Stress and Strain in Asphalt Pavements

ByByEng. Mohamed Hamdallah El-shaerEng. Mohamed Hamdallah El-shaer

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.

StressForce per unit area

Units: MPa, psi, ksi

Types: bearing, shearing , axial

PA

LoadArea

=

Strain

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

Units: Dimensionless

Change in Length

Original Length

LL

=

StiffnessStiffness = stress/strain =

For elastic materials :

oModulus of Elasticity

o Elastic Modulus

o Young’s Modulus

Str

ess,

Strain,

E

1

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 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

Wheel Load

Hot-mix asphalt

Base

Subbase

Natural soil

Distribution of Wheel Load

Subgrade Soil

Base/Subbase

Surface

SUR

SUB

SUR

AxleLoad

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 :

1. Displacement coefficient Iz

2. Vertical stress influence coefficient z/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 .

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

2. This difficulty can be overcome by using the finite element method

3. 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 1 D1

E2 2 D2

E3 3

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()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 viscoelastic

Damage analysis up to 12 periods

Thank You for Your Attention!