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CE 563 Airport Design

  A  model  that  defines  the  response  of  the  pavement  to  loading  in  terms  of  stresses,  strains,  and  deflections  

P  

L/2   L/2  

δmax

EIPL48

3max =δ

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  Differ  in:    Capabilities    Complexity   Material  input  requirements    Underlying  assumptions  

  Provide  σ,  ε,  δ  anywhere  and  in  any  direction  in  the  pavement  structure  

  Handle  dynamic  loading    HMA  modeled  as  visco-­‐elastic    Base  and  subgrade  modeled  as  non-­‐linear  inelastic    Consider  temperature  stresses  

  Multi-­‐layer  elastic  theory    Finite  element  methods    Visco-­‐elastic  theory    Dynamic  analysis    Thermal  models  

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  Complexity  of  model    Material  property  input  requirements    Computational  time    Relative  accuracy  

  Flexible  pavements    Fatigue  cracking    Rutting    Thermal  cracking    Others  

Base Course HMA

Subgrade

Compression

Tension

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  Cracking  in  HMA    Horizontal  tensile  strain  at  the  bottom  of  the  HMA  

  Base  material  will  not  take  tension    Limit  tensile  strain  in  HMA  

Base  Course  

HMA  

Subgrade  

σc

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  Pavement  behavior  under  wheel  loads  is  characterized  by  considering  it  to  be  a  homogeneous  half-­‐space  subjected  to  a  circular  load  of  radius  “a”  and  uniform  pressure  “p”  

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  Homogeneous  Material  Properties    Finite  Layer  Thickness    Layers  Infinite  in  Lateral  Directions    Isotropic  Layers    Full  Friction  Between  Layers    No  Surface  Shearing  Forces    Solutions  Characterized  by  E,  µ

Stress-­‐strain  relationship   Strain  time  dependency  

Strain  recovery  

  Curling    Temperature  Differences  

  Friction    Volume  Changes  

  Wheel  Loads    Loss  of  Support  

  Pumping  

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k  =  Modulus  of  Subgrade  Reaction  

Assumes:  Plate  in  Contact  w/  Subgrade  

  Slab

  Slab and Subgrade ( )2

3

112EhD

µ−=

( )25.0

2

3

k112Eh

⎥⎦

⎤⎢⎣

⎡µ−

=

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  Warping  Increase  w/  Increased  k    High  k,  Subgrade  does  not  yield  

  Low  k,  Subgrade  Conforms  

  Friction  between  the  slab  and  the  subgrade  causes  tensile  stresses  in  the  slab  

  The  subgrade  attempts  to  restrain  the  slab  as  it  expands  and  contracts  

  Tensile  stress  is  maximum  at  slab  center  

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  Also  puts  stress  on  dowel  bars  at  joints  and  reduces  load  transfer  at  joints  that  rely  on  aggregate  interlock  for  load  transfer  

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σc  =  γcLfa  

2  

γc  ≡  Unit  Weight  of  Concrete    

fa  ≡  Average  Coefficient  of  Friction  

L  ≡  Slab  Length    

σc  ≡  Stress  in  Concrete    

  3  Cases  (Single  Wheel  Loads)    Corner  Loading    Interior  Loading    Edge  Loading  

  Depends  on:    Gross  load    Tire  pressures   Multiple  wheel  spacing    Loading  position  (corner,  etc.)    Efficiency  of  subgrade  support