with the objective of

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

PRESENTATION OUTLINE

• Research Teams, Objectives of SHRP2 R19B

and NCHRP 12-83

• Summary of WIM Data Analysis

• WIM Data Analysis for Fatigue Limit State

• Example of the Calibration Process Applied to

Service III Limit State

2

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.

Research Team – R19B

TRB/SHRP

Jerry DiMaggio

Implementation Coordinator

3

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.

Research Team – NCHRP 12-83

TRB

Dr. Waseem Dekelbab

Senior Program Officer

4

SHRP2 R19B and NCHRP 12-83

• Both projects have same core team – able to take advantage of synergy

• 12-83 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

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 12-76

• Total number of records about 60 million

– about 35 million used

• Some obviously bad data

6

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 3 – 14

7

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

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

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

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: 1.36

- COV: 0.09

11

Bias Table for ADTT 5000

Fatigue Limit State

• WIM data passing through all filters was

used for fatigue limit state

• For Fatigue I, the top 1-in-10000 vehicles

are eliminated and only the heaviest

remaining trucks are considered

12

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

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

•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

Live Load for Fatigue II

0 50 100 150 200 250 300-6

-4

-2

0

2

4

6

GVW [kips]

Sta

nd

ard

No

rma

l V

ari

ab

le

NCHRP Data - Indiana

Station - 9511

Station - 9512

Station - 9532

Station - 9534

Station - 9552

Ontario

Fatigue II

Damage Factor Compared to Current

Current =0.75

30 ft 60 ft 90 ft 120 ft 200 ft

0.52 0.71 0.66 0.68 0.73

0.57 0.74 0.71 0.73 0.78

0.55 0.78 0.73 0.73 0.80

3/ rcFat Trkeq

AASHTO

nM M

n

High = 0.87 or 116% of current

Fatigue II: Design Cycles Per Truck

Longitudinal Members n

Simple Span Girders 1.0

Continuous

Girders

near interior

support 1.5

elsewhere 1.0

Longitudinal Members Span Length

> 40 ft ≤ 40 ft

Simple Span Girders 1.0 2.0

Continuous

Girders

near interior

support 1.5 2.0

elsewhere 1.0 2.0

Current

Proposed

Fatigue II: Improved Damage Ratios Simple Support –

mid-span

Fatigue Damage Ratio (proposed)

30 60 90 120 200

Arizona (SPS-1) 0.81 0.87 0.83 0.84 0.85

Arizona (SPS-2) 0.83 0.81 0.77 0.81 0.85

Arkansas (SPS-2) 0.82 0.81 0.76 0.80 0.83

Colorado (SPS-2) 0.74 0.73 0.69 0.72 0.76

Delaware (SPS-1) 0.83 0.85 0.78 0.78 0.79

Illinois (SPS-6) 0.82 0.81 0.75 0.79 0.83

Kansas (SPS-2) 0.79 0.80 0.75 0.79 0.83

Louisiana (SPS-1) 0.77 0.78 0.73 0.74 0.76

Maine (SPS-5) 0.71 0.72 0.67 0.69 0.72

Maryland (SPS-5) 0.70 0.71 0.63 0.64 0.65

Minnesota (SPS-5) 0.74 0.73 0.68 0.70 0.72

Penn (SPS-6) 0.84 0.82 0.75 0.78 0.81

Tennessee (SPS-6) 0.82 0.78 0.73 0.76 0.79

Virginia (SPS-1) 0.77 0.76 0.71 0.74 0.77

Wisconsin (SPS-1) 0.77 0.80 0.73 0.75 0.77

Fatigue II:

Calculate COV and Mean + 1.5 Std Dev

Continuous

Spans Results

Similar

Fatigue Damage Ratio (proposed) for Fatigue II LS

Span Mean Mean+1.5σ COV

Simply Supported

Mid-span

30 ft 0.785 0.87 0.07

60 ft 0.78 0.86 0.06

90 ft 0.73 0.81 0.07

120 ft 0.76 0.84 0.07

200 ft 0.78 0.86 0.07

Continuous

Middle Sup.

30 ft 0.59 0.65 0.07

60 ft 0.74 0.82 0.07

90 ft 0.69 0.77 0.07

120 ft 0.71 0.78 0.06

200 ft 0.785 0.87 0.07

Continuous

0.4 L

30 ft 0.73 0.81 0.07

60 ft 0.72 0.80 0.07

90 ft 0.68 0.75 0.07

120 ft 0.72 0.79 0.06

200 ft 0.76 0.84 0.07

Site Moments Normalized to Design Truck

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

Find Corresponding Point in WIM Data

Site Moments Normalized to Design Truck

Simple Support - mid-

span

"1/10000 Moment" / Design Truck Moment

30 60 90 120 200

Arizona (SPS-1) 1.74 1.84 1.63 1.70 1.84

Arizona (SPS-2) 1.26 1.41 1.31 1.38 1.54

Arkansas (SPS-2) 1.44 1.58 1.41 1.52 1.65

Colorado (SPS-2) 1.38 1.50 1.38 1.48 1.58

Delaware (SPS-1) 1.86 2.31 2.12 1.98 1.87

Illinois (SPS-6) 1.43 1.55 1.37 1.48 1.64

Kansas (SPS-2) 1.69 1.87 1.84 1.92 1.99

Louisiana (SPS-1) 1.89 2.27 1.96 2.05 2.16

Maine (SPS-5) 1.63 1.77 1.59 1.68 1.81

Maryland (SPS-5) 1.69 1.91 1.66 1.60 1.65

Minnesota (SPS-5) 1.61 2.04 2.05 2.04 2.03

Pennsylvania (SPS-6) 1.65 1.84 1.60 1.62 1.73

Tennessee (SPS-6) 1.72 1.88 1.52 1.47 1.60

Virginia (SPS-1) 1.51 1.74 1.58 1.58 1.65

Wisconsin (SPS-1) 1.61 1.78 1.58 1.67 1.76

Same Process

Continuous

Spans Results

similar

The Maximum Moment Range Ratio for Fatigue I LS

Span Mean Mean+1.5 σ COV

Simple Supported

Mid-span

30 ft 1.6 1.90 0.13

60 ft 1.83 2.24 0.15

90 ft 1.6 1.96 0.15

120 ft 1.64 1.88 0.10

200 ft 1.7 2.15 0.18

Continuous

Middle Sup.

30 ft 1.35 1.61 0.13

60 ft 1.81 2.13 0.12

90 ft 1.92 2.18 0.09

120 ft 1.97 2.17 0.07

200 ft 2.27 2.47 0.06

Continuous

0.4 L

30 ft 1.54 1.86 0.14

60 ft 1.67 2.06 0.16

90 ft 1.6 1.92 0.13

120 ft 1.65 1.97 0.13

200 ft 1.72 2.11 0.15

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

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

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 29

Tension Compression Compression Compression

Compression Compression Decompression Tension

(a) Initial State (b) Dead Load State (c) Decompression (d) Uncracked Section

f t < Allowable Tensile Stress

Compression

Tension

(e) Cracked Section

f t > Allowable Tensile Stress





Compression

Tension

(e) Cracked Section






Compression

Tension

(e) Cracked Section






Compression

Tension

(e) Cracked Section






Compression

Tension

(e) Cracked Section


Decompression Limit State

Maximum Allowable Tensile Stress Limit State

Maximum Allowable Crack

Width Limit State with Specified

Maximum Cracking Width

(Service III Limit State)

29

Target reliability indices in other

specifications

30

Reliability Class

Reference Period

(years)

1 50

RC2 2.9 1.5

Irreversible Service Limit States Reliability

Indices (Adapted from Table (C2)-EN1990)

Target reliability indices in other

specifications

31

Relative Costs of

Safety Measures

Consequences of Failure

Small Some Moderate Great

High 0 1.5(a) 2.3 3.1 (b)

Moderate 1.3 2.3 3.1 3.8 (c)

Low 2.3 3.1 3.8 4.3

Target Reliability Indices (Adapted from Table E-2

of ISO 2394-1998)

(a) For serviceability limit states, use β = 0 for

reversible and β = 1.5 for irreversible limit states.

Reliability indices of existing

structures

32

Summary of Reliability Indices for Existing Bridges (30 I-Girders, 36

Spread Box Girder, and 31 Adjacent Box Girder) (1 Year of Return

Period)

Performance Levels ADTTs

ADTT=1000 ADTT=2500 ADTT=5000 ADTT=10000 Decompression 1.02 0.91 0.80 0.66

Maximum Tensile

Stress Limit

3 sqrt f'c 1.15 1.01 0.94 0.82 6 sqrt f'c 1.24 1.14 1.05 0.95

8 sqrt f'c 1.40 1.27 1.19 1.07

Maximum Crack Width

0.008 in 2.29 2.21 1.99 1.85 0.012 in 2.65 2.60 2.37 2.22 0.016 in 3.06 2.89 2.69 2.56

Example of the Calibration Process

33

Calibration Process

34

Original Bridge Database

Check Reliability Index, βave> βT

Load and Resistance Models

No

Yes

New Load & Resistance Factors

Check Uniformity

Redesign with New Live Load Factor

No

Redesign with New Tandem Model, Dead

Load or Resistance Factor

Yes

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

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 5000 - Beams designed for 3 SQRT f’c - Live Load factor = 0.8


Step 2: Design Using a Different Load Factor

Decompression



Reliability index of simulated

bridges -Assuming ADTT 5000- - Beams designed for 3 SQRT f’c - Live Load factor = 1.0


Step 3: Design Using a Different Stress Limit

Decompression



Reliability index of simulated bridges

-Assuming ADTT 5000- - Beams designed for 6 SQRT f’c - Live Load factor = 1.0

Summary

39

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

Documents

Calibration for the Service Limit States in AASHTO LRFD ... of the... · in AASHTO LRFD Bridge Design Specifications ... prestressed concrete superstructures with the objective of