Vulnerability Assessment of Arizona's Critical Infrastructure
9th International Conference on Short and Medium Span Bridges Calgary, Alberta, Canada, July 15-18, 2014
EXPERIMENTAL INVESTIGATION OF STEEL – REINFORCED PL-3 BRIDGE BARRIERS SUBJECTED TO TRANSVERSE STATIC LOADING Hamidreza Khederzadeh Ph.D Candidate, Ryerson University, Canada Khaled Sennah Professor, Ryerson University, Canada ABSTRACT Yield Line Theory of Analysis is used to design steel-reinforced bridge barrier walls in accordance with AAHSTOLRFD specifications (2012). Two yield-line patterns at interior and exterior locations are assumed based on the location of vehicle collision. On the basis of yield-line theory, triangular yield-line failure patterns develop at interior or exterior locations. However, the failure pattern observed in statically tested bridge barriers reinforced with GFRP bars as well as the actual steel-reinforced bridge barriers failed due to vehicle collision demonstrated a trapezoidal failure shape in the barrier walls. Thus, to further investigate this achievement, a full-scale PL-3 bridge barrier reinforced with conventional steel reinforcements was constructed at Texas Transportation Institution (TTI) site. The PL-3 barrier wall was tested under increasing monotonic loading to examine its failure pattern and ultimate load-carrying capacity. The PL-3 barrier had a geometry and barrier shape similar to the Standard PL-3 bridge barrier specified in Canadian Highway Bridge Design Code (CHDBC). The experimental test results confirmed the development of trapezoidal failure within the barrier wall. The ultimate flexural capacity of the barriers was found to be far greater than the limit specified in CHBDC. Furthermore, the barrier design was compared to the AASHTOLRFD design specifications based on yield-line theory and the results indicated additional capacity of the tested barrier walls.
1. INTRODUCTION Design of bridge barriers and bridge railings were required to meet the requirement for crash and safety in accordance with National Cooperative Highway Research Program (NCHRP) Report 350. The design forces for bridge rails specified in Canadian Highway Bridge Design Code (CSA, 2006a and CSA 2006b) is based on AASHTO-LRFD Guide Specification for Bridge Rails (AASHTO, 1989) that is corresponds to the test levels stipulated in NCHRP Report 350, "Recommended Procedures for the Safety Performance Evaluation of Highway Features" (Ross et al., 1993). Accordingly, Canadian Highway Bridge Design Code (CHBDC) requires that the suitability of bridge barrier anchorage system to the deck should be based on its performance during crash testing of the traffic barriers. The crash testing of the bridge barriers is carried out to investigate suitability of traffic barriers against structural adequacy, occupant risk and vehicle trajectory after the collision. CHDBC also specifies if crash testing of the traffic barriers is not available; the suitability of the traffic barriers shall be investigated based on the static test- to- complete collapse of the traffic barriers. However, the ultimate strength of traffic barriers tested under static load should be greater than the maximum transverse load limits specified in CHDBD, that is 357 kN for Performance Level 3 (PL-3). Ngan and Stiemer (2008) conducted an experimental program on the Performance Level 2 (PL-2) Precast Concrete Bridge Barriers reinforced with steel bars for the aim of investigating its structural behaviour and anchorage capacity in accordance with CHDBC. The test results proved that the precast concrete bridge barrier complied with the current code specifications in terms of strength and overall structural behaviour. The anchorage system of the tested barrier was sufficient as the failure occurred within the body of the barrier.
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However, the failure mode of the barrier was rather in trapezoidal shape compared to triangular shape stipulated in AASHTO - LRFD. Thus, based on the experimental investigation conducted by other researchers as well as the actual failure of the traffic barriers during vehicle crashes, an extensive study was performed herein on the failure mode and strength capacity of the traffic barriers on the basis of yield-line theory. The constructed PL-3 traffic barrier at Texas Transportation site was tested under monotonic static test to complete collapse and their failure mode and structural behaviour were investigated.
2. YIELD LINE THEORY OF ANALYSIS The design of conventional steel – reinforced bridge barriers is mainly based on AASHTO – LRFD Design Specifications (AASHTO, 2012) on the basis of yield – line theory of analysis. On this basis, it is assumed that yield – line develops within the barrier wall only and does not extend into the deck slab. If assumed that the yield – line penetrates into the deck slab, the AASHTO – LRFD yield – line procedure will not be valid. Thus, the deck slab should have sufficient strength to force the yield – line within the wall only. In addition, the AASHTO yield – line pattern is assumed to occur within certain longitudinal length of the barrier. As such, if sufficient longitudinal length of barrier is not provided the failure may be accompanied by one – way action failure by forming only longitudinal crack at deck – wall junction. The assumed yield – line pattern caused by vehicle crash that produce a force Ft over a longitudinal length Lt is shown in Figure 1. The yield – line equations were originally proposed by Hirsch (1978) and presented in AASHTO – LRFD. The equations can be derived by equating the external work due to the applied load to the internal load due to resisting plastic moments along the yield – line. The resisting plastic moments include the moment about the vertical axis due to longitudinal reinforcements, Mw, and the moment about horizontal axis due to transverse reinforcements, Mc. The angle of inclination of the yield – line can be expressed in terms of critical length, Lc. The applied force, Ft, can be minimized with respect to Lc to solve for the least value of this upper bound solution. By performing some algebraic solutions using principals of virtual work, the critical yield – line length, Lc, can be obtained. The following equations show the yield – line resistance forces and critical lengths at interior and exterior locations of the barrier wall.
Figure 1. AASHTO – LRFD yield line patterns at interior location (left) and exterior location(right).
The yield- line equations at a general region within the barrier length specified in AASHTO-LRFD as follow; 280-2
2
[1] L ci
Lt L 8HM b int M w int H) t 2 M c int 2
M L 2 2 8M b int 8M w int H c int ci [2] R wi H 2L ci L t
Where, Lci is critical length of interior yield line failure pattern, Lt is longitudinal length of distribution of impact force, Ft. H is height of barrier wall; Mbint is flexural resistance of the cap beam at interior location, Mwint is flexural resistance of the wall about its vertical axis at interior location, Mc. is the flexural resistance of the wall about a horizontal axis at interior location, and Rwi is total transverse resistance of the barrier wall at interior location. The critical barrier wall length at exterior location over which the yield line mechanism occurs can be taken as: 2
[3] L ce
M Lt M wendH) L t H bend 2 M cend 2
The nominal barrier wall resistance to transverse load at exterior location may be determined as:
2 [4] R we 2 L ce L t
M L 2 M bend M wendH cend ce H
Where: Lce is the critical length of exterior yield line failure pattern; Lt is longitudinal length of distribution of impact force, Ft; H is height of barrier wall; Mbend is flexural resistance of the cap beam at end region; Mwend is flexural resistance of the wall about its vertical axis at end region; Mcend. is the flexural resistance of the wall about a horizontal axis at end region; and Rwe is total transverse resistance of the barrier wall at end region.
3. EXPERIMENTAL INVESTIGATIONS 3.1 PL-3 Barrier Configurations The constructed PL-3 barrier had a geometry and barrier shape similar to the Standard PL-3 bridge barrier specified in CHDBC which is approved by Ministry of Transportation of Ontario (MTO- SS110-67 drawings). Figure 2 illustrates the tested PL-3 traffic barrier reinforced with conventional steel reinforcements. The proposed PL-3 barrier had an overall height of 1140 mm as per CHBDC recommendations. This is a minimum height specified in CHBDC specifications to prevent vehicles from rollover. The traffic barrier had a variable thickness with a wall thickness of 225 mm at the top, proportionally increased to 305 mm at the tapered portion of the wall, and further increased to 475 mm at the base. The wall was reinforced with 19M bars at 200 mm spacing as the vertical reinforcements. The horizontal reinforcements were placed at an average spacing of 250 mm using 19M steel bars. The deck slab beneath the traffic barrier had a uniform thickness of 360 mm reinforced with 19M bars at 150 mm spacing as the tension reinforcements. Conventional steel reinforcing bars were used as reinforcements in the wall and the deck slab. The specified yield strength of steel bars was 400 MPa. The concrete compressive strength was determined by taking core samples at time of the testing. A minimum of 10 concrete core samples were tested and the characteristic compressive strengths were determined. The characteristic concrete compressive strength of PL-3 traffic barrier was found to be as 34.5 MPa. In accordance with CHDBC requirements, a resistance factor of 0.9 was taken for steel reinforcing bars, while a resistance factor of 0.75 was considered for concrete.
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Figure 2. Configuration and steel reinforcement arrangements in the proposed PL-3 barrier.
3.2 Test Setups and Instrumentations The test setups for static load testing of the traffic barrier are shown in Figure 3. It consists of a table with two steel I-beams placed on the top to adjust the distance between load cell and jacking load to the front face of the wall. A timber plank of 250 mm height and 100 mm thick adjusted the gap between steel I-beam and the wall so that the load could be uniformly distributed to the wall. The equivalent crash load of the vehicle was simulated by a line load (Lt) of length 2400 mm for PL-3 traffic barriers. The hydraulic jack was supported on a steel column in which the column was tied down to the ground with 19 mm diameter bolts via base plate. The table was also bolted to the ground so that any lateral movement of the table and steel column would be prevented during testing. The jack was connected to the hydraulic pump that applied pressure to the system. Load cell was also connected to data acquisition system via cables along with other sensors attached to the wall so that the load and displacement could be captured. Before conducting the static test, the constructed barrier was instrumented at loaded regions. Figure’s 4 and 5 show views of the sensor designations on the wall and deck slab at interior and exterior regions of the tested barrier. Linear Variable Displacement Transducers (LVDTs) and Potentiometers (POTs) were installed to measure barrier transverse deflections at 990 mm height from the deck slab and at equal spacing of 1200 mm in the longitudinal direction of the barrier wall. Data acquisition equipment, System 6000, was used to record data from sensors at a rate of 10,000 scans per second.
4. EXPERIMENTAL RESULTS 4.1 Interior Location The PL-3 traffic barrier was tested to complete collapse under the increasing monotonic loadings. The load was applied at 990 mm above the deck slab as per CHBDC requirements for static load testing of PL-3 traffic barriers. The load was applied manually using hydraulic jack and the load increments were captured by load call attached to the system. The load was applied in the increment of 50 KN to observe the crack initiations in the barrier wall and the deck slab. At each load increment cracks were marks at front and back face of the wall.
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(a) Interior Location (b) Exterior Location Figure 3. Views of test setups for PL-3 traffic barrier testing under static – test.
Figure 4. Sensor designation in PL-3 barrier at interior location.
Figure 5. Sensor designation in PL-3 barrier at exterior location.
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At interior location, initial flexural crack was observed at tapered portion of the wall at 575 kN that was propagated further up into to the wall by increasing the applied load to 725 kN. In addition, at the load of 575 kN diagonal cracks appeared on each side of the loading patch, which were propagated downward within the wall body and reached the base of the wall at deck-wall junction at higher loads (700 -800 kN). At higher load levels, the cracks did not propagate further, but rather widened with increase in the load. Furthermore, a horizontal crack was observed at base of the wall under the loading patch area. This horizontal crack was noticed at a load close to the failure load of the wall and within a length about half of the loaded length of 2400 mm. The traffic barrier was loaded until it failed at a load of 885.9 kN. This ultimate load was far greater than the minimum transverse load limit of 357 kN specified in CHBDC. At back face of the traffic barrier, vertical cracks were observed that can be attributed as flexural behaviour in plane. Figure 6 depicts cracks pattern at front and back face of the wall. From the crack patterns at front face of the wall, it can be noticed that cracks propagated in a trapezoidal failure shape rather than triangular shape stipulated in AASHTO-LRFD on the basis of yield line failure pattern. The maximum wall lateral deformation at failure was 12.91 mm. Thus, it can be noted that this wall deformation is very small to force the yield lines into the deck slab. Also, the deck slab experienced a vertical displacement of 1.89 mm. This deformation of the deck slab was relatively very small representing sufficient strength of the deck slab against the yield – line failure. The traces of Load- wall lateral deformation and deck vertical for PL-3 barrier at interior location are shown in Figure 7. It can be seen from the graph that the load- deformation curve is linear at initial load followed by plastic deformation of the barrier wall.
(a) Front Face
(b) Back Face Figure 6. Crack pattern at interior location of the PL-3 traffic barrier.
(a) Wall Horizontal Deflection (b) Deck Vertical Deflection Figure 7. Load – deformation curve of the PL-3 traffic barrier at interior location. 280-6
4.2 Exterior Location The PL-3 traffic barrier was tested at exterior location under static load testing. In accordance with CHBDC requirements for static testing, the load was applied at 990 mm above the deck slab over a loaded length of 2400 for PL-3 barriers. The load was applied in 50 kN increments and was maintained for a few minutes to marks the crack initiations at front or back faces of the traffic barriers. Due to applied increasing loads, it was observed that the barrier experienced flexural cracks within the loaded region and diagonal-flexural cracks beyond the loaded region. Figure 8 shows view of the crack pattern at front and back faces of the PL-3 traffic barrier at exterior location. The first crack was observed at a load of 425 kN that is diagonally extended toward the top of the traffic barrier by increasing the applied load. At a load of 500 kN, a horizontal crack appeared at base of the wall. This crack appeared at about two-third of the 2400 mm loaded length which was diagonally extended into interior region of the barrier wall. By increasing the applied load, other diagonal cracks have been observed at front face of the wall toward the top of the wall and extended into wall thickness. The cracks also extended into the wall thickness at the tapered portion and corner base of the wall at loads between 525 to 625 kN. The test ended when the barrier could not absorb any further increase in the applied load beyond 627.13 kN. This ultimate load carrying capacity of the wall was greater than the minimum transverse load limit of 357 kN specified in CHBDC with a factor of safety of 1.76. At the back face of the traffic barrier, diagonal torsional cracks were observed which were extended down into the deck slab at failure load. No sing of vertical cracks due to in plane flexural behaviour were observed at the back face of the wall. From test observations, it can be noticed a trapezoidal failure pattern at front face of the wall rather than triangular failure pattern due to only one diagonal tension crack as stipulated in AASHTO-LRFD on the basis of yield-line theory. The traces of load- wall lateral deformation and deck vertical deformation are shown in Figure 9. It can be observed that the wall exhibited a maximum lateral deformation of 30.3 mm that can be regarded as flexural and torsional behaviour of the wall at exterior region. It can also be seen that the wall deformation linearly increased at the initial load followed by a plastic deformation with the increase in the applied load.
(a) Front Face
(b) Back Face
(c) Corner Cracks Figure 8. Cracks pattern in PL-3 traffic barrier at exterior location. 280-7
(a) Wall Horizontal Deflection (b) Deck Vertical Deflection Figure 9. Load – deformation curves for PL-3 traffic barrier at exterior location.
5. COMPARSION WITH YIELD – LINE THEORY The constructed PL-3 barrier was subjected to static load testing to complete collapse at both interior and exterior locations. The experimental test results showed that the barrier reinforcement detailing and configuration provided suffcicent strength. The ultimate load carrying capacity of the barrier was far greater than CHBDC limit of 357 kN for static testing of PL-3 barriers with a factor of safety of 2.48 and 1.76 at interior and exterior locations, respectively. The barrier did not expericend a large deformation at failure indicating also adequate strength of the barrier at serveceablity limit state. To validate the experimental test results, the proposed barrier were analytically investigated by yeild – line theroy of analysis for steel reinforced barriers. The triangular failure shape shown in Figure 1 which is presented in AASHTO – LRFD was assumed. Based on the reinforcement detailing shwon in Figure 2, the wall resistance moments, Mw, and cantiever resistance moments, Mc, at each of interior and exterior location have been determined. Equations 1 to 4 were then empoyed to calculate the critical yeild – line length and wall nominal resistances at interior and exterior locations. Table 1 summerizes the results obtained from yeild – line analysis which are compared with experimental test results and CHBDC limit. It can be seen from Table 1 that yield – line theroy predict the wall resistance close to the experimental test results. However, both the experiment and yield – line theory maintained relatively high capacity of the proposed barrier when they are compared with CHBDC. The ratio of nominal wall resistance by yield – line theroy and experimental test results to the CHBDC limit is also provided in Table 1. It can be observed that the wall maintained a very high capacity at interior location with a ratio of minimum 2.27. At exterior location, this ratio is somewhat smaller due to torsional effect of the wall during experimental testing. It should also be noted that experimental results were obtained without considering any reduction factor for concrete resistance. As per CHBDC, if assuming a concrete resitance factor or durablity factor of 0.75, the experimental test results will become 664.4 and 470.3 kN at interior and exterior locations, respectively. Thus, the ratio between experimental results and factored ultimate resistance by CHBDC will be 1.86 and 1.32 at interior and exterior locations, respectively. These ratios are still greater than one and indicate additional capacity of the proposed barrier. Thus. It can be concluded that the proposed barrier detailing shown in Figure 2 can be safely utilized as PL-3 barrier construction in practical purpose to simulate vehicle crash test.
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Table 1 : Comparsion of experimental and analytical test results with CHBDC limit. Yield - Line Experiment, CHBDC limit Rw / FCHBDC Fexp / FCHBDC PL -3 Barrier Fexp. FCHBDC Lc Rw (kN) (kN) (mm) (kN) Interior Location Exterior Location
4016 2658
810 536.1
885.9 627.13
357 357
2.27 1.50
2.48 1.76
6. CONCLUSIONS A full – scale PL-3 traffic barrier constructed at Texas Transportation Institution (TTI) was tested under monotonic static testing to compelete collapse. The experimental tests were carried out at both interior and exterir locations of the PL-3 barrier to investigate its ultimate load carrying capacity and failure mode. From experiumental investigations, it was observed that the barrier developed trapezodial failure shape that contradicts the triangular failure shape specified in AASHTO – LRFD. In addition, the ultimate load carrying capacity of the tested barrier was comparably greater than the CHBDC limit both at interior and exterior locations. The durabilty factor of 0.75 was applied to the experimental test results, thus, stll a factor of safety of 1.86 and 1.32 was obtained at interior and exterior locations, respectively. The yield – line theory of analysis was aslo conducted on the proposed barrier. The critical yield – line length and wall nominal resitances at both interior and exterior locations were determined. The analytical results were found to be greater than CHBDC limits with a factor of safety of 2.27 and 1.50 at interior and exterior locations, respectively. Based on experimental and analytical investigations performed on the PL-3 barrier, it can be concluded that the proposed barrier detailing can be safely used in PL-3 bridge barrier constructions with a large margin of safety again vehicle crash.
7. ACKNOWLEDGEMENTS The authors acknowledge funding from Ministry of Transportation of Ontario (MTO) to support this research. The authors would like to thank Mr. Nidal Jaalouk, the Senior Technical Officer of Ryerson University, for assisting in barrier instrumentation and data recording during the static tests.
8. REFERENCES AASHTO. 1989. AASHTO Guide Specifications for Bridge Railings. American Association of State Highway and Transportation Officials, Washington D.C. AASHTO. 2012. AASHTO-LRFD Bridge Design Specifications. Fifth Edition, American Association of State Highway and Transportation Officials, Washington, DC. CSA. 2006a. Canadian Highway Bridge Design Code. CAN/CSA-S6-06. Canadian Standard Association, Toronto, Ontario, Canada. CSA. 2006b. Commentaries on CAN/CSA-S6-06, “Canadian Highway Bridge Design Code, Canadian Standard Association, Toronto, Ontario, Canada. Hirsch, T. J. 1978. Analytical Evaluation of Texas Bridge Rails to Contain Buses and Trucks. Research report 20-2, Texas Transportation Institute, Texas A&M University. 105 pages. Ngan, C. L. 2008. Experimental Investigations of Anchorage Capacity of Precast Concrete Bridge Barrier for Performance Level 2.Thesis, University of British Columbia. 93 pages. Ross, H.E., Jr., Sicking, D.L., Zimmer, R.A., and Michie, J.D. 1993. Recommended Procedures for the Safety Performance Evaluation of Highway Features. Transportation Research Board, NCHRP Report 350.
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EXPERIMENTAL INVESTIGATION OF STEEL – REINFORCED PL-3 BRIDGE BARRIERS SUBJECTED TO TRANSVERSE STATIC LOADING Hamidreza Khederzadeh Ph.D Candidate, Ryerson University, Canada Khaled Sennah Professor, Ryerson University, Canada ABSTRACT Yield Line Theory of Analysis is used to design steel-reinforced bridge barrier walls in accordance with AAHSTOLRFD specifications (2012). Two yield-line patterns at interior and exterior locations are assumed based on the location of vehicle collision. On the basis of yield-line theory, triangular yield-line failure patterns develop at interior or exterior locations. However, the failure pattern observed in statically tested bridge barriers reinforced with GFRP bars as well as the actual steel-reinforced bridge barriers failed due to vehicle collision demonstrated a trapezoidal failure shape in the barrier walls. Thus, to further investigate this achievement, a full-scale PL-3 bridge barrier reinforced with conventional steel reinforcements was constructed at Texas Transportation Institution (TTI) site. The PL-3 barrier wall was tested under increasing monotonic loading to examine its failure pattern and ultimate load-carrying capacity. The PL-3 barrier had a geometry and barrier shape similar to the Standard PL-3 bridge barrier specified in Canadian Highway Bridge Design Code (CHDBC). The experimental test results confirmed the development of trapezoidal failure within the barrier wall. The ultimate flexural capacity of the barriers was found to be far greater than the limit specified in CHBDC. Furthermore, the barrier design was compared to the AASHTOLRFD design specifications based on yield-line theory and the results indicated additional capacity of the tested barrier walls.
1. INTRODUCTION Design of bridge barriers and bridge railings were required to meet the requirement for crash and safety in accordance with National Cooperative Highway Research Program (NCHRP) Report 350. The design forces for bridge rails specified in Canadian Highway Bridge Design Code (CSA, 2006a and CSA 2006b) is based on AASHTO-LRFD Guide Specification for Bridge Rails (AASHTO, 1989) that is corresponds to the test levels stipulated in NCHRP Report 350, "Recommended Procedures for the Safety Performance Evaluation of Highway Features" (Ross et al., 1993). Accordingly, Canadian Highway Bridge Design Code (CHBDC) requires that the suitability of bridge barrier anchorage system to the deck should be based on its performance during crash testing of the traffic barriers. The crash testing of the bridge barriers is carried out to investigate suitability of traffic barriers against structural adequacy, occupant risk and vehicle trajectory after the collision. CHDBC also specifies if crash testing of the traffic barriers is not available; the suitability of the traffic barriers shall be investigated based on the static test- to- complete collapse of the traffic barriers. However, the ultimate strength of traffic barriers tested under static load should be greater than the maximum transverse load limits specified in CHDBD, that is 357 kN for Performance Level 3 (PL-3). Ngan and Stiemer (2008) conducted an experimental program on the Performance Level 2 (PL-2) Precast Concrete Bridge Barriers reinforced with steel bars for the aim of investigating its structural behaviour and anchorage capacity in accordance with CHDBC. The test results proved that the precast concrete bridge barrier complied with the current code specifications in terms of strength and overall structural behaviour. The anchorage system of the tested barrier was sufficient as the failure occurred within the body of the barrier.
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However, the failure mode of the barrier was rather in trapezoidal shape compared to triangular shape stipulated in AASHTO - LRFD. Thus, based on the experimental investigation conducted by other researchers as well as the actual failure of the traffic barriers during vehicle crashes, an extensive study was performed herein on the failure mode and strength capacity of the traffic barriers on the basis of yield-line theory. The constructed PL-3 traffic barrier at Texas Transportation site was tested under monotonic static test to complete collapse and their failure mode and structural behaviour were investigated.
2. YIELD LINE THEORY OF ANALYSIS The design of conventional steel – reinforced bridge barriers is mainly based on AASHTO – LRFD Design Specifications (AASHTO, 2012) on the basis of yield – line theory of analysis. On this basis, it is assumed that yield – line develops within the barrier wall only and does not extend into the deck slab. If assumed that the yield – line penetrates into the deck slab, the AASHTO – LRFD yield – line procedure will not be valid. Thus, the deck slab should have sufficient strength to force the yield – line within the wall only. In addition, the AASHTO yield – line pattern is assumed to occur within certain longitudinal length of the barrier. As such, if sufficient longitudinal length of barrier is not provided the failure may be accompanied by one – way action failure by forming only longitudinal crack at deck – wall junction. The assumed yield – line pattern caused by vehicle crash that produce a force Ft over a longitudinal length Lt is shown in Figure 1. The yield – line equations were originally proposed by Hirsch (1978) and presented in AASHTO – LRFD. The equations can be derived by equating the external work due to the applied load to the internal load due to resisting plastic moments along the yield – line. The resisting plastic moments include the moment about the vertical axis due to longitudinal reinforcements, Mw, and the moment about horizontal axis due to transverse reinforcements, Mc. The angle of inclination of the yield – line can be expressed in terms of critical length, Lc. The applied force, Ft, can be minimized with respect to Lc to solve for the least value of this upper bound solution. By performing some algebraic solutions using principals of virtual work, the critical yield – line length, Lc, can be obtained. The following equations show the yield – line resistance forces and critical lengths at interior and exterior locations of the barrier wall.
Figure 1. AASHTO – LRFD yield line patterns at interior location (left) and exterior location(right).
The yield- line equations at a general region within the barrier length specified in AASHTO-LRFD as follow; 280-2
2
[1] L ci
Lt L 8HM b int M w int H) t 2 M c int 2
M L 2 2 8M b int 8M w int H c int ci [2] R wi H 2L ci L t
Where, Lci is critical length of interior yield line failure pattern, Lt is longitudinal length of distribution of impact force, Ft. H is height of barrier wall; Mbint is flexural resistance of the cap beam at interior location, Mwint is flexural resistance of the wall about its vertical axis at interior location, Mc. is the flexural resistance of the wall about a horizontal axis at interior location, and Rwi is total transverse resistance of the barrier wall at interior location. The critical barrier wall length at exterior location over which the yield line mechanism occurs can be taken as: 2
[3] L ce
M Lt M wendH) L t H bend 2 M cend 2
The nominal barrier wall resistance to transverse load at exterior location may be determined as:
2 [4] R we 2 L ce L t
M L 2 M bend M wendH cend ce H
Where: Lce is the critical length of exterior yield line failure pattern; Lt is longitudinal length of distribution of impact force, Ft; H is height of barrier wall; Mbend is flexural resistance of the cap beam at end region; Mwend is flexural resistance of the wall about its vertical axis at end region; Mcend. is the flexural resistance of the wall about a horizontal axis at end region; and Rwe is total transverse resistance of the barrier wall at end region.
3. EXPERIMENTAL INVESTIGATIONS 3.1 PL-3 Barrier Configurations The constructed PL-3 barrier had a geometry and barrier shape similar to the Standard PL-3 bridge barrier specified in CHDBC which is approved by Ministry of Transportation of Ontario (MTO- SS110-67 drawings). Figure 2 illustrates the tested PL-3 traffic barrier reinforced with conventional steel reinforcements. The proposed PL-3 barrier had an overall height of 1140 mm as per CHBDC recommendations. This is a minimum height specified in CHBDC specifications to prevent vehicles from rollover. The traffic barrier had a variable thickness with a wall thickness of 225 mm at the top, proportionally increased to 305 mm at the tapered portion of the wall, and further increased to 475 mm at the base. The wall was reinforced with 19M bars at 200 mm spacing as the vertical reinforcements. The horizontal reinforcements were placed at an average spacing of 250 mm using 19M steel bars. The deck slab beneath the traffic barrier had a uniform thickness of 360 mm reinforced with 19M bars at 150 mm spacing as the tension reinforcements. Conventional steel reinforcing bars were used as reinforcements in the wall and the deck slab. The specified yield strength of steel bars was 400 MPa. The concrete compressive strength was determined by taking core samples at time of the testing. A minimum of 10 concrete core samples were tested and the characteristic compressive strengths were determined. The characteristic concrete compressive strength of PL-3 traffic barrier was found to be as 34.5 MPa. In accordance with CHDBC requirements, a resistance factor of 0.9 was taken for steel reinforcing bars, while a resistance factor of 0.75 was considered for concrete.
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Figure 2. Configuration and steel reinforcement arrangements in the proposed PL-3 barrier.
3.2 Test Setups and Instrumentations The test setups for static load testing of the traffic barrier are shown in Figure 3. It consists of a table with two steel I-beams placed on the top to adjust the distance between load cell and jacking load to the front face of the wall. A timber plank of 250 mm height and 100 mm thick adjusted the gap between steel I-beam and the wall so that the load could be uniformly distributed to the wall. The equivalent crash load of the vehicle was simulated by a line load (Lt) of length 2400 mm for PL-3 traffic barriers. The hydraulic jack was supported on a steel column in which the column was tied down to the ground with 19 mm diameter bolts via base plate. The table was also bolted to the ground so that any lateral movement of the table and steel column would be prevented during testing. The jack was connected to the hydraulic pump that applied pressure to the system. Load cell was also connected to data acquisition system via cables along with other sensors attached to the wall so that the load and displacement could be captured. Before conducting the static test, the constructed barrier was instrumented at loaded regions. Figure’s 4 and 5 show views of the sensor designations on the wall and deck slab at interior and exterior regions of the tested barrier. Linear Variable Displacement Transducers (LVDTs) and Potentiometers (POTs) were installed to measure barrier transverse deflections at 990 mm height from the deck slab and at equal spacing of 1200 mm in the longitudinal direction of the barrier wall. Data acquisition equipment, System 6000, was used to record data from sensors at a rate of 10,000 scans per second.
4. EXPERIMENTAL RESULTS 4.1 Interior Location The PL-3 traffic barrier was tested to complete collapse under the increasing monotonic loadings. The load was applied at 990 mm above the deck slab as per CHBDC requirements for static load testing of PL-3 traffic barriers. The load was applied manually using hydraulic jack and the load increments were captured by load call attached to the system. The load was applied in the increment of 50 KN to observe the crack initiations in the barrier wall and the deck slab. At each load increment cracks were marks at front and back face of the wall.
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(a) Interior Location (b) Exterior Location Figure 3. Views of test setups for PL-3 traffic barrier testing under static – test.
Figure 4. Sensor designation in PL-3 barrier at interior location.
Figure 5. Sensor designation in PL-3 barrier at exterior location.
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At interior location, initial flexural crack was observed at tapered portion of the wall at 575 kN that was propagated further up into to the wall by increasing the applied load to 725 kN. In addition, at the load of 575 kN diagonal cracks appeared on each side of the loading patch, which were propagated downward within the wall body and reached the base of the wall at deck-wall junction at higher loads (700 -800 kN). At higher load levels, the cracks did not propagate further, but rather widened with increase in the load. Furthermore, a horizontal crack was observed at base of the wall under the loading patch area. This horizontal crack was noticed at a load close to the failure load of the wall and within a length about half of the loaded length of 2400 mm. The traffic barrier was loaded until it failed at a load of 885.9 kN. This ultimate load was far greater than the minimum transverse load limit of 357 kN specified in CHBDC. At back face of the traffic barrier, vertical cracks were observed that can be attributed as flexural behaviour in plane. Figure 6 depicts cracks pattern at front and back face of the wall. From the crack patterns at front face of the wall, it can be noticed that cracks propagated in a trapezoidal failure shape rather than triangular shape stipulated in AASHTO-LRFD on the basis of yield line failure pattern. The maximum wall lateral deformation at failure was 12.91 mm. Thus, it can be noted that this wall deformation is very small to force the yield lines into the deck slab. Also, the deck slab experienced a vertical displacement of 1.89 mm. This deformation of the deck slab was relatively very small representing sufficient strength of the deck slab against the yield – line failure. The traces of Load- wall lateral deformation and deck vertical for PL-3 barrier at interior location are shown in Figure 7. It can be seen from the graph that the load- deformation curve is linear at initial load followed by plastic deformation of the barrier wall.
(a) Front Face
(b) Back Face Figure 6. Crack pattern at interior location of the PL-3 traffic barrier.
(a) Wall Horizontal Deflection (b) Deck Vertical Deflection Figure 7. Load – deformation curve of the PL-3 traffic barrier at interior location. 280-6
4.2 Exterior Location The PL-3 traffic barrier was tested at exterior location under static load testing. In accordance with CHBDC requirements for static testing, the load was applied at 990 mm above the deck slab over a loaded length of 2400 for PL-3 barriers. The load was applied in 50 kN increments and was maintained for a few minutes to marks the crack initiations at front or back faces of the traffic barriers. Due to applied increasing loads, it was observed that the barrier experienced flexural cracks within the loaded region and diagonal-flexural cracks beyond the loaded region. Figure 8 shows view of the crack pattern at front and back faces of the PL-3 traffic barrier at exterior location. The first crack was observed at a load of 425 kN that is diagonally extended toward the top of the traffic barrier by increasing the applied load. At a load of 500 kN, a horizontal crack appeared at base of the wall. This crack appeared at about two-third of the 2400 mm loaded length which was diagonally extended into interior region of the barrier wall. By increasing the applied load, other diagonal cracks have been observed at front face of the wall toward the top of the wall and extended into wall thickness. The cracks also extended into the wall thickness at the tapered portion and corner base of the wall at loads between 525 to 625 kN. The test ended when the barrier could not absorb any further increase in the applied load beyond 627.13 kN. This ultimate load carrying capacity of the wall was greater than the minimum transverse load limit of 357 kN specified in CHBDC with a factor of safety of 1.76. At the back face of the traffic barrier, diagonal torsional cracks were observed which were extended down into the deck slab at failure load. No sing of vertical cracks due to in plane flexural behaviour were observed at the back face of the wall. From test observations, it can be noticed a trapezoidal failure pattern at front face of the wall rather than triangular failure pattern due to only one diagonal tension crack as stipulated in AASHTO-LRFD on the basis of yield-line theory. The traces of load- wall lateral deformation and deck vertical deformation are shown in Figure 9. It can be observed that the wall exhibited a maximum lateral deformation of 30.3 mm that can be regarded as flexural and torsional behaviour of the wall at exterior region. It can also be seen that the wall deformation linearly increased at the initial load followed by a plastic deformation with the increase in the applied load.
(a) Front Face
(b) Back Face
(c) Corner Cracks Figure 8. Cracks pattern in PL-3 traffic barrier at exterior location. 280-7
(a) Wall Horizontal Deflection (b) Deck Vertical Deflection Figure 9. Load – deformation curves for PL-3 traffic barrier at exterior location.
5. COMPARSION WITH YIELD – LINE THEORY The constructed PL-3 barrier was subjected to static load testing to complete collapse at both interior and exterior locations. The experimental test results showed that the barrier reinforcement detailing and configuration provided suffcicent strength. The ultimate load carrying capacity of the barrier was far greater than CHBDC limit of 357 kN for static testing of PL-3 barriers with a factor of safety of 2.48 and 1.76 at interior and exterior locations, respectively. The barrier did not expericend a large deformation at failure indicating also adequate strength of the barrier at serveceablity limit state. To validate the experimental test results, the proposed barrier were analytically investigated by yeild – line theroy of analysis for steel reinforced barriers. The triangular failure shape shown in Figure 1 which is presented in AASHTO – LRFD was assumed. Based on the reinforcement detailing shwon in Figure 2, the wall resistance moments, Mw, and cantiever resistance moments, Mc, at each of interior and exterior location have been determined. Equations 1 to 4 were then empoyed to calculate the critical yeild – line length and wall nominal resistances at interior and exterior locations. Table 1 summerizes the results obtained from yeild – line analysis which are compared with experimental test results and CHBDC limit. It can be seen from Table 1 that yield – line theroy predict the wall resistance close to the experimental test results. However, both the experiment and yield – line theory maintained relatively high capacity of the proposed barrier when they are compared with CHBDC. The ratio of nominal wall resistance by yield – line theroy and experimental test results to the CHBDC limit is also provided in Table 1. It can be observed that the wall maintained a very high capacity at interior location with a ratio of minimum 2.27. At exterior location, this ratio is somewhat smaller due to torsional effect of the wall during experimental testing. It should also be noted that experimental results were obtained without considering any reduction factor for concrete resistance. As per CHBDC, if assuming a concrete resitance factor or durablity factor of 0.75, the experimental test results will become 664.4 and 470.3 kN at interior and exterior locations, respectively. Thus, the ratio between experimental results and factored ultimate resistance by CHBDC will be 1.86 and 1.32 at interior and exterior locations, respectively. These ratios are still greater than one and indicate additional capacity of the proposed barrier. Thus. It can be concluded that the proposed barrier detailing shown in Figure 2 can be safely utilized as PL-3 barrier construction in practical purpose to simulate vehicle crash test.
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Table 1 : Comparsion of experimental and analytical test results with CHBDC limit. Yield - Line Experiment, CHBDC limit Rw / FCHBDC Fexp / FCHBDC PL -3 Barrier Fexp. FCHBDC Lc Rw (kN) (kN) (mm) (kN) Interior Location Exterior Location
4016 2658
810 536.1
885.9 627.13
357 357
2.27 1.50
2.48 1.76
6. CONCLUSIONS A full – scale PL-3 traffic barrier constructed at Texas Transportation Institution (TTI) was tested under monotonic static testing to compelete collapse. The experimental tests were carried out at both interior and exterir locations of the PL-3 barrier to investigate its ultimate load carrying capacity and failure mode. From experiumental investigations, it was observed that the barrier developed trapezodial failure shape that contradicts the triangular failure shape specified in AASHTO – LRFD. In addition, the ultimate load carrying capacity of the tested barrier was comparably greater than the CHBDC limit both at interior and exterior locations. The durabilty factor of 0.75 was applied to the experimental test results, thus, stll a factor of safety of 1.86 and 1.32 was obtained at interior and exterior locations, respectively. The yield – line theory of analysis was aslo conducted on the proposed barrier. The critical yield – line length and wall nominal resitances at both interior and exterior locations were determined. The analytical results were found to be greater than CHBDC limits with a factor of safety of 2.27 and 1.50 at interior and exterior locations, respectively. Based on experimental and analytical investigations performed on the PL-3 barrier, it can be concluded that the proposed barrier detailing can be safely used in PL-3 bridge barrier constructions with a large margin of safety again vehicle crash.
7. ACKNOWLEDGEMENTS The authors acknowledge funding from Ministry of Transportation of Ontario (MTO) to support this research. The authors would like to thank Mr. Nidal Jaalouk, the Senior Technical Officer of Ryerson University, for assisting in barrier instrumentation and data recording during the static tests.
8. REFERENCES AASHTO. 1989. AASHTO Guide Specifications for Bridge Railings. American Association of State Highway and Transportation Officials, Washington D.C. AASHTO. 2012. AASHTO-LRFD Bridge Design Specifications. Fifth Edition, American Association of State Highway and Transportation Officials, Washington, DC. CSA. 2006a. Canadian Highway Bridge Design Code. CAN/CSA-S6-06. Canadian Standard Association, Toronto, Ontario, Canada. CSA. 2006b. Commentaries on CAN/CSA-S6-06, “Canadian Highway Bridge Design Code, Canadian Standard Association, Toronto, Ontario, Canada. Hirsch, T. J. 1978. Analytical Evaluation of Texas Bridge Rails to Contain Buses and Trucks. Research report 20-2, Texas Transportation Institute, Texas A&M University. 105 pages. Ngan, C. L. 2008. Experimental Investigations of Anchorage Capacity of Precast Concrete Bridge Barrier for Performance Level 2.Thesis, University of British Columbia. 93 pages. Ross, H.E., Jr., Sicking, D.L., Zimmer, R.A., and Michie, J.D. 1993. Recommended Procedures for the Safety Performance Evaluation of Highway Features. Transportation Research Board, NCHRP Report 350.
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