STRUCTURAL SYSTEMS
RESEARCH PROJECT
Report No.
SSRP– 04/ 14
Final
SEISMIC RESPONSE OF SACRIFICIAL
EXTERIOR SHEAR KEYS IN
BRIDGE ABUTMENTS
by
AZADEH BOZORGZADEH
SAMI HANNA MEGALLY
SCOTT ASHFORD
JOSÉ I. RESTREPO
Final Report Submitted to the California Department of
Transportation ( Caltrans) Under Contract No. 59A0337
October 2007
Department of Structural Engineering
University of California, San Diego
La Jolla, California 92093- 0085
University of California, San Diego
Department of Structural Engineering
Structural Systems Research Project
Report No. SSRP– 04/ 14
Final
SEISMIC RESPONSE OF SACRIFICIAL EXTERIOR SHEAR
KEYS IN BRIDGE ABUTMENTS
by
Azadeh Bozorgzadeh
Graduate Student Researcher
Sami Hanna Megally
Graduate Student Researcher
Scott A. Ashford
Professor of Structural Engineering
José I. Restrepo
Professor of Structural Engineering
Final Report Submitted to the California Department of Transportation
( Caltrans) Under Contract No. 59A0337
Department of Structural Engineering
University of California, San Diego
La Jolla, California 92093- 0085
October 2007
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Technical Report Documentation Page
1. Report No.
2. Government Accession No.
3. Recipient’s Catalog No.
4. Title and Subtitle
Seismic Response of Sacrificial Exterior Shear Keys in Bridge
Abutments
5. Report Date
April 2005
6. Performing Organization Code
7. Author( s)
Azadeh Bozorgzadeh, Sami Hanna Megally, José I. Restrepo, Scott A. Ashford
8. Performing Organization Report No.
UCSD / SSRP- 04/ 14
9. Performing Organization Name and Address
Department of Structural Engineering
School of Engineering
10. Work Unit No. ( TRAIS)
University of California, San Diego
La Jolla, California 92093- 0085
11. Contract or Grant No.
59A0337
12. Sponsoring Agency Name and Address
California Department of Transportation
13. Type of Report and Period Covered
Final Report – July 2002 / May 2003
Division of Engineering Services
1801 30th St., West Building MS- 9
Sacramento, California 95807
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared in cooperation with the State of California Department of Transportation.
16. Abstract
Seismic response and capacity evaluation of sacrificial exterior shear keys are the main objectives of this work. Shear
keys are used in bridge abutments to provide transverse support for the superstructure. However, it has been recognized
that to protect abutment piles from severe damage under transverse forces, shear keys must be designed as a locking
mechanism that limits the magnitude of the transverse force that can be transmitted into the abutment. In philosophical
terms, a shear key could transversely be designed as a sacrificial element to limit transverse inertial forces in the abutment
walls and supporting piles. If shear keys are designed as sacrificial elements within a capacity design framework, their
overstrength must be accurately determined to ensure other elements can be designed to remain elastic.
An experimental program to study the seismic behavior of shear keys was carried out at University of California, San
Diego. These specimens were built at a 40% scale of the exterior shear keys of a prototype abutment. The design
philosophy was to force a shear sliding failure at the interface of the shear key- abutment stem wall to control damage to
the abutment walls and the piles under transverse seismic force. This report presents recommendations for design and
construction details of sacrificial exterior shear keys based on test results
Several factors were considered in this experimental program such as including construction joints between the abutment
stem wall and the shear key, different amount and configuration of the vertical reinforcement crossing the abutment stem
wall- shear key interface, and different amounts and configuration of the horizontal reinforcement in the stem wall. A total
of five specimens were built and tested at UCSD; each specimen included two exterior shear key test units. Experimental
results of specimens 4 and 5 are given in this report.
17. Key Words
Abutments, sacrificial, shear keys, experimental test, seismic
18. Distribution Statement
No restrictions
19. Security Classification ( of this report)
Unclassified
20. Security Classification ( of this page)
Unclassified
21. No. of Pages
82
22. Price
Form DOT F 1700.7 ( 8- 72) Reproduction of completed page authorized
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DISCLAIMER
The contents of this report reflect the views of the authors who are responsible for the facts and
accuracy of the data presented herein. The contents do not necessarily reflect the official views
or policies of the California Department of Transportation or the Federal Highway
Administration. This report does not constitute a standard, specification or regulation.
- iii -
ACKNOWLEDGEMENTS
This study was made possible by funding from the California Department of Transportation
under contract No. 59A0337.
As in any other research program there are several people that made this work possible. We
would like to thank Dr. Charles Sikorsky from Caltrans for his technical participation during the
design and testing phases of this research program.
The experiments presented in this report were tested at the Charles Lee Powell Laboratory of the
University of California- San Diego ( UCSD). A number of technical personnel at UCSD assisted
in the experimental investigation. Among them Mr. Lawrence Berman and Dr. Christopher
Latham deserve special mention for their contribution in construction and testing of the shear key
units. Thanks are also due to Mr. Charles Stearns and Alex Sherman for their invaluable
assistance.
- iv -
LIST OF SYMBOLS
Avf = area of vertical reinforcement crossing
the shear key- abutment stem wall;
Ash = area of horizontal tie reinforcement in
the abutment stem wall;
a = distance from the location of the applied
force to the surface of the stem wall;
b = distance between the top surface of the
stem wall and center line of the lowest
horizontal tie reinforcement;
d = length of shear key- stem wall interface;
db = diameter of reinforcement bar;
f’c = specified concrete compressive strength;
fsu = ultimate tensile strength of steel;
fy = yield strength of steel;
y f = mean value of yield strength of steel;
h = height of the abutment stem wall;
ldh = development length of reinforcing steel;
u v = ultimate shear strength ( Vu / bd);
V = applied lateral force;
Vu, t = shear force capacity observed in the
tests;
Vn, Calt = shear force capacity calculated from
caltrans equation;
Vn = calculated shear force capacity using
Eq.( 8);
Vo = overstrength shear key capacity;
Vu = ultimate shear force capacity;
α = angle of kinking of shear key vertical
bars with respect to the vertical axis;
α = mean value of angle of kinking of shear
key vertical bars with respect to the
vertical axis;
β = angle of inclined face of shear key with
respect to the vertical axis;
φ = strength reduction factor;
φ o = overstrength factor;
μf = kinematic coefficient of friction for
concrete;
f μ
= mean value of kinematic coefficient of
friction for concrete;
μ = static coefficient of friction for concrete
- v -
TABLE OF CONTENTS
DISCLAIMER..................................................................................................................... .......... ii
ACKNOWLEDGEMENTS........................................................................................................... iii
LIST OF SYMBOLS ..................................................................................................................... iv
TABLE OF CONTENTS................................................................................................................ v
LIST OF FIGURES ...................................................................................................................... vii
LIST OF TABLES......................................................................................................................... x
ABSTRACT....................................................................................................................... ........... xi
1 INTRODUCTION .................................................................................................................. 1
2 SCOPE.......................................................................................................................... ......... 1
3 SUMMARY OF RESEARCH WORK................................................................................... 2
3.1 MODES OF FAILURE................................................................................................... 2
3.1.1 UNITS 4A AND 4B................................................................................................ 2
3.1.2 UNITS 5A AND 5B................................................................................................ 2
4 RECOMMENDATIONS FOR CONSTRUCTIONS............................................................. 4
4.1 Discussion of Experimental Results ............................................................................... 4
5 EVALUATION OF THE CAPACITY OF EXTERIOR SHEAR KEYS .............................. 6
6 RECOMMENDATIONS FOR FUTURE RESEARCH....................................................... 11
7 APPENDIX A- 1.................................................................................................................... 12
8 APPENDIX A- 2.................................................................................................................... 18
9 APPENDIX A- 3.................................................................................................................... 25
9.1 Analytical Studey of Sacrificial Shear Keys................................................................. 25
10 APPENDIX A- 4................................................................................................................ 29
10.1 Evaluation of the Capacity of the Test Series IV.......................................................... 29
10.1.1 Strut- and- Tie Mechanism and Hysteretic Model:................................................. 29
10.1.2 Horizontal Reinforcement Strain Profiles............................................................. 34
10.1.3 Vertical Reinforcement Strain Profiles................................................................. 42
10.1.4 Shear friction capacity model proposed by Mattock ............................................ 45
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10.1.5 Capacity Evaluation of Exterior Shear Key with Shear Friction Capacity Model
Proposed by Walraven et al. ( 1987) ..................................................................................... 46
10.1.6 Capacity Evaluation of Exterior Shear Key with Caltrans Sliding Shear Friction
Model 47
10.2 Evaluation of the Capacity of the Test Series V ........................................................... 48
10.2.1 Strut- and- Tie Model: ............................................................................................ 48
10.2.2 Horizontal Reinforcement Strain Profiles............................................................. 50
10.2.3 Vertical Reinforcement Strain Profiles................................................................. 65
10.2.4 Shear friction capacity model proposed by Mattock ............................................ 68
10.2.5 Capacity Evaluation of Exterior Shear Key with Shear Friction Capacity Model
Proposed by Walraven et al. ( 1987) ..................................................................................... 69
11 Appendix A- 5.................................................................................................................... 71
11.1 Geometry and Reinforcement Details of Test Series IV .............................................. 71
Reinforcement Layout .......................................................................................................... 71
11.2 Geometry and Reinforcement Details of Test Series V................................................ 73
11.3 Instrumentation ............................................................................................................. 76
12 REFERENCES ................................................................................................................. 82
- vii -
LIST OF FIGURES
Figure 3- 1 Test Observations.......................................................................................................... 3
Figure 4- 1 Schematic of Reinforcement Configuration with Hanger Bars .................................... 6
Figure 5- 1 Mechanistic Model of Exterior Shear Key.................................................................... 8
Figure 5- 2 Frequency Distribution of V / Asv Obtained from a Monte- Carlo Simulation. ............ 9
Figure A1- 1 Elevation View of the Reinforcement Layout......................................................... 14
Figure A1- 2- Observation at First Yield of Hanger Bars of Test Unit 4- A................................. 15
Figure A1- 3- Observation at the End of Test Unit 4- A ............................................................... 15
Figure A1- 4- Observation at First Yield of Hanger Bars of Test Unit 4- B ................................. 16
Figure A1- 5- Observation at the End of Test Unit 4- B ............................................................... 16
Figure A1- 6- Exterior Shear Keys Test Units 4- A and 4- B: Load vs. Displacement at top of
shear key ............................................................................................................................... 17
Figure A1- 1 Elevation View of the Reinforcement Layout......................................................... 14
Figure A1- 2- Observation at First Yield of Hanger Bars of Test Unit 4- A................................. 15
Figure A1- 3- Observation at the End of Test Unit 4- A ............................................................... 15
Figure A1- 4- Observation at First Yield of Hanger Bars of Test Unit 4- B ................................. 16
Figure A1- 5- Observation at the End of Test Unit 4- B ............................................................... 16
Figure A1- 6- Exterior Shear Keys Test Units 4- A and 4- B: Load vs. Displacement at top of
shear key ............................................................................................................................... 17
Figure A2- 1- Elevation View of the Reinforcement Layout ....................................................... 20
Figure A2- 2- Observation at Peak Load of Test Unit 5- A........................................................... 21
Figure A2- 3- Observation at 0.6 in. Displ. of Test Unit 5- A....................................................... 21
Figure A2- 4- Observation at 103 kips lateral Load with 1.0 in. Displ. of Shear Key in Test Unit
5- A ............................................................................................................................... ........ 22
Figure A2- 5- Observation of Specimen at Failure....................................................................... 22
Figure A2- 6- Observation of Specimen at Failure After Removing the Keys ............................ 22
Figure A2- 7- Observation at Peak Load of Test Unit 5................................................................ 23
Figure A2- 8- Observation at 1.6 in. Displ. of Test Unit 5 ........................................................... 23
Figure A2- 9- Observation at 44 kips lateral Load with 2.0 in. Displ. of Shear Key in Test Unit 5
............................................................................................................................... ............... 23
Figure A2- 10- Exterior Shear Keys Test Units 5- A and 5- B: Load vs. Displacement at
top of shear key..................................................................................................................... 24
Figure A3- 1- Strut- and- Tie Model for Shear Key ....................................................................... 25
Figure A3- 2- A Fractured Vertical Bar in Unit 5B, Removed from Inside of Concrete ............. 26
Figure A4- 1- Schematic of Strut- and- Tie Model for Exterior Shear Key ................................... 30
Figure A4- 2- Hysteresis Model for Exterior Shear Key.............................................................. 32
Figure A4- 3- Horizontal Strain Profiles, Layer x, Line 1, Unit 4A............................................. 34
- viii -
Figure A4- 4- Horizontal Strain Profiles, Layer x, Line 2, Unit 4A............................................. 35
Figure A4- 5- Horizontal Strain Profiles, Layer x, Line 3, Unit 4A............................................. 35
Figure A4- 6- Horizontal Strain Profiles, Layer x, Line 4, Unit 4A............................................. 35
Figure A4- 7- Horizontal Strain Profiles, Layer y, Line 1, Unit 4A............................................. 36
Figure A4- 8- Horizontal Strain Profiles, Layer y, Line 2, Unit 4A............................................. 36
Figure A4- 9- Horizontal Strain Profiles, Layer y, Line 3 Unit 4A.............................................. 37
Figure A4- 10- Horizontal Strain Profiles, Layer y, Line 4, Unit 4A........................................... 37
Figure A4- 11- Horizontal Strain Profiles, Layer x, Line 1, Unit 4B ........................................... 38
Figure A4- 12- Horizontal Strain Profiles, Layer x, Line 2, Unit 4B ........................................... 38
Figure A4- 13- Horizontal Strain Profiles, Layer x, Line 3, Unit 4B ........................................... 39
Figure A4- 14- Horizontal Strain Profiles, Layer x, Line 4, Unit 4B ........................................... 39
Figure A4- 15- Horizontal Strain Profiles, Layer y, Line 1, Unit 4B ........................................... 40
Figure A4- 16- Horizontal Strain Profiles, Layer y, Line 2, Unit 4B ........................................... 40
Figure A4- 17- Horizontal Strain Profiles, Layer y, Line 3, Unit 4B ........................................... 41
Figure A4- 18- Horizontal Strain Profiles, Layer y, Line 4, Unit 4B ........................................... 41
Figure A4- 19- Vertical Strain Profiles, Layer x, Line 1, Unit 4A ............................................... 42
Figure A4- 20- Vertical Strain Profiles, Layer x, Line 2, Unit 4A ............................................... 42
Figure A4- 21- Vertical Strain Profiles, Layer y, Line 1, Unit 4A ............................................... 43
Figure A4- 22- Vertical Strain Profiles, Layer y, Line 2, Unit 4A ............................................... 43
Figure A4- 23- Vertical Strain Profiles, Layer x, Line 1, Unit 4B ............................................... 44
Figure A4- 24- Vertical Strain Profiles, Layer x, Line 2, Unit 4B ............................................... 44
Figure A4- 25- Vertical Strain Profiles, Layer y, Line 1, Unit 4B ............................................... 45
Figure A4- 26- Vertical Strain Profiles, Layer y, Line 2, Unit 4B ............................................... 45
Figure A4- 27- Strut- and- Tie Model for Exterior Shear Key Unit 5A ........................................ 49
Figure A4- 28- Strut- and- Tie Model for Exterior Shear Key Unit 5B ........................................ 49
Figure A4- 29- Horizontal Strain Profiles, Layer 1, Line 1, Unit 5A........................................... 51
Figure A4- 30- Horizontal Strain Profiles, Layer 1, Line 2, Unit 5A........................................... 51
Figure A4- 31- Horizontal Strain Profiles, Layer 1, Line 3, Unit 5A........................................... 52
Figure A4- 32- Horizontal Strain Profiles, Layer 1, Line 4, Unit 5A........................................... 52
Figure A4- 33- Horizontal Strain Profiles, Layer 1, Line 5, Unit 5A........................................... 53
Figure A4- 34- Horizontal Strain Profiles, Layer 1, Line 6, Unit 5A........................................... 53
Figure A4- 35- Horizontal Strain Profiles, Layer 1, Line 7, Unit 5A........................................... 54
Figure A4- 36- Horizontal Strain Profiles, Layer 2, Line 1, Unit 5A........................................... 54
Figure A4- 37- Horizontal Strain Profiles, Layer 2, Line 2, Unit 5A........................................... 55
Figure A4- 38- Horizontal Strain Profiles, Layer 2, Line 3, Unit 5A........................................... 55
Figure A4- 39- Horizontal Strain Profiles, Layer 2, Line 4, Unit 5A........................................... 56
Figure A4- 40- Horizontal Strain Profiles, Layer 2, Line 5, Unit 5A........................................... 56
Figure A4- 41- Horizontal Strain Profiles, Layer 2, Line 6, Unit 5A........................................... 57
Figure A4- 42- Horizontal Strain Profiles, Layer 2, Line 7, Unit 5A........................................... 57
Figure A4- 43- Horizontal Strain Profiles, Layer 1, Line 1, Unit 5B ........................................... 58
Figure A4- 44- Horizontal Strain Profiles, Layer 1, Line 2, Unit 5B ........................................... 58
Figure A4- 45- Horizontal Strain Profiles, Layer 1, Line 3, Unit 5B ........................................... 59
Figure A4- 46- Horizontal Strain Profiles, Layer 1, Line 4, Unit 5B ........................................... 59
Figure A4- 47- Horizontal Strain Profiles, Layer 1, Line 5, Unit 5B ........................................... 60
Figure A4- 48- Horizontal Strain Profiles, Layer 1, Line 6, Unit 5B ........................................... 60
Figure A4- 49- Horizontal Strain Profiles, Layer 1, Line 7, Unit 5B ........................................... 61
- ix -
Figure A4- 50- Horizontal Strain Profiles, Layer 2, Line 1, Unit 5B ........................................... 61
Figure A4- 51- Horizontal Strain Profiles, Layer 2, Line 2, Unit 5B ........................................... 62
Figure A4- 52- Horizontal Strain Profiles, Layer 2, Line 3, Unit 5B ........................................... 62
Figure A4- 53- Horizontal Strain Profiles, Layer 2, Line 4, Unit 5B ........................................... 63
Figure A4- 54- Horizontal Strain Profiles, Layer 2, Line 5, Unit 5B ........................................... 63
Figure A4- 55- Horizontal Strain Profiles, Layer 2, Line 6, Unit 5B ........................................... 64
Figure A4- 56- Horizontal Strain Profiles, Layer 2, Line 7, Unit 5B ........................................... 64
Figure A4- 57- Vertical Strain Profiles, Layer 1, Unit 5A ........................................................... 65
Figure A4- 58- Vertical Strain Profiles, Layer 2, Unit 5A ........................................................... 65
Figure A4- 59- Vertical Strain Profiles, Layer 3, Unit 5A ........................................................... 66
Figure A4- 60- Vertical Strain Profiles, Layer 4, Unit 5A ........................................................... 66
Figure A4- 61- Vertical Strain Profiles, Layer 1, Unit 5B............................................................ 67
Figure A4- 62- Vertical Strain Profiles, Layer 2, Unit 5B............................................................ 67
Figure A4- 63- Vertical Strain Profiles, Layer 3, Unit 5B............................................................ 68
Figure A4- 64- Vertical Strain Profiles, Layer 4, Unit 5B............................................................ 68
Figure A5- 1- Elevation View of the Reinforcement Layout- Test Series IV ............................... 72
Figure A5- 2- Reinforcement Layout ( Section A- A)- Test Series IV ........................................... 72
Figure A5- 3- Reinforcement Layout ( Section B- B)- Test Series IV............................................ 73
Figure A5- 4- Elevation View of the Reinforcement Layout- Test Series V ................................ 74
Figure A5- 5- Reinforcement Layout ( Section C- C)- Test Series V ............................................. 74
Figure A5- 6- Reinforcement Layout ( Section A- A)- Test Series V............................................. 75
Figure A5- 7- Reinforcement Layout ( Section B- B)- Test Series V ............................................. 75
Figure A5- 8- Labels of Displacement Transducers- Test Series IV............................................ 76
Figure A5- 9- Labels of Displacement Transducers- Test Series V ............................................. 76
Figure A5- 10- Labels of Strain Gages on U Shape Vertical Bars, in Diagonal Direction- Test
Series IV............................................................................................................................. .. 77
Figure A5- 11- Labels of Strain Gages on U Shape Vertical Bars, in Horizontal direction- Test
Series IV............................................................................................................................. .. 78
Figure A5- 12- Labels of Strain Gages on Horizontal Hanger Bars- Test Series IV.................... 78
Figure A5- 13- Location of Strain Gages on Horizontal and Vertical Bars- Test Series IV ........ 79
Figure A5- 14- Labels of Strain Gages on Vertical Shear Key Reinforcement- Test Series V.... 80
Figure A5- 15- Labels of Strain Gages on Horizontal Headed Bars- Test Series V .................... 80
Figure A5- 16- Location of Strain Gages on Horizontal and Vertical Bars- Test Series V ......... 81
- x -
LIST OF TABLES
Table 5- 1 Summary of Statistic Analysis for Variables μf, α, and fsu/⎯ fy........................................ 8
Table A1- 1: Experimental and Calculated Maximum Load Carrying Capacities of Shear Key
( Units 4- A and 4- B) .............................................................................................................. 17
Table A2- 1: Experimental and Calculated Maximum Load Carrying Capacities of Shear Key
( Units 5- A and 5- B) .............................................................................................................. 24
Table A4- 1: Calculated the Steel Contribution to the Capacity of Exterior Shear Key Test Units
4A and 4B ............................................................................................................................. 31
Table A4- 2: Calculated Capacity of Exterior Shear Key Test Units 4A and 4B......................... 31
Table A4- 3: Calculated Load andDisplacement of Test Series IV at Each Damage Level ........ 33
Table A4- 4: Capacity Evaluation of Exterior Shear key Test Units 4A and 4B with
Mattock Equation.................................................................................................................. 46
Table A4- 5: Capacity Evaluation of Exterior Shear key Test Units 4A and 4B with Walraven et
al. ( 1987)’ s Equations........................................................................................................... 47
Table A4- 6: Capacity Evaluation of Exterior Shear key Test Units 4A and 4B with Caltrans
Sliding Shear Friction Equation............................................................................................ 48
Table A4- 7: Calculated Load andDisplacement of Test Series V at Each Damage Level.......... 50
Table A4- 8: Capacity Evaluation of Exterior Shear key Test Units 5A and 5B with Mattock
Equation ............................................................................................................................... 69
Table A4- 9: Capacity Evaluation of Exterior Shear key Test Units 5A and 5B with Walraven et
al. ( 1987)’ s Equations........................................................................................................... 70
- xi -
ABSTRACT
Seismic response and capacity evaluation of sacrificial exterior shear keys are the main
objectives of this work. Shear keys are used in bridge abutments to provide transverse support
for the superstructure. However, it has been recognized that to protect abutment piles from
severe damage under transverse forces, shear keys must be designed as a locking mechanism that
limits the magnitude of the transverse force that can be transmitted into the abutment. In
philosophical terms, a shear key could transversely be designed as a sacrificial element to limit
transverse inertial forces in the abutment walls and supporting piles. If shear keys are designed as
sacrificial elements within a capacity design framework, their overstrength must be accurately
determined to ensure other elements can be designed to remain elastic.
An experimental program to study the seismic behavior of shear keys was carried out at
University of California, San Diego. These specimens were built at a 40% scale of the exterior
shear keys of a prototype abutment. The design philosophy was to force a shear sliding failure at
the interface of the shear key- abutment stem wall to control damage to the abutment walls and
the piles under transverse seismic force. This report presents recommendations for design and
construction details of sacrificial exterior shear keys based on test results
Several factors were considered in this experimental program such as including construction
joints between the abutment stem wall and the shear key, different amount and configuration of
the vertical reinforcement crossing the abutment stem wall- shear key interface, and different
amounts and configuration of the horizontal reinforcement in the stem wall. A total of six
specimens were built and tested at UCSD; each specimen included two exterior shear key test
units. Experimental results of specimens 4 and 5 are given in report.
- 1 -
1 INTRODUCTION
Seismic response and capacity evaluation of sacrificial exterior shear keys are the main
objectives of this work. Shear keys are used in bridge abutments to provide transverse support
for the superstructure. However, it has been recognized that to protect abutment piles from
severe damage under transverse forces, shear keys must be designed as a locking mechanism that
limits the magnitude of the transverse force that can be transmitted into the abutment. In
philosophical terms, a shear key could transversely be designed as a sacrificial element to limit
transverse inertial forces in the abutment walls and supporting piles. If shear keys are designed as
sacrificial elements within a capacity design framework, their overstrength must be accurately
determined to ensure other elements can be designed to remain elastic.
Damage to abutments under a major seismic event is admissible provided that any abutment
damage is repairable and there is no damage to the piles ( ACI, 2005).. Therefore, transfer of
seismic forces to the abutments is controlled by design of sacrificial shear keys such that the
capacity of the shear keys does not exceed the smaller of 30% of the dead load vertical reaction
at the abutment or 75% of the total shear capacity of the piles plus one of the wing walls
( Caltrans, 1993a)..
2 SCOPE
An experimental program to study the seismic behavior of shear keys was carried out at
University of California, San Diego. These specimens were built at a 40% scale of the exterior
shear keys of a prototype abutment. The design philosophy was to force a shear sliding failure at
the interface of the shear key- abutment stem wall to control damage to the abutment walls and
the piles under transverse seismic force. This report presents recommendations for design and
construction details of sacrificial exterior shear keys based on test results
Several factors were considered in this experimental program such as including construction
joints between the abutment stem wall and the shear key, different amount and configuration of
the vertical reinforcement crossing the abutment stem wall- shear key interface, and different
amounts and configuration of the horizontal reinforcement in the stem wall. A total of five
specimens were built and tested at UCSD; each specimen included two exterior shear key test
- 2 -
units. Experimental results of specimens 4 and 5 are given in Appendices A- 1 and A- 2,
respectively.
3 SUMMARY OF RESEARCH WORK
Construction details and experimental results of Test Units 4A, 4B, 5A, and 5B are described in
Appendices A- 1 and A- 2. Test Units 4A and 4B represented the standard shear key design.
Caltrans provided the design and construction details for Test Units 4A and 4B. Design of Test
Units 5A and 5B was proposed by UCSD. Design of Units 5A and 5B developed based on strut-and-
tie modeling.
3.1 MODES OF FAILURE
3.1.1 UNITS 4A AND 4B
A large diagonal crack developed in the stem wall for both test units. Thus, failure occurred in
the stem wall rather than at the interface of the shear key- abutment stem wall as intended. No
shear sliding was observed at the interface of the shear key- stem wall during these tests
[ Appendix A- 1]. Figure 3- 1a shows Test Unit 4A after failure.
3.1.2 UNITS 5A AND 5B
A horizontal shear sliding at the interface of the shear key- abutment stem wall developed in Test
Units 5A and 5B. Capacity of the shear key of Unit 5B was very close to that initially estimated.
Few hair line cracks developed in the stem wall during the test, but the width of these hair line
cracks was very small throughout the test [ Appendix A- 2]. Figure 3- 1b shows Test Unit 5B after
failure.
- 3 -
( a) Failure mode of Test Unit 4A.
( b) Failure mode of Test Unit 5B
Figure 3- 1 Test Observations
V V
- 4 -
4 RECOMMENDATIONS FOR CONSTRUCTIONS
4.1 Discussion of Experimental Results
Based on the results of the experimental work performed at the University of California, San
Diego, several recommendations are proposed in this section for construction details of
sacrificial exterior shear keys.
• A smooth construction joint should be considered at the interface of the shear key-abutment
stem wall, to effectively create a weaker plane at the shear key- abutment stem
wall interface. Similarly, the smooth construction joint should exist between the shear
key and the abutment back wall for the same reason. The abutment stem and back walls
should be constructed first followed by smooth finishing of all surfaces.
• A bond breaker film should be applied on the abutment stem wall and back wall at the
location of their interface with the shear keys. The purpose of bond breaker is to prevent
any chemical bond between concretes of shear keys and abutments at the interface of the
shear key- stem or back wall. Form oil could be used as a bond breaker. Other alternatives
include use of available commercial products ( used for Test Unit 5B). Another option
could be the use of a mix of soap and talc, as used in precast segmental practice to break
the bond between the match cast segments.
• Shear key vertical reinforcement should be lumped in a single group and be placed as
close as possible to center of the shear key. These vertical reinforcing bars should be the
only ones that connect the shear key to the abutment stem wall. Temperature and
shrinkage reinforcement should be provided as standard design in the shear key and
abutment wall. However, temperature and shrinkage reinforcement should not cross the
shear key- abutment wall interface. No reinforcement should be used to connect the shear
key to the abutment back wall.
• Horizontal reinforcement, required to carry the tension force in the stem wall arising from
the force transmitted by the shear key, can be headed bars or standard hanger bars. These
reinforcement should be placed in the stem wall as close as possible to the shear key. If
headed bars are provided, the bars should be as long as possible; minimum concrete
- 5 -
cover should be maintained at the ends of the headed bars. If hanger bars are used,
minimum length should be provided from the intersection of the lowest layer of the
hanger bars and the shear key vertical reinforcement. Figure 4.1 shows a schematic of
reinforcement configuration for hanger bars.
In order to be conservative the coefficient of friction, μ, is assumed to be equal to 0.6,
which is the static coefficient of friction for concrete placed against hardened concrete
surface not intentionally roughened ( ACI, 2005). Hence the angle θ is equal to 31°( μ =
tan θ) .
The basic development length of standard hooks ( hanger bars) in tension is given by
Crisafulli et al., 2002:
c
b
dh f
d
l
′
=
1200
( 1)
Where db ( in.) is the bar diameter and f'c ( psi) is the compressive strength of concrete.
The basic development length should be multiplied by the appropriate correction factors
to account for specified yield strength different than 60 ksi, concrete cover, presence of
ties or stirrups around the bars, excess reinforcement, light weight aggregate concrete and
epoxy coating of reinforcement ( Crisafulli et al., 2002). Thus, for hanger bars:
L = tan ( a + b) + ldh min θ ( 2)
dh L = 0.6( a + b) + l min ( 3)
Where “ a” is the distance from the location of the applied force to the surface of the wall
and “ b” is the distance between the top surface of the stem wall to centroid of the lowest
horizontal reinforcement layer. For headed bars Lmin is equal to:
L = 0.6( a + b) + c min ( 4)
Where “ c” is recommended as 3 in ( 76 mm). Lmin should be satisfied for the lowest layer
of horizontal hanger bars or headed bars so that these reinforcing bars would be effective
in transferring the tensile force.
- 6 -
Figure 4- 1 Schematic of Reinforcement Configuration with Hanger Bars
• The horizontal reinforcement should be concentrated close to top surface of the stem
wall. If they are distributed along the height of the wall, the lower layers will not be
effective in carrying any tension force. On the other hand Lmin is a function of the
location of the lowest layer of hanger bars or headed bars, indicating of the need to place
the hanger bars close to top surface of the abutment stem wall.
5 EVALUATION OF THE CAPACITY OF EXTERIOR SHEAR
KEYS
The capacity evaluation of exterior shear keys can be performed using Strut- and- Tie models. As
reference the Strut- and- Tie model for shear keys at the failure is discussed in Appendix A- 3. A
mechanism model was developed for shear key 5B because this shear key performed as a
sacrificial element with sliding shear failure at the expected load. Figure 5.1 shows the model of
an exterior shear key, which is based on that proposed by Crisafulli et al., 2002. The nominal
capacity of shear key is given by:
Lowest layer of reinforcement
carrying the shear force, V
L min
l dh
V
a
b
θ
V
- 7 -
vf su
f
f
n V A f
μ β
μ α α
1 tan
cos sin
−
+
= ( 5)
where α is an angle of kinking of the vertical bars with respect to the vertical axis; β is an angle
of inclined face of shear key with respect to the vertical axis ( see Fig. 5.1); μf is a kinematic
coefficient of friction of concrete; and fsu is an ultimate tensile strength of the vertical
reinforcement. Due to the kinematics of the sliding shear key, the vertical bars which connect the
shear key to the stem wall must kink. Experimental tests indicate the average kink angle, α, to be
37° at failure ( Fig. A3- 2). By back- calculating the tensile force of vertical reinforcement and kink
angle, α, from displacement data ( measured during the test in unit 5B) and substituting in Eq.
( 5), the value of μf for concrete with smooth finishing was determined to be 0.36. A smooth
construction joint should be considered at the interface of the shear key- abutment stem wall, to
effectively create a weaker plane at the shear key- abutment stem wall interface and enable
occurrence of sliding shear failure at the interface. In shear key 5B, the ultimate tensile strength
of the vertical reinforcement (# 4 bars) was 103.9 ksi ( 710 MPa) and the total area of vertical bars
crossing the shear key- abutment stem wall was 0.8 in2 ( 516.1) mm2. The angle of inclined face
of the shear key, β, in all shear key units was equal to 16.3°. By substituting values of these
variables in Eq. ( 5), the nominal shear force capacity of unit 5B is equal to 82.5 kips ( 364 kN),
which is 8% greater than the shear force measured in the experiment for shear key 5B.
Capacity design to protect abutment system requires evaluation of over- strength capacity, Vo.
Over- strength evaluation can be obtained from Eq. ( 5) by considering for uncertainty
C = ( Avf fsu cosα + Vn tan β)
Vc = μ f
C α
Vn/ cos β
Avf fsu
Kinked bar
β
- 8 -
Figure 5- 1 Mechanistic Model of Exterior Shear Key
and variability on the independent variables, using a Monte- Carlo simulation. Independent
variables in Eq. ( 5) are α, the angle of kinked vertical bars with respect to vertical axis, μf, the
kinematic coefficient of friction for concrete with smooth finishing, and fsu, the ultimate tensile
strength of the vertical reinforcement. The independent variables are assumed to follow a
truncated normal distribution as described in Table 5.1. Since there is only limited available test
data for variables μf and α, the mean, upper, and lower values for these variables are assumed
based on the limited test data. However, there are some available test data for yield strength of
steel, fy, that have been done at University of California, San Diego. Based on these data, it is
assumed that the mean value for yield strength of steel ( Grade 60), f ¯
y, is equal to 64.8 ksi.
Figure 5.2 shows the frequency distribution of ( Vn / Avf) as evaluated by using Eq. ( 5) for a
number of randomly generated values of the independent variables. This distribution can be
assumed as normally distributed with a mean value ( Vn / Avf) = 95.95 ksi and a standard
deviation equal to 7.214 ksi:
Table 5- 1 Summary of Statistic Analysis for Variables μf, α, and fsu/⎯ fy
* COV=
Coefficient of Variation
Extreme Value
Variable Mean COV*
Upper Lower
( 1) ( 2) ( 3) ( 4) ( 5)
μf 0.36 6.8% 0.40 0.32
α 37° 4.9% 40° 34°
f s u / ⎯ f y 1.55 5.9% 1.70 1.40
- 9 -
Figure 5- 2 Frequency Distribution of V / Asv Obtained from a Monte- Carlo Simulation.
( )
μ β
φ μ α α
φ
1 tan
cos sin
f
y
y
su
o f vf
o o n
f
f
f
A
V V
−
⎟ ⎟ ⎟
⎠
⎞
⎜ ⎜ ⎜
⎝
⎛
+
= =
−
−
( 6)
For 95% confidence, the value of φo is equal to 1.13. By substituting values for ⎯ μf, ⎯ α,
⎟ ⎟ ⎟
⎠
⎞
⎜ ⎜ ⎜
⎝
⎛
−
−
y
su
f
f
( from Table 5.1) and β:
( )
( 1 ( 0.36) tan16.3 )
( 1.13) ( 0.36) cos37 sin 37 ( 1.55)
o
o o
−
+
= vf y
o
A f
V ( 7)
The ratio of mean value for yield strength of Grade 60 reinforcement to the specified yield strength results
in:
= 1.08
y
y
f
f
( 8)
Where fy is the specified yield strength ( fy = 60 ksi for Grade 60 steel). Hence, by substituting
Eq. ( 8) into Eq. ( 7) and rounding up gives the following for design purposes:
o vf y V = 1.88A f ( 9)
However, the capacity of a shear key should not exceed the smaller of 30% of the dead load vertical
reaction at the abutment, Wa, or 75% of the total shear capacity of the piles, Vpiles, plus one of the wing
walls, Vwingwall, ( Caltrans, 1993a). Therefore:
V / Avf, ksi
0
500
1000
1500
2000
2500
75
78
80
83
85
88
90
93
95
98
100
103
105
108
110
113
115
118
120
Frequency
Test Unit 5B
Test Unit 3A [ 3]
96.4 107.7
94.4
Test Unit 3B [ 3]
- 10 -
min( 0.3 ,0.75 ) o a piles wingwall V ≤ W V + V ( 10)
By substituting Eq. ( 9) into Eq. ( 10) and solving for Avf:
y
a piles wingwall
vf f
W V V
A
1.88
min( 0.3 ,0.75 + )
≤ ( 11)
The horizontal tie reinforcement in the stem wall below the shear key must be designed to carry the
overstrength force, Vo, elastically. Thus, the area of reinforcement, Ash, required in this region is equal to:
y
o
sh f
A V
φ
= 1 ( 12)
where φ, the strength reduction factor, is equal to 1.0, if capacity design has been used ( Mattlock, 1974).
Eq. ( 9) and Eq. ( 12) are the proposed design equations to determine the required amounts of shear key
vertical reinforcement and horizontal tie reinforcement in the stem wall, respectively.
- 11 -
6 RECOMMENDATIONS FOR FUTURE RESEARCH
As mentioned above, Eq. ( 9) is recommended for design of sacrificial exterior shear keys with a
smooth construction joint at the interface of the shear key- abutment stem wall. Future research
would be recommended to:
1. Investigate the effect of the size and amount of vertical reinforcement on the capacity of
shear keys.
2. Investigate the effect of changing the location of vertical reinforcement on capacity.
3. Use of standard hanger bars instead of headed bars with sufficient development length as
reinforcement in the abutment stem wall.
4. Define the variation of the coefficient of friction, μf, for different types of construction
joints.
- 12 -
7 APPENDIX A- 1
Caltrans Contract No. 59A0337
Seismic Response of Sacrificial Exterior Shear Keys
in Bridge Abutments
Summary of the Experimental Results:
Test Units 4- A and 4- B
by
Azadeh Bozorgzadeh
Graduate Student Researcher
of
Department of Structural Engineering
University of California, San Diego
August 21, 2002
- 13 -
This report presents the results of the tests of two shear key Units 4- A and 4- B. These tests were
held on August 21, 2002, at the University of California, San Diego ( UCSD). Units 1- A to 3- B
were tested earlier at UCSD under Caltrans Contract 59A0051 ( Research report No. SSRP-
2001/ 23).
Caltrans provided the main part of these specimens’ design. Based on that design, eight # 4
hanger bars were used horizontally close to the top surface of the abutment stem wall. In Test
Unit 4- A, the shear key was built monolithically with the abutment stem wall. In Test Unit 4- B,
there was a rough construction joint between the shear key and the wall. Figure A1- 1 shows the
schematic of the specimen.
In Test Unit 4- A, the first crack occurred at the lateral load of 100 kips, which was initiated at
the interface between the shear key inclined face and the stem wall. The crack was inclined to the
support ( toe of the wall). The first yield occurred in one of the hanger bars at the load of 191
kips. The maximum load carrying capacity of the Unit 4- A was 329.3 kips. The first crack was
the major crack during the test. The width of the major crack was around 0.4 in. at the maximum
load carrying capacity. Figures A1- 2 and A1- 3 show the Test Unit 4- A at the first yield of the
hanger bars and end of the test, respectively.
In Test Unit 4- B, the first crack occurred at the lateral load of 88 kips, which was initiated at the
interface between the shear key inclined face and the stem wall. The crack was inclined to the
support ( toe of the wall). The first yield occurred in one of the hanger bars at the load of 147
kips. The maximum load carrying capacity of the Unit 4- B was 298.7 kips. The first crack was
the major crack during the test. The width of the major crack was around 0.625 in. at the
maximum load carrying capacity. Figures A1- 4 and A1- 5 show the Test Unit 4- B at the first
yield of the hanger bars and end of the test, respectively.
Table A1- 1 shows the experimental and calculated maximum load carrying capacities of the
shear keys. In these calculations, f'c was the strength of the concrete on date- of- test. A
comparison of the values in columns 3 and 4 shows that the current Caltrans shear friction model
severely underestimates the capacity of the shear keys. Column 5 represents the calculated
maximum load carrying capacity of shear keys based on the Strut- and- Tie analogous model ( Eqs.
- 14 -
5.2 to 5.4 in UCSD Research Report No. SSRP- 2001/ 23 submitted to Caltrans on May 2002).
Columns 6 and 7 show the ratio of the experimental and calculated maximum capacity of the
shear keys based on the Caltrans model ( shear friction) and Strut- and- Tie analogous model,
respectively.
Figure A1- 1- Elevation View of the Reinforcement Layout
17" ( 0.433 m)
7"
( 178.3 mm)
24" ( 0.61 m)
24" ( 610 mm) 30 1/ 2" ( 0.77 m) 18" ( 457 mm)
. ( 229 mm)
9"
1" ( 25.4 mm)
clearance
15"
( 381 mm)
4-# 3
4-# 3
8 - # 4
# 3 @ 4 3/ 4" ( 121 mm)
1" ( 25.4 mm)
12 - # 5
12 - # 5
Clearance
# 3 @ 4 3/ 4"
( 121 mm)
4-# 3
# 5 Stirrups
3/ 4"
Rough Construction Joint
4 - # 3
5 - # 3
4 - # 3
16 - # 3
6 - # 3 1" ( 25.4 mm)
6 - # 3
. 48" ( 1.22m)
# 3
4 - # 3
114" ( 2896 mm)
4-# 3
B A
- 15 -
Figure A1- 2- Observation at First Yield of Hanger Bars of Test Unit 4- A
Figure A1- 3- Observation at the End of Test Unit 4- A
- 16 -
Figure A1- 4- Observation at First Yield of Hanger Bars of Test Unit 4- B
Figure A1- 5- Observation at the End of Test Unit 4- B
- 17 -
Results of this experiment indicate that the maximum load carrying capacity can be estimated
using the Strut- and- Tie analogous model.
Table A1- 1: Experimental and Calculated Maximum Load Carrying Capacities of Shear Key ( Units 4- A
and 4- B)
Figure A1- 6 shows the Load vs. Displacement at top of the shear key Units 4- A and 4- B in one
graph. Test Unit 4- B ( with construction joint) has less capacity than that in Unit 4- A.
0
50
100
150
200
250
300
350
0 1 2 3 4 5
Displacemnet ( in.)
Load ( kip)
Unit 4- A ( Monolithic)
Unit 4- B ( with
Construction Joint)
Figure A1- 6- Exterior Shear Keys Test Units 4- A and 4- B: Load vs. Displacement at top of shear key
TEST
UNIT
f'c
psi
( Mpa)
Vu, t
Kips
( kN)
Vn, Calt
Kips
( kN)
Vn, Strut- and- Tie
kips ( kN)
Vn, Calt
Vu, t
Vn, Strut- and- Tie
Vu, tt
4- A 5780
( 39.8)
329.3
( 1464.8)
222.5
( 989.7)
316
( 1405.6)
0.68 0.96
4- B 5780
( 39.8)
298.7
( 1328.7)
160
( 711.7)
297
( 1321.1)
0.54 0.99
- 18 -
8 APPENDIX A- 2
Caltrans Contract No. 59A0337
Seismic Response of Sacrificial Exterior Shear Keys
in Bridge Abutments
Summary of the Experimental Results:
Test Units 5- A and 5- B
by
Graduate Student Researcher
of
Department of Structural Engineering
University of California, San Diego
December 20, 2002
- 19 -
This report presents the results of the tests of two shear key Units 5- A and 5- B. These tests were
held on December 16, 2002, at the University of California, San Diego ( UCSD). Units 1- A to 4-
B were tested earlier at UCSD under Caltrans Contract 59A0051.
The design model and analysis of shear key units 5A and 5B were submitted to Caltrans
previously. Based on strut- and- tie model, fourteen # 4 headed bars were used horizontally close
to the top surface of the abutment stem wall. In Test Unit 5- A, the foam was used at interface of
the shear key and the wall. An 8x8 hole was provided at center of the foam. There was a rough
construction joint between the shear key and the wall at the location of the hole and a smooth
construction joint between the foam and the wall. All shear key vertical reinforcing bars are
lumped at one location close to the side of the hole that is closer to the inclined face of the shear
key. In Test Unit 5- B, there was a smooth construction joint between the shear key and the wall.
A bond breaker is applied at interface to create a weak plane of failure. All shear key vertical
reinforcing bars are lumped at one location near the centerline of the shear key. Figure A2- 1
shows the schematic of the specimen.
In Test Unit 5- A, the first hair crack at surface of the wall occurred at the lateral load of 80 kips,
which was initiated at the interface close to location of vertical bars. The crack was inclined to
the support ( toe of the wall). Several inclined hair cracks occurred during the test but the width
of all cracks did not exceed 0.01 in. The maximum load carrying capacity of the Unit 5- A was
165.0 kips. The main slippage at interface occurred after the unit 5- A reached to the maximum
load carrying capacity. Figures A2- 2 and A2- 3 show the Test Unit 5- A at the peak load and 0.6
in. displacement, respectively. Figure A2- 4 shows the slippage of the test unit 5- A at 1.0 in.
displacement and 103 kips load. The mode failure was shear failure at interface of the shear key
and the stem wall. No damage was observed on the stem wall. Figure A2- 5 and A2- 6 show the
specimen after failure with and without shear keys.
- 20 -
Figure A2- 1- Elevation View of the Reinforcement Layout
In Test Unit 5- B, the first hair crack occurred at the lateral load of 10 kips, which was the
horizontal crack at the interface between the shear key and the stem wall. Few inclined hair
cracks occurred during the test on the stem wall close to interface but the width of all cracks
didn’t exceed 0.01 in. The length of these hair cracks was shorter than those in test unit 5- A. The
slippage between the shear key and the wall started at the load of 30 kips. The maximum load
carrying capacity of the Unit 5- B was 75.5 kips which was very close to what was predicted.
Figures A2- 7 and A2- 8 show the Test Unit 5- B at the peak load and 1.6 in. displacement,
respectively. Figure A2- 9 shows the slippage of the test unit 5- B at 2.0 in. displacement and 44
kips load. The mode failure was shear failure at interface of the shear key and the stem wall. No
damage was observed on the stem wall. Figure 5 and 6 shows the specimen after failure with and
without shear keys.
Table A2- 1 shows the experimental and calculated maximum load carrying capacities of the
shear keys. In these calculations, f'c was the strength of the concrete on date- of- test. A
comparison of the values in columns 3 and 4 shows that the current Caltrans shear friction model
underestimates the capacity of the shear keys. In test unit 5- A the capacity was twice as what was
Rough Construction Joint
114" ( 2896 mm)
48" ( 1.22m)
3/ 4" ( 19.05 mm)
30 1/ 2" ( 0.77 m)
clearance
9"
( 229 mm)
18" ( 457 mm)
.
Foam( 1/ 2" thick)
21 - # 3
( 121 mm)
# 3 @ 4 3/ 4"
24" ( 610 mm)
6 - # 3
4 - # 3
6 - # 3 17" ( 0.433 m.)
C
4 - # 4
# 3
A
# 3
( 178.3 mm)
4-# 3
7"
Clearance
1" ( 25.4 mm)
12 - # 5
12 - # 5
# 5 Stirrups
6 - # 3
24" ( 0.61 m)
14 - # 4
Headed bars
4 - # 4
C
B
with Bond Breaker ( form oil)
Smooth Construction Joint
3/ 4" recess
clearance
3/ 4" ( 19.05 mm)
# 3 @ 4 3/ 4" ( 121 mm)
# 3
6 - # 3
4-# 3
- 21 -
estimated. It is believed that the high strength was achieved due to cohesion of concrete at rough
construction joint. More investigation and data analysis is required for more details. Column 5
shows the ratio of the experimental and calculated maximum capacity of the shear keys based on
the Caltrans model ( shear friction).
Figure A2- 2- Observation at Peak Load of Test Unit 5- A
Figure A2- 3- Observation at 0.6 in. Displ. of Test Unit 5- A
- 22 -
Figure A2- 4- Observation at 103 kips lateral Load with 1.0 in. Displ. of Shear Key in Test Unit 5- A
Figure A2- 5- Observation of Specimen at Failure
Figure A2- 6- Observation of Specimen at Failure After Removing the Keys
- 23 -
Figure A2- 7- Observation at Peak Load of Test Unit 5
Figure A2- 8- Observation at 1.6 in. Displ. of Test Unit 5
Figure A2- 9- Observation at 44 kips lateral Load with 2.0 in. Displ. of Shear Key in Test Unit 5
- - - B
- - - B
- B
- 24 -
Results of this experiment indicate that the maximum load carrying capacity can be estimated
using the Strut- and- Tie analogous model for exterior shear keys with smooth construction joint.
Table A2- 1: Experimental and Calculated Maximum Load Carrying Capacities of Shear Key ( Units 5- A
and 5- B)
Figure A2- 10 shows the Load vs. Displacement at top of the shear key Units 5- A and 5- B in one
graph. Test Unit 5- B ( with smooth construction joint) has less capacity than that in Unit 5- A.
0
20
40
60
80
100
120
140
160
0 0.5 1 1.5 2
Displacement ( in.)
Load ( kip)
Unit 5- A ( using foam)
Unit 5- B( with bond
breaker)
Figure A2- 10- Exterior Shear Keys Test Units 5- A and 5- B: Load vs. Displacement at
top of shear key
TEST
UNIT
f'c
psi
( Mpa)
Vu, t
Kips
( kN)
Vn, Calt
Kips
( kN)
Vn, Calt
Vu, t
5- A 4900
( 33.8)
165.5
( 736.2)
50.4
( 224.1)
0.3
5- B 4900
( 33.8)
75.5
( 335.8)
30.24
( 134.5)
0.4
- 25 -
9 APPENDIX A- 3
9.1 Analytical Study of Sacrificial Shear Keys
In order to estimate the capacity of shear keys, a Strut- and- Tie model is developed. The model
takes into account the deformed shape of the shear key. Figure A3- 1 shows the strut- and- tie
Figure A3- 1- Strut- and- Tie Model for Shear Key
model. In order to measure the angle of kinked vertical bars, fractured vertical bars were
removed from inside shear key and stem wall. Figure A3- 2 shows one of the kinked vertical bars
after putting together the two fractured pieces. The forces in struts and ties are found as
described below. The ultimate force in the shear key vertical reinforcement, T1, is calculated by:
C4
φ
0.5 l
1 "
x
3.375"
3.3"
0.5 l
E
C5
C3
θT2 γ V
D
δu
T4 T3
A
α β
T1
C1 B
T4
4.375"
C2
10.7"
C P
dv
dh
1"
- 26 -
Figure A3- 2- A Fractured Vertical Bar in Unit 5B, Removed from Inside of Concrete
vf su T = A f 1 ( A- 1)
Where Asv is the amount of the vertical reinforcement connecting the shear key to the abutment
stem wall and fsu is the ultimate tensile strength of the vertical reinforcement. For Test Unit 5B,
Avf= 0.8 in2, and fsu= 103.9 ksi ( measured). Thus,
( 0.8)( 103.9) 82.472 1 T = = kips
The experimental shear key capacity of Unit 5B, V [ see Fig. A3- 1] was 75.5 kips and the angle
of deformed reinforcement with respect to vertical axis was measured asα = 37o .
The development length of reinforcing bars is given by the following equation [ 5]:
c
b y
d f
d f
l
′
=
0.025
( lb and in. units) ( A- 2)
Where db is the bar diameter; fy is the yield strength and f'c is the concrete compressive strength.
For Unit 5B, db= 0.5 in ( No. 4 bars); f'c ( abutment stem wall) = 4930 psi; f'c ( shear key) = 4870
psi; fy ( vertical bars) = 62.97 ksi and fy ( tension tie reinforcement) = 66.02 ksi. Thus, the
development length of vertical reinforcement, ldv, is given by:
Location of the Fractured Bar
- 27 -
5.64"
2
11.28"
4870
( 0.025)( 0.5)( 62970)
=
= =
dv
dv
l
l
Similarly, the development length of the tension tie reinforcement ( headed bars), ldh, is given by:
5.88"
2
11.75"
4930
( 0.025)( 0.5)( 66020)
=
= =
dh
dh
l
l
Thus,
0.5l − u = 5.88 − 1.4 = 4.48" dh δ
Where δu is the measured displacement at failure ( δu = 1.4 in. for Unit 5B). From geometries, the
angles between struts and ties can be determines as follows:
o
o
o
o
) 21.36
5.88
tan ( 3.3 1
) 24.26
3.3 1 3.375 2.265
tan ( 4.48
) 17.5
10.7
tan ( 3.375
) 11.95
10.7
tan ( 5.64 3.375
1
1
1
1
= − =
=
+ + +
=
= =
= − =
−
−
−
−
φ
θ
β
γ
In order to find the force in each individual strut and tie, it is needed to solve the force
equilibrium equations at each node as follows:
At node “ A”:
Σ = 0 ⇒ cosβ = sinα 1 1 H C T
49.6 1 C = kips
At node “ B”:
- 28 -
Σ = 0 ⇒ = cosβ + cosγ 1 2 H V C C
75.5 ( 49.6) cos17.5o cos11.95o 2 = + C
28.8 2 C = kips
Σ = 0 ⇒ = sinβ − sinγ 1 2 V P C C
P = ( 49.6) sin17.5o − ( 28.8) sin11.95o
P = 8.95 kips
At node “ C”:
Σ = 0 ⇒ sinθ = cosγ 3 2 H C C
68.57 3 C = kips
At node “ D”:
Σ = 0 ⇒ cosφ = sinα 4 1 H C T
50.79 4 C = kips
At node “ E”:
Σ = 0 ⇒ = cosθ + sinφ 5 3 4 V C C C
81.01 5 C = kips
Σ = 0 ⇒ = cosφ + sinθ 4 4 3 H T C C
75.5 4 T = V = kips
( ) s s ε 929.8μ
( 14)( 0.2)( 29000)
= 75.5 =
The maximum measured strain in the tension reinforcement was 974 μs, which agrees with the
strain value calculated above. This indicates that the Strut- and- Tie model shown in figure ( A3- 1)
is reasonable.
- 29 -
10 APPENDIX A- 4
10.1 Evaluation of the Capacity of the Test Series IV
Capacity estimation of exterior shear keys series IV was evaluated using three different existing
models.
10.1.1 Strut- and- Tie Mechanism and Hysteretic Model:
The strut- and- tie mechanism and hysteretic model presented in report SSRP 2001/ 23 ( Megally et
al., 2001) was used to evaluate the capacity of shear keys unit 4A and 4B. The hysteric model is
composed of two components, which represent the concrete behavior and steel behavior. The
steel reinforcement is assumed as a tension tie where concrete is acting as compressive struts.
Figure A4- 1illustrates the schematic of the strut- and- tie behavior of shear key under lateral load.
The diagonal concrete struts and steel reinforcement ties which are the horizontal and vertical bar
in the abutment stem wall are shown clearly. A diagonal crack develops in the abutment stem
wall below the shear key by applying lateral load. The load is transferred from the shear key to
the footing by the diagonal strut as shown in Figure A4- 1. The capacity of Test Units 4A and 4B
was calculated using equilibrium of the shear key along this diagonal crack. Therefore, based on
this model the capacity of the shear key is equal to:
where C V and S V are the concrete and reinforcing steel contribution to the strength of the shear
key respectively. C V , the concrete contribution can be calculated by:
where h is height of the abutment stem wall; b is width of the abutment stem wall and fc’ is the
concrete compressive strength. By substituting h = 30.5 in ( 775 mm); b = 16.75 in. ( 425 mm)
and fc’ = 5,780 psi ( 34.5 MPa), the contribution of the concrete is equal to:
N C S V = V + V ( A4. 1)
⎪⎩ ⎪⎨
⎧
=
0.2 ( )
2.4 ( )
'
'
f b h MPa
f b h psi
V
c
c
C ( A4. 2)
= 93.2 C V Kips ( 414.6 KN)
- 30 -
The reinforcing steel contribution to the capacity of the shear key, S V , is obtained by taking
summation of moments about point A. All reinforcing bars intersecting the crack are assumed to
yield. Thus the contribution of steel S V is calculated as follows:
Figure A4- 1- Schematic of Strut- and- Tie Model for Exterior Shear Key, After Megally et al.,
2001
⎟ ⎟⎠
⎞
⎜ ⎜⎝
⎛
+ ⎥⎦
⎤
⎢⎣
⎡
= + + + +
s h a
n A f d
s
V A f d A f h A f d n A f h S vf y s y s y h s s y s v s s y s
1
2 2 2
2
, ,
2
,1 ,1 ,2 ,2 , , ( A4.3)
where vf A is the total vertical reinforcement which connect the shear key to the stem wall and
cross the crack, As, 1 is the total area of steel of hanger bars; As, 2 is the total area of steel along T2
( see Figure A4- 1). In general horizontal and vertical side reinforcement are same in amount and
As, s is the cross sectional area of the side reinforcement ( Megally et al., 2001). For the test units
4A and 4B of this experimental program, a = 4 in. ( 102 mm) and s = 4.75 in. ( 121 mm). Table
A4- 1 shows the calculated S V , given by Eq.( A4.3) for Test Units 4A and 4B. Total Shear key
capacity, given by Eq. ( A4. 1), which is based on the proposed model in report SSRP 2001/ 23, is
calculated and presented in Table A4- 2. The idealized load- displacement envelope, which
d
s
Ti
s
V
T 2
a
h
A
Cc, 1
Cc, 2
P
T1
B
- 31 -
describes the behavior of exterior shear key under lateral load in terms of five damage level, is
presented in Figure A4- 2. Damage level I is characterized by onset of cracking at the shear- key
abutment stem wall interface.
Vertical Steel
Area Crossing
Interface of
Shear Key &
Wall
Steel Areas for
Strut- and- Tie
Model
Cross
Sectional Area
of the Side
Test Reinforcement
Series
Test
Unit
No.
of
Bars
Avf
in2.
( mm2)
As, 1
in2.
( mm2)
As, 2
in2.
( mm2)
Bar
Size
As, s
in2.
( mm2)
VS
Steel
Contribution
to Shear Key
Capacity
kips ( KN)
Eq. ( 1.4)
4A 24# 3 2.64
( 1,703)
1.6
( 1,032)
0.44
( 284) # 3 0.11
( 71)
222.5
IV ( 989.7)
4B 24# 3 2.64
( 1,703)
1.6
( 1,032) ------- # 3 0.11
( 71)
203.8
( 906.5)
Table A4- 1: Calculated the Steel Contribution to the Capacity of Exterior Shear Key Test
Units 4A and 4B
Test
Series
Test
Unit
Vc
Concrete Contribution to
Shear Key Capacity
kips ( KN)
Eq. ( A4. 2)
VS
Steel Contribution to
Shear Key Capacity
kips ( KN)
Eq. ( A4.3)
VN
Shear Key
Capacity
kips ( KN)
Eq. ( A4. 1)
4A 93.2
( 414.6)
222.5
( 989.7)
315.7
IV ( 1404.3)
4B 93.2
( 414.6)
203.8
( 906.5)
297
( 1321.1)
The required shear force to cause crack in shear key is given by:
3 9 4
7.5
2
'
+ +
=
k k
f bd
V c
cr ( A4. 5)
where a = kd , is the distance from the top of the stem wall to center of application of the laeral
load, V. The shear key top displacement at damage level I is:
y
cr
I II V
V Δ = Δ ( A4. 6)
Table A4- 2: Calculated Capacity of Exterior Shear Key Test Units 4A and 4B
- 32 -
VIII
VS = VIV = VIV
VC
VI
ΔI ΔII ΔIII ΔIV ΔV ΔD
V
Hysteresis Rule
Concrete Component
Steel Component
Δ
ko, I
ko, II ko, III
VII
VIV = VIV
ko
ko, III = ko, V
A
B
C
D E
F
Figure A4- 2- Hysteresis Model for Exterior Shear Key, After Megally et al., 2001
which II Δ and y V is the shear key to displacement and shear force at level II, respectively. Level
II represent to onset of yielding of the shear key reinforcement. The shear force at level II is
computed by:
III
II
II S C V V V
Δ
Δ
= + ( A4. 7)
where C V which is given by Eq ( A4. 2), is the concrete component to the shear resisting
mechanism. II Δ and III Δ are the shear keys top displacement at level II and III. The
displacement at top of the shear key at Level II is calculated by:
( )
2 2
2 ( )
h d
L L h d II y d a +
Δ = ε + + ( A4. 8)
where Ld is the reinforcement development length given by:
[ , ]
25 '
psi in
f
d f
L
c
b y
d = ( A4. 9)
where db is the bar diameter and La in Eq. ( A4. 8) is the cracked region and based on the test
observations this value is about the width of the stem wall, b. Level III is corresponding to the
- 33 -
peak load. Increase in width of the diagonal crack results in decreasing the contribution of
concrete to the shear key capacity. At this level the peak load is calculated by Eq ( A4. 1), and the
displacement at top of the key is computed by:
( )
s
L L h d III y d a
Δ = 2ε ( + ) + ( A4. 10)
where s is the reinforcement spacing in the stem wall. At the level III it is assumed that all the
rebars crossing the crack zone have been yielded. At the damage level IV the shear key capacity
is equal to the steel contribution to the resisting mechanism and concrete contribution is small
enough to be neglected. Thus, the capacity of the shear key is IV S V = V . It is assumed that the
degradation of the concrete contribution to the shear resisting mechanism occurs likely at a steel
strain of 0.005. Therefore, the displacement at this level is calculated by:
( )
s
L L h d IV d a
Δ = 2 ( + ) + 0.005 ε ( A4. 11)
Finally, level V represents fracture of reinforcement crossing the cracking zone. The capacity of
the shear key does not change from damage level IV since the shear key capacity is equal to just
steel contribution. Investigation on test results show that the steel strain at onset of fracture is
equal to approximately to 0.007. Thus, the displacement at top the shear key is computed by:
( )
s
L L h d V d a
Δ = 2 ( + ) + 0.007 ε ( A4. 12)
Test Unit 4A Test Units 4B
Load
kips( KN)
Displacement
in.( mm)
Load
kips( KN)
Displacement
in.( mm)
LEVEL I 89.40( 397.7) 0.060( 1.52) 71.55( 318.3) 0.052( 1.32)
LEVEL II 233.8( 1,040) 0.157( 3.99) 215.1( 956.8) 0.157( 3.99)
LEVEL III 315.7( 1,404.3) 1.30( 33.02) 297( 1,321.1) 1.30( 33.02)
LEVEL IV 222.5( 989.7) 2.66( 67.56) 203.8( 906.5) 2.66( 67.56)
LEVEL V 222.5( 989.7) 3.72( 94.49) 203.8( 906.5) 3.72( 94.49)
Table A4- 3: Calculated Load and Displacement of Test Series IV at Each Damage Level
- 34 -
Table A4- 3 shows the calculated load and displacement at each level for Test series IV.
10.1.2 Horizontal Reinforcement Strain Profiles
Figures A4- 3 to A4- 18 show the horizontal profiles of strains in the two layers of horizontal
reinforcement ( hanger bars) nearest to the top surface of the abutment stem wall in Unit 4A and
Unit 4B. The high strain after level 3 shows the agreement with the crack pattern in test 4A and
4B, which indicates significant diagonal cracking in the abutment stem wall started from the toe
of the shear key.
0
5000
10000
15000
20000
25000
5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B C D E
B C D E
Layer x
Line 1
Figure A4- 3- Horizontal Strain Profiles, Layer x, Line 1, Unit 4A
- 5000
0
5000
10000
15000
20000
25000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C D E
A A B C D E
Layer x
Line 2
- 35 -
Figure A4- 4- Horizontal Strain Profiles, Layer x, Line 2, Unit 4A
- 5000
0
5000
10000
15000
20000
25000
30000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
C
E
A A C E
Layer x
Line 3
Figure A4- 5- Horizontal Strain Profiles, Layer x, Line 3, Unit 4A
0
5000
10000
15000
20000
25000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
C E
A
A C E
Layer x
Line
Figure A4- 6- Horizontal Strain Profiles, Layer x, Line 4, Unit 4A
- 36 -
- 5000
0
5000
10000
15000
20000
25000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Distance from End of Hanger Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B C D
E
A A B C D E
Layer y
Line 1
Figure A4- 7- Horizontal Strain Profiles, Layer y, Line 1, Unit 4A
- 5000
0
5000
10000
15000
20000
25000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Distance from End of Hanger Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C D E
A
A B C D E
Layer y
Line 2
Figure A4- 8- Horizontal Strain Profiles, Layer y, Line 2, Unit 4A
- 37 -
- 5000
0
5000
10000
15000
20000
25000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Distance from End of Hanger Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
C E
A
A C E
Layer y
Line 3
Figure A4- 9- Horizontal Strain Profiles, Layer y, Line 3 Unit 4A
0
5000
10000
15000
20000
25000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Distance from End of Hanger Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
C E
A
A C E
Layer y
Line 4
Figure A4- 10- Horizontal Strain Profiles, Layer y, Line 4, Unit 4A
- 38 -
0
500
1000
1500
2000
2500
3000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
D
E
A
A B C D E
Layer x
Line 1
Figure A4- 11- Horizontal Strain Profiles, Layer x, Line 1, Unit 4B
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
Level 1 level 2 level 3
B
C
D
A E A B C D E
Layer x
Line 2
Figure A4- 12- Horizontal Strain Profiles, Layer x, Line 2, Unit 4B
- 39 -
- 500
0
500
1000
1500
2000
2500
3000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
level 1 level 2 level 3
C
E
A
A C E
Layer x
Line 3
Figure A4- 13- Horizontal Strain Profiles, Layer x, Line 3, Unit 4B
0
500
1000
1500
2000
2500
3000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
C
E
A
Layer x
Line 4
A C E
Figure A4- 14- Horizontal Strain Profiles, Layer x, Line 4, Unit 4B
- 40 -
0
500
1000
1500
2000
2500
3000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
level 1 Level 2 level 3 level 4
B
C
A D E A B C D E
Layer y
Line 1
Figure A4- 15- Horizontal Strain Profiles, Layer y, Line 1, Unit 4B
0
500
1000
1500
2000
2500
3000
3500
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4
B
C
D
A E
Layer y
Line 2
A B C D E
Figure A4- 16- Horizontal Strain Profiles, Layer y, Line 2, Unit 4B
- 41 -
0
500
1000
1500
2000
2500
3000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
level 1 level 2 level 3
C
E
A
A C E
Layer y
Line 3
Figure A4- 17- Horizontal Strain Profiles, Layer y, Line 3, Unit 4B
- 500
0
500
1000
1500
2000
2500
3000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Distance from End of Hanger Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
C
E
A A C E
Layer y
Line 4
Figure A4- 18- Horizontal Strain Profiles, Layer y, Line 4, Unit 4B
- 42 -
10.1.3 Vertical Reinforcement Strain Profiles
Figures A4- 19 to A4- 26 show the vertical strain profiles of the U shape reinforcing bars of the
shear keys. Figures A4- 19, A4- 20, A4- 23, and A4- 24 show a very high strain in the vertical bars
nearest the toe of the shear key. However the strain gages far from the toe of the shear key had a
very low strain which is indicating that the crack started from the toe of the shear key and grew
diagonally to the toe of the stem wall. The strain profiles along “ y” direction show the agreement
with the crack pattern observed in Test Unit 4A and 4B.
- 1000
0
1000
2000
3000
4000
5000
6000
0 5 10 15 20 25 30 35
Distance from Toe of the Shear Key, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
A C
D
F
Layer x
Line 1
A C D F
Figure A4- 19- Vertical Strain Profiles, Layer x, Line 1, Unit 4A
- 500
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
Distance from Toe of the Shear Key, inch
Strain ( με) Level 1 Level 2 Level 3 Level 4 Level 5
B C
D E
F
A
Layer x
Line 2
A B C DE F
Figure A4- 20- Vertical Strain Profiles, Layer x, Line 2, Unit 4A
- 43 -
- 2000
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
5 10 15 20 25 30 35 40 45 50
Diagonal Distance from Toe of the Wall, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
E F
D
B
C
A
Layer y
Line 1
A B C DE F
Figure A4- 21- Vertical Strain Profiles, Layer y, Line 1, Unit 4A
- 2000
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
5 10 15 20 25 30 35 40 45 50
Diagonal Distance from Toe of the Wall, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
A
B
C
D
F
Layer y
Line 2
A BC DE F
E
Figure A4- 22- Vertical Strain Profiles, Layer y, Line 2, Unit 4A
- 44 -
- 5000
0
5000
10000
15000
20000
25000
5 10 15 20 25 30
Distance from End of Shear Key, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B C
D E
A
F Layer x
Line 1
A B C DE F
Figure A4- 23- Vertical Strain Profiles, Layer x, Line 1, Unit 4B
- 5000
0
5000
10000
15000
20000
25000
5 10 15 20 25 30
Distance from End of Shear Key, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
A B C D E
F Layer x
Line 2
A B C DE F
Figure A4- 24- Vertical Strain Profiles, Layer x, Line 2, Unit 4B
- 45 -
- 5000
0
5000
10000
15000
20000
25000
5 10 15 20 25 30 35 40 45 50 55
Diagonal Distance from Bottom Corner of Wall, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
D E
A
F
Layer y
Line 1
A B C DE F
Figure A4- 25- Vertical Strain Profiles, Layer y, Line 1, Unit 4B
- 5000
0
5000
10000
15000
20000
25000
5 10 15 20 25 30 35 40 45
Diagonal Distance from Bottom Corner of Wall, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B C
D
E
A
Layer y
Line 2
A BC DE
Figure A4- 26- Vertical Strain Profiles, Layer y, Line 2, Unit 4B
10.1.4 Shear friction capacity model proposed by Mattock
Mattock proposed model ( Mattock, 1974) includes a cohesion term in shear friction evaluation.
From a physical point of view, his model corresponds to a crack model where the crack is
characterized by a general roughness and a local roughness. The local shearing off of a
roughness surface is considered in cohesion term of his model which is given by:
- 46 -
400 0.8( ) s v y n v = + ρ f + σ ( psi) ( A4. 13)
where n σ is the externally applied compressive stress perpendicular to the crack. The calculated
capacity of exterior shear key Test Units 4A and 4B, using Mattock model is summarized in
Table A4- 4. For this experimental units, b= 16.75 in. ( 425.5 mm) and d= 24 in. ( 610 mm). It can
be noticed that the concrete strength is not included in Mattock model. It has been shown that in
reality the transmission of forces across a crack takes place at areas between aggregate particles
( Walraven et al., 1987). Therefore strength of concrete should play an important role in
developing shear capacity. Walraven et al. ( 1987) proposed a model considering the concrete
strength which is presented in the following section.
Test
Unit
As
in2.
( mm2)
ρv fy
ksi
( MPa)
bd
v
V = s
kips ( KN)
4A 4.4
( 2,839) .011 61.1
( 421.3)
375.87
( 1,672)
4B 2.64
( 1,703) .007 61.1
( 421.3)
289.84
( 1,289)
10.1.5 Capacity Evaluation of Exterior Shear Key with Shear Friction Capacity Model
Proposed by Walraven et al. ( 1987)
Walraven et al. ( 1987)’ s proposed shear friction equations to determine the shear capacity of
reinforced concrete were used to reevaluate the capacity of exterior shear keys. This model takes
into consideration the influence of concrete strength as a basic parameter. The proposed equation
is given by:
( 0.007 ) 4 , 3
C
u th v y v = C ρ f ( psi) ( A4. 14)
Table A4- 4: Capacity Evaluation of Exterior Shear key Test Units 4A and 4B with
Mattock Equation
- 47 -
where for psi units:
where cc f ′ is the concrete compressive strength of 5.9 in. ( 150 mm) cubes. cc f ′ can be assumed as
a
0.85
'
c f . The calculated capacity of exterior shear key Test Units 4A and 4B are summarized in
Table A4- 5 ( b= 16.75 in. ( 425.5 mm) and d= 24 in. ( 610 mm)).
10.1.6 Capacity Evaluation of Exterior Shear Key with Caltrans Sliding Shear Friction
Model
According to Caltrans Bridge Design Specifications ( Caltrans, 1993a) the shear key capacity
shall be computed by:
where μ is the coefficient of friction and shall be taken as 1.4λ for concrete placed
monolithically such as in Test Unit 4A. As indicated in Caltrans Design Specifications ( Caltrans,
1993a) the coefficient of friction, μ, is considered as 1.0λ at the interface between two concretes
cast at different times, such as in Test Unit 4B. λ shall be taken as 1.0 for normal- weight
concrete. Avf and fyf are the area and the yield strength of the vertical shear reinforcement
0.30
4
0.406
3
0.0353
15.686
cc
cc
C f
C f
= ′
= ′
( A4. 15)
Test
Unit
As
in2. ( mm2)
ρv fy
ksi
( MPa)
f’c
psi
( MPa)
f’cc
psi
( MPa)
C3
C4
bd
v
V s 0.82 =
kips ( kN)
4A 4.4
( 2,839) .011 61.1
( 421.3)
5780
( 39.8)
6800
( 46.5) 564.3 0.498 410. 44
( 1,825.7)
4B 2.64
( 1,703) .007 61.1
( 421.3)
5780
( 39.8)
6800
( 46.5) 564.3 0.498 311.22
( 1,384.4)
Table A4- 5: Capacity Evaluation of Exterior Shear key Test Units 4A and 4B with
Walraven et al.( 1987)’ s Equations
( ) vf yf vs ys V = μ A f + A f ( A4. 16)
- 48 -
crossing the shear key- abutment stem wall interface, respectively. In Eq ( A4. 16) Avs and fys are,
respectively, the area and the yield strength of the vertical reinforcement on the sides of the
abutment back and wing walls crossing the shear key- abutment stem wall interface. Table A4- 6
summarized the calculation to evaluate the capacity of the exterior shear key Test Unit 4A and
4B. The capacity of the exterior shear key specimens was considered with and without the side
Reinforcement steel which are for temperature control.
Vertical Steel
Area Crossing
Interface of
Shear Key &
Wall
Vertical Steel
Area of the Side
Reinforcement
Crossing the
Interface of
Shear Key & Wall
VS
Steel Contribution
to Shear Key
Capacity
kips ( KN)
Eq. ( 1.3)
Test
Series
Test
Unit
No.
of
Bars
Avf
in2.
( mm2)
No.
of
Bars
Avf ( add)
in2. ( mm2)
Including
Avf ( add)
Without
Avf ( add)
4A 24# 3 2.64
( 1,703) 16# 3 1.76
( 1,135)
375.8
( 1,672)
225.5
( 1,003)
IV
4B 24# 3 2.64
( 1,703)
161.3
( 717.5)
161.3
( 717.5)
10.2 Evaluation of the Capacity of the Test Series V
After observed failure in test series IV, test series V was designed with substantially different
amount and configuration of steel reinforcement. In following, the capacity of exterior shear key
was evaluated using three different models.
10.2.1 Strut- and- Tie Model:
Strut- and- tie model is considered as a very appropriate basis for the design of reinforced concrete
loaded in shear by researchers and practitioners. Since the exterior shear key should act as fuse
element by shear sliding under later seismic load during the earthquake, it was proposed to use
this analogy. The design criteria in designing of sacrificial shear keys are ( 1) to have shear
Table A4- 6: Capacity Evaluation of Exterior Shear key Test Units 4A and 4B with Caltrans
Sliding Shear Friction Equation
- 49 -
sliding failure at the shear key- abutment stem wall interface, ( 2) to determine amount of vertical
shear key reinforcement and horizontal steel ties close to surface of the stem wall. The developed
model which illustrates the path of transferred load is shown in Figures A4- 27 and A4- 28.
8"
2.5"
10.9"
5.5" 9" 10"
4.25"
31.4" 31.4" 7.3"
75.5 k V ( V= 75.5 k)
A
B
C
E
F H
D G I K
J
31.5 k 31.5 k 31.5 k
69.6 k 34.8 k
34.8 k
31.5 k
5.8 k 34.8 k
47 k
47 k
45.8 k
113 k
6.1 k
26.3 k
65.5 k
10"
103 k
84 k
α γ γ
θ
β
γ
δ
ζ
θ= 48.1 α= 43.4
γ= 42.1 β= 62.2
δ= 62.8 ζ= 83.4
31.5 k
Figure A4- 27- Strut- and- Tie Model for Exterior Shear Key Unit 5A
δ= 88.1 ζ= 72.2
θ= 46.5 α= 55.8
γ= 40.6 β= 35.9
A
B
C
E
G
D
H F
K I
J
6.9" 5.1"
4.4"
3.3"
10.1"
5.6" 32.2" 32.2" 14" 5.9" 6.1"
33 k
50.7 k
38.5 k 76.9 k
33 k 33 k
50.7 k
56.3 k
11.5 k
22.1 k
74.9 k
115.9 k
79.8 k
84 k
122.6 k
38.5 k 38.5 k 2.75 k
33 k
V ( V= 79.8 k)
α
θ
ζ δ
γ β
Figure A4- 28- Strut- and- Tie Model for Exterior Shear Key Unit 5B
- 50 -
Solid Lines represent struts, the compression members of a strut- and- tie model and dot lines are
the tension members of a strut- and- tie model. The capacity of shear key Unit 5A and 5B was
calculated as 75.5 kips and 79.8 kips, respectively. After solving for the truss members,
reinforcing steel was selected to provide the necessary tie capacity. Fourteen # 4 headed bars
were used horizontally close to the top surface of the abutment stem wall. In Test Unit 5A, the
foam with an 8” x8” hole at center was used at interface of the shear key and the wall. There was
a rough construction joint between the shear key and the wall at the location of the hole and a
smooth construction joint between the foam and the wall. All shear key vertical reinforcing bars
are lumped at one location close to the side of the hole, which is closer to the inclined face of the
shear key. In Test Unit 5B, there was a smooth construction joint between the shear key and the
wall. A bond breaker is applied at interface to create a weak plane of failure. All shear key
vertical reinforcing bars are lumped at one location near the centerline of the shear key. Four # 4
bars were used as the shear key vertical reinforcement.
Table A4- 7 shows the observed load and displacement of test series V at five damage levels as
described in section 10.1.1. The failure mode in series V was shear sliding, the equations
described in section 10.1.1 for prediction the load and displacement for each level cannot be
applied.
Test Unit 5A Test Units 5B
Load
kips( KN)
Displacement
in.( mm)
Load
kips( KN)
Displacement
in.( mm)
LEVEL I 9.20( 40.9) 0.004( 0.1) 9.6( 40.9) 0.002( 0.05)
LEVEL II 130.3( 579.5) 0.14( 3.5) 37.2( 165.6) 0.32( 8.2)
LEVEL III 123.7( 550.4) 1.50( 38.2) 75.1( 333.9) 1.40( 35.6)
LEVEL IV 35.9( 159.5) 1.70( 42.8) 29.3( 130.3) 1.60( 40.4)
LEVEL V 35.4( 157.6) 1.80( 45.4) 32.1( 142.8) 1.70( 44.3)
Table A4- 7: Calculated Load and Displacement of Test Series V at Each Damage Level
10.2.2 Horizontal Reinforcement Strain Profiles
Figures A4- 29 to A4- 56 show the horizontal strain profiles in the two layers of horizontal
reinforcement ( headed bars) close to the top surface of the abutment stem wall in Unit 5A and
- 51 -
Unit 5B. The strain profiles in these figures had a good agreement with the crack pattern in test
5A and 5B, which indicates shear sliding occurred initiated from the toe of the shear key.
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30 35 40 45 50 55
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B C D E
A
F
Layer 1
A B C D E F
Line 1
Figure A4- 29- Horizontal Strain Profiles, Layer 1, Line 1, Unit 5A
y ( )
- 200
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30 35 40 45 50 55
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
D E
A F
Layer 1
Line 2
A B C D E F
Figure A4- 30- Horizontal Strain Profiles, Layer 1, Line 2, Unit 5A
- 52 -
- 200
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30 35 40 45 50 55
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C D E
A
F Layer 1
Line 3
A B C D E F
Figure A4- 31- Horizontal Strain Profiles, Layer 1, Line 3, Unit 5A
, y , ( )
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30 35 40 45 50 55
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
E
A
F
Layer 1
Line 3
A B CD E F
Figure A4- 32- Horizontal Strain Profiles, Layer 1, Line 4, Unit 5A
- 53 -
0
200
400
600
800
1000
1200
10 15 20 25 30 35 40
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
C
E
Layer 1
C E
Line 5
Figure A4- 33- Horizontal Strain Profiles, Layer 1, Line 5, Unit 5A
0
200
400
600
800
1000
1200
5 10 15 20 25 30 35 40 45
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
E
Layer 1
BC E
Line 6
Figure A4- 34- Horizontal Strain Profiles, Layer 1, Line 6, Unit 5A
- 54 -
0
200
400
600
800
1000
1200
1400
5 10 15 20 25 30 35 40 45
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
E
Layer 1
B C E
Line 7
Figure A4- 35- Horizontal Strain Profiles, Layer 1, Line 7, Unit 5A
, y , ( )
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 5 10 15 20 25 30 35 40 45 50 55
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B D
E
A F
Layer 2
AB DE F
Line 1
Figure A4- 36- Horizontal Strain Profiles, Layer 2, Line 1, Unit 5A
- 55 -
- 200
0
200
400
600
800
1000
1200
1400
1600
0 5 10 15 20 25 30 35 40 45 50
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
D E
A
Layer 2
AB C D E
Line 2
Figure A4- 37- Horizontal Strain Profiles, Layer 2, Line 2, Unit 5A
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 10 20 30 40 50
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
D
E
A F
Layer 2
AB C D E
Line 2
Figure A4- 38- Horizontal Strain Profiles, Layer 2, Line 3, Unit 5A
- 56 -
0
500
1000
1500
2000
2500
0 10 20 30 40 50
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
D
E
A F
Layer 2
ABC D E F
Line 4
Figure A4- 39- Horizontal Strain Profiles, Layer 2, Line 4, Unit 5A
0
200
400
600
800
1000
1200
1400
1600
1800
2000
5 10 15 20 25 30 35 40 45
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
E Layer 2
C E
Line 5
B
Figure A4- 40- Horizontal Strain Profiles, Layer 2, Line 5, Unit 5A
- 57 -
0
200
400
600
800
1000
1200
1400
1600
5 10 15 20 25 30 35 40 45
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B C
E
Layer 2
B C E
Line 6
Figure A4- 41- Horizontal Strain Profiles, Layer 2, Line 6, Unit 5A
0
200
400
600
800
1000
1200
1400
5 10 15 20 25 30 35 40 45
Distance from End of Headed Bar, inch
Strain ( με)
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
E
Layer 2
B C E
Line 7
Figure A4- 42- Horizontal Strain Profiles, Layer 2, Line 7, Unit 5A
- 58 -
, y , ( )
0
100
200
300
400
500
600
0 5 10 15 20 25 30 35 40
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
D E
A
Layer 1
AB C D E
Line 1
Figure A4- 43- Horizontal Strain Profiles, Layer 1, Line 1, Unit 5B
0
100
200
300
400
500
600
700
0 5 10 15 20 25 30 35 40 45 50
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
E
A
F
Layer 1
AB C E F
Line 2
Figure A4- 44- Horizontal Strain Profiles, Layer 1, Line 2, Unit 5B
- 59 -
0
100
200
300
400
500
600
700
800
900
0 5 10 15 20 25 30 35 40 45 50
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
D
E F
Layer 1
B C D E F
Line 3
Figure A4- 45- Horizontal Strain Profiles, Layer 1, Line 3, Unit 5B
- 200
- 100
0
100
200
300
400
500
600
700
800
0 5 10 15 20 25 30 35 40 45 50
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
D
A
F
Layer 1
AB C D F
Line 4
Figure A4- 46- Horizontal Strain Profiles, Layer 1, Line 4, Unit 5B
- 60 -
0
100
200
300
400
500
600
700
800
900
0 5 10 15 20 25
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
Layer 1
B C
Line 5
Figure A4- 47- Horizontal Strain Profiles, Layer 1, Line 5, Unit 5B
0
100
200
300
400
500
600
700
800
900
0 5 10 15 20 25
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
Layer 1
B C
Line 6
Figure A4- 48- Horizontal Strain Profiles, Layer 1, Line 6, Unit 5B
- 61 -
0
100
200
300
400
500
600
0 5 10 15 20 25 30 35 40 45 50
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
E
Layer 1
B C E
Line 7
Figure A4- 49- Horizontal Strain Profiles, Layer 1, Line 7, Unit 5B
0
100
200
300
400
500
600
0 5 10 15 20 25 30 35 40 45 50
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
C
D
A
F
Layer 2
A CD F
Line 1
Figure A4- 50- Horizontal Strain Profiles, Layer 2, Line 1, Unit 5B
- 62 -
- 200
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30 35 40 45 50
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
D
E
A
F
Layer 2
AB C D E F
Line 2
Figure A4- 51- Horizontal Strain Profiles, Layer 2, Line 2, Unit 5B
0
100
200
300
400
500
600
700
800
0 5 10 15 20 25 30 35 40 45 50
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
D
E
A
F
Layer 2
AB C D E F
Line 3
Figure A4- 52- Horizontal Strain Profiles, Layer 2, Line 3, Unit 5B
- 63 -
0
100
200
300
400
500
600
700
800
900
0 5 10 15 20 25 30 35 40 45 50
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
D
E
A
F
Layer 2
AB C D E F
Line 4
Figure A4- 53- Horizontal Strain Profiles, Layer 2, Line 4, Unit 5B
0
100
200
300
400
500
600
700
800
0 5 10 15 20 25 30 35 40 45
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
E
Layer 2
B C E
Line 5
Figure A4- 54- Horizontal Strain Profiles, Layer 2, Line 5, Unit 5B
- 64 -
0
100
200
300
400
500
600
700
800
900
1000
0 5 10 15 20 25 30 35 40 45
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B
C
E
Layer 2
B C E
Line 6
Figure A4- 55- Horizontal Strain Profiles, Layer 2, Line 6, Unit 5B
0
100
200
300
400
500
600
700
0 5 10 15 20 25 30 35 40 45
Distance from End of Headed Bar, inch
Strain ( με)
level 1 level 2 level 3 level 4 level 5
B C
E
Layer 2
B C E
Line 7
Figure A4- 56- Horizontal Strain Profiles, Layer 2, Line 7, Unit 5B
- 65 -
10.2.3 Vertical Reinforcement Strain Profiles
Figures A4- 57 to A4- 64 show the vertical profiles of the “ L” shape vertical reinforcing bars of
the shear keys Test Units 5A and 5B. A very high strain in gages located at the interface of shear
key- stem wall is indicating that the crack started from the toe of the shear key and grew
horizontally through the interface of the shear key- stem wall.
0
10
20
30
40
50
60
- 10000 10000 30000 50000 70000 90000 110000 130000
Strain ( με)
Distance from Bottom of Bar, inch
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
D
E
A
F Layer 1
AB
CDEF
Figure A4- 57- Vertical Strain Profiles, Layer 1, Unit 5A
0
10
20
30
40
50
60
- 10000 10000 30000 50000 70000 90000 110000 130000
Strain ( με)
Distance from Bottom of Bar, inch
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
D
E
A
F
Layer 2
AB
CDEF
Figure A4- 58- Vertical Strain Profiles, Layer 2, Unit 5A
- 66 -
0
10
20
30
40
50
60
- 2500 2500 7500 12500 17500 22500
Strain ( με)
Distance from Bottom of Bar, inch
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
D
E
A
F
Layer 3
AB
CDEF
Figure A4- 59- Vertical Strain Profiles, Layer 3, Unit 5A
0
10
20
30
40
50
60
0 20000 40000 60000 80000 100000 120000
Strain ( με)
Distance from Bottom of Bar, inch
Level 1 Level 2 Level 3 Level 4 Level 5
B
C
D
E
A
F
Layer 4 AB
CDEF
Figure A4- 60- Vertical Strain Profiles, Layer 4, Unit 5A
- 67 -
- 30
- 25
- 20
- 15
- 10
- 5
0
5
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Strain ( με)
Distance from Bottom of Bar, inch
Level 1 level 2 level 3 level 4 level 5
B
C
D
E
F
Layer 1
B
CDEF
Figure A4- 61- Vertical Strain Profiles, Layer 1, Unit 5B
- 30
- 25
- 20
- 15
- 10
- 5
0
5
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Strain ( με)
Distance from Bottom of Bar, inch
level 1 level 2 level 3 level 4 level 5
B
C
D
E
A
F
Layer 2
AB
CDEF
Figure A4- 62- Vertical Strain Profiles, Layer 2, Unit 5B
- 68 -
- 30
- 25
- 20
- 15
- 10
- 5
0
5
- 1000 1000 3000 5000 7000 9000 11000 13000 15000 17000 19000
Strain ( με)
Distance from Bottom of Bar, inch
level 1 level 2 level 3 level 4 level 5
B
C
D
E
A
F
Layer 3
AB
CDEF
Figure A4- 63- Vertical Strain Profiles, Layer 3, Unit 5B
- 25
- 20
- 15
- 10
- 5
0
5
10
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Strain ( με)
Distance from Bottom of Bar, inch
level 1 level 2 level 3 level 4 level 5
B
C
D
E
A
Layer 4 AB
CDE
Figure A4- 64- Vertical Strain Profiles, Layer 4, Unit 5B
10.2.4 Shear friction capacity model proposed by Mattock, 1974
This model is used to calculate the shear capacity of test units 5A and 5B. According to section
10.1.4 ( Eq. ( A4.13)), the shear capacity of the Test Unit 5A and 5B are calculated and shown in
Table A4- 8.
- 69 -
Test
Unit
As
in2.
( mm2)
ρv fy
ksi
( MPa)
bd
v
V = s
kips ( KN)
5A 0.8
( 516) 0.002 63
( 434.4)
40.9
( 182)
5B 0.8
( 516) 0.002 63
( 434.4)
40.9
( 182)
Test Unit 5A had the shear key- stem wall interface with rough and smooth surface area.
However, the Mattock equation, Eq. ( A4.13), does not take into account the situations with
different surface conditions. In his proposed model, the coefficient of friction is assumed equal to
one for the area with general roughness. In Test Unit 5B, the effect of smooth concrete surface
on contact area was disregarded.
10.2.5 Capacity Evaluation of Exterior Shear Key with Shear Friction Capacity Model
Proposed by Walraven et al. ( 1987)
Walraven et al. ( 1987)’ s proposed shear friction equations to determine the shear capacity of
reinforced concrete were used to reevaluate the capacity of exterior shear keys Series V. As
mentioned in previous section, this model also does not consider the different concrete contact
surface area. In his model the contact surface area of concrete was assumed to be rough. The
calculated shear capacity of test specimen, using Eq. ( A4.14) and Eq. ( A4.15), is given in Table
A4- 9.
Table A4- 8: Capacity Evaluation of Exterior Shear key Test Units 5A and 5B with
Mattock Equation
- 70 -
Test
Unit
As
in2.
( mm2)
ρv fy
ksi
( MPa)
f’c
psi
( MPa)
f’cc
psi
( MPa)
C3
C4
V v bd s = 0.82
kips ( KN)
5A 0.8
( 516) 0.0125 63
( 434.4)
4870
( 33.6)
5729
( 39.5) 526.4 0.47 198.7
( 884)
5B 0.8
( 516) 0.002 63
( 434.4)
4870
( 33.6)
5729
( 39.5) 526.4 0.47 192.1
( 855)
Table A4- 9: Capacity Evaluation of Exterior Shear key Test Units 5A and 5B with
Walraven et al. ( 1987)’ s Equations
- 71 -
11 Appendix A- 5
11.1 Geometry and Reinforcement Details of Test Series IV
All test specimens were designed at a 2/ 5- scale with respect to a prototype abutment design
provided by Caltrans. Figure A5- 1 illustrates the elevation view of the test setup of Test Series
IV. The simulated lateral load was applied to test units, by means of two servo- controlled. A
hold- down frame was used to prevent any upward movement of the loading arm.
The foundation was post- tensioned to the strong floor by using ten tie- down bars in two rows on
the sides of the shear key specimens. One central tie- down bar, at top of the stem wall was post-tensioned
to the strong floor to simulate the vertical load corresponding to the weight of the
bridge superstructure. The post- tensioned force at each bar was 150 kips ( 667 KN). In Test Unit
4- A, the shear key was built monolithically with the abutment stem wall, whereas the Test Unit
4- B was built with a rough construction joint between the shear key and the wall.
Reinforcement Layout:
Caltrans provided the main part of these specimens’ design. The reinforcement amount and
distribution were scaled down to % 40 to match a regularly used in abutment design, provided by
Caltrans. Based on that design, eight # 4 hanger bars were used horizontally in two rows close to
the top surface of the abutment stem wall. In test series IV, the U shape shear reinforcement
consisted of 4 rows each of 6-# 3 bars which were extended to the foundation block. The
horizontal and vertical reinforcement on the sides of the shear key and abutment wall were
placed at 4.75 in. ( 121 mm) spacing with # 3 bars. The vertical side reinforcement in Test Unit
4B stopped below the shear key- abutment stem wall interface. Figure A5- 1 to A5- 3 show the
schematic of the specimen reinforcement details at different cross sections.
- 72 -
Figure A5- 1- Elevation View of the Reinforcement Layout- Test Series IV
Figure A5- 2- Reinforcement Layout ( Section A- A)- Test Series IV
7"
( 178.3 mm)
24" ( 0.61 m)
24" ( 610 mm) 30 1/ 2" ( 0.77 m) 18" ( 457 mm)
. ( 229 mm)
9"
1" ( 25.4 mm)
clearance
15"
( 381 mm)
4-# 3
4-# 3
8 - # 4
# 3 @ 4 3/ 4" ( 121 mm)
1" ( 25.4 mm)
12 - # 5
12 - # 5
Clearance
B A
# 3 @ 4 3/ 4"
( 121 mm)
4-# 3
# 5 Stirrups
3/ 4"
Rough Construction Joint
4 - # 3
5 - # 3
4 - # 3
16 - # 3
6 - # 3 1" ( 25.4 mm)
6 - # 3
. 48" ( 1.22m)
# 3
4 - # 3
114" ( 2896 mm)
4-# 3
17"
( 0.432 m)
16 3/ 4"
( 425 mm)
72 1/ 2"
( 1842 mm )
18" ( 475 mm)
15"( 381 mm)
# 3 @ 4 3/ 4" ( 121 mm)
# 3 @ 4 3/ 4" ( 121 mm)
4 - # 3
4 - # 3
1" ( 25.4 mm)
Clearance
12 - # 5
12 - # 5
54 1/ 2" ( 1.38 m)
24 5/ 8"
( 625 mm)
24 5/ 8"
( 625 mm)
8 - # 4
( Two Layers)
- 73 -
11.2 Geometry and Reinforcement Details of Test Series V
In all previous shear key test units, except test series III, significant damage of the abutment stem
wall could not be prevented. However it was shown in test series III, increasing the amount of
tension tie reinforcement in the abutment stem wall can control damage of the abutment stem
wall. The shear key in Test Unit 5A was separated from the abutment stem wall by foam, except
for a central interface area of 8in. x 8in. ( 203mm x 203mm). In both test Units 5A and 5B, the
abutment stem wall surface had smooth finish. Concrete surface of the abutment wall surface at
the location of the hole had a rough finish. The 0.5” ( 12.7 mm) thick foam with an 8 in. ( 203
mm) square central hole was placed at the center of shear key- abutment interface area in Test
Unit 5A. The smooth shear key- abutment stem wall interface was painted by a bond breaking
material before casting the shear key on top it in Test Unit 5B to create a weak plane of failure.
Reinforcement Layout:
Based on strut- and- tie model, fourteen # 4 headed bars were used horizontally close to the top
surface of the abutment stem wall. The headed bars provide mechanical anchorage at ends of the
Figure A5- 3- Reinforcement Layout ( Section B- B)- Test Series IV
16 3/ 4"
( 425 mm)
72 1/ 2"
( 1842 mm )
18"
( 475 mm)
24"
30 1/ 2"
( 610 mm)
( 775 mm)
# 3 @ 4 3/ 4" ( 121 mm)
Construction Joint
3/ 4"
( 0.75 mm)
# 3 @ 4 3/ 4" ( 121 mm)
3/ 4" ( 19.1 mm) Concrete Cover
8-# 4 ( Two Layer)
# 5 Stirrups # 5 Stirrups
12- # 5 ( Top
& Bottom)
1" ( 25.4 mm) Concrete Cover
66" ( 1676 mm)
5 3/ 8"
# 3 @ 4 3/ 4" ( 121 mm)
15"
4 - # 3
- 74 -
bars, which makes it possible for the bars to develop their full yield strength close to the welded
ends. All shear key vertical reinforcing bars are lumped at one location close to the side of the
hole that is closer to the inclined face of the shear key in Test Unit 5A while all shear key
vertical reinforcing bars are lumped at one location near the centerline of the shear key in Test
Unit 5B. Figure A5- 4 illustrates the elevation view of the test setup of Test Series V. Figure A5- 4
to A5- 7 show the schematic of the specimen reinforcement details at different cross sections.
Figure A5- 4- Elevation View of the Reinforcement Layout- Test Series V
Figure A5- 5- Reinforcement Layout ( Section C- C)- Test Series V
Headed Bars
# 3
3/ 4" ( 19.1 mm) clearance Headed Bras
4-# 4
# 3 @ 4 3/ 4" ( 121 mm)
4-# 4 # 3 @ 4 3/ 4" ( 121 mm)
Rough Construction Joint
114" ( 2896 mm)
48" ( 1.22m)
3/ 4" ( 19.05 mm)
30 1/ 2" ( 0.77 m)
clearance
9"
( 229 mm)
18" ( 457 mm)
.
Foam( 1/ 2" thick)
21 - # 3
( 121 mm)
# 3 @ 4 3/ 4"
24" ( 610 mm)
6 - # 3
4 - # 3
6 - # 3 .
C
4 - # 4
# 3
A
# 3
4-# 3
7"
Clearance
1" ( 25.4 mm)
12 - # 5
12 - # 5
# 5 Stirrups
6 - # 3
24" ( 0.61 m)
Headed bars14 - # 4
4 - # 4
C
B
with Bond Breaker ( form oil)
Smooth Construction Joint
3/ 4" recess
clearance
3/ 4" ( 19.05 mm)
# 3 @ 4 3/ 4" ( 121 mm)
# 3
6 - # 3
4-# 3
17"
( 177.8 mm)
- 75 -
Figure A5- 6- Reinforcement Layout ( Section A- A)- Test Series V
Figure A5- 7- Reinforcement Layout ( Section B- B)- Test Series V
Concrete Cover
Concrete Cover
# 3
4-# 4
5 1/ 2"
5.0"
2 1/ 2"
1/ 2"
Rough Construction Joint
# 3 @ 4 3/ 4" ( 121 mm)
6"
66" ( 1676 mm)
1" ( 25.4 mm)
& Bottom)
12- # 5 ( Top
# 5 Stirrups # 5 Stirrups
14-# 4 ( Two Layer)
3/ 4" ( 19.1 mm)
# 3 @ 4 3/ 4" ( 121 mm)
Foam
# 3
( 775 mm)
( 610 mm)
30 1/ 2"
24"
( 475 mm)
18"
( 1842 mm )
72 1/ 2"
( 425 mm)
16 3/ 4"
2 1/ 2"
5 1/ 2"
Concrete Cover
Concrete Cover
4-# 4
# 3
5 1/ 2"
5.0"
2 1/ 2"
30 1/ 2"
24"
6.0"
# 3 @ 4 3/ 4" ( 121 mm)
66" ( 1676 mm)
1" ( 25.4 mm)
& Bottom)
12- # 5 ( Top
# 5 Stirrups # 5 Stirrups
14-# 4 ( Two Layer)
3/ 4" ( 19.1 mm)
# 3 @ 4 3/ 4" ( 121 mm)
Smooth Construction Joint
# 3
( 775 mm)
( 610 mm)
( 475 mm)
18"
( 1842 mm )
72 1/ 2"
( 425 mm)
16 3/ 4"
- 76 -
11.3 Instrumentation
External Instrumentation:
Linear potentiometers and inclinometer were attached to the test units to record displacement and
rotation of the exterior shear key specimens. Displacement transducers were placed at location of
expected large displacement or undesirable movement of the test units. These locations were
along the centerline of the key at top and the interface level. Figures A5- 8 and A5- 9 show the
potentiometers on test series IV and V, respectively.
3"
TM- A 61"
3"
3"
3"
LPB- A
TM- B LPWH- A
LPFV- A
LPT- A
LPFH- A
LPWV- A
LPB- B LPRH- A
LPWV- B
LPWH- B
LPFV- B
LPFH- B
LPRV- A
LPT- B
LPRV- B
LPRH- B
3"
TM- B 61"
3"
3"
3"
LPB- B
TM- A LPWH- B
LPFV- B
LPT- B
LPFH- B
LPWV- B
LPB- A LPRH- B
LPWV- A
LPWH- A
LPFV- A
LPFH- A
LPRV- B
LPT- A
LPRV- A
LPRH- A
Figure A5- 8- Labels of Displacement Transducers- Test Series IV
Figure A5- 9- Labels of Displacement Transducers- Test Series V
Unit 4B Unit 4A
Unit 5A Unit 5B
- 77 -
Internal Instrumentation:
Test units were instrumented with electrical resistance strain gauges. Most of the strain gauges
were mounted on the reinforcing steel of the test units close to the shear key- stem wall interface
and along the expected diagonal crack. The major locations of strain gauges for series IV and V
are shown in Figures A5- 10 to A5- 16.
4B 4A
E
D
C B A
A
B
C
D
E
A
B
C
D
E
E
D
A B C
1
2
1
2
Figure A5- 10- Labels of Strain Gages on U Shape Vertical Bars, in Diagonal Direction- Test
Series IV
- 78 -
E
A
B C
D
4B
D
B
C E F
F
B
D
C
E
C
4A
E
D
A
B
F
A
A
F
1
2
E F
D
C
A B
3 4
B A
C
D
F E
4
32
1
Figure A5- 11- Labels of Strain Gages on U Shape Vertical Bars, in Horizontal direction- Test
Series IV
1
4
4B
A B C D E
4A
1
4
E D C B A
2
3
x y
2
3
y x
Figure A5- 12- Labels of Strain Gages on Horizontal Hanger Bars- Test Series IV
- 79 -
Figure A5- 13- Location of Strain Gages on Horizontal and Vertical Bars- Test Series IV
F 42
E 35
D 34
C 29
B 28
A 21
Vertical Distance
from Bottom of
Strain
Gauge
A B C D E F
x
y
y
x
48.5
A B C D E
13
22
31
40
4
A B C D E
12
21
30
39
3
x y
- 80 -
F
D
C
B
A
F
E
D
C
B
A
E
1
2
3
4
1
2
3
4
Figure A5- 14- Labels of Strain Gages on Vertical Shear Key Reinforcement- Test Series V
A B C D E F F E D C B A
1
2
3
1
2
46 75 7 6
42
3
5
1
2
1
Figure A5- 15- Labels of Strain Gages on Horizontal Headed Bars- Test Series V
- 81 -
Figure A5- 16- Location of Strain Gages on Horizontal and Vertical Bars- Test Series V
F
A
B
C
D
E
20
27
35.1
45
48.5
52.75
E D C F
B A
4
8.8
14.5
32
20
26
a: 5A- 5B Vertical Shear Key Bars
b: 5A- 5B Horizontal Headed Bars
- 82 -
12 REFERENCES
American Concrete Institute ( ACI). ( 2005). Building Code Requirements for Structural Concrete ( ACI
318- 05) and Commentary ( ACI 318R- 05), Farmington Hills, MI.
Caltrans, Bridge Design Specifications, 1993a.
Caltrans, Bridge Memo to Designers Manual, Section 5, 1993b.
Crisafulli, F. J., Restrepo, J. I., Park, R. ( 2002). “ Seismic design of lightly reinforced precast concrete
rectangular wall panels.” PCI Journal, 47( 4), July- August, 104- 121.
Mattock, A. H. ( 1974). “ Shear transfer in concrete having reinforcement at an angle to the shear plane.”
Shear in Reinforced Concrete, ACI Special Publication 42, 17- 42.
Megally, S. H., Silva, P. F., and Seible, F., Seismic Response of Sacrificial Shear Keys in Bridge
Abutments, Structural Systems Research Report SSRP- 2001/ 23, Department of Structural
Engineering, University of California San Diego, La Jolla, CA, May 2001, 198 pp.
Priestley, M. J. N. and Seible, F., Calvi, G. M., Seismic Design and Retrofit of Bridges.
John Wiley & Sons, New York 1996.
Walraven, J. C., Frénay, J., Pruijssers, A. ( 1987). “ Influence of concrete strength and load history on the
shear friction capacity of concrete members.” PCI Journal, January- February, 66- 83.