2appendices_II

Constant Stress Vs Constant Strain Analysis

N_f = Ck₁(1/ε_t)^k2(1/E)^k3 (2)

where:

The most commonly used fatigue cracking models are those developed by Shell Oil (6) and the Asphalt Institute (MS-1) (7). The overall general form of each model is the same mathematical model form shown above. However, the difference is in the laboratory regression coefficients in the equation and the laboratory to field adjustment factor. In the following section these two models will be discussed, showing the difference between the two models and the effect of the laboratory testing procedure on the models.

It has to be noted that the fatigue-cracking model, which calculates the number of cycles to failure is only expressing the stage of fatigue cracking described as the crack initiation stage. The second stage, or vertical crack propagation stage, is accounted for in these models by using the field adjustment factor. Other models in the literature use two different equations to express each stage of the fatigue cracking. For example, Lytton et al. (8) used fracture mechanics based upon the Paris law to model the crack propagation stage in his development of the theoretical Superpave Model. Finally, another (third) stage of fatigue fracture is associated with the growth in longitudinal area, in which fatigue cracking occurs. In general, true field fatigue failure is generally associated with a percentage of fatigue cracking along the roadway.

Constant Stress Vs Constant Strain Analysis

In the laboratory, two types of controlled loading are generally applied for fatigue characterization: constant stress and constant strain. In constant stress (load) testing, the applied stress during the fatigue testing remains constant. As the repetitive load causes damage in the test specimen, the stiffness of the mix is decreased due to the micro cracking observed. This, in turn, leads to an increase in tensile strain with load repetitions. In the constant strain test, the strain remains constant with the number of repetitions. Because of specimen damage due to the repetitive loading; the stress must be reduced to obtain the same strain. This leads to a reduced stiffness as a function of repetitions. The constant stress and constant strain phenomena are shown in Figure 1.

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Acknowledgment of Sponsorship

This work was sponsored by the American Association of State Highway and Transportation Officials (AASHTO) in cooperation with the Federal Highway Administration and was conducted in the National Cooperative Highway Research Program which is administered by the Transportation Research Board of the National Research Council.

Disclaimer

This is the final draft as submitted by the research agency. The opinions and conclusions expressed or implied in this report are those of the research agency. They are not necessarily those of the Transportation Research Board, the National Research Council, the Federal Highway Administration, AASHTO, or the individual States participating in the National Cooperative Highway Research program.

Acknowledgements

The research team for NCHRP Project 1-37A: Development of the 2002 Guide for the Design of New and Rehabilitated Pavement Structures consisted of Applied Research Associates, Inc., ERES Consultants Division (ARA-ERES) as the prime contractor with Arizona State University (ASU) as the primary subcontractor. Fugro-BRE, Inc., the University of Maryland, and Advanced Asphalt Technologies, LLC served as subcontractors to either ARA-ERES or ASU along with several independent consultants.

Research into the subject area covered in this Appendix was conducted at ASU. The authors of this Appendix are Dr. M.W. Witczak and Mr. M. M. El-Basyouny.

Foreword

This appendix is the first in a series of three volumes on Calibration of Fatigue Cracking Models for Flexible Pavements. This volume concentrates on the selection, development, of calibration and validation aspects of the fatigue cracking models selected for the Design Guide. Both types of fatigue cracking (bottom up and top down) are discussed separately in the following sections. The fatigue cracking discussion will consist of: an overview of two widely used fatigue models evaluated for inclusion in the Design Guide. For each model evaluated, fatigue-cracking comparisons of data collected from the LTPP database will be discussed. Finally the calibration of the final fatigue cracking model and the reliability of the model selected are explained in detail.

The other volumes are:

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Table of Contents

Appendix II-1

Calibration of Fatigue Cracking Models for Flexible Pavements

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Annex A – Calibration of Fatigue Cracking Models For Flexible Pavements

Introduction

Load-associated fatigue cracking is one of the major distress types occurring in flexible pavement systems. The action of repeated traffic loads induces tensile and shear stresses in all chemically stabilized layers, which eventually lead to a loss in the structural integrity of the stabilized layer. Repeated load or fatigue cracks initiate at points where the critical tensile strains and stresses occur. The location of the critical strain/stress is dependent upon several factors. The most important is the stiffness of the layer and the load configuration. In addition, it should be realized that the maximum tensile strain developed within the pavement system might not be the most critical or damaging value. This is because the critical strain is a function of the stiffness of the mix. Since the stiffness of an asphalt mix in a layered pavement system varies with depth, these changes will eventually effect the location of the critical strain that causes fatigue damage. Once the damage initiates at the critical location, the continued action of traffic eventually causes these cracks to propagate through the entire bound layer.

Propagation of the cracks throughout the entire layer thickness will eventually allow water to seep into the lower unbound layers, weakening the pavement structure and reducing the overall performance. This will result in increased roughness of the pavement system, causing a decrease in pavement serviceability. This phenomenon of crack initiation and then propagation through the entire layer occurs not only in the surface layer but also in all the stabilized layers underneath. Cracking in an underlying layer, such as a cement stabilized subbase, also reduces the overall structural capacity of the layer (and pavement) and may induce reflective cracking in the upper layers.

Over the last 3 to 4 decades of pavement technology, it has been common to assume that fatigue cracking normally initiates at the bottom of the asphalt layer and propagates to the surface (bottom-up cracking). This is due to the bending action of the pavement layer that results in flexural stresses to develop at the bottom of the bound layer. However, numerous recent worldwide studies (1, 2, 3, 4) have also clearly demonstrated that fatigue cracking may also be initiated from the top and propagate down (top-down cracking). This type of fatigue is not as well defined from a mechanistic viewpoint as the more classical "bottom-up" fatigue. However, it is a reasonable engineering assumption, with the current state of knowledge, that this distress may be due to critical tensile and/or shear stresses developed at the pavement surface and, perhaps, caused by extremely large contact pressures at the tire edge-pavement interface; coupled with highly aged (stiff) thin surface layer that have become oxidized. In this initial mechanistic attempt to model top-down cracking in the Design Guide; the failure mechanism for this distress is hypothesized to be a result of tensile surface strains leading to fatigue cracking at the pavement surface.

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Asphalt Mixture Fatigue Cracking Models

This chapter concentrates on the selection, development, of calibration and validation aspects of the fatigue cracking models selected for the Design Guide. Both types of fatigue cracking (bottom up and top down) are discussed separately in the following sections. The fatigue cracking discussion will consist of: an overview of two widely used fatigue models evaluated for inclusion in the Design Guide. For each model evaluated, fatigue-cracking comparisons of data collected from the LTPP database will be discussed. Finally the calibration of the final fatigue cracking model and the reliability of the model selected are explained in detail.

Fatigue cracking prediction is normally based on the cumulative damage concept given by Miner's (5). The damage is calculated as the ratio of the predicted number of traffic repetitions to the allowable number of load repetitions (to some failure level) as shown in equation 1. Theoretically, fatigue cracking should occur at an accumulated damage value of 1. If a normal distribution is assumed for the damage ratio calculated, the percentage of area cracked can be computed and checked with field performance.

D = ∑_i=1^T n_i/N_i (1)

where:

D = damage.

T = total number of periods.

n_i = actual traffic for period i.

N_i = allowable failure repetitions under conditions prevailing in period i.

The fatigue life of an asphalt concrete mixture is influenced by many factors. Several key mix properties such as asphalt type, asphalt content and air-void content are well known to influence fatigue. Other factors such as temperature, frequency, and rest periods of the applied load also are known to influence fatigue life. Other material properties may also affect the fatigue life. It is obvious that mix properties need to be carefully balanced to optimize fatigue cracking of any mixtures.

In the literature, the most commonly used model form to predict the number of load repetitions to fatigue cracking is a function of the tensile strain and mix stiffness (modulus). The critical locations of the tensile strains may either be at the surface (result in top-down cracking) or at the bottom of the asphaltic layer (result in bottom-up cracking).

The general mathematical form of the number of load repetitions used in the literature is shown in equation 2. The form of the model is a function of the tensile strains at a given location and modulus of the asphalt layer.

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Constant Stress Vs Constant Strain Analysis

N_f = Ck₁(1/ε_t)^k2(1/E)^k3 (2)

where:

The most commonly used fatigue cracking models are those developed by Shell Oil (6) and the Asphalt Institute (MS-1) (7). The overall general form of each model is the same mathematical model form shown above. However, the difference is in the laboratory regression coefficients in the equation and the laboratory to field adjustment factor. In the following section these two models will be discussed, showing the difference between the two models and the effect of the laboratory testing procedure on the models.

It has to be noted that the fatigue-cracking model, which calculates the number of cycles to failure is only expressing the stage of fatigue cracking described as the crack initiation stage. The second stage, or vertical crack propagation stage, is accounted for in these models by using the field adjustment factor. Other models in the literature use two different equations to express each stage of the fatigue cracking. For example, Lytton et al. (8) used fracture mechanics based upon the Paris law to model the crack propagation stage in his development of the theoretical Superpave Model. Finally, another (third) stage of fatigue fracture is associated with the growth in longitudinal area, in which fatigue cracking occurs. In general, true field fatigue failure is generally associated with a percentage of fatigue cracking along the roadway.

Constant Stress Vs Constant Strain Analysis

In the laboratory, two types of controlled loading are generally applied for fatigue characterization: constant stress and constant strain. In constant stress (load) testing, the applied stress during the fatigue testing remains constant. As the repetitive load causes damage in the test specimen, the stiffness of the mix is decreased due to the micro cracking observed. This, in turn, leads to an increase in tensile strain with load repetitions. In the constant strain test, the strain remains constant with the number of repetitions. Because of specimen damage due to the repetitive loading; the stress must be reduced to obtain the same strain. This leads to a reduced stiffness as a function of repetitions. The constant stress and constant strain phenomena are shown in Figure 1.

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