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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!
