stress and strain in asphalt pavement

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Cairo UniversityPost GraduateHighway Engineering Technical ReportStresses And Strains In Flexible PavementUsing Computer Program : 

Cairo UniversityPost GraduateHighway Engineering Technical ReportStresses And Strains In Flexible PavementUsing Computer Program By Eng. Mohamed Hamdallah El-shaer

Outline : 

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. 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 .

Slide 4: 

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).

Slide 5: 

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 : 

Stress Force per unit area Units: MPa, psi, ksi Types: bearing, shearing , axial P A s = Load Area =

Strain : 

Strain Ratio of deformation caused by load to the original length of material Units: Dimensionless

Stiffness : 

Stiffness Stiffness = stress/strain = For elastic materials : Modulus of Elasticity Elastic Modulus Young’s Modulus Stress, ? Strain, ? E 1

Stress vs. Strain of a Material in Compression : 

Stress vs. Strain of a Material in Compression

Poisson’s Ratio : 

Poisson’s Ratio

Slide 11: 

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.

Slide 12: 

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.

Slide 13: 

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.

Slide 14: 

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.

Slide 15: 

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.

Slide 16: 

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).

Slide 17: 

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.

Slide 18: 

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 (D) : 

Deflection (D) Change in length. Deformation. Units: mm, mils (0.001 in).

Slide 20: 

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 :

Slide 21: 

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).

Slide 22: 

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.

Slide 23: 

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.

Slide 24: 

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).

Slide 25: 

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.

Slide 26: 

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

Slide 27: 

Structural Response Models Different analysis methods for AC and PCC . Layered system behavior. All layers carry part of load. Slab action predominates. Slab carries most load.

Slide 28: 

Wheel Load Hot-mix asphalt Base Subbase Natural soil Distribution of Wheel Load

Slide 29: 

Subgrade Soil Base/Subbase Surface d SUR SUB SUR Axle Load Pavement Responses Under Load

Slide 30: 

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 ? subjected to a static point load P .

Slide 31: 

As can be seen, the elastic modulus does not influence any of the stresses and the vertical normal stress z s 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.

Slide 32: 

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.

Slide 33: 

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

One-Layer System(Cylindrical Coordinates) : 

One-Layer System(Cylindrical Coordinates)

Slide 36: 

Formulas for Calculating Stresses

Slide 37: 

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.

Slide 38: 

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)

Slide 39: 

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.

Slide 40: 

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)

Slide 41: 

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 s 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.

Slide 42: 

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

Slide 43: 

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).

Slide 44: 

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

Slide 45: 

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 :

Slide 46: 

Displacement coefficient IDz

Slide 47: 

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

Slide 48: 

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.

Slide 49: 

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.

Slide 50: 

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.

Slide 51: 

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 (?i), and thickness (hi).

Slide 52: 

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

Slide 53: 

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

Slide 54: 

Advantages and Disadvantages of Layered Elastic Analysis

Slide 55: 

Multi-Layer Computer Program

Slide 59: 

Typical input : Material properties: modulus and m Layer thickness Loading conditions: magnitude of load, radius, or contact pressure. Typical output : Stress s Strain e Deflection ?

Example AC Fatigue Criterion : 

Example AC Fatigue Criterion

Slide 69: 

Problem No. 1 Relation bet. Depth & Hz. tensile strain which predict the Fatigue Cracking

Slide 70: 

Problem No. 3 Relation bet. Depth & Hz. tensile strain which predict the Fatigue Cracking

Example Subgrade Strain Criterion for Rutting : 

Example Subgrade Strain Criterion for Rutting

Slide 75: 

Problem No. 1 Relation bet. Depth & Vl. Comp. strain which predict the Rutting

Slide 76: 

Problem No. 3 Relation bet. Depth & Vl. Comp. strain which predict the Rutting

Example Pavement (6” Base) : 

Example Pavement (6” Base)

Example Pavement (10” Base) : 

Example Pavement (10” Base)

Example Pavement (14” Base) : 

Example Pavement (14” Base)

Slide 85: 

New Approaches for Stresses Analysis Falling Weight Deflectometer (FWD): Deflections measured from (FWD) field were used to approximate layer moduli of all pavement sections.

Slide 86: 

NDT Sensors NDT Load Measurement of Surface Deflection

Typical FWD Equipment : 

Typical FWD Equipment KUAB Dynatest JILS

BackcalculationTypical Pavement Case : 

Layer Characteristics Surface NDT Load r BackcalculationTypical Pavement Case E1 m1 D1 E2 m2 D2 E3 m3 ¥ Base / Subbase Subgrade Soil

Backcalculation Programs : 

Backcalculation Programs BISDEF MODCOMP ELSDEF BOUSDEF CHEVDEF ELMOD MODULUS EVERCALC COMDEF ILLI-BACK WESDEF

KENPAVE Software : 

KENPAVE Software Four separate programs LAYERINP KENLAYER SLABSINP KENSLABS Program installation - CD

Everstress Software : 

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 : 

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(?)K2

Everstress Software : 

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.

Everstress (1)—Click on File to get started : 

Everstress (1)—Click on File to get started

Everstress (2)—Change from Metric to US Units : 

Everstress (2)—Change from Metric to US Units

Everstress (3)—Input Layer Thicknesses and Material Properties : 

Everstress (3)—Input Layer Thicknesses and Material Properties

Everstress (4)—Load Locations and Pavement Response Evaluation Locations (points) : 

Everstress (4)—Load Locations and Pavement Response Evaluation Locations (points)

Everstress (5)—Save Data File : 

Everstress (5)—Save Data File

Everstress (6)—Output File : 

Everstress (6)—Output File

Everstress (7)—try the Everstrs.out output file to view typical results : 

Everstress (7)—try the Everstrs.out output file to view typical results

Everstress (7)—try the Everstrs.out output file to view typical results : 

Everstress (7)—try the Everstrs.out output file to view typical results HMA 3.1 inches Stabilized Base 6.0 inches Subbase 12.0 inches Subgrade 6” 6” x y 1 2 3 4

Everstress (8)—Class Example : 

Everstress (8)—Class Example

Everstress (9)—Class Example : 

Everstress (9)—Class Example

Everstress (10)—Class Example : 

Everstress (10)—Class Example

Everstress (11)—Class Example : 

Everstress (11)—Class Example

Everstress (12)—Class Example : 

Everstress (12)—Class Example

Everstress (13)—Class Example : 

Everstress (13)—Class Example

Everstress (14)—Class Example : 

Everstress (14)—Class Example

Everstress (15)—Class Example : 

Everstress (15)—Class Example

Everstress (16)—Class Example : 

Everstress (16)—Class Example

Everstress (17)—Class Example : 

Everstress (17)—Class Example

Everstress (18)—Class Example : 

Everstress (18)—Class Example

Everstress (19)—Class Example : 

Everstress (19)—Class Example

KENLAYER Program : 

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

Thank You for Your Attention! : 

Thank You for Your Attention!