ByByEng. Mohamed Hamdallah El-Eng. Mohamed Hamdallah El-

shaershaer

OutlineIntroduction .

Background on Stress and strain in flexible pavements.

Review of Multi-Layer Computer Program and comparison between them.

Distress analysis for Flexible Pavement.

New Approaches for stresses analysis.

Everstress Software & KENLAYER Program.

Introduction

The first asphalt road was constructed in

the US about 100 years ago in New Jersey.

There are currently about 2.2 million miles

of roadway surfaced by asphalt concrete

Pavements (Huang, 1993).

Flexible pavements are made up of

bituminous and granular Materials .

A typical flexible pavement section can be

idealized as a multi-layered system

Consisting of asphalt layers resting on soil

layers having different material properties

Methods of designing flexible pavements

can be classified into several categories :

Empirical method with or without a soil test,

limiting shear failure, and the mechanistic

empirical method (Huang, 1993).

Currently, the design of flexible pavements

is largely empirical (Helwany et al, 1998;

Huang, 1993). However, mechanistic design

is becoming more prevalent, which requires

the accurate evaluation of stresses and

strains in pavements due to wheel and axle

loads.

Stress

Force per unit area

Units: MPa, psi, ksi

Types: bearing, shearing , axial

PAσ =

LoadArea =

Strain

Ratio of deformation caused by load to the original length of material

Units: Dimensionless

Change in Length

Original Length ε =

∆LL=

StiffnessStiffness = stress/strain =

For elastic materials :

oModulus of

Elasticity

oElastic Modulus

oYoung’s Modulus

Str

ess,

σ

Strain, ε

E

1

σε

Stress vs. Strain of a Material in Compression

Poisson’s Ratio

• Since the mid-1960s, pavement

researchers have been refining

mechanistically based design methods.

• While the mechanics of layered systems

are well developed, there remains much

work to be done in the areas of material

characterization and failure criteria.

• The horizontal strain is used to predict and

control fatigue cracking in the surface layer.

• With respect to asphalt concrete

pavements, the current failure criteria used

are the horizontal tensile strain at the

bottom of the asphalt concrete layer and

the vertical strain at the top of the subgrade

layer .

• While test methods and failure criteria for

predicting fatigue cracking are maturing.

• There has been very little effort placed on

the refinement of the subgrade failure

criteria.

• The development of the current subgrade

failure criteria, which limits the amount of

vertical strain on top of the subgrade, is based

primarily on limited data from the AASHO

Road Test (Dormon and Metcalf 1965).

• Similarly the vertical strain at the top of the

subgrade is used to predict and control

permanent deformation (rutting) of the

pavement structure caused by shear

deformation in the upper subgrade.

In general, there are 3 approaches that

can be used to compute the stresses and

strains in pavement structures:

Layered elastic methods.

Two-dimensional (2D) finite element

modeling.

Three-dimensional (3D) finite element

modeling.

The layered elastic approach :

is the most popular and easily understood procedure. • In this method, the system is divided into an arbitrary number of horizontal layers (Vokas et al. 1985). • The thickness of each individual layer and material properties may vary from one layer to the next.• But in any one layer the material is assumed to be homogeneous and linearly elastic. • Those shortcomings make it difficult to simulate realistic scenarios.

• Although the layered elastic method is

more easily implemented than finite

element methods, it still has severe

limitations: materials must be homogenous

and linearly elastic within each layer, and

the wheel loads applied on the surface must

be axi-symmetric.

• For example, it is very hard to rationally

accommodate material non-linearity and

incorporate spatially varying tire contact

pressures, which can significantly affect the

behavior of the pavement systems (de Beer

et al. 1997; Bensalem et al, 2000).

For 2D finite element analysis :

• plane strain or axis-symmetric conditions are generally assumed.• Compared to the layered elastic method, the practical applications of this method are greater, as it can rigorously handle material anisotropy, material nonlinearity, and a variety of boundary conditions (Zienkiewicz and Taylor, 1988).• Unfortunately, 2D models can not accurately capture non-uniform tire contact pressure and multiple wheel loads.

• To overcome the limitations inherent in 2D

modeling approaches, 3D finite

element models are becoming more

widespread.

•With 3D FE analysis, we can study the

response of flexible pavements under

spatially varying tire pavement contact

pressures.

For 3D finite element analysis :

Deflection (∆)

Change in length.

Deformation.

Units: mm, mils (0.001 in).

∆

Pavement structural analysis includes

three main issues: material

characterization , theoretical model

for structural response, and

environmental conditions.

Background on Stress and strain in flexible pavements :

Three aspects of the material behavior

are typically considered for pavement

analysis (Yoder and Witczak, 1975):

• The relationship between the stress and

strain (linear or nonlinear).

• The time dependency of strain under a

constant load (viscous or non-viscous).

• The degree to which the material can

recover strain after stress removal (elastic

or plastic).

Theoretical response models for the

pavement are typically based on a

continuum mechanics approach.

The model can be a closed-formed

analytical solution or a numerical

approach.

Various theoretical response models have

been developed with different levels of

sophistication from analytical solutions

such as Boussinesq’s equations based on

elasticity to three-dimensional dynamic

finite element models.

Environmental conditions :

• Can have a great impact on pavement

performance.

Two of the most important environmental

factors included in pavement structural

analysis are temperature and moisture

variation.

Frost action, the combination of high

moisture content and low temperature can

lead to both frost heave during freezing

and then loss of subgrade support during

thaw significantly weakening the structural

capacity of the pavement leading to

structural damage and even premature

failures.

In addition, both the diurnal temperature cycle and moisture gradient have been shown experimentally and analytically to cause significant curling and warping stresses in the concrete slab of rigid pavements (NHI, 2002).

This study will focus on the second

issue:

The theoretical model for pavement

analysis. Environmental conditions are

not considered in the pavement model

and the pavement materials are

assumed to be linear elastic.

Flexible and rigid pavements respond to loads in very different ways. Consequently, different theoretical models have been developed for flexible and rigid pavements.

Pavement Response models

Structural Response ModelsDifferent 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

Wheel Load

Hot-mix asphalt

Base

Subbase

Natural soil

Distribution of Wheel Load

Subgrade Soil

Base/Subbase

Surface

ε

δSUR

SUB

SUR

AxleLoad

ε

Pavement Responses Under Load

Response models for flexible pavements

Single Layer Model :

Boussinesq (1885) was the first to examine

the pavement's response to a load.

A series of equations was proposed by

Boussinesq to determine stresses, strains,

and deflections in a homogeneous, isotropic,

linear elastic half space with modulus E and

Poisson’s ration ν subjected to a static point

load P .

As can be seen, the elastic modulus does not influence any of the stresses and the vertical normal stress z σ and shear stresses are independent of the elastic parameters.

Boussinesq's equations were originally developed for a static point load.

Later, Boussinesq's equations were further extended by other researchers for a uniformly distributed load by integration (Newmark, 1947; Sanborn and Yoder, 1967). Although Boussinesq’s equations are seldom used today as the main design theory.

His theory is still considered a useful tool

for pavement analysis and it provides the

basis for several methods that are being

currently used.

Yoder and Witczak (1975) suggested that

Boussinesq theory can be used to estimate

subgrade stresses, strains, and deflections

when the modulus of base and the

subgrade are close.

Pavement surface modulus, the equivalent

“weighted mean modulus” calculated from

the measured surface deflections based on

Boussinesq’s equations, can be used as an

overall indicator of the stiffness of

pavement (Ullidtz, 1998).

One-Layer System

One-Layer System(Cylindrical Coordinates)

Formulas for Calculating Stresses

Burmister’s Two-layer Elastic Models :

Pavement systems typically have a

layered structure with stronger/stiffer

materials on top instead of a homogeneous

mass as assumed in Boussinesq’s theory.

Therefore, a better theory is needed to

analyze the behavior of pavements.

Burmister (1943) was the first to develop solutions to calculate stresses, strains and displacement in two-layered flexible pavement systems (Figure 1.1).

Figure 1.1 Burmister’s Two Layer System (Burmister, 1943)

The basic assumptions for all

Burmister’s models include:

1.The pavement system consists of several

layers; each layer is homogeneous,

isotropic, and linearly elastic with an

elastic modulus and Poisson’s ratio

(Hooke’s law).

2. Each layer has a uniform thickness and

infinite dimensions in all horizontal

directions, resting on a semi-infinite elastic

half-space.

3. Before the application of external loads,

the pavement system is free of stresses

and deformations.

4. All the layers are assumed to be

weightless.

5. The dynamic effects are assumed to be

negligible.

6. Either of the two cases of interface

continuity boundary conditions given

below is satisfied (Fig. 1.2)

fully bonded: at the layer interfaces, the

normal stresses, shear stresses, vertical

displacements, and radial displacements

are assumed to be the same. There is a

discontinuity in the radial stresses r σ since

they must be determined by the respective

elastic moduli of the layers.

frictionless interface: the continuity of

shear stress and radial displacement is

replaced by zero shear stress at each side

of the interface.

Figure 1.2 Boundary and Continuity Conditions for Burmister’s Two Layer System

Burmister derived the stress and displacement equations for two-layer pavement systems from the equations of elasticity for the three-dimensional problem solved by Love (1923) and Timeshenko (1934).

To simplify the problem, Burmister assumed Poisson's ratio to be 0.5.

He found the stresses and deflections were dependent on the ratio of the moduli of subgrade to the pavement (E 2/E 1).

The ratio of the radius of bearing area

to the thickness of the pavement layer (r/h

1). For design application purpose,

equations for surface deflections were also

proposed:

Flexible load bearing:

W = 1. 5 pr/ E2

 * Fw

Rigid load bearing:

W = 1. 18 pr/ E2  *

Fw

where:

W: the surface deflection at the center of a

circular uniform loading . 

p: pressure of the circular bearing .

E2 : elastic modulus of the subgrade layer .

Fw : deflection factor .

 Influence curves of deflection factor were

proposed for a practical range of values of

these two ratios :

• Displacement coefficient I∆z

• Vertical stress influence coefficient σz/p, for a=h

Multi-layer Elastic Models :To attain a closer approximation of an

actual pavement system, Burmister extended his solutions to a three-layer system (Burmister, 1945) and derived analytical expressions for the stresses and displacements.

Acum and Fox (1951) presented an extensive tabular summary of normal and radial stresses in three-layer systems at the intersection of the axis of symmetry with the interfaces.

The variables considered in their work were the radius of the uniformly loaded circular area, the thickness of the two top layers, and the elastic moduli of the three layers.

Jones (1962) extended Acum and Fox’s work to cover a much wider range of the same parameters.

Peattie (1962) presented Jones’s table in graphical form and brought convenience in analysis and design of pavement for engineers before the modern computer was widely available.

The above cited research considered the pavement to be either a 2 or 3 layer system with a concentrated normal force or a uniformly distributed normal load.

Therefore, vehicle thrust (tangential loads) and non-uniform loads were not considered.

Poisson’s ratio of 0.5 was assumed in most cases.

Schiffman (1962) developed a general solution to the analysis of stresses and displacements in an N-layer elastic system.

His solution provides an analytical theory

for the determination of stresses and

displacements of a multi-layer elastic

system subjected to non-uniform normal

surface loads, tangential surface loads,

rigid, semi-rigid and slightly inclined plate

bearing loads.

Schiffman presented the equations in an

asymmetric cylindrical coordinate system

(Figure 1.3). Each layer has its separate

properties.

including elastic modulus (Ei), Poisson’s ratio

(νi), and thickness (hi).

Figure 1.3 Element of Stress in a Multi-layer Elastic System (Schiffman, 1962)

Figure 1.4 N-layer Elastic System (Schiffman, 1962)

Advantages and Disadvantages of Layered Elastic Analysis

Advantages Disadvantages

1. high-performance computers2. elastic method can be

extended to multiple-layer system with any number of layers

3. Layered elastic models are widely accepted and easily implemented

4. accurately approximate the response of the flexible pavement systems.

5. each layer is homogenous .

• This assumption makes it difficult to analyze layered systems consisting of non-linear such as untreated sub-bases and sub-grade angular materials.

• This difficulty can be overcome by using the finite element method

• All wheel loads applied on the top of the asphalt concrete have to be axi-symmetric which is not true for actual wheel loads.

Multi-Layer Computer Program

Computer programs

Notes

KENLAYER

Can be applied to layered systems under single, dual, dual-tandem wheel loads with each layer's material properties being linearly elastic , non-linearly elastic or visco-elastic.Based on the computed stresses .ELSYM5 was developed by FHWA to analyze pavement structures up to five different layers under 20 multiple wheel loads (Kopperman et al., 1986).

CHEVRON was developed by the Chevron research company and is based on linear elastic theory. The original program allowed up to five structural layers with one circular load area (Michelow, 1963). Revised versions now accept more than 10 layers and up to 10 wheel loads (NHI, 2002).

EVERSTRS

This software is capable of determining the stresses, strains, and deflections in a layered elastic system (semi-infinite) under a circular surface loads. It can be used to analyze up to 5 layers, 20 loads, and 50 evaluation points .

WESLEA is a multi-layer linear elastic program developed by the U.S. Army Corps of Engineers Waterways Experiment Station (Van Cauwelaert et al., 1989). The current versions have the capability of analyzing more than ten layers with more than ten loads .

ILLI-PAVE Several numerical programs have been developed to model flexible pavement systems. Raad and Figueroa (1980) developed a 2-D finite element program.Nonlinear constitutive relationships were used for pavement materials and the Mohr-Coulomb theory was used as the failure criterion for subgrade soil in ILLI-PAVE.

DAMA can be used to analyze a multiple-layered elastic pavement structure under a single- or dual-wheel load The number of layers can not exceed five.In DAMA, the sub-grade and the asphalt layers are considered to be linearly elastic and the untreated sub-base to be non-linear.MnPAVE MnPAVE is a computer program that combines known empirical relationships with a representation of the physics and mechanics behind flexible pavement behavior .The mechanistic portions of the program rely on finding the tensile strain at the bottom of the asphalt layer, the compressive strain at the top of the subgrade, and the maximum principal stress in the middle of the aggregate base layer .

BISAR BISAR 3.0 is capable of calculating :Comprehensive stress and strain profiles.Deflections. Horizontal forces .Slip between the pavement layers via a shear spring compliance at the interface.

CIRCLY5 CIRCLY software is for the mechanistic analysis and design of road pavements.CIRCLY uses state-of-the-art material properties and performance models and is continuously being developed and extended.CIRCLY has many other powerful features, including selection of: cross-anisotropic and isotropic material properties; fully continuous (rough) or fully frictionless (smooth) layer interfaces. a comprehensive range of load types, including vertical, horizontal, torsional, etc. non-uniform surface contact stress distributions. automatic sub-layering of unbound granular materials.

MICHPAVE

is a user-friendly, non-linear finite element program for the analysis of flexible pavements. The program computes displacements, stresses and strains within the pavement due to a single circular wheel load.

Typical input :

• Material properties: modulus and m• Layer thickness• Loading conditions: magnitude of load, radius, or contact pressure.

Typical output :

• Stress σ• Strain ε• Deflection Δ

Example AC Fatigue Criterion

Problem No. 1

Relation bet. Depth & Hz. tensile strain which predict the Fatigue Cracking

Problem No. 3

Relation bet. Depth & Hz. tensile strain which predict the Fatigue Cracking

Example Subgrade Strain Criterion for Rutting

Problem No. 1

Relation bet. Depth & Vl. Comp. strain which predict the Rutting

Problem No. 3

Relation bet. Depth & Vl. Comp. strain which predict the Rutting

Example Pavement (6” Base)

Example Pavement (10” Base)

Example Pavement (14” Base)

New Approaches for Stresses Analysis

Falling Weight Deflectometer (FWD):

Deflections measured from (FWD) field were

used to approximate layer moduli of all

pavement sections.

NDT SensorsNDTLoad

Measurement of Surface Deflection

Typical FWD EquipmentKUABDynatest

JILS

LayerCharacteristics

Surface

NDT Loadr

E1 µ1 D1

E2 µ2 D2

E3 µ3∞

Base /Subbase

SubgradeSoil

Backcalculation Programs BISDEF MODCOMP

ELSDEF BOUSDEF

CHEVDEF ELMOD

MODULUS EVERCALC

COMDEF ILLI-BACK

WESDEF

KENPAVE SoftwareFour separate programs

LAYERINPKENLAYERSLABSINPKENSLABS

Program installation - CD

Everstress SoftwareReference: WSDOT Pavement Guide, Volume

3, “Pavement Analysis Computer Software and Case Studies,” June 1999. Specific interest is on Section 1.0 “Everstress—Layered Elastic Analysis.”

Download from WSDOThttp://www.wsdot.wa.gov/biz/mats/pavement/pave_tools.

htm

Everstress SoftwareThis software is capable of determining

the stresses, strains, and deflections in a layered elastic system (semi-infinite) under a circular surface loads. It can be used to analyze up to 5 layers, 20 loads, and 50 evaluation points.

Material properties can be either stress dependent or not.E = K1(θ)K2

Everstress SoftwareFiles

Prepare Input Data: This menu option allows creation of a new file or start with an existing file.

Analyze Pavement: This menu option performs the actual analysis and requires an input data file.

Print/View Results: This menu option lets the user view the output on the screen or print.

HMA 3.1 inches

Stabilized Base 6.0 inches

Subbase 12.0 inches

Subgrade

6”6”

x

y

1

2

3

4

KENLAYER ProgramSolution for an elastic multilayer system

under a circular load; superposition principles were used for multiple wheels

Linear elastic, nonlinear elastic, or viscoelasticDamage analysis up to 12 periods

Thank You for Your Attention!