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UBC Theses and Dissertations

A study of bridge coating maintenance Tam, Chun Kwok 1994

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A STUDY OF BRIDGE COATING MAINTENANCE by CHUN KWOK TAM B.A.Sc, The University of British Columbia, 1992 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTERS OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Civil Engineering We accept this thesis as conforimg to the required standard THE UNIVERSITY OF BRITISH COLUMBIA MARCH, 1994 © Chun Kwok Tarn, 1994 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my writ ten permission. (Signature) Department of Civil Engineering The University of British Columbia Vancouver, Canada Date March 10, 1994 DE-6 (2/88) ABSTRACT Two analysis methods are presented in this thesis to minimize the cost of coating maintenance for steel bridges. The first method is incorporated into the Bridge Corrosion Cost Model. This model performs a life-cycle cost analysis using equivalent annual costs to compare the three maintenance strategies: spot repair, overcoat, and recoat. The strategy that provides the minimum equivalent annual cost is considered to be optimal. A computer application has been developed to reduce the work required to implement the procedures described in this model. The flexibility of this program allows the user to adjust key parameters in order to account for variability in costs and environmental conditions between different regions in British Columbia. In addition, an on-line help feature is provided to reduce the time needed to operate this program. The second method presented in this thesis uses the dynamic programming approach. The procedures are implemented into the Bridge Coating Maintenance Model. In this model, the sum of the costs resulting from a sequence of rehabilitation choices is rninimized. The procedures developed in this analysis can easily be converted into algorithms for possible computer applications. On the basis of the preliminary analysis using these two approaches, spot repair is the most cost effective rehabilitation method. Overcoating is the second most effective strategy and recoating is usually the most expensive solution. However, the difficulty in obtaining adequate deterioration and cost functions for the coating systems will significantly reduce the accuracy of these analysis techniques. Therefore, a uniform data collection system should be implemented so that a database will be available for these models. ii TABLE OF CONTENTS Page Abstract ii Table of Contents in List of Tables vi List of Illustrations vii Acknowledgements ix Chapter 1. Introduction 1 Chapter 2. Literature Review 7 2.1 Coating Maintenance 7 2.1.1 Repair Considerations 8 2.1.1.1 Type ofFailure 8 2.1.1.2 Level ofFailure 9 2.1.1.3 Adhesion 10 2.1.1.4 Coating Type 10 2.1.2 Maintenance Strategies 11 2.1.3 Advantage of Shorter Maintenance Periods 13 2.1.4 Application Strategies 14 2.2 Coating Systems For Steel Bridges 14 2.2.1 History 14 2.2.2 Coating Systems 15 2.2.2.1 The Inhibitive Primers 15 2.2.2.2 The Sacrificial Primers 15 2.2.2.3 The Barrier Coatings 16 2.3 Surface Preparation 16 2.3.1 Hand and Power Tool Cleaning 16 2.3.2 Solvent Cleaning 17 2.3.3 Dry Abrasive Blasting 17 2.3.4 Wet Abrasive Blasting 18 2.3.5 Wet Blasting 18 2.4 Costs 19 hi Chapter 3. Bridge Corrosion Cost Model 20 3.1 Introduction 20 3.2 Overview of Analysis Procedure 20 3.3 Simulation of Coating System Deterioration 21 3.4 Optimization of Coating System 24 3.4.1 Equivalent Annual Cost Method 24 3.4.2 Optimization Process 25 3.4.3 Application to Maintenance Strategies 28 3.4.4 Inflation 29 3.4.5 Cost Factors 30 3.4.6 Application of Cost Factors to Equivalent Annual Cost Equations 31 3.4.7 Condition Limits of Maintenance Strategies 31 3.4.8 Probability of Success Analysis 32 3.4.9 Effectiveness 33 3.4.10 Cost-Effectiveness Ratio 34 3.5 Problems Associated With Model Formulation 35 3.6 Assumptions and Limitations 36 Chapter 4. Bridge Coating Maintenance Model 38 4.1 Introduction 38 4.2 Solution Strategy 38 4.3 Problem Description 39 4.4 Organization 39 4.4.1 Step 1 39 4.4.2 Step 2 40 4.4.3 Step 3 43 4.4.4 Step 4 44 4.5 Formula 44 4.6 Constraints 45 4.7 Solution 45 4.8 Example 45 4.8.1 Organization of Problem 45 4.8.2 Decision Choices 46 4.8.3 Stage Return Function g(dns,n,s) 47 4.8.4 Solution 49 4.9 Assumptions and Limitations 51 Chapter 5. Conclusions and Future Developments 56 5.1 Conclusions 56 5.2 Future Developments 57 iv Bibliograhy 59 Appendix A Program Description and Layout 61 A.1 Introduction 61 A.2 Cover 61 A 3 Index 62 A.4 Input Module 64 A.5 Optimization Module 71 A.6 Risk Assessment Module 73 A.7 Output Module 74 A 8 Macro Module 74 A.9 Database 74 A.10 Results 74 A l l Summary 77 Appendix B. Program Documentation 78 Appendix C. Example Using Bridge Corrosion Cost Model 93 Example 1 93 v LIST OF TABLES Table Page Table 1. ASTM Standards for Coating Systems 9 Table 2. Cleaning Methods 16 Table 3. Corrosion Performance Rating ASTM D610 20 Table 4. Adhesion Performance Rating ASTM D3359 21 Table 5. Cost Factors For Bridge Height 29 Table 6. Cost Factors For Bridge Type 29 Table 7. Cost Factors For Maintenance Strategy 30 Table 8. Condition Limits 31 Table 9. Decision Choices at Each State 40 Table 10. Table of Costs for Each Decision Choice dns 42 Table 11. Decision Sets, Dns, for Each State s 46 Table 12. Stage Return Function 47 Table 13. Environmental Classification 64 vi LIST OF ILLUSTRATIONS Figure Page Figure 1. Different Maintenance Periods 12 Figure 2. Simulation of Deterioration Using Field Data 22 Figure 3. Illustration of Optimization Procedure 26 Figure 4. Effectiveness 33 Figure 5. Coating Condition of a Steel Bridge Over Its Service Life 38 Figure 6. Bridge Coating Maintenance Model in a Dynamic Programming Framework 39 Figure 7. Decision Choices at Stagenand State s 40 Figure 8. Deterioration Function of a Coating System 41 Figure 9. Organization of Simplified Problem Using Dynamic Programming Approach 45 Figure 10. Deterioration Function of Coating System. 46 Figure 11. Diagram of Stage Return Function g(dns,n,s) Applied to Each Decision SetDns 47 Figure 12. Partial Optimization of Problem 48 Figure 13. Detailed Evaluation of Cumulative Return Function at Stage 4 and State 3 49 Figure 14. Optimal Maintenance Strategies for Simplified Bridge Coating Maintenance Problem 50 Figure 15. Possible Deterioration Paths 51 Figure 16. Comparison of Actual and Assumed Deterioration Processes 52 Figure 17. Partial Dynamic Programming Framework for Analyzing Multiple Coating Systems 53 Figure 18. Dynamic Programming Framework to Account for Changes in Environmental Conditions 54 Figure 19. Cover Page and Introduction of Bridge Corrosion Cost Model 61 Figure 20. Index Section ofProgram 62 Figure 21. Dialogue B ox For the Selection of Coating Simulation Procedure 63 Figure 22. Dialogue Box For Environmental and Structural Description 65 Figure 23. Dialogue Box for Coating Parameters Using Service Life 66 Figure 24. Dialogue Box for Coating Parameters Using Corrosion Functions in Program Database 66 Figure 25. Dialogue Box for Cost and Financial Information 67 Figure 26. Dialogue Box for Cost Factors 68 Figure 27. Dialogue Box for Condition Limits 69 Figure 28. Dialogue Box for Probability of Success Parameters 72 Figure 29. Dialogue Box for Optimal Maintenance Strategies 74 Figure 30. Dialogue Box for Probability of Success Results 75 Figure 31. Dialogue Box for Results Section 76 Figure 32. Dialogue Box for Structural and Environmental Information 92 vii Figure 33. Dialogue Box for Choosing Method of Simulating Coating Deterioration 93 Figure 34. Dialogue Box for Coating Parameters 93 Figure 35. Dialogue Box for Cost and Financial Information 94 Figure 36. Dialogue Box for Results of Life Cycle Cost Analysis 94 Figure 37. Dialogue Box for Probability of Success of Rehabilitated Coating 95 Figure 38. Graph of Equivalent Annual Cost for Spot Repair 95 Figure 39. Graph of Equivalent Annual Cost for Overcoat 96 Figure 40. Graph of equivalent annual cost for Recoat 96 viii ACKNOWLEDGMENTS I would like to thank my mom and dad for providing me with food and shelter over all these years. I am also very grateful of Dr. Stiemer for his guidance, patience and for introducing to me this thesis topic. Furthermore, I want to thank Mr. Russ Raine for his expert advice. Finally, I want to thank Orlando Tisot, Bob Dick, and Ministry of Transportation and Highways for their financial support. ix CHAPTER 1 INTRODUCTION In the past few years, the cost of maintenance and rehabilitation of existing coating systems on steel bridges has risen dramatically. This increase can be attributed to stricter environmental constraints and higher safety standards for the workers. In addition, reduced government funding and inefficient maintenance scheduling have contributed to increasing deterioration of these structures. Eventually, the corrosive action can reduce the cross section of the steel member and decrease its load capacity. Due to these problems, a research project between the Ministry of Transportation and Highways of British Columbia and the University of British Columbia was conducted to investigate current rehabilitation methods and incorporate these procedures into a computer application in order to minimize the cost of coating maintenance. The Province of British Columbia owns over 700 structures that are classified as steel bridges. Most of these structures are coated with lead-based alkyds that have a life span ranging from a few years to over 20 years depending on the type of environmental conditions. These structures are subjected to environmental conditions ranging from highly corrosive such as in the coastal regions to less aggressive environments such as the interior regions of British Columbia. The Ministry of Transportation and Highways had to drastically reduce the recoating of steel bridges in the past two years for financial reasons. As a result, some steel structures may have been damaged by corrosion. Furthermore, the longer these maintenance activities are delayed the more the total cost will be. One of the strategies employed by bridge managers is to allow the coating system to deteriorate without implementing any maintenance activities. This option is certainly feasible under specific situations. For example, if the structure is near its expected design life, it is more economical to replace the structure. In most cases, this option will reduce the service life of the structure. The reason for the decreased lifespan is attributed to the I durability of the coating systems. Most coating systems have lifespans that he in the range between several years to approximately 30 years depending on the environmental conditions. However, Hiroshi (1988) has found that the average lifespan of steel bridges is approximately 35 years. Therefore, most structures must require at least one rehabilitation activity during its service life. The service life of the steel bridge is limited by several factors such as fatigue, loading capacity, and corrosion. The first two factors, fatigue and loading capacity, depend on the loading conditions and require either replacement of certain components or the entire structure to maintain service. The third factor, corrosion, can be controlled by preventative maintenance. Application of rehabilitation activities can extend the service life of structure. However, the cost of rehabilitation may sometimes be less economical then replacing the structure. The most economical choice will depend on the costs of these two options and their relative service lives. Therefore, some decision analysis techniques such as life-cycle cost analysis can be used to assist bridge managers in choosing the best strategy for an existing or proposed steel bridge. Several researchers have begun to incorporate life-cycle cost analysis or discounted cash flow methods to minimize the cost of bridge maintenance. Weyers et al (1988) have applied this approach to compare the equivalent uniform annual cost of various rehabilitation activities during the service life of a bridge. Rajagopal and George (1990) have applied this approach to road pavement in order to reduce maintenance cost. In this thesis, a life-cycle cost analysis using equivalent annual cost is developed to compare the cost of three maintenance strategies: spot repair, overcoat, and recoat. Life-cycle cost analysis is a relatively simple approach for minimizing coating maintenance costs. The general objective of this approach is to determine all the costs associated with the corrosion protection of the structure throughout its remaining service life. The total cost for a combination of a particular maintenance strategy is compared to 2 the total cost of another strategy. The strategy which yields the lowest cost is considered to be the optimal maintenance strategy for the specific structure. The basic components required in the life-cycle cost analysis using equivalent annual cost are: 1. Database ~ deterioration functions and maintenance costs 2. Formula for equivalent annual costs 3. Correlation between condition upgrades and rehabilitation activities 4. Constraints ~ condition limits for each activities The most difficult problem associated with this approach is developing a database. Some government bridge branches have programs to collect the necessary information. However, most of these programs are based on the standards from the American Society for Testing and Materials (ASTM). One of these standards, ASTM D610, rates the condition of the coating system according to a visual inspection. As a result, the data will contain significant variations. In addition, some of the newer coating systems may have insufficient data to formulate a deterioration function. To compensate for these inadequacies, estimates based on accelerated weathering tests can be used as a substitute. The basic formula used in the life-cycle cost analysis can be obtained from any basic economics textbook. The equation for equivalent annual cost is: 4 = F 's ( 1 + 0 * - l where F = future cost i= interest rate N= maintenance period A = annuity 3 The basic formula is not sufficient for this analysis. Several key elements have been added to this formula to account for factors such as inflation and bridge characteristics. A detailed description of these alterations will be presented in Chapter 3. In order to simplify the implementation of this approach, a spreadsheet application is developed. The program follows the analysis procedure by first separating the structure into its basic components to simulate the deterioration process more accurately. The user then must enter various financial parameters into the program After all these parameters are entered, the program automatically determines the rehabilitation strategy with the minimum equivalent annual cost. Furthermore, a risk associated with this strategy is also presented to the user. Finally, the program has on-line help features to assist the user. Life-cycle cost analysis is a relatively simple method for comparing different maintenance strategies. Unfortunately, this approach cannot determine the optimal maintenance strategy. Jiang and Sinha (1989) have applied optimization techniques such as linear programming and dynamic programming to minimize maintenance cost. In this thesis, the dynamic programming methodology is applied to find the optimal sequence of maintenance activities for a specific steel bridge. Dynamic programming is an optimization technique used in systems analysis to minimize or maximize the sum of values resulting from a sequence of decisions. In the Bridge Coatings Maintenance Model, the objective is to find the combination of rehabilitation strategies that has the lowest total cost over the service life of the structure. In the Bridge Corrosion Cost Model as described previously, only one particular maintenance strategy is minimized. For example, the most cost effective maintenance strategy is to spot repair at every five year interval. However, in the Bridge Coating Maintenance Model, a combination of these strategies that yields the lowest cost can be determined. For example, the most cost effective maintenance strategy is to spot repair at every two year interval and then overcoat the entire bridge in ten years. 4 To obtain the optimal solution by dynamic programming, the problem must have the following four elements: • organization of the problem, • formulation of the partial optimizations, • constraint, and • solution. The first element, organization of the problem, can be obtained in three steps. These steps are: 1. representation of stages and states, 2. determination of the possible set of decision choices, D n s , and 3. formulation of the stage return function. The second element, formulation of the partial optimizations, can be produced by the cumulative return function, fn(s). fn(s) - min ormax[g(dw,s,n)+fn+i t(dm,s,n)] Dm where Dm = set of decision choices at stage n and state s This function systematically finds the optimal decision path at every state and stage position. The third element, constraints, is applied to the to the framework of the problem. This is accomplished by limiting the number of decision choices at every state level. Finally, the solution of the problem can be obtained by finding the sequence of decisions that lead to the optimal value. Detailed explanations of these elements are given in Chapter 4 of this thesis. The two methods proposed in this thesis are still at the developmental stage. However, these models provide two different analyses options to maintenance engineers for planning purposes. By incorporating these procedures into computer applications, life-5 cycle cost analysis and dynamic prograrriming approach can be incorporated into any rehabilitation program. CHAPTER 2. LITERATURE REVIEW 2.1 Coating Maintenance Maintenance of coatings is important in the visual and physical preservation of steel bridges. Often, rehabihtation of these structures is more difficult than coating a new structure or repairing one that have been completely sandblasted. The problem is mainly caused by the complicated surface preparation of the existing coating. For example, in spot painting only isolated rust spots have to be removed. The contractor must locate these areas and remove the defects without damaging the adjacent coating that is still in good condition. Furthermore, there should be a transition zone between the existing coating and the edges of the blast cleaned areas to increase the mechanical connection between the old and new coatings. This zone, which receives a lower degree of blast cleaning, will improve the appearance of the rehabilitated areas. Choosing the proper rehabihtation method at the most economical time is critical in coating maintenance. Overcoating a bridge before there is significant rusting on the surface can be both uneconomical and detrimental to the existing coating. The thick and heavy buildup of the coating will eventually lead to delamination and cracking. Historically, most of the efforts in coating maintenance have concentrated on the development of new coating systems. These advances in coating technology are very important in coating maintenance; however, optimizing the maintenance schedule can also significantly reduce the cost of rehabilitating a steel bridge. Unfortunately, optimization techniques such as dynamic prograinming and linear programming in coating maintenance are still relatively new and analysis tools that assist the coating maintenance engineer are still at the developmental stages. 7 2.1.1 Repair Considerations The decision to rehabilitate a bridge depends on economical and structural factors. However, other considerations such as appearance or political influences also contribute to the decision process. Some of these factors are: • type of failure, • level of failure, • adhesion, and • coating type. 2.1.1.1 Type of Failure Coating failures are caused by many factors such as incorrect application procedures or incompatibility between the existing coating and the repair coating. Once a problem is detected, a proper repair procedure must be chosen and applied to the damage. Following the repair work, the treated areas should be periodically inspected to analyze the performance of the rehabilitation. Several types of failures are described in the next few paragraphs. Corrosion undercutting or corrosion beneath the coating system is one of the most common contributor to coating failure. This type of failure usually occurs at breaks in the coating system, but can also appear under areas where the coating is intact. This problem is due to a lack of adhesion between the coating and the steel substrate. The corrosive action can be intensified in this type of failure because moisture and salts are allowed to be trapped at these areas. At the intersection between the steel and coating system, the corrosion process forces the two materials away from each other. To decrease the damage caused by undercutting, strong adhesion between the coating and substrate is necessary. Blistering is another common defect that can result in early failure of improper rehabilitation work. Blisters are generally round, hemispherical projections on the surface 8 of the coating. They are sometimes filled with a liquid or a gas. Depending on the adhesion and the pressure in the blister, the size of the blister can vary from a few millimetres to several centimetres. Bhsters can occur at the substrate and coating interface or between the coating layers. The usual cause of this failure is caused by the "penetration of moisture through the coating into areas of poor adhesion" (Munger, 369). Pinpoint rusting is often the most common failure of coating systems. It occurs on both organic and inorganic coatings due to aging. However, this type of failure can also occur if the formulation or application procedure is incorrect. Fortunately, pinpoint rusting is relatively easy to remove if the damage is repaired at an early stage. Delamination is not as common as the previously described types of failures. This failure is caused by inadequate adhesion between coatings. In most cases, delamination occurs when rehabilitation work is being done on the existing coating. The three possible causes of this failure are contamination, chalking, and overcured surfaces. Chalking is "the formation on a pigmented coating of a friable powder evolved from the film itself at or just beneath the surface" (ASTM, 725). This failure is found on most types of coatings and is a major contributor to delamination. Checking of the coating can be described as small breaks on the coating surface that do not penetrate to the steel substrate. This failure occurs as the coating ages and becomes more brittle. The extent of checking is dependent on the formulation of the coating system and the weather conditions. 2.1.1.2 Level of Failure The level of failure is important in determining the type and extent of rehabilitation work that is required. In order to quantify these coating failures, the American Society for Testing and Materials (ASTM) has developed a set of standards to simplify this procedure (see Table 1). However, the ASTM Standards are based on a visual evaluation and the results may vary between various inspectors. Sometimes, even the same inspector will 9 provide different results. Several types of these standards relating to evaluation of existing coating can be found in the ASTM standards. ASTM Standard D610 D660 D661 D662 D3359 D4214 D5043 D5064 D5065 Description Test Methods for Evaluating Degree of Rusting on Painted Steel Surfaces Test Method for Evaluating Degree of Checking of Exterior Paints Test Method for Evaluating Degree of Cracking of Exterior Paints Test Method for Evaluating Degree of Erosion of Exterior Paints Test Method for Measuring Adhesion by Tape Test Test Methods for Evaluating the Degree of Chalking of Exterior Paint Films Test Methods for Field Identification of Coatings Practice for Conducting a Patch Test to Assess Coating Compatibility Guide for Assessing the Condition of Aged Coatings on Steel Surfaces Table 1. ASTM Standards for Coating Systems 2.1.1.3 Adhesion Adequate adhesion between the coating layers and between the steel substrate and the original coating is required for any repair activities. A lack of adhesion will result in early failure and wasted effort. Sometimes, surface preparation or the additional weight of the new coating can reduce the adhesion of the original coating and eventually lead to delamination or blisters. 2.1.1.4 Coating Type The type of coating on an existing bridge will limit the types of coating that can be used to repair the damaged areas. Incompatible coating systems will result in adhesion problems such as delamination and blistering. Sometimes, the existing coating system may be damaged. Often, records are not kept on the type of coating used on the bridge. This can create a problem in choosing a compatible repair system for the existing coating 10 system. One method used to assess the compatibility of the two systems is to conduct a patch test (ASTM D5064 Standard). Here, a small section on the existing coating is cleaned, coated with the new system, and checked for failures. 2.1.2 Maintenance Strategies There are three techniques used in bridge maintenance: • spot cleaning, • overcoating, and • complete recoating. In spot cleaning, only rusted or delaminated areas are removed from the surface and a new coating is applied. Areas which have minor defects will not be removed until they deteriorate to a specific condition. This approach is only applicable for existing coatings that have limited corrosion and adequate adhesion. For upgrading, Kline and Corbett (1991) recommend an existing coating to have less than 10 percent of corroded surface area or rust grade 4 according to ASTM D610. They also recommend that there is satisfactory adhesion (adhesion classification 2B based on ASTM D3359 Standard) between the steel substrate and the existing coating. In addition, adequate adhesion between existing coating layers is necessary to prevent delamination. In overcoating or encapsulation, all defective areas are removed and the entire steel structure is finished with a new coating that is compatible to the existing coating system. This technique can be cost effective for apphcation on existing lead based paints because removal of the lead can be delayed until new methods are developed to contain and dispose the lead contaminated blast abrasives in a safe and economical manner. Along with the same apphcation constraints that govern spot cleaning, several important considerations must also be addressed in this approach. One of the concerns associated with encapsulation is shrinkage during the curing process of the new coating. Coating systems with excessive shrinkage will result in cracking or delamination within the existing 11 coating system. Another concern is the softening of the underlying layer from solvent penetration. This problem can be rninimized by using coatings that have high solids content. In a study on overcoating techniques conducted by Kline and Corbett (1991), the five types of coatings tested performed as well or better on surfaces which had been clean by air blow down than on surfaces which had brush-offblast cleaning (see Table 2). Previously, most experts thought that the higher degree of surface preparation removed more loose rust and, therefore, improves performance. However, this is not always true. In accordance with ASTM D610, it was shown that surfaces cleaned by brush-offblasting (see Table 2) ranged from four to five. For air blow down cleaning, the values ranged from five to seven. This unexpected result "may be attributed to a fracturing and weakening of the old alkyd due to the impact of the abrasives" (Kline and Corbett, 55). As a result of this finding, limited surface preparation should be used instead of the more expensive brush-offblasting for coating systems which have similar characteristics to the ones used in the study. In addition to the increased performance, the expense and health concerns due to removal of lead contaminated abrasives are eliminated. The third strategy, complete recoating, was the method used in the past to maintain bridges. The reasoning for using this method was to allow the coating system to deteriorate until structural damage due to corrosion is imminent. When the condition of the coating system has reached this level, the surface is cleaned and a new coating is applied. Currently, this method is considered to be less cost effective than the first two methods due to the extremely high cost in the containment and disposal of lead contaminated abrasives. 12 2.1.3 Advantage of Shorter Maintenance Periods In addition to lower annual costs, a shorter maintenance period will provide a higher level of service. This fact is illustrated in Figure 1. In Figure la, the coating system is allowed to deteriorate to a condition level of CI before it is rehabilitated. The strategy, displayed in Figure lb, allows the coating system to deteriorate to a lower condition level, C2. The difference, d, between the two maintenance strategies can be calculated by using the following equation: d = average condition a - average condition b 1 average condition = — \f(f)dt P 0 K >K » Figure 1 a average condition a C2 Time (years) t2 Figure 1 b average condition b • t Time (years) Figure 1. Different Maintenance Periods 13 2.1.4 Application Strategies Bridge maintenance engineers in the past have generally coated bridges with one type of coating system. This approach was acceptable because there were a limited number of types of systems available for coating steel bridges. However, nowadays there is a large variety of coating system available. Different elements of steel bridge can be coated with different systems to suit the purpose. Regions of the structure which are subjected to more severe environmental conditions can be protected with an expensive, durable coating system. The regions which corrode at a slower rate can be coated with a less expensive system. The cheaper system will reduce the cost of the rehabilitation but increase the frequency of the maintenance activities. For some types of coating systems, their service lives depend on the coating thickness. This characteristic can be effectively used in coating maintenance. For example, regions that are subjected to more severe conditions can be protected with a thicker coating layer or several layers. 2.2 Coating Systems For Steel Bridges 2.2.1 History Protection of steel bridges started as early as the first steel bridges were built. These early coatings used a red lead/linseed oil primer, red oxide intermediate coat and one red oxide topcoat. These systems were very effective in protecting the steel and also required lrnnimal surface preparation which reduced costs and increased flexibility. Today, lead based coatings are still present in many of the steel bridges. However, the health and environmental problems caused by these coating systems have lead to developments of alternatives such as zinc based systems and other inhibitive or barrier type systems. 14 2.2.2 Coating Systems The three types of coatings used to reduce corrosion of steel bridges are paint, galvanizing, and oxidized steel formed on weathering steel or a combination of these coatings. Due to the difficulty in galvanizing large sections and problems from weathering steel, the industry has generally used paints for protection. Paints or high performance coatings, as some of the newer systems are known, are separated into three categories: the inbibitive primer, the sacrificial primer, and the barrier coat. These categories are based on the mechanisms employed by the coating system to control corrosion. Generally, a combination of these systems can be used, but compatibility problems can occur between certain types of coatings in the system. 2.2.2.1 The Inhibitive Primers The inhibitive primers control corrosion by decreasing the "potential difference between the anode and the cathode and/or increases the electrical resistance across the (corrosive) cell" (Hare, 11). The inhibitive properties of the coating are mainly contributed by the pigment which were traditionally chromium or lead compounds. By the early eighties, these compounds were replaced with pigments which have reduced "toxicological profiles" (Hare, 13). 2.2.2.2 The Sacrificial Primers The sacrificial primer is based on the same principal as sacrificial anodes used to protect ship hulls and pipes. They protect the steel from corrosion by becoming anodic. The zinc in the primer will oxidize or lose electrons to the electrolyte, thereby, preventing oxidation to occur in the steel. However, the steel surface must be free from any contaminants to allow contact between the zinc and the steel. 15 2.2.2.3 The Barrier Coatings The barrier coating prevents the corrosion of the steel substrate by severely limiting the amount of water and oxygen from penetrating. Any water that does reach the steel will have very little ions to allow significant oxidation to occur. An important characteristic of barrier systems is that they perform better with thinner multiple coats rather than thick single or double coats (Hare, 23). Some types of these coatings are vinyl, chlorinated rubbers, and coal tar systems. 2.3 Surface Preparation Surface preparation of existing bridges contributes a significant portion to the high cost of bridge maintenance. In the past, lead-based alkyd bonded to less prepared surfaces with little problem. However, new high performance coating systems require a higher degree of surface preparation for proper adhesion. The cleaner surface quality required by these systems forced the industry to use abrasive blasting procedures instead of hand and power tools. In order to decrease the high costs in the preparation of the surfaces, manufacturers are constantly developing new paint systems that may not last as long as the traditional zinc based systems, but require a lower quality surface that will decrease the present value of the system over their service life. 2.3.1 Hand and Power Tool Cleaning These tools mechanically remove loose rust, loose mill scale, and paint from the surface of the steel substrate. Some of these devices are wire brushes, hand scrappers, grinders, and sanders. These labour intensive methods are also useful in removing heavy rust scale prior to blasting. Needle descaling, one of the most widely used power tooling 16 technique, can be used effectively to remove corrosion at intricate areas such as rivet heads, seams, and weld splatter (Hare, 41). 2.3.2 Solvent Cleaning Solvents are used to remove oil, grease, wax, dirt, and other types of contaminants. Some of these methods are solvents, vapours, emulsions, alkalis, and steam. 2.3.3 Dry Abrasive Blasting This method uses air propelled abrasives such as sand to clean the steel surface of contaminants and paints. The problem associated with this technique is containing the air borne pollutants. To solve this problem, extensive containment apparatuses are necessary in sensitive areas such as over salmon spawning streams and in residential neighbourhoods. The American Society for Testing and Materials (ASTM) and the Steel Structures Painting Council (SSPC) developed a standard for various types of surface preparation. Some of these preparation techniques are shown in Table 2. Cleaning Method solvent cleaning hand tool cleaning power tool cleaning brush-offblast commercial blast near-white metal blast white-metal blast SSPC Standard SSPC-SP-1 SSPC-SP-2 SSPC-SP-3 SSPC-SP-7 SSPC-SP-6 SSPC-SP-10 SSPC-SP-5 Description removes oil, grease, wax, dirt removes loose rust, millscale, and coating removes loose rust, millscale, and coating does not remove tightly adhering mill scale, rust or old coating minimum for most government agency for bridge maintenance, leaves 66% of surface area free of all visible residue 95% free of all visible residue complete removal of all visible residue Table 2. Cleaning Methods 17 2.3.4 Wet Abrasive Blasting This method provides the most acceptable results in terms of meeting both surface preparation requirements and environmental concerns. In wet abrasive blasting, air and water are mixed together with abrasives and sent through a nozzle onto the steel surface. This procedure produces very little pollution to the surrounding environment. One of the major problems with this method is from flash rusting which occurs shortly after blasting. Rust inhibitors such as chromates and phosphates can be added, but these compounds make the technique less cost effective. 2.3.5 Wet Blasting Traditionally, water blasting or hydroblasting, operating at pressures between 5000-20000 psi, was used to remove old paint, rust and chlorides. However, operator fatigue prevented wide use of this technique at the higher pressures. Recently, a new type of high pressure system, which operates at pressures of 35000 pounds per square inch, was developed to solve the problem of operator fatigue. This apparatus solved the problem by reducing the amount of water used during this cleaning procedure. The reduced water flow decreased the force applied to the operator. In addition, this type of surface preparation removes virtually all contaminants such as sulphates from the surface. The absence of an electrolyte prevents corrosion cells from developing without the aid of corrosion inhibitors. Another method has been used to remove sulphates from the steel structure. In the past, water blasting was used; however, only the surface was free of these contaminants. As soon as the contractor finished blasting, the surface was corroded by "flash rusting." The problem was sulphates which were imbedded in the steel rose to the surface, dissolved in the water and formed the electrolyte. To solve this problem, large quantities of water can be used wash the structure and draw the sulphates out of the steel. 18 2.4 Costs The unit cost of the coating system is the most difficult variable to obtain in the Bridge Corrosion Cost Model. Up to now, the contractors only provided a single cost for rehabilitation of the coating system. This cost includes all activities necessary to rehabilitate the bridge. However, some regional managers of the Ministry of Transportation and Highways in British Columbia require the cost of these activities to be separated from each other. The unit cost of the coating system depends on the contractor, material cost, labour cost, equipment costs, productivity rate, the market situation (work available), disposal costs, and surface preparation. Depending on their overhead costs and profit margin, there will always be variations in the unit cost between different contractors. This variability can also be caused by the expertise of the contractor and its workers in their estimation techniques. The second variable, material cost, depends on the availability of the coating system. If the coating system is widely available and supplied by various manufacturers, the cost of the coating system will be generally lower. The third variable, labour cost, is the wages paid to the workers. This cost is related to the productivity rate of the workers. The productivity rate depends on the expertise of the workers and the management skills of the supervisors. Finally, surface preparation depends on the type of coating system used to rehabilitate the steel bridge. Some coating systems require more extensive surface preparation and will have a higher surface preparation cost. Generally, most coating systems will perform better on a surface which was treated with a higher level of surface preparation. 19 CHAPTER 3 BRIDGE CORROSION COST MODEL 3.1 Introduction A computer program has been developed in the framework of this thesis to assist the engineer or other individuals who are involved in the rehabilitation of steel bridges in their decision making process. The program performs a life-cycle cost analysis of a coating system for a specific steel structure. Basically, this approach compares the equivalent annual cost of the three maintenance strategies throughout the design life of the structure. The rehabilitation method that has the lowest equivalent annual cost will be the optimal procedure. This analysis procedure relies mainly on the corrosion and adhesion functions that are supplied by manufacturers, experts, experimental testing and field data of various sources. The program attempts to provide answers to the following questions. • When is the optimal time to rehabilitate an existing coating system for a specific steel bridge? • What is the optimal rehabilitation method for the specific bridge? • What is the estimated equivalent annual cost for the rehabilitation? • What is the probability that the rehabilitation will fail prematurely? 3.2 Overview of Analysis Procedure The analysis procedure is divided into two parts. In the first part of the procedure, the deterioration of the coating system is simulated. In the second part, life-cycle cost analysis using equivalent annual cost is applied to the rehabilitation strategies in order to determine the optimal result. 20 3.3 Simulation of Coating System Deterioration The most critical part of the simulation, which is providing realistic estimates, depends on the accuracy of the corrosion curves. These functions, which show the condition of the coating system at a specific time, can be derived from field data, laboratory weathering test results, or expert estimates (Hare). Due to the lack of an adequate database at the time of developing the tool, the deterioration functions used in the database depends mainly on the estimates from experts in this field. Provisions are made that new data can be easily implemented and updated. Then as more data become available, the results from weathering tests can be correlated to field data and these estimated functions will be updated. The first part of the simulation is to identify various components of the entire structure to provide a more accurate description of the coating condition. The coating system on each component can be individually simulated by a single corrosion and adhesion function. These functions are based on the corrosion performance rating system from the American Society for Testing and Materials (ASTM) D610 and D3359 Standards. The key tables of the two standards are displayed in Table 3 and Table 4. Corrosion Rating 10 9 8 7 6 5 4 3 2 1 0 Description no rust or less than 0.01% rust minute rust, less than 0.03% rust few isolated rust spots, less than 0.1% rust less than 0.3% rust extensive rust spots, less than 1% rust less than 3% rust less than 10% rust approximately 1/6 of surface rusted approximately 1/3 of surface rusted approximately 1/2 of surface rusted approximately 100% of surface rusted Area to be Painted (%) 0 0 0 0 8 18 40 60 100 100 100 Table 3. Corrosion Performance Rating ASTM D610 21 Adhesion Classification 5B 4B 3B 2B IB OB Description smooth edges, no coating is removed small flakes are detached at intersections small flakes are detached at edges and intersections flaking along edges and on parts of the squares flaking in large ribbons and detachment of whole squares flaking and detachment worse than Grade IB Area Removed (%) 0 1-5 6-15 16-35 36-65 >65 Table 4. Adhesion Performance Rating ASTMD3359 The corrosion performance rating system is based on visual inspection; therefore, variations can occur between different surveyors. In addition, visually quantifying the amount of corroded area can be very difficult even for a well-trained surveyor. To reduce the amount of discrepancy in the data collection, a set of photographs showing different corrosion ratings on actual bridge components can be used with schematic representation of the ASTM D610 Standard. Adhesion is also a very important factor governing the condition of the coating system. The procedure described in ASTM D3359 standard is used to determine the level of adhesion in the existing coating system. There are two different methods described in this standard. Only test method B, Cross-Cut Tape Test, is used in the model to determine the level of adhesion. In this test, a series of cuts in a grid pattern is made through the coating to the steel substrate. Next, tape is placed over the grid and is rapidly removed at a constant rate. The percentage of coating removed by the tape determines the adhesion classification of the coating system. Since the field data on coating deterioration on steel bridges in British Columbia are limited to the last four to five years, an alternate method was used to formulate the deterioration functions of the coating system. The database in the Ministry of Transportation and Highways provides the age of the coating system and condition ratings 22 of the structure. Unfortunately, the condition ratings are only available for the last three or four years and is inadequate to formulate deterioration functions for the particular structure. However, by grouping various structures that have the same coating systems and are exposed to similar environmental conditions, a deterioration function can be formulated. In Figure 2, the data for three bridges are plotted together to simulate the deterioration rate of a coating system subjected to similar environmental conditions. i Coating Condition (C) i V\ • \ X X *C* • Bridge #1 X Bridge #2 • Bridge #3 ^^- Deterioration Function n ^ \ D Coating Age (j) Figure 2. Simulation of Deterioration Using Field Data 23 3.4 Optimization of Coating System 3.4.1 Equivalent Annual Cost Method The strategy used in the model to obtain the optimal painting schedule is to minimize the equivalent annual cost of the coating system over the design life of the bridge. The equivalent annual cost method is used to compare alternatives that have unequal lifespans by converting a lump sum into an equivalent annuity (see example below). The basic equation is shown below: A = A(AIF,i,N) = F '-j; (1 + 0 - i where: F = future cost i = interest rate N = maintenance period A = annuity Example: Comparison of Alternatives with Unequal Lives The cost of bridge maintenance depends on the condition of the existing coating. One alternative is overcoating which costs $20,000 at 10 year intervals. Another alternative is to allow the existing coating system to deteriorate completely and recoat the entire structure. This strategy results in a higher cost of $60,000, but the time interval between recoating is 20 years. The question is which alternative is less expensive when the discount rate is 6 percent annually. 24 a) Equivalent annual cost for overcoating: 0.06 Aovercoat = 20000 x 10 = $1517-36 (1+0.06) - 1 b) Equivalent annual cost for recoating: 0.06 Arecnat = 6 0 0 0 0 x on = $ 1631.07 20 _ The implied assumption is that the two maintenance strategies will be repeated consecutively to provide the same length of service. The example shows that in this case, overcoating the bridge is a more cost effective method for bridge maintenance. 3.4.2 Optimization Process The equivalent annual cost method is applied in the model by transforming the future cost of the rehabilitation process into an equivalent annual cost. These costs can be used to compare with the results from different rehabilitation processes. This methodology is explained in the following procedure. 1. At time,y, the condition of the component, category j , is given as Qv (see Figure 3). 2. Using this rating, CH, the approximate percentage of rusted area, ARu(%), and the percentage of area that require rehabilitation APfj(%) can be obtained from Table 3. (e.g. if Cyj2=5; th<mARJ>2(%)=3%, APJ2(%)=1S%) 25 3. The actual area needed to be recoated APu is calculated by using the equation below. APy(%) APU = x area J 100 where: area. = surface area of component i = component number j = time interval (in years) 4. At each time interval, j , the areas, APu, from all of the components, categoryi, are added together. APj is the total area which must be painted at the specific time interval./. APj = Z APj,-eg. at; = 1: AP = AP +AP2 +...+AP 5. At this point, the method of equivalent annual cost can be applied to the total area, areoj, at the time interval, j , which will yield the minimum annual value, EACj. min EACj=AP xCFxcostx -• J J (\ + ir)J - 1 where: cost = unit cost of rehabilitation ($ / unit area) CF = cost factor 26 i 10 0 L \ > \ ^ - i _ C 1 , 1 1 -\_Jci,2 "~\4jC2,2 2 Cij = condit ion o f member i a t time j c a t e g o r y i = component i = component number j = time interval C1j ~~~~- — _ c a t e g o r y ^C2j ^~~~~—~ c a t e g o r y Cij 2 ~^~~~ c a t e g o r y . j Time Figure 3. Illustration of Optimization Procedure Example: Numeric Example of Optimization Procedure A steel bridge, which is situated in a marine environment, was recoated 7 years ago at a cost of $30.00/m2. The inspection team divided the bridge components into three different categories: category j , category2, and category3. The first category, category j , has a corrosion rating of 7 and a surface area of 200m2. The second category, category2, has a corrosion rating of 6 and a surface area of 235m2. The third category, category3, has a corrosion rating of 5 and a surface area of 240m2. Discount rate is 6%. The question is what is the equivalent annual cost at this time interval. 27 a) surface area which requires rehabilitation: i) For category j : Cl,7 = 7 APl 7 (%) = 0% (refer to Table 3) 0% 2 2 AP, 7 = x 200/M = 0/» 1'/ 100% ii) For category2'. cr, „ = 6 2,7 ^ P 2 7 ( % ) = 8% ^P„ „ = - ^ - x 235m2 = 18.8w2 2,7 100% iii) For category3: Q = 5 3,7 18% "7 1 AP = x 240/M = 43.2/w 3,7 100% b) total area to be painted: AP7 =APl7+AP27+AP37 =0+18.8 + 43.2= 62. Om2 c) equivalent annual cost at the seventh year: ir 0.06 EAC = AP xCFxcostx = 62.0 x 1.0 x 30.00 x = $221.59 7 7 7 (l + / > ) 7 - l (1+0.06) - 1 3.4.3 Application to Maintenance Strategies The equivalent annual costs of the three maintenance strategies differ depending on the size of the area to be removed and the area to be painted. The process described previously is only applicable to spot repair maintenance. In spot repair, only the rusted 28 areas require both rust removal and painting activities. For overcoating, the calculation of the equivalent annual cost is similar to those for spot repair, except, the area to be painted is the total surface area of all the components. Finally, the equivalent annual cost for recoating is based on the entire surface area for both surface preparation and coating application. The following equations describe the three maintenance strategies used for this model. For spot repair: ir min EACS • = AP • x (cost_s + cost_ m) x -• J J (l + ? > ) 7 - l where: AP.- = total area to be painted cost__s = unit cost for surface preparation cost_ m = unit cost for coating system For overcoat: min EACO j = (AP • x cost_s+ areax cost_m) ir (\ + ir)J - \ where area= total surface area of entire structure For recoat: min EA CR • = area x (cost_ s + cost_ m) ir (l + ir)J - 1 3.4.4 Inflation The effect of inflation on the unit cost for both surface preparation and coating system application is incorporated into the program. Basically, inflation is accounted for by adding an extra "term" to the previous equations. 29 For spot repair: min EACS.• = AP}- x (cost _s + cost_m) x -• J J (l + ir)J-1 For overcoat: ir(l + ir)J min EACO 7- = (AP • x cost_s+ areax cost_m) -• J J (1 + iry - 1 For recoat: ir(\ + ir)J min EA CR .• = area x (cost_ s + cost_ tri) -• J (l + ir)J - 1 3.4.5 Cost Factors Cost factors are used in the analysis to account for the differences as a result of bridge height, bridge type, and type of maintenance strategy. These cost factors increase the base cost by a factor depending on the extent of extra effort required to rehabiUtate the steel bridge. The cost factors used in analysis are hsted below; however, these factors can be altered by the user. Description 0 to 30 feet over ground 0 to 60 feet over any surface over 60 feet Cost Factor 1.25 1.5 1.75 Table 5. Cost Factors For Bridge Height Description beam/girder lattice/truss Cost Factor 1 2 Table 6. Cost Factors For Bridge Type 30 Description spot repair overcoat recoat Cost Factor 1 1.2 1.35 Table 7. Cost Factors For Maintenance Strategy 3.4.6 Application of Cost Factors to Equivalent Annual Cost Equations For spot repair: ir(\ + iry min EACS • = CFheight x CFstructurex CFstrategyx AP- x (cost _s + cost _m) x -• J J (\ + ir)J-I where: CFheight = cost factor for height of bridge CFstructure= cost factor for type of bridge structure CFstrategyx cost factor for type of maintenance strategy For overcoat: ir(\ + iry min EACO • = CFheightx CFstructurex CFstrategyx (AP,- x cost_s + areax cost_m) = J J (l + ir)J - 1 For recoat: ir(l + ir)J min EA CR 7- = CFheight x CFstructurex CFstrategyx area x (cost_ s + cost_ m) = J (l + jr)j-I 3.4.7 Condition Limits of Maintenance Strategies The optimization of the maintenance strategy is accomplished by detennining the minimum equivalent annual cost of the existing coating system within specific condition intervals. These intervals are governed by two main parameters: corrosion and adhesion. Each maintenance strategy has a certain corrosion limit before the method is considered ineffective or inefficient. For example, overcoating the component that has a corrosion 31 grade below four is not recommended because premature failure will occur. In this condition, the optimal strategy is to allow the existing coating system to deteriorate completely and recoat the whole component. This method increases the time interval and lowers the equivalent annual cost. For this model, the corrosion and adhesion limits, which are based on ASTM D610 and ASTM D3359 standards, respectively, are presented in Table 8. Maintenance Strategy spot repair overcoat recoat Lower Corrosion Limit 6.0 (average condition) 4.0 (average condition) 0.0 (minimum condition) Upper Corrosion Limit 8.0 (average condition) 7.0 (average condition) not applicable Table 8. Condition Limits The corrosion condition limits for spot repair and overcoat are based on the average corrosion condition of the bridge. The maintenance strategy, recoating, is limited by the ininimum corrosion condition of any component of the bridge. In addition to these corrosion limits, rehabilitation will also depend on the adhesion of the existing coating. The suggested limit of adhesion used for spot repair and recoating is 3B (refer to Table 8) according to ASTM D3359 Standards. The suggested limit of adhesion for recoating is 0B. Finally, the strategy which has the lowest equivalent annual cost and falls within these condition limits is considered to be the optimal maintenance strategy. 3.4.8 Probability of Success Analysis Any rehabilitation technique involves a certain level of risk. The probability that the rehabilitated coating system can fail prematurely depends on adhesion and the coating 32 thickness. An existing system with an adhesion rating over 3B (refer to Table 4) and a coating thickness over ten mils can be successfully spot repaired or overcoated with a small chance of premature failure. Trimber and Neal developed a procedure that correlates film thicknesses with adhesion results. The method uses five categories of adhesion levels and three categories of coating thicknesses. Each adhesion level/coating thickness category is assigned a risk level to assist district bridge engineers in choosing the best rehabilitation procedure. A similar approach is adopted into this analysis to give an indication of the risk involved in salvaging an existing coating system. The major difference between the two approaches is the description of the level of risk. Trimber and Neal (1987) uses descriptive indicators such as low risk and high risk to quantify the level of risk. The model of this thesis uses probabilities to describe the risk associated with the rehabilitation. Using probabilities provides a better indicator by more effectively transferring the statistical results from field and laboratory data. 3.4.9 Effectiveness The effectiveness of a rehabilitation strategy provides a non monetary ranking system to choosing the best rehabilitation alternative. It is represented by the area under the maintenance curve as shown in Figure 4. As the area increases within a specific time interval, the damage caused by corrosion will decrease. In addition, a maintenance strategy which has a high effectiveness value will increase the aesthetics of the bridge. The effectiveness can be determined by the following equation. Eff= jf(j)dj J = 0 where: Eff = effectiveness j = time interval k = design life of bridge f(j) = deterioration function of rehabilitation strategy 33 Effectiveness time interval, j Figure 4. Effectiveness 3.4.10 Cost-Effectiveness Ratio The cost-effectiveness ratio (Haas, Turay, and Austin) can be used to compare different maintenance strategies and determine the optimal rehabilitation procedure. This method of comparison is similar to the benefit/cost ratio which was used to compare alternatives. A higher cost-effectiveness ratio will result in a better alternative. The cost effectiveness ratio of a maintenance strategy can be calculated by the following equation: CE = Eff EAC where: CE = cost - effectiveness ratio Eff = effectiveness EAC = equivalent annual cost of maintenance strategy 34 3.5 Problems Associated With Model Formulation A major problem in formulating an accurate Bridge Corrosion Cost Model is the description of the coating condition. This can be attributed to the variability in the deterioration rates of the coating system throughout the structure. An area that accumulates debris and water will corrode at a faster rate than areas which are protected from chlorides and ultra-violet radiation. To account for these variations, the model separates the entire structure into individual components. Each component's coating system is assigned a corrosion and an adhesion function. After each component is analyzed, they are combined to simulate the condition of the bridge. Another problem to be solved is the large amount of variables that affect the life of the coating system. These variables can be caused by natural forces or human influences. Some of these variables are: • environmental conditions ~ de-icing salts, ultra-violet radiation, wind, amount of participation, humidity, and abrasion, • type of coating system, • manufacture expertise, • shape of section, • application procedure, • surface preparation, and • coating thickness. Environmental conditions may vary throughout the life of the coating system. For a coating system which has a short life span, these effects are more significant. For example, if the expected coating life is approximately five years, the bridge might be subjected to abnormal weather conditions for that time period. The coating system will deteriorate at a faster rate than if the structure was exposed to drier weather conditions. 35 Even though the chemical compounds of the coating system are essentially the same, differences in the performance can occur due to quality control problems within the coating manufacturers. In addition, variability between different contractors is also present (e.g. quality control or expertise). In addition, the application procedure can affect the performance of the coating. For example, all types of coatings require an adequate period for proper curing. If the coating is not allowed to cure properly before a topcoat is applied, the lower coating layer will never attain its optimal performance level. Finally, quantifying the condition of the existing coating system can be very comphcated due to the variety of the different kinds of defects. These surface defects can be caused by corrosion, chalking, cracking, lack of adhesion, erosion, blistering, and checking. In the Bridge Corrosion Cost Model, only corrosion defects are used to quantify the amount of surface area that requires rehabilitation in order to simplify the analysis. More importantly, this simplification is justified because eventually all the other surface defects will lead to corrosion. 3.6 Assumptions and Limitations The approach used in this thesis assumes that the rehabilitation process will restore the coating system back to its original condition. This assumption is not correct for spot repair because only the corroded areas are removed and replaced. The rest of the coating is not rehabilitated and will not be at its original condition. In overcoating, the new coating is placed on top of the original coating. This will result in different deterioration rates that are not accounted for in this type of analysis. As a result of these assumptions, the estimates for the equivalent annual cost will be lower than the actual cost for these two strategies. 36 The method of comparison used here assumes that the bridge will be rehabilitated with the same type of coating system or with a system that has similar deterioration characteristics. If different types of coatings are applied throughout the design life of the structure, all the possible variations must be individually evaluated. The maintenance strategy that yields the minimum cost over the design life of the structure will be the optimal solution. Structural considerations are not incorporated into the program. For example, if the remaining life of the bridge is ten years, the program cannot account for this limitation and might suggest recoating the bridge in ten years. In this case, the best strategy is to allow the bridge to deteriorate and replace the structure. The life-cycle cost analysis used in this program is a deterministic approach. This means that probabilistic techniques are currently not incorporated into the analysis procedures. For example, the deterioration curves of the coating systems are determined by linear and nonlinear regression techniques. These functions are assumed to represent the actu3eal deterioration of the coating under a certain set of environmental conditions. However, the change of coating condition from one year to the next cannot be determined exactly due to variations in the environmental conditions during the life of the coating system. This change follows a Markov Chain that applies probabilities to the transitions from one event to the next (Jiang, et al). For example, the condition of a coating system may lower by either one or two ratings in one year. The probability associated with a reduction of one condition rating in one year can be 0.8 or 80%. The probability associated with a reduction of two condition ratings can be 0.2 or 20%. This approach account for all the possible events which may occur due to variations in climate or maintenance procedures. This technique can be applied to the decay model to provide a more realistic simulation; however, all probabilistic techniques require an adequate amount of data to provide useful results. 37 CHAPTER 4 BRIDGE COATING MAINTENANCE MODEL 4.1 Introduction Dynamic programming is an optimization technique that is used in systems analysis to minimize or lnaximize the sum of values resulting from a sequence of decisions. This method drastically reduces the number of computations and comparisons required to obtain the optimal sequence. It reduces the computational effort by systematically eliminating many sets of possible solutions that are shown to be inferior (de NeufiUe, 141). An analysis procedure using dynamic prograinming is proposed to determine the optimal maintenance strategy for the coating system during the service life of the steel structure. Finally, a simplified version of the Bridge Coating Maintenance Model will be analyzed using the proposed technique. 4.2 Solution Strategy Dynamic programming provides the analyst with an approach rather than a formulation to optimize a system. In order to obtain an optimal solution using dynamic programming, the problem must have the following four elements: • organization of the problem, • formula to be used in the partial optimizations, • constraints, and • solution. Each of these elements will be described in further details later. In addition, these elements will be used to formulate the Bridge Coating Maintenance Model. 38 4.3 Problem Description In coating maintenance, the coating condition over the service life of the bridge can be represented by a graph similar to the one shown in Figure 5. • Coating Condition Service Life w l ime, t Figure 5. Coating Condition of a Steel Bridge Over Its Service Life Each increase in the condition of the coating system represents a specific type of rehabilitation activity. The problem is to find the sequence of rehabilitation activities that will minimi 7& the total cost of protecting the steel bridge over its lifetime. 4.4 Organization 4.4.1 Step 1 The first and most important step is to organize the problem into a dynamic prograrmning framework consisting of stages and states. In the Bridge Coating 39 Maintenance Model, the stages are represented by the age of the bridge component or the entire bridge and the states are represented by the condition level of the coating system A representation of the dynamic programming framework is shown in Figure 6. Stages 1 2 3 4 5 6 7 States Initial State Time Figure 6. Bridge Coating Maintenance Model in a Dynamic Programming Framework 4.4.2 Step 2 The second step in organizing the problem into a dynamic programming framework is to determine the possible set of decision choices, Dns, at a particular stage n and state s. Each of these decision set at stage n and state s is composed of one or more individual decision choices which is represented by dns (see Figure 7). The decision 40 10 9 8 7 6 5 4 2 1 0 10 9 8 7 6 5 4 3 2 1 0 Coating Condition Rating Final State choices at each stage n and state s for the Bridge Coating Maintenance Model are tabulated in Table 9. Starting r~~\ State V _ A dns ,-~-~~^^ dns \\dns J\ , Following // States Figure 7. Decision Choices at Stage n and State s Initial State (Initial Condition) 10 9 8 7 6 5 4 3 2 1 0 Following State (Following Condition) 10 10,9 10,9,8 10,9,8,7 10,8,6 10,8,5 10,8 10, 10 10 10 Table 9. Decision Choices at Each State 41 The decision choices hsted in Table 9 require a level of rehabilitation work to maintain or upgrade the condition level of the existing coating system In addition to these choices, the decision set will also include a decision choice of "zero" maintenance. The change in condition level from this decision is dependent on the deterioration function of the coating system. • Coating Condition ^xf(t)=deterioration function p t Coating Age Figure 8. Deterioration Function of a Coating System At a specific coating age, t, the deterioration rate (k) of the coating system is: k _ dfjt) dt 42 Therefore, the change of coating condition (8) from one stage i to the next stage i+1 can be determined by: S=kAt where At = time interval between two consecutive stages 4.4.3 Step 3 The third step in organizing the problem into a dynamic programming framework is to formulate the stage return function. This function, denoted as g(dns, s, n), specifies how the benefits, costs, et cetera are to be calculated. It only depends on the current stage n, state s, and the decision choice dns. For the Bridge Coating Maintenance Model, the stage return function is decretized into a tabular form as shown in Table 10. Starting State i 0 1 2 3 4 5 6 7 8 9 10 Following State i+1 0 c^ o Ci o 1 Co 1 C M 2 3 4 5 C^5 Cf^ 6 C^fi Cfi6 7 8 9 10 where Cj^+^cost of decision choice or maintenance Table 10. Table of Costs for Each Decision Choice dm 43 4.4.4 Step 4 The final step is to formulate the state transformation function. This function, denoted as s', determines the new state if a particular decision, dns, is chosen at a specific stage n and state s. In addition, the state transformation function depends only on the stage n, state s, and decision choice dns. s,= t(dw,s,n) 4.5 Formula The solution of the problem can be obtained by: 1. finding the optimal decision choice for every stage n and state s position 2. and finding the optimal sequence of decisions choices over all stages. The optimal decision at every stage n and state s (or partial optimization) is obtained by the cumulative return function fn(s). fn(s) = min or max[g(dw, s,ri)+fn+it(dns,s,n)] Dns where Dm = set of decision choices at stage n and state s This function is built up sequentially from one stage to the next. This means, the quantity of the cumulative return function for the following stages, fn+it(dns,s,n), must be known before the current function, fn(s), can be quantified. As a result of this process, the optimal quantity for any level or state at the end of a specific number of stages is known. 44 4.6 Constraints The constraints found in dynamic programming are built into the organization of the problem. In most cases, the constraints are applied to the problem by limiting the number of decision choices at a particular stage n and state s. For example, in the Bridge Coating Maintenance Model, the decision choices from one stage to the next stage are constrained by the deterioration rate (see Figure 8) and a limited number of rehabilitation activities (see Table 9). 4.7 Solution The solution of the problem is obtained by finding the optimal sequence of decisions which lead to the optimal value of the cumulative return function, fn(s). As stated previously, the cumulative return function can keep tract of the optimal solution of the previous stages. Therefore, the decision choice which leads to this value can be derived from the cumulative function for the previous stage. This process is repeated for all the previous stages to obtain the optimal solution. 4.8 Example In this example, a simplified version of the Bridge Coating Maintenance problem will be analyzed using the dynamic programming approach as described previously. 4.8.1 Organization of Problem The condition of the coating system is separated into four levels ranging from one to four. Each of these levels represents one state. The stages of the problem represent the time increments in the maintenance schedule. For this problem, each stage represents one year 45 and there is a total of six stages. The following figure shows the layout of this problem in a dynamic programming framework. Stages 1 2 3 4 5 6 4 - r -r -r - r T ~r T 4 States 2 Coating Condition 1 _L J_ -L _L _L _L _L 1 0 1 2 3 4 5 6 Time Figure 9. Organization of Simplified Problem Using Dynamic Programming Approach 4.8.2 Decision Choices The constraints are applied to the problem by limiting the number of decision choices at each stage n and state s. The increase in condition level from one stage to the next is governed by the type of rehabilitation activities applied to the coating system. The decrease in condition rating is governed by the deterioration rate of the coating system. To simplify this problem, a constant deterioration rate is used (see Figure 10). Therefore, the coating will decrease by one condition level after one stage for zero maintenance. The decision sets, D n s , for each state are tabulated in Table 11. 46 • 4 Condition 1 0 \ \ \ 3 Coating Age (years) ^ t Figure 10. Deterioration Function of Coating System Starting State at Beginning of Stage n 4 3 2 1 Following State(s) at End of Stagen 4,3 4,3,2 4,3,1 4 Table 11. Decision Sets, Dm, for Each State s 4.8.3 Stage Return Function g(dns,n,s) The stage return function in this problem represents the cost required to upgrade or maintain the condition of the existing coating system. These costs depend on various variables such as the type of coating system and the level of surface preparation. In this 47 example, the process of obtaining these values is ignored and only a final value is used. Table 12 discretizes the stage return function into a tabular format. Initial State (8) 4 3 2 1 Following State (s+1) 4 1 2 8 10 3 0 1.5 7 N/A 2 N/A 0 1.8 N/A 1 N/A N/A 0 N/A N/A = not applicable Table 12. Stage Return Function Starting State g(dns,n,s) i 10 Following State Figure 11. Diagram of Stage Return Function g(dm,n,s) Applied to Each Decision Set D ns 48 4.8.4 Solution The first step in obtaining the solution is to minimize the cumulative return function fn(s). The process begins from stage six and proceeds one stage at a time until it reaches stage one. Figure 12 summarizes this whole process. Figure 13 provides a detailed evaluation of the cumulative return function at stage 4 and state 3. Stages 1 2 3 4 5 6 4 -K3 -- -K2- "Tr i " - -;;wp ~rtp- - 7F& - w 4 States 1:5 ^6.5 Time ?yo ^ . 5 vo Coating Condition ^10 ^10 "MO ^ 1 2 3 4 5 6 Decision Choice Figure 12. Partial Optimization of Problem 49 f4(3)=1.5 C 3 X — 2 ^ -1.5 ^Q) f5(4)=° — 0 f5(3)=0 ~ " \ 2 ) f (2)=6.5 v _ ^ 5 ya) = min[g(dns,s,n)+fn+1t(dns,s,n)] = mm 2 + 0 1.5 + 0 0 + 6.5 = 1.5 Figure 13. Detailed Evaluation of Cumulative Return Function at Stage 4 and State 3 The second step is to trace the optimal path using the cumulative return function. From Figure 12, it is shown that the optimal value of the problem is fj(4)=3. There are two decision choices available at this point. From the partial optimization performed previously, both decision choices result in this optimal value. This leads to the conclusion that there are two or more possible optimal maintenance pohcies for this problem. As the procedure is repeated for the following stages, several other optimal paths are discovered. Figure 14 displays the various strategies which will minimize the maintenance cost over a specific time period. 50 States Stages Time Coating Condition Optimal Path Decision Choice Figure 14. Optimal Maintenance Strategies for Simplified Bridge Coating Maintenance Problem 4.9 Assumptions and Limitations Several aspects of coating maintenance were not accounted for in the Bridge Coating Maintenance Model. Firstly, this approach does not take into account the probabihstic behavior of the coating deterioration. The model only assigns fixed paths in the dynamic programming framework based on the deterioration function. Figure 11 shows the actual behavior of the deterioration and the assumed process used in the model. 51 Stage 5_ 4 ^ States 3_ 2 -1 _ n \ \ \ \ V \ Actual Deterioration Process Stage 5_ 4 -States 3 -2 , 1 _ n _ s Assumed Deterioration Process deteriration path Figure 15. Possible Deterioration Paths Secondly, this approach does not account for the effects on the deterioration rates caused by different rehabihtation options. This means the deterioration rate of the coating system will not be affected by the previous rehabihtation activity. The deterioration rate will only be based on the current state (condition level). Figure 16 shows the actual deterioration process and the process assumed in the model. 52 Stages 5_ 4 -States 3_ 2_ 1 ^ - — s ^ * — * / 2 "^v:—— Actual Deterioration Process Stages 5_ 4 States 3" 2_ 1 ^ ^ ^ V .^ ^ * ^^ ^ * _^^ * • * * 2 Assumed Deterioration Process _ „ ___. . ._. rehabilitation type 1 r P h a h i l i t a t i n n hmo 9 Figure 16. Comparison of Actual and Assumed Deterioration Processes Thirdly, only one coating parameter (corrosion or adhesion) can be used in the analysis. However, these two important parameters may be combined to create a single rating system Fourth, only one coating system can be analyzed. A combination of paint systems can be analyzed only if each system is manually incorporated into the dynamic programming framework. This approach does not provide the optimal coating combinations, but only provides the optimal sequence of decisions for the specific framework. In addition, possible failures may occur due to incompatibihty between different coating systems. Figure 17 shows a partial dynamic prograinming framework of a combination of two coating systems applied to a single bridge. 53 rehabilitaion choice A with existing systen 5. States 2-c 1 rehabilitaion choice B with existing system rehabilitaion choice C with new system Stages deterioration of new system as a result of rehabilitation choice D rehabilitation choice D with new system deterioration of combined system as a result of rehabilitation choice C Figure 17. Partial Dynamic Programming Framework for Analyzing Multiple Coating Systems Finally, this model does not account for the variations in the environmental conditions caused by changes in weather patterns and industrial pollutants. The solution of this problem is to alter the deterioration function according to the predicted environmental conditions during the service life of the structure. Figure 18 shows an example of different deterioration functions apphed to the dynamic framework of the problem 54 States environmental condition type A environmental condition type B environmental condition type C Coating Condition Figure 18. Dynamic Programming Framework to Account for Changes in Environmental Conditions The approach described in this thesis is only in its developmental stages. Some of the problems mentioned previously should be addressed before this method can be used effectively. In addition, these procedures described in this model can be easily converted into algorithms and incorporated into a computer application. However, some of the solutions described previously to reduce the magnitude of the sources of errors may create some difficulties in the computer programming. Despite the assumptions associated with this approach, dynamic programming will at least provide the bridge coating manager with another analysis technique to minimize rehabilitation costs. 55 CHAPTER 5. CONCLUSIONS AND FUTURE DEVELOPMENTS 5.1 Conclusions On the basis of this investigation, spot repair is the most cost effective method for rehabilitation of a steel bridge. This maintenance strategy is more effective than the others because the corrosion rates are not uniform throughout the entire structure. Therefore, rehabilitating only the corroded areas will require less effort and will reduce the cost of maintenance. In addition to reduced labour and material cost, the disposal and containment costs are also drastically reduced. In spot repair, power tools, instead of the more environmentally hazardous sandblasting, can be used to remove rust and old coatings on the steel surface. This is not possible in overcoating and recoating because power tools are too labour intensive for cleaning large areas. Even though the transportation and setup costs are higher for spot repair due to shorter maintenance intervals, the savings in containment and disposal cost effectively eliminate this disadvantage. The preliminary indication that spot repair is the most cost effective strategy corresponds to the beliefs of other bridge maintenance engineers. However, spot repair is not a cost effective solution if the structure is severely corroded. Generally, the second most cost effective maintenance strategy is to overcoat the existing steel bridge. The savings are contributed by delaying the removal and disposal cost of the lead-based paints. Unfortunately, the performance of the new system is decreased due to bonding between old coating system and the new coating system. In addition, coating failure may occur as a result of coating incompatibility. Recoating is usually the least cost effective rehabilitation strategy. However, if the existing coating system has deteriorated substantially, recoating the entire structure is the only solution. In addition, some coating systems such as zinc-based systems can not be overcoated or spot repaired. 56 All analysis techniques can only provide useful solutions or decisions if the input values are accurate. The two techniques described in this thesis can assist the maintenance engineer in reducing the rehabilitation cost for corrosion protection of steel bridges. However, the information necessary to implement these approaches are currently inadequate for providing accurate results. Therefore, the preliminary analysis was performed using data derived from expert estimates. Proper validation of these techniques will be completed when cost information and coating deterioration functions for the coating systems are available. In conclusion, the most important aspect of coating maintenance is to maintain a good database on rehabilitation costs and deterioration rates of coating systems. This allows the maintenance engineer to apply various techniques in order to optimize the maintenance schedules for coating steel bridges. Without a coordinated effort by all the regional managers in collecting information for the bridge coating database, the optimization techniques described previously will be difficult to implement and may lead to inefficient decisions. 5.2 Future Developments This thesis specifically deals with optimizing the maintenance schedule for one bridge. This is a logical first step in understanding the complex and relatively new field of coating maintenance. However, most government agencies are concerned with the overall cost of mamtaining their entire steel bridge inventory. They want to either minimize the annual cost of all rehabilitation activities or maximize their efforts based on a fixed annual budget. As a result of this thesis work, many techniques developed in the analysis of a single structure can be used to solve the global problem. Some of these techniques are 57 simulation of coating deterioration by individual components and simulation of coating deterioration using Markov Chain. The analysis technique used in the Bridge Corrosion Cost Model to compare the different maintenance alternatives is not a true optimization procedure. However, life-cycle cost analysis was more than adequate for this type of comparison. Unfortunately, life-cycle cost analysis cannot be applied in finding an optimal solution to the global problem. Some researchers in coating maintenance have begun to use optimization techniques such as dynamic programming and linear programming to determine their annual maintenance budget. These techniques should be further investigated and possibly incorporated into a computer application. The deterioration functions used in the analysis are based on estimates by experts. These functions should be replaced by functions which are based on data collected from the field. In addition, the accuracy of this model should be determined by analyzing a rehabilitation project which contains all the necessary information. The equivalent annual cost for the rehabilitation strategy, spot repair, may be somewhat misleading to the user. The extremely low values generated by the program for this strategy can be attributed to the assumption that the rehabilitation will bring the existing coating back to its original condition. As discussed previously, this assumption is incorrect. Therefore, subsequent Bridge Corrosion Cost Models should incorporate approaches which can account for this problem. The dynamic programming approach presented in this thesis is a more accurate analysis technique than the equivalent annual cost approach. This analysis can determine the optimal sequence of rehabilitation activities over the service life of the structure. By addressing the problems mention previously, this approach can be incorporated into a computer application. Therefore, future work should be concentrated in the refinement of this approach. 58 BIBLIOGRAPHY Al-Subhi, KM., D.W. Johnston, and F Farid. "OPBRJDGE: An Integrated Bridge Budget Forcasting and Allocation Module at the State Level", Transportation Research Record 1268. 1990 pp. 95-109. Al-Subhi, KM., D.W. Johnson, andF. Farid. "Resource-Constrained Capital Budgeting Model for Bridge Maintenance, Rehabilitation, and Replacement," Transportation Reserch Record 1276. 1990, pp. 110-117. Aldinger T.I., J. Byrd, and D.E. Abbott. "Problem Solving Forum: Defining Standard Service Environments for Coatings", Journal of Protective Coatings & Linings. Vol. 5, No. 9, 1988, pp. 11-14. Chen, C. and D.W. Johnston. "Forecasting Optimum Bridge Management Decisions and Funding Needs on the Basis of Economic Analysis", Transportation Research Record 1268. 1990, pp. 84-94. de Neufville, Richard. Applied Systems Analysis. McGraw-Hill Inc., New York, 1990. Hare, Clive H. Painting of Steel Bridges and Other Structures. Van Nostrand Reinhold, New York, 1990. Harper, W. V. et al. "Selection of Ideal Maintainance Strategies in a Network-Level Bridge Management System", Transportation Research Record 1268. 1990, pp. 59-67. Hass, Ralph, S. Turay, and H. Austin. Pavement Rehabilitation Life-Cycle Economic Analysis Model Ministry of Transportation of Ontario, Project No. 21180, 1991. Hiroshi, fizuka. "Statistical Study On Life Time of Bridges," University of Niigata, Japan, 1988. Jiang, J. and KC. Sinha. "Dynamic Optimization Model for Bridge Manangement Systems", Transportation Research Record 1211. 1989, pp. 92-100. Kline, E. S. and W.D. Corbett. "Beneficial Procrastination: Delaying Lead Paint Removal Projects by Upgrading the Coating System," Journal of Protective Coatings & Linings. Vol. 9, No.3, pp. 48-56. MarkowM.J. "Life-Cycle Cost Evaluations of the effects of Pavement Maintenance," Transportation Research Record 1276. 1990, pp. 37-47. 59 McNeil, S. and A.M. Finn. "Expert System to Cost Feasible Bridge-Painting Strategies," Transportation Research Record 1145. 1987, pp. 54-60. Munger, C.G. Corrosion Prevention by Protective Coatings. National Association of Corrosion Engineers, Houston, 1984. Munger, C.G. "The Philosophy of Long-Term Coating Protection", Journal of Protective Coatings & Linings. Vol. 3, No. 6, 1986, pp. 24-27. Phull, B.S. and W.W. Kirk. "Monitoring the corrosiveness of Atmospheric Exposure Sites," Journal of Protective Coatings & Linings. Vol. *, No. 10, pp. 152-162. RajagopaL, A.S. and KP. George. "Pavement Maintenance Effectiveness," Transportation Research Record 1276. 1990, pp.62-68. Riggs, J.L., et al., Engineering Economics. McGraw-Hill Ryerson Limited, Toronto, 1986. Smith, L., RP. Calvo, J. Lunardini, D.P. Adley. "Problem Solving Forum: Factors to Consider When Preparing to Spot Clean Structures Containing Lead-Based Paint", Journal of Protective Coatings & Linings. Vol. 8, No. 10, 1991, pp. 11-19. Trimber, KA. and T.W. Neal. "New Procedure for Field Classification of Paint Condition." Journal of Protective Coatings & Linings. Vol.4, No. 10, 1987, pp. 120. Weyers, RE., P.D. Cady, and J.M. Hunter. "Cost-Effective Bridge Maintenance and Rehabilitation Procedures." Transportation Research Record 1184. 1988, pp. 31-40. Windier, F.J. "Conpromising Long-Term Coating Protection of Steel Structures", Journal of Protective Coatings & Linings. Vol. 3, No. 6, pp. 28-36. 1991 Annual Book of ASTM Standards. Volume 06.01: Paints, Related Coatings, and Aromatics, American Society for Testing and Materials, Philadelphia, PA., 1991. 60 APPENDIX A PROGRAM DESCRIPTION AND LAYOUT A.1 Introduction This computer program is developed in a spreadsheet environment. In order to operate this template, Quattro Pro For Windows by Borland International is required. The program is separated into various modules. Each of these modules performs a specific task but is interconnected to each other through cell references and macros. The various modules representing individual parts of the program are Cover, Index, Input Section, Optimization Section, Output Section, Database, Macro Section, Results, and Summary. Only the cover, index, and results will be accessible to the user. The program also has an on-line help feature to assist the user in understanding some of the other features of this program. All data entries are performed by the user through dialogue boxes. The following paragraphs describe in detail each of these sections. A.2 Cover This is the first screen that will appear after the program is started. The user has an option to stop the program by chcking on the Exit button. If the user wishes to know more about the program, there is an Information button. Finally, the user can press the Continue button to begin the analysis procedure. 61 Figure 19. Cover Page and Introduction of Bridge Corrosion Cost Model A.3 Index This module schematically displays the steps required to perform the analysis. Each button performs a different task using macros to display dialogue boxes. A dialogue box provides an easy communication link between the user and the program. There are a total of six buttons shown on the screen. The first four buttons are used in data entry and analysis and the other two buttons terminate the program and provide on-line help. After the user starts the program, the sequence as shown by the layout should be followed to avoid missing any important coating parameters. However, the user can make changes to any of the parameters at anytime by chcking on one of the buttons. Each of these buttons is described in the next few paragraphs. 62 Figure 20. Index Section of Program Environmental and Structural Parameters: After this button is pressed, a dialogue box will be displayed. In this dialogue box, the user has to specify the environmental conditions affecting the structure and its structural characteristics. A detailed explanation of these parameters is shown in the Input Module. Choosing Method of Coating Deterioration Simulation: The program provides two options in simulating the deterioration of the coating system. One of the options allows the user to specify service lives of the coating system for each component of the structure. This will allow the user to analyze a coating system which is not found in this program's database. The second option uses the decay functions from the database within the program. 63 Figure 21. Dialogue Box For the Selection of Coating Simulation Procedure Cost Parameters: A dialogue box containing five coating parameters will be displayed after this button is pressed. The dialogue box contains a help feature to explain some of these parameters. In addition, there is an adjust button which alters the cost factors used in the analysis. A detailed explanation of the coating parameters and the cost factors is shown in the Input Module. Analysis and Results: This button will begin the analysis process and will automatically proceed to the Result Section after the analysis is complete. A.4 Input Module The information entered into the dialogue boxes as previously described are sent to this section of the program This module is inaccessible to the user unless the user alters the display setup by using the menu. This should only be possible if the user is familiar 64 with the spreadsheet application. The Input Module is separated into 6 categories: environmental and structural description, option, coating description, cost parameters, cost factors, and condition limits. Each of these categories contains one or more variables that are dynamically linked to one or more dialogue boxes. In addition, the layout of this section is in the form of a formatted spreadsheet. Environmental and Structural Description: The environmental condition parameter (ec) is separated into four different types: industrial, marine, urban/rural, and desert. These categories are used by the American Society for Testing and Materials and the Structural Steel Painting Committee. Each type of environmental condition is explained below. Environmental Classification marine industrial urban/rural desert Description located near ocean, high levels of chloride located near industries with atmospheric emissions, principle pollutants are oxides such as sulfur and nitrogen main contaminants are automobile emissions dry conditions with small amounts of pollutants Table 13. Environmental Classification The next parameter, type of structure (ts), is separated into two categories: truss/lattice and beam/girder. Generally, a truss or lattice type of structure is more costly to rehabilitate than a simple beam/girder system due to complexity and over spray. The height of the structure also affects the cost of rehabilitation. In the program, there are three height classifications (hs): 0 to 10 metres, 10 to 20 metres and over 30 metres. The cost increases as the height of the structure increases. Deicing salt (deice) which is used 65 to remove ice on the bridge deck dramatically decrease the life expectancy of the coating system. Finally, the last parameter, rw, indicates the purpose of the bridge. This parameter is separated into two different categories: over water and over roadway. The rehabilitation cost is higher if the structure spans over water due to accessibihty problems. 1 Enter information about the structure and the environment - TEST MODE UWWMUWUUU 088611; * V** ttaadarVtater? ¥ HHHaAHAMflMHH UMMMMMMtH Help lAudtinttiui rtifflftimtiftn^ift^ + 3»-* * tym wet* -Example "**•"—(MwwwmnnnnnnnnnnnnnnryvwwMMWiWvvvvvw Figure 22. Dialogue Box For Environmental and Structural Description Coating Description: This section is used to describe the condition of the coating system on each component of the bridge. The parameters in this section are component name (namej), corrosion rating (corrj), adhesion rating (adhj), surface area (areaj), service life (Hfej), coating age (age), coating system (type), and coating thickness (thick). These parameters are provided by the user through dialogue boxes: Compl and Comp2. 66 Enter Coating Parameters For Each Component [If] J3T| PI Figure 23. Dialogue Box for Coating Parameters Using Service Life Enter Coating Parameters For Each Component Figure 24. Dialogue Box for Coating Parameters Using Corrosion Functions in Program Database 67 Cost Parameters: This category contains five variables which provide the necessary financial information to perform the life-cycle cost analysis. These variables are: discount rate {if), inflation rate (infl), unit cost for surface preparation (cost s), unit cost for coating system (costm), and number of years to iterate (number). The unit cost for the coating system includes the cost of the coating system, the labour, and any other costs that are necessary in the apphcation of the coating system The unit cost of surface preparation includes the cost of the blast abrasives, containment apparatus, disposal of the waste materials, and any other costs that are required for surface preparation. Note that the discount rate is not the interest rate charged by financial institutions. It should always be higher than the interest rate. The rate most often used by public agencies in the United States is approximately 10% (de Neufville, 231). The rate of inflation can be incorporated into the discount rate; however, the separation of these two parameters will clarify the analysis procedure and will avoid any possible confusion. The last parameter specifies the length of the analysis. For example, if the design life of the bridge is 30 years then the length of analysis should be 30 years. Figure 25. Dialogue Box for Cost and Financial Information 68 Cost Factors: Cost factors are necessary to account for the variations in the cost of rehabihtation due to bridge height (CFht), structure type (CFstr), and maintenance strategy (CFtype). These factors are apphed to the base cost of the rehabihtation. In addition, there is an Adjust button that allows the user to change the cost factors. This feature was incorporated into the program to allow for variability in the cost of rehabihtation activities between different regions in the Province of British Columbia. However, the user should understand how these factors are apphed to the analysis procedures before any alterations are made. Figure 26. Dialogue Box for Cost Factors 69 Condition Limits: These limits are used in the model to eliminate strategies that are inefficient or will fail prematurely due to a lack of adhesion. Each strategy is given corrosion limits and an adhesion limit. Spot repair is bounded by an upper average corrosion limit (maxs), a lower average corrosion limit (mins), and a rmnimum adhesion limit (minadso). Overcoating has an upper average corrosion limit (max 6), a lower average corrosion limit (mino), and a minimum adhesion limit (minadso). Recoating has only a minimum corrosion limit (minr) and a minimum adhesion limit (minadr). These limits can also be adjusted by the user through a dialogue box which can be displayed by pressing the Adjust button in the Input Module or in the Index Module. Condition Limits S^ftspait !—BUM l+l IT""" • • M I ' l l M I W " " ' ! UOOOUOUWUUWA J m'"""\ f"K$ |3—i waaaat..'' •lfl»»mw3U.iiJoooada & \ M 0 SI t \M '° imwrnfiwYVAWwri? Figure 27. Dialogue Box for Condition Limits 70 A.5 Optimization Module The main purposes of this module are to utilize the information from the input section to simulate the deterioration of the coating system and to calculate the equivalent annual cost of the maintenance strategies at each time interval. This module is separated into several categories: Simulation of Coating Deterioration, Cost Factors, and Output Variables. Simulation of Coating Deterioration: This category simulates the deterioration of the coating system by either using the corrosion and adhesion functions in the Database Section or by using the service lives of the coating system provided by the user. All the decay functions depend on the variable, time interval (/'). As the time interval or age of the coating increases, the condition rating decreases. The first two sections, Corrosion Functions for Each Component Based on Coating Type and Corrosion Functions for Each Component Based on Service Life, are used to simulate the corrosion of the coating system based on the option chosen by the user. The next section, Corrosion Functions for Modeling Coating Deterioration, determines the method of modeling the corrosion rates based on the option. The next step, Corrosion Grade At Time Intervalj, determines the corrosion rating of the coating on each component of the structure. In addition, the minimum corrosion grade of the structure is provided at the time interval,/ The weighted corrosion grade is used to calculate an average corrosion grade for the bridge. The equation for the weighted corrosion grade is: 71 area WCij=Cij — J area where: C2/ = corrosion grade of component* at time interval/ area; = surface area of component/ area - total surface area of structure The average corrosion grade of the structure is: j To determine the area which requires rehabilitation, a correlation between the condition rating and the percentage of area which requires rehabilitation is necessary. The correlation used in this program is based on the deterioration models developed by Fontisdou-Yannis (McNeil and Finn). The procedure used to simulate the corrosion rate is also applied to the adhesion decay of the coating system Cost Factors: This category determines the cost factors which are applied to the base cost of the rehabilitation. The variable, CFht, is the cost factor for the height of the structure. The height is separated into three categories: 0 -10 metres over roadway, 0 -20 metres over any surface, and over 20 metres. The second variable, CFstr, is used to determine the structural type of the bridge. This parameter is divided into two categories: beam/girder (CFstr 1) and truss/lattice (CFstr2). Output Variables: In this category, the equivalent annual costs of the three maintenance strategies are calculated according to the time interval. The five variables in this section are time 72 interval (J), total surface area of structure (area), equivalent annual cost for spot repair (EACS), equivalent annual cost for overcoat (EACO), and equivalent annual cost for recoat (EACR). These variables are sent to the Output Section to determine the minimal value. A.6 Risk Assessment Module In this module, the risk involved with salvaging existing coating systems is determined. The first set of variables is the probabilities associated with a specific adhesion rating and coating thickness category. These variables can be altered by the Adjust button in the Risk Assessment Module or the Index Module. The next sets of variables determine the probability of success for each component based on its adhesion rating and coating thickness (see Appendix B for program documentation). Adjusting Probability of Success Parameter: <18«&* f75 |imiyimifcW iY*Wnim,i1IWffi.,m)rtWf m Li m W f t f f l i i-i 111111111 fio A^VkVk'LlUVlVllllllllWtV *^35j&+J^W£!§L&!SEjt-, HMMMM'V"iiii| s Iwwfl. >WIPIII |m"J'I IJi '" <m [75 5 <t i n »VrtYffi m m 4HHH00W F~ 5 1ST"" J i m~~ WYffliiiiijJUj;|i,ui 55 iJimWiiri'Hwtw J — -^ J m . . a . ^ . ^ J m v m m m m m m •• j m . . . J » . J W > J . . J i m , J , . ^ J I ^ M M M M , j M A ^ m m M M M M M M , . ^ ^ . ^ • j m > IttWI^^dWIMi JfC«ne*l . "^«^«^«^ WHHfflhWfflpHHHHHHWi ...VL-L ..••••• —innn1 Figure 28. Dialogue Box for Probability of Success Parameters 73 A.7 Output Module This module is composed of a number of tables used to determine the minimum equivalent annual cost for each maintenance strategy. The Output Variable Table is a summary of the output from the optimization section. The macro, \I, transfers these variables at each time interval, j , to the Result Table. The macro then copies the equivalent annual costs to the Application of Condition Constraints Table where the condition limits are applied to the three strategies. These formulas are converted to values and placed into the Converted Values Table. These values are then sorted in ascending order and placed into the Sorted Values Table. Finally, the minimum equivalent annual costs for the three strategies are sent to the Decision Table. A.8 Macro Module All the macros used in this program are located in this module. The first two macros, \Z"and \d, are used to create variables for the formatted spreadsheet. The other macro, \I, is used in the program to perform the analysis. A.9 Database The database contains all the corrosion and adhesion functions used in the program. These functions are derived from field data, laboratory data, or expert estimates. A. 10 Results In this section the user can see the results from the analysis. By pressing the first button, Optimal Results for Each Maintenance Strategy, a dialogue box, similar to the one shown in Figure 29, will be displayed. This dialogue box provides the minimum 74 equivalent annual cost of the three maintenance strategies and the corresponding time intervals. These time intervals, which are the age of the coating system, are the optimal time for the implementation of these maintenance strategies. Figure 29. Dialogue Box for Optimal Maintenance Strategies The second button, Probability of Success of Rehabilitated Coating, displays a dialogue box that provides an estimate of the risk involved with the rehabilitation of the existing coating system. A sample of this dialogue box is displayed below. 75 t l l t i i ^ 5 & t jj65 |65 Ire" * ri £m&. Figure 30. Dialogue Box for Probability of Success Results The next four buttons display the graphs of the equivalent annual cost of the three maintenance strategies at each time interval. In addition, these graphs show the condition of the coating system at these time intervals. The results of the analysis can be printed by clicking on the Print buttons 76 Figure 31. Dialogue Box for Results Section A.11 Summary This module contains the final results from the analysis. The tables displayed will be printed after the user presses the Print button in the Index Section. 77 APPENDIX B PROGRAM DOCUMENTATION INPUT SECTION: Environmental and Structure Description: (from Dialog Box Environment) ec = environmental conditions ts = type of structure hs = height of structure deice = Is de-icing used? rw = Is structure over road or water? Industrial Truss above 60 f Yes Over water <input< <input< <input< <input< <input< Option: (from Dialog Box Option) option = Option 1 or Option 2? = Option 1 <input< Coating Description: (from Dialog Boxes Component 1 or Component 2) Component Name: namel = name of component 1 name2 = name of component 2 name3 = name of component 3 name4 = name of component 4 name5 = name of component 5 name6 = name of component 6 name7 = name of component 7 name8 = name of component 8 name9 = name of component 9 Corrosion Rating: corrl corr2 corr3 corr4 corr5 corr6 corr7 corr8 corr9 corrosion rating of component 1 corrosion rating of component 2 corrosion rating of component 2 corrosion rating of component 4 corrosion rating of component 5 corrosion rating of component 6 corrosion rating of component 7 corrosion rating of component 8 corrosion rating of component 9 Adhesion: adhl = adhesion rating of component 1 adh2 = adhesion rating of component 2 adh3 = adhesion rating of component 3 adh4 = adhesion rating of component 4 adh5 = adhesion rating of component 5 adh6 = adhesion rating of component 6 adh7 = adhesion rating of component 7 adh8 = adhesion rating of component 8 adh9 = adhesion rating of component 9 Surface Area: areal = surface area of component 1 area2 = surface area of component 1 area3 = surface area of component 1 area4 = surface area of component 1 area5 = surface area of component 1 area6 = surface area of component 1 area7 = surface area of component 1 area8 = surface area of component 1 area9 = surface area of component 1 bracing 1 bracing2 beaml beam2 beam3 beam4 bearing 1 bearing2 8 8 9 9 8 8 6 6 4 4 5 5 4 4 3 3 65 75 200 200 175 175 30 30 <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< 79 Service Life: lifel Iife2 Iife3 Iife4 Iife5 Iife6 Iife7 Iife8 Iife9 service service service service service service service service service life of coating life of coating life of coating life of coating life of coating life of coating life of coating life of coating life of coating for component 1 for component 2 for component 3 for component 4 for component 5 for component 6 for component 7 for component 8 for component 9 Name of Structure: name = name of structure Coating Age: age = age of the coating system Coating System: type = type of coating system Coating Thickness: thick = coating thickness (mil) 11 years 11 years 15 years 14 years 15 years 14 years 9 years 10 years years = example alkyd 3 years 6 mils <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< Cost Parameters: ir = interest rate infl = inflation rate cost_s = unit cost for surface preparation cost_m = unit cost for materials number = number of years to iterate 6 % <input< 2 % <input< 10 $/unitar <input< 4 $/unitar <input< 40 years <input< Cost Factors: CFhtl = for bridge height (0 - 30' over ground) CFht2 = for bridge height (0 - 60' over any surface) CFht3 = for bridge height (above 60') CFstrl = for type of bridge structure (beam/girder) CFstr2 = for type of bridge structure (lattice/truss) CFtypel = for type of maintenance strategy (spot repair) CFtype2 = for type of maintenance strategy (overcoat) CFtype3 = for type of maintenance strategy (recoat) CFratel = to account for deterioration rate (spot repair) CFrate2 = to account for deterioration rate (overcoat) CFrate3 = to account for deterioration rate (recoat) Condition Limits: max_s min_s max_o min_o min_r minad_ minad r so upper average corrosion limit - spot repair = lower average corrosion limit - spot repair = upper average corrosion limit - overcoat = lower average corrosion limit - overcoat = minimum corrosion limit - recoat = minimum adhesion limit - spot repair and overcoat = minimum adhesion limit - recoat = 1.25 1.5 1.75 1 2 1 1.2 1.35 10 1.2 1 8 6 7 4 0 3 0 <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< 0 <input< <input< <input< <input< <input< <input< <input< 80 OPTIMIZATION SECTION: Simulation of Coating Deterioration: Corrosion Functions for Each Component Based on Coating Type (Option 2): cfctl = @IF(type=,,alkyd,#AND#ec="industrial'#A cfct2 = @IF(type="alkyd'*AND#ec="industriar«A cfct3 = @IF(type="alkyd'*AND#ec="industrial,*A cfct4 = @IF(type="alkyd'«AND#ec="industrial'WA cfct5 = @IF(type="alkyd'WAND#ec="industrial'WA cfct6 = @IF(type="alkyd'«AND#ec="industriar*A cfct7 = @IF(type="alkyd,*AND#ec="industrial'*A cfct8 = @IF(type=,,alkyd'WAND#ec="industriarttA cfct9 = @IF(type="alkyd'WAND#ec="industrial'*A -40 -40 -40 -40 -40 -40 -40 -40 -40 Corrosion Functions for Each Component Based on Service Life (Option 1): cfsM = @IF(life1="","",10-(10/life1)*j) = -26.36364 cfsl2 = @IF(life2="","",10-(10/life2)*j) = -26.36364 cfsl3 = @IF(life3="","",10-(10/life3)*j) = -16.66667 cfsl4 = @IF(life4="","",10-(10/life4)*j) = -18.57143 cfsl5 = @IF(life5="","",10-(10/life5)*j) = -16.66667 cfsl6 = @IF(life6="","",10-(10/life6)*j) = -18.57143 cfsl7 = @IF(life7="","",10-(10/life7)*j) = -34.44444 cfsl8 = @IF(life8="","",10-(10/life8)*j) = -30 cfsl9 = @IF(life9="","",10-(10/life9)*j) Corrosion cfcdl cfcd2 cfcd3 cfcd4 cfcd5 cfcd6 cfcd7 cfcd8 cfcd9 Functions for the = @IF(option-= @IF(option-= @IF(option = @IF(option = @IF(option = @IF(option = @IF(option= = @IF(option= = @IF(option=' Modeling Coating Deterioration: "Option 1",cfsl1,cfctl) Option 1",cfsl2,cfct2) "Option 1",cfsl3,cfct3) "Option 1",cfsl4,cfct4) "Option 1",cfsl5,cfct5) "Option 1",cfsl6,cfct6) Option 1",cfsl7,cfct7) "Option 1",cfsl8,cfct8) Option 1",cfsl9,cfct9) Corrosion Grade At Time Interval j : C1j = @IF(life1="","",@ROUND(cfcd1,0)) C2j = @IF(life2="","",@ROUND(cfcd2,0)) C3j = @IF(life3="","",@ROUND(cfcd3,0)) C4j = @IF(life4="","",@ROUND(cfcd4,0)) C5j = @IF(life5="","",@ROUND(cfcd5,0)) C6j = @IF(life6="","",@ROUND(cfcd6,0)) C7j = @IF(life7="","",@ROUND(cfcd7,0)) C8j = @IF(life8="","",@ROUND(cfcd8,0)) C9j = @IF(life9="",'"',@ROUND(cfcd9,0)) -26.36364 -26.36364 -16.66667 -18.57143 -16.66667 -18.57143 -34.44444 -30 -26 -26 -17 -19 -17 -19 -34 -30 Corrosion Grade At Time Interval j (For Minimum Corrosion Grade): C1ja C2ja C3ja C4ja C5ja C6ja C7ja C8ja C9ja @IF(life1=" @IF(life2=" @IF(life3=" @IF(life4=" @IF(life5=" @IF(life6=" @IF(life7=" @IF(life8=" @IF(life9=" \10,C1j) •,10,C2j) M0.C3J) •,10,C4j) M0,C5j) ',10,C6j) ',10,C7j) ,10,C8j) ',10,091) Minimum Corrosion Grade: Cmin = @MIN(F49..F57) -26 -26 -17 -19 -17 -19 -34 -30 10 -34 <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< 81 Weighted Corrosion Grade: WC1j WC2j WC3j WC4j WC5j WC6j WC7j WC8j WC9j = = = = = = = = = C1j*area1/area C2j*area2/area C3j*area3/area C4j*area4/area C5j*area5/area C6j*area6/area C7j*area7/area C8j*area8/area C9j*area9/area Average Corrosion Grade: Cavg = Rusted Area AR1j% AR2j% AR3j% AR4j% AR5j% AR6j% AR7j% AR8j% AR9j% = = = = = = = = = Rusted Area: AR1j AR2j AR3j AR4j AR5j AR6j AR7j AR8j AR9j = = = = = = = = = @SUM(F62..F70) {%)• @IF(life1="","",@VLOOKUP(@IF(C1j<0,0, @IF(life2="","",@VLOOKUP(@IF(C2j<0,0, @IF(life3="","",@VLOOKUP(@IF(C3j<0,0, @IF(life4="","",@VLOOKUP(@IF(C4j<0,0, @IF(life5="","",@VLOOKUP(@iF(C5j<0,0, @IF(life6="","",@VLOOKUP(@IF(C6j<0,0, @IF(life7="","",@VLOOKUP(@IF(C7j<0,0, @IF(life8="","",@VLOOKUP(@IF(C8j<0,0, @IF(life9="","",@VLOOKUP(@IF(C9j<0,0, area1*AR1j%/100 area2*AR2j%/100 area3*AR3j%/100 area4*AR4j%/100 area5*AR5j%/100 area6*AR6j%/100 area7*AR7j%/100 area8*AR8j%/100 area9*AR9j%/100 Total Rusted Area: ARj = @SUM(D86..D94) Area to be Painted (%): AP1j% AP2j% AP3j% AP4j% AP5j% AP6j% AP7j% AP8j% AP9j% = = = = = = = = = @IF(life1="","",@VLOOKUP(@IF(C1j<0,0, @IF(life2="","",@VLOOKUP(@IF(C2j<0,0, @IF(life3="","",@VLOOKUP(@IF(C3j<0,0, @IF(life4="","",@VLOOKUP(@IF(C4j<0,0, @IF(life5="","",@VLOOKUP(@IF(C5j<0,0, @IF(life6=,,","",@VLOOKUP(@IF(C6j<0,0, @IF(life7="","",@VLOOKUP(@IF(C7j<0,0, @IF(life8="","",@VLOOKUP(@IF(C8j<0,0, @IF(life9="","",@VLOOKUP(@IF(C9j<0,0, Area to be Painted: AP1j AP2j AP3j AP4j AP5j AP6j AP7j AP8j AP9j = = = = = = = = = area1*AP1j%/100 area2*AP2j%/100 area3*AP3j%/100 area4*AP4j%/100 area5*AP5j%/100 area6*AP6j%/100 area7*AP7j%/100 area8*AP8j%/100 area9*AP9j%/100 Total Area to be Painted: = = = = = = = = = ~ = = = = = = = = — = = = = = = = = = = = = = = = = = = ~ = = = = = = = = = -1.778947 -2.052632 -3.578947 -4 -3.131579 -3.5 -1.073684 -0.947368 0 -20.06316 100 % 100 % 100 % 100 % 100 % 100 % 100 % 100 % % 65 unit 75 unit 200 unit 200 unit 175 unit 175 unit 30 unit 30 unit 0 unit 950 unit 100 % 100 % 100 % 100 % 100 % 100 % 100 % 100 % % 65 unit 75 unit 200 unit 200 unit 175 unit 175 unit 30 unit 30 unit 0 unit area area area area area area area area area area area area area area area area area area area <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< 82 APj = @SUM(F110..F118) 950 unit area <calc< Adhesion Functions for Each Component Based on Coatii afctl afct2 afct3 afct4 afct5 afct6 afct7 afct8 afct9 = = = = = = = = = @IF(type="alkyd'*AND#ec="industrial'*A @IF(type="alkyd,*AND#ec="industrial'WA @IF(type="alkyd'V!IAND#ec="industrial,#A @IF(type="alkyd'*AND#ec="industrial'*A @IF(type="alkyd'*AND#ec="industrial,WA @IF(type="alkyd'*AND#ec="industrial,*A @IF(type="alkyd'«AND#ec="industrial'*A @IF(type="alkyd'WAND#ec="industrial'V!IA @IF(type="alkyd,*^ND#ec="industrial'*A i g l = = = = = = = = ™ Type (Option2): -20 -20 -20 -20 -20 -20 -20 -20 -20 Adhesion Grade for Each Component Based on Service Life (Option 1): afsll afsl2 afsl3 afsl4 afsl5 afsl6 afsl7 afsl8 afsl9 = = = = = = = = = @IF(life1="","",5-(5/life1)*j) @IF(life2="","",5-(5/life2)*j) @IF(life3="","",5-(5/life3)*j) @IF(life4="","",5-(5/life4)*j) @IF(life5="","",5-(5/life5)*j) @IF(life6="","",5-(5/life6)*j) @IF(life7="","",5-(5/life7)*j) @IF(life8="","",5-(5/life8)*j) @IF(life9="","",5-(5/life9)*j) Adhesion Functions for Modeling Coating Deterioration: afcdl afcd2 afcd3 afcd4 afcd5 afcd6 afcd7 afcd8 afcd9 Adhesion AD1j AD2j AD3j AD4j AD5j AD6j AD7j AD8j AD9j Adhesion AD1ja AD2ja AD3ja AD4ja AD5ja AD6ja AD7ja AD8ja AD9ja = = = = = = = = = @IF(option="Option 1 ",af si 1,afctl) @IF(option="Option 1 ",afsl2,afct2) @IF(option="Option 1 ",afsl3,afct3) @IF(option="Option 1 ",afsl4,afct4) @IF(option="Option 1 ",afsl5,afct5) @IF(option="Option 1 ",afsl6,afct6) @IF(option="Option 1 M,afsl7,afct7) @IF(option="Option 1 ",afsl8,afct8) @IF(option="Option 1 ",afsl9,afct9) Grade At Time Interval j : = = = = = = = = = @IF(life1="","",@ROUND(afcd1,0)) @IF(life2="",'",,@ROUND(afcd2,0)) @IF(life3="","",@ROUND(afcd3,0)) @IF(life4="","",@ROUND(afcd4,0)) @IF(life5="","",@ROUND(afcd5,0)) @IF(life6="","",@ROUND(afcd6,0)) @IF(life7="","",@ROUND(afcd7,0)) @IF(life8="","",@ROUND(afcd8,0)) @IF(life9="","",@ROUND(afcd9,0)) s = = = = = = = = = = = = = = = = = = = = = = = = = = -13.18182 -13.18182 -8.333333 -9.285714 -8.333333 -9.285714 -17.22222 -15 -13.18182 -13.18182 -8.333333 -9.285714 -8.333333 -9.285714 -17.22222 -15 -13 -13 -8 -9 -8 -9 -17 -15 Grade At Time Interval j (For Minimum Adhesion Grade): = = = = = = = = = @IF(life1="",5,AD1j) @IF(life2="",5,AD2j) @IF(life3="",5,AD3j) @IF(life4="",5,AD4j) @IF(life5="",5,AD5j) @IF(life6="",5,AD6j) @IF(life7="",5,AD7j) @IF(life8="",5,AD8j) @IF(life9="",5,AD9j) = = = = = = = = = -13 -13 -8 -9 -8 -9 -17 -15 5 <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< Minimum Adhesion Grade: ADmin = @MIN(F167..F175) -17 <calc< Weighted Adhesion Grade: 83 WAD1J = AD1j*area1/area WAD2J = AD2j*area2/area WAD3J = AD3j*area3/area WAD4J = AD4j*area4/area WAD5J = AD5j*area5/area WAD6J = AD6j*area6/area WAD7J = AD7j*area7/area WAD8J = AD8j*area8/area WAD9J = AD9j*area9/area Average Adhesion Grade: ADavg = @SUM(F180..F188) Cost Factors: CFht = @IF(hs="0-30feet",CFht1,@IF(hs="30-CFstr = @IF(ts="Beam/Girder",CFstr1,CFstr2) Output Variables: j = time interval Total Surface Area of Structure: area = areal +area2+area3+area4+area5+area6+ •0.889474 •1.026316 •1.684211 •1.894737 •1.473684 •1.657895 •0.536842 •0.473684 0 •9.636842 1.75 2 <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< 40 years <input< 950 unit area <calc< Equivalent Annual Cost for Spot Repair: EACS = APj*(cost_m+cost_s)*((ir/100)*(1+(ir/100)) Equivalent Annual Cost for Overcoat: EACO = (APj*cost_s+area*cost_m)*((ir/100)*(1+(ir/ Equivalent Annual Cost for Recoat: E A C R = area*(cost_s+cost_m)*((ir/100)*(1+(ir/100) = 30937.84 $ <calc< 4455.05 $ <calc< = 4176.609 $ <calc< 84 Risk Assessment In this section, the probability of success in salvaging an existing coating system is asse Risk Assessment: Risk Designations (probability of success): from Dialog Box # rdnl = Adhesion = 5 & Thickness < 10 mils = rdn2 = Adhesion = 5 & Thickness 10-20 mils = rdn3 = Adhesion = 5 & Thickness > 20 mils = rdn4 = Adhesion = 4 & Thickness < 10 mils = rdn5 = Adhesion = 4 & Thickness 10-20 mils = rdn6 = Adhesion = 4 & Thickness > 20 mils = rdn7 = Adhesion = 3 & Thickness < 10 mils = rdn8 = Adhesion = 3 & Thickness 10-20 mils = rdn9 = Adhesion = 3 & Thickness > 20 mils = rdn10 = Adhesion = 2 & Thickness < 10 mils = rdnl 1 = Adhesion = 2 & Thickness 10-20 mils = rdn12 = Adhesion = 2 & Thickness > 20 mils = rdn13 = Adhesion = 1 & Thickness < 10 mils = rdn14 = Adhesion = 1 & Thickness 10-20 mils = rdn15 = Adhesion = 1 & Thickness > 20 mils = rdn16 = Adhesion = 0 & Thickness < 10 mils = rdn17 = Adhesion = 0 & Thickness 10-20 mils = rdn18 = Adhesion = 0 & Thickness > 20 mils = For Component 1: d - 1 d - 2 d - 3 d - 4 d - 5 d - 6 d - 7 d - 8 d - 9 d-10 d-11 d-12 d-13 d-14 d-15 d-16 d-17 d-18 riskl @IF(adh1; @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1 = @IF(adh1= @IF(adh1 = @IF(adh1 = @IF(adh1 = For Component 2: c2-1 c2-2 c2-3 c2-4 c2-5 c2-6 c2-7 c2-8 c2-9 C2-10 C2-11 C2-12 @IF(adh2= @IF(adh2= @IF(adh2= @IF(adh2= @IF(adh2= @IF(adh2= @IF(adh2= @IF(adh2= @IF(adh2= @IF(adh2= @IF(adh2= @IF(adh2= =5 #AND# thick<10,rdn1,0) 5 #AND# thick>=10 #AND# thic 5 #AND# thick>20,rdn3,0) 4 #AND# thick<10,rdn4,0) •4 #AND# thick>=10 #AND# thic 4 #AND# thick>20,rdn6,0) 3 #AND# thick<10,rdn7,0) 3 #AND# thick>=10 #AND# thic •• 3 #AND# thick>20,rdn9,0) =2#AND#thick<10,rdn10,0) •2 #AND# thick>=10 #AND# thic = •2 #AND# thick>20,rdn12,0) =1#AND#thick<10,rdn13,0) •1 #AND#thick>=10#AND#thic = :1 #AND#thick>20,rdn15,0) =0 #AND# thick<10,rdn16,0) 0 #AND# thick>=10 #AND# thic = 0 #AND# thick>20,rdn18,0) !"","",@SUM(D27..D44)) =5#AND#thick<10,rdn1,0) =5 #AND# thick>=10 #AND# thic •• =5#AND#thick>20,rdn3,0) •4 #AND# thick<10,rdn4,0) =4 #AND# thick>=10 #AND# thic •• •4 #AND# thick>20,rdn6,0) 3^ #AND# thick<10,rdn7,0) •3 #AND# thick>=10 #AND# thic ' 3#AND#thick>20,rdn9,0) 2 #AND# thick<10,rdn10,0) 2 #AND# thick>=10 #AND# thic = 2 #AND# thick>20,rdn12,0) 75 % 85 % 100 % 60 % 75 % 85 % 55 % 65 % 75 % 35 % 45 % 55 % 10 % 20 % 25 % 0 % 0 % 0 % 0 % 0 % 0 % 60 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 60 % 0 % 0 % 0 % 60 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <input< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< 85 c2-13 = @IF(adh2=1#AND#thick<10,rdn13,0) c2-14 = @IF(adh2=1*AND#thick>=10#AND#thic^ c2-15 = @IF(adh2=1#AND#thick>20,rdn15,0) C2-16 = @IF(adh2=0#AND#thick<10,rdn16,0) C2-17 = @IF(adh2=0#AND#thick>=10#AND#thic> c2-18 = @IF(adh2=0#AND#thick>20,rdn18,0) risk2 = @IF(adh2="","",@SUM(D48..D65)) For Component 3: c3-1 = @IF(adh3=5#AND#thick<10,rdn1,0) c3-2 = @IF(adh3=5#AND#thick>=10#AND#thic' c3-3 = @IF(adh3=5 #AND# thick>20,rdn3,0) c3-4 = @IF(adh3=4#AND#thick<10,rdn4,0) c3-5 = @IF(adh3=4*AND#thick>=10#AND#thic = c3-6 = @IF(adh3=4 #AND# thick>20,rdn6,0) c3-7 = @IF(adh3=3#AND#thick<10,rdn7,0) c3-8 = @IF(adh3=3#AND#thick>=10#AND#thic = c3-9 = @IF(adh3=3 #AND# thick>20,rdn9,0) c3-10 = @IF(adh3=2#AND#thick<10,rdn10,0) C3-11 = @IF(adh3=2#AND#thick>=10*AND#thic = C3-12 = @IF(adh3=2#AND#thick>20,rdn12,0) C3-13 = @IF(adh3=1#AND#thick<10,rdn13,0) c3-14 = @IF(adh3=1#AND#thick>=10#AND#thic = c3-15 = @IF(adh3=1#AND#thick>20,rdn15,0) c3-16 = @IF(adh3=0#AND#thick<10,rdn16,0) c3-17 = @IF(adh3=0#AND#thick>=10#AND#thic = C3-18 = @IF(adh3=0#AND#thick>20,rdn18,0) risk3 = @IF(adh3="","",@SUM(D69..D86)) For Component 4: c4-1 = @IF(adh4=5#AND#thick<10,rdn1,0) c4-2 = @IF(adh4=5#AND#thick>=10#AND#thic = c4-3 = @IF(adh4=5 #AND# thick>20,rdn3,0) C4-4 = @IF(adh4=4#AND#thick<10,rdn4,0) c4-5 = @IF(adh4=4#AND#thick>=10MND#thic = c4-6 = @IF(adh4=4 #AND# thick>20,rdn6,0) c4-7 = @IF(adh4=3#AND#thick<10,rdn7,0) c4-8 = @IF(adh4=3#AND#thick>=10#AND#thic = c4-9 = @IF(adh4=3#AND#thick>20,rdn9,0) C4-10 = @IF(adh4=2#AND#thick<10,rdn10,0) c4-11 = @IF(adh4=2#AND#thick>=10#AND#thic = C4-12 = @IF(adh4=2#AND#thick>20,rdn12,0) c4-13 = @IF(adh4=1#AND#thick<10,rdn13,0) c4-14 = @IF(adh4=1#AND#thick>=10*AND#thic = c4-15 = @IF(adh4=1#AND#thick>20,rdn15,0) C4-16 = @IF(adh4=0#AND#thick<10,rdn16,0) c4-17 = @IF(adh4=0#AND#thick>=10#AND#thic = c4-18 = @IF(adh4=0#AND#thick>20,rdn18,0) risk4 = @IF(adh1="","",@SUM(D90..D107)) For Component 5: c5-1 = @IF(adh5=5#AND#thick<10,rdn1,0) c5-2 = @IF(adh5=5#AND#thick>=10#AND#thic = c5-3 = @IF(adh5=5#AND#thick>20,rdn3,0) c5-4 = @IF(adh5=4#AND#thick<10,rdn4,0) c5-5 = @IF(adh5=4#AND#thick>=10#AND#thic = c5-6 = @IF(adh5=4 #AND# thick>20,rdn6,0) c5-7 = @IF(adh5=3#AND#thick<10,rdn7,0) c5-8 = @IF(adh5=3#AND#thick>=10#AND#thic = c5-9 = @IF(adh5=3 #AND# thick>20,rdn9,0) 0 % 0 % 0 % 0 % 0 % 0 % 60 % 75 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 75 % 75 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 75 % 0 % 0 % 0 % 60 % 0 % 0 % 0 % 0 % 0 % <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< 86 c5-10 = @IF(adh5=2#AND#thick<10,rdn10,0) C5-11 = @IF(adh5=2#AND#thick>=10#AND#thic> c5-12 = @IF(adh5=2#AND#thick>20,rdn12,0) c5-13 = @IF(adh5=1#AND#thick<10,rdn13,0) c5-14 = @IF(adh5=1#AND#thick>=10#AND#thic: 05-15 = @IF(adh5=1#AND#thick>20,rdn15,0) C5-16 = @IF(adh5=0#AND#thick<10,rdn16,0) C5-17 = @IF(adh5=0#AND#thick>=10#AND#thic' c5-18 = @IF(adh5=0#AND#thick>20,rdn18,0) risk5 = @IF(adh5="","",@SUM(D111..D128)) For Component 6: c6-1 = @IF(adh6=5#AND#thick<10,rdn1,0) c6-2 = @IF(adh6=5#AND#thick>=10#AND#thic-c6-3 = @IF(adh6=5#AND#thick>20,rdn3,0) c6-4 = @IF(adh6=4#AND#thick<10,rdn4,0) c6-5 = @IF(adh6=4#AND#thick>=10#AND#thic = c6-6 = @IF(adh6=4#AND#thick>20,rdn6,0) c6-7 = @IF(adh6=3#AND#thick<10,rdn7,0) c6-8 = @IF(adh6=3#AND#thick>=10#AND#thic = c6-9 = @IF(adh6=3 #AND# thick>20,rdn9,0) C6-10 = @IF(adh6=2#AND#thick<10,rdn10,0) C6-11 = @IF(adh6=2#AND#thick>=10#AND#thic = C6-12 = @IF(adh6=2#AND#thick>20,rdn12,0) c6-13 = @IF(adh6=1#AND#thick<10,rdn13,0) c6-14 = @IF(adh6=1 #AND# thick>=10 #AND# thic = C6-15 = @IF(adh6=1#AND#thick>20,rdn15,0) c6-16 = @IF(adh6=0#AND#thick<10,rdn16,0) c6-17 = @IF(adh6=0#AND#thick>=10#AND#thic = c6-18 = @IF(adh6=0#AND#thick>20,rdn18,0) risk6 = @IF(adh6="","",@SUM(D132..D149)) For Component 7: c7-1 = @IF(adh7=5#AND#thick<10,rdn1,0) c7-2 = @IF(adh7=5#AND#thick>=10#AND#thic = c7-3 = @IF(adh7=5#AND#thick>20,rdn3,0) c7-4 = @IF(adh7=4#AND#thick<10,rdn4,0) c7-5 = @IF(adh7=4#AND#thick>=10#AND#thic = c7-6 = @IF(adh7=4 #AND# thick>20,rdn6,0) c7-7 = @IF(adh7=3#AND#thick<10,rdn7,0) c7-8 = @IF(adh7=3#AND#thick>=10#AND#thic = c7-9 = @IF(adh7=3 #AND# thick>20,rdn9,0) c7-10 = @IF(adh7=2#AND#thick<10,rdn10,0) c7-11 = @IF(adh7=2#AND#thick>=10#AND#thic = c7-12 = @IF(adh7=2#AND#thick>20,rdn12,0) c7-13 = @IF(adh7=1#AND#thick<10,rdn13,0) C7-14 = @IF(adh7=1#AND#thick>=10#AND#thic = c7-15 = @IF(adh7=1#AND#thick>20,rdn15,0) c7-16 = @IF(adh7=0#AND#thick<10,rdn16,0) c7-17 = @IF(adh7=0#AND#thick>=10#AND#thic = c7-18 = @IF(adh7=0#AND#thick>20,rdn18,0) risk7 = @IF(adh7="","",@SUM(D153..D170)) For Component 8: c8-1 = @IF(adh8=5#AND#thick<10,rdn1,0) c8-2 = @IF(adh8=5#AND#thick>=10#AND#thic = c8-3 = @IF(adh8=5#AND#thick>20,rdn3,0) c8-4 = @IF(adh8=4#AND#thick<10,rdn4,0) c8-5 = @IF(adh8=4*AND#thick>=10#AND#thic = c8-6 = @IF(adh8=4 #AND# thick>20,rdn6,0) 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 60 % 0 % 0 % 0 % 60 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 60 % 0 % 0 % 0 % 0 % 0 % 0 % 55 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 55 % 0 % 0 % 0 % 0 % 0 % 0 % <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< 87 c8-7 = @IF(adh8=3#AND#thick<10,rdn7,0) c8-8 = @IF(adh8=3#AND#thick>=10#AND#thic c8-9 = @IF(adh8=3 #AND# thick>20,rdn9,0) c8-10 = @IF(adh8=2#AND#thick<10,rdn10,0) c8-11 = @IF(adh8=2#AND#thick>=10#AND#thic c8-12 = @IF(adh8=2#AND#thick>20,rdn12,0) c8-13 = @IF(adh8=1#AND#thick<10,rdn13,0) C8-14 = @IF(adh8=1#AND#thick>=10#AND#thic c8-15 = @IF(adh8=1#AND#thick>20,rdn15,0) c8-16 = @IF(adh8=0#AND#thick<10,rdn16,0) c8-17 = @IF(adh8=0#AND#thick>=10#AND#thic c8-18 = @IF(adh8=0#AND#thick>20,rdn18,0) risk8 = @IF(adh8="","",@SUM(D174..D191)) For Component 9: c9-1 = @IF(adh9=5#AND#thick<10,rdn1,0) c9-2 = @IF(adh9=5#AND#thick>=10#AND#thic c9-3 = @IF(adh9=5 #AND# thick>20,rdn3,0) c9-4 = @IF(adh9=4#AND#thick<10,rdn4,0) c9-5 = @IF(adh9=4#AND#thick>=10#AND#thic c9-6 = @IF(adh9=4#AND#thick>20,rdn6,0) c9-7 = @IF(adh9=3#AND#thick<10,rdn7,0) c9-8 = @IF(adh9=3*AND#thick>=10#AND#thic c9-9 = @IF(adh9=3 #AND# thick>20,rdn9,0) c9-10 = @IF(adh9=2#AND#thick<10,rdn10,0) c9-11 = @IF(adh9=2#AND#thick>=10#AND#thic c9-12 = @IF(adh9=2#AND#thick>20,rdn12,0) c9-13 = @IF(adh9=1#AND#thick<10,rdn13,0) C9-14 = @IF(adh9=1#AND#thick>=10#AND#thic C9-15 = @IF(adh9=1#AND#thick>20,rdn15,0) c9-16 = @IF(adh9=0#AND#thick<10,rdn16,0) c9-17 = @IF(adh9=0#AND#thick>=10#AND#thic c9-18 = @IF(adh9=0#AND#thick>20,rdn18,0) risk9 = @IF(adh9="","",@SUM(D195..D212)) 55 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 55 % <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % 0 % % <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< <calc< Macro Section Macro Name Keystrokes ~/bnc{?}~ {Left 1} {PutCell =} {Right 2} {PutCell "Please enter units:'} {?}-{Right 1} {PutCell "<input<'} {Down 1XLeft6}~ \d -{Right 2} /bnc{?}~ {Left 1} {PutCell =} {Left} {EditCopy} {Right 2} {EditPaste} {EditKHomeKDelete}+~ {Right 1} {PutCell "Please enter units:'} {?}-{Right 1} {PutCell "<calc<*} {Down 1}{Left6} \l {; Iteration for Results Table} {SelectBlock OUTPUT:G5..CA15} {EditClear} {FOR COUNTER1,1,NUMBER,1,LOOP1} {SelectBlock OUTPUT:G5..CA15} {Setproperty Shading,"7,0,Blend4'} {DECISION} {SelectBlock RESULTS.A1} COUNTER1 41 LOOP1 {;this loop transfers the output values to Results Table {LETJ.COUNTER1} {SelectBlock OUTPUT:C5..C15KEditCopy} {RIGHT COUNTER1+3}{EditPaste} {FOR COUNTER2,1,11,1,LOOP2} COUNTER2 12 LOOP2 {;this loop changes the output formulas into values} /bv~ {DOWN} {DECISION} {;this macro determines the optimal strategy} {SelectBlock OUTPUT:F30..AJ37} {EditClear} {SelectBlock OUTPUT:F41..M71} 89 {EditClear} {BlockValues OUTPUT:F19..AJ26,OUTPUT:F30} {BlockTranspose OUTPUT:F30..AJ37,OUTPUT:F41} {Sort. Reset} {Sort.Block OUTPUT:F42..G71} {Sort.Key_1 OUTPUT:G46}{Sort.Key_2 OUTPUT:F46} {Sort.Order_1 Ascending}{Sort.Order_2 Ascending} {Sort. Go} {Sort. Reset} {Sort.Block OUTPUT:I42..J71} {Sort.Key_1 OUTPUT:J42}{Sort.Key_2 OUTPUT: 142} {Sort.Order_1 Ascending}{Sort.Order_2 Ascending} {Sort. Go} {Sort. Reset} {SortBlock OUTPUT:L42..M71} {Sort.KeyJ OUTPUT:M42}{Sort.Key_2 OUTPUT:L42} {Sort.Order_1 Ascending}{Sort.Order_2 Ascending} {Sort. Go} \0 {;Adjusts Diaplay} {Application. Display "None,No,No,No,A..B:A1 ..B2"} {Notebook. Display "No, No, No'} {Window/Maximize} 90 SUMMARY Description of Structure Name of Structure: Type of Structure: Environmental Condition: De-icing: Age of Existing Coating System example Truss Industrial Yes 3 Decision Table Maintenance Strategy spot repair overcoat recoat Optimal Time (year) 4 4 9 Equivalent Annual Cost $2,262.56 $5,759.82 $9,239.24 Probability of Success Component Number 1 2 3 4 5 6 7 8 9 Probability of Success (%) 60 60 75 75 60 60 55 55 91 APPENDIX C EXAMPLE USING BRIDGE CORROSION COST MODEL Example 1 Stepl: Start Quattro Pro For Windows and retrieve file BCCM.WB1. Step 2: Press the Continue button to proceed to the Index. Step 3: Press the Environmental and Structural button to display the following dialogue box: Cfticr Information about the structure and Ihc environment 8'3t>f*$t • y«* 8* $t«W«f S*FMCt*W> fexample jfttttxi • *! Figure 32. Dialogue Box for Structural and Environmental Information In this dialogue box, choose the parameters that best describes the situation. Then press the OK button. 92 Step 4: Press the button Choosing Method of Coating Deterioration Simulation to display the following dialogue box: d h i k fctftfeA tetSfMiMB dtJfiftrt S«Wfefc tJfe PhMt ItMtt ^ • ^ • X U U . . A . . J M ~ ~ ~ ^ ^ ^ SeatettlrfefctHHian £aatfo8?g|M< %£am» iwmimiimi ' Figure 33. Dialogue Box for Choosing Method of Simulating Coating Deterioration There are two options for the user to choose. By choosing the first option, Service Life From the User, the following dialogue will be displayed. '§^^i^^^^^0^i&^MM^^W^iM^^^ Figure 34. Dialogue Box for Coating Parameters 93 Step 5: Figure 35. Dialogue Box for Cost and Financial Information Step 6: Press the analysis button to start the analysis process. After the analsys is completed, the Results Section will appear. By pressing the various buttons shown on the screen, the following dialogue boxes will be displayed. t tmm i ffj \ {237 48 Figure 36. Dialogue Box for Results of Life Cycle Cost Analysis The most cost effective rehabihtation strategy for this bridge is to spot repair at every three year intervals. Since the coating age is three years old, this strategy should be implemented immediately. 94 Ilpifsliljjl^^ 3 * V 9 J60 m— m— |GO J55 |55 Figure 37. Dialogue Box for Probability of Success of Rehabilitated Coating The probability of success of the rehabilitation for each component is shown in Figure 37. The values provided are based on the specific type of coating system, the level of adhesion, and the thickness of the coating system The user has to specify these values in the spreadsheet for their coating system by using the Adjust button. Equivalent Annual Cost for Spot Repair _0) i or LLI ' f I I I I I I I 1 4 7 10 13 Time (years) 10 8 6 4 2 0 -2 c ra a: a o '+± TJ C o O • equivalent annual cost -«- average corrosion rating -»- average adhesion rating Figure 38. Graph of Equivalent Annual Cost for Spot Repair 95 Equivalent Annual Cost for Overcoat .2 1' cr HI 0 I ' l 'WWl 'WWWl ' l " ! I I I I I I 1 4 7 10 13 Time (years) i i i i M i i 10 8 6 4 2 • Equivalent Annual Cost -»- average corrosion rating -»- average adhesion rating Figure 39. Graph of Equivalent Annual Cost for Overcoat Equivalent Annual Cost for Recoat 7 10 13 Time (years) i i i i i i i i i i i i + 10 5 g 13 n a: 5 | 4-10 1 -15 • equivalent annual cost -»- minimum corrosion rating -=- average adhesion rating Figure 40. Graph of equivalent annual cost for Recoat The three graphs shown previously provide all the equivalent annual costs for each rehabilitation strategy. In order to obtain the optimal maintenance strategy for this structure, only some of the equivalent annual costs can be considered. The maintenance intervals which exceed the condition constraints are eliminated in the analysis. For example, spot repairing the structure at every four year interval will cost approximately $100 per year. At this maintenance interval, the average corrosion rating of the coating system is approximately 7 which Ues between the corrosion limits of 6 to 8 for spot repair. 96 Therefore, this maintenance interval can be considered for this structure. If the structure is spot repaired at every eight year intervals, the equivalent annual cost will be approximately $500. This maintenance interval cannot be considered because the average corrosion rating of the coating (rating of 4) exceeds the corrosion limits for spot repair. Furthermore, the average adhesion rating of the coating (rating of 2) for this maintenance interval also exceeds the adhesion limit of 3. In addition to the cost savings, the average condition of the coating system will be higher for the shorter maintenance interval. The negative values in the condition ratings are not correlated to the degree of corrosion on the structure. However, a negative condition rating indicates that the coating system is no longer protecting the steel from corrosion. Therefore, some maintenance activity should be applied before any of the condition ratings becomes negative. 91 

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