Why Dynamic Analysis Is Needed?

Impact of Wide-Base Tires on Pavement and Trucking Operation: Advanced Analysis Imad L. Al-Qadi Founder Professor of Engineering Illinois Center for Transportation Why Dynamic Analysis Is Needed? Quasi-static analysis: Does not consider mass inertia and damping forces Dynamic analysis: Considers mass inertia and damping forces Pavement responses are loading-time dependent Focus Point Primary objective of this part of the presentation is to investigate flexible pavement dynamic responses due to moving loads of dual-tire assembly and wide-base tire. 1

Overall Research Approach Instrumentation (Al-Qadi et al., 2-27) Field test (Al-Qadi et al., 2-27) 3-D Finite element modeling Study Approach 3D Finite Element Modeling Analysis Considerations Material Constitutive Models Loading Amplitude Surface Tangential Stresses Layer Interface Condition Implicit Dynamic Analysis Model Calibration Validation of FE Models (w/ Field Measurements) Pavement Response Analysis Smart Road Pavement Design A B C D E F G H I J K L SM-12.5D SM-9.5D SM-9.5E SM-9.5A SM-9.5D SM-9.5D SM-9.5D SM-9.5D SM-9.5A* SM-9.5D OGFC (19mm) SMA-12.5 (38mm) (38mm) (38mm) (38mm) (38mm) (38mm) (38mm) (38mm) (38mm) (38mm) SM-9.5D (38mm) (19mm) CRCP BM-25. BM-25. BM-25. Concrete (25mm) BM-25. BM-25. BM-25. BM-25. BM-25. (1mm) (1mm) (1mm) BM-25. (15mm) (15mm) (15mm) (15mm) BM-25. (15mm) BM-25. (15mm) (225mm) SM-9.5A SM-9.5A SM-9.5A (225mm) BM-25. (5mm) (5mm) (5mm) (225mm) Cement OGDL OGDL OGDL OGDL 21A 21A OGDL OGDL OGDL Cement Cement Cement 21A Cement Stabilized Stabilized OGDL OGDL OGDL OGDL Cement (15mm) (15mm) 21A 21A 21A 21A Stabilized 21A 21A 21A Cement Cement Cement Cement (15mm) Cement Cement Cement Stabilized Stabilized Stabilized Stabilized Stabilized Stabilized Stabilized (15mm) (15mm) (15mm) (15mm) 21B 21B (15mm) (15mm) 21B 21B (15mm) 21A Cement 21B (15mm) (15mm) (15mm) (15mm) Stabilized (15mm) 21B 21B 21B 21B 21B 21B 21B 21B (175mm) (175mm) (175mm) (175mm) Modeled Section 2

3 in (76mm) 12 in (35 mm) Pavement Designs CASE 1 CASE 2 6in (152 mm) Aggregate Base 12 in (35 mm) Aggregate Base 12 in (35 mm) CASE 3 Subgrade 12 in Aggregate Base Subgrade (35 mm) 3 in (762 mm) 3 in (762 mm) Subgrade Infinite Foundation Infinite Foundation 3 in (762 mm) Infinite Foundation 11.4 Importance of Tire Dimension (mm) 14.6 14.6 14.6 14.6 11.4 11.4 11.4 Radial-ply truck tire 122.1 33.8 29.9 32.4 29.9 33.8 333.9 33.8 29.9 32.4 29.9 33.8 9.6 9.6 1.3 11.4 11.4 1.3 9.6 9.6 Center to Center Space Code: 455/55R22.5 Tire width, mm/ Tire aspect ratio, %/ Radial ply, R/ Rim-diameter, in 38.4 3.8 3.8 31.5 35.1 31.6 3.8 3.8 38.4 Surface Contact Stresses Compressive Stresses Transverse Stresses Longitudinal Stresses Entrance Aspect of Tire Imprint Rib 1 Rib 2 Rib 3 Rib 4 Rib 5 Exit Aspect of Tire Imprint 3

Nonuniform Stresses of Each Rib Ribs 1 and 5 (Outer ribs): Shorter contact length and smaller contact stress Ribs 2, 3, and 4 (Inner ribs): Longer contact length and higher contact stress Entrance Imprint Exit Imprint Entrance Imprint Exit Imprint Transverse Strain (µ) 2 Slow Recovery: Transverse Strain -2.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6-4 -6-8 -1-12 -14-16 -18 Time (sec) Field Responses Residual strain condition: 5 mph and 34 ºC Greater residual strain in transverse direction Smaller residual strain Longitudinal Strain (µ) 8 Fast Recovery: Longitudinal Strain 6 4 2.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6-2 11-4 Time (sec) Hot-Mix Asphalt Linear Viscoelasticity Creep Compliance from Lab sin(nπ) E(t)D(t) = D(t) = D + D (1 e t/τ ),i = 1, 9 nπ i Log(time), E(t), K(t), and G(t) Curve Fitting Finding Prony Series Coefficients Bulk and Shear Moduli ABAQUS 4

Moving Load Simulation Traditional method Triangular, trapezoidal, rectangular amplitude Impulsive loading (hammering) All the tire imprint elements have same loading history Continuous loading: Newly developed method Loading amplitudes are linearly varied by time within entrance and exit parts of tire imprint. 3D FE Model Pavement Design In-Plane Dimension (mm) Infinite Domain 3D FE Model: Convergence Determination of element thickness: Convergence Vertical Stress (kpa) 8 6 Bisar 4 Finite Element 2 5% -5% 38.1 19.5 9.5 4.76 2.38 Element Thickness (mm) Interface Sensitivity: Stress-jump Vertical Strain (µ) 6 4 2 Bisar Finite Element 5% -5% 38.1 19.5 9.5 4.76 2.38 Element Thickness (mm) Case ID Element Thickness (mm) Model Size (*DOF) Number of Elements Data Storage (Gbytes) *Computation Time (sec) Jump at WS BM Interface (kpa) A 38.1 172,476 42,916 2.35 3145 93.2 B 19.5 212,226 55,656 3.9 4871 52.2 C 9.5 291,726 81,136 4.19 6599 25.6 D 4.76 45,726 132,96 7.26 18565 9.9 E 2.38 76,776 231,468 12.91 3551 6.97 (DOF: Degree of freedom-number of equation) 5

Boundary Effect Check for Dynamic Analysis Location of infinite element: No stress-wave reflection At least six times of tire loading radius in both directions Roller Roller Roller Roller 3D Dynamic Analysis: Transient Moving Loads Simulation Example: Moving dual-tire assembly loading Field Response vs. Calculation Bottom of the wearing surface (38.1mm) Longitudinal Strain (µ) 15 15 6 15-3.1.2-75 Measured Calculated Time (sec) Longitudinal Strain (µ) Bottom of the (188 mm) 1 Measured 8 Calculated 6 4 2-2.1.2.3-4 Time (sec) 6

Flexible Pavement Responses and Damage Potentials Depth (mm) Strain (µ) -3-2 -1 1 2 3 2 4 Thickness Dependency (Vertical distribution) Transverse Strain-76 mm 6 Transverse Strain-152 mm Transverse Strain-35 mm 8 Strain (µ) -3-2 -1 1 2 3 E32 E33 E31 E21 Depth (mm) 2 4 E11 E12 E13 E23 E22 Longitudinal Strain-76 6mm Longitudinal Strain-152 mm Longitudinal Strain-35 mm 8 Surface Tensile Strain (µ) Surface Tangential Stress Effect at Surface Dual-tire Wide-base Without Tangential Stresses 3 2 1 E33 5 51 52 53 54 55-1 E31 E32-2 E21 E12-3 E22 Transverse Distribution E23 E11 E13 3 Dual-tire Wide-base With Tangential Stresses Surface Tensile Strain (µ) 2 1-1 5 51 52 53 54 55-2 -3 Transverse Distribution 7

76 mm Vertical Shear Strain Occurs below Surface 152 mm E33 E32 E12 E11 E13 E31 E21 E22 E23 35 mm Flexible Pavement Responses and Damage Potentials Dual-Tire vs. Wide-base Tire Vertical Contact Stress (kpa) Vertical Contact Stress (kpa) 12 1 8 6 4 2 12 1 8 6 4 2 Dual-tire Wide-base Tire Dual-tire Wide-base Tire 35.5 kn 45.5 kn Equivalent Surface Contact Stresses Dual-tire Wide-base Tire Vertical Contact Stress (kpa) 12 1 8 6 4 2 Dual-tire Wide-base Tire Edge Middle Right Edge Left 53.4 kn S11 S32 S12 S13 S33 S31 S21 S23 S22 8

Transverse Strain (µ) Transverse Strain (µ) 2 16 12 8 4 2 16 12 8 4 Dual-tire assembly Wide-base tire Dual-tire assembly Wide-base tire 35.5 kn 45.5 kn Transverse Strain at the bottom of 25 ºC (188 mm) Dual-tire Wide-base Tire Transverse Strain (µ) 2 16 12 8 4 Dual-tire assembly Wide-base tire 53.4 kn E11 E32 E12 E33 E13 E31 E21 E23 E22 Longitudinal Strain (µ) Longitudinal Strain (µ) 2 16 12 8 4 2 16 12 8 4 Dual-tire assembly Wide-base tire Dual-tire assembly Wide-base tire 35.5 kn 45.5 kn Longitudinal Strain at the bottom of 25 ºC (188 mm) Dual-tire < Widebase Tire 2 Dual-tire assembly Wide-base tire E33 Longitudinal Strain (µ) 16 12 8 4 53.4 kn E11 E32 E12 E13 E31 E21 E23 E22 Vertical Shear Strain (µ) Vertical Shear Strain (µ) Vertical Shear Strain (µ) 8 6 4 2 2 16 12 8 4 16 12 8 4 Dual-tire Wide-base Tire 35.5 kn 45.5 kn 53.4 kn Dual-tire Wide-base Tire 35.5 kn 45.5 kn 53.4 kn Dual-tire Wide-base Tire 35.5 kn 45.5 kn 53.4 kn 5 ºC 25 ºC 4 ºC Vertical Shear Strain Dual-tire > Wide-base Tire E32 E12 E11 E13 E33 E31 E21 E23 E22 9

3 2 4Outside Rib 3 2 1 2 1 1 Strain Strain (µ) (µ) Strain Distribution with Depth Critical strain within (One Tire of a Dual-Tire Assembly Loading) Strains from 4.75mm to bottom of 114mm Inside Rib 3 6 9 12 15-1 3 3 6 6 9 12 15-1 -2 114mm-Shear Strain 76mm-Shear Strain -2 38mm-Shear Strain -2 76mm-Transverse 114mm-Transverse Tensile Strain -3 4.75 mm-shear Strain 38mm-Transverse Tensile Strain 4.75 mm-transverse Tensile Strain 76mm-Longitudinal 114mm-Longitudinal Tensile Strain 4.75 mm-longitudinal Tensile Strain38mm-Longitudinal Tensile Strain -3-4 Transverse Rib Position Rib Position Strain Distribution Strains at the bottom of 15mm : Dual-tire 25 Outside Rib 2 Inside Rib 15 Strain (µ) 1 5 3 6 9 12 15-5 15mm-Shear Strain -1 15mm-Transverse Tensile Strain 15mm-Longitudinal Tensile Strain -15 25 Rib Position 2 Strains at the bottom of 15mm : Wide-base 15 Strain (µ) 1 5 3 6 9 12 15 18 21 24 27-5 15mm-Shear Strain -1 15mm-Lateral Tensile Strain 15mm-Longitudinal Tensile Strain -15 Rib Positions Vertical Shear Strain Distribution with Depth Four critical straining points Two critical straining points Depth (mm) Transverse Vertical Shear Strain (µ) -4-2 2 4 2 4 6 8 1 Left Edge Inner Edge Depth (mm) Transverse Vertical Shear Strain (µ) -4-2 2 4 2 4 6 8 Left Edge 1 Right Edge 1

Fatigue Damage Potential DR: Damage Ratio= Allowable Load Repetitions due to Dual-tire/ due to Wide-base tire Wheel Load (kn) Dual-Tire Assembly *Shear Strain N FC Wide-Base Tire Shear Strain N FC DR FC 5 ºC 35.5 44.27 1.4E+8 35.74 2.3E+8.49 45.5 44.43 9.917E+7 39.98 1.43E+8.71 53.4 53.56 5.361E+7 5.54 6.489E+7.83 Wheel Load (kn) Dual-Tire Assembly *Shear Strain N FC Wide-Base Tire Shear Strain N FC DR FC 25 ºC 35.5 244.19 7.33E+5 194. 1.5E+6.47 45.5 276.12 4.694E+5 247.77 6.74E+5.7 53.4 366.7 1.845E+5 353.48 2.82E+5.89 Wheel Load (kn) Dual-Tire Assembly *Shear Strain N FC Wide-Base Tire Shear Strain N FC DR FC 4 ºC 35.5 2351.21 8.57E+2 195. 1.491E+3.54 45.5 2527.79 6.348E+2 2267.2 9.84E+2.7 53.4 3275.33 2.76E+2 327.64 2.719E+2 1. Rutting Potential Wheel Load (kn) Dual-Tire Assembly *Comp. Strain N PR Wide-Base Tire Comp. Strain N PR DR PR 5 ºC 35.5-99.28 1.3E+9-94.87 1.4E+9.92 45.5-99.3 1.3E+9-95.3 1.39E+9.93 53.4-99.62 1.29E+9-95.7 1.38E+9.93 Wheel Load (kn) 35.5 Dual-Tire Assembly *Comp. Strain N PR -789.62 1.2E+5 Wide-Base Tire Comp. Strain N PR -827.44 1.11E+5 DR PR 1.8 25 ºC 45.5-855.27 1.5E+5-875.65 1.E+5 1.4 53.4-95.97 9.46E+4-958.63 8.58E+4 1.1 Wheel Load (kn) Dual-Tire Assembly *Comp. Strain N PR Wide-Base Tire Comp. Strain N PR DR PR 4 ºC 35.5-1945.1 2.36E+2-11237.3 2.26E+2 1.5 45.5-11383.25 2.21E+2-11591.1 2.14E+2 1.3 53.4-11689.7 2.11E+2-12225.3 1.95E+2 1.8 Summary 3D FE Model Surface contact stresses were incorporated into the developed 3D FE model (along w/continuous moving load and viscoelastic characteristics). Pavement Actually Subjected to a Moving Wheel Load Continuous loading amplitude Simulation of moving wheel load Surface Tangential Stress Effect Significant variance in strains at shallow depth The effect diminishes as the depth increases 11

Conclusions Flexible pavement responses are affected by pavement designs,, tire characteristics, applied load, temperature, and vehicle speed. Critical shear strains within depth are significantly higher than the tensile strain at the bottom of. Tangential surface stresses may affect the prediction of top-down cracking, primary rutting, and occasionally fatigue damage. Future Researches Brake-Maneuvering Effect: Effect of High Inertia Force on Pavement Responses Effect of High Frictional Force on Pavement Response Differential Tire Pressure Distribution: Feasibility Study on Asymmetry Tire Pressure Effect on Pavement Responses Development of Real Tire Model: Two Solid (Tire and Pavement) Model Deformable + Solid Illinois Pool-Fund Study 12

Main Research Tasks Task 1 State-of-Art Literature Survey Task 2: Pavement Test Sections and Instrumentation Task 3: Accelerated Load Testing Task 4: Three-Dimensional Tire-Pavement Contact Stress Measurement Task 5: Material Laboratory Characterization Task 6: Pavement Response Prediction Using Finite Element Model Task 7: Quantification of Pavement Damage due to Various Vehicle-Tire Factors Thank You 13