By Eng. Mohamed Hamdallah Elshaer
Outline Introduction
.
Background
on Stress and strain in flexible pavements.
Review
of Multi-Layer Computer Program and comparison between them.
Distress
analysis for Flexible Pavement.
Outline Introduction
.
Background
on Stress and strain in flexible pavements.
Review
of Multi-Layer Computer Program and comparison between them.
Distress
analysis for Flexible Pavement.
Introduction
The
first asphalt road was constructed in
the US about 100 years ago in in New Jersey. There
are currently about 2.2 million miles
of roadway surfaced by asphalt concrete Pavements (Huang, 1993). Flexible
pavements
are
made
bituminous and granular Materials .
up
of
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
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
Load P = Area A Units: Types:
MPa, psi, ksi bearing, shearing , axial
Strain Ratio
of deformation caused by load to the original length of material Change in Length Original Length
Units:
Dimensionless
=
L L
Stiffness
σ Stiffness = stress/strain = ε σ , s s e r t S
E 1
For elastic materials : o
Modulus of Elasticity
Strain, ε
o
Elastic Modulus
Stress
vs. Strain of a Material in Compression
Poisson’s
Ratio
•
Since
researchers
the
mid-1960s, have
pavement
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
•
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.
•
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
pavement
structure
(rutting)
caused
deformation in the upper subgrade.
by
of
the shear
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.
• Although the layered elastic method is
more
easily
element
implemented
methods,
it
still
than has
finite 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
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
For 3D
finite element analysis :
• 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 spatially
of
flexible
varying
tire
pavements pavement
under contact
Deflection Change
(∆)
in length.
Deformation. Units:
∆
mm, mils (0.001 in).
Background on Stress and strain in flexible pavements :
Pavement
three
structural main
analysis
issues:
includes material
characterization , theoretical model for
structural
response,
environmental conditions.
and
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
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
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
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
assumed to be linear elastic.
are
Pavement Flexible
Response models
and rigid pavements respond to loads in very different ways. Consequently, different theoretical models have been developed for flexible and rigid pavements.
Structural
Response
Models Different analysis methods for AC and PCC .
AC
PCC Slab
Base Subgrade Subgrade
•Layered system behavior. • All layers carry part of load.
• Slab action predominates. • Slab carries most
Distribution
of Wheel
Load Wheel Load
Hot-mix asphalt Base Subbase Natural soil
Pavement
Responses Under
Load Axle Load
Surface
ε SUR
Base/Subbase Subgrade Soil
δ SUR
ε SUB
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
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,
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
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
pavement (Ullidtz, 1998).
stiffness
of
One-Layer
System
One-Layer
System(Cylindrical Coordinates)
Formulas
Stresses
for Calculating
Burmister’s
Two-layer Elastic
Models : Pavement
layered
systems
structure
typically with
have
a
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; isotropic, elastic
each and
layer
is
linearly
modulus
and
homogeneous, elastic
with
Poisson’s
an
ratio
(Hooke’s law). 2. Each layer has a uniform thickness and infinite
dimensions
in
all
horizontal
directions, resting on a semi-infinite elastic
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
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
ure 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
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
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
• Displacement coefficient I∆z
• Vertical stress influence coefficient σ 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
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
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
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
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
1. high-performance computers • 2. 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 .
Disadvantages
This assumption makes it difficult to analyze layered systems consisting of nonlinear such as untreated subbases 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
Multi-Layer Computer programs KENLAYE R
ELSYM5
Computer Program Notes
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 . 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,
EVERSTR S
WESLEA
ILLI-PAVE
This software is capable of determining the stresses, strains, and deflections in a layered elastic system (semiinfinite) under a circular surface loads. It can be used to analyze up to 5 layers, 20 loads, and 50 evaluation points . 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 . 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
MnPAVE
BISAR
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 subbase to beisnon-linear. MnPAVE a computer program that combines known empirical relationships relationships with a represen representation tation 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 stress in the middle BISAR 3.0principal is capable of calculating : of the aggregate base layer . ve stress and strain profiles. Comprehensive Comprehensi Deflections. Horizontal forces . Slip between the pavement layers via a shear spring compliance at the interface. i nterface.
CIRCLY5
MICHPAV E
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. is a user-friendly, non-linear finite element program for non-uniform surface contact stress distributions. the analysis sub-layering of flexible pavements. The program automatic of unbound granular materials. 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 Typical
contact pressure.
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
for Rutting
Subgrade Strain Criterion
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
Base)
Pavement (10”
Example
Base)
Pavement (14”
New
Approaches for Stresses Analysis Falling Weight Deflectometer (FWD):
Deflections measured from (FWD) field were used to approximate layer moduli of all pavement sections.
Measurement of Surface Deflection NDT Load
NDT Sensors
Typical Dynatest
JILS
FWD Equipment KUAB
NDT Load
r
Layer Characteristics
Surface
E1
µ1
D1
Base / Subbase
E2
µ2
D2
Subgrade Soil
E3
µ3
Backcalculation Programs
BISDEF
MODCOMP
ELSDEF
BOUSDEF
CHEVDEF
ELMOD
MODULUS EVERCALC
COMDEF
WESDEF
ILLI-BACK
KENPAVE Software Four
separate programs
LAYERINP KENLAYER SLABSINP KENSLABS
Program
installation - CD
Everstress Software Reference:
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 WSDOT http://www.wsdot.wa.gov/biz/mats/pavement/pave_tools.
htm
Everstress Software 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. Material properties can be either stress dependent or not. E
= K1(θ)K2
Everstress Software Files 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.
x 6”
6” HMA 3.1 inches
y 1
Stabilized Base 6.0 inches
Subbase 12.0 inches
Subgrade
KENLAYER Program Solution
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
