National Academies Press: OpenBook

MASH Railing Load Requirements for Bridge Deck Overhang (2023)

Chapter: Chapter 2 - Overview of LS-DYNA Modeling Practices

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Suggested Citation:"Chapter 2 - Overview of LS-DYNA Modeling Practices." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
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Suggested Citation:"Chapter 2 - Overview of LS-DYNA Modeling Practices." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
×
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Suggested Citation:"Chapter 2 - Overview of LS-DYNA Modeling Practices." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
×
Page 7
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Suggested Citation:"Chapter 2 - Overview of LS-DYNA Modeling Practices." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
×
Page 8
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Suggested Citation:"Chapter 2 - Overview of LS-DYNA Modeling Practices." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
×
Page 9
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Suggested Citation:"Chapter 2 - Overview of LS-DYNA Modeling Practices." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
×
Page 10
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Suggested Citation:"Chapter 2 - Overview of LS-DYNA Modeling Practices." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
×
Page 11
Page 12
Suggested Citation:"Chapter 2 - Overview of LS-DYNA Modeling Practices." National Academies of Sciences, Engineering, and Medicine. 2023. MASH Railing Load Requirements for Bridge Deck Overhang. Washington, DC: The National Academies Press. doi: 10.17226/27422.
×
Page 12

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5   Overview of LS-DYNA Modeling Practices LS-DYNA (4) was used to create models of railing and overhang specimens for the analytical program. In this chapter, key aspects of LS-DYNA modeling practices used in this project are described, including material models, reinforcement modeling, and calibration criteria. Concrete Material Models Three potentially applicable concrete material models were identified at the beginning of NCHRP Project 12-119: the Karagozian and Case (K&C) model (5), the Continuous Surface Cap (CSC) model (6), and the Winfrith model (7). Although the formulations of each model are similar, each model may provide a different result; the model that provides the most accurate result is specific to application. For a demonstration of variable results produced by the three different concrete models, damage contours at the failure of a barrier model are shown in Figure 1. Although the CSC model is the most commonly used concrete model in vehicle impact applications, limitations in its ability to accurately capture shear failure have been identified in the literature (8). This limitation was also observed during this project. For barrier, which typically fail in flexure, this limitation is largely insignificant. For overhangs supporting posts, however, this limitation has a pronounced effect on predicted behavior as deck failure in those cases is typically due to a combination of flexure, shear, and torsion. Thus, the CSC model alone was deemed insufficient for this project, hence, the introduction of additional concrete models. Although the Winfrith model produced accurate results in preliminary modeling efforts, this model was eliminated from consideration due to its use of smeared reinforcement. In the Winfrith model, reinforcement is specified as an effective unit-length steel area, rather than dis- cretely modeled. This feature of the Winfrith model, while convenient in applications regarding slabs with grid reinforcement, rendered the model ineffectual for this project. Overhangs and concrete railings typically include unique steel details that require discrete bar modeling, and bar strains at particular locations require calculation for comparison to strain gage measurements in the eventual model calibration process. Thus, only the CSC and K&C concrete models were used in this project. Modeling Reinforcement Reinforcing bars were modeled as beam elements embedded in the concrete matrix via the Constrained-Beam-in-Solid (CBIS) keyword in LS-DYNA. In this formulation, beam node velocities and accelerations are forced to be equal to those of the nodes of the concrete solid element that contains them. The CBIS formulation used herein corrected energy imbalances identified in the Constrained-Lagrange-in-Solid formulation, which was previously common practice for constraining rebar in concrete (9). C H A P T E R 2

6 MASH Railing Load Requirements for Bridge Deck Overhang A notable limitation of modeling reinforcement using CBIS is its neglect of the eects of bar development length. As beam elements are essentially locked into the surrounding concrete matrix, bars are able to reach their yield stress over very short embedment lengths. Using the CBIS formulation, if the overall tensile breakout strength of the bar (assuming a perfect bond) is sucient, the bar can develop its full yield stress. is is unrealistic, as bar stresses must be progressively developed along the embedment length of a bar through bearing stresses on ribs and cohesion. To approximately represent the eects of incomplete bar development, a method of allowable stress tapering (Figure 2) was used. For bars that were not fully developed at a critical section, the maximum developable stress in the bar was varied from zero at the free end to the nominal tension yield stress, fy, at the end of the AASHTO LRFD BDS development length. K&C concrete model CSC concrete model Winfrith concrete model Figure 1. Barrier pushover damage predictions with various concrete material models. AASHTO LRFD BDS development length Figure 2. Model of incomplete bar development.

Overview of LS-DYNA Modeling Practices 7   Material Properties Both nominal and as-tested material properties were used in LS-DYNA models depending on the objective of the model. For models that were created to represent a physical test for accuracy evaluations, as-tested material properties were used, and steel strain hardening was included. For models created to aid in the development of design methodologies, nominal material properties were used, and steel was modeled as elastic-perfectly plastic. Thus, consistent with AASHTO LRFD BDS, the design methodology proposed herein conservatively assumes no load can develop in reinforcing steel beyond the yield stress. Model Evaluation Criteria and Calibration Process Models corresponding to physical tests were used to evaluate the accuracy of modeling practices to establish confidence in the analytical program results. If models did not predict test behavior to a reasonable degree of accuracy, they were calibrated until tolerable accuracy was achieved. In this context, “accuracy” is a somewhat subjective term. As a general rule, error in the peak load and corresponding lateral deflection of the test article were limited to 5% for post tests and 10% for barrier tests. Target accuracies for barrier tests were slightly relaxed due to the more complex, distributed nature of the behavior. The general process of evaluating the accuracy of a model began with an initial energy validation in which energy conservation was confirmed, and hourglass energy was limited to 10% of the total energy. Then, the model’s general depiction of the event, including deflection behavior and damage, was qualitatively compared to the physical test. If the general response of the model appeared reasonable, force-time and force-deflection histories were then compared, at which point the 5% and 10% limits on peak force and corresponding lateral deflection were imposed. Models that passed the preceding evaluations were deemed, at a minimum, to be rea- sonably accurate in predicting the global behavior of the specimen. After this distinction was made, physical test strain gage measurements were compared to model strain calculations in rebar beam elements at corresponding locations. At a minimum, strain agreement was required at the point in time when the first bar yield occurred in the physical test. It was also desired that strain agreement was maintained throughout the entire event; however, in cases of extreme damage, accuracy requirements were relaxed slightly, as the accuracy of the concrete models is significantly less reliable in these cases. Prevalidation Efforts At the onset of this project, prevalidation exercises were performed to evaluate the accuracy of the applied modeling practices before test specimen development. This process included modeling physical tests found in literature of railings or railing components attached to over- hangs. Modeled tests included strip specimen tests performed by Trejo et al. (10); safety-shape barrier tests performed by Williams et al. (11) and Alberson et al. (12); concrete-post tests performed by Arnold and Hirsch (13) and Williams et al. (11); and steel-post tests performed by Arnold and Hirsch (13). Results of barrier test models indicated that both the autogenerated K&C and CSC concrete models were capable of producing reasonably accurate behavior for this system type. The K&C model provided more accurate results in tests performed by Williams et al. (11) in which punching shear failure governed the barrier response. Initial errors in peak load prediction for both baseline models ranged from 20% to 30% across three barrier tests. In this initial calibration exercise,

8 MASH Railing Load Requirements for Bridge Deck Overhang slight modifications were applied to both the CSC and K&C models to produce better agreement with physical test results. For the CSC model, tensile and shear fracture energies were reduced relative to the compressive fracture energy; for the K&C model, the shear dilation factor and tensile damage evolution coefficient were modified. Barrier model results produced after these modifications were applied as shown in Figures 3, 4, and 5. As shown, the precalibrated models of interior load tests produced reasonably accurate rep- resentations of barrier damage mechanisms and ultimate lateral capacities. For test A, which was an interior test but was near the free end, the K&C and CSC models underpredicted capacity by 8% and overpredicted capacity by 7%, respectively. For test B, which was an interior test, the K&C model underpredicted capacity by 4%. Test C, which was performed at a free end of the barrier, was also modeled in this exercise. Damage contours at peak loads in each model are compared to physical test damage in Figures 6, 7, 8, and 9. It should be noted that the tests performed in this series were partial end regions in which the barrier was terminated, but the slab continued beyond the barrier. Damage prediction in these models was reasonably accurate, although the modified CSC model overpredicted horizontal damage at the slope breakpoint of the safety-shape barrier. (The modified CSC model 67.0 kips 61.8 kips 67.0 kips 71.9 kips Figure 3. Texas Department of Transportation (TxDOT) T501 test A comparison (K&C concrete model). Figure 4. TxDOT T501 test A comparison (CSC concrete model).

Overview of LS-DYNA Modeling Practices 9   75.0 kips 71.9 kips Figure 5. TxDOT T501 test B comparison (K&C concrete model). 40.0 kips 40.5 kips 40.0 kips 40.5 kips Figure 6. TxDOT T501 end-region test C results (K&C concrete model). Figure 7. TxDOT T501 end-region test C results—field side (K&C concrete model).

10 MASH Railing Load Requirements for Bridge Deck Overhang 40.0 kips 41.6 kips 41.6 kips 40.0 kips Figure 8. TxDOT T501 end-region test C results (CSC concrete model). Figure 9. TxDOT T501 end-region test C results—field side (CSC concrete model). used reduced tensile and shear fracture energies relative to autogenerated values. Also, the modulus recovery parameter was reduced to 75%, and a 5% erosion strain was specified.) After slightly calibrating the CSC and K&C models to the results of barrier tests, their ability to predict the behavior of overhangs supporting concrete posts was evaluated. In this evalu- ation, bogie impact testing of the Texas Department of Transportation (TxDOT) T223 open concrete railing was used. One interior impact and one end-region impact were modeled. For the interior test, the K&C model underpredicted the peak lateral load exerted on the bogie vehicle by 7%. Model damage is compared to physical test specimen damage for the interior impact in Figure 10. For the end-region test, the K&C model overpredicted the peak lateral load exerted on the bogie vehicle by 25%. Model damage is compared to physical test specimen damage for the interior impact in Figure 11. Based on the results of the concrete-post modeling exercise, it was determined that the CSC model was inaccurate in predicting the behavior of overhangs supporting posts. For the two test models shown above, CSC models predicted virtually zero damage in the railing and overhang, which was not consistent with test results. CSC models also overpredicted the interior and end-region impact forces by 36% and 29%, respectively.

Overview of LS-DYNA Modeling Practices 11   No modifications were applied to the K&C model following the concrete-post modeling exercise. However, it was found that the accuracy of the model was significantly improved by reducing the mesh size. Contrary to the guidance provided in the LS-DYNA Keyword User’s Manual, which suggests that a mesh size of at least three times the maximum aggregate diameter be used (4), improved results were produced when a 1-in. mesh size was used. The results shown above correspond to a 2-in. mesh size, which proved too large to accurately depict crack locations and orientations. Following the concrete-post modeling exercise, the accuracy of the models in steel-post appli- cations was evaluated. This evaluation was performed using pushover testing of the TxDOT T101 post on a deck overhang (13). As expected, the CSC model overpredicted the peak load achieved in the post-pushover test, as shear damage in the slab was not captured. The CSC model with previously applied modifica- tions overpredicted the system capacity by 56%. At this point in the prevalidation effort, the CSC model was eliminated from consideration for applications involving steel and concrete posts. The K&C model with previously applied modifications predicted the peak load within 5% but did not accurately predict damage mechanisms in the slab and the overall force-deflection response to an acceptable level of accuracy. The response of the model was too brittle, under- estimating the total energy dissipation of the system by roughly 50%. Figure 10. TxDOT T223 interior test damage—model and physical test (K&C concrete model). Figure 11. TxDOT T223 end-region test damage—model and physical test (K&C concrete model).

12 MASH Railing Load Requirements for Bridge Deck Overhang It was found that reducing the K&C model’s localization width, which controls the relationship between mesh size and fracture energy, resulted in a significantly improved model response. The K&C user’s manual recommends that the localization width be set at three times the maximum aggregate diameter, which was 2.25 in. for this system (0.75-in. aggregate diameter). Modifying the localization width to 0.75 in. resulted in improved results, accurately predicting the ductile response of the overhang and predicting the peak lateral load within 5% of the test value. The results of this exercise suggest that the localization width must be less than the element size for accurate behavior predictions at significant damage levels. Damage predicted in the LS-DYNA model is compared to damage sustained in the physical TxDOT T101 test in Figure 12. Based on the results of these three modeling exercises, it was determined that the selected material models and modeling practices were capable of producing acceptably accurate results. Thus, the material models calibrated in this prevalidation effort were used to perform portions of the analytical program and to plan physical test specimens used in this project. Figure 12. TxDOT T101 pushover test damage—LS-DYNA model (left) and physical test (right) (K&C concrete model).

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State highway agencies across the country are upgrading standards, policies, and processes to satisfy the 2016 AASHTO/FHWA Joint Implementation Agreement for MASH.

NCHRP Research Report 1078: MASH Railing Load Requirements for Bridge Deck Overhang, from TRB's National Cooperative Highway Research Program, presents an evaluation of the structural demand and load distribution in concrete bridge deck overhangs supporting barriers subjected to vehicle impact loads.

Supplemental to the report are Appendices B through E, which provide design examples for concrete barriers, open concrete railing post on deck, deck-mounted steel-post, and curb-mounted steel-post.

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