1. Image Aided Discrete Element Modeling (DEM) for Railroad Ballast By Erol Tutumluer Hai Huang Youssef Hashash Jamshid Ghaboussi Association of American Railroads

2. Outline BackgroundBackground Problem Statement Current Railroad Track Analysis Approach –Finite Element (FEM) –Discrete Element (DEM) »DEM Theory »Discrete Element Modeling for Railroad Track Analysis Image Aided DEM ApproachImage Aided DEM Approach – Research in University of Illinois Digitalized Image Technique for Aggregates Image Aided DEM Approach Approach Validation Applications on Railroad Ballast –Ballast Strength in terms of Aggregate Shapes –Ballast Settlement under Moving Load Conclusions and Future WorkConclusions and Future Work AcknowledgementAcknowledgement

3. Problem Statement A large portion of a railroad company’s annual budget to sustain the railway track system goes into maintenance and renewal of track ballastA large portion of a railroad company’s annual budget to sustain the railway track system goes into maintenance and renewal of track ballast A better basic understanding of the ballast behavior is essential for mitigating track problems and failures due to: Ballast movement and instability causing track buckle Ballast deformation and degradation Factors affecting ballast strength and stability includes: ballast aggregate gradation, aggregate shape properties, and loading characters A more realistic computational tool is needed to consider all factors which may have impact on ballastA more realistic computational tool is needed to consider all factors which may have impact on ballast

4. Current Railroad Track Analysis Approach : - Finite Element Finite element based numerical solution techniques used for the analysis of railroad tracks assume the railroad ballast bed to be an elastic homogeneous continuum ILLI-TRACK and GEO-TRACK

5. Longitudinal & Transverse 2-D Finite Element Meshes – IILI-TRACK Current Railroad Track Analysis Approach : - Finite Element

6. 3-D Finite Element Model – GEO – TRACK Continuum Solution: Elastic Layers, E and Unbound Aggregate Layers “Track Geotechnology and Track Management,” 2000, by Ernest T. Selig and John M. Waters

7. Railroad ballast layers are actually particulate media where individual aggregate particles are surrounded by other particles in contact with air voids in between When ballast is strained due to rail buckle and train wheels, motion takes place that may involve one or all of the following modes: Inter-particle slippage, Particle rotation, particle separation, and Even fracture at particle contacts Current Railroad Track Analysis Approach : - Discrete Element

8. Discontinuous Ballast Layer √ × Discrete Element Analysis Continuum Analysis Current Railroad Track Analysis Approach : - Discrete Element

9. DEM Theory: A DEM model simulates the mechanical response of a particulate medium by explicitly accounting for the dynamics of each particle in the system F1F1 F1F1 F2F2 F2F2 F3F3 F3F3 F4F4 F4F4 F5F5 F5F5 F6F6 F6F6 Current Railroad Track Analysis Approach : - Discrete Element

10. The interaction forces between two particles are represented by a damped spring in the normal direction and a spring in series with a frictional slider in the tangential (shear) direction DEM Theory: Fs Fn A B F F F Current Railroad Track Analysis Approach : - Discrete Element

11. The acceleration forces of each particle is computed by dividing the net force caused by interactions among neighboring particles Having found the acceleration, the particles velocity and displacement are computed for each time step using explicit integration Newton’s laws of motion DEM Theory: Current Railroad Track Analysis Approach : - Discrete Element

12. Current DEM Research (3D): Research, using ITASCA’s “PFC3D” to model the ballast-geogrid interlock effect, is currently underway Current Railroad Track Analysis Approach : - Discrete Element

13. Current DEM Research (3D): Tie was modeled by several big balls in the upper layer. Colors represent gradation. Ballast and geogrid system. (UK) Current Railroad Track Analysis Approach : - Discrete Element

14. Can only use spherical particles to model aggregate Particle rotation becomes dominant in contact between particles due to the spherical shape Calculation time is relatively long PLUS Current Railroad Track Analysis Approach : - Discrete Element

15. AREMA (2000) requires ballast material to be angular particles with sharp corners and cubic fragments with a minimum of flat and elongated pieces. Visual Inspection cause error and fairly low reliable result. Uncompacted Voids method is time and labor intensive, subjective, and has inter-lab variability and low repeatability. SOLUTION? ------- Image-DEM Approach Current Railroad Track Analysis Approach : - Discrete Element

16. Flat & Elongated (F&E) Ratio - ASTM D 4791 F&E ratio = Maximum to minimum dimensionF&E ratio = Maximum to minimum dimension –5:1 –3:1 –2:1 IntermediateMaximum Minimum AREMA specs require maximum 5% by weight over 3:1 ratio Digitalized Image Technique for Aggregates

17. n = 1 2 3 n 4 a1a1 a2a2 a3a3 0% Crushed 100% with 2 or More Crushed Faces Crushed Faces 0 100200300400500 Angularity Index  (degrees) 40 41 42 43 44 45 46 47 Crushed Stone Gravel 50-50 Blend AREMA specs require ballast aggregates to be angular particles with sharp corners and cubical fragments Digitalized Image Technique for Aggregates

18. University of Illinois Aggregate Image Analyzer - UIAIA Conveyor speed of 3 in./second Particles placed 10 in. apart Images captured within 0.1 second in succession Progressive Scan Video Camera

19. Angularity: 570 Angularity: 570 F&E Ratio: 1:1 F&E Ratio: 1:1 Top, front, and side images Top, front, and side images of an aggregate particle of an aggregate particle Image Aided DEM Approach

20. Library 2 AI = 570 F&E = 1:1 Library 1 AI = 630 F&E = 1:1 Library 3 AI = 448 F&E = 1:1 Library 4 AI = 390 F&E = 1:1 Library 6 AI = 570 F&E = 3 :1 Library 5 AI = 620 F&E = 3 :1 Library 7 AI = 454 F&E = 3 :1 Library 8 AI = 347 F&E = 3 :1 Library 10 AI = 490 F&E = 5 :1 Library 11 AI = 360 F&E = 5 :1 Library 9 AI = 573 F&E = 5 :1 Three orthogonal views of a single aggregate particle obtained using University of Illinois Aggregate Image Analyzer to construct 3D Shape libraries for DEM F&E: 1:1 F&E: 3:1 F&E: 5:1 Image Aided DEM Approach

21. Some applications of Image Aided DEM Approach 1.Drop Particles 2.Compaction 3.Tamping Image Aided DEM Approach

109. Tie Pull-out Test Results – Before & After Tamping F&E = 1:1 AI: 630-390 F&E = 3:1 AI: 620-347 F&E = 5:1 AI: 573-360

110. Tie Pull-out Tests – Effect of Tamping Ballast With Aggregate From Library 5 Before Tamping Wheel Load Ballast

111. Ballast With Aggregate From Library 5 After Tamping Wheel Load Ballast Tie Pull-out Tests – Effect of Tamping

112. Validation of Image Aided DEM Approach Direct Shear Box laboratory tests characters Humboldt HM-2560A direct shear device with 100 by 100 mm box Aggregate size: 4.75 – 9.5 mm Laboratory sample has an average AI of 535 and F&E ratio of 1.4:1 Need sensitivity analysis to decide DEM parameters including: Normal Contact Stiffness Shear Contact Stiffness Final set of parameters should make all DEM simulation results close to the laboratory results

113. Real aggregate picture compared to Discrete Element Validation of Image Aided DEM Approach

114. Sensitivity Analysis - First Trial Normal Stiffness: 300000 N/m Shear Stiffness: 300000 N/m Validation of Image Aided DEM Approach

115. Sensitivity Analysis - Second Trial Normal Stiffness: 300000 N/m Shear Stiffness: 500000 N/m Validation of Image Aided DEM Approach

116. Sensitivity Analysis - First Trial Normal Stiffness: 500000 N/m Shear Stiffness: 300000 N/m Validation of Image Aided DEM Approach

117. Final Validation Results Validation of Image Aided DEM Approach

118. Validated Parameters Normal Contact Stiffness500 KN/m Shear Contact Stiffness300KN/m Particle Size4.75~9.5 mm Angularity Index535 Flat & Elongated Ratio1:1.4 Tangent Surface Friction Angle0.7 Validation of Image Aided DEM Approach

119. Ballast Strength in Terms of Aggregate Shapes Direct shear box simulations to investigate the effect of Surface Texture and Angularity Fs Fn A B F F F 

120. Ballast Strength in Terms of Aggregate Shapes AI =570, Surface Friction Angle = 40 AI =390, Surface Friction Angle = 15 AI =390, Surface Friction Angle = 40 AI =570, Surface Friction Angle = 15

121. Ballast Strength in Terms of Aggregate Shapes Rough and Angular

122. Ballast Strength in Terms of Aggregate Shapes Rough and Round

123. Ballast Strength in Terms of Aggregate Shapes Smooth and Angular

124. Ballast Strength in Terms of Aggregate Shapes Smooth and Round

125. - Plan View of Ballast Settlement DEM Simulation Center PlaneRail SeatTransverse Vertical Plane Half Tie 0.61 m Application on Railroad Ballast Settlement

126. Ballast Layer Preparation - Ballast Sample of a Half Railroad Section with Angular and Cubical Aggregates of Shape Library 1

127. Need to solve “Moving Load on Track” problem to obtain the load profile on the top of one single tie Application on Railroad Ballast Settlement Observation Tie Load: P; Speed: V; Duration: t Close Form Solution Unequal Tie Spacing Different Tie-Ballast Structure Thermal Stress Arbitrary Excitation

128. Moving Load on Track Observation Tie Load: P; Speed: V; Duration: t Tie Mass Ballast Mass

129. Parameters: EI rail bending rigidity u rail vertical deflection Trail axial thermal force ρ rail unit mass ε rail damping f(t) excitation function δ delta function a m reaction force from substructure mnumber of ties u t tie vertical deflection u b ballast mass deflection K p rail pad stiffness K b ballast stiffness D p rail pad damping D b ballast damping Moving Load on Track

131. Load Pulse in DEM Loading Magnitude and Frequency in DEM Single Tie Load Pulse of a 286 kip Car Moving @ 28 km/h

132. Simulation Test Matrix Load Magnitude (kN) Frequency (Hz) (Train Speed, km/h) Shape Library 1 (Cubical - Angular) Shape Library 3 (Cubical - Rounded) Shape Library 8 (Elongated - Rounded) 90 1 (28)X X 5 (140)X X 10 (280)X X 120 1 (28)XXX 5 (140)XXX 10 (280)XXX 150 1(28)X X 5 (140)X X 10 (280)X X

133. Repeated Loading – Longitudinal view CYCLE 0

134. Repeated Loading – Longitudinal view CYCLE 0

135. Repeated Loading – Longitudinal view CYCLE 0

136. Repeated Loading – Longitudinal view CYCLE 20

137. Repeated Loading – Longitudinal view CYCLE 20

138. Repeated Loading – Longitudinal view CYCLE 20

139. Repeated Loading – Longitudinal view CYCLE 40

140. Repeated Loading – Longitudinal view CYCLE 40

141. Repeated Loading – Longitudinal view CYCLE 40

142. Repeated Loading – Longitudinal view CYCLE 60

143. Repeated Loading – Longitudinal view CYCLE 60

144. Repeated Loading – Longitudinal view CYCLE 60

145. Repeated Loading – Longitudinal view CYCLE 80

146. Repeated Loading – Longitudinal view CYCLE 80

147. Repeated Loading – Longitudinal view CYCLE 80

148. Repeated Loading – Longitudinal view CYCLE 100

149. Repeated Loading – Longitudinal view CYCLE 100

150. Repeated Loading – Longitudinal view CYCLE 100

151. Repeated Loading – Longitudinal view CYCLE 200

152. Repeated Loading – Longitudinal view CYCLE 200

153. Repeated Loading – Longitudinal view CYCLE 200

154. Repeated Loading – Longitudinal view CYCLE 400

155. Repeated Loading – Longitudinal view CYCLE 400

156. Repeated Loading – Longitudinal view CYCLE 400

157. Repeated Loading – Longitudinal view CYCLE 600

158. Repeated Loading – Longitudinal view CYCLE 600

159. Repeated Loading – Longitudinal view CYCLE 600

160. Repeated Loading – Longitudinal view CYCLE 800

161. Repeated Loading – Longitudinal view CYCLE 800

162. Repeated Loading – Longitudinal view CYCLE 800

163. Repeated Loading – Side View CYCLE 0

164. Repeated Loading – Side View CYCLE 0

165. Repeated Loading – Side View CYCLE 0

166. Repeated Loading – Side View CYCLE 20

167. Repeated Loading – Side View CYCLE 20

168. Repeated Loading – Side View CYCLE 20

169. Repeated Loading – Side View CYCLE 40

170. Repeated Loading – Side View CYCLE 40

171. Repeated Loading – Side View CYCLE 40

172. Repeated Loading – Side View CYCLE 60

173. Repeated Loading – Side View CYCLE 60

174. Repeated Loading – Side View CYCLE 60

175. Repeated Loading – Side View CYCLE 80

176. Repeated Loading – Side View CYCLE 80

177. Repeated Loading – Side View CYCLE 80

178. Repeated Loading – Side View CYCLE 100

179. Repeated Loading – Side View CYCLE 100

180. Repeated Loading – Side View CYCLE 100

181. Repeated Loading – Side View CYCLE 200

182. Repeated Loading – Side View CYCLE 200

183. Repeated Loading – Side View CYCLE 200

184. Repeated Loading – Side View CYCLE 400

185. Repeated Loading – Side View CYCLE 400

186. Repeated Loading – Side View CYCLE 400

187. Repeated Loading – Side View CYCLE 600

188. Repeated Loading – Side View CYCLE 600

189. Repeated Loading – Side View CYCLE 600

190. Repeated Loading – Side View CYCLE 800

191. Repeated Loading – Side View CYCLE 800

192. Repeated Loading – Side View CYCLE 800

193. Simulation Results and Analysis - Permanent Settlement of Ballast with Aggregate Shape Library 1 (Cubical – Angular) at three Different Loading Frequencies Library 1 Rutting Trend Line

194. Critical Loading Frequency (?) for maximum rutting f = 1 - 5 Hz Library 1 Aggregate 120 kN Load Simulation Results and Analysis - Permanent Deformation Produced by the Static Load and the Same Magnitude Dynamic Loads Applied at Different Frequencies

195. Simulation Results and Analysis - Comparisons of Ballast Settlement between Aggregate Shape Library 1 (Cubical – Angular) and Shape Library 8 (Elongated – Rounded) at Three Loading Frequencies Library 8 Rutting Trend Line

196. Simulation Results and Analysis - Comparisons of Ballast Settlement between Aggregate Shape Library 1 (Cubical – Angular) and Shape Library 3 (Cubical – Rounded) at Three Loading Frequencies Library 3 Rutting Trend Line

197. Simulation Results and Analysis Only one tie is simulated in the train moving direction, the interactions between ties are not considered in the DEM simulations and the ballast aggregate movement along the traffic direction is limited by the transverse plane 20000 25000 30000 35000 40000 45000 020406080100120 Loading Cycle Library 3 Library 1 Residual Force on Transverse Vertical Plane (The Middle Plane between Two Ties) (N) More rounded Library 3 has higher lateral confinement to reduce permanent deformation tendency Transverse Vertical Plane 0.61 m

198. Conclusions Aggregate angularity was found to have significant impact on strength of aggregate assembly. Aggregate surface texture, defined as the friction between two particles in contact, was quantified from direct shear box DEM simulations to have even more pronounced impact on the strength of the assembly when compared to aggregate angularity. Reducing the train speed, such as in the slow orders, (or decreasing the applied loading frequency by increasing the load pulse durations) often results in a significant increase in the rut accumulation. However, static loading induced smaller permanent deformations than the 1-Hz loading. Therefore, a critical loading frequency to give maximum rutting was found to be between 1 and 5 Hz loadings. Effects of ballast aggregate shape was also found to influence ballast settlement. The DEM simulations that considered single tie tests resulted in lower ballast settlements for rounded aggregate particles possible due to lesser tendency to shakedown and consolidate. For future ballast settlement simulations, it will be worthwhile to consider a modified ballast box for the half tie and half ballast width railroad track geometry with at least three ties included to model longitudinal confinement and movement of ballast aggregate.

199. Future Work Fouling study by combining Image Aided DEM Simulation with Large Direct Shear Box Tests. Field Validation of Image Aided DEM Approach in TTCI “FAST” Track.

200. The Authors would like to thank the Association of American Railroad for their financial support of this research study through the AAR Affiliated Research Laboratory established at the University of Illinois at Urbana-Champaign The Authors would like to thank the Association of American Railroad for their financial support of this research study through the AAR Affiliated Research Laboratory established at the University of Illinois at Urbana-Champaign Acknowledgement Association of American Railroads