2appendices_BB

Step 2. Compute descriptive statistics for each group of data

For each predicted cracking group the following parameters were computed:

1. Mean predicted percentage of cracked slabs.

2. Mean measured percentage of cracked slabs.

2. Standard deviation of measured percentage of cracked slabs.

These parameters are presented in table 2.

Figure 2 shows very good correspondence between predicted and mean measured faulting for each group.

Figure 2. Mean predicted vs. mean measured cracking for each group of data.

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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 both ARA-ERES and ASU. The authors of this Appendix are Mr. Jagannath Mallela, Dr. Manuel Ayres, Dr. Lev Khazanovich, Dr. Chetana Rao, Mr. Leslie Titus-Glover, Dr. Matthew Witzak and Dr. Michael Darter.

Foreword

This appendix describes the design reliability approach as incorporated into the design guide. It is a supporting reference to the performance model reliability discussions presented in PART 3, Chapters 3, 4, 6, and 7 of the Design Guide. Some equations and expressions presented in the referenced chapters are repeated here for emphasis and continuity.

The appendix begins with an introduction to the design reliability approach as incorporated into the design guide followed by its application to the rigid and flexible pavement design models.

Application to the rigid pavement design models includes: (1) the development of the variance models for estimating reliability of JPCP fatigue cracking, joint faulting, and smoothness models, and (2) the development of the variance models for estimating reliability of CRCP punchouts and smoothness models.

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Application to flexible pavement design models includes the development of the variance models for estimating reliability of fatigue (bottom up) cracking, longitudinal (top down) cracking, rutting, thermal cracking, and smoothness models. Note that the same variance and reliability models are used for new pavement and rehabilitated pavement design.

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DESIGN RELIABILITY

INTRODUCTION

Pavement design and construction is a very complex process that involves many uncertainties, variabilities, and approximations. Even though mechanistic concepts provide a more rational and realistic methodology for pavement design, a consistent and practical method to consider these uncertainties and variations is needed so that a new or rehabilitated pavement can be designed for a desired level of reliability.

Practically everything associated with the design of new and rehabilitated pavements is variable or uncertain in nature. Perhaps the most obviously uncertain of all is estimating truck axle loadings many years into the future. Materials and construction also introduce a measure of variability. Practically every existing pavement exhibits significant variation in condition along its length. Each of these variations must be considered properly in a reliability-based design. For the design to be effective, reliability must be incorporated in a consistent and uniform fashion for all pavement types and rehabilitation.

DESIGN RELIABILITY FOR JPCP FATIGUE CRACKING

The information presented in this section is applicable for new JPCP as well as for JPCP restoration and PCC overlays with JPCP.

Introduction

The definition of reliability for slab cracking for a given project under design is as follows:

R = P [ Cracking of Design Project < Critical Level of Cracking Over Design Life ]

The mean slab cracking (percent slabs) of the design project over time depends on many factors including the design of various aspects of the pavement and particularly joint spacing, slab thickness, strength of PCC, traffic loadings, climate (temperature gradients), construction curling, and climate during construction. Project slab cracking is a stochastic or probabilistic variable whose prediction is uncertain. For example, if 100 projects were designed and constructed with the same design and specifications, they would ultimately over time exhibit a wide range of slab cracking. Data from previous field studies shows that the coefficient of variation of mean slab cracking from project to project within a group of similar designs within a given state averaged 97 percent. (“Long-Term Pavement Performance Pre-Implementation Activities,” technical report prepared for SHRP by J. B. Rauhut, M. I. Darter, R. L. Lytton, and R. E. DeVor, 1986.)

Mean slab cracking between similar projects follows some type of distribution. After considerable analyses, it is believed that the error in prediction of mean slab cracking is approximately normally distributed on the upper side of the mean cracking (not on the lower side, especially near zero cracking). Thus, the likely variation of cracking around

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the mean prediction can be defined by the mean of the prediction model (at any time over the design life) and a standard deviation. The standard deviation is a function of the error associated with the data used to calibrate the cracking model.

This memo summarizes development of the slab cracking design reliability procedure based on the normal distribution assumption. This procedure is based on analysis of the predicted versus measured cracking (see figure 1) and estimation of parameters of the corresponding error distribution.

Figure 1. Predicted versus. measured JPCP cracking.

Step-by-Step Approach to Derive Parameters of the Error Distribution

Step 1 – Group all data points by the level of predicted cracking

All data points in the calibration database were divided into subgroups based on the level of predicted cracking. Table 1 shows the groups established after inspecting the data plots with residual (predicted – measured) on the y-axis versus predicted cracking on the x-axis (not shown here):

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Step 2. Compute descriptive statistics for each group of data

For each predicted cracking group the following parameters were computed:

1. Mean predicted percentage of cracked slabs.

2. Mean measured percentage of cracked slabs.

2. Standard deviation of measured percentage of cracked slabs.

These parameters are presented in table 2.

Figure 2 shows very good correspondence between predicted and mean measured faulting for each group.

Figure 2. Mean predicted vs. mean measured cracking for each group of data.

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