J.6 Overheight_Countermeasures_Final Report.pdf

i

MARCH 2022

FHWA-RC-22-0003

IMPLEMENTATION OF CRASH

SIMULATION TECHNOLOGY TO

DEVELOP COUNTERMEASURES

STRATEGIES FOR OVER-HEIGHT

IMPACT PROTECTION SYSTEM ON

CONCRETE GIRDERS

ii

Foreword

This report presents a performance-based approach to develop a comprehensive methodology for the demand model and the design of supplemental protection beam against bridge strikes due to over-height heavy vehicles (OHV) impact. This work is important because recent survey indicated

OHV impact on bridge superstructure has been recognized as a serious problem across the country.

However, there is no standard design or knowledge base on the OHV impact demand that can be used by engineers to design the protection systems for bridge girders. The effectiveness of current retrofit approaches, such as carbon-fiber reinforced polymers (CFRP) wrapping for pre-stressed concrete girders damaged during OHV impact, has not been systematically studied.

The work reported herein evaluated the efficacy of wrapping concrete girders with CFRP for protection against significant damages due to OHV impact in detail. To minimize damage to fascia girders, installing energy-absorbing materials such as aluminum honeycombs in front of the girder or as sacrificial beam is proposed. The effectiveness and capabilities of these supplemental systems in protecting pre-stressed fascia girders of bridges were investigated through high fidelity computational simulation and large scaled drop-hammer tests. This report will be of interest to bridge program personnel from Federal, State, and local agencies as well as to parties engaged in bridge-related research, and the practicing bridge engineering community. The findings and recommendations will also serve as pertinent resources to the ongoing transportation pooled fund study TPF-5(484), “Develop countermeasure strategies for protecting bridge girders against over-height vehicles impact.”

Shay K. Burrows P.E.

Resource Center Director

Federal Highway Administration

Office of Innovation Implementation

Disclaimer

This document is a preliminary draft for information purposes only. It is not to be considered as the final report, and all information contained herein is subject to change upon further peer review by the Federal Highway Administration. Unless FHWA provide express prior written consent, no part of this report should be reproduced, distributed or communicated to any third party. FHWA does not accept any liability if this report is used for an alternative purpose from which it is intended, nor to any third party in respect of this report.

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TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HIF-xx-xxx

2. Government Accession

No.

3. Recipient’s Catalog No.

4. Title and Subtitle

Implementation of crash simulation technology to develop countermeasures strategies for over-height impact protection system on concrete girders

5. Report Date

6. Performing Organization Code:

7. Author(s)

Agrawal, A.K., El-Tawil, S., Cao, R., and Wong, W.

8. Performing Organization Report No.

9. Performing Organization Name and Address

The City College of New York

160 Convent Ave, New York, NY 10031

10. Work Unit No.

11. Contract or Grant No.

DTFH61-14-D-00010/0003

12. Sponsoring Agency Name and Address

Office of Research, Development, and Technology

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101-2296

13. Type of Report and Period

Final Report, 04/10/2019-

07/26/2020

14. Sponsoring Agency

Code

15. Supplementary Notes

16. Abstract

Based on the 2016 National Bridge Inventory (NBI) database available at the FHWA, there are a total of

614,387 bridges in the United States. It has been observed from previous research that collision, both caused by vessel and vehicles, is the second leading cause of bridge failures. Recently, over-height impact on bridge superstructure has been recognized as a serious problem across the country. However, there is no standard design or knowledge base on the overheight impact demand that can be used by engineers to design the protection systems for bridge girders. The effectiveness of current retrofit approaches, such as carbon-fiber reinforced polymers (CFRP) wrapping for pre-stressed concrete girders damaged during overheight impact, has not been systematically studied. Hence, the objective of the proposed research was to use crash simulation technology for developing a comprehensive approach for the demand model and performance-based design of supplemental protection beams. The efficacy of wrapping concrete girders with CFRP for protection against significant damage by overheight impact was also evaluated in detail. To minimize damage to fascia girders, energy-absorbing materials, such as aluminium honeycombs, have been proposed to be installed in front of the girder or sacrificial beams. The effectiveness and capabilities of these supplemental systems in protecting pre-stressed fascia girders of bridges were investigated through high fidelity computational simulation and scaled drop-hammer tests.

17. Key Words

Vehicular impacts, overheight impact with bridges, impact protection

18. Distribution Statement

No restrictions. This document is available to the public through the National Technical Information

Service, Springfield, VA 22161.

http://www.ntis.gov

19. Security Classif. (of this report) Unclassified

20. Security Classif. (of this page) Unclassified

21. No. of

Pages

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized http://www.ntis.gov/ iv v

TABLE OF CONTENTS

LIST OF FIGURES .............................................................................................VII

LIST OF TABLES ............................................................................................. VIII

CHAPTER 1. INTRODUCTION

BACKGROUND

OBJECTIVES

CHAPTER 2. DEVELOPMENT OF A SUPPLEMENTAL PROTECTIVE

SYSTEM FOR OVER-HEIGHT IMPACT

HAZARD LEVEL COMPARISON

Material Model

Validation

Simulation Results

PARAMETRIC STUDIES

SIMPLIFIED PULSE MODEL FOR OVERHEIGHT IMPACT

PERFORMANCE-BASED DESIGN

PROPOSED DESIGN PROCEDURE

VALIDATION OF THE PROPOSED FRAMEWORK

CHAPTER 3. RETROFIT OF GIRDERS DAMAGE DURING

OVERHEIGHT IMPACT USING CARBON-FIBER REINFORCED

POLYMERS

MODEL OF THE TRUCK AND BRIDGE

Bridge Model

Material Model

SIMULATION RESULTS

PARAMETRIC STUDY

PUSHOVER ANALYSIS SIMULATION

CHAPTER 4. OVERHEIGHT IMPACT ON GIRDERS WITH

HONEYCOMB LAYERS

Energy Method for Honeycomb Device Design

Validation of the Honeycomb Modeling

Truck Impact Simulation vi

CHAPTER 5. LARGE SCALE TESTING OF A GIRDER WITH

HONECOMB BLOCK

CHAPTER 6. CONCLUSIONS, LIMITATIONS AND FUTURE WORK

SUMMARY AND CONCLUSIONS

LIMITATIONS AND FUTURE WORK

REFERENCES

vii

LIST OF FIGURES

Figure 1. Chart. Causes of bridge failures in the United States Figure 2. Map. Seriousness of bridge hits problem in the United States during 2005-2008 Figure 3. Graph. Types of overheight vehicles impacting bridge superstructures in New York State.

Figure 4. Drawing. Installation of overheight protection beams on a bridge Figure 5. Photo. Original tractor-semitrailer model Figure 6. Photo. Collapse scene of the Skagit River bridge (reprinted from NTSB 2014) Figure 7. Photo. Damaged mode of the accident trailer in the Skagit river bridge collapse.

(reprinted from NTSB report)

Figure 8. Photo. Simulation setup of overheight impact with Skagit River bridge in LS-DYNA. 7

Figure 9. Photo. Simulated progress of the impact and damage mode of the trailer

Figure 10. Photo. Comparison of the collapse scenario between FE simulation and the accident. 8 Figure 11. Photo. Example concrete bridge model subject to the modified semi-rigid trailer impact.

Figure 12. Photo. Typical severe damage mode of the concrete girder subject to semi-rigid trailer impact Figure 13. Photo. Typical scratch damage mode of the concrete girder subject to normal trailer impact Figure 14. Photo. Simulation setup of overheight impact with steel box beam Figure 15. Graph. Impact force time history for steel beams: (a) W20; (b) V70

Figure 16. Graph. Displacement time history for steel beams: (a) W40; (b) V55 Figure 17. Graph. Simplified triangle pulse loading model

Figure 18. Photo. Loading application of the pulse model

Figure 19. Graph. Comparison of the beam displacement caused by the truck impact and pulse loading: (a) V40-W40; (b) V55-W40; (c) V70-W40; (d) V55-W20 Figure 20. Graph. Capacity calculation model for steel box beams Figure 21. Graph. Performance based design chart for the steel box beam

Figure 22. Photo. Example concrete bridge model subject to the modified semi-rigid trailer impact.

Figure 23. Photo. Example prestressing concrete bridge (a) before the impact; (b) post-impact scene Figure 24. Illustration. Illustration of CFRP wrapping on prestressing concrete girders

Figure 25. Photo. Typical damage mode of the CFRP wrapped girders subject to overheight impact from actual accidents and simulations Figure 26. Photo. Localized damage of the CFRP wrapping from the simulation

Figure 27. Graph. Effects of CFRP on the girder deformations subject to overheight impact (V55-

W40) Figure 28. Graph. Deformation of the CFRP wrapped girder subject to different truck impact: (a) speed effects; (b) weight effects Figure 29. Graph. Impact force time history for a 40-ton truck at different speeds Figure 30. Damage mode of the CFRP wrapped girder: (a) V30-W40; (b) V50-W40; (c) V70-W40

Figure 31. Illustration. Pushover loading setup on the concrete girder

Figure 32. Graph. Pushover curve from the simulation viii

Figure 33. Graph. Patterns of the yield lines of concrete girder under pushover loading

Figure 34. Illustration. Illustration of the yield line method

Figure 35. Photo. Simulation setup of pushover on the honeycomb sample Figure 36. Pushover curve of the honeycomb: (a) testing results for strength of 190 psi; (b) simulation results for strength of 190 psi; (c) testing results for strength of 80 psi; (d) simulation results for strength of 80 psi Figure 37. Photo. Simulation setup of honeycomb modular subject to the overheight impact

Figure 38. Graph. Crushing behavior of the honeycomb Figure 39. Graph. Impact force time history of the honeycomb beam subject to the overheight impact Figure 40. Graph. Comparison of peak deformation of the girder protected by CFRP and honeycomb blocks: (a) V50; (b) W40

Figure 41. Photo. Minor damage mode of bridge girder protected by the honeycomb modular.. 31

Figure 42. Photo. Simulation setup of the drop-hammer test

Figure 43. Illustration. Two configurations of the honeycomb: (a) single honeycomb block; (b) two honeycomb blocks Figure 44. Photo. Impact process of the 20-mph case: (a) testing; (b) simulation Figure 45. Graph. Deformation time history of the beam under the 20-mph drop-hammer impact:

(a) steel beam; (b) honeycomb beam Figure 46. Graph. Impact force time history of the 20-mph drop hammer impact: (a) steel beam;

(b) honeycomb beam Figure 47. Graph. Deformation time history of the beam under the 10-mph drop-hammer impact:

(a) steel beam; (b) honeycomb beam

Figure 48. Graph. Impact force time history of the 10-mph drop-hammer impact: (a) steel beam;

(b) honeycomb beam

Figure 49. Graph. Damage mode of the beam under 20-mph drop-hammer impact: (a) steel beam;

(b) honeycomb beam

Figure 50. Graph. Deformation mode of the beam under 10-mph drop-hammer impact: (a) steel beam; (b) honeycomb beam Figure 51. Graph. Strain of the beam at point A (Figure 42) under: (a) 10-mph drop-hammer impact; (b) 20-mph drop-hammer impact

LIST OF TABLES

Table 1. Comparison of calibrated pulse demands in FEM and proposed equation results Table 2. Computed ductility ratio for the impact beams subject to truck impact Table 3. Performance levels, corresponding damage state, and rotation

Table 4. Beam geometry for validation study

Table 5. Selected cases for validation of proposed method Table 6. Computed energy of the trailer and honeycombs Table 7. Displacement results for each testing case

CHAPTER 1. INTRODUCTION

BACKGROUND

Based on the 2016 National Bridge Inventory database available at the FHWA1, there are a total of 614,387 bridges in the United States. A 1994 National Transportation Safety Board (NTSB) study noted that “The National Highway Traffic Safety Administration (NHTSA) estimates that annually 1,000 trucks and buses with gross weight greater than 10,000 pounds gross collide with bridge structures” (Zimmerman 2012). Based on bridge failure data compiled by the New York

State Department of Transportation, figure 1 shows the leading causes of bridge failures in the

United States during the period from 1969 to 2006. It is observed that collision, both caused by vessel and vehicles, has been recognized as the second leading cause of bridge failures after hydraulic failures.

Figure 1. Chart. Causes of bridge failures in the United States.

A recent study by Agrawal et al. (2011) has shown the impact of overheight trucks on bridge superstructure is a “high likelihood” event that causes damages to steel or concrete components of bridges and creates significant traffic congestion in the aftermath of the impact. The survey by

Agrawal et al. (2011) in figure 2 asked the States whether the impact of bridges is a serious problem in the United States. It is observed that the overheight impact on bridge superstructure has generally been considered as a serious problem across the country. It should also be noted that the number of impacts for the period of 2005-2008 shown in figure 2 might not directly show the seriousness of the impact. For example, Missouri had a large number of impacts (1,691). However, a majority of hits resulted in minor damages or scratches on bridges. Therefore, Missouri considered bridge impacts a minor problem. Also, Virginia data had been updated based on recent information. Based on the analysis of data from the New York State Department of Transportation

(NYSDOT) on impacts by overheight vehicles, figure 3 shows that tractor-semitrailers were impacting bridge superstructures the most frequently.

1 https://www.fhwa.dot.gov/bridge/nbi/ascii.cfm

Figure 2. Map. Seriousness of bridge hits problem in the United States during 2005-2008.

Figure 3. Graph. Types of overheight vehicles impacting bridge superstructures in New

York State.

Although most of the States use an over-height detection system to warn over-height trucks from impacting bridge superstructure, the superstructure/tunnels could still be damaged if the driver does not follow the warning signs or the detention systems malfunctions. In such cases, some

States install protection beams at the entrance of bridges/tunnels. These protection beams are designed as a supplemental structure to prevent over-height portions of trucks from impacting vehicle_count

8 11 9 boat car construction equipment trailer train truck vehicle type h it f re q vehicle_count fascia girders of the bridges or for preventing overheight trucks from entering a tunnel. Error!

Reference source not found. shows an example of such a system installed at the entrance of a bridge. The design of such protection beams was based on approximate impact analysis. Currently, there is no standard design or knowledge base on impact force demand that can be used by engineers to design the protection beam. Qiao et al. (2008) conducted simulations and testing on

FRP sandwich as overheight impact protection system but did not provide a demand model for impacting tractor-semitrailers. Hence, further studies are needed to develop a demand model of over-height impact for the design of impact protection systems. Based on such demand model, a supplemental system (such as a protection beam) could be designed to prevent any significant damage to the fascia girder of bridges. This protection beam could be replaced after an impact event if it suffered any damage. It has been recognized by State DOT engineers that pre-stressed concrete girders are at an increased risk of failure due to over-height impact, which can be prevented by installing such protection systems. Hence, the main objective of the proposed research is to develop a comprehensive approach for the demand model and performance-based design of protection beams for bridges at risk of impacts by over-height trucks.

Figure 4. Drawing. Installation of overheight protection beams on a bridge.

OBJECTIVES

The Federal Highway Administration (FHWA) has recently developed a technology for crash simulation using the enhanced non-linear finite element model of the tractor-trailer as well as the single unit truck (SUT) in LS-DYNA. This technology is being used extensively for investigating the safety of bridge piers for frontal impact by heavy trucks, as well as side collisions on superstructure due to over-height vehicles. The main objective of this research is to use this technology for developing a comprehensive approach for the demand model and performance-based design of supplemental protection beams. These protection beams have also been made of energy-absorbing materials, such as aluminum honeycombs, to minimize damage to fascia girders in the event of over-height trucks moving at high speeds. The efficacy of wrapping concrete girders with carbon-fiber-reinforced polymers (CFRP) for protection against overheight impact has also been evaluated through high-fidelity truck collision simulations. Based on the simulation results, the effectiveness and capabilities of these supplemental systems in protecting pre-stressed fascia girders of bridges were investigated in detail. The objectives of this research have been achieved through the following eight tasks.

• Task 1: Conceptual development of a supplemental protective system for over-height impact.

• Task 2: Literature search and data collection on Carbon Fiber Reinforced Plastic (CFRP) wrapping protection for over-height impact.

• Task 3: Modeling replaceable aluminum honeycombs filled with energy-dissipative materials.

• Task 4: Simulating over-height impact on the protection devices installed on the pre-stressed girders.

• Task 5: Material behavior and damage mechanisms of the honeycomb through laboratory testing.

• Task 6: Design of field test setup through numerical simulations.

• Task 7: Scaled impact testing on the honeycomb devices.

• Task 8: Theoretical verifications with test results.

Detailed work performed towards achieving these eight tasks is described in different chapters of this report as follows:

Chapter 2 describes the development of a supplemental protection system for over-height impact, including the demand model and the performance-based design framework.

Chapter 3 describes survey results of CFRP usage among State DOTs for protecting concrete girders against overheight impact and other retrofits. Simulation results have also been presented to evaluate the effectiveness of the CFRP wrapping on the impact performance of the pre-stressed concrete girders subject to truck impact.

Chapter 4 describes the modeling of honeycomb materials and presents simulation results of truck collisions with honeycomb beams installed on a full-scale bridge model. A simple design method of the honeycomb beam was also proposed for engineer use in a practical setting. The efficacy of honeycomb beams was compared with the CFRP wrapping for protecting pre-stressed concrete girders against overheight truck impact.

Chapter 5 presents the testing results of drop-hammer impact with steel beams installed with honeycombs. Simulation verification is also presented in this chapter.

Chapter 6 presents conclusions and recommendations for future work.

CHAPTER 2. DEVELOPMENT OF A SUPPLEMENTAL PROTECTIVE

SYSTEM FOR OVER-HEIGHT IMPACT

An advanced tractor-semitrailer model developed recently by the Federal Highway Administration and used extensively by the authors was further modified for developing a demand model of over-height impact for the design of impact protection systems. Figure 5 shows the truck model used in the simulations. The truck model was originally developed by the National Crash Analysis

Center (NCAC) and updated by Battelle (Plaxico et al. 2008). The trailer model was developed at

Battelle and the overall model was validated against several full-scale barrier impact tests (Plaxico et al. 2009 and Miele et al. 2010). The truck model is a van-type tractor-semitrailer with dimensions of 66 ft x 9 ft x 13 ft, and is representative of models such as 1991 White GMC tractor with a 1988 Pines 14.6-m semitrailer, 1979 International TranStar 4200 tractor with a 1977

Pullman van-trailer, and 1992 Freightliner FLD120 with integral sleeper cabin or a 1990 Stoughton box semitrailer (Miele et al. 2010). The finite element model of the truck is composed of approximately 472,000 finite elements, including shell, beam, and solid elements for different parts of the truck. This model has also been used for hundreds of simulations for cases within the scope of TL-5 speeds and impact angles in NCHRP Report 350 (Ross et al. 1993) and has been shown to be reasonably representative and accurate. Further details about this model can be found in Miele et al. (2010) and at the National Transportation Research Center website

(https://thyme.ornl.gov/fhwa/tractortrailer/).

In the original trailer model, the trailer body was comprised of roof and side panels that were light and were mostly constructed of thin plywood, aluminum, and steel sheets. Therefore, the original trailer’s main body was not strong or stiff enough to represent a severe overheight impact hazard.

For example, Figure 6 shows a steel truss bridge over the Skagit River near Mount Vernon, Washington, that collapsed due to the overheight impact. Figure 7 shows that the impacting trailer carried a special cargo comprised of a heavily reinforced container-like structure without side panels. It is clear that the trailer behaved mostly as a rigid body during the impact, as evinced by the presence of minor damage in the trailer’s top part. Hence, the original trailer model shown in

Figure 5 was modified to be more rigid (adjusting material strength and thickness) and it was calibrated against the damage mode of the semi-rigid trailer in the Skagit River bridge collapse.

Figure 5. Photo. Original tractor-semitrailer model.

Figure 6. Photo. Collapse scene of the Skagit River bridge (reprinted from NTSB 2014).

Figure 7. Photo. Damaged mode of the accident trailer in the Skagit river bridge collapse.

(reprinted from NTSB report)

Based on the as-built drawings, Figure 8 shows the simulation setup of the overheight impact with the Skagit River bridge model in LS-DYNA (Hallquist 2006). The main trusses of the bridge were modeled using shell elements. The truss members were connected to the gusset plates using the nodal rigid body command in LS-DYNA (Hallquist 2006). This implies that connection failure was not permitted to occur, which is consistent with field observations after the incident. The mesh size of the bridge superstructure was 1.5 inch. The piers were modeled using rigid materials and fully fixed at the bottom. The total number of elements in the model was approximately 1.1 million.

Plastic kinematic material (MAT 3) in LS-DYNA (Hallquist 2006) was used to model the steel members, with a failure strain of 0.2. The yielding strength of the steel was assumed to be 50 ksi based on the design drawings. More detailed information of the bridge model can be found in Cao et al. (2020a).

Based on the calibration, Figure 9 shows the damage mode of the calibrated trailer model after the impact. It can be seen from Figure 9 that the trailer corner suffered localized damage, the area and location of which matched the damage in the actual trailer shown in Figure 7. The calibrated truck was believed to deliver a similar level of hazard to the bridges as that from the semi-rigid trailer, which caused the Skagit River bridge to collapse. Figure 10 shows the comparison of the collapse mode of the bridge from the accident and simulations. A more detailed explanation of the collapse mechanisms can be found in Cao et al. (2020a).

Figure 8. Photo. Simulation setup of overheight impact with Skagit River bridge in LS-

DYNA.

Figure 9. Photo. Simulated progress of the impact and damage mode of the trailer.

Figure 10. Photo. Comparison of the collapse scenario between FE simulation and the accident.

HAZARD LEVEL COMPARISON

To further compare the hazard level represented by the calibrated semi-rigid trailer and the original trailer model, a full-scale prestressed concrete girder bridge model was developed in LS-DYNA

(Hallquist 2006). Figure 11 shows the simulation setup of the concrete girder subject to the overheight impact from the semi-rigid trailer model. The weight of the truck was assumed to be

80 kips and the velocity of the truck was 55 mph. The bridge model was developed based on the as-built drawing of a highway bridge in Texas that had been subjected to several overheight impacts. More details about this bridge will be presented in the next chapter.

Material Model

Concrete behavior was modeled by the Continuous Surface Cap Model (CSCM MAT159) in LS-

DYNA (Hallquist 2006). The model can capture key aspects of inelastic concrete behavior, including post-peak softening and confinement effects. It is based on an elasto-plastic damage formulation that accounts for rate effects. Default material parameters were used in this study, which were generated based on the compressive strength and the maximum aggregate size of the concrete (Murray et al. 2007). Steel rebars were modeled using Hughes-Liu beam elements and were represented using material MAT 3, which accounts for yielding and kinematic hardening plasticity. Steel rebar elements were assumed to fracture and removed after the strain reached 0.20.

The general mesh size used was 1.5 inch. Perfect bond was enforced between the steel and concrete components by using the coupling method in LS-DYNA, *CONSTRAINED_BEAM_IN_SOLID.

The tendons in the bridge girder were unbonded. In the FE simulation, the

*CONSTRAINED_BEAM_IN_SOLID command was used to model the tendons and their interaction with the surrounding concrete. The selected model ensures kinematic coupling (in displacement, velocity, and acceleration) between the tendons and concrete only in the direction normal to the tendon’s axis but permits slip along the tendon’s axis. Prestressing was achieved by cooling the tendons, which applied a prestressing force because of shrinkage in pre-stressing tendons. A similar approach has been used in many studies with reasonable simulation results

(Nakalswamy 2010, Jiang and Chorzepa 2015, Do et al. 2018, Cao et al. 2019d). The pre-stressing tendons were modeled using ELASTIC_PLASTIC_THERMAL material (MAT 4), which can simulate the thermal deformations of the material based on provided temperature time history curves and a given coefficient of thermal expansion.

Validation

The concrete (Mat 159) and rebar (MAT 3) models have been validated for simulating the flexure/shear behavior of reinforced concrete (RC) specimens in multiple publications, including

Moutoussamy et al. (2011), Liu (2012), and Murray et al. (2007). In these studies, multiple sets of experimental data of RC beams subject to static or impact loading were used to prove the effectiveness of the RC modeling scheme. It has been shown that the selected modeling scheme yielded reasonable comparisons to the test results. The authors have used the same general modeling scheme described above in several previous studies where they conducted their own validation studies (Cao et al. 2019a, b, c, 2020b and Xu et al. 2019). The validation efforts in those research studies, which are not repeated here in the interest of saving space, provide confidence in the authors’ nonlinear modeling approach.

Figure 11. Photo. Example concrete bridge model subject to the modified semi-rigid trailer impact.

Simulation Results

Figure 12 shows the simulated damage mode of the concrete girder subject to semi-rigid trailer impact and its comparison with damages to concrete girders because of overheight impacts. It can be seen from Figure 12 that the simulation results well captured the typical trapezoidal-shape yielding line patterns observed in many overheight impact accidents. Figure 13 shows the damage mode of the bridge girders subject to normal (soft) trailer impact. In Figure 13, the top of the trailer was crushed and only some minor spalling was found in concrete girders. Such scratch type damage mode was also observed in some accidents shown in Figure 13 when the colliding cargo was believed to be either soft or light in weight.

The objective of this study is to develop a demand model for designing a protection beam against severe overheight impacts. Therefore, the calibrated semi-rigid trailer model was used in parametric studies to develop a demand model that can be used for designing these protection beams.

Figure 12. Photo. Typical severe damage mode of the concrete girder subject to semi-rigid trailer impact

Figure 13. Photo. Typical scratch damage mode of the concrete girder subject to normal trailer impact.

PARAMETRIC STUDIES

Figure 14 shows the setup of the prototype impact beam subjected to the semi-rigid trailer impact.

The impact beam prototype was a steel box beam with a dimension of 40-inch x 40-inch x 2 inch.

The size of the beam was consistent with the depth of the example prestressed concrete girder shown in Figure 11 so that it could be aligned with the protected girder after installation. The span of the beam was around 66 ft (which is also the same as that of the example girder in Figure 11).

The steel beam was modeled using shell elements and was represented by material model MAT 3, which is the same as that for rebars in the concrete girders. The yield strength of the steel was 60 ksi.

To develop the demand model during an overheight impact, three different truck velocities were considered: 40 mph, 55 mph, and 70 mph, and three different truck weights were considered: 20

US ton, 30 US ton, and 40 US ton. In the following discussion, the name for each simulation case is described in the format of V-W, where V is the impact velocity (mph), W is the truck weight

(US ton).

Figure 15 shows the impact force time histories for different velocities and truck weights. In Figure

15a, the peak impact force increased from 1,250 kips to 2,100 kips as the velocity was increased from 40 mph to 70 mph for a 20-ton truck. The effects of truck weights on the peak impact forces are shown in Figure 15b, where the peak impact force increased from 2,100 to 3,050 kips as the truck weight was increased from 20 ton to 40 ton at a velocity of 70 mph.

Figure 16 shows the displacement time histories of the impact beam subjected to the trailer impact at different velocities and weights. In Figure 16a, the peak deformation of the beam increased from

4.2 inch to 8.0 inch as the velocity of the truck was increased from 40 mph to 70 mph at a total truck weight of 40 ton. Figure 16b shows the effects of the truck weight on the beam deformations for a velocity of 55 mph, where the peak deformation of the beam increased from 2 inch to 6 inch as the weight of the truck was increased from 20 ton to 40 ton.

Figure 14. Photo. Simulation setup of overheight impact with steel box beam.

Figure 15. Graph. Impact force time history for steel beams: (a) W20; (b) V70.

Figure 16. Graph. Displacement time history for steel beams: (a) W40; (b) V55.

SIMPLIFIED PULSE MODEL FOR OVERHEIGHT IMPACT

Based on the analysis of the impact force time histories for various truck weight/velocity combinations, a simplified triangular pulse is proposed and is shown in Figure 17 to represent the demand model of overheight impact from semi-rigid trailers. Based on the observations from parametric simulation cases with a truck velocity varying from 40 mph to 70 mph and truck weight varying from 20 ton to 40 ton, the duration of the pulse was assumed to be 0.02 sec and the peak loading, F, was dependent on the truck velocities and weight. Figure 18 illustrates the loading scheme for the proposed pulse model, where the pulse was applied as a distributed force on the impact beam over a length of 8 ft, representing the width of the standard trailer used in this study.

Figure 17. Graph. Simplified triangle pulse loading model.

Figure 18. Photo. Loading application of the pulse model.

The peak force of the proposed pulse model was calibrated so that the pulse model causes the same displacement of the beam as that from truck impact. Based on a systematic parametric study, where all key parameters have been varied, a general equation for the peak impact, that is similar to that in AASHTO (2017) for vessel collisions, can be obtained through nonlinear regression of simulation results as, 𝐹 = 0.75𝑉0.84𝑊1.35 (1) where, F is the peak force (kips), V is the truck impact velocity (mph), W is the truck weight (US ton).

It should be noted that the form of the demand model in equation (1) is similar to that for the impact of trucks on bridge piers defined in Agrawal et al. (2018), Cao et al. (2019b), and Xu et al.

(2019).

Figure 19 shows the comparison of the beam displacement from the truck and pulse simulations.

It can be seen from Figure 19 that the pulse simulation results match the truck simulation results reasonably well. Table 1 lists the results of the calibrated pulse force from the FE simulations and that from the proposed demand model based on equation (1).

Figure 19. Graph. Comparison of the beam displacement caused by the truck impact and pulse loading: (a) V40-W40; (b) V55-W40; (c) V70-W40; (d) V55-W20

It should be noted that the peak force from equation (1) is impulsive in nature and has a relatively short duration. As such, direct use of the estimated dynamic load in the traditional static design framework may lead to overconservative results. Instead, the dynamic load from equation (1) for a particular impact velocity and truck weight could be used in a performance-based framework to directly obtain the required capacity to satisfy a certain performance level as done in the next section.

Table 1. Comparison of calibrated pulse demands in FEM and proposed equation results

Simulation FEM (kips) Equation 1

(kips)

Equation 1/FEM

V40-W40 2305.35 2418.65 1.05

V55-W40 3040.01 3160.44 1.04

V70-W40 3749.21 3870.12 1.03

V40-W30 1922.04 1640.23 0.85

V55-W30 2573.89 2143.28 0.83

V70-W30 3080.70 2624.56 0.85

V40-W20 765.83 948.82 1.24

V55-W20 1053.77 1239.81 1.18

V70-W20 1162.71 1518.22 1.31

Average 1.04

PERFORMANCE-BASED DESIGN

A performance-based design framework requires determination of three things: 1) demand (D), 2) capacity (C), and 3) a performance objective for a given hazard level. In general, the computation of demand for the vehicular impact problem is complicated because it entails running a full vehicle model. However, that can be greatly simplified by using the proposed demand equation and exploiting the previously discussed observation that the force time histories have similar characteristics and loading effects on the impact beams.

The proposed performance-based design method correlates the ductility of the girder with the demand to capacity (D/C) ratio, where D is the dynamic impact force from equation (1) and C is the plastic capacity of the steel beam, as illustrated in Figure 20 and Equation 2. The proposed approach has conceptual similarities to a method proposed by the authors for the design of bridge piers impacted by both single unit (SU) and TS trucks (Agrawal et al. 2018 and Cao et al. 2019b).

In the design of structures against vehicular impact, the performance objective is typically a qualitative one, e.g., minor or major damage, as defined in Liu (2012). In this study, the performance was quantified using the ductility ratio of the impact beam, which is the maximum deformations over the yielding deformation. The yielding deformation was determined based on the pushover simulation, where an 8-ft distributed pushover load was applied in the middle of the impacted beam (similar to the loading application in Figure 18). Impact beams with minor damage, i.e., ductility ratio less than 1.0, are fully functional after the impact and do not need immediate attention. Yielding damage is associated with the ductility ratio larger than 1.0 with permanent damage in the beams and may need temporary closure of the road for immediate repair or replacement after the impact event. A steel beam with yielding damages will not collapse and the impacting trailer will be stopped or effectively deformed so that it would not impact the protected concrete girders.

Figure 20. Graph. Capacity calculation model for steel box beams.

1 2

1 3 1 3

1 1 p p p

M M C P P M

L L L L = + = + = + (2) where, L2 = width of the trailer, 8 ft.

L1 = L3 = 0.5x(L4 – L2).

L4 = span length of the beam.

Mp = plastic moment of the steel beam.

C = lateral capacity of the beam.

Table 2 lists the ductility ratios calculated for each truck-impact beam simulation. Figure 21 shows the plot of the ductility of the impacted beam as a function of the D/C ratio for the nine cases of semi-rigid trailer impact on the barrier. It is observed from Figure 21 that two levels of performance, i.e., minor and yielding damage, can be clearly distinguished in terms of the D/C ratio.

Table 2. Computed ductility ratio for the impact beams subject to truck impact

Simulation Ductility Damage level

V40-W20 0.24 Minor

V55-W20 0.33 Minor

V70-W20 0.37 Minor

V40-W30 0.63 Minor

V55-W30 0.86 Minor

V70-W30 1.04 Yielding

V40-W40 0.77 Minor

V55-W40 1.03 Yielding

V70-W40 1.33 Yielding

Figure 21. Graph. Performance based design chart for the steel box beam

The performance levels in terms of ductility and D/C ratios are listed in Table 3 below. The information presented in Table 3 can be used to design an impact beam to achieve the desired performance level as discussed in the next section.

Table 3. Performance levels, corresponding damage state, and rotation.

Performance level

Damage state D/C Ductility

Immediate use Minor damage [0.00, 1.75] [0.0, 1.0]

Need repair/ replacement

Yielding damage but stopped the trailer

[1.75, 2.75] [1.0, 1.8]

PROPOSED DESIGN PROCEDURE

The information from Figure 21 and Table 3 can be used to establish a performance-based design methodology that applies to impact beam designs. The proposed design steps are as follows:

1. Select the speed and weight of the impacting tractor-semitrailer based on local traffic conditions and owner requirements.

2. Determine the desired performance level: Immediate use (minor damage) or Need repair/replacement (yielding damage). Select from the ranges in Table 3 an acceptable D/C ratio.

3. Compute the demand, D, using design equation (1) for the selected truck speed, weight through dynamic analysis using any commercial structural analysis software.

4. Determine the required capacity of the beam, C = D/(selected D/C ratio).

5. Select the section size and steel strength to satisfy C. Compute the actual capacity of the beam, Cdesign, using the plastic capacity analysis shown in equation (2).

VALIDATION OF THE PROPOSED FRAMEWORK

Three impact beams with characteristics that are different than those used during the calibration of the demand model were selected to validate the proposed performance-based design framework.

The geometries and strengths of the selected beams are shown in Table 4. The steel beams were designed according to the procedure detailed above. These steel beams were then impacted by the calibrated tractor-semitrailer with different combinations of weight and approach speeds, as outlined in Table 5, creating a total of 7 cases that cover a broad range of design scenarios. A unique descriptive name is given to each case of simulation in Table 4. For example, V-W, where

V is the impact velocity (mph), W is the truck weight (US ton). The actual deformation and ductility ratios were computed for each case. These values are listed in Table 5 along with the computed damage states according to the criteria in Table 3. As shown in Table 5, the predictions are accurate for all the cases. This shows that the proposed framework is reasonable and can be used to achieve the desired performance level for a bridge at a risk of being impacted by a truck, given the complexity of the collision process being modeled.

Table 4. Beam geometry for validation study

Beam

ID

Beam section dimension

(inch)

Beam section thickness

(inch)

Beam span

(ft)

Steel strength

(ksi)

Cdesign

(kips)

1 40 2.0 32 60 3543

2 30 1.5 32 60 1495

3 40 2.0 48 60 2113

Table 5. Selected cases for validation of proposed method

Case Truck characteristics

Beam

ID

D/C

Predicted damage level

Ductility

Actual damage level

1 V55-W20 1 0.53 Minor 0.38 Minor

2 V55-W30 1 0.76 Minor 0.91 Minor

3 V40-W40 2 1.63 Minor 0.77 Minor

4 V55-W40 2 2.14 Yield 1.11 Yield

5 V70-W40 2 2.62 Yield 1.69 Yield

6 V60-W30 3 1.10 Minor 0.88 Minor

7 V50-W30 3 0.95 Minor 0.80 Minor

CHAPTER 3. RETROFIT OF GIRDERS DAMAGE DURING

OVERHEIGHT IMPACT USING CARBON-FIBER REINFORCED

POLYMERS

Composites such as carbon fiber-reinforced polymer (CFRP) have been widely used to increase the ultimate strength of reinforced concrete (RC) and pre-stressed concrete members through externally bonded FRP systems (Belarbi et al. 2012; Rosenboom et al. 2009). More recently, the use of composite materials in the strengthening, rehabilitation, and repair industry has been gaining popularity due to their excellent material behavior and ease of application. However, the effectiveness of CFRP in protecting pre-stressed girders impacted by over-height vehicles is not well established because of the lack of guidance on the application of CFRP and evaluation of its effectiveness. Hence, the proposed research used high-fidelity simulations to investigate the behavior of several pre-stressed concrete girders wrapped by CFRP when impacted by over-height vehicles.

MODEL OF THE TRUCK AND BRIDGE

Bridge Model

Figure 22 shows the full-scale prestressed concrete girder bridge model developed in LS-DYNA

(Hallquist 2006). The bridge model was developed based on the as-built drawing of a highway bridge in Texas that has been subjected to several overheight impact accidents (Figure 23). Figure

24 shows the application of carbon fiber reinforced polymer (CFRP) wrap on the example bridge girders. In Figure 24, the total length of the CFRP was around 1/3 of the total span of the bridge, which is close to the width of the roadway underneath the girder. The CFRP wrapping was applied from the bottom of the girder to the web of the girder.

Figure 22. Photo. Example concrete bridge model subject to the modified semi-rigid trailer

Figure 23. Photo. Example prestressing concrete bridge (a) before the impact; (b) post-impact scene

Figure 24. Illustration. Illustration of CFRP wrapping on prestressing concrete girders.

Material Model

As shown in Figure 22, the concrete behavior was modeled by the Continuous Surface Cap Model

(CSCM MAT159) in LS-DYNA (Hallquist 2006). Steel rebars were modeled using Hughes-Liu beam elements with material model MAT 3, which accounts for yielding and kinematic hardening plasticity. Steel rebar elements were assumed to fracture and removed after the strain reached 0.20.

More details about the material models and validations for the concrete, steel rebars, and tendons can be found in Chapter 2.

The CFRP sheet was modeled using ENHANCED_COMPOSITE_DAMAGE (MAT55) in LS-

DYNA (Hallquist 2006). The material was defined as elastic before reaching its failure strain and elements would be deleted (fracture) after reaching the maximum allowable strain. The young’s modulus of the CFRP was 32,915 ksi and the failure strain was around 0.0167 based on the manufacture information provided by TXDOT. Shell elements were used to model the CFRP wrapping, which were fully merged with the concrete girders. The failure mode of debonding was not modeled in this study. The thickness of the CFRP wrapping was 0.08 inch based on the manufacture's information.

SIMULATION RESULTS

Based on the setup in Figure 22, numerical simulations were carried out to identify the typical damage mode of CFRP wrapped concrete girders subject to overheight truck impact. In the simulation, the velocity of the truck was 55 mph and the weight of the truck was 40 US ton. Based on the simulation, Figure 25 shows the comparison of the simulated damage mode of the girder and the actual damaged girder during the overheight impact accident in Figure 23. It can be seen from Figure 25 that diagonal cracking was developed in the front face of the girder’s web. Most of these inclined cracks were developed outside the wrapping area. Also, horizontal yield lines were developed between the web and top/bottom flanges, which indicated the typical weak locations of I-girders in the lateral direction.

Figure 26 shows some localized damage of the CFRP sheet (fracture) caused by the edge of the impinging semi-rigid trailer. In Figure 25, similar patterns of CFRP fracture were also observed in the bottom flange of the damaged girder.

Figure 25. Photo. Typical damage mode of the CFRP wrapped girders subject to overheight impact from actual accidents and simulations

Figure 26. Photo. Localized damage of the CFRP wrapping from the simulation

PARAMETRIC STUDY

Figure 27 shows the effects of CFRP thickness on the deformation of concrete girders, where the velocity and weight were the same as the example above, i.e., 55 mph and 40 US ton. In Figure

27, the peak deformation of the girder without CFRP wrapping was 13.8 inches and the permanent deformation was around 7 inches. After applying the 0.08-inch thick CFRP, the peak deformation was reduced from 13.8 inch to 11 inches, while the permanent deformation of the CFRP girder was similar to the results without CFRP wrapping. To investigate the effect of CFRP thickness on the girder deformations, the thickness of CFRP sheet was changed from 0.08 inch to 0.80 inch. In

Figure 27, it can be seen that the peak deformation of the girder decreased from 11 inches to 6.2 inches (44% less) as the thickness was increased from 0.08 inch to 0.80 inch, which shows certain confinement effects from the thick CFPR sheets. However, the permanent deformation was still large for the 0.80-inch CFRP wrapping case, and was only reduced by 36% as the thickness was increased by 10 times, and the concrete girder was found significantly damaged, showing a damage mode similar to that in Figure 25.

Figure 27. Graph. Effects of CFRP on the girder deformations subject to overheight impact

(V55-W40)

Figure 28 shows the deformation of the 0.08-inch thick CFRP wrapped girder subjected to different truck velocities and truck weights. In Figure 28a, the permanent deformation of the girder increased from 4 inch to 9 inch as the velocity of the truck was increased from 30 mph to 70 mph.

Also, in Figure 28b, the girders’ permanent deformation increased from 2 inch to 8 inch as the weight of the truck was increased from 20 US ton to 40 US ton for a truck speed of 50 mph.

Figure 29 shows the impact force time histories for a 40-ton truck impacting the CFRP girder at different velocities. In Figure 29, the impact force shows impulsive nature and the peak impact force increased from 1,350 kips to 1,978 kips as the velocity was increased from 30 mph to 50 mph. The peak impact force was found to be decreased from 1,978 kips to 1,619 kips as the velocity was increased from 50 mph to 70 mph. This is because the girder was more severely damaged by the 70-mph truck than that by the 50-mph truck. Figure 30 shows the damage mode of the CFRP wrapped girder subject to an overheight truck at different speeds. The simulation results show that the CFRP wrapped girder doesn’t have sufficient capacity to resist the impact load from the overheight truck.

Figure 28. Graph. Deformation of the CFRP wrapped girder subject to different truck impact: (a) speed effects; (b) weight effects.

Figure 29. Graph. Impact force time history for a 40-ton truck at different speeds.

Figure 30. Damage mode of the CFRP wrapped girder: (a) V30-W40; (b) V50-W40; (c)

V70-W40

PUSHOVER ANALYSIS SIMULATION

The simulation results shown in Figure 25 and Figure 27 indicated that CFRP wrapping was not effective in preventing severe damage or large deformations of concrete girders under the overheight impact. To better study the lateral capacity enhancement by the CFRP wrapping, pushover simulations were conducted on the concrete girders with and without CFRP. Figure 31 shows the setup of the pushover loading in LS-DYNA, where the loading length was around 8 ft representing the width of the trailer. Based on the simulation, Figure 32 shows the load-deflection curves for the concrete girder with and without CFRP. It can be seen from Figure 32 that the peak loading of the girder was increased from 261 kips to 354 kips (0.04-inch thick CFRP) and 384 kips for 0.08-inch thick CFRP, which is still much less than the peak dynamic loading from the truck impact shown in Figure 29, even for a low-speed impact of 30 mph.

Figure 31. Illustration. Pushover loading setup on the concrete girder.

Figure 32. Graph. Pushover curve from the simulation.

Figure 33 shows the yield line patterns of the concrete girder obtained from the pushover simulations. In Figure 33, several inclined yield lines have been seen to develop in the front face and back face of the girder. Also, a horizontal yield line occurred at the interface between the deck and the girder. The overall damage pattern appeared to be a W-shape based on the simulations. To estimate the lateral capacity of the concrete girder, Figure 34 shows the yield line method calculations based on the W-shape damage patterns obtained from the simulations. Based on the energy balance method, Equation (3) shows the calculation of the lateral capacity of the concrete girder using the yield line method.

Using Equation (3), the calculated capacity of the concrete girder was around 254 kips, which matched the pushover simulation results reasonably well (Figure 32). It should be noted that similar W-shape yield line patterns have also been seen in concrete barriers subject to lateral loading and a similar yield line method was developed recently by Cao et al.