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Publication Number: FHWA-HRT-05-063
Date: May 2007

Evaluation of LS-DYNA Concrete Material Model 159

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Foreword

This report documents the evaluation of a concrete material model that has been implemented into the dynamic finite element code, LS-DYNA, beginning with version 971. This material model is in keyword format as MAT_CSCM for Continuous Surface Cap Model. This model was developed to predict the dynamic performance-both elastic deformation and failure-of concrete used in safety structures when involved in a collision with a motor vehicle. An example of a roadside safety structure is a concrete safety barrier that divides opposing lanes of traffic on a roadway. Default input parameters for concrete are stored in the model and can be accessed for use. This material model only replicates the concrete aggregate. Appropriate reinforcement bars or rods must be included in the structure model separately.

This report is the second of two that completely documents this material model. This report documents the testing performed to review the model's performance and accuracy of results. The first report is Users Manual for LS-DYNA Concrete Material Model 159, which documents the theoretical basis and required input format, and includes limited hypothetical problems for the user.

This report will be of interest to research engineers who are associated with the evaluation and crashworthy performance of roadside safety structures, particularly engineers responsible for predicting the crash response of such structures when using the finite element code, LS-DYNA.

Michael Trentacoste

Director, Office of Safety R&D

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document.

The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear in this report only because they are considered essential to the objective of the document.

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Technical Report Documentation Page
1. Report No.
FHWA-HRT-05-063
2. Government Accession No. 3. Recipient's Catalog No.
4. Title and Subtitle
Evaluation of LS-DYNA Concrete Material Model 159
5. Report Date
May 2007
6. Performing Organization Code
7. Author(s)
Yvonne D. Murray Akram Abu-Odeh and Roger Bligh
8. Performing Organization Report No.
9. Performing Organization Name and Address
APTEK, Inc.
1257 Lake Plaza Dr. Suite 100
Colorado Springs, CO 80906

Texas Transportation InstituteTexas
A &M University System
3135 TAMU
College Station, TX 77843
10. Work Unit No. (TRAIS)
11. Contract or Grant
No.DTFH61-98-C-00075
12. Sponsoring Agency Name and Address
Volpe National Transportation Systems Center
55 Broadway, Kendall Square
Cambridge, MA 02142-1093

Federal Highway Administration
6300 Georgetown PikeMcLean, VA 22101-2296
13. Type of Report and Period Covered
Final Report September 27, 2001 through December 26, 2004
14. Sponsoring Agency Code
15. Supplementary Notes
The Contracting Officer's Technical Representative (COTR) for this project is Martin Hargrave, Office of Safety Research and Development, HRDS-04, Turner-Fairbank Highway Research Center.
16. Abstract
An elastoplastic damage model with rate effects was developed for concrete and implemented into ls-dyna, a commercially available finite element code. This manual documents the evaluation of the concrete material model, including the selection of the concrete model input parameters. The model is evaluated through correlations with test data: drop tower impact of ⅓-scale beams (plain and reinforced), bogie vehicle impact of full-scale reinforced beams, pendulum impact of bridge rails, and quasi-static loading of a safety-shaped barrier. Although the model was developed and evaluated for roadside safety applications, it should also be applicable to many dynamic problems.

The companion manual to this report is Users Manual for ls-dyna Concrete Material Model 159, FHWA-HRT-05-062.
17. Key Words concrete, LS-DYNA, material model, reinforced beam, New Jersey barrier, bridge rail, pendulum, bogie vehicle 18. Distribution Statement
No restrictions. This document is available through the National Technical Information Service, Springfield, VA 22161.

19. Security Classif. (of this report)
Unclassified

20. Security Classif. (of this page)
Unclassified
21. No. of Pages
206

22. PriceN/A

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized.

TABLE OF CONTENTS

Chapter 5. Size Effect

References

List of Figures

Figure 1. The default behavior of the concrete model in uniaxial tensile stress and pure shear stress is linear to the peak, followed by brittle softening

Figure 2. Strength and ductility increase with confining pressure in these triaxial compression simulations

Figure 3. The concrete model simulates volume expansion in uniaxial compressive stress, in agreement with typical test data (strains and stress positive in compression)

Figure 4. The modulus of concrete degrades with strength, as demonstrated by this cyclic loading simulation.

Figure 5. The difference in pressure at a given volumetric strain for these isotropic compression and uniaxial strain simulations is due to shear enhanced compaction

Figure 6. The increase in strength with strain rate is significant in tension at a strain rate of 100 per second

Figure 7. The increase in strength with strain rate in pure shear stress is similar to that modeled in uniaxial tensile stress

Figure 8. The increase in strength with strain rate in uniaxial compression stress is less pronounced than in uniaxial tensile stress or pure shear stress

Figure 9. Application of kinematic hardening simulates prepeak nonlinearity accompanied by plastic volume expansion

Figure 10. Realistic damage modes are simulated in concrete cylinders loaded in tension and compression

Figure 11. Two bands of damage initiate symmetrically about the axial midplane, then one band of damage rapidly dominates

Figure 12. Damage modes observed in cylinder compression tests as a function of end conditions. Source: CRC Press

Figure 13. The damage mode calculated for compression cylinders with fixed ends agrees with the X-shaped damage bands observed in tests

Figure 14. Concrete cylinder tested as part of the bogie vehicle impact test series

Figure 15. A diagonal band of damage is calculated with frictional end constraints if both end caps are allowed to rotate and slide (no end cap constraints)

Figure 16. A diagonal band of damage is calculated with frictional end constraints if one end cap is allowed to rotate and slide relative to the other (bottom cap constrained from rotating and sliding)

Figure 17. A double diagonal band of damage is initially calculated if both end caps are prevented from rotating and sliding (bottom and top caps constrained from rotating and sliding)

Figure 18. A double diagonal band of damage is initially calculated if one end cap is free to rotate (bottom cap restrained from rotating and sliding, top cap restrained from sliding)

Figure 19. A single diagonal band of damage initiates, but is not retained, if the cylinder is over-constrained (bottom and top caps restrained from sliding)

Figure 20. Diagonal damage bands are calculated using the *contact_automatic_surface_to_surface option, although the diagonal band location varies with scale factor

Figure 21. Differences in initial slope are primarily due to differing amounts of contact surface penetration between the concrete cylinder and end caps

Figure 22. End cap versus concrete displacement with penetration (SFS = 1)

Figure 23. End cap versus concrete displacement with little penetration (SFS = 10)

Figure 24. The relative displacement between the ends of the concrete cylinder depends on the amount of interface penetration present

Figure 25. The stress-displacement histories are in reasonable agreement if the relative displacement of the cylinder is used

Figure 26. Early time tensile damage occurs in some compressive cylinder calculations in the vicinity of the contact surface interface

Figure 27. The fracture energy, which is the area under the softening portion of the stress-displacement curve, is independent of element size in the direct pull simulations (not shifted)

Figure 28. The fracture energy, which is the area under the softening portion of the stress-displacement curve, is independent of element size in the direct pull simulations (shifted to displacement at peak stress)

Figure 29. Although the fracture energy is constant, the softening curves vary slightly with element size in the unconfined compression simulations (not shifted)

Figure 30. Although the fracture energy is constant, the softening curves vary slightly with element size in the unconfined compression simulations (shifted to displacement at peak stress)

Figure 31. Refinement of each mesh used in sensitivity analyses

Figure 32. The stress-displacement curves calculated in direct pull with an unregulated softening formulation do not converge as the mesh is refined

Figure 33. The damage mode calculated in direct pull with an unregulated softening formulation is damage within a single band of elements

Figure 34. The stress-displacement curves calculated in unconfined compression with an unregulated softening formulation are similar for the basic and refined meshes (fixed ends)

Figure 35. The damage mode calculated in unconfined compression with an unregulated softening formulation is a double diagonal (in the basic and refined meshes with fixed end conditions)

Figure 36. The stress-displacement curves calculated in direct pull with a regulated softening formulation converge as the mesh is refined

Figure 37. The damage modes calculated in direct pull with a regulated softening formulation are in agreement for the basic and refined mesh simulations

Figure 38. The stress-displacement curves calculated in unconfined compression with a regulated softening formulation nearly converge as the mesh is refined (fixed ends)

Figure 39. The X-shaped damage mode calculated in unconfined compression with a regulated softening formulation is similar for the basic and refined mesh simulations (fixed ends)

Figure 40. A crisp X-shaped band of damage is calculated for the very refined mesh, with or without regulation of the softening response

Figure 41. The stress-displacement curves calculated in unconfined compression without a regulated softening formulation become more brittle as the mesh is refined (fixed ends)

Figure 42. The stress-displacement curves calculated in unconfined compression with a regulated softening formulation become more ductile as the mesh is refined (fixed ends)

Figure 43. Schematic of the size effect, as suggested by Bazant and Planas.(9)

Figure 44. Refinement of the concrete beam mesh used in the size effect analyses

Figure 45. The damage simulated in the full-scale beam is more severe than that simulated in the ⅓-scale beam, which is consistent with the size effect

Figure 46. The stress-deflection behavior of the full-scale beam is softer than that of the ⅓-scale beam, which is consistent with the size effect

Figure 47. Without regulation of the softening formulation, the damage simulated in the full-scale and ⅓-scale beams is nearly the same, which is inconsistent with the size effect

Figure 48. Without regulation of the softening formulation, the stress versus relative deflection curves of the full and ⅓-scale beams are nearly identical, which is inconsistent with the size effect

Figure 49. Sketch of four-point bend tests, showing dimensions in millimeters.(10)

Figure 50. Six of the eight plain concrete specimens initially failed with two major cracks in the impact regime

Figure 51. Two of the eight plain concrete specimens initially failed with one major crack in the impact regime

Figure 52. All plain concrete specimens impact the bottom of the test fixture

Figure 53. Four of the eight plain concrete specimens ultimately break into five pieces

Figure 54. The plain concrete beam initially breaks into three large pieces in all baseline calculations performed (shown at 12 msec for impact at 5.8 m/sec (19.0 ft/sec))

Figure 55. The plain concrete beam ultimately breaks into five pieces in three of four calculations performed (shown at 26 msec for impact at 5.8 m/sec (19.0 ft/sec))

Figure 56. The plain concrete beam ultimately broke into four pieces in one of four calculations performed (shown at 26 msec for impact at 5.0 m/sec (16.4 ft/sec))

Figure 57. This preliminary calculation demonstrates the formation of one primary crack

Figure 58. The over-reinforced concrete beam has localized tensile cracks and concrete crushing in the impactor regime (test 15 conducted at 5 m/sec (16.4 ft/sec))

Figure 59. The damage mode of the over-reinforced concrete beam at peak deflection is localized tensile cracks and concrete crushing in the impactor regime (shown at 16 msec for impact at 5 m/sec (16.4 ft/sec))

Figure 60. The simulated damage fringes for impact at 10.6 m/sec (34.8 ft/sec) are less extensive than those simulated at 5.0 m/sec (16.4 ft/sec)

Figure 61. The measured displacement histories are accurately simulated by ls-dyna concrete material model MAT 159

Figure 62. The processed velocity histories drift once the impactor separates from the beam during rebound at about 17 msec

Figure 63. The damage mode measured for half of the under-reinforced beam specimens is two major cracks beneath the impactor points, without rebar breakage

Figure 64. The damage mode simulated for all under-reinforced beam specimens is two major cracks beneath the impactor points, with additional damage toward the ends of the beam

Figure 65. About half of the under-reinforced beam specimens exhibited cracks originating on the top of the specimen, and located halfway between the impactor points and ends of the beam

Figure 66. Good displacement history and peak deflection comparisons of ls-dyna drop tower impact simulations with test data for plain and reinforced concrete beams

Figure 67. Schematic of bogie vehicle impacting reinforced concrete beam

Figure 68. The beam rests on greased supports and reacts against two load frames

Figure 69. The beam tested at an impact velocity of 33.1 km/h (20.5 mi/h) exhibits inclined shear cracks, localized crushing, and bond failure

Figure 70. Inclined shear cracks, localized crushing, and bond failure are simulated in the calculation conducted at 33 km/h (20.5 mi/h)

Figure 71. The beam tested at an impact velocity of 15.9 km/h (9.9 mi/h) exhibits inclined shear cracks, localized crushing, and bond failure

Figure 72. Damage dominates one side of the beam impacted at 15.9 km/h (9.9 mi/h)

Figure 73. Tensile damage, inclined shear damage, and bond failure are simulated in the calculation conducted at 15.9 km/h (9.9 mi/h) with erosion set to 10 percent strain

Figure 74. The beam breaks into two major pieces and does not rebound when impacted at 18 km/h (11.2 mi/h)

Figure 75. This damage modeled at 15.9 km/h (9.9 mi/h) with erosion set to 1 percent strain is more extensive than when erosion is set to 10 percent strain

Figure 76. Cracks form on the tensile face of the beam impacted at 8.6 km/h (5.3 mi/h) and propagate toward the compression face

Figure 77. The beam rebounds when impacted at 8.6 km/h (5.3 mi/h), pushing the bogie vehicle backward.

Figure 78. The simulation of the beam impacted at 8.6 km/h (5.3 mi/h) exhibits substantial damage, but retains its integrity and rebounds

Figure 79. The displacement histories from the ls-dyna bogie vehicle impact simulations compare well with the test data

Figure 80. The calculations conducted at 8.6 km/h (5.3 mi/h) correlate best with the test data if the supports are modeled

Figure 81. Strain histories measured on the compressive face of each beam peak around 0.23 percent strain.

Figure 82. The strain histories from the ls-dyna bogie vehicle impact simulations vary with impact velocity.

Figure 83. Details of T4 rail with four-bolt anchorage and 254-mm- (10-inch-) wide parapet

Figure 84. Details of T4 rail with three-bolt anchorage and 317.5-mm- (12.5-inch-) wide parapet

Figure 85. Parapet before test P3

Figure 86. Parapet before test P5

Figure 87. Parapet damage after test P3

Figure 88. Parapet damage after test P4

Figure 89. Parapet damage after test P5, side

Figure 90. Parapet damage after test P5, rear

Figure 91. Parapet damage after test P7

Figure 92. Original pendulum model

Figure 93. Modified pendulum model

Figure 94. Comparison of the SBP model to rigid pole calibration test

Figure 95. Force-time histories for benchmark tests and spring models

Figure 96. Force-displacement relationships for benchmark tests and SBP2 model

Figure 97. Model of T4 bridge rail specimen with four-bolt anchorage and 254-mm- (10-inch-) wide parapet

Figure 98. Model of T4 bridge rail specimen with three-bolt anchorage and 317.5-mm- (12.5-inch-) wide parapet

Figure 99. Closeup view of steel rail system with four-bolt anchorage

Figure 100. Steel reinforcement and anchor bolts for T4 bridge rail specimen with four-bolt anchorage and 254-mm- (10-inch-) wide parapet

Figure 101. Steel reinforcement and anchor bolts for T4 bridge rail specimen with three-bolt anchorage and 317.5-mm- (12.5-inch-) wide parapet

Figure 102. Right end view of parapet-only model for four-bolt design and three-bolt design

Figure 103. Original parapet mesh used for merging nodes with steel reinforcement

Figure 104. Revised parapet mesh with steel reinforcement

Figure 105. Linear mesh biasing along the height of parapet and width of deck

Figure 106. Bell curve mesh biasing along length of parapet and uniform meshing along length of deck

Figure 107. Boundary conditions used for the full system model with deck and for the parapet-only model

Figure 108. Anchor bolt constraint to base plate

Figure 109. Contacts definitions for the T4 bridge rail model

Figure 110. Damage fringe for baseline simulation of T4 with four-bolt anchorage and 254-mm- (10-inch-) wide parapet

Figure 111. Element erosion profile (simulation case02, ERODE =1) on traffic side

Figure 112. Element erosion profile (simulation case02, ERODE =1)

Figure 113. Damage fringes for simulation case02 (ERODE =1)

Figure 114. Parapet failure with fracture energies at 20 percent of baseline values

Figure 115. Energy-time histories for pendulum impact of T4 bridge rail with fracture energies at 20 percent of baseline values

Figure 116. Parapet failure with fracture energies at 50 percent of baseline values

Figure 117. Parapet failure with fracture energies at 27.5 percent of baseline values

Figure 118. Energy-time histories for pendulum impact of T4 bridge rail with fracture energies at 27.5 percent of baseline values

Figure 119. Enhanced anchor bolt-to-base plate connection model

Figure 120. Fracture profile of modified T4 system at 0.080 seconds

Figure 121. Fracture profile of modified T4 system at 0.115 seconds

Figure 122. Fracture profile of modified T4 system at 0.250 seconds

Figure 123. Profile of damaged T4 bridge rail system with four-bolt anchorage after pendulum impact

Figure 124. Fracture profile for T4 bridge rail with four-bolt anchorage for parapet and eroded elements

Figure 125. Pendulum bogie accelerations for impact of T4 bridge rail with four-bolt anchorage and 254-mm- (10-inch-) wide parapet

Figure 126. Pendulum bogie velocities for impact of T4 bridge rail with four-bolt anchorage and 254-mm- (10-inch-) wide parapet

Figure 127. Profile of T4 bridge rail system with three-bolt anchorage after pendulum impact

Figure 128. Damage to 317.5-mm- (12.5-inch-) wide parapet after pendulum impact showing element erosion

Figure 129. Damage to 317.5-mm- (12.5-inch-) wide parapet after pendulum impact showing damage fringes

Figure 130. Pendulum bogie accelerations for impact of T4 bridge rail with three-bolt anchorage and 317.5-mm- (12.5-inch-) wide parapet

Figure 131. Pendulum bogie velocities for impact of T4 bridge rail with three-bolt anchorage and 317.5-mm- (12.5-inch-) wide parapet

Figure 132. Test setup for static load tests on safety-shaped barriers

Figure 133. Failure mode at end of the safety-shaped barrier

Figure 134. Measured load versus displacement for the safety-shaped barrier

Figure 135. Cross section of the Florida safety-shaped barrier with New Jersey profile.(8)

Figure 136. Cross section of Florida barrier model concrete mesh and reinforcement layout

Figure 137. Isometric view of steel reinforcement in Florida barrier model

Figure 138. Model of quasi-static load test setup

Figure 139. Fracture profile of Florida safety-shaped barrier

Figure 140. A damage concentration is simulated in the parapet due to application of the steel/timber spreader plate that is not observed in the post-test parapet

Figure 141. The damage concentration is relieved if the timber is realistically modeled as an elastoplastic damaging material

Figure 142. A realistic damage and erosion pattern is simulated if the timber remains in contact with the parapet (ERODE = 1.05)

Figure 143. The primary erosion agrees with the measured crack pattern if the timber remains in contact with the parapet (ERODE = 1.0)

Figure 144. The primary erosion agrees with the measured crack pattern if the timber remains in contact with the parapet (ERODE = 1.0)

Figure 145. The calculated force versus deflection history is in reasonable agreement with the measured curve for the first 12 mm (0.5 inches) of deflection

Figure 146. The computed damage mode is similar to that measured if the load is applied via concentrated nodal point forces (at 11- to 12-mm (0.43- to 0.5-inch) deflection)

Figure 147. The computed force versus displacement unloads, when the load is applied via concentrated nodal point forces (ERODE = 1.05)

Figure 148. Single element under compressive loading, developer

Figure 149. Single element under compressive loading, user

Figure 150. Single element under tensile loading, developer

Figure 151. Single element under tensile loading, user

Figure 152. Single element under pure shear loading, developer

Figure 153. Single element under pure shear loading, user

Figure 154. Concrete cylinder model with inclined cross section

Figure 155. Damage fringe t = 13.498 msec

Figure 156. Damage fringe t = 13.598 msec

Figure 157. Damage fringe at t = 40 msec

Figure 158. Cross-sectional force (developer)

Figure 159. Cross-sectional force (user)

Figure 160. Plain concrete damage fringe at 1 msec (developer)

Figure 161. Plain concrete damage fringe at 4 msec (developer)

Figure 162. Plain concrete damage fringe at 20 msec (developer)

Figure 163. Plain concrete damage fringe at 30 msec (developer)

Figure 164. Plain concrete damage fringe t =1 msec (user Linux)

Figure 165. Plain concrete damage fringe t = 4 msec (user Linux)

Figure 166. Plain concrete damage fringe t = 20 msec (user Linux)

Figure 167. Plain concrete damage fringe t = 30 msec (user Linux)

Figure 168. Plain concrete damage fringe t = 1 msec (user Windows)

Figure 169. Plain concrete damage fringe t = 4 msec (user Windows)

Figure 170. Plain concrete damage fringe t = 20 msec (user Windows)

Figure 171. Plain concrete damage fringe t = 30 msec (user Windows)

Figure 172. Reinforced concrete damage fringe t = 1 msec (developer)

Figure 173 Reinforced concrete damage fringe t = 4 msec (developer)

Figure 174. Reinforced concrete damage fringe t = 16 msec (developer)

Figure 175. Reinforced concrete damage fringe t = 20 msec (developer)

Figure 176. Reinforced concrete damage fringe t = 1 msec (user Linux)

Figure 177. Reinforced concrete damage fringe t = 4 msec (user Linux)

Figure 178. Reinforced concrete damage fringe t = 16 msec (user Linux)

Figure 179. Reinforced concrete damage fringe t = 20 msec (user Linux)

Figure 180. Displacement of node 49,072 in millimeters (developer)

Figure 181. Displacement of node 49,072 in millimeters (user Linux)

Figure 182. Bogie damage, t = 4 msec (developer)

Figure 183. Bogie damage t = 8 msec (developer)

Figure 184. Bogie damage, t = 48 msec (developer)

Figure 185. Bogie damage, t = 80 msec (developer)

Figure 186. Damage fringes t = 4 msec (user Windows)

Figure 187. Damage fringe t = 8 msec (user Windows)

Figure 188. Damage fringe t = 48 msec (user Windows)

Figure 189. Damage fringe t = 80 msec (user Windows)

Figure 190. Damage, t = 4 msec (user Linux)

Figure 191. Damage, t = 8 msec (user Linux)

Figure 192. Damage, t = 48 msec (user Linux)

Figure 193. Damage t = 80 msec (user Linux)

Figure 194. Finite element model of the pendulum, rail, and fixed end of parapet

Figure 195. Damage fringes calculated with baseline properties for a fixed end parapet

Figure 196. The deformed configuration and damage of the Texas T4 bridge rail (four-bolt design) from impact with the simplified pendulum model (without a crushable nose) at 25 percent maximum available kinetic energy is similar to that observed during the tests

Figure 197. Stiffening the spring increases the maximum deceleration and decreases the time at which the maximum deceleration occurs

Figure 198. Good comparison of measured and calculated acceleration histories for the reduced fixed parapet mesh (spring stiffened using 80 percent deflection scale factor)

Figure 199. Addition of the deck model improves correlations with the test data (spring stiffened using 80 percent deflection scale factor)

Figure 200. All calculations run with baseline or slightly reduced properties (repow = 0.5 and Gfs / Gft = 0.5) produce rail deflections within two standard deviations of the measured results

Figure 201. Deflection and damage calculated with baseline properties using a stiffened spring (80 percent displacement scale factor)

Figure 202. Closeup of damage calculated with baseline properties using a stiffened spring (80 percent displacement scale factor)

Figure 203. Deflection and damage calculated with slightly reduced properties using a stiffened spring (80 percent displacement scale factor)

Figure 204. Closeup of damage calculated with slightly reduced properties using a stiffened spring (80 percent displacement scale factor)

Figure 205. Larger rail deflections are calculated at 9,835 mm/sec (large dots) compared with 9,556 mm/sec (solid and large dashed lines)

Figure 206. The tensile damage at the base of the parapet is eliminated if a flexible joint is modeled (80 percent displacement scale factor with baseline properties)

List of Tables

Table 1. Over-reinforced beam test matrix.

Table 2. Under-reinforced beam test matrix.

Table 3. Plain concrete beam test matrix.

Table 4. Primary crack analysis of test 15 conducted at 5 m/sec (16.4 ft/sec).

Table 5. Comparison of measured and computed deflections for the over-reinforced beams.

Table 6. Crack analysis for one under-reinforced beam tested with an impactor mass of 31.75 kg (70 lb).

Table 7. Comparison of measured and computed deflections for the under-reinforced beams.

Table 8. Short input format for parapet concrete material model.

Table 9. Short input format for bridge deck concrete material model.

Table 10. Long input format for parapet concrete material model.

Table 11. Long input format for bridge deck concrete material model.

Table 12. Force comparison between tests and simulation for T4 rail system with four-bolt anchorage.

Table 13. Force comparison between tests and simulation for T4 rail system with three-bolt anchorage.

Table 14. Rail deflection and pendulum crush in the Texas T4 bridge rail tests.

Table 15. Rail deflection as a function of maximum kinetic energy available.

Table 16. Rail deflection, pendulum crush, and crush energy as a function of spring stiffness and concrete properties for the fixed end parapet model.

Table 17. Rail deflection, pendulum crush, and crush energy as a function of spring stiffness and concrete properties for the full deck model.

Table 18. Rail deflection, pendulum crush, and crush energy for calculations conducted with increased impact velocity (9,835 mm/sec) for the full deck model.

Acronyms and Abbreviations
CEB Comite Euro-International Du Beton
COTR Contracting Officer's Technical Representative
CSCM continuous surface cap model
FHWA Federal Highway Administration
FIP Fédération Internationale de la Précontrainte
FOIL Federal Outdoor Impact Laboratory
LSTC Livermore Software Technology Corporation
NCAC National Crash Analysis Center
NCHRP National Cooperative Highway Research Program
SBP spring-based pendulum
SGI Silicon Graphics, Inc.

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