This work was aimed at providing the most appropriate Nigerian Empirical-Mechanistic Flexible Pavement Analysis and Design method (NEMPAD) by incorporating Reliability, using First order reliability method (FORM), considering all the input variabilities, uncertainties, and seasonal variations, with the aid of Matlab to express the algorithms. A frame work was developed for computation of component reliability index (R.I), system reliability index (R.I), and probability of failure. Inputs parameters considered includes: traffic load, material properties, and environmental conditions. Four seasons were considered in the design namely: Hunturu(1 week Dec-2 week Feb), Bazara(2 week Feb-2 week May), Damina(2 week may-1 week Oct), and Kaka(1 week Oct-1 week Dec) seasons, for the North West geographical zone, and the cumulated damage was computed for each season. Comparism was made between deterministic and reliability methods. The results indicates that at coefficient of variation (COV) of 25% , a surfacing thickness of 100mm (representing wearing and binder course), 165mm thickness of Base course material, and 180mm thickness of sub base course material, are adequate, while at coefficient of variation (COV) of 42% a surfacing thickness of 100mm (representing wearing and binder course), 200mm thickness of Base course material, and 250mm thickness of sub base course material, are adequate, as against the deterministic method cited in Olowosulu (2005),where higher thicknesses were used, under the same traffic load and conditions. The results also indicated that highest level of damage with respect to fatigue was recorded during Bazara season due to the effects of Temperature, while highest level of damage with respect to Rutting was recorded during Damina season due to the effects of water in the subgrade.
TABLE OF CONTENTS
Title page i Dedication ii Declaration iii Certification iv Acknowledgement v Abstract vi Table of contents vii List of tables x List of Figures xii List of symbols/abbreviation xiii CHAPTER ONE: INTRODUCTION 1 1.1 Background 1 1.2 Statement of the problem 3 1.3 Aim and objectives 4 1.3.1 aim 4 1.3.2 objectives 4 1.4 Scope of the study 5 1.5 Methodology 5
1.6 Significance of the Study 5 CHAPTER TWO: LITERATURE REVIEW 6 2.1 General 6 2.2 Transfer functions 10 2.3 Reliability Method 10 2.3.1 First order reliability method (Form) 10 CHAPTER THREE: METHODOLOGY 12 3.1 Introduction 12 3.2 Methodology 14 3.3. Failure Mode-1 (Fatigue) 17 3.4 Failure Mode-2 (Rutting) 20 3.5 Probability Distribution of N and n 21 3.6 Traffic Data Input for E-M procedure 22 3.7 Material Characterization 24 CHAPTER FOUR: ANALYSIS AND DISCUSSION OF RESULTS 28 4.1 Fatigue failure 28 4.2 Rutting failure 34 CHAPTER FIVE: CONCLUSION AND RECOMMENDATION 51 5.1 Conclusion 51 5.2 Recommendations 52 REFERENCES 53
APPENDIX A:Elysym-5 output(showing stresses and strains) 58 APPENDIX B:MatLab output (showing Reliability Index and Probability of Failure) 64
INTRODUCTION 1.1 BACKGROUND Traditionally, flexible pavement thickness design has been accomplished throughempirically based procedures. One well-known procedure, the American Association ofState Highway and Transportation Officials (AASHTO,1993) method, was based upon theAASHTO Road Test held in Illinois between 1958 and 1960. The designprocedure utilized empirical relationships developed from the AASHTO road test and istherefore limited to the conditions of that test. In fact, all empirically based methodsshare the same common disadvantage in that they are limited to the conditions andobservations of the particular road sections on which the procedure was based. This factmay require engineers to extrapolate outside the original inference space, which could beproblematic.As a result of this limitation, many pavement sections failed prematurely while other sections far outlived their design lives(Rutherford, 2012)
Conversely, Empirical-Mechanistic (M-E) design is more robust since it combinesthe elements of mechanical modeling and performance observations in determining therequired pavement thickness for a set of design conditions. The Empirical-Mechanistic Empirical-Mechanisticbased method of pavement design is based on the mechanics of materials,which relates inputs such as wheel loadsto output such as pavement response.The response is then used to predict pavement distresses(including cracking)and other performance based laboratories and field testing outcomes.In essence, M-E design has the capability of changing andadapting to new developments in pavement design by relying primarily on the mechanicsof material (Timmet al, 1999).
The induced state of stress and strain in a pavement structure due to traffic loading and
environmental conditions is predicted using theory of mechanics. Empirical models link
these structural responses to distress predictions. The Analytical-Empirical (or Empirical-
Mechanistic) approach to design of flexible pavements has two steps, as implied by the name.
In the first step the critical stresses or strains (the response) in the individual pavement layers
are calculated using an analytical model, and in the second step they are compared to
permissible stresses or strains. In the more sophisticated versions, the critical stresses or
strains are used for determining the rate of deterioration (the performance).
Fig. 1.1: Pavement response (analytical) and performance (empirical)
On the other hand,there are many definitions concerning the term reliability.” In the general
sense,reliability implies trustworthiness or dependability. When applied to structural
pavementdesign, the 1993 AASHTOGuide defines reliability in this way (AASHTO,
1993):”The reliability of a pavement design-performance process is the probability that a
pavement section designed using the process will perform satisfactorily over thetraffic and
environmental conditions for the design period.”
“To provide uniformity, pavement design reliability is defined as the probabilitythat the pavement’s traffic carrying capacity exceeds the cumulative traffic loading onthe pavement during a selected design life.”The above statement may be expressed mathematically as Kulkarni1994) R = P[N > n] (1.1) Where “N” is the traffic load capacity of the pavement structure and “n” is the actualnumber of load applications. Design of flexible pavement involves many uncertainties, variabilities, and approximations regarding material properties, traffic loads, subgrade strength,drainage conditions, construction and compaction procedures and climatic factorssuch as temperature, rainfall, and snowfall, etc.The combination of the variances associated with inputvariables contributes to components and system uncertainty, and this combinationof variances can have a significant effect on the predicted performanceof the pavement. Reliability in pavement design isintroduced to consider these uncertainties..Advantages of usingreliability includes the calibration of new design methods, developing rational designspecifications, optimizing resources, and assessing the damage and remaining life of thepavement. For example, M-E methods can adapt to new design conditions (e.g., heavierloads, new pavement materials) by relying primarily upon mechanistic pavementmodeling.
While Monte carlo simulation (MCS) is by far the most accurate reliability approximationtechnique available, several other techniques have been employedin the structural reliability community, including those that haveachieved accuracy close to that of MCS for many practical engineeringdesign problems but require few model evaluations toimplement. Some examples includes:Point Estimate methods(PEM), the Mean value First-order secondmoment (MVFOSM), first-order reliability methods (FORMs),Rosenblueth, and advanced mean value (AMV) (Cornel et al, 1975).
1.2 STATEMENT OF PROBLEM A Empirical-Mechanistic (M-E) pavement analysis and design has been proposed for use in Nigeria (Olowosulu, 2005;Murana, 2010;and Yakubu,2011). There is statistical variation in the input parameters. Consequently, there is variability in the calculated stresses and strains that lead to variations in the number of allowable loads. There is also variability in the number of expected loads during the design period. Finally, there is variability in regard to the transfer functions that predict pavement life (Timmet al, 1999). So there is need to incorporate reliability analysis into the design of pavement systems in order to improve the accuracy of pavement life prediction. 1.3 AIM AND OBJECTIVES 1.3.1 Aim Theaim of this research is to improve the Nigerian Empirical- Mechanistic pavement analysis and design system (NEMPADS) by incorporating reliability into the methodology. 1.3.2 Objectives
i. To generate stresses and strains using a Multilayer elastic computer programme,ELSYM-5.
ii. To compute the allowable stresses in terms of Fatigue and Rutting failures using distress sub-models developed in NEMPAD.
iii. To calculate theaccumulated damage in each season due tofatigue and rutting.
iv. To calculate the reliability index usingFirst order Reliability method(FORM)andthrough a developed program in MatLab.
v. To perform systemreliability analysis using fatigue and rutting data as inputs.
In order to achieve these objectives, the relevant design input variables were identified and there variability statistically characterized.
1.4 SCOPE OF THE STUDY The First order reliability method(FORM) is used to incorporate reliability into the existing Nigerian Empirical-Mechanistic pavement analysis and design, using NEMPAD Fatigue and Rutting distress model equations, and the data is obtained from Kaduna – Kano road project ,1987 (CH 25+000 TO CH35+000). 1.5METHODOLOGY Material properties, Traffic load, and climatic condition, are enteredinto a load-displacement model (ELSYM-5) that calculates stresses and strains at critical locations.The calculated stresses and strains are used to compute the number of allowable loadsuntil failure, while the number of expected loads for each particular condition is also determined, the effects of variabilities of the inputs are determined using Reliability(first order reliability method, FORM). 1.6 SIGNIFICANCE OF THE STUDY The significance of this study is to improve the accuracy of the pavement life prediction by incorporating reliability analysis into the design of pavement system.
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