Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
2/28/14
1
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
2/28/14
2
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
2/28/14
3
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
2/28/14
4
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
2/28/14
5
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”
2/28/14
6
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
2/28/14
7
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−
=
2/28/14
8
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
2/28/14
9
Also puts stress on dowel bars at joints and reduces load transfer at joints that rely on aggregate interlock for load transfer
2/28/14
10
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