Transportation Research Record 1647

TRANSPORTATION RESEARCH RECORD 1647

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Finite-Element Modeling and Model Verification of Steel W-Beam Guardrails Subject to Pendulum Impact Loading T. RUSSELL GENTRY AND LAWRENCE C. BANK The experimental and simulated response of steel W-beam guards to pendulum impact loading for impact velocities of 20 km / h, 30 km / h, and 35 km / h are presented. The guardrails were supported by four posts and cable-anchored at each end to ensure that the full tension capacity of the rail could be developed. Experiments carried out with a 912-kg impact pendulum are compared with LS-DYNA finite-element simulations of the impact events. Pendulum tests were completed at the Turner Fairbank Highway Research Center of the Federal Highway Administration. Acceleration, velocity, and displacement time histories are compared for the pendulum impact test and the LS-DYNA simulations. Comparison of the experimental and simulation acceleration records is made using the Numerical Analysis of Roadside Design time-domain statistics. The comparative statistics show that the simulations are in good agreement with the experiments. Guardrail tension data and cable tension data are presented from the LS-DYNA simulations. Results show that the guardrail was close to its tension yield point when impacted at an initial velocity of 35 km / h.

Research at the Federal Highway Administration and at the Catholic University of America has focused on the development of fiberreinforced plastic composite materials for highway guardrails. As a preliminary and necessary step toward the characterization of composite guardrails, it was decided to develop a set of standard procedures that would be used to test current steel W-beam guardrails and the prototype composite guardrails. Included in these tests was pendulum impact testing carried out at the Federal Outdoor Impact Laboratory (FOIL) at the Turner Fairbank Highway Research Laboratory. Initial tests were carried out on steel guardrail sections that were supported by two posts (1). From the results of these two-post tests, it was concluded that the two posts were not capable of adequately restraining the guardrail. As a consequence of this lack of restraint, the full tension capacity of the guardrails was not developed during the pendulum testing, and the guardrail system was unable to withstand a pendulum impact with an initial velocity of 35 km /h. From energy calculations, it can be shown that the 35-km /h pendulum impact using the 912-kg pendulum perpendicular to the guardrail is roughly equivalent to an NCHRP Report 350 Test 3–10 with an impact angle of 20 degrees (2). Modifications to the pendulum test fixture were completed to allow for four-post testing with the guardrail section anchored with steel cables (Figure 1). A series of impact tests on steel W-beam guardrails was completed in this fixture using a 912-kg mass pendulum. The tests were completed in early 1996 and are numbered 96P001 through 96P006. Impact velocities were 20 km /h and 30 km /h for tests

T. R. Gentry, College of Architecture, Georgia Institute of Technology, Atlanta, GA 30332-0155. L. C. Bank, Department of Civil and Environmental Engineering, University of Wisconsin–Madison, Madison, WI 53706.

96P001 and 96P002, respectively. The impact velocity for tests 96P003 through 96P006 was 35 km /h. The results of these fixed-end guardrail tests are discussed by Brown (3). The focus of this paper is the finite-element modeling of the fixedend steel W-beam guardrail tests. The steel guardrail, supporting fixtures, and pendulum impactor were modeled in LS-DYNA, and simulations at the three initial velocities (20, 30, and 35 km /h) were completed. LS-DYNA is an explicit finite-element code capable of tracking the inelastic material behavior and large displacements associated with impacts into highway safety structures (4). LS-DYNA is a commercial version of the public-domain LLNL-DYNA (coded and maintained by Lawrence Livermore National Laboratory). Previous finite-element modeling of the two-post guardrail experiments, completed using LLNL-DYNA, has been reported by Bank et al. (5). In the current work, time history and animation results from the simulations are compared with experimental results. The sensitivity of the model to changes in element formulation, material properties, and geometric modeling is discussed. Comparative statistics from the Numerical Analysis of Roadside Design (NARD) validation procedures are presented for the 35-km /h experiments and the LS-DYNA simulations (6 ).

DESCRIPTION OF PENDULUM IMPACT TESTS The setup and execution of the pendulum impact tests are described briefly in the section below. A more detailed description of the tests can be found in the report by Brown (3). A photograph of the steel guardrail installed in the test fixture is included as Figure 1. The impact pendulum carries a mass of between 850 and 920 kg, depending on the nose fitted for the impact experiment. For these impact events, the pendulum was fitted with a triangular wood nose, with a height of 300 mm and a radius of approximately 75 mm. The mass of the pendulum for Experiments 96P001 to 96P006 was 912 kg. The pendulum is suspended by four steel cables and swings on a circular radius. It is constructed of reinforced concrete with steel-plate weights. The guardrails were placed at the bottom of the circular path of the pendulum. The guardrail was connected to two inboard posts and two outboard posts. The inboard posts were standard strong steel posts with blockouts. The outboard posts were large steel tubes that were designed to remain absolutely rigid during testing. The guardrail was installed in three 1.9-m sections. A standard eight-bolt splice that straddles the inboard posts was used to join the three sections of rail. One 16-mm bolt with washer was used to connect the guardrail to each post, and two 16-mm bolts with washers were used to connect the post to blockout.

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results of the tests are summarized below. Additional discussion is provided along with results of the LS-DYNA simulations. 20-km /h Test At 20 km / h, the pendulum was stopped at a peak displacement of 0.23 m at a time of 0.075 s after impact. The posts and blockouts deformed little during this event. Most of the inelastic damage to the guardrail was contained in the middle “span” of the rail and consisted of flexural damage at the point of impact. The input energy and strain energy exerted to stop the pendulum for Test 96P001 were 13 800 N-m. 30-km /h Test FIGURE 1

Steel W-beam guardrail in pendulum test fixture.

The 25-mm cables were fabricated with threaded male studs at each end. At the end closest to the inboard post, the threaded end of the cable passed through a standard cable-end anchor that was bolted to the guardrail with eight 16-mm bolts. The outboard end of the cable passed through the large tube posts. The cables were 6×19 independent wire rope core (IWRC) and have a nominal tensile strength of 400 kN for a 25-mm diameter. The strands are galvanized and are constructed of improved plow steel. The cables were tensioned using a turn-of-the-nut method before the test. The magnitude of the pre-tension was not measured before the tests. Instead, the voltage from the amplifier connected to the strain gauges on the guardrail were monitored to ensure that the cable pre-tension was roughly equal from test to test. RESULTS FROM PENDULUM IMPACT TESTS Six pendulum tests were completed on the steel guardrails. The first experiment (96P001) was run with an impact velocity of 20 km/h. The second experiment (96P002) was run with an impact velocity of 30 km /h. The final four experiments were run at an impact velocity of 35 km /h. In Experiment 96P005, one of the anchor cables snapped. An older cable had been reused for this experiment, and this may have contributed to the failure. An additional test at 35 km /h was completed to provide three good tests at 35 km /h. The overall

FIGURE 2

At 30 km/h, the pendulum was stopped at a peak displacement of 0.45 m at a time of 0.125 s after impact. The posts and blockouts deformed considerably during this event. The input energy and strain energy exerted to stop the pendulum for Test 96P002 were 31 400 N-m. 35-km/h Tests At 35 km/h, the pendulum was stopped at a peak displacement of 0.6 m at a time of 0.12 s after impact (data reported are the average of three experiments). The post and blockouts deformed considerably during these events. The input energy and strain energy exerted to stop the pendulum for Tests 96P003, 96P004, and 96P006 were 43,000 N-m. LS-DYNA FINITE-ELEMENT MODEL The finite-element model consisted of six major parts: guardrail, post, blockout, cable-end anchor, cable, and the pendulum impactor. Reflective half symmetry was used to reduce the size of the model. The model and its major parts are shown in Figure 2. LS-DYNA Version 936, running on a Sun Ultra-Sparc 1 workstation, was used to perform the simulation calculations. Various parts of the model were built in AUTOCAD, COSMOS-M, and HYPERMESH modelers and merged togther into one input deck. The guardrail itself was modeled using 1,242 four-node shell elements with five integration points through the thickness. Material

Finite-element model of pendulum and guardrail.

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properties for the guardrail steel were taken from test results published by Wright and Ray (7 ). An elastic-plastic material law with strain hardening was used for the guardrail steel (Material Model 24 in LS-DYNA). Strain rate effects were not included. Mesh density was increased in areas where large amounts of inelastic behavior were expected. The posts and blockouts were also modeled using four-node shell elements with five integration points through the thickness. Material Model 24 was also used for the post and blockouts. An effective plastic stress-strain curve appropriate for mild steel was used for the post and blockouts (7 ). The base of the post was modeled to be completely fixed. In the pendulum test fixture, the steel posts were dropped into large receiving tubes and wedged into place, approximating a fully fixed base. The cable-end anchor was modeled using the same material properties as the posts and blockouts. The cables were modeled as tension-only truss elements with linear elastic properties. The modulus of elasticity of the cables was set to 140 GPa, following recommendations by Costello for 6×19 IWRC cables (8). Theory predicts that the effective modulus of cable will be about 70 percent of the modulus of the base metal from which it is manufactured. The stiffness of cable drops dramatically if it is allowed to twist as it is loaded. An initial tension of 38 kN was input to account for the tightening of the cable using the turn-of-the-nut method used in the impact experiments. In the discussion that follows, the effect of varying the level of pre-tension in the cable will be discussed. None of the major parts shared nodes. Connection of the parts was achieved through constrained node pairs at the locations where bolts existed in the experiment. Additional compression-only connections were achieved through the contact algorithms used in the simulation.

Elements Omitted from Finite-Element Model The goal for any finite-element model is to develop sufficient detail in the model to capture the structural response with sufficient accuracy, without including excessive detail that increases modeling effort and computational expense. In the finite-element model of the steel guardrail, the bolts joining the three 1.9-m guardrail sections were omitted; instead, the guardrail was modeled as one continuous section 5.7 m long. Additionally, the bolts connecting the cable-end anchor to the guardrail were omitted. In this case, each bolt was replaced by a nodal constraint that forced the guardrail and the cable-end anchor to move together. The rail-to-blockout and blockout-to-post connections were also modeled with nodal constraints. The outboard posts present in the experiment were also omitted from the finite-element model. In trials of the modified impact fixture, strain gauge data showed that the outboard posts behaved elastically and were essentially rigid. Potential errors induced by these modeling simplifications are discussed below.

Parameters Output from Finite-Element Model Output from the finite-element model includes acceleration, velocity, and displacement time history data. These data are of primary importance as they can be directly compared with results from the impact experiments. Time histories presented below were taken from pendulum nodal data. Each data point represents the average of eight points sampled throughout the body of the pendulum. Acceleration data from the LS-DYNA simulations were digitally

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filtered using a 300-Hz low-pass filter to match the filter used in data processing at FOIL. A time history of cable tension forces and guardrail tension forces was also taken from the finite-element models. These are of special interest because they represent key design parameters that could not be observed during the experiments. In this case, the rail tension force is taken at a location just inside the inboard post; in other words, between the inboard post and the pendulum. Finally, deformed animation snapshots were taken at various intervals. These can be compared anecdotally with high-speed film taken from the experiments to confirm that key behavior witnessed in the experiments was also occurring in the simulation. These data are presented below and, when possible, are compared with data taken from the impact experiments.

COMPARISON OF EXPERIMENTAL AND SIMULATION RESULTS Figures 3 and 4 depict five steps in the deformation sequence of the guardrail undergoing the 35-km /h impact. Figures 5 and 6 present the pendulum time histories and rail/cable force time histories respectively for the 20-km /h experiment and simulation. Figures 7 and 8 present the pendulum time histories and rail/cable force time histories for the 35-km /h experiments and simulation. In general, three major phases of behavior were observed in both the experiments and in the simulation: 1. Just after impact, the rail begins to deform locally around the impact point. Later in this phase, the rail begins to bend at the two inboard posts, forming three plastic hinges and, thus, a flexural mechanism. This mechanism continues to actuate until the total deformation reaches about 0.30 m. During this initial deformation phase, the rail tension force increases almost linearly with time and displacement. The initial cable pre-tension dissipates early in this phase. As the pendulum displaces about 0.1 m into the guardrail, the tension is renewed and continues to increase during this phase. Note that for the 20-km /h experiment and simulation, the pendulum is stopped during this phase; therefore, the next two phases do not occur. 2. As the pendulum reaches a displacement of approximately 0.30 m into the guardrail, the posts begin to yield in a flexural/ torsional mode. This causes a significant loss of stiffness in the system. The deceleration of the pendulum drops, and both the guardrail and cable shed nearly 50 percent of their previous tension. The top of the posts move backward about 0.1 m and twist through 45 degrees during this phase. 3. At a displacement of about 0.45 m, the system restiffens sharply in a tension mode. The cable forces and rail tension forces return to their previous levels, and the pendulum is brought to a stop at a displacement of about 0.60 m. In comparing the acceleration time history records for the 20-km /h and 35-km /h impacts, it can be concluded that two differences exist in the actual and simulated behavior. First, the stiffness of the system in the initial phase of the impact event is slightly lower in the LSDYNA simulation compared with the experiments. Also, the initial flexural phase ends earlier in the LS-DYNA simulation (Figure 7). Second, the stiffening that occurs in the third phase is more dramatic in the LS-DYNA simulation than in the experiments. It appears that the cable/rail axial stiffness of the LS-DYNA model in the third phase is higher than the stiffness of the experiments. To quantify the extent of these differences, the acceleration time histories for the

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FIGURE 3

Front view animation of 35-km/h LS-DYNA simulation.

35-km /h experiments were compared with the LS-DYNA simulation using the NARD validation procedures (6).

STATISTICAL COMPARISON OF 35-km / h EXPERIMENTS AND LS-DYNA SIMULATIONS Figure 9 depicts the three acceleration time histories for the 35-km /h experiments along with the average curve. From the figure, it can be concluded that the repeatability of the experiments compared with themselves is quite good. All area moments for the three individual time histories are within 0.10 of one another (see below). The first five area moments for the three experiments, the average of the three experiments, and the LS-DYNA simulation are presented in Table 1. According to the NARD validation procedure, two time histories compare with reasonable accuracy if the difference in the relative absolute moments is less than 0.20. For the 35-km /h simu-

lation compared with the average of the three experiments, this criterion is met for all moments except the fourth moment. Ray (9) has suggested that higher-order moments may not be a good comparison of time history records. Table 2 contains additional comparison statistics. These “area” statistics show that the root mean square log areas of the two time histories are within 12 percent of each other, and the energy correlation coefficient is 0.89. From the comparative statistics presented above, it can be concluded that the simulation provides reasonable results. Avenues for improving the simulation and coming to a better agreement are discussed below.

MODEL SENSITIVITY ANALYSIS The sensitivity of various input parameters was considered by increasing and decreasing the parameters and rerunning the simulation. The

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wide range with no significant change in response. Cable preload was varied from 0 kN to 200 kN, again with no significant change in response. Finally, the angle of the cable relative to the guardrail was varied slightly front to back to observe whether cable geometry would affect the response. No change in response resulted. These findings do not prove conclusively that the cable is modeled properly in LS-DYNA. If the cable in the experiments did unwind at high loading levels, then the stiffness of the cables would drop dramatically as the cable unwound (8). In LS-DYNA, no constitutive models exist to capture such an unwinding, and, consequently, it will be difficult to simulate such behavior in a finite-element model.

MODEL IMPROVEMENTS To improve the agreement between the two simulations, the following modeling changes are being considered. To better capture the yielding and twisting of the post and blockouts, the bolts between the post and blockouts could be modeled. The current LS-DYNA model appears to need stiffening in this area. Additionally, the slots for the bolts that connect the guardrail to the inboard and outboard posts could be modeled. Currently, the slotted connections are modeled as nodal constraints that prevent slip entirely. Some slip at these locations was noted in the pendulum impact experiments. The current LS-DYNA model appears too stiff in the third phase of the time history. Some of this stiffness might be released by adding the slots to the guardrail models.

FIGURE 4 Top view animation of 35-km /h LS-DYNA simulation.

model was found to be insensitive to changes in guardrail steel material properties or element formulation. Though an increase in the yield point of the guardrail steel did slightly increase the energy absorbed in the initial or flexural phase of the response, it had little effect on the overall response. The response of the guardrail was primarily as a tension element and, as the guardrail did not yield in tension in either the experiments or the simulations, increasing the yield point had no effect on the outcome of the simulation (see below). The model was rerun with fully integrated shell elements to determine the effect of numerical instability or hourglassing. No change in the time histories was noted. Various optional contact algorithms, including the automatic single-surface contact (LS-DYNA Type 13) and automatic surface-to-surface contact, were explored, again with no change in model response. The model was sensitive to changes in post and blockout material strengths and element thicknesses. An increase in the yield point of the steel or the thickness of the shell elements in the post and blockout stiffened the initial response of the LS-DYNA simulation and improved the agreement between the simulation and experiments. From this result, it may follow that the connections between the guardrail and the blockout and the blockout and the post are not adequately stiff in the LS-DYNA model. If these connections are too flexible and the post and blockouts twist too early in the LS-DYNA model, it may explain the time offset noted in the acceleration time history response (Figure 7). The model was insensitive to changes in cable element properties. The axial stiffness (modulus × area) of the cable was varied over a

GUARDRAIL TENSION AND CABLE TENSION FORCES Global response of the guardrail to the pendulum impact forces can be observed in the element force time histories given in Figures 6 and 8. The cable force time histories contained a large amount of high-frequency information. The time histories for cable forces were filtered at 300 Hz to remove these high-frequency components. The guardrail tension time histories contained little high-frequency noise and are presented unfiltered. The guardrail tension peaks at approximately 400 kN for the 20-km /h simulation and 480 kN for the 35-km /h experiments. The guardrail should yield in tension at a tension force of approximately 500 kN (yield point of 415 MPa × cross-sectional area of 1240 mm2). Strain gauges on guardrails tested at 35 km /h showed peak strains between 800 and 1,800 microstrain—below the yield strain of 2,000 microstrain for guardrail steel. Only one gauge in the three 35-km /h experiments appeared to detect yielding in the guardrail. From the experimental and simulation results, it can be concluded that the 35-km/h experiment applies a tension load quite close to the maximum load that the steel W-beam can resist. This may be an important consideration in the design of future test fixtures intended to apply loads sufficient to break highway guardrails in a tension mode. The cables carry maximum tension forces of 160 kN and 200 kN for initial velocities of 20 km /h and 35 km /h, respectively. These loads are well below the predicted axial capacity of 400 kN for the cable. Axial stresses in cable wires are amplified dramatically if the cable is subject to bending deformation along with tension (8). Some bending in the cable is possible; in Figure 4, it can be observed that at high levels of guardrail deflection, the cable comes quite close to the edge of cable-end anchor. Contact between the anchor and the cable may have been the reason for the cable breakage

FIGURE 5 Acceleration, velocity, and displacement time histories for 20-km / h pendulum experiments and LS-DYNA simulation.

FIGURE 6 Rail tension force and cable tension force time histories for 20-km / h LS-DYNA simulation.

FIGURE 7 Acceleration, velocity, and displacement time histories for 35-km / h pendulum experiments (average of 3) and LS-DYNA simulation.

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FIGURE 8

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Rail tension force and cable tension force time histories for 35-km/h LS-DYNA simulation.

observed in Experiment 96P005. Assuming that local bending of the cables was avoided, the cable anchors performed as expected and should have the capacity required to anchor guardrails tested at higher input energies.

CONCLUSIONS The LS-DYNA models presented in this paper provide good agreement with the pendulum impact experiments modeled. The guard-

rails under 35-km /h impact exhibit an initial flexural resistance mode, followed by a softening behavior as the posts and blockouts yield, followed by dramatic stiffening in tension. The LS-DYNA simulation provides insight into important design parameters that are not available from the test data; in this case, overall rail tension forces and cable tension forces. Finally, the newly modified fixture at FOIL appears to have nearly the capacity required to fracture steel W-beam guardrails in tension. A small increase in pendulum mass should provide the input energy required to fracture steel W-beam guardrails in tension.

FIGURE 9 Acceleration time histories for 35-km / h FOIL Tests 96P003, 96P004, and 96P006 and average acceleration time history.

TABLE 1

Validation Statistics for 35-km/h Experiments and LS-DYNA Simulation

TABLE 2 Root Mean Square and Correlation Statistics for 35-km /h Experiments (Average of 3) and LS-DYNA Simulation

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ACKNOWLEDGMENTS This material is based on work supported by the Federal Highway Administration under two cooperative agreements. The authors acknowledge the technical oversight of Martin Hargrave of FHWA in this research. The technical assistance of Chris Brown, who provided and interpreted data from the pendulum experiments, is also appreciated.

REFERENCES 1. Svenson, A. L., and C. Brown. Pendulum Impact Testing of Steel W-Beam Guardrail: FOIL Test Numbers 94P023-94P027, 94P030, and 94P031. Draft FHWA Report. FHWA, U.S. Department of Transportation, 1997. 2. Ross, H. E., D. L. Sicking, R. A. Zimmer, and J. D. Michie. NCHRP Report 350: Recommended Procedures for the Safety Performance Evaluation of Highway Features. TRB, National Research Council, Washington, D.C., 1993. 3. Brown, C. M. Pendulum Testing of Fixed-End W-Beam Guardrail: FOIL Test Numbers 96P001, 96P002, 96P003, 96P004, 96P005, and 96P006. Report FHWA-RD-97-079 (Draft). FHWA, U.S. Department of Transportation, 1997.

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4. LS-DYNA Version 940 User’s Manual. Livermore Software Technology Corporation, Livermore, Calif., 1997. 5. Bank, L. C., T. R. Gentry, J. Yin, and J. D. Lamtenzan. DYNA3D Simulations of Pendulum Impact Tests on Steel Guardrails. In Crashworthiness and Occupant Protection in Transportation Systems (H. F. Mahmood and M. R. Baccouche, eds.), AMD-Vol. 218, ASME, New York, 1996, pp. 51–64. 6. Basu S., and A. Haghighi. Numerical Analysis of Roadside Design (NARD): Validation Manual, Vol. 3. Report FHWA-RD-88-214. FHWA, U.S. Department of Transportation, Sept. 1988. 7. Wright, A. E., and M. H. Ray. Characterizing Guardrail Steels for LSDYNA3D Simulations. Report FHWA-RD-96-108. FHWA, U.S. Department of Transportation, Feb. 1997. 8. Costello, G. A. Theory of Wire Rope. Springer-Verlag, Inc., New York, 1990. 9. Ray, M. H. Repeatability of Full-Scale Crash Tests and Criteria for Validating Simulation Results. In Transportation Research Record 1528, TRB, National Research Council, Washington, D.C., 1996, pp. 155–160.

Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the Federal Highway Administration. Publication of this paper sponsored by Committee on Roadside Safety Features.