Criteria for Restoration of Longitudinal Barriers, Phase II (2021)

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109 CHAPTER 7 – DEVELOPMENT AND VALIDATION OF THE G4(2W) GUARDRAIL MODEL Model Development A detailed finite element model of the G4(2W) guardrail system was developed and the finite element analysis code LS-DYNA was used to conduct crash analyses of the barrier system. The G4(2W) guardrail system includes many of the same components used in other common strong-post guardrail systems, thus valid models for most of the guardrail components were readily available from previous projects conducted by the authors. The development of the components of the G4(2W) model were based largely on the modeling methodology used for G4(2W) and G4(1S) models developed at Worcester Polytechnic Institute in the late 1990’s and early 2000’s. [Plaxico98; Plaxico02; Plaxico07] The improvements of the current model were primarily related to mesh refinement of critical components. The guardrail model consisted of 13.5 ft (4.13 m) lengths of 12-gauge w-beam rail (RWM02a), 6x8 inch cross-section wood posts with lengths of 64 inches (PDE01), and 6x8x13 inch wood blockouts (PDB01). The splice bolts (FBB01) connecting the w-beam rail elements together were modeled in geometric detail with rigid material properties. The bolts fastening the w-beam rail to the posts (FBB04) were modeled with beam elements with material properties modeled as piecewise linear plasticity. The nuts and the bolt heads were modeled with rigid material properties since deformations of those components were considered insignificant to the results. [Component designators refer to the AASHTO-ARTBA-AGC hardware Guide AASHTO04]. The nuts were tightened onto the bolts using nonlinear springs and dampers. The posts were spaced at 75 inches (1.905 m) center-to-center. The w-beam rail was positioned such that the top of rail was 27-5/8 inches (650.9 mm) above ground. The boundary conditions on the upstream and downstream ends of the guardrail model were modeled with nonlinear springs attached to the ends of the w-beam rail. The stiffness properties of the boundary springs were intended to correspond to a two-BCT post anchor system with foundation tubes and groundline strut, as defined in [Plaxico03]. The post-soil interaction was modeled with the post model supported by an array of non-linear springs based on the subgrade reaction approach. Figure 72 shows the overall dimensions of the guardrail model, and Figure 73 shows a close up view illustrating the level of detail in the geometry and finite element mesh. W-Beam The cross-sectional dimensions of the rails were modeled according to the standard drawing RWM02a for 12-gauge w-beam (designation from AASHTO’s A Standardized Guide to Highway Barrier Hardware). The material properties were characterized based on the properties determined in an earlier study by Wright and Ray.[Wright96] This model has been used in numerous analyses over the past decade by members of the research team and others, and has been validated based on full-scale crash testing.[Engstrand00; Plaxico02]

110 Figure 72. Finite element model of the G4(2W) guardrail. Figure 73. Angle perspective view illustrating typical components of guardrail model. Post 4 Post 27 64 in 28 in 27.6 in

111 Splice Connection Model An important consideration in modeling the w-beam rails is the splice connections that fasten the individual rail sections together. The splice is often the point where structural failure occurs during impact. W-beam guardrails are connected by overlapping the ends of the rail sections and clamping them together using eight 16-mm diameter bolts and nuts, as shown in Figure 74. In a study conducted by Ray et al., the performance of w-beam splices were analyzed using the results of full-scale crash tests, laboratory experiments and finite element simulation.[Ray01a; Ray01b] In the G4(2W) and many other guardrails and guardrail terminal systems, the w-beam splice is located at the posts where the splice is subjected to a combination of axial tension, torsion in the guardrail section about its longitudinal axis, and lateral bending of the splice against the guardrail posts. Incorporating failure into the model of the splice connection would require a very fine mesh in order to capture the local stress concentrations around the splice bolt connections, as demonstrated by Engstrand.[Engstrand00] The finite element model of the splice and guardrail used in their study is shown in Figure 74. Using such a fine mesh in the current model would require a time-step on the order of 0.1 microseconds which was not feasible for analysis of a full-scale impact event which lasts 0.6 to 1.2 seconds (e.g., the analysis would require 6,000,000 to 12,500,000 time-steps to complete the simulation). In order to approximate the behavior of the splice connection, the mesh around the splice hole was modeled with a moderately refined mesh (element size 7 mm nominally). This mesh size provides reasonable accuracy up to the point of failure, but will not properly capture the fracture of the material around the hole when ultimate stress of the material is exceeded. A refined mesh (with null material properties) was overlaid and tied to the deformable mesh around the slice connection hole in the rail element, in order to provide sufficient load points between the w-beam and bolt hardware to more accurately model the force distribution at these critical locations. The splice connection details are shown in Figure 75 (note that the null mesh for the top-right bolt hole is hidden from view in order to show the mesh for the deformable elements). The bolt hardware is the same as that shown in Figure 74. At the start of the analysis the w-beam rails are in an unstressed state and positioned such that the overlapping rails in the splice connection are only in “slight” contact with each other. As the analysis begins, the splice bolts tighten and clamp the w-beam splice together, resulting in a pre-stressed state of the w-beam material which approximates that of the actual splice connection. More details on modeling of the splice bolts are provide in the following section. The behavior of the splice connection was validated by comparing model results to physical laboratory tests. In the study by Engstrand, the force-displacement relationship of the splice connection in pure tension was determined by conducting a series of quasi-static laboratory uniaxial tensile tests of the guardrail splice connection using a Tinus-Olsen 400,000- lb uniaxial load test machine.[Engstrand00] The splice-test conducted by Engstrand was simulated using the finite element model shown in Figure 76. The FE results are accurate up to approximately 89.9 kips (400 kN) – the point when the splice bolts began to tear through the holes in the laboratory tests. The model experiences severe element distortion at this load, which is an apparent indication of the potential for rupture. Since the model does not incorporate failure directly, the results from the model must be carefully monitored at critical locations, such as splice connections, to evaluate model results and discern onset of potential failure.

112 Figure 74. Components of the finite element model of a weak-post w-beam guardrail splice used in Ray et al. [Ray01a] Figure 75. Splice connection model used in current study.

113 Figure 76. Test setup and axial force-displacement graphs from uniaxial tension tests of guardrail splices. [Engstrand00] Bolt Hardware Splice-bolt hardware seldom fails during impact, thus the material properties for the bolts and nuts were modeled with rigid material behavior. Failure of the splice connection is generally due to the “rigid” bolts rotating and tearing through the relatively thin w-beam material. Therefore, the bolts were modeled with geometric fidelity in order to obtain accurate force distribution and stress concentrations in the w-beam splice holes. The dimensions of the bolt hardware were modeled according to the standard drawing FBB01 for guardrail bolt and recessed nut (designation from AASHTO’s A Standardized Guide to Highway Barrier Hardware). The details of the splice bolts, however, do not include the bolt-threads. Non-linear springs and damper elements are used to tighten nut onto the bolts. The stiffness of bolt springs was set to achieve an appropriate clamping force applied to each bolt, while linear dampers were used control the speed of the clamping process (i.e., prevent the nut from impacting against the w-beam during clamping). For example, the clamping process occurs over a 0.001 second time interval. Once the nut is in the desired clamped position, it is necessary to ensure that it is securely “fixed” to the bolt (i.e., simulate the nut being locked to the bolt by threads) to prevent the nut from “backing off” during crash simulations. A set of non-linear one-way dampers were included on the bolt model for this purpose, which was more than sufficient to hold the nut in place during the crash simulations. Fixed Constraint FEA (a) Model (b) Test setup (c) Force-displacement results

114 Guardrail Posts The cross-section dimensions of the wood guardrail posts and blockouts were 6 x 8 inches; the length of the posts was 64 inches. The wood material was modeled with mechanical properties consistent with Southern Yellow Pine. Two different LS-DYNA material models were used for the posts. In the impact region of the guardrail, the material model *Mat_Wood (material type 143) was used, which is a transversely isotropic elasto-plastic damage model with rate effects. In the non-impact regions of the guardrail, a much simpler and less computationally demanding constitutive model called *Mat_Isotropic_Elastic_Plastic_Failure (material type 13) was used. The material model *MAT_WOOD (i.e., material type 143 in LS-DYNA) was developed by APTEK through a study sponsored by the Federal Highway Administration.[Murray07] This material model was developed specifically for conducting finite element analyses of vehicle collisions into wooden guardrail posts. The constitutive model in *MAT_WOOD is characterized as a transversely isotropic material with yield surfaces. The model effectively simulates the stiffness, strength and post-peak softening behavior in the two primary directions of wood (i.e., parallel and perpendicular to wood grain). The model also includes rate effects which effectively increase the strength properties of the material as a function of strain rate. The user has the option of inputting his or her own material properties or requesting default material properties for Southern Yellow Pine or Douglas Fir. The material property data stored in LS-DYNA for MAT 143 corresponds to clear wood properties for these two species, whereas most structural wood, such as guardrail posts, are graded. Clear wood properties correspond to the highest strength properties for the wood material (i.e., no knots or defects). In order to obtain the appropriate strength reduction for graded wood, MAT 143 applies quality factors (e.g., strength-reduction factors) to the clear-wood property values. In particular, two quality factor parameters may be defined, QT and QC, whose values range from 0 to 1. QT is applied to the tensile and shear strength properties, and QC is applied to the compressive strength properties. Predefined values for these quality factors are provided with this material model for Pine and Douglas Fir. These values were developed based on correlation to static bending tests and bogie impact tests of guardrail posts.[Murray07] The default quality factors for Grade 1 and DS-65 Southern Yellow Pine are:  Grade 1: QT=0.47 and QC=0.63  Grade DS-65: QT=0.80 and QC=0.93 Table 28 shows a summary of the resulting material property values for *MAT_WOOD_PINE in LS-DYNA for clear wood, DS-65 and Grade 1. (NOTE: Table 28 lists the values for the material parameters in the units used in the FE model (i.e., Mg, mm, sec, N and MPa)). These properties correspond to Southern Yellow Pine under saturated conditions (e.g., moisture content is greater than or equal to 30 percent). Wood Post Model Calibration/Validation The material properties for the baseline guardrail post model were determined through the process of trial and error by comparing the dynamic impact response of the post model to the results of full-scale pendulum tests. The tests used for this evaluation were conducted as part of Task 4A-3 of this study (see Chapter 8) to assess the dynamic failure properties of deteriorated guardrail posts. The tests were performed at the FOIL. The nominal impact conditions for the

115 tests involved a 2,372-lb rigid-nose pendulum striking the posts at 21.5 inches above grade. The posts were 66 inches long and were embedded 38 inches inside a 12x12 inch steel tubular sleeve with “rigid” fixity. See Chapter 8 for more details regarding the test setup. Figure 77 shows a side-by-side view of the physical test set-up and the finite element model. Two series of tests were performed: Series 1 included 22 tests with impact speed of 20 mph and Series 2 included 31 tests with impact speed of 10 mph. The tests specimens ranged from highly deteriorated posts (e.g., rot and insect damage) to relatively sound posts. Unfortunately, only two of the posts tested were new, unused posts. These were labeled as Post A and Post B and were tested in Series 1 at 20 mph; the corresponding test numbers are 13009L and 13009K, respectively (see Chapter 8). The finite element model of the wood post was used to simulate these test conditions and the results are presented below. Additional validation/calibration of the model was also made based on comparison to pendulum tests performed on guardrail posts embedded in soil. The results of those comparisons are presented in the following section of this report. The posts used in Tests 13009K and 13009L were very similar in that both had a diameter of 7.24 inches; the mass densities were 44.8 lb/ft3 and 45.4 4 lb/ft3 for 13009K and 13009L, respectively; and the moisture content for both cases was greater than 30 percent (i.e., saturated condition). The most notable difference between the two tests was the ring density of the posts. The post in test 13009K had an average ring density of 5.8 rings/inch and the post in Test 13009L had an average ring density of 9.4 rings/inch. The force vs. deflection and the energy vs. deflection results from the tests are shown in Figure 78 and Figure 79, respectively. Post A, which had the higher ring density, resulted in a peak impact force of 19 kips and total energy absorption of 37 kip-inches. Post B resulted in a peak impact force of 16 kips and total energy absorption of 24.9 kip-inches. These impact conditions were simulated using the finite element model shown in Figure 77. As a starting point, the pre-defined material parameters in LS-DYNA for clear wood, Grade DS-65 and Grade 1 were used to model the wood material (refer to Table 28). The results from those three analysis cases are shown in Figures 80 through 82. The dashed lines in the plots correspond to the results from the physical tests. The analysis results using Grade 1 properties matched reasonably close to the results from the physical tests. The peak impact force for the analysis was 20.8 kips and the total energy absorption was 34 kip-inches. The Grade 1 properties also resulted in a more brittle failure response of the post, as illustrated in the sequential views in Figure 82. The peak impact forces for the Grade DS-65 and clear wood material properties were 20.7 kips and 23.9 kips, respectively; while the total energy absorption was 72 kip-in and 95 kip- in, respectively. The higher strength properties also resulted in a more ductile failure of the post with significantly more energy absorption after reaching peak force. The initial peak in the force- deflection plots, which accounted for a notable portion of the energy in the event, was attributed in part to the impulse of the rigid pendulum head impacting the post and in part to the post’s boundary conditions. This spike was generally of lower force magnitude and larger displacement in the tests but varied slightly from test to test; whereas in the FEA analyses, the spike was exactly the same in every analysis case conducted since the material properties at the top of the post (i.e., DS65) and the boundary conditions were modeled the same in every analysis case.

116 The differences between the FEA results and tests indicate that the pendulum head, as well as the boundary conditions, were softer in the test. Table 28. Predefined material parameters values for *MAT_WOOD_PINE in LS-DYNA for various quality factor settings (units: Mg, mm, sec, N, MPa). Variable Description Clear Wood DS-65 Grade 1 User Defined (QT=0.8 QC=0.93) (QT=0.47 QC=0.63) (QT=0.60 QC=0.70) General RO Density (Mg/mm3) 6.73E-10 6.73E-10 6.73E-10 6.73E-10 NPLOT Parallel damage written to D3PLOT 1 1 1 1 ITERS Number of plasticity iterations 1 1 1 1 IRATE Rate effects (0=off; 1=on) 1 1 1 1 GHARD Perfect plasticity override (0=perfect plasticity) 0.05 0.05 0.05 0.05 IFAIL Erosion perpendicular to grain (0=No; 1=Yes) 1 1 1 1 IVOL Erode on negative volume (0=No; 1=Yes) 0 0 0 0 Stiffness EL Parallel Normal Modulus (MPa) 11352 11352 11352 11352 ET Perpendicular Normal Modulus (MPa) 246.8 246.8 246.8 246.8 GLT Parallel Shear Modulus (MPa) 715.2 715.2 715.2 715.2 GTR Perpendicular Shear Modulus (MPa) 87.5 87.5 87.5 87.5 PR Parallel Major Poisson's Ration 0.157 0.157 0.157 0.157 Strength XT Parallel Tensile Strength (MPa) 85.1 68.1 40 51.1 XC Parallel Compressive Strength (MPa) 21.1 19.7 13.3 14.8 YT Perpendicular Tensile Strength (MPa) 2.05 1.6 0.96 1.23 YC Perpendicular Compressive Strength (MPa) 4.08 3.8 2.6 2.9 SXY Parallel Shear Strength (MPa) 9.1 7.3 4.3 5.5 SYZ Perpendicular Shear Strength (MPa) 12.7 10.2 6 7.6 Damage GF1∥ Parallel Fracture Energy in Tension (MPa-mm) 42.7 34.1 20 25.6 GF2∥ Parallel Fracture Energy in Shear (MPa-mm) 88.3 70.6 41.5 53 BFIT Parallel Softening Parameter 30 30 30 30 DMAX∥ Parallel Maximum Damage 0.9999 0.9999 0.9999 0.9999 GF1⊥ Perpendicular Fracture Energy in Tension (MPa-mm) 0.4 0.4 0.4 0.4 GF2⊥ Perpendicular Fracture Energy in Compression (MPa-mm) 0.83 0.83 0.83 0.83 DFIT Perpendicular Softening Parameter 30 30 30 30 DMAX⊥ Perpendicular Maximum Damage 0.99 0.99 0.99 0.99 Rate Effects FLPAR Parallel Fluidity Parameter Tension/Shear 9.42E-06 7.54E-06 4.43E-06 5.65E-06 FLPARC Parallel Fluidity Parameter Compression 9.42E-06 8.76E-06 5.94E-06 6.60E-06 POWPAR Parallel Power 0.107 0.107 0.107 0.107 FLPER Perpendicular Fluidity Parameter Tension/Shear 1.97E-04 1.58E-04 9.27E-05 1.18E-04 FLPERC Perpendicular Fluidity Parameter Compression 1.97E-04 1.84E-04 1.24E-04 1.38E-04 POWPER Perpendicular Power 0.104 0.104 0.104 0.104 Hardening NPAR Parallel Hardening Initiation 0.50 0.50 0.50 0.5 CPAR Parallel Hareding Rate (/s) 400.0 462.5 1010.0 816.3 NPER Perpendicular Hardening Initiation 0.40 0.40 0.40 0.4 CPER Perpendicular Hardening Rate (/s) 100.0 115.6 252.0 204.08

117 Figure 77. Test set-up and FEA model used in wood-model validation. Figure 78. Force vs. deflection plots from dynamic impact tests 13009K and 13009L at impact speed of 20 mph. (a) Test 13009L (b) FEA Model

118 Figure 79. Energy vs. deflection plots from dynamic impact tests 13009K and 13009L at impact speed of 20 mph. An additional analysis was conducted using a set of quality factors with slightly higher values than those pre-defined for Grade 1. For this case, the quality factor QT was set to 0.60 and the quality factor QC was set to 0.7. The purpose for this analysis will become apparent in the next section which compares model results to pendulum impact tests on posts embedded in soil. The results for this analysis case are shown in Figure 83 and Figure 84, where the peak forces are identical to those for the Grade 1 analysis case. The post-peak response, however, was somewhat less brittle for the analysis case using QT = 0.60 and the quality factor QC = 0.7. Soil Model The posts of the G4(2W) guardrail were 6x8 inches in cross-section and were embedded 36 inches into the soil. There are several approaches that may be used for modeling the soil in analyses of guardrail posts embedded in soil. Some common approaches include: 1. Post embedded in a soil continuum of solid finite elements, 2. Post embedded in a continuum of meshless finite elements, 3. Subgrade reaction approach in which the post is supported by an array of uncoupled springs. The finite element formulations available in LS-DYNA include: 1. Lagrangian, 2. Eulerian, 3. Arbitrary Lagrangian-Eulerian (ALE), 4. Element Free Galerkin (EFG), 5. Smooth Particle Hydrodynamics (SPH), and 6. Discrete springs and dampers.

119 Figure 80. Force vs. deflection plots from dynamic impact analysis with pre-defined properties in MAT143 for (a) clear wood, (b) grade DS-65 and (c) grade 1. Figure 81. Energy vs. deflection plots from dynamic impact analysis with pre-defined properties in MAT143 for (a) clear wood, (b) grade DS-65 and (c) grade 1.

120 Figure 82. Sequential views of (a) Test 13009L and analyses for post model with pre- defined MAT143 properties for (b) clear wood, (c) grade DS-65 and (d) grade 1. (a) Test 13009L 0.024 sec 0.036 sec 0.048 sec0.012 sec (c) Grade DS-65 (d) Grade 1 (b) Clear Wood

121 Figure 83. Force vs. deflection plots from dynamic impact analysis using properties for (1) Grade 1 and (2) quality factors set to QT=0.60 and QC=0.7. Figure 84. Energy vs. deflection plots from dynamic impact analysis using properties for (1) Grade 1 and (2) quality factors set to QT=0.60 and QC=0.7. 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 Fo rc e ( ki p ) Displacement (in) Test 13009K Test 13009L FEA (Grade 1) FEA (Qt60, Qc70) 0 10 20 30 40 50 60 0 2 4 6 8 10 12 En e rg y (k ip /i n ) Displacement (in) Test 13009K Test 13009L FEA (Grade 1) FEA (Qt60, Qc70)

122 The Lagrangian and Eulerian element types are the traditional formulations used in stress analysis as well as crash analysis; although ALE, EFG and SPH formulations may be better suited to modeling fluid type behavior. All these element formulations can be mixed and often are to model fluid-structure interactions. The research team has used each of these methods to model soil in various projects with limited success. The most commonly used method for modeling guardrail posts in soil is to model the soil as a continuum of solid Lagrangian elements. However, the solid Lagrangian based meshes generally do not provide very accurate response for the case of large soil deformation, where the post is shearing through the soil (e.g., typical of wood post systems). In these cases the soil often demonstrates more fluid like behavior. For the current study, the soil model was developed based on the subgrade reaction approach and validated through comparison with full-scale pendulum tests. The subgrade modulus is influenced by many factors such as the relative density and moisture content of the soil, the cohesiveness of the soil, the overburden pressure, the nature of the applied load, the post deflection, and the properties and geometry of the post. Refer to Plaxico et al. for more details on the development of the force-deflection relationship of the soil springs.[Plaxico98] The soil for NCHRP Report 350 and MASH tests is assumed to be non- cohesive. The parameters that are needed to characterize the soil model include: – Unit weight of soil – Void ratio – Relative density – Degree of saturation – Moisture content of soil at saturation – Critical moisture content – Current moisture content (calculated using void ratio and degree of saturation) – Effective unit weight of soil (calculated based on unit weight of soil, moisture content and degree of saturation) – Angle of internal friction – Post shape – Depth of each layer of springs – Distance between rows of springs Patzner et al. used the subgrade reaction approach to model the post-soil interaction for wooden guardrail posts used in the Modified Eccentric Loader Terminal (MELT) with reasonable success.[Patzner99] In their model the soil springs were attached directly to the post, as illustrated in Figure 85, which provides adequate response for low to moderate rotation of the guardrail post. However, as post rotation continues to increase and the post begins to extract from the soil, the accuracy of the model starts to decline. This is because the force-deflection curves for the discrete spring elements were defined based on their initial position (e.g., initial overburden stress). When these springs are attached directly to the post, their vertical position will change as the posts rotate during loading (e.g., they generally rise toward the ground surface). The lateral resistance of the springs in such a model will not automatically readjust as the post rotates in the “soil.”

123 Figure 85. Soil springs attached directly to post. [Patzner99] To correct this issue, a shell element interface was included to separate the soil springs from the post, as shown in Figure 86. The shell elements were meshed such that the element size was consistent with the element size of the posts and each line of nodes of the mesh was spaced at 1.97 inches (50 mm). A single discrete spring element was attached to each row of nodes at the center of the shell section. The shell elements were modeled with null material properties so that the resistance to the elements movement/deformation was due solely to the discrete springs. Each row of nodes was constrained to move as a rigid body with its corresponding spring element. That is, for the elements representing y-direction displacement of the soil, each individual row of nodes were constrained in the x- and z-directions using the *CONSTRAINED_NODAL_RIGIDBODY_SPC option in LS-DYNA. Figure 87 shows sequential views illustrating the typical response of the post-soil model to an impact load at approximately 21.6 inches (550 mm) above grade with a post embedment depth of 44 inches. Soil Model Validation The soil model was qualitatively validated based on comparison with impact tests of guardrail posts embedded 40 inches in soil with impact height of approximately 25 inches. Test 13010F involved a 2,372-lb rigid-nose pendulum impacting a W6x16 steel post at an impact speed of 20 mph. The post was 72 inches long and embedded 40 inches in the soil. The impact point was 24.88 inches above ground. The soil conformed to Grading B of AASHTO M147-95 and was compacted in 6-inch lifts using a pneumatic tamper. The density, moisture content and degree of compaction of the soil was measured in front of and behind the post after each compaction process using a Troxler- model 3440 Surface Moisture-Density Gauge. There were a total of twelve readings which were averaged to determine the effective soil conditions, which were a 92 percent soil compaction with average soil density of 138 pcf.

124 Figure 86. Soil modeled with non-linear springs and contact plates. Figure 87. Sequential views illustrating typical model response to simulated bogie impact load. A finite element model was developed to simulate Test 13010F using the soil-spring model. The properties of the spring elements were defined according to [Plaxico98] using a soil density of 134 pcf. The striker head used in the simulation was modeled with rigid material Soil Springs at center of each line of nodes NRB w/ z-constraint at each line of nodes Null shells for contact with post

125 properties with the dimensions similar to those of the physical device. The pendulum model struck the face of the post at 24.88 inches above grade at an impact speed of 20.0 mph. Acceleration data was collected at the rear of the pendulum model and used to compute the force-displacement response. The results from the finite element analysis are compared to those from full-scale Test 13010F in Figure 88 and Figure 89. The response of the soil-spring model with the stiffness of the soil-springs adopted directly from [Plaxico98] matched very well with the test results. The total energy absorption for the analysis was 288 kip-in compared to 274 kip- in in the test. Figure 88. Force vs. displacement results from FE analysis compared with Test 13010F. Figure 89. Energy vs. displacement results from FE analysis compared with Test 13010F. 0 2 4 6 8 10 12 14 16 0 20 40 60 Fo rc e ( ki p ) Displacement (in) Test 13010F FEA W6x16 post 0 50 100 150 200 250 300 350 400 450 0 20 40 60 En e rg y (k ip -i n ) Displacement (in) Test 13010F FEA W6x16 post

126 Limitations of the model  The effects of dynamic loading of the soil (e.g., inertial spikes) are not accounted for in this model, although they could be modeled using discrete damper elements with empirically defined properties.  The springs only provide lateral resistance for the posts. For the soil-plate model described here, the vertical resistance to pull-out comes from the vertical constraint on the plates. That is, the nodes of the soil-plates can move laterally but not vertically. It is assumed that this would become less of an issue as the vertical distance between springs is reduced (i.e., mesh refinement); however, accuracy in simulating large post rotation would likely be improved if the vertical response of the soil were included in the model. Vehicle Model C2500D-v5b The C2500D-v5b vehicle model was developed through the process of reverse engineering by the National Crash Analysis Center (NCAC).[NCAC08] The model version used in these analyses is version 5b. Minor modifications were made to the model by RoadSafe to improve hourglass modes, contact stability and wheel assembly failure. The FE model was developed based on a 1994 Chevrolet C2500 pick-up truck and corresponds to the 2000P large passenger vehicle specification in NCHRP Report 350. The C2500D-v5b model closely matches the mass and dimensional properties of the test vehicle used in the full-scale crash test of the G4(2W) guardrail in Test No. 471470-26.[Mak99] Validation of the G4(2W) Guardrail Model A finite element model of the standard G4(2W) (SGR04b) wood post guardrail system was developed. In order to gain confidence in the model’s results, it was necessary to validate the model’s predictions against full-scale crash test results. The validation procedures presented in NCHRP Web Document 179 were used to assess the fidelity of the model. Full-scale crash test 471470-26 conducted by the Texas Transportation Institute (TTI) in College Station, Texas on May 25, 1994 was used for the validation.[Mak99] The test was conducted under NCHRP Report 350 Test 3-11 impact conditions. The guardrail system successfully passed Report 350 performance criteria; however, the test was classified as “marginally acceptable” due to severe wheel snag and subsequent vehicle instability after redirection from the system.[Mak99] Simulation of Test 471470-26 TTI Test 471470-26 involved an impact with a 1989 Chevrolet C-2500 pickup truck striking a standard G4(2W) wood post guardrail system. The gross static mass of the test vehicle was 4,568 lbs including a restrained 50th percentile male anthropomorphic dummy placed in the driver’s position. The test guardrail system included 150 ft of standard G4(2W) guardrail, with a Modified Eccentric Loader Terminal (MELT) at the upstream end of the system and a Breakaway Cable Terminal (BCT) at the downstream end to provide anchorage. The total length of the complete system, including terminals, was 225 ft. The test vehicle struck the G4(2W) guardrail at an angle of 24.3 degrees and a speed of 62.6 mph (100.8 km/h), traveling in the

127 downstream direction. The initial point of contact was approximately 2-ft upstream of the w- beam rail splice connection at Post 14. The guardrail model consisted of twelve 13.5 ft (4.13 m) lengths of 12-gauge w-beam rail, twenty-four 6x8x64 inch wood posts, and twenty-four 6x8x13 inch wood blockouts. The posts were spaced at 75 inches (1.905 m) center-to-center and the w-beam rail was positioned such that the top of rail was 27-5/8 inches (650.9 mm) above ground. The posts were embedded 36 inches in the ground. The total length of the guardrail model, excluding end anchors, was 151 ft. The vehicle model used in the analysis was the NCAC C2500D version 5B. The model was modified in order to calibrate the mass inertial properties of the vehicle to the properties of the test vehicle. This was achieved through the use of the *Constrained_Nodal_Rigid_Body_Inertia card in LS-DYNA, with the added mass concentrated at the center of gravity of the vehicle model. The mass of the vehicle model was increased by 573 lb to match the gross static mass of the test vehicle. However, the mass moments of inertia of the test vehicle were not measured, so the inertial properties of the model were calibrated to a similar vehicle type (i.e., 1998 Chevrolet C1500) which were documented in a NHTSA report.[Garret98] A comparison of the physical and inertial properties of the test and analysis vehicles is provided in Figure 90. The most notable difference was the location of the center of gravity of the vehicle in the longitudinal direction. The c.g. of the vehicle model was located approximately 10 inches forward of that measured for the test vehicle, which corresponded to a 17 percent error. Additional modifications to the model included remeshing various parts in the impact region of the model and changing the element type to the fully integrated shell element (i.e., type 16 in LS-DYNA). A failure condition was also included on the spherical joints which simulate the attachment of the wheel assembly to the upper and lower A-Frames. The failure force for the joint was set to 14.6 kips based on the tests conducted at the FOIL by Stefano Dolci of Polytechnico di Milano.[Dolci12] Dolci measured the static load required to fail the wheel assembly joint of a 2007 Chevrolet Silverado 1500 Crew-Cab pickup, where the joint failed at a static load of 9.98 kips. The failure load used in the finite element model was approximated, by assuming a strain-rate magnification factor of 1.5 for the component. The analysis was conducted with a time-step of 1.26 microseconds for a time period of 0.6 seconds. The exact timing of phenomenological events was not possible, because plot states were only collected at 0.005 second intervals throughout the analysis. Therefore, a 0.005 second time window corresponding to range of time for which the event could have occurred in the analysis was reported.

128 Figure 90. Comparison of properties for the test and analysis vehicle. The vehicle model impacted the guardrail at 22 inches upstream of Post 14, traveling at a speed of 62.6 mph and at an angle of 24.3 degrees. Redirection began at 0.044 seconds. The vehicle contacted Post 15 at 0.085 – 0.090 seconds and tire contact with Post 15 occurred at 0.100 - 0.105 seconds. The front impact side tire assembly separated shortly after wheel impact with Post 15 from the vehicle at 0.124 seconds. The vehicle contacted Post 16 at 0.155 – 0.160 seconds and tire contact with Post 16 occurred at 0.190 – 0.195 seconds. The rear of the vehicle made contact with the guardrail at 0.190 – 0.195 seconds. The vehicle contacted Post 17 at 0.240 – 0.245 seconds. The vehicle was parallel to the guardrail at 0.256 seconds, traveling at 41.0 mph. The vehicle lost contact with the installation at 0.600 seconds, traveling at a speed of 37 mph and at an exit angle of 26 degrees. As the vehicle exited the rail, its roll angle was 30.3 degrees. The analysis was terminated at 0.6 seconds, at which time:  The roll angle of the vehicle was 30.3 degrees and increasing, Vehicle Geomerty (inches) Test Vehicle FE Model Error % A 73.2 73.3 0.2 B 31.5 35.6 12.9 C 131.9 144.3 9.4 D 70.9 73.2 3.3 E 52.8 52.8 0.1 F 216.1 232.7 7.7 G 60.7 50.3 -17.1 H - 27.8 - J 41.1 42.3 2.8 K 25.6 26.0 1.5 L 3.5 4.1 16.7 M 16.9 18.0 6.3 N 61.8 65.2 5.4 O 63.8 65.2 2.2 P 31.1 28.0 -9.9 Q 17.3 16.4 -5.5 R 28.0 27.6 -1.4 S 40.6 - - T 59.1 54.6 -7.5 U 163.8 - - Mass -Properties Test Vehicle FE Model Error % Test Vehicle FE Model Error % Test Vehicle FE Model Error % M1 2,394 - - 2,381 - - 2,478 - M2 1,682 - - 2,028 - - 2,094 - MTotal 4,076 3,995 -2.0 4,409 - - 4,572 4,568 -0.1 I11 - - - - - - 18,082 17,997 -0.5 I22 - - - - - - 103,985 104,080 0.1 I33 - - - - - - 111,650 111,341 -0.3 *Properties for 1998 C1500 [NHTSA] (lb - ft2) (lb - ft2) (lb - ft2) Curb Test Inertial Gross Static (lb) (lb) (lb)

129  The pitch angle was 9.1 degrees and decreasing,  The yaw angle was 26.15 degrees relative to the barrier, and  The forward velocity of the vehicle was 37.3 mph. Damage to Test Installation The installation received moderate damage as shown in Figure 91. None of the posts were broken in either simulation or the test but there was significant deflection of some of the posts as they were pushed back in the soil. The groundline deflections of the posts are shown in Table 29. The post displacements in the impact region in the simulation showed good correlation with the full-scale test; whereas the post deflections just outside the impact region were slightly lower in the analysis compared to the test measurements. Although it cannot be confirmed, it also appears from visual inspection that the posts in the full-scale test showed greater rotation angles compared to the simulation. The W-Beam rail element was deformed from Posts 13 through 18 as shown in Figure 91. The maximum deformation of the guardrail during the simulated impact event was 27.2 inches between Posts 15 and 16, which correlates exactly to the rail deformation reported in the full-scale test. Overall, the simulated barrier response was essentially identical to that observed in the full-scale test. Qualitative Validation Sequential Views A qualitative assessment was made by comparing sequential snapshots of the full-scale crash test with the results of the simulation to verify vehicle kinematic response as well as sequence and timing of key phenomenological events. The results from the FE analysis compare reasonably well with the results from full-scale crash test 471470-26. Figure 92, Figure 93 and Figure 94 show sequential snapshots of the impact event from an overhead viewpoint, a downstream viewpoint, and from an oblique (downstream and behind the barrier) viewpoint, respectively. The model appears to simulate the basic kinematic behavior of the pickup and adequately captures the basic phenomenological events that occur during impact. Table 2 provides a list of phenomenological events and their corresponding time of occurrence for both the full-scale test and the FE analysis. Occupant Risk Measures Acceleration-time histories and angular rate-time histories were collected from several locations in the model using the *Element-Seatbelt-Accelerometer option in LS-DYNA, which is the preferred method suggested by LS-DYNA for collecting acceleration data.[LSDYNA13] The accelerometers were connected to the vehicle model using *Nodal-Rigid-Body-Constraints (NRBs). The time-history data was collected from each accelerometer in a local reference coordinate system that was fixed to the vehicle with the x-direction coincident with the forward direction of the vehicle; which is consistent with the way the test data was collected from physical accelerometers. The data was collected at a frequency of 30 kHz which was determined to be sufficient to avoid aliasing of the data. The model was instrumented with eight accelerometers with one positioned near the center of gravity of the vehicle on the cabin floor, as identified in Figure 95.

130 Figure 91. Comparison of G4(2W) guardrail after crash event for Test 471470-26 and FE analysis. Table 29. Groundline deflections of posts for Test 471470-26 and FE analysis. Post Number Test FEA 471470-26 (in) (in) Post 13 2.0 0.5 Post 14 5.0 5.0 Post 15 13.0 13.0 Post 16 13.5 12.5 Post 17 4.75 4.0 Post 18 1.5 0.25 Post 19 0.25 0.00 Post 15 Post 14 Post 16 Post 17 Post 14 Post 15 Post 15 Post 14 Post 16 Post 17 Post 14 Post 15

131 The occupant risk assessment measures were computed using the three acceleration time- histories and the three angular-rate time histories collected at the center of gravity of the vehicle. The Test Risk Assessment Program (TRAP) calculates standardized occupant risk factors from vehicle crash data in accordance with the National Cooperative Highway Research Program (NCHRP) guidelines and the European Committee for Standardization (CEN).(TTI98) The analysis results obtained from TRAP for the full-scale test and the FE analysis are shown in Table 31. The acceleration data used in the TRAP program was filtered using the SAE Class 180 filter. The table shows the two occupant risk factors recommended by NCHRP Report 350: 1) the lateral and longitudinal components of Occupant Impact Velocity (OIV) and 2) the maximum lateral and longitudinal component of resultant vehicle acceleration averaged over 10 millisecond interval after occupant impact called the Occupant Ridedown Acceleration (ORA). Also provided in the table are the CEN risk factors: the Theoretical Head Impact Velocity (THIV), the Post Impact Head Deceleration (PHD) and the Acceleration Severity Index (ASI). The results indicate that the occupant risk factors for both the full-scale test and the simulation are similar. The occupant impact velocity in the longitudinal direction was predicted from the simulation to be 5.3-m/s (15 percent higher than the test OIV of 4.6 m/s) at 0.1442 seconds. In the transverse direction, the occupant impact velocity predicted in the simulation was 5.8-m/s (same as test OIV). The highest 0.010-second occupant ridedown acceleration in the longitudinal direction was 10.2 g (11.3 percent lower than test ORA of 11.5 g) between 0.1791 and 0.1891 seconds. In the transverse direction, the highest 0.010-second occupant ridedown acceleration was 11.1 (0.9 percent lower than test ORA of 11.2) between 0.2152 and 0.2248 seconds. The THIV, PHD and ASI predicted from the simulation were 7.4 m/s (7.3 percent higher), 13.6 g’s (16 percent higher), and 0.99 (2 percent higher), respectively. With the exception of the PHD, both the test and the simulation values agree within ±15 percent. The most notable differences between the analysis and the test were the angular displacements of the vehicle. The increased pitch of the vehicle in the analysis allowed the rear bumper to pass over the top of the rail. Refer to Figure 94 starting at time 0.241 seconds. This event resulted in an increased yaw angle of the vehicle during redirection in the analysis and was likely caused by too high of friction between the vehicle and barrier. Time-History Data Comparison Figure 96, Figure 97, and Figure 98 show a comparison of the 10-millisecond moving average and the 50-millisecond moving average acceleration-time history at the c.g. of the pickup (i.e., longitudinal, transverse and vertical channels, respectively) for the test and FE analysis. Figure 99, Figure 100, and Figure 101 show comparisons of the yaw, roll, and pitch rates and displacements at the c.g. of the pickup for the test and FE analysis. Values for the quantitative evaluation metrics are also shown on the time-history plots. These quantities were computed from the raw acceleration data and are shown with these plots only for reference. The values in red font indicate poor correlation between test and analysis results, while the values in black font indicate good correlation. The quantitative metrics are discussed in more detail in the Quantitative Evaluation section of this chapter.

132 Figure 92. Sequential views of TTI Test 471470-26 and FE analysis from overhead viewpoint. 0.061 seconds 0.119 seconds 0.180 seconds 0.000 seconds

133 Figure 92. [CONTINUED] Sequential views of TTI Test 471470-26 and FE analysis from overhead viewpoint. 0.361 seconds 0.480 seconds 0.599 seconds 0.241 seconds

134 Figure 93. Sequential views of TTI Test 471470-26 and FE analysis from downstream viewpoint. 0.061 seconds 0.119 seconds 0.180 seconds 0.000 seconds

135 Figure 93. [CONTINUED] Sequential views of TTI Test 471470-26 and FE analysis from downstream viewpoint. 0.361 seconds 0.480 seconds 0.599 seconds 0.241 seconds

136 Figure 94. Sequential views of TTI Test 471470-26 and FE analysis from an oblique viewpoint behind the system. 0.061 seconds 0.119 seconds 0.180 seconds 0.000 seconds

137 Figure 94. [CONTINUED] Sequential views of TTI Test 471470-26 and FE analysis from an oblique viewpoint behind the system. 0.361 seconds 0.480 seconds 0.599 seconds 0.241 seconds

138 Table 30. Summary of phenomenological events of full-scale test 471470-26 and FEA simulation. Event Test 471470-26 FE Analysis Start of redirection 0.056 sec 0.044 sec Vehicle contact with Post 15 0.086 sec 0.085 - 0.090 sec Tire contact with Post 15 0.104 sec 0.100 – 0.105 sec Wheel assembly separated 0.104 – 0.193 sec 0.124 seconds Vehicle contacts Post 16 0.157 sec 0.155 – 0.160 sec Tire contact with Post 16 0.193 sec 0.190 – 0.195 sec Rear of vehicle contacts rail 0.203 sec 0.190 – 0.195 sec Vehicle contact with Post 17 0.236 sec 0.240 – 0.245 sec Vehicle parallel with guardrail 0.249 sec 0.256 sec Speed at parallel 46.3 mph (74.5 km/h) 41.0 mph (66.0 km/h Vehicle contact with Post 18 0.356 sec N.A. Maximum deflection of guardrail 27.2 in (691 mm) 27.2 in (691 mm) Vehicle loses contact with guardrail 0.513 sec 0.600 sec Speed at exit 44.0 mph (70.8 km/h) 37.3 mph (60.0 km/h) Angle at exit 8.1 deg 26.0 deg Roll angle at exit 25 deg 30.3 deg Maximum roll angle 39 deg @ 0.709 s N.A. Total contact length 22.7 ft (6.92 m) 25.1 ft (7.65 m)

139 Figure 95. Location of accelerometer in FE model. 53 in 36.7 in 36.7 in 29.1 in

140 Table 31. Summary of occupant risk measures computed from Test 471470-26 and FEA simulation. Event Test 471470-26 FE Analysis Start of redirection 0.056 sec 0.044 sec Vehicle contact with Post 15 0.086 sec 0.085 - 0.090 sec Tire contact with Post 15 0.104 sec 0.100 – 0.105 sec Wheel assembly separated 0.104 – 0.193 sec 0.124 seconds Vehicle contacts Post 16 0.157 sec 0.155 – 0.160 sec Tire contact with Post 16 0.193 sec 0.190 – 0.195 sec Rear of vehicle contacts rail 0.203 sec 0.190 – 0.195 sec Vehicle contact with Post 17 0.236 sec 0.240 – 0.245 sec Vehicle parallel with guardrail 0.249 sec 0.256 sec Speed at parallel 46.3 mph (74.5 km/h) 41.0 mph (66.0 km/h) Vehicle contact with Post 18 0.356 sec N.A. Maximum deflection of guardrail 27.2 in (691 mm) 27.2 in (691 mm) Vehicle loses contact with guardrail 0.513 sec 0.600 sec Speed at exit 44 mph (70.8 km/h) 37.3 mph (60.0 km/h) Angle at exit 8.1 deg 26.0 deg Roll angle at exit 25 deg 30.3 deg Maximum roll angle 39 deg @ 0.709 s N.A. Total contact length 22.7 ft (6.92 m) 25.1 ft (7.65 m)

141 Figure 96. Longitudinal acceleration-time history plot from accelerometer at c.g. for full- scale Test 471470-26 and FEA (10-ms and 50-ms moving averages). Figure 97. Lateral acceleration-time history plot from accelerometer at c.g. for full-scale Test 471470-26 and FEA (10-ms and 50-ms moving averages). Figure 98. Vertical acceleration-time history plot from accelerometer at c.g. for full-scale Test 471470-26 and FEA (10-ms and 50-ms moving averages). -15 -10 -5 0 5 10 0 0.2 0.4 0.6 0.8 1 A cc e le at io n ( G 's ) Time (seconds) x-acc (10-ms Avg.) Test 471470-26 FEA -7 -6 -5 -4 -3 -2 -1 0 1 2 0 0.2 0.4 0.6 0.8 1 A cc e le at io n ( G 's ) Time (seconds) x-acc (50-ms Avg.) Test 471470-26 FEA S-G (M) = 5.2 S-G (P) = 38.4 ANOVA = 1.75 SD = 29.1 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 0 0.2 0.4 0.6 0.8 1 A cc e le at io n ( G 's ) Time (seconds) y-acc (10-ms Avg.) Test 471470-26 FEA -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 0 0.2 0.4 0.6 0.8 1 A cc e le at io n ( G 's ) Time (seconds) y-acc (50-ms Avg.) Test 471470-26 FEA S-G (M) = 1.8 S-G (P) = 30.7 ANOVA = 1.12 SD = 25.92 -20 -10 0 10 20 30 40 0 0.2 0.4 0.6 0.8 1 1.2 A cc e le at io n ( G 's ) Time (seconds) z-acc (10-ms Avg.) Test 471470-26 FEA -6 -4 -2 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 1.2 A cc e le at io n ( G 's ) Time (seconds) z-acc (50-ms Avg.) Test 471470-26 FEA S-G (M) = 60.6 S-G (P) = 51.0 ANOVA = 1.02 SD = 17.27

142 Figure 99. Yaw-time history plot from accelerometer at c.g. for full-scale test 471470-26 and FEA (angular rate and displacement). Figure 100. Roll-time history plot from accelerometer at c.g. for full-scale test 471470-26 and FEA (angular rate and displacement). Figure 101. Pitch-time history plot from accelerometer at c.g. for full-scale test 471470-26 and FEA (angular rate and displacement). -200 -150 -100 -50 0 50 100 0 0.2 0.4 0.6 0.8 1 Ya w R at e ( d e g) Time (seconds) Test 471470-26 FEA -60 -50 -40 -30 -20 -10 0 10 0 0.2 0.4 0.6 0.8 1 Ya w A n gl e ( d e g) Time (seconds) Test 471470-26 FEA S-G (M) = 15.7 S-G (P) = 8.3 ANOVA = 8.99 SD = 11.8 -200 -150 -100 -50 0 50 100 150 200 250 300 0 0.2 0.4 0.6 0.8 1 R o ll R at e ( d e g) Time (seconds) Test 471470-26 FEA -5 0 5 10 15 20 25 30 35 40 45 0 0.2 0.4 0.6 0.8 1 R o ll A n gl e ( d e g) Time (seconds) Test 471470-26 FEA S-G (M) = 4 S-G (P) = 23.3 ANOVA = .12 SD = 20.2 -14 -12 -10 -8 -6 -4 -2 0 2 4 0 0.2 0.4 0.6 0.8 1 P it ch A n gl e ( d e g) Time (seconds) Test 471470-26 FEA -300 -200 -100 0 100 200 300 0 0.2 0.4 0.6 0.8 1 P it ch R at e ( d e g) Time (seconds) Test 471470-26 FEA P it ch A n gl e (d e g) -300 -200 -100 0 100 200 300 400 0 0.2 0.4 0.6 0.8 1 P it ch R at e ( d e g) Ti e (seconds) Test 471470-26 FEA S-G (M) = 51.7 S-G (P) = 41.1 ANOVA = 1.7 SD = 28.0

143 Summary The intent of this qualitative evaluation was to verify overall model response through a general comparison with a full-scale crash test. The general response of the FE model seemed reasonable in that the model provided the basic chain of phenomenological events that occurred in the full-scale crash test. The occupant risk measures computed from the time-history data collected at the c.g. of the vehicle also correlated reasonably well with the test data. As mentioned earlier, the higher pitch of the vehicle in the analysis in turn caused error in the yaw angle. The pitch angle was only 4 degrees higher in the analysis, but this was enough to allow the bumper to pass over the top of the rail. It was theorized that the increased pitch may have been a result of too high of friction forces between the vehicle and guardrail. Quantitative Validation The quantitative validation assessment of the model’s results was based on validation procedures of NCHRP Web Document 179 (W179). [Ray10] The purpose of these guidelines is to establish accuracy, credibility, and confidence in the results of crash test simulations that are intended to support policy decisions, and to be used for approval of design modifications to roadside safety devices that were originally approved with full-scale crash testing. The validation procedure has three steps: 1. Solution verification: Indicates whether the analysis solution produced numerically stable results (ensures that basic physical laws are upheld in the model). 2. Time-history evaluation: Quantitative measure of the level of agreement of time-history data (e.g., x, y, z accelerations and roll, pitch, and yaw rates) between the analysis and test. 3. Phenomena Importance Ranking Table (PIRT): A table that documents the types of phenomena that a numerical model is intended to replicate and verifies that the model produces results consistent with its intended use. The PIRTs for the individual components were presented earlier in the “Calibration/Validation of Guardrail Components” section of this report. The following is a discussion of the time-history evaluation metrics, their acceptance criteria, and the Phenomena Importance Ranking Table (PIRT) for crash simulation. Time-History Evaluation The RSVVP (Roadside Safety Verification and Validation Program) software, which was developed as part of NCHRP Project 22-24, was used to compute the comparison metrics between analysis and full-scale test data. RSVVP computes fifteen different metrics that quantify the differences between a pair of curves. Since many of the metrics share similar formulations, their results are often identical or very similar. Because of this, it is not necessary to include all of the variations. The metrics recommended in Report W179 for comparing time- history traces from full-scale crash tests and/or simulations of crash tests are the Sprague & Geers metrics and the ANOVA metrics. The Sprague-Geers metrics assess the magnitude and phase of two curves while the ANOVA examines the differences of residual errors between them. The definitions of these metrics are shown below:

144 Sprague & Geers: 22 22 1 2 2 )( iveComprehens cos1)( Phase 1)( Magnitude PMC mc mc P m c M ii ii i i           ANOVA: 2 max )(1)(Deviation Standard 1)()(Error Residual r ii iir ecm n nm cm e      Where, deviation standard relative error residual average relative valuealexperiment measured maximum quanties measured quantities calculated max       r i i e m m c Time-History Evaluation Acceptance Criteria Once a measure of comparison is obtained using a quantitative metric, it is necessary to establish an acceptance criterion for deciding if the comparison is acceptable. Because of the highly nonlinear nature of crash events, there are often considerable differences in the results of essentially identical full-scale crash tests – this was demonstrated in the W179 report. Likewise, a computational model may not match “exactly” the results of a physical test, but the difference should be no greater than what is expected between physical tests. The approach taken in the W179 was to determine the realistic variation in the deterministic shape comparison metrics for a set of identical physical experiments and use that variation as an acceptance criterion. The current acceptance criteria is based on the results of a quantitative comparison of ten essentially identical full-scale crash tests that were performed as part of the ROBUST project involving small car impact into a vertical rigid wall at 100 km/hr and 25 degrees.[ROBUST02; Ray08] The resulting acceptance criteria recommended by W179 for assessing the similarity of two time- history curves are:  Sprague-Geers o Magnitude should be less than 40 percent

145 o Phase should be less than 40 percent  ANOVA metrics o Mean residual error should be less than 5 percent o Standard deviation should be less than 35 percent. Phenomena Importance Ranking Tables (PIRT) The PIRT includes evaluation criteria corresponding to NCHRP Report 350 for TL-3 impacts and is patterned after the full-scale crash test evaluation criteria listed in Table 5.1 in NCHRP Report 350.[Ross93] The values for the individual metrics from the full-scale test and the computer analysis were reported and both the relative difference and absolute difference for each phenomenon were computed. If the relative difference is less than 20 percent or if the absolute difference is less than 20 percent of the acceptance limit in NCHRP Report 350, then the phenomena are considered to be replicated. Results The quantitative evaluation was based on comparison of acceleration-time histories and angular rate-time histories computed in the analysis to those measured in full-scale crash test 471470-26. The impact conditions for the simulation matched exactly those from the full-scale test (i.e., a 4572-lb pickup impacting the guardrail system at 62.6 mph (100.7 km/hr) at an angle of 24.3 degrees, at an impact point 2 ft (0.61 m) upstream of Post 14 in the guardrail system). These impact conditions correspond to NCHRP Report 350 Test 3-11. A summary of the quantitative comparison results are provided herein. Additional comparison data can be found in Appendix C. Solution Verification The first step in the validation process is to perform global checks of the analysis to verify that the numerical solution is stable and is producing physical results (e.g., results conform to the basic laws of conservation). The analysis was modeled as a closed system, which means that energy is not being added or removed during the analysis. Thus, the total energy should remain constant throughout the analysis and should be equal to the initial kinetic energy of the impacting vehicle. The one exception in this case is any kinetic energy generated due to the gravity load (which should be minimal during the short time period of the crash event relative to the initial kinetic energy of the vehicle). Table 32 shows a summary of the global verification assessment based on criteria recommended in Report W179. Figure 102 shows a plot of the global energy-time histories from the analysis. As shown in Table 32, all the solution verification parameters were satisfied except; for the hour glass energies in the truck model. The largest hourglass energies came from the frame rail of the pickup. The hourglass modes on the frame rail may have influenced the kinematics of the vehicle to some degree, but it is not likely that the error would have a significant influence on the overall results since the deformations and associated internal energies of the pickup are small compared to those of the guardrail system. Upon review of the truck model materials, the frame rail and many other components of the pickup model are modeled with under-integrated elements with no hourglass control. These were corrected prior to subsequent use of the model in this study.

146 Table 32. Analysis solution verification table. Verification Evaluation Criteria Change (%) Pass? Total energy of the analysis solution (i.e., kinetic, potential, contact, etc.) must not vary more than 10 percent from the beginning of the run to the end of the run. 5% Y Hourglass Energy of the analysis solution at the end of the run is less than five percent of the total initial energy at the beginning of the run. 5.2% N Hourglass Energy of the analysis solution at the end of the run is less than ten percent of the total internal energy at the end of the run. 9.7% Y The part/material with the highest amount of hourglass energy at the end of the run is less than ten percent of the total internal energy of the part/material at the end of the run. Blockout (9.7%) Truck Frame (50%) N Mass added to the total model is less than five percent of the total model mass at the beginning of the run. 39 lb Y The part/material with the most mass added had less than 10 percent of its initial mass added. Y The moving parts/materials in the model have less than five percent of mass added to the initial moving mass of the model. 0.3% Y There are no shooting nodes in the solution? Y Y There are no solid elements with negative volumes? Y Y Figure 102. Plot of global energy-time histories from the analysis.

147 Time-History Validation The RSVVP computer program was used to compute the Sprague-Geer metrics and ANOVA metrics using time-history data from the full-scale test (i.e., true curve) and analysis data (i.e., test curve). The multi-channel option in RSVVP was used since this option computes metrics for each individual channel as well as for the weighted composite of the combined channels. The data from each of the six data channels, which were located at the center of gravity of the vehicle, were input into RSVVP. These data included the x-acceleration, y-acceleration, z- acceleration, roll-rate, pitch-rate and yaw-rate. From Report W179 it was recommended that the raw data be used as input into the program. The data was then filtered in RSVVP using a CFC Class 60 filter. The shift and drift options in RSVVP were not used for the physical test data. From visual inspection, the physical test data appeared to show no initial offset of acceleration magnitude or drift. Since both the test and analysis data started at the time of impact with the barrier the synchronization of curves was determined to be unnecessary. The default metrics evaluation options in RSVVP were used, which included the Sprague & Geers and the ANOVA metrics, as shown in Figure 103. The curves were evaluated over 0.6 seconds of the impact event, corresponding to the termination time of the analysis. Figure 103. RSVVP metric selection for validation assessment. Based on the validation metrics, a comparison of the individual components of acceleration indicated that the simulation was in good agreement for the x- and y-channels of acceleration, and for the roll-rate channel as well. The yaw-rate channel and the pitch-rate channel showed mixed results, while the z-acceleration channel showed poor correlation. The results are shown in Table 33 and are summarized below: Sprague-Geers Metrics  The Sprague-Geers metrics for the x-acceleration were good regarding both magnitude (i.e., M=1.3%) and phase (i.e., P=33.7%), which indicates that the simulation is in agreement with the test.

148  The Sprague-Geers metrics for the y-acceleration were good regarding both magnitude (i.e., M=6.0%) and phase (i.e., P=31.7%), which indicates that the simulation is in agreement with the test.  The Sprague-Geers metrics for the z-acceleration were poor for both magnitude (i.e., M=59.6%) and phase (i.e., P=51.1%), which indicates that the simulation is not in agreement with the test for this channel.  The Sprague-Geers metrics for the yaw-rate were good regarding both magnitude (i.e., M=15.7%) and phase (i.e., P=8.3%), which indicates that the simulation is in agreement with the test.  The Sprague-Geers metrics for the roll-rate were good regarding both magnitude (i.e., M=4%) and phase (i.e., P=23.3%), which indicates that the simulation is in agreement with the test.  The Sprague-Geers metrics for the pitch-rate were poor for magnitude (i.e., M=51.7%) and phase (i.e., P=41.1%), which indicates that the simulation is in not agreement with the test. ANOVA  The ANOVA metrics for the x-acceleration were good regarding both the mean residual error (i.e., 1.42%) and the standard deviation of residual error (i.e., 26.4%), which indicated that the simulation is in agreement with the test.  The ANOVA metrics for the y-acceleration were good regarding both the mean residual error (i.e., 1.29%) and the standard deviation of residual error (i.e., 27.3%), which indicated that the simulation is in agreement with the test.  The ANOVA metrics for the z-acceleration were good regarding both the mean residual error (i.e., 0.92%) and the standard deviation of residual error (i.e., 17.4%), which indicated that the simulation is in agreement with the test.  The ANOVA metrics for the yaw-rate were poor for the mean residual error (i.e., 8.99%) but good regarding the standard deviation of residual error (i.e., 11.8%).  The ANOVA metrics for the roll-rate were good regarding both the mean residual error (i.e., 0.12%) and the standard deviation of residual error (i.e., 20.2%), which indicated that the simulation is in agreement with the test.  The ANOVA metrics for the pitch-rate were good regarding both the mean residual error (i.e., 1.7%) and the standard deviation of residual error (i.e., 28.3%), which indicated that the simulation is in agreement with the test. Since the metrics computed for the individual data channels did not all satisfy the acceptance criteria, the multi-channel option in RSVVP was used to calculate the weighted Sprague-Geer and ANOVA metrics for the six channels of data. The Area II method is the default method used in RSVVP for weighting the importance of each data channel. The Area (II) method determines the weight for each channel based on a pseudo momentum approach using the area under the curves. Table 34 shows the results from RSVVP for the multi-channel option using the Area (II) method. The resulting weight factors computed for each channel are shown in both tabular form and graphical form in the tables. The results indicate that the x-, y-, yaw rate-, and roll-rate channels dominate the kinematics of the impact event. Which implies that the velocity change in the z-direction was insignificant compared to the change in velocity in the x- and y-directions.

149 Similarly, the pitch angle magnitude was comparatively less than that for the yaw and roll channels (refer to Figure 99, Figure 100 and Figure 101). The weighted metrics computed in RSVVP in the multi-channel mode all satisfy the acceptance criteria; therefore, the time history comparison can be considered acceptable. Table 33. Roadside safety validation metrics rating table – time history comparison (single-channel option). Evaluation Criteria Time interval [0.00 – 0.6 sec] OSprague-Geers Metrics List all the data channels being compared. Calculate the M and P metrics using RSVVP and enter the results. Values less than or equal to 40 are acceptable. RSVVP Curve Preprocessing Options M P Pass? Filter Option Sync. Option Shift Drift True Curve Test Curve True Curve Test Curve X acceleration CFC 60 none none none none none 1.3 33.7 Y Y acceleration CFC 60 none none none none none 6.0 31.7 Y Z acceleration CFC 60 none none none none none 59.6 51.1 N Roll rate CFC 60 none none none none none 4 23.3 Y Pitch rate CFC 60 none none none none none 51.7 41.1 N Yaw rate CFC 60 none none none none none 15.7 8.3 Y 4 P ANOVA Metrics List all the data channels being compared. Calculate the ANOVA metrics using RSVVP and enter the results. Both of the following criteria must be met:  The mean residual error must be less than five percent of the peak acceleration ( Peakae  05.0 ) and  The standard deviation of the residuals must be less than 35 percent of the peak acceleration ( Peaka 35.0 ) M ea n R es id ua l S ta nd ar d D ev ia tio n o f R es id ua ls Pass? X acceleration/Peak 1.4 26.4 Y Y acceleration/Peak 1.29 27.3 Y Z acceleration/Peak 0.92 17.4 Y Roll rate 0.12 20.2 Y Pitch rate 1.7 28.0 Y Yaw rate 9.0 11.83 N

150 Table 34. Roadside safety validation metrics rating table – (multi-channel option). Evaluation Criteria (time interval [0.0 – 0.6 seconds]) Channels (Select which were used) X Acceleration Y Acceleration Z Acceleration Roll rate Pitch rate Yaw rate Multi-Channel Weights - Area II method - X Channel: 0.190 Y Channel: 0.249 Z Channel: 0.061 Yaw Channel: 0.249 Roll Channel: 0.185 Pitch Channel: 0.065 O Sprague-Geer Metrics Values less or equal to 40 are acceptable. M P Pass? 13.4 26.5 Y P ANOVA Metrics Both of the following criteria must be met:  The mean residual error must be less than five percent of the peak acceleration ( Peakae  05.0 )  The standard deviation of the residuals must be less than 35 percent of the peak acceleration ( Peaka 35.0 ) M ea n R es id ua l St an da rd D ev ia tio n of R es id ua ls Pass? 2.8 21.4 Y PIRT – Crash Specific Phenomena The last step in the validation procedure was to compare the phenomena observed in both the crash test and the numerical solution. Table 35 contains the Report 350 crash test criteria with the applicable test numbers. The criteria that apply to Test 3-11 (i.e., corresponding to this particular test case) are marked with a red square. These include criteria A, D, F, L and M. Table 36 through Table 38 contain an expanded list of these same criteria including additional specific phenomena that were measured in the test and that could be directly compared to the numerical solution. Table 36 contains a comparison of phenomena related to structural adequacy, Table 37 contains a comparison of phenomena related to occupant risk, and Table 38 contains a comparison of phenomena related to vehicle trajectory.

151 Table 35. Report 350 crash test criteria with the applicable test numbers. Evaluation Factors Evaluation Criteria Applicable Tests  Stru ctural Adequacy A Test article should contain and redirect the vehicle; the vehicle should not penetrate, under-ride, or override the installation although controlled lateral deflection of the test article is acceptable. 10, 11, 12, 20, 21, 22, 35, 36, 37, 38 B The test article should readily activate in a predictable manner by breaking away, fracturing or yielding. 60, 61, 70, 71, 80, 81 C Acceptable test article performance may be by redirection, controlled penetration or controlled stopping of the vehicle. 30, 31,, 32, 33, 34, 39, 40, 41, 42, 43, 44, 50, 51, 52, 53 Occupant Risk D Detached elements, fragments or other debris from the test article should not penetrate or show potential for penetrating the occupant compartment, or present an undue hazard to other traffic, pedestrians or personnel in a work zone. All E Detached elements, fragments or other debris from the test article, or vehicular damage should not block the driver’s vision or otherwise cause the driver to lose control of the vehicle. (Answer Yes or No) 70, 71 F The vehicle should remain upright during and after the collision although moderate roll, pitching and yawing are acceptable. All except those listed in criterion G G It is preferable, although not essential, that the vehicle remain upright during and after collision. 12, 22 (for test level 1 – 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44) H Occupant impact velocities should satisfy the following: Occupant Impact Velocity Limits (m/s) Component Preferred Maximum 10, 20, 30,31, 32, 33, 34, 36, 40, 41, 42, 43, 50, 51, 52, 53, 80, 81 Longitudinal and Lateral 9 12 Longitudinal 3 5 60, 61, 70, 71 I Occupant ridedown accelerations should satisfy the following: Occupant Ridedown Acceleration Limits (g’s) Component Preferred Maximum 10, 20, 30,31, 32, 33, 34, 36, 40, 41, 42, 43, 50, 51, 52, 53, 60, 61, 70, 71, 80, 81 Longitudinal and Lateral 15 20 Vehicle Trajectory L The occupant impact velocity in the longitudinal direction should not exceed 40 ft/sec and the occupant ride-down acceleration in the longitudinal direction should not exceed 20 G’s. 11,21, 35, 37, 38, 39 M The exit angle from the test article preferable should be less than 60 percent of test impact angle, measured at the time of vehicle loss of contact with test device. 10, 11, 12, 20, 21, 22, 35, 36, 37, 38, 39 N Vehicle trajectory behind the test article is acceptable. 30, 31, 32, 33, 34, 39, 42, 43, 44, 60, 61, 70, 71, 80, 81

152 Table 36. Roadside safety phenomena importance ranking table (structural adequacy). Evaluation Criteria Known Result Analysis Result Difference Relative/ Absolute Agree? St ru ct ur al A de qu ac y A A 1 Test article should contain and redirect the vehicle; the vehicle should not penetrate, under-ride, or override the installation although controlled lateral deflection of the test article is acceptable. (Answer Yes or No) Y Y Y A 2 Maximum dynamic deflection: - Relative difference is less than 20 percent or - Absolute difference is less than 6 inches 27.2 in 27.2 in 0 % 0 in Y A 3 Length of vehicle-barrier contact: - Relative difference is less than 20 percent or - Absolute difference is less than 6.6 ft 22.7 ft 25.1ft 10.6 % 2.4 ft Y A 4 Number of broken or significantly bent posts is less than 20 percent. 0 0 Y A 5 Did the rail element rupture or tear (Answer Yes or No) No No Y A 6 Number of detached post-rail connections. 2 2 Y A 7 Was there significant snagging between the vehicle wheels and barrier elements (Answer Yes or No). Y Y Y A 8 Was there significant snagging between vehicle body components and barrier elements (Answer Yes or No). N N Y

153 Table 37. Roadside safety phenomena importance ranking table (occupant risk). Evaluation Criteria Known Result Analysis Result Difference Relative/ Absolute Agree? O cc up an t R isk D Detached elements, fragments or other debris from the test article should not penetrate or show potential for penetrating the occupant compartment, or present an undue hazard to other traffic, pedestrians or personnel in a work zone. (Answer Yes or No) N N Y F F 1 The vehicle should remain upright during and after the collision although moderate roll, pitching and yawing are acceptable. (Answer Yes or No) Y Y Y F 2 Maximum roll of the vehicle at 0.6 seconds: - Relative difference is less than 20 percent or - Absolute difference is less than 5 degrees. 25 deg 30 deg 20% 5 deg Y F 3 Maximum pitch of the vehicle at 0.6 seconds: - Relative difference is less than 20 percent or - Absolute difference is less than 5 degrees. 10.7 deg 9.1 deg 15% 1.6 deg Y F 4 Maximum yaw of the vehicle at 0.6 seconds: - Relative difference is less than 20 percent or - Absolute difference is less than 5 degrees. 41.2 deg 50.4 deg 22% 9.2 deg N L L 1 Occupant impact velocities: - Relative difference is less than 20 percent or - Absolute difference is less than 2 m/s.  Longitudinal OIV (m/s) 4.6 5.3 15 0.7 m/s Y  Lateral OIV (m/s) 5.8 5.8 0% 0 m/s Y  THIV (m/s) 6.9 7.4 7.2% 0.5 m/s Y L 2 Occupant accelerations: - Relative difference is less than 20 percent or - Absolute difference is less than 4 g’s.  Longitudinal ORA 11.5 10.2 11.3 % 1.3 g Y  Lateral ORA 11.2 11.1 0.9 % 0.1 g Y  PHD 11.7 13.6 16.2 % 1.9 g Y  ASI 1.01 0.99 2% 0.02 g Y

154 Table 38. Roadside safety phenomena importance ranking table (vehicle trajectory). Evaluation Criteria Known Result Analysis Result Difference Relative/ Absolute Agree? V eh ic le T ra je ct or y M M 1 The exit angle from the test article preferable should be less than 60 percent of test impact angle, measured at the time of vehicle loss of contact with test device. 55% 106% N M 2 Exit angle at loss of contact: - Relative difference is less than 20 percent or - Absolute difference is less than 5 degrees. 13.5 deg 25.7 deg 90% 12.2 deg N M 3 Exit velocity at loss of contact: - Relative difference is less than 20 percent or - Absolute difference is less than 6.2 mph. 44 mph 37.3 mph 15% 6.7 mph Y M 4 One or more vehicle tires failed or de-beaded during the collision event (Answer Yes or No). Y Y Y All the applicable criteria in Table 36 through Table 38 agree (i.e., the relative difference between the numerical solution and the test was less than 20%) except for the criteria involving the vehicle yaw angle. As discussed earlier, the slight increase in pitch of the vehicle allowed the rear bumper to pass over the top of the w-beam during redirection, which significantly increased the yaw angle as the vehicle exited the system. Conclusions In general, the finite element analysis of the G4(2W) guardrail system under NCHRP Report 350 Test Level 3 conditions demonstrated that the finite element model replicates the basic phenomenological behavior of the system in a redirection impact with a 2000P vehicle. There was good agreement between the test and the simulations with respect to event timing, overall kinematics of the vehicle, guardrail damage and guardrail deflections; although, the model did experience slightly higher pitch angle and higher yaw angle than occurred in the test. There were some components of the truck model that experienced higher than acceptable zero-energy modes (i.e., hourglass energies). Although it is not likely that slight errors in the response of those components would affect overall results, it is possible that they could lead to further instability in the model. These issues were corrected and the vehicle model is thus considered stable for subsequent analyses in this study. Quantitative comparison of the time- history data indicated that the finite element model accurately replicates the results of the baseline crash test. Thus, the model is considered valid for use in assessing the effects of incremental modifications to the guardrail system.