Stresses Inflexible Pavements

8/2/2019 Stresses Inflexible Pavements

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Stresses in FlexiblePavement Systems


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Multi-layered Elastic Theory

Pavement behavior under wheelloads is characterized by consideringit to be a homogeneous half-space

subjected to a circular load of radiusa and uniform pressure p


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Multi-layered Elastic System


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Assumptions

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,


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Assumptions

Most Not Valid Reasonable for Small Strains


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Stresses

Normal Stresses (Perpendicular)z, t, r

Shear Stresses (Parallel)rt = trzt = tzrz = zr


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Strains


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One Layer System

Boussinesq EquationsStress, Strains, Deflections

AssumesHomogeneous

IsotropicElastic Media

Point Load at Surface


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Vertical Stress Distribution

c

r

z


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Boussinesqs Formula

Note: z is not a functionof E (materials stiffness)


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One Layer Theory

Need Theory for Circular LoadFoster & Ahlvin

Charts, pp. 49-51 = 0.5

Waterway Experiment Station Equations & Tables


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One Layer Elastic Equations


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Example

Givena = 5 inches

z = 10 inchesr = 20 inches

FindRadii for Functions A and B


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Example

z/a = 10/5 = 2 r/a = 20/5 = 4


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Example

A = 0.01160 B = -0.00401


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Example

GivenLoad = 9000 lbs.

Tire Inflation = 80 psiE = 10,000 psi

= 0.4 Find

z1

, z2

,

z1,z2

1

2

r1 = 0

r2 = 6 in.

z2 = 6 in.

z1 = 0


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Burmister Influence Curves


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Available Solutions

Vertical DeflectionsRutting

Interface DeflectionsRutting in Layers

Tensile Strain at Bottom of HMA

Fatigue Analysis


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Influence Values


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Example 1

1 Given (Flexible)p = 80 psi

E1 = 500,000 psiE2 = 10,000 psi

a = 6 inches

Find

max

6


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Example 2

1 Given (Flexible)p = 80 psi

E1 = 50,000 psiE2 = 10,000 psi

a = 6 inches

Find

max

6


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Interface Deflections

Deflections at Layer Intersections

s = paE2

F


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Interface Deflections


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Example 3

Givenp = 80 psi

E1 = 500,000 psi

E2 = 10,000 psi

a = 6 inches

max = 0.022 Find HMA Contribution to

max

max 6s


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Tensile Strains

t at Bottom of HMA Controls FatigueCracking For a Single Tire

t

=

p

E1F

e


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Strain Factors


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Example 4

GivenP = 9000 lbs.

p = 67.7 psi

E1 = 150,000 psi

E2

= 15,000 psi

Find

t

t8

Stresses Inflexible Pavements

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