MATERIAL MODELS FOR CRUMB RUBBER AND TDA. California State University, Chico

Transcription

1 MATERIAL MODELS FOR CRUMB RUBBER AND TDA California State University, Chico

2 Waste Tire Products for CE Applications Whole Tires Tire Shreds (TDA) Crumb Rubber/Tire Buffings

3 Whole Tires

4 TIRE DERIVED AGGREGATE (TDA) Definition: Pieces of shredded tires that are generally between 25mm (1 in.) and 300mm (12 in.) in largest dimension. Small Shred Size Large Shred Size

5 Crumb Rubber Sample

6 Rubber Tire Buffings

7 Side by Side Comparison

8 CIVIL ENGINEERING APPLICATIONS: Whole Tires Crash Barriers Retaining walls Fences Culverts Others?

9 CIVIL ENGINEERING APPLICATIONS: Tire Derived Aggregate (TDA) Subgrade and Embankment Fill Backfill for Wall and Bridge Abutments Subgrade Insulation for Roads Lateral Edge Drains Vibration Damping Layer Beneath Rail Lines Landfill Daily Cover and Drainage Septic System Drain Fields

10 CIVIL ENGINEERING APPLICATIONS: Crumb Rubber/Tire Buffings Rubberized Asphalt Concrete Rubberized Portland Cement Concrete Running Tracks Others?

11 Engineering Properties of TDA (After Humphrey, 2003) 1. Gradation 2. Specific Gravity and Absorption Capacity 3. Compressibility 4. Resilient Modulus 5. Time Dependent Settlement of TDA Fills 6. Lateral Earth Pressure Characteristics 7. Shear Strength 8. Hydraulic Conductivity (Permeability) 9. Thermal Conductivity

12 Mechanics of Materials Background Continuum Mechanics Uniform distribution of matter No voids Cohesive (all portions are connected together, and have no breaks, cracks, or separations) Crumb Rubber and TDA Discrete material Contains air voids Cohesionless Similar properties to sands and gravels

13 Continuum Mechanics Deformable bodies develop both Normal (tension and compression) and Shear Stresses when acted on by applied loads Brittle materials fail in tension perpendicular to the maximum tensile stress Ductile materials fail in shear parallel to the maximum shear stress Poisson s s ratio relates the transverse contraction to the longitudinal elongation (or vice versa) 0.25< μ < 0.34 for most CE materials

14 TDA STRENGTH TDA can support compressive but not tensile stresses and typically fails in shear The Shear Strength of TDA is affected by five factors: 1. Size and shape of the tire shreds The density (packing) of the sample at the beginning of the test 3. Magnitude of the compressive normal loading 4. The orientation of the tire shreds in the specimen 5. Cohesion 5.

15 Material Model: Elastoplastic Unload and Load along same path

16 More General Material Model Nonlinear Inelastic Model

17 More Realistic General Model Energy is lost in unloading and reloading process (hysteresis( hysteresis) σ Energy Dissipated = Heat ε

18 Closer Look at Elasticity Linear Elastic Behavior- makes things easy True up to Elastic Limit σ ε

19 Non-Linear Elastic (Rubber) Nonlinear load path Still loads and unloads along same path σ ε

20 Anelastic Behavior Does not load and unload along the same path σ Thermal energy- Dissipates to the surroundings without damaging material Useful for vibration damping Examples Mounts for motors and other rotating machinery Subbase under railroads (TDA application) Just think about applications for earthquakes if we could get concrete to behave this way by adding waste tire rubber ε

21 Poisson Effect After Yielding, values of engineering and true stress deviate appreciably σ Eng. stress (compression) True stress Eng. stress (tension) ε

22 Possible Material Models Hookean Linear Elastic σ x Hookean Material, σ x =Eε x E = Spring Constant Hencky Material Hencky Material Nonlinear Spring In either case, energy is conserved if Loading and Unloading curves coincide ε x

23 Viscous Materials Named viscous because of fluid-like like behavior Material is viscous if stress determines strain rate i.e. strain rate is a function of stress. dε/dtdt = ε x = g(σ x ) Strain is not recovered upon removal of stress

24 Viscous Materials If stress is a linear function of the strain rate, then we call it a Newtonian fluid. Use linear dashpot to model behavior: σ x η=damping constant Newtonian η = Damping constant. σ x =ηε x Ideal Viscous (Newtonian). ε x In this model, we consider σ x to be the force on the system. while ε x is the speed of the piston. Therefore η = Damping constant

25 When Force and Speed are Not Linearly Related We have a Non-Newtonian Newtonian or Quasi-Viscous case. Also referred to as a Stoke s Material σ x Stokes Quasi-viscous (Stokes). ε x

26 Viscoelastic Materials Materials that posses viscous and elastic properties Many materials are viscoelastic Examples: Structural Metals and Rock at high temperatures Plastics at room temperature Use combinations of springs and dashpots to model viscoelastic materials

27 Linear Maxwell Model E η Linear spring and dashpot in series, therefore F spring =F dashpot Strain rate composed of two parts 1. Strain rate in spring, ε x =σ x /E 2. Strain rate in dashpot, ε x =σ x /η Add them using superposition to get total strain rate of system.. ε x =σ x /E + σ x /η...

28 Graphical Linear Maxwell Model Constant Stress Constant stress gives a nearly instantaneous spring displacement plus a constant strain-rate rate from the dashpot ε E σ x = σ x = Constant o η t (time)

29 Kelvin Model E η Spring and dashpot are in parallel Strains are equal, but forces are not Stress components: σ spring = Eε x. σ dashpot = ηε x Therefore, by superposition. σ total = Eε x + ηε x

30 Kelvin Relaxation When the spring relaxes, energy is dissipated in the dashpot

31 More General Model (Burgers Fluid) Combine Maxwell and E 1 Kelvin model in Series Some permanent η 1 deformation Some perfect elasticity E 2 η 2 Some vibration damping Many additional spring- dashpot combinations possible

32 General Model Behavior σ Energy Dissipated = Heat ε

33 General Model- Kelvin Model in Series with Nonlinear Dashpot σ ε

34 Potential Applications Energy Dissipation Earthquake Energy Absorption Vibration Mitigation Machinery Mounts Train and Truck Traffic Loads

35 Vibration Mitigation Application- Vasona Light Rail Line and Test Track TDA used as subbase beneath train track ballast Goal: Reduce vibration for local residence and businesses

36 Case History VTA Light Rail Project Reduce ground borne vibrations that affect adjacent businesses and residences 12 of Type A Tire Shreds below 12 of subballast and 12 of ballast for 1591 feet of track Tests indicated a significant reduction in vibration with TDA section

37 Test Track Cross-Section

38 TDA Test Track Construction

39 Test Track Construction

40 Finished Test Track

41 Vibration Sensor Mounted Under Ground

42 Measuring Devices Strain gages to measure strains in rail Dial gage to measure deflections

43 Rail Line Cross Section Drawing

44 Rail Line Construction Pictures

45 Results - Vibration

46 Tie Deflections Elastic Deflections in ties less than 0.2 in. Which is acceptable Minor permanent deflection may mean more frequent releveling of the ties.

47 Cost Savings Cost of conventional track = $100 per track-ft Cost of track with TDA vibration mitigation = $121 per track-ft Cost of floating slab vibration mitigation = $ per track-ft Cost savings = $479-$879 $879 per track-ft Total savings = $1 to $2-million

48 Summary Presented practical material models applicable to TDA for vibration mitigation TDA can save money in these applications More data and studies are needed to calibrate these material models

49 THANK YOU Questions?

50 References Elastic and Inelastic Stress Analysis,, Irving H. Shames, Francis A. Cozzarelli.. Prentice Hall, Englewood Cliffs, New Jersey Civil Engineering Applications Using Tire Derived Aggregate.. Presented by Dr. Dana Humpherey.. Sponsored by: California Integrated Waste Management Board E Wall System at Kembla Grange: leid=3069