Lesson 2-1 Structural Responses in Flexible Pavements

7/28/2019 Lesson 2-1 Structural Responses in Flexible Pavements

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Lesson 2Structural Responses in Flexible

Pavements

ECE 5813

Nishantha Bandara


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Outline

What is stress and strain? Stress and strain in flexible pavements

KENPAVE software


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Stress

Force per unit area

Units: MPa, psi, ksi

Types: bearing, shearing, axial

P

ALoad

Area=


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Strain

Ratio of deformation caused by load to theoriginal length of material

Units: Dimensionless

Change in Length

Original Length LL=


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Stiffness

Stiffness = stress/strain =

For elastic

materials: Modulus of Elasticity

Elastic Modulus

Youngs ModulusStress,

Strain,

E

1


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Stress vs. Strain of a Material inCompression


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Poissons Ratio


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Typical Modulus (E) Values

Material E (psi)

Rubber 1,000

Wood 1,000 2,000,000

Aluminum 10,000,000

Steel 30,000,000Diamond 170,000,000


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Material Range (ksi) Typical (ksi)

PCC 3,000 - 8,000 4,000

HMA 200 - 800 450

ATB 70 - 450 150

Granular soil 7 - 22 15

Fine-grained soil 3 - 10 4

Granular base 14 - 50 30

CTB 500 - 1,000 700

Lean concrete 1,000 - 3,000 1,500

Typical Modulus Values


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Typical E Values AsphaltConcrete

Material E (psi)

Asphalt concrete (32F) 2,000,000Asphalt concrete (70F) 500,000

Asphalt concrete (120F) 20,000


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Material Range Typical

PCC 0.10 - 0.20 0.15

HMA / ATB 0.15 - 0.45 0.35Cement Stab. 0.15 - 0.30 0.20

Base

Granular 0.30 - 0.40 0.35Base / Subbase

Subgrade Soil 0.30 - 0.50 0.40

Typical Poissons Ratios


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Deflection ()

Change in length Deformation

Units: mm, mils (0.001 in)


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Structural Response Models

Different analysis methods for AC and PCC

Layered system behavior

All layers carry part of load

Subgrade

PCC Slab

Slab action predominates

Slab carries most load

Subgrade

AC

Base


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Flexible Pavement Model


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Layered Elastic Systems

The basic assumptions: Each layer is homogeneous, isotropic, and

linearly elastic with an elastic modulus and The material is weightless

Each layer has a finite thickness, except thelowest layer

A uniform pressure is applied over a circulararea

Interface condition (continuity vs frictionless)


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Pavement Response Locations

Used in Evaluating Load Effects


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Stresses and Strains in Flexible

Pavements

Function of the following: Material properties of each layer

Thickness of each layer

Loading conditions Pavement responses generally of interest:

Surface deflection

Horizontal tensile strains at bottom of AC layer Vertical compressive strain on top of

intermediate layer (base or subbase)

Vertical compressive strain on top of thesubgrade


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One-Layer System (Boussinesq)

The original elastic theory published byBoussinesq in 1885

For computing stresses and deflections in

a half-space (soil) composed ofhomogeneous, isotropic, and linearly

elastic material

Still widely used in soil mechanics andfoundation design


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One-Layer System


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Solutions at Axis of Symmetry-

Stresses

5.122

31

za

zqz

trrz ,0

5.122

3

5.022

1221

2 za

z

za

zqr


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Strains

5.122

3

5.022

2211

za

z

za

zE

qz

5.122

3

5.022

1221

2

1

za

z

za

z

E

qr


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Deflections

zzaaza

a

E

qa

w

5.022

5.022

211

5.0222

2

3

zaE

qaw

When =0.5 the above can be simplified to

At the surface of the half-space E

qaw2

12


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Example 1:Given

Load P=9000 lbs

Pressure q=80 psi

E=5,000 psi,

=0.3

Find vertical stress z at z=6 and r=0


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Example 2.2 (page 51)

Determine the stresses, strains and deflections at point A.


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Two-Layer System (Burmister)

Burmister extended the one-layersolutions to two and three layers in 1943

Assumed layers have full frictional contact

at the interface and =0.5 Equation and graphs are used to compute

deflection


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Two-Layer System

Vertical stress influence coefficient z/p, for a=h


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Vertical Stress

Vertical stress on the top of the subgrade

is an important factor in pavement design To combine stress and strength, vertical

compressive strain used as a design

criterion Figure 2.14 Burmister

Figure 2.15 Huang

Example 2.5


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Vertical Deflections

Used as design criterions

Vertical Surface Deflections Figure 2.17

Example 2.6

Vertical Interface Deflections

Figure 2.19

Example 2.7

22

0

5.1F

E

qaw

FE

qaw

2


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Critical Tensile Strain

Asphalt fatigue cracking design criterion

Tensile strain at the bottom of asphaltlayer

Single wheel use Figure 2.21

Dual Wheels use Figures 2.23 and 2.21

Dual Tandem Wheels use Figures 2.25 or2.26 or 2.27 and 2.21

eFE

ae

1


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Multi-Layer System


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Multi-Layer System

Computer programs

KENLAYER

ELSYM5

LEAP2

EVERSTRS

Typical input

Material properties: modulus and Layer thickness

Loading conditions: magnitude of load, radius, orcontact pressure


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Viscoelastic Solutions HMA is a visco-elastic material (behavior

depends on the time of loading)

Two methods to characterize 1. Mechanical

2. Creep-compliance

Mechanical (Elastic., viscous, Maxwell, Kelvin,mBurgers, Generalized) stress-strain

relationships can be physically visualized

Creep-Compliance Creep-compliance curve canbe easily obtained by a laboratory creep test

Example 2.13

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Lesson 2-1 Structural Responses in Flexible Pavements