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Age-dependent reliability analysis and development of a fuzzy based condition rating tool for timber… Aslam, Hafiz Sohail Hasan 2016

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AGE-DEPENDANT RELIABILITY ANALYSIS AND DEVELOPMENT OF A FUZZY BASED CONDITION RATING TOOL FOR TIMBER UTILITY POLES  by  Hafiz Sohail Hasan Aslam  BSc. Civil Engineering, University of Engineering & Technology, Lahore 2004   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  in  THE COLLEGE OF GRADUATE STUDIES  (Civil Engineering)   THE UNIVERSITY OF BRITISH COLUMBIA  (Okanagan)   January 2016   © Hafiz Sohail Hasan Aslam, 2016  ii Abstract Timber is the most commonly used material for supporting utility power lines, with an estimated quantity of over 165 million across North America. Timber Poles provide a safe and cost effective mean to supply electricity and communication to vast majority of consumers, and are considered to be the most important asset by utility companies. Due to significantly large investment in timber poles across North America, there is need to investigate their structural reliability. Within the past few decades, different parts of the world have experienced significant climate changes. Specifically in North America, Hurricanes and strong winds have caused tremendous damage to infrastructure including Timber utility pole structures. Therefore, there is an urgent need to understand the performance of timber poles to mitigate damage during extreme climatic hazards. This research presents a fragility based methodology to assess and compare the vulnerability of timber poles exposed to wind hazards models for selected locations. Timber poles are designed as per both CSA 22.3 No.1 deterministic design wind loads and probabilistic wind loads. Wind hazard models for selected locations are developed using Extreme value analysis. Reliability of timber poles is determined through convolution of structural fragility models with the wind hazard models. Strength degradation with time due to decay was also taken into account for a holistic approach towards risk assessment of Timber poles.  In addition to reliability analysis, a framework for development of a fuzzy logic based condition rating tool is also proposed in this research. Fuzzy synthetic evaluation technique, which is based on fuzzy logic theory has been utilized for the proposed framework. External decay, internal decay, wood pecker damage and mechanical damage were selected as performance indicators. A five tuple fuzzy linguistic evaluation set having levels of Very good, Good, Fair, Poor and Very Poor was used to assess the performance indicators. The proposed framework was validated through an illustrative example of ten timber poles. Analytical hierarchy process (AHP) was used to calculate weights for the four performance indicators. The proposed framework also provides the ability to prioritize timber poles according to their respective level of deterioration.    iii Table of Contents Abstract .................................................................................................................................... ii List of Tables .......................................................................................................................... vi List of Figures ........................................................................................................................ vii List of Illustrations ............................................................................................................... viii Acknowledgements ................................................................................................................. x Dedication ............................................................................................................................... xi  Introduction ..................................................................................................... 1 1.1. Background ........................................................................................................................... 1 1.2. Objective of this research ...................................................................................................... 4 1.3. Organization of Thesis .......................................................................................................... 5  Literature Review ........................................................................................... 6 2.1. Design of Timber Utility Poles ............................................................................................. 6 2.1.1. Deterministic Design Approach (CSA 22.3 No. 01) ........................................................ 6 2.1.1.1. Load Factors ............................................................................................................. 9 2.1.1.2. Minimum Grades of Construction ......................................................................... 10 2.1.1.3. Classification of Timber poles ............................................................................... 10 2.1.1.4. P-∆ (Second Order) Effects.................................................................................... 12 2.2. Reliability Theory in Engineering Analysis ........................................................................ 14 2.2.1. Fragility Analysis ........................................................................................................... 16 2.2.2. Previous Studies in Reliability Analysis of Timber Poles .............................................. 16 2.3. Condition Assessment of Timber Utility Poles ................................................................... 18 2.3.1. Structure of Wood........................................................................................................... 19 2.3.2. Preservation of Timber Poles .......................................................................................... 20 2.3.2.1. Seasoning of Wood Poles ...................................................................................... 20 2.3.2.2. Pre-treatment Procedures ....................................................................................... 21 2.3.2.3. Preservative Treatment .......................................................................................... 22 2.3.2.3.1. Oil based preservatives: ................................................................................... 22 2.3.2.3.2. Water based preservative ................................................................................. 23 2.4. Degradation of Timber Poles .............................................................................................. 24  iv 2.4.1. Decay Fungi .................................................................................................................... 25 2.4.1.1. Brown Rot .............................................................................................................. 25 2.4.1.2. White Rot ............................................................................................................... 26 2.4.1.3. Soft Rot .................................................................................................................. 26 2.4.2. Wood Pecker Damage .................................................................................................... 26 2.4.2.1. Exploratory and feeding damage ........................................................................... 27 2.4.2.2. Nesting damage ...................................................................................................... 27 2.5. Timber Pole Inspection Methods ........................................................................................ 27 2.5.1. Manual inspection methods ............................................................................................ 28 2.5.1.1. Visual Inspection ................................................................................................... 28 2.5.1.2. Sounding ................................................................................................................ 28 2.5.1.3. Drilling ................................................................................................................... 28 2.5.2. Non-destructive Evaluation (NDE) Methods ................................................................. 29 2.5.2.1. Resistance Drilling ................................................................................................. 29 2.5.2.2. Stress Wave Methods ............................................................................................. 30 2.5.2.3. X-Ray Tomography method .................................................................................. 30 2.5.2.4. Radar Method ......................................................................................................... 31 2.6. Fuzzy Logic and Fuzzy Synthetic Evaluation Technique ................................................... 31 2.6.1. Fuzzy set theory .............................................................................................................. 31 2.6.2. Fuzzy Synthetic Evaluation ............................................................................................ 34 2.6.2.1. Development of Framework for Fuzzy Synthetic Evaluation ................................ 34 2.6.2.1.1. Fuzzification ..................................................................................................... 35 2.6.2.1.2. Determination of Criteria Weights ................................................................... 37 2.6.2.1.3. Aggregation ...................................................................................................... 39 2.6.2.1.4. Defuzzification ................................................................................................. 39 2.7. Summary ............................................................................................................................. 40  Reliability Assessment of Timber Utility Poles using Fragility Analysis . 41 3.1. General ................................................................................................................................ 41 3.2. Pole Model .......................................................................................................................... 42 3.2.1. Design Load on Timber Pole .......................................................................................... 44 3.2.2. Design Capacity of Timber Pole ..................................................................................... 45 3.2.3. In-service deterioration of Timber Poles ........................................................................ 46 3.3. Wind Fragility Analysis ...................................................................................................... 49 3.4. Annual Probability of Failure ............................................................................................. 50  v 3.5. Results of Fragility Analysis ............................................................................................... 56  Development of Fuzzy based Condition Assessment Tool for Timber Utility Poles 74 4.1. General ................................................................................................................................ 74 4.2. Application of FSE technique to Condition Rating of Timber Utility Poles. ..................... 75 4.2.1. Description of defect criteria and development of membership functions ..................... 75 4.2.1.1. Bio-degradation (External and Internal Decay) ..................................................... 77 4.2.1.2. Wood Pecker Damage ............................................................................................ 80 4.2.1.3. Mechanical Damage ............................................................................................... 82 4.2.1.4. Membership Functions for Defect Indicators ........................................................ 83 4.2.1.5. Determination of Neutral Axis (NA) ..................................................................... 88 4.3. Validation of Timber Pole Condition Rating Framework ................................................... 90 4.3.1. Fuzzification of basic criteria into five tuple fuzzy sets ................................................. 91 4.3.2. Determination of weights for basic criteria .................................................................... 92 4.3.3. Aggregation of Criteria ................................................................................................... 93 4.3.4. Defuzzification ............................................................................................................... 95 4.4. Prioritization and ranking of poles ...................................................................................... 95 4.5. Summary ............................................................................................................................. 98  Conclusions & Recommendations ............................................................... 99 5.1. Conclusion .......................................................................................................................... 99 5.2. Limitations & Future Recommendations .......................................................................... 100 References ............................................................................................................................ 102 Appendix-A: Extreme Value Analysis .............................................................................. 108   vi List of Tables Table 2.1: Deterministic Weather Load Intensities (CSA C22.3 2015) ................................... 7 Table 2.2: Minimum Load Factors for Linear and Non-Linear analysis of Timber Poles (CSA C22.3 2015) .............................................................................................................. 9 Table 2.3: Minimum Circumference of Western Red Cedar (CSA O15 2015) ...................... 11 Table 2.4: Values obtained after Fuzzification ....................................................................... 36 Table 2.5  Fundamental scale used to develop priority matrix for AHP (Saaty 1988) ........... 38 Table 3.1: Probabilistic Parameters for Wind Loading .......................................................... 51 Table 3.2: Wind Speeds (m/s) at various Return Periods ....................................................... 52 Table 3.3: Statistical Parameters for Fragility analysis .......................................................... 57 Table 3.4: Climatic Parameters for selected locations ............................................................ 57 Table 3.5: COV of Capacity (C) of timber poles for class 1 to 5 at various ages .................. 58 Table 3.6: Lognormal Parameters for Wind Fragility ............................................................ 70 Table 3.7: Annual Probability of Failure & Reliability Index values for Timber Poles ......... 71 Table 3.8: Relationship between return period and reliability index (CSA C22.3 No.60826 2010) ....................................................................................................................... 72 Table 4.1: Inspection Results of basic categories ................................................................... 91 Table 4.2: Fuzzy sets corresponding to results of basic criteria ............................................. 92 Table 4.3: Weights estimated using AHP ............................................................................... 93 Table 4.4: Fuzzy Synthetic Evaluation results of ten timber poles ......................................... 97   vii List of Figures Figure 2.1: Wind Force acting on Typical Timber Pole ........................................................... 8 Figure 2.2: Radial Ice Thickness over Conductors ................................................................... 9 Figure 2.3: P-Delta Effect in Timber Utility Poles ................................................................. 12 Figure 2.4: Cross-section of a Tree (USDA-FPL 2010) ......................................................... 19 Figure 2.5: Drilling Patterns for Pre-treatment of Timber Poles (Morrell 2012) ................... 22 Figure 3.1: Configuration & Layout of the Timber Distribution Pole .................................... 43 Figure 3.2: Horizontal and Vertical Spans (USDA-RUS 2009) ............................................. 44 Figure 3.3:  Flow Chart for Reliability Analysis .................................................................... 55 Figure 4.1: Hierarchical Structure for Timber Pole Condition Assessment (WP refers to wood pecker) .................................................................................................................. 76 Figure 4.2  Possible decay patterns at ground line a) Internal decay (Core Rot);  b) External decay (shell rot) .................................................................................................... 79 Figure 4.3: Hypothetical manifestation of Wood Pecker Damage (a) Exploratory (b) Feeding (c) Nesting. w and d are width and depth of Wood Pecker holes respectively (Adapted from Steenhof 2011) ............................................................................ 81 Figure 4.4: Proposed Hierarchical Framework of Fuzzy Synthetic Evaluation ..................... 87 Figure 4.5: Neutral Axis of a Timber Pole (Ausgrid 2014) .................................................... 88 Figure 4.6  Neutral Axis of an in-line Timber pole (Ausgrid 2014) ....................................... 89 Figure 4.7  Neutral Axis of Timber Pole with services (Ausgrid 2014) ................................. 89 Figure 4.8  Neutral Axis for an Angle Timber Pole (Ausgrid 2014) ...................................... 89 Figure 4.9  Neutral Axis for a Dead End Timber Pole (Ausgrid 2015) .................................. 90     viii List of Illustrations Illustration 2.1: Weather Loading Map of Canada ................................................................... 7 Illustration 2.2: Seasoning of Timber Poles (Morrell 2012) ................................................... 21 Illustration 2.3: Triangular Membership Function.................................................................. 32 Illustration 2.4: Trapezoidal Membership Function ............................................................... 33 Illustration 3.1: Wind Hazard Chart for Vancouver ............................................................... 52 Illustration 3.2: Wind Hazard Chart for Victoria .................................................................... 53 Illustration 3.3: Wind Hazard Chart for Kelowna .................................................................. 53 Illustration 3.4: Wind Hazard Chart for Castlegar .................................................................. 54 Illustration 3.5: Fragility Curves for Vancouver (a) Deterministic Wind Load (b) Probabilistic Wind Load ............................................................................... 60 Illustration 3.6: Fragility Curves for Victoria (a) Deterministic Wind Load (b) Probabilistic Wind Load .................................................................................................... 61 Illustration 3.7: Fragility Curves for Kelowna (a) Deterministic Wind Load (b) Probabilistic Wind Load .................................................................................................... 62 Illustration 3.8: Fragility Curves for Castlegar (a) Deterministic Wind Load (b) Probabilistic Wind Load .................................................................................................... 63 Illustration 3.9: Lognormal Probability Plot for Timber Poles in Vancouver at 0 years (a) Deterministic (b) Probabilistic ...................................................................... 64 Illustration 3.10: Lognormal Probability Plot for Timber Poles in Vancouver at 25 years (a) Deterministic (b) Probabilistic.................................................................... 64 Illustration 3.11: Lognormal Probability Plot for Timber Poles in Vancouver at 50 years (a) Deterministic (b) Probabilistic.................................................................... 65 Illustration 3.12: Lognormal Probability Plot for Timber Poles in Victoria at 0 years (a) Deterministic (b) Probabilistic.................................................................... 65 Illustration 3.13: Lognormal Probability Plot for Timber Poles in Victoria at 25 years (a) Deterministic (b) Probabilistic.................................................................... 66 Illustration 3.14: Lognormal Probability Plot for Timber Poles in Victoria at 50 years (a) Deterministic (b) Probabilistic.................................................................... 66 Illustration 3.15: Lognormal Probability Plot for Timber Poles in Kelowna at 0 years (a) Deterministic (b) Probabilistic.................................................................... 67  ix Illustration 3.16: Lognormal Probability Plot for Timber Poles in Kelowna at 25 years (a) Deterministic (b) Probabilistic.................................................................... 67 Illustration 3.17: Lognormal Probability Plot for Timber Poles in Kelowna at 50 years (a) Deterministic (b) Probabilistic.................................................................... 68 Illustration 3.18: Lognormal Probability Plot for Timber Poles in Castlegar at 0 years (a) Deterministic (b) Probabilistic.................................................................... 68 Illustration 3.19: Lognormal Probability Plot for Timber Poles in Castlegar at 25 years (a) Deterministic (b) Probabilistic.................................................................... 69 Illustration 3.20: Lognormal Probability Plot for Timber Poles in Castlegar at 50 years (a) Deterministic (b) Probabilistic.................................................................... 69 Illustration 3.21: Reliability Index of Timber Poles designed according to deterministic wind loads ............................................................................................................ 73 Illustration 3.22: Reliability Index of Timber Poles designed according to Probabilistic wind loads ............................................................................................................ 73 Illustration 4.1: Example of Damage caused by motor vehicle collisions (1. Dstar.org & 2. [Public domain], via Wikimedia Commons)) ............................................... 83 Illustration 4.2: Membership Function for External Decay .................................................... 84 Illustration 4.3: Membership Function of Internal Decay ...................................................... 84 Illustration 4.4: Membership Function of Wood Pecker Hole Depth ..................................... 85 Illustration 4.5: Membership Function of Width of Opening ................................................. 85 Illustration 4.6: Membership Function of Mechanical Damage ............................................. 86 Illustration 4.7: Condition rating results using FSE................................................................ 95  x Acknowledgements First and foremost, praise and thanks to Allah almighty for giving me the strength and ability to complete my thesis. I would like to express my sincere gratitude to my academic supervisors Dr. Kasun Hewage and Dr. Shahria Alam, for providing me with this opportunity and for extending their continuous guidance, encouragement and support to accomplish this academic endeavor.  I would like to thank Dr. Anjuman Shahriar and Mr. Dave Walden from Fortis BC for initiating this research project and providing necessary resources. I would specially like to appreciate the time and effort put forth by Dr. Anjuman Shahriar, during project work as well as in the review process of my thesis. Her valuable feedback, suggestions and insightful comments helped significantly to improve and shape my thesis. I would also like to acknowledge National Engineering and Research Council of Canada (NSERC) for providing financial assistance for this research.  Last but not the least, I would like to thank my parents for their unconditional love and support, and also my wife and kids for their tremendous patience, love, and comprehension especially during the later stage of my thesis.      xi Dedication   Dedicated to my loving Parents, my wife, & my kids    1  Introduction 1.1. Background The supply of electricity to potential customers is accomplished through two major systems. First is the transmission system, which consists of high voltage lines through which electricity travels from the generating source such as dams, nuclear power plants etc. to substations. Second is the distribution systems, which transfers electricity from substations directly to the customers. Timber poles have been extensively utilized as support structures for overhead electric transmission and distribution lines across Canada since the late 19th century (Shahi 2008; Tallavo 2009). Timber is a preferred choice for utility poles primarily due to its high initial strength, low electrical conductivity, economy, reliability and ease of availability. Manufacturing of wood poles generate lesser greenhouse gases compared to concrete and steel poles, rendering them more sustainable and environmentally friendly (Sedjo 2002). Wood Poles are long round timber members, behaving as typical structural cantilever beams, designed to support component dead loads such as conductors, insulators, cross arms and others accessories. In addition to dead loads, wooden poles are also designed to have sufficient capacity to resist climatic loads of ice and wind, live loads during routine maintenance and inspections and other forces corresponding to earthquakes or imbalanced cable loads (broken cable condition (Datla and Pandey 2006).  The terms “Risk” and “Reliability” are assumed to have identical implications, when used to describe the state of any particular system. Lower reliability corresponds to a higher risk and vice versa. Risk and reliability assessment of utility wood poles is particularly important to any power supply system owing to the economic consequences associated with interruptions due to utility pole failures (Li 2005). The structural design of utility timber poles contains considerable amount of uncertainties which stems to our inability to accurately specify material properties, limitations of design methods, lack of knowledge regarding future loadings, the use of simplified assumptions to predict behavior of structures and human factors such as errors, omissions etc. (Ayyub and Haldar 1985).  The power industry has employed the deterministic approach for years to design utility timber poles. This approach is based on a set of prescriptive criteria, providing a straightforward procedure to design and ensure safety of timber poles during extreme loading conditions (wind  2 and ice). Although, timber poles designed using deterministic design approaches have remained in service for considerable amount of time, however, their actual performance or reliability achieved through such methods remains unknown (Li et al. 2006). The true performance of timber poles is controlled by the uncertainties associated with the load and resistance parameters. Due to such uncertainties, there might be a probability that the timber pole may not perform as intended. Deterministic design approach does not account for such uncertainties and hence is unable to specify the probability of non-performance of a timber pole structure (Foschi 2004). The application of probabilistic design methods provide a systematic approach to reduce the probability of non-performance by establishing appropriate design parameters, thereby increasing reliability of the component to an acceptable level. Since 1990, several countries around the world have incorporated probabilistic or reliability based design methods into their national design standards.  Distribution poles are highly vulnerable to failure during extreme winds. The deterministic wind loads as specified in CSA 22.3 No.1 have been used for decades for design of timber utility poles. These specified wind loads are assumed to be equally applicable to very large areas without considering the local climatic conditions. This tends to create doubts regarding performance or reliability of timber poles designed using deterministic wind loads. To address the concerns, reliability assessment of timber poles designed using deterministic wind loadings will be carried out using fragility analysis. The reliability values thus obtained will be compared with target reliability values specified in CSA 22.3 No.60826 Reliability based design code. Li et al. (2006) conducted a study to evaluate the reliability of timber poles across selected locations of British Columbia, Canada using first order/ second order reliability methods. However, in this research, Fragility analysis will be used determine the reliability index of timber poles. Fragility analysis provides a realistic and appropriate solution, to evaluate functional and safety performance of a structural system or component by taking into account potential uncertainties associated with its behavior. Fragility analysis approach has been used effectively in the past (Bjarnadottir et al. 2013; Li and Ellingwood 2006; Rosowsky and Ellingwood 2002) to determine the probability of failure of structures against extreme hazards. This research provides a probabilistic approach to assess the risk of wind loads on probability of failure and reliability of timber utility poles.   3 Being a natural material, wood is quite susceptible to physical deformation and deterioration with the passage of time resulting from decay due to fungus or insect attacks and woodpecker damage. The deterioration process causes significant loss to the structural capacity and service life of pole structures and its corresponding components. The sudden failure of these pole structures may jeopardize the overhead network performance through unplanned interruptions in power supply, causing safety and economic implications (Gustavsen and Rolfseng 2005). It is therefore imperative for the analysis to account for changes in the resistance of timber poles with time. The work presented in this research incorporates time dependent strength degradation of timber poles through a probabilistic decay model. This holistic approach of considering the simultaneous effect of decay and natural hazard on failure probability will help to effectively address reliability issues of aging timber poles by deriving effective pole management strategies.  In view of time dependent degradation, utility providers are also quite keen to develop effective mechanisms for proper management of their timber pole assets. Timber utility poles usually have a service life of 35 – 50 years, which is mainly dependent upon the type of wood, preservative treatment, atmospheric conditions and maintenance cycle (Datla and Pandey 2006; Morrell 2008). Power lines consist of wooden poles connected in series. Failure of any pole may constitute a weak link within the power line, leading to a cascading failure and causing devastating consequences. Deterioration of wooden poles may also lead to fatalities to line workers performing inspection and maintenance operations. Maintaining optimal performance and adequate structural capacity of timber poles has always been a major concern for utility companies. Line managers nowadays, have a profound focus towards optimizing the lifecycle of timber pole assets so that utility lines continue to supply electricity without any interruption. It is therefore, quite imperative for utility providers to develop effective preventative maintenance programs to identify deficiencies and defects in wooden poles in order to circumvent their degradation and subsequent failure (Nelson and Sinclair 2005).  Condition assessment may be defined as “a process of systematically evaluating an organization’s capital assets in order to project repair, renewal, or replacement needs that will preserve their ability to support the mission or activities they were assigned to serve” (Ahluwalia 2008). The efficacy of any timber pole condition assessment program depends  4 upon its ability to identify potential defects and allow line managers to make informed decision regarding maintenance and rehabilitation. In addition, it should also facilitate to rank timber poles depending upon their respective condition. Condition assessment of timber poles is performed by inspectors using variety of techniques and procedures. The information obtained can sometimes be imprecise and subjective due to lack of experience of site inspectors and cause poles to be condemned, which still exhibit adequate strength. Adoption of more refined inspection methods and development of new technology can help to make more objective assessment. However, interpretation of results from advanced methods also requires engineering judgment and hence requires considerable skill and experience (Nelson and Sinclair 2005). The inherent subjectivity involved in the condition assessment process provides an impetus to account for uncertainty. In this regard, a decision support tool for condition assessment of timber poles based on fuzzy logic theory is proposed. The motivation behind developing such a tool is based on the hypothesis that if uncertainty associated with condition assessment results can be removed, then this information can be effectively used by asset managers and line engineers to make efficient maintenance decision regarding their timber pole assets.   The cost associated with replacing timber poles is considerably higher as compared to replacing single component. Line managers are therefore interested in allocating funds for pole assets, which require immediate repair. For this reason, the fuzzy based tool would not only provide a mechanism to assess the condition of timber poles in a particular line, but also subsequently rank them according to their level of deterioration. This will allow the line managers to decide cost effective mitigations actions for pole maintenance. 1.2. Objective of this research The objectives of this research are as follows: 1. To evaluate and study the difference in achieved reliability of timber distribution poles designed according to both CSA 22.3 No.1 deterministic as well as probabilistic wind loadings.  2. To study the effect of time dependent degradation on reliability of timber poles due to decay.   5 3. To develop a decision support tool for condition based rating of timber poles using fuzzy logic based technique.  1.3. Organization of Thesis Chapter 1 includes a brief introduction to timber poles, background of the research and underlying objective to be achieved. Chapter 2 provides a comprehensive literature review pertaining to design, reliability analysis, structure, preservation, degradation and condition assessment of timber utility poles. It also provides an introduction to fuzzy logic and its application to the condition rating of timber poles. Chapter 3 presents a reliability based assessment for utility timber poles designed according to deterministic wind design loadings as mentioned in CSA 22.3 No.1 and Probabilistic wind loadings. The assessment is performed for timber pole at selected locations using the concept of wind fragility. Probabilistic wind load models for the selected locations are created using extreme value analysis. The conditional probability of failures for timber poles determined through fragility analysis are convolved with wind load models to estimate the annual probability of failure for selected locations. Finally, the reliability index of timber poles for both deterministic as well as a probabilistic loadings for selected locations are determined and compared subsequently. Chapter 4 focuses on the development of a fuzzy based decision support tool for condition assessment of timber poles. This chapter starts off with an introduction to the performance indicators, which are used to develop the hierarchical framework for condition assessment of timber poles using Fuzzy synthetic evaluation (FSE) technique.  Eventually, application of the proposed methodology is validated through an illustrative case study and results are presented herewith. Finally, chapter 5 presents conclusions and provides recommendation for future research.     6   Literature Review 2.1. Design of Timber Utility Poles In Canada, two standards are currently being used for design of overhead structures. These include: CAN/CSA C22.3 No. 1-10 “Overhead Systems” and CAN/CSA C22.3 60826-06 “Design Criteria of Overhead Transmission Lines”.  CAN/CSA C22.3 No. 1 is based on deterministic design procedure, whereas CAN/CSA C22.3 No. 60826 is based on probabilistic or reliability based design procedure. Currently, CSA C22.3 No. 1 is the most widely used standard in Canada for design of overhead structures. It is therefore, imperative to understand the archived performance and reliability of overhead timber poles using deterministic design loads to allow comparison with probability based design loadings. This knowledge will not only help to improve the current design practices but would also allow to establish a target reliability.  2.1.1. Deterministic Design Approach (CSA 22.3 No. 01) The main premise of deterministic design procedure is the utilization of pre-specified material strengths and loading conditions without considering the inherent variability associated with them. Depending upon experience of local conditions, factors have been derived to modify strength and loads based on the perceived level of safety, however, they are subjective in nature. The CSA 22.3 No. 1 provides a loading map of Canada (see illustration 2.1), which is used to determine the type load, which a utility structure will be subjected to for design purposes. The map is divided into four zones: Severe, Heavy, Medium A and Medium B. Medium A loading region is not shown in Fig and can be found in the province specific maps.    7  Illustration 2.1: Weather Loading Map of Canada (CSA C22.3 No.1 2015) The abovementioned loading region have specified values related to different weather conditions, which include amount of ice accretion on conductors, intensity of wind loading and temperature. Once the loading region is selected, the corresponding values of weather conditions can be determined. Table 2.1 provides the values for deterministic weather loads corresponding to each of the loading region. Table 2.1: Deterministic Weather Load Intensities (CSA C22.3 No.1 2015)   Loading Zone     Loading Condition Severe Heavy Medium A Medium B Wind Pressure (N/m2) 400 400 400 300 Radial Ice Thickness (mm) 19 12.5 6.5 12.5   8 Wind acts in the horizontal direction, either longitudinally or transversely to the line direction, on the pole structure including conductors and any additional equipment. Wind acting in the transverse direction to pole and conductors is considered most critical for design purposes. Fig 2.1 shows wind acting horizontally on a typical pole with conductors and transformer.  Figure 2.1: Wind Force acting on Typical Timber Pole Ice accretion over conductors is not uniform and can be manifested in different complex shapes. However, for simplicity it is assumed that ice accretes on conductors with uniform radial thickness (Fig 2.2) and having value as specified in Table 2.1. The radial thickness of ice increases the vertical forces due to increased weight and also instigates additional horizontal forces due to increased wind surface area of ice covered conductors. Temperature variations are used in sag and tension calculations for conductors. Wind on TansformerWind on Conductors Wind on Pole G.L. 9 Conductor Accreted ice over conductor  Figure 2.2: Radial Ice Thickness over Conductors  2.1.1.1. Load Factors In the deterministic design approach, safety factor have been derived which are used to magnify the applied loads. CSA 22.3 No. 1 provides minimum load factors for both linear and non-linear analysis. In case of linear analysis, load factors are categorized based on type of load (vertical or horizontal) and construction grade. However, in case of non-linear analysis, coefficient of variation (COV) of material strength is also taken into account for categorization of load factors. Dead weight of poles, conductors and any attachment such as transformer may constitute vertical loads. Wind pressure acting on pole, conductors and equipment corresponds to horizontal load. Table 2.2 shows Load factors to be used for linear and non-linear analysis.  Table 2.2: Minimum Load Factors for Linear and Non-Linear analysis of Timber Poles (CSA C22.3 No.1 2015) Type of Load Construction Grade Minimum Load Factor Linear Non-Linear Vertical 1 4 2  2 2.7 1.5  3 2 1.2 Transverse 1 2 1.9  2 1.5 1.3   3 1.2 1.1  10 2.1.1.2. Minimum Grades of Construction  Overhead utility structures are designed to be utilized for different purposes and also to be installed in a variety of surrounding. In order to establish the importance of timber poles based upon purpose and type of surrounding, CSA 22.3 No.1 specifies three construction grades i.e. Construction Grade 1 (CG-1), Construction Grade 2 (CG-2), and Construction Grade 3 (CG-3). In other words, these grades categorize utility structures based on severity of consequences in the event of failure. Construction grades are established keeping in view various factors which include proximity of utility poles to type and nature of nearby structures or facilities, use of communications cables on utility poles in addition to supply conductors as part of joint use and types of facilities over which utility lines are passing. CG-3 is usually considered for typical construction near roads and highways, whereas CG-1 is used for poles near railway control facilities.  2.1.1.3. Classification of Timber poles Numerous species of timber is used to manufacture transmission and distribution poles in North America. The most common species include Southern Yellow Pine (SYP), Western Red Cedar (WRC), Douglas Fir (DF) and Red Pine (RP). For this research, only western red cedar was considered for reliability analysis. The primary reason for choosing WRC was due the fact that it is the most widely available species in British Columbia (BC). Furthermore, majority of distribution poles throughout different utility companies of BC comprised of WRC species. As our selected location were in BC, hence it was pertinent to use WRC for analysis purposes in this research. CSA 015-05 (CSA O15 2005) provides information regarding strength and dimensional properties of various species and classes of timber utilized for timber poles in Canada. The dimensional properties for WRC are given in Table 2.3.     11 Table 2.3: Minimum Circumference of Western Red Cedar (CSA O15 2015) CLASS 1 2 3 4 5 6 7 CIRC AT TOP (IN) 27 25 23 21 19 17 15 LENGTH (FT) SET DEPTH (FT) Minimum circumference at 6 ft. from butt, in 20 4 33.5 31.5 29.5 27 25 23 21.5 25 4.5 37 34.5 32.5 30 28 25.5 24 30 5 40 37.5 35 32.5 30 28 26 35 5.5 42.5 40 37.5 34.5 32 30 27.5 40 6 45 42.5 39.5 36.5 34 31.5  45 6.5 47.5 44.5 41.5 38.5 36 33  50 7 49.5 46.5 43.5 40 37.5   55 7.5 51.5 48.5 45 42    60 8 53.5 50 46.5 43.5    65 8.5 55 51.5 48 45    70 9 56.5 53 49.5 46    75 9.5 58 54.5 51     80 10 59.5 56 52     85 10.5 61 57 53.5     90 11 62.5 58.5 54.5     95 11.5 63.5 59.5      100 12 65 61      105 12.5 66 62      110 13 67.5 63      115 13.5 68.5 64      120 14 69.5 65      125 14.5 70.5 66             12 2.1.1.4. P-∆ (Second Order) Effects Historically, overhead structures were designed using linear analysis i.e. considering the effect of vertical and horizontal loads only. Now CSA 22.3 No. 1 specifies to adopt non-linear analysis for design purposes. Non-linear analysis takes in to account the P-∆ (second order) effects, which is moment produced due to horizontal displacement of pole top resulting from vertical forces. The second order effects are produced once the pole is deflected due to horizontal forces and vertical forces (due to conductor and equipment) induce additional moments in the non-linear state. (Fig. 2.3)  Figure 2.3: P-Delta Effect in Timber Utility Poles  The timber pole is generally designed as a cantilever structure. The deflection at the free end of the pole due to horizontal forces can be calculated by the following equation (IEEE 1991): ∆𝑚𝑎𝑥=6.78 ×𝐹× ℎ3𝐸 ×𝐷𝐺𝐿3  ×𝐷𝐿.……………………………………………………..…..(2.1)  Where, F = Horizontal Force (due to wind) ∆PFSecondary Moment = P∆ 13 L = Height of loading point from ground line E = Modulus of Elasticity DGL = Dia. of Pole at ground line DL = Dia. of pole at loading point  The vertical unbalance causes the pole to lean further to resist the loads, which cause an additional increase in deflection. Eq. 2.1 does not take into account the additional deflection and hence an amplification factor is used as shown below (Gaiotti and Smith 1989):  ∆𝑇𝑜𝑡𝑎𝑙=  ∆𝑚𝑎𝑥 [1 −𝑃𝑣𝑃𝑒]−1…………………………………………………………………(2.2) Where,  Pe = Euler’s Buckling Load  Pv = Vertical load acting on the pole For a circular tapered column with fixed-free end conditions, the Euler’s buckling load is given by the equation (Gaiotti and Smith 1989; IEEE 1991): 𝑃𝑒 =𝜋2𝐸𝐼4𝐿2(𝐷𝐺𝐿𝐷ℎ)2.7………………………………………………………………………….(2.3)  Where, L = Length of Column E = Modulus of Elasticity I = Moment of Inertia DGL = Dia. of Pole at fixed end Dh = Dia. of pole at free end  Therefore, the bending moment induced at ground line due to P-∆ effect can be calculated as (IEEE 1991): 𝑀𝑃−∆ =  𝑃𝑣. ∆𝑇𝑜𝑡𝑎𝑙  ……………………………………………………………………...(2.4)  14 2.2. Reliability Theory in Engineering Analysis Structural reliability is the application of probabilistic methods to study the safety of structures. The reliability of a structure refers to the probability that the structure will perform its intended function for a specified amount of time-period (Ellingwood 2004; Foschi et al. 2002; Li 2005). The introduction of probabilistic methods in engineering analysis provide an impetus to reduce the risk of failure to a tolerable level by enhancing the level of performance or reliability. Traditional deterministic methods use empirical or semi-empirical safety factors to address safety issues for acceptable performance, which have deemed to be inadequate under extreme natural hazards. On the contrary, performance or reliability based approach provide a hierarchical system to explicitly state the functional objectives of the structure, strength or stiffness criteria to meet those objectives and evaluation methods to measure the satisfaction of criteria (Ellingwood 2004). A performance or limit state function can be used in general to describe the reliability or performance of an engineering system, which may be expressed as (Foschi 2004). 𝐺(𝑥) = 𝐶(𝑥𝑐, 𝑑𝑐) − 𝐿(𝑥𝐿 , 𝑑𝐿)…………………………………………………………………….(2.5) Where,  G(x) = performance function C = Capacity L = Load xc = uncertain parameters (variables) related to capacity dc = deterministic parameters related to capacity xL = uncertain parameters (variables) related to load dL = deterministic parameters related to load From the above equation, it is clear that the vectors x and d associated with capacity C and load L respectively may include random variables as well as deterministic quantities. The probability of the structure not performing its intended function will be the probability that G < 0 or L > C. Such a situation corresponds to the probability of failure, PF. The reliability can then be calculated as 1-PF.  15 Statistical information for each random variable related to capacity and load is required to calculate the reliability of a structural system. Capacity of a structural system involves random variables depending upon the type and nature of material used and can be obtained from statistical analysis of test data. Information regarding load or demand related variables such as maximum wind speed, accretion of ice on conductors, earthquake intensities, etc. can be obtained from historical data. Subjective estimates can be made for variables, with less or no data is available. Sensitivity analysis can also be performed for values of these assumed variables, in order to study their effect on the overall reliability (Foschi 2004). Several methods can be employed to calculate the probability of failure and subsequent reliability of a structural system. These methods include First-Order Reliability Method (FORM), Second-Order Reliability Method (SORM) and Monte Carlo simulation. The FORM/SORM are very efficient but approximate methods for calculation of reliability index and involve complex algorithms. The non-linearity of the performance function G(x) also effects the outcome of these method. The Monte Carlo simulation, on the other hand is quite a straightforward computer simulation technique. In this technique, the capacity and load variables are generated randomly for a specified number of iterations based on their distribution. The performance function G(x) can be evaluated for each iteration. For values of G(x) > 0, it can be concluded that performance criterion is met, however values of G(x) < 0 correspond to a failure event Nf. If N is the total number of iterations, then the probability of failure is given by: 𝑃𝑓 =𝑁𝑓𝑁………………………………………………………………………………….(2.6) The accuracy of the Monte Carlo simulation depends on the number of iterations. It can also prove to be data intensive for systems with very low probability of failure. In such situations, more efficient techniques such as Importance Sampling or Adaptive Sampling Simulation can also be used. The reliability index (β) can be estimated by the following relationships (Zhai and Stewart 2009): 𝛽 = 𝜙−1(−𝑃𝑓)……………………………………………………..………………..…...(2.8) Where Ф(.) is the standard normal cumulative distribution.  16 2.2.1. Fragility Analysis The plot between probabilities of failure i.e. the number of times the load exceeds capacity for a particular performance function using Monte Carlo Simulation against a specific range of intensity measure or load is known as fragility curve. In other words, Fragility curves are functions that describe the conditional probability of failure of a structural system as a function of the intensity measure (Schultz et al. 2010).  The fragility curves provide comprehensive perspective on reliability of a structural system. The shape of the fragility curve describes the uncertainty associated with capacity of the structure to resist load. In case of Complex or poorly understood systems, fragility curves take the form of s-shaped functions, which is indicative of variability associated with the capacity of system (Schultz et al. 2010). Fragility curve for timber poles can be used to make informed decision regarding asset management. In addition, they can also be used to investigate the effectiveness of various retrofitting measures on structures.  2.2.2. Previous Studies in Reliability Analysis of Timber Poles Li et al. 2006 conducted a study to assess the reliability of wood utility poles designed according to CAN/CSA-C22.3 No. 1 deterministic design approach. Western Red Cedar poles for all 3 grades of construction were designed for 15 locations across Canada using both linear and non-linear design approaches. Climatic loads based on 50-year return period as given in CSA C22.3 No. 1. Gumbel distribution was assumed to model climatic loads. Annual reliability index for each location and design scenario was determined using a reliability analysis program known as RELAN. The results of the study showed that design using linear approach yielded structures with lower reliability as compared to non-linear approach. This showed the significance of second-order effects even though linear approach possessed higher load factors. Furthermore, reliability index of structures was not uniform across all locations, which attributed to the disparity between the code specified climatic load and actual weather loads at each selected location. Daigle (2013) conducted a similar research to study the effect of construction grades, height of pole, end of life criterion (60% remaining life) and wood pecker damage on reliability of timber poles. Red pine species was considered for analysis in this research.   17 Bjarnadottir et al. (2013) proposed a probabilistic framework to assess the vulnerability of timber distribution poles exposed to hurricane hazards under the impact of climate change. Both NESC and ASCE methods with different safety factors were employed in the study to design timber pole and Fragility analysis was used to determine the reliability. Effect of degradation was also investigated in the analysis. The results of the study showed that changing patterns of hurricane hazards due to climate change had a significant impact on the reliability of timber poles. The probability of failure further increases when effect of degradation is considered. Ryan et al. (2014) developed a probabilistic methodology to carry out reliability assessment of treated and untreated timber poles under wind loads incorporating deterioration and network maintenance in accordance with Australian standards. Monte Carlo simulation was used for analysis purposes. The results of the study revealed similar failure rates and structural reliability for both treated and untreated timber poles maintained in accordance with Australian studies over a period of 100 years. However, untreated poles experienced twice as much replacements over the same period. In addition, effect of four different maintenance strategies on network performance was also investigated, suggesting significant improvements in network performance through minor changes in maintenance and design practices. Salman (2014) proposed a framework to fragility analysis of timber and steel poles subject to extreme wind hazards. Deterioration of timber and steel poles with time was also considered in the analysis. The poles were assumed to be located in Florida and Iowa for analysis purposes. A life-cycle cost analysis framework was also proposed to compare both steel and timber poles. The results of the analysis suggested that steel poles were more reliable and depicted lower life cycle cost as compared to timber poles. Fu et al. (2016) presented a study to conduct fragility analysis of transmission towers subjected to wind and rain loads. In addition, the concept of critical collapse to evaluate the collapse status of transmission towers was also presented. The results of the study showed that fragility and critical collapse were greatly influenced by the wind attack angle and wind spectrum. The study also suggested that rain load contributed significantly to the tower collapse and should be paid added attention during severe thunderstorms and gales.   18 2.3. Condition Assessment of Timber Utility Poles Timber Poles are not only exposed to operational loads but also experience varying environmental condition during their service life. In general, new timber poles with proper preservative treatment do not require regular inspection during the first 10 to 15 year of their installation. However, with passage of time, ageing and weathering effects will cause the pole to lose its mechanical strength. Ageing in timber is poles manifested in two ways: Firstly, due to constant effect of applied loads, the poles experience a gradual decrease in fiber strength. Furthermore, continuous wetting and drying cycles and environmental changes can cause cracks to develop in poles. The second form ageing occurs when barrier created by preservative treatment is broken by microorganisms resulting in bio-degradation of timber poles due to decay fungi. Wood peckers and motor vehicle accidents also contribute to the ageing process (Endrenyi and Anders 2006; Sandoz and Vanackere 1997): Timber poles provide mechanical support to overhead line components such as conductors and insulators. Ageing and deterioration can cause failure of timber poles, which in return can cause forced interruptions in power supply. Such interruptions are highly undesirable for utility companies as they readily effect their reputation and integrity. In addition, considerable cost is incurred to rectify such situations. Weak poles also pose safety issues to linemen and people in its vicinity. In order to avoid these intricacies, utility companies have devised inspection programs to assess the condition and structural integrity of timber utility poles on a regular basis (Brown and Willis 2006). A literature review is performed regarding structure, preservation treatment, degradation mechanisms and inspection techniques of timber poles. This knowledge may prove essential towards condition assessment and subsequent ranking of timber poles.    19 2.3.1. Structure of Wood The cross-section of a tree is shown in Fig. 2.4 (USDA-FPL 2010).  Figure 2.4: Cross-section of a Tree (USDA-FPL 2010) The outer dead layer of the tree is known as the outer bark (A). The outer bark prevents the tree from drying and also serves as a protective layer for Fungi and insect attacks. The outer bark is usually removed during pole manufacturing to as it can affect proper drying and preservation treatment and may also attract various wood-boring insects.  The inner bark (B) is a thin living layer which transports food from leaves produced from photosynthesis to roots and other growing parts of the tree.  The thin microscopic layer separating bark from the wood is known as vascular cambium (C) and is responsible for producing both outer and inner bark tissues each year.  Sapwood (D) is the living part of the tree forming a white to cream coloured band, and carries sap (water) from roots to the leaves. It is also responsible for storage and synthesis of bio-chemicals in the living tree. The depth of sapwood depends upon the health of the tree and varies widely within and among wood species.   20 Hardwood (E) is the portion containing dead and inactive sapwood and may be more durable than sapwood. The colour of heartwood is either red or brown depending on the wood species.  Pith (F) is the central part of the tree trunk and signifies the place of early growth of the initial wood.  Wood rays (G) are tissues that are horizontally oriented through the radial plane of the tree. Rays vary in size and connect various layers from pith to bark for storage and transfer of food. Douglas-fir (DF) and western red cedar (WRC) are the most widely used species for wood poles by utilities in western Canada. Douglas-fir has thicker sapwood (1-3 inches), whereas sapwood for WRC is relatively thin (3/4 inches). Chemical indicators such as difference in pH can be used to distinguish between sapwood and hardwood. As long as the sapwood is wet, it shows little resistance to fungal and insect attacks. However, dying cells of aging sapwood in some species are converted into compounds called extractives, which are highly toxic to decay fungi and insects, thereby protecting the hardwood for a longer period of time (Morrell 2012). Heartwood of DF and WRC is more durable as compared to their sapwood. Hence, Poles manufactured from species having durable heartwood and supplemented with preservative treatment in the sapwood usually have a longer service life. 2.3.2. Preservation of Timber Poles Wood poles are treated with preservative treatment to protect it from attacks by decay fungi, insects and marine borers. The preservative treatment enhances the service life and reduces cost associated with replacement of wood poles. The effectiveness of the preservation treatment depends upon its penetration and retention and varies with wood species and use requirements. Wood species with thin layer of sapwood such as western red cedar require less penetration as compared to wood with thicker sapwood e.g. Southern pine (Morrell 2012; USDA-FPL 2010).  2.3.2.1. Seasoning of Wood Poles Seasoning is performed in order to dry wood poles before applying preservative treatment. Air seasoning is the simplest method for this purpose, in which poles are stacked one foot above ground in well ventilated open spaces with spacers to facilitate air circulation for 1 to 12  21 months (Illustration 2.6). Although inexpensive, the poles may be susceptible fungi and insect attacks due to direct exposure to climatic conditions. Despite this, air seasoning commonly adopted for WRC and DF poles before treatment. Air seasoning can prove to be time consuming. Hence, alternate seasoning methods such as Boulton seasoning, steam conditioning and kiln drying have been developed to reduce production times.  Kiln drying is the most commonly used method for wood seasoning nowadays (Morrell et al. 2009).  Illustration 2.2: Seasoning of Timber Poles (reproduced by permission Morrell 2012) 2.3.2.2. Pre-treatment Procedures In addition to seasoning, Utility providers can also adopt certain methods such as pre-boring, incising, deep incising, radial drilling, through boring and kerfing, to improve the pole performance and reduce long term maintenance costs. Incision (Fig 2.5) improves the depth and effectiveness of preservative treatments in wooden poles. Incising is carried for the outer ¾ inch of the wood pole and is mostly recommended for western red cedar poles. Deep incising (Fig 2.5) involves making 3 inch deep cuts along the ground line area of wood pole. Similarly, radial drilling (Fig 2.5) involves drilling series of 3 to 5 deep inch holes in diamond-shaped pattern in the ground line zone. These both processes ensure preservative treatment to percolate deeper into wood poles. Through-drilling is an extension of radial drilling holes completely through the pole and can reduce almost total treatment of the ground line zone. (Fig 2.5).  22 Incising, radial drilling and through boring are only facilitate preservative treatment up to the zone to which they are applied and not above or below that zone (Morrell 2012).    Figure 2.5: Drilling Patterns for Pre-treatment of Timber Poles (reproduced by permission Morrell 2012) 2.3.2.3. Preservative Treatment Wood preservatives are considered as a type of pesticides, hence, in addition to providing protection to wood for its intended use, they should also not pose any adverse risk to the environment. Wood preservatives are generally classified into two categories (1) Oil based preservatives (2) Water-based preservatives. 2.3.2.3.1. Oil based preservatives:  Most common Oil based preservative for treatment of wood poles include creosote, pentachlorophenol (penta) and copper nephthenate.  Creosote was developed in 1838 by John Bethel and is one of the oldest preservative used for protection of wood. Creosote is a black or brownish oil produced from destructive distillation of coal. It is highly effective against wood destroying organisms and ensures longer service life of wood poles. Some drawbacks of creosote solutions include unpleasant odour and skin sensitization in contact. Creosote was rendered a restricted use pesticide and is only employed in pressure treatment facilities (Morrell et al. 2009). Pentachlorophenol (penta) was developed in 1930 as a substitute for creosote and is used along with a heavy hydrocarbon solvent (APWA Standard P9 type) for treatment of wood poles. The solvent play an important role in the performance of penta. It is quite effective against wood  23 decay fungi, molds and insects. Results of field tests of wood poles treated with penta have found to be similar with those of creosote. Due to presence of dioxins, vapour or solution can prove be highly toxic for humans. In November 1986, Pentachlorophenol became a restricted-use pesticide and is currently only available for use in pressure treatment (CSA-O80 2011; USDA-FPL 2010). Copper Nephthenate was introduced in 1900 as a reaction product of copper salts and naphthenic acids. It imparts a light green colour to poles, which turns light brown due to weathering. Copper nephthenate has also been found quite effective against insects and wood decay organisms. Higher cost and non-standardization as compared to creosote or penta, has restricted its use. It is generally recommended for repair of hole and cuts that expose untreated portion of wood (CSA-O80 2011; Morrell et al. 2009).  In addition to the chemicals mentioned above, research is under development for less toxic preservative such as chlorothalonil and isothiazolone. Utility companies are however reluctant in accepting new chemicals, until they are completely sure regarding their effectiveness (Morrell 2012).   2.3.2.3.2. Water based preservative  Water based preservatives are used to provide clean and residue free surfaces of wood poles. Common types of water based preservatives for treatment of wood poles include chromated copper arsenate (CCA), ammoniacal copper zinc arsenate (ACZA), copper azole (CA), and ammoniacal copper quaternary (ACQ) (Morrell 2012).   Chromated copper arsenate (CCA) is an acid system first developed in 1930 containing chromium trioxide, arsenic pent oxide and copper oxide. The acid system undergoes chromium reactions with wood, which may continue for several days or weeks to fix arsenic and copper. CCA has being used quite effectively for treatment of southern pine poles, however is has shown lesser degree of permeability for Douglas fir species. Trials testing may be performed before recommending the chemical for this species (CSA-O80 2011; Morrell 2012; USDA-FPL 2010).  24 Ammoniacal copper zinc arsenate (ACZA) is a combination of copper oxide (50%), zinc oxide (25%) and arsenic pentoxide (25%). It was originally developed without zinc as Ammoniacal copper arsenate (ACA) in 1930, which is no longer available. The presence of ammonia in ACZA is used to solubilize the metals. When the heated ACZA solution is applied to wood, ammonia evaporates and metal precipitate, resulting in deeper penetration than other water borne preservatives (CSA-O80 2011; Morrell 2012; USDA-FPL 2010).  Ammoniacal copper quaternary (ACQ) is a recently developed water based preservative solution to address the issue of arsenic and chromium in treated wood poles. The formulation utilizes ammonia or ethanol amine to solubilize copper which acts as primary fungicide and insecticide. The solution further utilizes quaternary ammonium compounds (‘quats’), which provide added protection against fungi tolerant to fungi. At present, the used of ACQ has rapidly increased in Canada and United States (CSA-O80 2011; USDA-FPL 2010). Copper azole Type B (CA-B) is another recently developed and standardized water based preservative solution. It utilizes copper as a primary biocide and organic trizaole as co-biocide. The copper in copper azole systems provides the primary fungicide and insecticide activity, whereas the azole component provides protection against fungi that are tolerant to copper. Copper azole is widely being used in North America, Australia, New Zealand and Europe (CSA-O80 2011; USDA-FPL 2010). 2.4. Degradation of Timber Poles Timber poles usually have high initial strength and can survive over a longer period of time under proper environmental conditions. However, environmental conditions are not constant and vary in different regions of the world. Wet and humid environmental conditions encourage the development of organisms which results in degradation of wood. Wood decay can be considered as the most significant cause damage to Timber poles throughout the world. The term decay in timber poles describes the process pertaining to different stages of fungal attack i.e. from initial penetration to complete destruction. Principally, the organisms responsible for bio-degradation of wood poles include fungi and insects (Wang and Wang 2012; Wareing 2005).  25 2.4.1. Decay Fungi Decay fungi are the most destructive organisms, when it comes to damaging the structural integrity of timber poles. Decay fungi decompose wood by releasing enzymes and acids, which dissolve cellulose, lignin and other constituents of wood in presence of moisture. The decomposed matter serves as nutrients and is absorbed by fungi. Decay fungi requires favorable conditions to decay wood which include: moisture content (20% to 30%), sufficient availability of oxygen, temperature (60o to 80o Fahrenheit) and food (the wood itself). Wood decay can literally be prevented by altering any of the aforementioned conditions (Shupe et al. 2008). The decay of timber poles occurs in various stages. In the earliest stage of decay, known as the incipient or initial stage, the wood appears to be firm and hard and fungal attack can only be detected by microscopic examination of culture. As the wood continues to decay further, the changes in appearance and condition of wood become more apparent and strength of wood is considerably reduced. This is known as the advanced stage of decay and marks the formation of rot (Brischke and Rapp 2008; Li et al. 2007; Nguyen et al. 2004).  Change in wood colour from normal is indicative of decay presence, however, it is often absent in the incipient stage. Another indication of decay is the softening of wood when checked with a sharp object. Strength of wood reduces considerably even at slight incipient decay. Due to decomposition of wood by decay fungi, the density of wood also reduces as compared to sound wood. Wood affected by decay fungi can also be detected by presence of a mushroom odour. However, this kind of odour can also be indicative of damp conditions and not necessarily the presence of decay. In addition, excessive shrinkage can also provide some clue fungal decay, as decayed wood shrinks more than sound wood. Depending upon the mode of attack, decay fungi can be grouped into three types (Brischke and Rapp 2008; Li et al. 2007; Nguyen et al. 2004). 2.4.1.1. Brown Rot Brown Rot is a type of advanced decay most common in soft woods. The brown rot fungi  decompose the cellulose, leaving lignin in cell walls more or less unchanged, thus giving a characteristic brown colour to wood attacked by these fungi. Brown rot is also sometimes  26 referred to as dry rot, which is misleading considering the fact that wood must sufficiently damp for the decay to occur. Brown rot are responsible for substantial strength loss even in the incipient stage, due to removal of cellulose. Wood affected by brown rot can shrink, crack across grain and crumble under dry conditions (Shupe et al. 2008; USDA-FPL 2010). 2.4.1.2. White Rot White Rot differs from brown rot as it attacks both cellulose and lignin simultaneously. The wood attacked by white rot may lose colour and generally provides a white or bleached appearance. White rot is usually associated with hardwood, however it can also affect softwoods as well. White rot on wood cells can be characterized at the microscopic level through presence of bore holes through walls and general thinning of cell walls at advanced stage of decay (Morrell 2012; Shupe et al. 2008). 2.4.1.3. Soft Rot Soft Rot fungi generally attacks the exposed superficial surface of both softwood and hardwoods, especially the area where the preservative treatment has lost its efficacy.  As opposed to white and brown rot, which occur internally within the timber, Soft rot fungi cause external softening of treated wood, causing considerable damage at ground line and below. This damage results in significant decline in flexural strength due to reduction of wood pole circumference. Some soft rot fungi are tolerant to wood preservative that provide sufficient protection against brown and white rot. Some soft rot fungi can also tolerate extreme conditions such as high temperature and high moisture content, and survive for fairly longer periods as compared to other decay fungi (Morrell 2012; Shupe et al. 2008). 2.4.2. Wood Pecker Damage Woodpeckers peck tress for a variety of reasons. These reasons include drumming, foraging, and nesting and roosting (Harness and Walters 2005). Drumming is used for communication purposes and does not produce significant mechanical damage. Foraging is done in order to search for food. Finally, nesting and roosting cavities are used to lay and roost eggs. The primary reason for woodpecker to target utility poles is thought to be for nesting. The area surrounding wood poles is often cleared which offers woodpecker’s great visibility of their surroundings (Harness and Walters 2005).   27 In order to do a structural evaluation of these damaged wood poles, their sectional properties must be determined. In order to do this, attention must first be place on the sectional resistances which are required. In this case, flexural and shear resistances are of interest. Work by Steenhof (2011) has shown that it is important to consider the orientation of the damage when determining a particular sectional resistance. Orienting the damage with the extreme fibers (i.e., the tension or compression fibers) will have the greatest impact on the flexural resistance whilst orienting the damage with the neutral axis will have the greatest impact on the shear resistance. Thus, to properly evaluate the effect of woodpecker damage on the structure, section properties reflecting both damage orientations must be calculated. 2.4.2.1. Exploratory and feeding damage  The exploratory damage category exhibits the lowest amount of damage of all three categories. It is believed that these holes are made by woodpeckers in search of food. The shape of the hole is roughly cylindrical with an opening size ranging from 25 to 75 mm and a depth ranging between 25 to 150 mm. It is believed that these holes are made at locations where woodpeckers think they have found food. The shape of the hole is similar to that found in exploratory holes. However, the opening has an elliptical shape with a height ranging from 75 to 200 mm and a width ranging from 50 to 75 mm. The depth of hole ranges from 150 to 175 mm.  2.4.2.2. Nesting damage  Nesting damage exhibits a form of damage that is different from exploratory and feeding damage. As the name implies, nesting damage are holes used by woodpeckers to build their nests. The hole consists of a 100 to 175 mm opening into a large cavity. The cavity can be seen as a hollowing of the core of the pole leaving a shell approximately 25 to 75 mm in thickness. 2.5. Timber Pole Inspection Methods Effective and reliable inspection methods can undoubtedly play a pivotal role in the proper management of timber poles. A successful inspection program should account for various factors such as climatic conditions, pole species, system age and type of initial preservative treatment. Although bio-degradation may be more eminent in regions with moist and wet climates, equal importance should be given areas with drier climate as it may be conducive to development of checks and cracks (Nelson 1998). Two methods are used by utility companies  28 to perform inspection of timber poles. These methods include manual inspections and Non-destructive evaluation (NDE) methods. 2.5.1. Manual inspection methods Manual methods of inspection have been consistently used for years by utility companies for condition assessment of timber poles. The manual methods of inspection generally include the following procedures: 2.5.1.1. Visual Inspection Visual inspection is performed by experienced and qualified linemen to assess the condition of the structure and its components, right of way obstructions and to identify any other irregularities. Visual inspection can be performed either on foot, on vehicle or aerially on helicopters. Due to the direct involvement of a skilled personnel, visual inspection provides valuable information regarding safety and integrity of the line. Defects such as wood pecker damage, pole top deterioration, pole leaning, missing or loose hardware can be detected through visual inspection. However, defects such as internal decay cannot be detected through visual inspection. Sometimes, linemen perform climbing or bucket inspection to closely assess wood pecker damage and defects not clear from ground (Nelson 1998; USDA-FPL 2014).     2.5.1.2. Sounding Sounding provides and effective way to detect the presence of decay in timber poles if used by an experienced inspector. A hammer is used to perform sounding and the feel of the sound produced is used to assess the pole condition. A hollow sound would indicate the presence of rot whereas, a sharp sound would indicate sound wood. This method is only suitable for detecting potential hollow areas in portions of the pole above ground and may not be applicable for below ground areas (Morrell 2012; Nelson 1998).  2.5.1.3. Drilling Portions of the utility pole which are identified as hollow, can be further investigated by drilling series of hole in those particular areas. Drilling is used assess the pole in the critical zone, i.e. 6 inches above and 18 inches below the ground line, as this zone provides the most conducive environment for attack by decay fungi. In order to perform drilling, the area around the pole at  29 the ground line is excavated to a depth of 18 inches for humid climates. Further excavation beyond 18 inches can be made, if pole is located in a drier climate. Holes are drilled at 90o in the above ground portion and 45o in the excavated portion. Depending upon the sound of the drill, resistance offered by the pole to the penetration of drilling bit and smell of the wood shavings, an experienced will assess the condition of the timber pole. Cores (3/8 in.) can also be extracted from poles, which can cultured to ascertain the presence of decay fungi or to evaluate the retention and penetration levels of preservative treatments (Nelson 1998; USDA-FPL 2014). The manual methods mentioned above for the inspection and assessment of timber poles greatly rely on the experience and skill of the inspector. Hence any decision regarding the condition or structural capacity of the timber poles using these methods will involve subjective judgment. Manual methods only detect damages that are apparent or near surface and do not possess the capability to identify internal decay.  2.5.2. Non-destructive Evaluation (NDE) Methods Due to inherent amount of in-accuracy and subjectivity associated with manual inspection methods, equal possibility exists that either a timber poles adequate capacity may be condemned prematurely or a weaker poles remains in service. These limitation have led to the development of more advanced inspections methods, which provide a much higher degree of reliability in assessing the nature and extent of damage. These advanced inspection methods include devices which operate on a certain technology principle to measure defects using non-destructive evaluation. The following sections give brief descriptions of the various NDE technologies. 2.5.2.1. Resistance Drilling The method is quite similar to the conventional method of drilling but provides more accuracy in mapping and detecting voids and hollow areas in timber poles. This method uses a relatively smaller dia (1/8 inch) drilling bits as compared to larger dia bits used in conventional drilling. The resistance offered to the bit rotation is recorded and printed as a graph. A slow change in resistance is indicative of change in density due to moisture or initial stages of decay. A sudden change in resistance can be correlated with a decay pocket or void. The measurement obtained  30 from this method depends upon the relationship between the drill resistance and penetration depth. The devices used in this method were originally developed to detect decay and voids in living trees. The inspection holes drilled in trees by this method usually close down due to natural healing and growth. However, such natural phenomenon does not occur in utility timber poles. Hence, holes made in timber poles should be filled with chemicals to stop the ingress of decay and insects (Morrell 2012; Nelson 1998; Nelson and Sinclair 2005).    2.5.2.2. Stress Wave Methods The method utilizes the stress wave (speed of sound) propagation principle to assess the material. The technique involves measurement of time taken by a sound wave to travel between two sensors attached on both sides of the timber pole. The principle behind the use of this method is that stress waves propagate at a lower speed in a decayed or low quality timber. However, it has been observed that good quality inhomogeneous materials allow faster propagation of stress waves as compared to the ones with low quality. As timber is an inhomogeneous material, the reliability of this technique is debatable. Nevertheless, it can be viewed as a method that provides a prompt assessment regarding the quality of the timber pole (Nelson 1998; Seavey and Larson 2002).  Apart from stress wave measurement, stress wave analysis technique provides a more reliable method for estimation pole condition. This method is the based on the concept that in inhomogeneous materials like timber, stress wave not only propagates at different speeds but also attenuate differently at various frequencies. The stress wave devices are not capable to detect decay, rather they use the sound wave parameter and relate them with modulus of rupture and modulus of elasticity to estimate the residual strength of timber poles. Hence, they will give similar strength values for both weak and sound poles. In such a case, stress wave method may be supplemented by conventional methods to come up with a final decision regarding strength of timber poles (USDA-FPL 2014).  2.5.2.3. X-Ray Tomography method    The X-Ray tomography method is similar to the method of x-ray used in the medical field. Timber poles possess considerable variation in density throughout its length. In general, variation in density depends upon the presence of moisture, however, decay and other defects  31 can also complement to this variation. The x-ray tomography method can be used to detect these variations in densities in different portions of the timber pole. The method has been used since 1970 for in-situ inspection of timber poles. However, due to heavy equipment, slow process and relatively higher cost, this method is rendered unsuitable for field use. The device used in this method emits radiations, which pass through the timber pole and are measured by a sensor on the opposite side. The amount of radiation received at the sensor will fluctuate depending upon the density of timber poles i.e. higher the density, lesser will be amount of radiations received by the sensor. Measurements can be taken from different direction for accuracy (Morrell 2012; Nelson and Sinclair 2005). 2.5.2.4. Radar Method In this method, a radar antenna transmits electromagnetic waves, which provide three dimensional images of timber poles. These images are used to interpret various characteristics such as variation in density and presence of internal defects such as decay. The radar system is either mounted on a truck or helicopter and can be used to perform detailed analysis of pole structures. Due to cost issues, it is not feasible for regular or frequent inspection  (Nelson and Sinclair 2005; Seavey and Larson 2002). 2.6. Fuzzy Logic and Fuzzy Synthetic Evaluation Technique 2.6.1. Fuzzy set theory Subjective judgment (cognitive uncertainty) is inherent with human decision making. Uncertainty can be classified into two forms i.e. fuzziness (vagueness) and ambiguity (conflicting possibility). Fuzziness may be defined as the lack of clarity or sharp distinction among deliberations or decisions. Fuzzy set theory provides an ideal approach to effectively formalize and handle such uncertainties in decision making.(Klir and Yuan 1995; Sadiq et al. 2004) Ambiguity, on the other hand arises when there are several alternatives to the same problem or proposition due to partially ignorant or missing information. Problems pertaining to ambiguous information can be ideally solved using evidential reasoning (Rajani et al. 2006). In this thesis, uncertainty associated with fuzziness will only be considered.   Fuzzy set theory was first introduced by Lotfi Zadeh (1965), as an extension to the traditional set theory and since then has been used to solve complex real world problems. In the traditional  32 set theory, an element x either has full membership to a particular set or no membership at all. In a fuzzy set, however, an element x can have a partial degree of membership µ, which ranges between 0 and 1. An element x having a value closer to unity signifies higher degree of membership within a specified fuzzy set and vice versa. Thus a fuzzy sets enables to characterize quantitatively, the degree to which an element belongs to a set. A fuzzy set can be characterized by a membership function (MF) that defines how each point in the input space, also referred to as universe of discourse, is mapped to a membership value between 0 and 1. Based upon available data and experience, fuzzy numbers can be represented by MF of various shapes.  In general, triangular and trapezoidal shapes are used to represent fuzzy numbers due to their simplicity and computational efficiency. A triangular MF is shown in Illustration 2.3:    Illustration 2.3: Triangular Membership Function The above triangular MF is specified by three parameters a (smallest possible value), b (most likely value) and c (largest possible value). These parameters indicate the x-coordinate of the three corners of the triangular MF. The membership of any value x, mapped on the triangular function can be determined by relationships given in eq. 2.9 below:  33 ……….………………………… (2.9)  Similarly, a trapezoidal MF can be represented by four parameters a, b, c and d as shown in Illustration 2.4 below:  Illustration 2.4: Trapezoidal Membership Function Mathematical representation of a trapezoidal membership function can be given by Eq. 2.10.  34 ……….………………………… (2.10)  Fuzzy set theory has been successfully used in studies related to water quality assessment (Lu et al. 1999; Sadiq and Rodriguez 2004; Sadiq et al. 2004), industrial applications (Kabir and Hasin 2012), deterioration of water main pipes (Najjaran et al. 2004; Sadiq et al. 2004), Condition assessment of water main pipes (Al-barqawi and Zayed 2006; Rajani et al. 2006; Yan and Vairavamoothy 2004), Seismic risk assessment of RC buildings (Tesfameriam 2008), Condition evaluation of RC bridges (Sasmal and Ramanjaneyulu 2008), Pavement condition evaluation (Fwa and Shanmugam 1998; Sun and Gu 2011) and Urban infrastructure management (Tesfameriam and Vanier 2005). 2.6.2. Fuzzy Synthetic Evaluation Multi criteria decision making (MCDM) methods have been used for years to solve real life problems. However, these methods do not have the capability to account for uncertainty and imprecision arising from human perception. Integration of fuzzy logic in MCDM methods enables to incorporate subjectivity to provide a rational approach to decision making. Fuzzy synthetic evaluation is a type fuzzy MCDM method and consists of the following distinct three step process referred to as fuzzification, aggregation and defuzzification (Rajani et al. 2006; Sadiq et al. 2004). The following sections give a detailed step by step description of the fuzzy synthetic evaluation technique (Sadiq et al. 2004). 2.6.2.1. Development of Framework for Fuzzy Synthetic Evaluation The first step of FSE is to identify of criteria and alternatives which directly influence the decision making process. The criteria for decision making can be broken down into sub criteria to account for detailed analysis. This results in hierarchical structure of criteria, which may be broken down further until no subdivision is possible. The composite number obtained by grouping sub-criteria provides a final score, which forms the basis of decision making. The  35 basic criteria can either be estimated quantitatively in the forms fuzzy or crisp values or may be expressed as qualitative linguistic terms e.g. the efficiency of a certain machine can be defined as “moderate” or “satisfactory”. The FSE has the advantage to deal with such data that is qualitative, imprecise and involves inherent amount of subjective judgment.   2.6.2.1.1. Fuzzification The fuzzification process is the most important part of the proposed methodology and converts criteria into a homogenous scale by assigning memberships with respect to an evaluation set. The number of qualitative levels of the evaluation set, also known as the granularity, may be defined by expert opinion or industry choice. Other methods such as heuristic and fuzzy c-means (cluster analysis) may also be used generate fuzzy evaluation sets. In general, the granularity of a fuzzy evaluation sets can be defined by 5 – 11 qualitative levels depending upon the type of application. In this study, a five granular fuzzy evaluation set has be defined heuristically to be assigned to each basic criteria: B = {Very Good, Good, Fair, Poor, Very Poor}……………………………………………   (2.11) The scope of this study is to classify each pole in a particular utility line segment into an appropriate evaluation category according to a predefined set of criteria or defect indicators. The shape of the fuzzy evaluation sets for a corresponding criteria represent a membership function. The development of a membership function depends upon how a particular defect indicator is measured and the shape is defined either by expert opinion using Delphi methods or through available literature. The observed value of a criteria is mapped on the corresponding scale of its respective membership function to obtain a 5-tuple fuzzy set (μVG, μG, μF, μP, μVP), where μ refers to the degree of membership to each category in the fuzzy evaluation set. The sum of degree of membership of all values is known as the cardinality of the fuzzy set.   36  Illustration 2.5: Performance Scale for Fuzzification Iluustration 2.5 shows an example of membership function in which a criteria X is defined over a range of 0 to 1. The shape fuzzy evaluation set for the criteria X are also defined. Suppose the observed value for the criteria X is 0.65 which is represented by X1. After Fuzzification, a 5-tuple fuzzy set is obtained, i.e. (0, 0, 0.75, 0.25, 0), where the values represent the membership to each category of evaluation set – Very Good (0), good (0), fair (0.75), poor (0.25) and Very Poor (0). Table 2.4: Values obtained after Fuzzification  μ Very Good μ Good μ Fair μ Poor μ Very PoorPerformance Scale, X (<0.2,0.2,0.4) (0.2,0.4,0.6) (0.4,0.6,0.8) (0.6,0.8,1) (0.8,1,1)Observed Value, X1X1 = (0.65) 0 0 0.75 0.25 0X1 (5-tuple fuzzy set) ( 0, 0, 0.75, 0.25, 0) 37 2.6.2.1.2. Determination of Criteria Weights The impact and contribution of each criteria towards the final rating or goal is reflected through its corresponding weight co-efficient. The value of weight coefficient depends upon the relative importance of criteria and is established through a set of preference weights and trade-offs among each criteria. This process requires sufficient information regarding criteria, careful deliberation and subjective judgment. The set of weights obtained represents a weight vector, which satisfies the normalized condition as shown in Eq. 2.12 below: W= (w1, w2, w3,…….., wn)………………………………………………………..………(2.12) Where,        ∑ 𝑤𝑗 = 1𝑛𝑗=1      In this study, Analytical hierarchy process (AHP) will be applied to determine the weight coefficients of each criteria.  AHP was proposed by Saaty (1988) and provides a manageable approach to estimate the relative importance of each criteria one at a time using pair wise comparison. Pair wise comparison allows equal opportunity to each criteria to serve as reference point and relies heavily on engineering judgment.  Table 2.5 shows the scale by which relative importance of different criteria is established using intensity of importance. As a result of pair wise comparison, an importance matrix I can be established (Fig 2.13) given by I= (Iij)mxm  where m = number of criteria and Iij = importance intensity of a criterion i with respect to criterion j. Consider the example of an importance matrix I as shown below. It is evident that the criteria a11 has been assigned a relative importance of three times greater than a12 and 1.5 times greater than a13 respectively. Similarly, importance intensities can be assigned to other criteria in this manner. It should also be noted the values in the upper triangle of the matrix are reciprocal to the values in the lower triangle.        38 …………………………………………......(2.13) Table 2.5  Fundamental scale used to develop priority matrix for AHP (Saaty 1988) Intensity of Importance Definition  Explanation 1 Equal importance  Two activities contribute equally to the objective 2 Weak  – 3 Moderate importance Experience and judgement slightly favour one 4 Moderate plus – 5 Strong importance Experience and judgement strongly favour one 6 Strong plus – 7 demonstrated importance An activity is favoured very strongly over another 8 Very, very strong  – 9 Extreme importance The evidence favouring one activity over another is of highest possible order of affirmation   The importance intensities to each criteria should be assigned based on expert opinion and judgement. The importance intensity values can be modified at a later stage on availability of more reliable data or new expert judgement. There are several methods to derive weight vector a 1 a 2 a 3a 1 1.00 3.00 1.50I = a 2 0.33 1.00 4.00a 3 0.67 0.25 1.00 39 ………………………..…… (2.14) (2.16) ………………………………………………………….………… (2.15) ……………..……… (2.17) W form the pair wise comparison matrix I. These methods include the least square method (Xu 2000), geometric mean method (Buckley 2012), extent analysis (Chang 2004) and eigenvector method (Saaty 1988). The geometric mean method proposed by Buckley will be utilized in this research.  After taking the geometric mean of each row in the importance matrix I, a matrix J is obtained. The weight vector W can be determined by normalizing the matrix J.     2.6.2.1.3. Aggregation The five-tuple fuzzy set for each criteria established as a result of fuzzification are arranged in a five-tuple fuzzy matrix R. The weight vector as determined in the previous step is multiplied with the Fuzzy matrix R, which gives a final fuzzy set F. This process is known as aggregation and represented by the following relations:    F = W      R   2.6.2.1.4. Defuzzification The final fuzzy set F provides an overall membership corresponding each qualitative level in the fuzzy evaluation set. Decision makers are more interested in crisp value and are often not 1.64 w 1 0.50J = 1.10 => W = w 2 = 0.330.55 w 3 0.17μ1VG μ1G μ1F μ1P μ1VPF = w 1 w 2 w 3 μ2VG μ2VG μ2VG μ2VG μ2VGμ3VG μ3VG μ3VG μ3VG μ3VGF = μ VG μ G μ F μ P μ VP 40 comfortable with results expressed in fuzzy values. The process to calculate a crisp value of the final fuzzy set F is known as defuzzification. There are several methods to perform defuzzification. Centre of Area method (Yager 1980), maximum operator method (Chen and Hwang 1992) and weighted average approach (scoring method) (Lu et al. 1999; Sadiq and Rodriguez 2004).  In this research, the maximum operator method, also known as maximum grade principle (Sun and Gu 2011) will be used for defuzzification. The maximum operator principle implies that the entry in the final fuzzy set, whose membership corresponds to the highest qualitative linguistic level in the evaluation set, is assigned as the crisp value and may be defined as the overall evaluation outcome. 2.7. Summary This chapter presents a detailed review pertaining to the state-of-the-art knowledge and research available on reliability assessment of timber utility poles. In Canada, two standards are used to design overhead utility support structures. These standards include CAN/CSA 22.3 No.1 Deterministic design code and CAN/CSA 22.3 No.60826 Probabilistic design code. CAN/CSA 22.3 No.1 is the most commonly used design code in Canada for overhead structures. Previous reliability assessment studies in Canada have been carried out using CSA 22.3 No.1. These studies have concluded that reliability of structures is mainly dependent upon the geographical conditions and is not uniform across all locations. In this research, reliability of timber poles achieved through CSA 22.3 No.1 deterministic code will be evaluated using fragility analysis, the procedure for which has been outlined. Furthermore, time dependent degradation of timber poles due to decay, not considered in previous studies, shall be accounted for in this research. In addition to reliability analysis, this chapter provides as insight to structure, manufacturing, preservation, degradation mechanism and condition assessment methods for timber utility poles. This chapter also provides an introduction to fuzzy logic based fuzzy synthetic evaluation technique, which will be employed in this research to develop a condition rating tool for timber utility poles.          41  Reliability Assessment of Timber Utility Poles using Fragility Analysis 3.1. General Fragility of a system is a key component in defining the damage state of a structural system exposed to extreme wind hazards. The probability that a structure is not able to meet its prescribed performance criterion conditioned on an intensity measure, can easily be described by a fragility curve (Shafieezadeh et al. 2013). In this research, damage state has been specified as the flexural failure of timber poles at ground level. Here, the probability that a timber pole will break at ground level, conditioned on an intensity measure (wind pressure) will be estimated through fragility analysis of timber poles. The general performance function for timber poles is given by: 𝐺 = 𝐶 − 𝐿…………………………………………………………………………….…..(3.1) Where, C = Actual capacity of timber pole (N-m) L = Load or demand on the timber pole (N-m) Although, there are several failure modes for timber poles such as foundation failure, failure due to unbalanced forces (broken wire condition), failure due to torsion etc. (Datla and Pandey 2006; Datla 2007), however, only flexural failure mode at the ground level due to wind speed is considered in this research. According to ASCE (2006), for timber poles (<60 ft in height) such as distribution poles, bending stresses are critical at the ground level (Salman 2014). Hence, the general equation for performance function can be written in terms of flexural stress at the ground level as: 𝐺 = 𝐶 − 𝐿 = 𝜎𝐶 − 𝜎𝐿………………………………………………………...……….(3.1a) Where, σC = Flexural capacity of timber pole at ground level (N-m) σL = Flexural stress or load on the timber pole at ground level (N-m) Failure of any structural system or component is an uncertain event. This uncertainty is directly associated with the uncertainties inherent with the capacity of the structural components and  42 demand (whether natural or manmade). Fragility assessment provides solid framework to evaluate the performance of the structure by incorporating uncertainties with both capacity and demand. In order to obtain fragility curves to estimate reliability of timber poles, it is imperative to establish the capacity and demand model for timber pole under consideration (Shafieezadeh et al. 2014). The effect of age dependent deterioration or decay due to fungal attack on reliability of poles designed as per deterministic approach shall also be investigated in this research. 3.2. Pole Model Fig 3.1 shows a typical distribution timber pole considered in this study for performing reliability analysis.  The timber pole is assumed to be a tangent structure without any guy supports. Timber poles connected in a line are categorized by vertical and horizontal spans, which are important in determining the transverse and vertical resultant loads on the pole. Vertical span (VS as depicted in Fig 3.2), or weight span is the horizontal distance between the lowest points of the conductor sag on adjacent spans. Whereas, the horizontal span (HS as depicted in Fig 3.2), or wind span is the horizontal distance to mid points of adjacent spans (Steenhof 2011).  For this research, the timber pole is considered to be located on flat terrain i.e. Weight span = Wind span, i.e. VS = HS. Construction Grades ranging from 1 through 3 have been specified in CSA 22.3 code for deign of utility poles. Grade 1 is the strongest, whereas Grade 3 is the weakest. In this research, Grade 2 construction was assumed, which depicts the majority of distribution poles. For wind pressure calculations, the span length is taken as 100 m. Timber Poles were assumed to be located in four cities in the province of British Columbia (BC) namely Vancouver, Victoria, Kelowna and Castlegar. According to the weather loading map of Canada as given in CSA 22.3 No.1 code (CSA C22.3 No.1 2010), all the selected locations fall in the Medium B loading zone (Fig. 2.1). The deterministic wind pressure specified in the code for Medium B loading zone is 300 N/m2. As the selected locations fall under the same loading zone, hence the analysis will be considered more representative in terms of comparison of reliabilities.    43    Figure 3.1: Configuration & Layout of the Timber Distribution Pole  44  Figure 3.2: Horizontal and Vertical Spans (USDA-RUS 2009) 3.2.1. Design Load on Timber Pole The wind force acting on each component produces certain amount of moment at the ground line. The intensity of wind force acting on timber poles is a direct function of its geometric features, which primarily include the free length of the pole above ground, diameter of pole at top and ground line, span between adjacent poles, number of conductors attached to the poles, conductor diameters and their height above ground line. Similarly, any additional component attached to the pole such as transformers and switches will also influence the magnitude and intensity of wind force. Depending upon the class of poles, CSA 015-05 (CSA O15 2005) provides the geometric properties such as length and diameter of timber utility poles.  In addition to wind loads, Vertical loads such as dead load of timber pole, conductors and other components also contribute towards the total moment at ground line. Hence, the total design  45 load on the pole is the summation of moments due to horizontal load on components as well as vertical loads due to dead weights, and is given by. 𝐿 =  ∑(𝐹𝑛. ℎ𝑛 + 𝑄. 𝑒)…………………………………………………………………….(3.2) Where,  L = Design Load (N-m)  F = Horizontal force due to wind acting on the component n (N)  h = Distance from ground level to the centroid of component n (m)  Q = Vertical dead load due to components (N)  e = eccentricity of vertical loads (m) CSA 22.3 No.1 specifies both linear as well as non-linear (considering P-Δ effect) approaches for design of timber poles. Hence, reliability analysis will be performed using both these approaches. In this research, wind load on timber pole is assumed to act in the transverse direction, which is the worst case scenario and produces maximum bending moment at the ground level. The pressure that wind exerts on the pole, conductors or other components is given by (CSA C22.3 No.1 2010):  𝑃 =  𝐶𝑑 .  12⁄  𝜌 .  𝑉2……………………………………………………………………...(3.3) Where, P = Wind Pressure (N/m2) Cd = Drag Coefficient or shape factor = 1.0 (for cylindrical objects)  ρ = air density (kg/m3) V = Wind Speed (m/s) 3.2.2. Design Capacity of Timber Pole The CAN/CSA 015-05 categorizes the capacity or resistance of different species of timber poles in terms of their fiber stress values. The geometry of timber poles include its total length and circumferences at different heights. During erection of timber poles, some portion remains embedded in ground, which experiences a distributed lateral soil pressure under wind loads. As the circumference of the pole increases linearly from top to bottom, the moment capacity  46 increases. Lateral wind pressure acting on the face of the pole and conductors horizontally tend to cause deflection at pole top, thus producing moments near the ground line. Failure of the timber pole occurs when the induced moment due to wind exceeds the moment capacity of the pole at ground line. The ultimate bending strength (𝜎𝑏) of the timber pole at ground level, also known as the Modulus of Rupture (MOR) is given by: 𝜎𝑏 =  𝑀𝑆………………………………………………………………………………….(3.4) Where, M = Ultimate moment capacity at ground level (N-m) S = Section modulus (m3)  Eq. 3.4 can also be written as, 𝑀 =  𝜎𝑏 . 𝜋𝐷332…………………………………………………………………………...(3.5) Where D is the diameter of timber pole at ground level. 3.2.3. In-service deterioration of Timber Poles Timber poles are naturally occurring materials and possess a high tendency to lose strength with time under the effect of climatic conditions. Timber absorbs moisture from the atmosphere and instigate the development of decay by fungi attack which are the main contributors to the deterioration of timber poles. Decay is usually facilitated by moisture, humidity and lack of oxygen. The region of timber pole in the vicinity of ground line provides such ambient conditions for fungal growth; and hence, can be considered the most vulnerable to decay. The decrease in capacity or resistance of timber poles resulting from deterioration at any specific time during its service life can be characterized by a degradation function (Bjarnadottir et al. 2013) and can be written as: 𝐶(𝑡) =  𝛼(𝑡).  𝐶……………………………………………………………………...…...(3.6)  47 Where,  C(t) = Capacity of pole at time t  α(t) = Degradation function  C = Design capacity of timber pole Wang et al. (2008) developed a model to estimate the loss in capacity of timber poles at ground level subject to attack by decay fungi. The model was developed in Australia on the basis of tests carried out on 77 untreated species of heartwood between 1968 and 2004. Although, the decay model was developed in Australia, it will be used as starting point in Canada to estimate the strength loss of timber poles resulting from fungal deterioration with time. Wang et al. (2008) assumed that the decay in the timber pole occurred in the region 100-200 mm below ground level and progressed inwards from the outer parameter. This results in loss of section and can be estimated as: 𝛼(𝑡) =  𝜋32 [𝐷 − 2𝑑(𝑡)]3…………………………………………………………………(3.7) Where,  D = Initial Diameter of Pole   d(t) = decay depth Timber poles do not consist of homogenous sections throughout its entire length. Depending upon the type of species, timber poles can either have a combination of sapwood and heartwood or solely heartwood. Western red cedar is found to possess considerably thin sapwood, as compared to other species such as Douglas Fir and southern Pine etc. (Lassen and Okkonen 1969). For this particular research, it is assumed that timber poles are only composed of untreated heartwood, and therefore, the deterioration model as proposed by Wang et al. (2008) can be implemented directly. The decay model is based on survey of timber poles in Australia. According to Australian Standard AS 5604 (2005) on durability of timber poles, western red cedar corresponds to a durability class of 2 and classified as softwood. Australian standards have been assumed applicable in Canada due to non-availability of such characteristic data in Canada. These assumptions may be modified in future as more information become available.    48 The rate of decay of untreated heartwood can be estimated as follows:(Wang and Wang 2012) 𝑟 =  𝑘𝑤𝑜𝑜𝑑𝑘𝑐𝑙𝑖𝑚𝑎𝑡𝑒(mm/year)……………………………………………………………(3.8) The climate parameter depends upon the temperature and rainfall occurring in a particular area. Hence, Eq. 3.8 can be written as:   𝑟 =  𝑘𝑤𝑜𝑜𝑑 . 𝑓 (𝜆)0.3. 𝑔(𝜏)0.2 (mm/year)…………………………………………………(3.9) Where, 𝑘𝑤𝑜𝑜𝑑 =  {0.23,      𝑓𝑜𝑟 𝐶𝑙𝑎𝑠𝑠 10.48,      𝑓𝑜𝑟 𝐶𝑙𝑎𝑠𝑠 20.76,     𝑓𝑜𝑟 𝐶𝑙𝑎𝑠𝑠 3……………………..……………………………....…(3.9a) 𝑓(𝜆) = {10[1 − 𝑒−0.001(𝜆−250)] (1 −𝑁𝑑𝑚6) ,  𝑖𝑓 𝑅 > 250𝑚𝑚 𝑎𝑛𝑑 0 ≤ 𝑁𝑑𝑚 ≤ 6;0,                                                                                                          𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒…….(3.9b) g(𝜏) =  {0,                    𝑖𝑓 𝜏 ≤ 5℃−1 + .2𝜏,                   𝑖𝑓 5℃ < 𝜏 < 20℃−25 + 1.4𝜏,                           𝑖𝑓 𝜏 > 20℃……………………………….…….(3.9c) 𝑓(𝜆) and  g(𝜏) are the functions of annual rainfall (mm/year) and average annual temperature (oC), respectively. 𝑁𝑑𝑚  refers to number of dry months per year during which total rainfall does not exceed 5 mm.  Wang et al. (2008) found out that the decay in timber poles did not commence immediately after installation, in fact there was a certain period initially, in which the timber poles experienced negligible or no decay. This period is referred to as time lag and can be estimated in terms of decay rate as follows: 𝑡𝑙𝑎𝑔 =  5.5𝑟−0.95…………………………………………………………………………(3.10) The decay depth can be calculated on the basis of decay rate as follows: 𝑑(𝑡) =  (𝑡 −  𝑡𝑙𝑎𝑔)𝑟……………………………………………………………………..(3.11) According to Wang et al. (2008), uncertainties within the predictive decay model arising from the variability in timber and climatic parameters must be accounted for in estimating the  49 deterioration of strength with time. The coefficient of variation (COV) of decay depth is given by: 𝑉𝑑 =  √𝑉𝑘𝑤𝑜𝑜𝑑2 + 𝑉𝑘𝑐𝑙𝑖𝑚𝑎𝑡𝑒2 ………………………………………..………………………(3.12) Where, VKwood = COV of wood parameter VKclimate = COV of climate parameter The COV values of both wood and climate parameters pertaining to timber poles of durability class 2 are the same, i.e. 0.55. Therefore, the COV of decay depth for durability class 2 timber after incorporating the above values in Eq. 3.12 comes out to be 0.78. The uncertainty in the strength of timber pole at any time t is directly related to its initial strength and the uncertainty arising from the decay depth. The COV of pole strength at any time t is given as: (Wang et al. 2008) 𝑉𝐶(𝑡)2 =  𝑉𝐶(0)2 +  [6𝑉𝑑𝑑(𝑡)𝐷−2𝑑(𝑡)]2…………………………………………………..…….(3.13) Where, VC (0) = COV of initial strength Vd = COV of decay depth D = Initial diameter of pole d(t) = Decay depth at time t 3.3. Wind Fragility Analysis The conditional probability of failure of a structural system as a function of wind speed is defined as the wind fragility (Bjarnadottir et al. 2013; Li and Ellingwood 2006). Monte Carlo simulation (MCS) has been utilized in this study to estimate the conditional probability of failure of timber utility poles. To account for uncertainty, variables associated with the design of timber poles are randomly generated 50,000 times in the MCS. For each run of the MCS, wind speed is increased monotonically from 0 to 100, and the number of cases where the demand exceed the capacity (i.e. pole fails) are counted. The results are then used to develop fragility curves.  50 Previous studies (Li and Ellingwood 2006; Rosowsky and Ellingwood 2002; Schultz et al. 2010) have shown that Fragility of a structural system can be described by a lognormal distribution. 𝐹𝑅(𝑉) =  𝛷 [𝑙𝑛(𝑉𝑚𝑅)𝜁𝑅]…………………………….…………………………………...(3.14) Where, V = Wind Speed mR = Median Capacity or Resistance ζR = Logarithmic Standard Deviation of the Capacity or Resistance  Φ(.) = Standard normal cumulative distribution function 3.4. Annual Probability of Failure Fragility analysis provides the conditional probability of failure over a range of wind speeds to which the timber pole can be subjected to. For reliability analysis, the expected or actual annual probability of failure of a timber pole has to be estimated using probabilistic wind speed data for a particular location based on a desired return period. CSA Standard for reliability based design (CSA C22.3 No.60826 2006) suggests that annual wind speed can be modelled using Gumbel Type-1 distribution in Canada. The probability density function (PDF) for extreme wind speed using Gumbel Type-1 distribution is given as: 𝑓𝑉(𝑉) =1𝛼 exp [− (𝑉−𝜇𝛼) − exp [− (𝑉−𝜇𝛼)]]………………………………………..(3.15) Where, V = Extreme gust/wind speed (m/s) µ = Location parameter α = Scale parameter Wind speed data for the four selected locations was obtained from the Environment Canada website (weather.gc.ca). Extreme Value analysis (Goel 2008) was performed to estimate the parameters for Gumbel Type-1 distribution and has been provided in Appendix 1. Table 3.1 shows the parameters of Gumbel Type-1 distribution for each location.  51 Table 3.1: Probabilistic Parameters for Wind Loading Location Mean Wind Speed (m/s) COV (%) Gumbel Parameters µ α Vancouver 24.60 15.55 22.80 3.27 Victoria 23.27 13.32 21.80 2.68 Kelowna 21.10 12.93 19.76 2.50 Castlegar 23.07 13.94 21.40 3.39 The extreme wind speed corresponding to a specific return period (T) in case of Gumbel Type-1 distribution can be calculated by the following equation: (Goel 2008) 𝑉 =  𝑉𝑚 −  𝜎𝑐2𝑐1 +  𝜎𝑐1 [− ln (− ln {1 −1𝑇})]…………………………………..(3.16) Where, Vm = Mean value of wind speed σ = Standard deviation of wind speed C1 & C2 = Parameters depending upon the no. of observations T = Return Period  Based on the parameters of Gumbel Type-1 distribution in Table 3.1 and Eq.3.16, extreme wind speeds at different return periods are given in Table 3.2. Illustrations 3.1 to 3.4 show the wind hazard curves for the selected locations.    52 Table 3.2: Wind Speeds (m/s) at various Return Periods Location Return Period (Years) T=10 T=25 T=50 T=100 T=200 T=300 T=400 T=500 Vancouver 30.16 33.26 35.56 37.85 40.12 41.45 42.39 43.13 Victoria 27.83 30.37 32.25 34.12 35.98 37.07 37.84 38.44 Kelowna 25.39 27.75 29.51 31.26 33.00 34.01 34.73 35.29 Castlegar 28.49 31.45 33.64 35.82 37.99 39.26 40.16 40.86   Illustration 3.1: Wind Hazard Chart for Vancouver  53    Illustration 3.2: Wind Hazard Chart for Victoria  Illustration 3.3: Wind Hazard Chart for Kelowna  54  Illustration 3.4: Wind Hazard Chart for Castlegar The expected annual probability of failure for extreme wind speed can be determined by convolution of cumulative distribution function (CDF) of wind fragility (Eq. 3.15) described in section 3.3 and probability density function (PDF) of the extreme wind speed model (Eq. 3.16) mentioned in section 3.4: (Bjarnadottir et al. 2013; Li and Ellingwood 2006) 𝑃𝑓 =  ∫ 𝐹𝑅(𝑉). 𝑓𝑉(𝑉)𝑑𝑉∞0……………………………………………………………..(3.17) Where, FR(V) = Cumulative distribution function (CDF) of wind fragility  fV(V) = Probability density function (PDF) annual wind speed model   The above equation can be solved using numerical integration. The reliability index (β) can be estimated by the following relationship: (Zhai and Stewart 2010) 𝛽 = 𝜙−1(−𝑃𝑓)………………………………….……..…………..…………………...(3.19) Fig 3.3 shows a flow chart of estimating reliability of timber poles using fragility analysis.     55  Figure 3.3:  Flow Chart for Reliability Analysis Select the Grade of Construction, Pole height, no of attachments and span lengthDesign Pole based on CSA 22.3 No.1 considering Non-Linear Analysis (P-∆ Effect)Select a Pole Class Capacity > LoadYesNoEstablish values of random variables for Capacity (C) Consider Degradation with TimeC(t) = CC(t) =Δ(t).CConduct Monte Carlo Simulation i.e. Randomize Capacity and Load variables for N runs Determine Annual Probability of Failure and Reliability IndexNoYesChoose Failure Mode (Flexural, Torsional,Foundation etc.)Design is Ok. Proceed for Fragility AnalysisEstablish values of random variables for Load (L)Estimate degradation function Δ(t)Develop Fragility Curves Fragility Analysis  56 3.5. Results of Fragility Analysis Fragility analysis was carried out by considering wind speed as the intensity measure. Wind fragility curve shows the conditional probability of failure of a timber pole for a defined range of wind speed. As stated previously in Section 3.3, the probability of failure can be estimated by counting the number of times the Load (L) exceeds Capacity (C) for N runs of a Monte Carlo Simulation. For each iteration of Monte Carlo simulation, the wind speed is increased monotonically (0 to 100 m/s), while uncertain parameters associated with capacity and load are randomly generated according to their respective distribution. Pole class for the reference structure as shown in Fig. 3.2 was selected according to the CSA 22.3 No.1 non-linear design requirements. CAN/CSA-015 specifies a COV of 20% for strength of timber poles. For this analysis, bending strength of timber poles was assumed to follow a lognormal distribution, which was also previously suggested by Li et al. (2006) and Wolfe et al. (2001).  The magnitude of wind load on the pole structure is determined by the geometry of the pole and conductors. The statistical parameter of random variables for both capacity of timber poles and wind load to be used for fragility analysis are shown in Table 3.3. Fragility curves were also developed for poles at the age of 25 and 50 years. Eqs. 3.6 to 3.13 were used to calculate the strength of timber under the effect of degradation. As decay occurs, the effective diameter of timber pole decreases and also causes a decrease in bending strength with time. The decrease in bending strength depends upon the rate of decay, which further depends upon two parameters; Wood parameter (kWood) and Climatic parameter (kClimate) as given in Eq. 3.8 and Eq. 3.9. According to Australian Standard (AS 5604 2005), Western red cedar falls under the durability class 2. Hence, the value of wood parameter can be taken as 0.48 from Eq. 3.9a. Similarly, the climatic parameter for a specific location can be calculated by using Eq. 3.9b and 3.9c. This involves the analysis of actual rainfall and temperature data for that particular location. The climatic parameters for the selected locations are given in Table 3.4.    57 Table 3.3: Statistical Parameters for Fragility analysis Variable  Description Unit Probability Distribution Mean Value COV Remarks Source σb Fiber Stress  MPa Lognormal 39 Varies WRC CSA 015-05 E Modulus of Elasticity  MPa Normal 7720 0.14 WRC CSA 015-05 DPole Dia of Pole m Normal Varies 0.06 WRC Bjarnadottir et al. 2013 (for COV values) DConductor Dia of Conductors mm Normal 20.7 0.06 477 ACSR Pelican DNeutral Dia of Neutral mm Normal 7.82 0.06 # 2 ACSR Haddock DComm Dia of Communication Cable mm Normal 60.59 0.06 8mm 1x200 pair Cu +2x50 pair Cu hPole Distance to Centriod of pole from GL m Normal 5.3 0.03   Bjarnadottir et al. 2013 (for COV values) hConductor Distance to Centriod of Conductor from GL m Normal 11.66 0.03 hNeutral Distance to Centriod of Neutral wire from GL m Normal 10.66 0.03 hComm Distance to Centriod of Comm Cable from GL m Normal 7.74 0.03 WRC = Western Red Cedar  GL = Ground level Table 3.4: Climatic Parameters for selected locations Location KClimate Vancouver 1.66 Victoria 1.50 Kelowna 0.60 Castlegar 1.18  58 The variation in climatic parameter would result in different values for decay rate. This suggests that the reduction in strength or capacity of timber poles with time due to degradation depends upon the climatic conditions. The COV of capacity of timber poles at different ages is calculated by Eq. 3.13. Table 3.5 shows the COV of timber poles from class 1 to 5 at 0, 25 and 50 years respectively. Table 3.5:  COV of Capacity (C) of timber poles for class 1 to 5 at various ages Location Service Life Pole Class 1 2 3 4 5 COV (%) COV (%) COV (%) COV (%) COV (%) Vancouver 0 20.00 20.00 20.00 20.00 20.00 25 29.84 31.06 32.53 34.30 36.07 50 62.57 67.29 72.90 79.69 86.54 Victoria 0 20.00 20.00 20.00 20.00 20.00 25 27.62 28.58 29.75 31.16 32.58 50 55.22 59.14 63.81 69.43 75.07 Kelowna 0 20.00 20.00 20.00 20.00 20.00 25 20.32 20.36 20.42 20.48 20.56 50 24.24 24.81 25.49 26.32 27.17 Castlegar 0 20.00 20.00 20.00 20.00 20.00 25 23.88 24.40 25.03 25.80 26.58 50 41.97 44.50 47.51 51.12 54.73 It may be noted from Table 3.5 that uncertainty in capacity of timber increases with age, which translates into a higher COV. Similarly, timber poles of lower class (i.e. Class 5) experience greater uncertainty with age as compared to higher class (i.e. Class 1). This is due to the fact that decay depth remains the same, irrespective of the initial diameter of pole, resulting in profound dimensional changes for lower class poles as compared to higher class poles.          59 Illustrations 3.5 to 3.8 show the wind fragility curves for timber pole in Vancouver, Victoria, Kelowna and Castlegar designed using both deterministic and probabilistic wind loads. Strength degradation with age due to decay was also considered in the analysis. It is evident from the fragility curves at each location that probability of failure of timber poles designed as per CSA 22.3 No.1 deterministic wind loadings is much higher as compared to those designed as per probabilistic wind loads. This is attributed to the fact that probabilistic wind loads yield a higher class pole than deterministic wind loads, resulting in a higher capacity and lower probability of failure. This statement implies that the actual wind speed data for locations in consideration comes out to be greater than that mentioned in the CSA deterministic code for the same region. Design using probabilistic wind loads will result in the selection of a higher pole class. Hence, for a particular wind speed, probability of failure of higher class poles is always less than lower class poles. This fact is also evident from the fragility curves.  Furthermore, the probability of failure of timber poles with age is not consistent across the four selected locations, with Vancouver being the most and Kelowna being the least vulnerable. The reason behind this inconsistency stems to the variation in climate parameter across the selected locations. Vancouver has the highest value of climatic parameter (1.66), which corresponds to a higher rate of decay. A higher rate of decay would translate to a greater decay depth resulting in higher strength degradation with time and consequently, higher probability of failure as evident from fragility curves. This variation in probability of failure with time can also be validated by the corresponding values of COV calculated for different ages and for different pole classes as given in Table 3.5.        60   Illustration 3.5: Fragility Curves for Vancouver (a) Deterministic Wind Load (b) Probabilistic Wind Load (a) (b)  61   Illustration 3.6: Fragility Curves for Victoria (a) Deterministic Wind Load (b) Probabilistic Wind Load (a) (b)  62   Illustration 3.7: Fragility Curves for Kelowna (a) Deterministic Wind Load (b) Probabilistic Wind Load (a) (b)  63   Illustration 3.8: Fragility Curves for Castlegar (a) Deterministic Wind Load (b) Probabilistic Wind Load Eq. 3.14 shows that the wind fragility model can be fully described by two parameters i.e. mR, median capacity or resistance, and ζR, logarithmic standard deviation of capacity or resistance.  In order to verify the suitability of lognormal CDF to define wind fragility curves, the CDF’s (a) (b)  64 determined from fragility analysis were plotted on lognormal paper (Li and Ellingwood 2006), The lognormal probability plot for timber poles in Vancouver at 0 years designed using both deterministic and probabilistic loads is shown in Illustration 3.9.   Illustration 3.9: Lognormal Probability Plot for Timber Poles in Vancouver at 0 years (a) Deterministic (b) Probabilistic The linearity of the plot and correlation coefficient value of close to 1 (0.9878 and 0.9987) were presumptive indications for suitability of lognormal distribution. Similar linearity trends were observed for fragility curves of timber poles at 0, 25 and 50 years for other cities as well (Illustrations 3.10 to 3.20). In addition to probability plots, Kolmogorov- Smirnov test for goodness of fit was also carried out to confirm the validity of lognormal distribution.  (b) (a) (a) (b) Illustration 3.10: Lognormal Probability Plot for Timber Poles in Vancouver at 25 years (a) Deterministic (b) Probabilistic  65               (a) (b) (b) (a) Illustration 3.11: Lognormal Probability Plot for Timber Poles in Vancouver at 50 years (a) Deterministic (b) Probabilistic Illustration 3.12: Lognormal Probability Plot for Timber Poles in Victoria at 0 years (a) Deterministic (b) Probabilistic  66              (a) (b) (a) (b) Illustration 3.13: Lognormal Probability Plot for Timber Poles in Victoria at 25 years (a) Deterministic (b) Probabilistic Illustration 3.14: Lognormal Probability Plot for Timber Poles in Victoria at 50 years (a) Deterministic (b) Probabilistic  67                (a) (b) (a) (b) Illustration 3.15: Lognormal Probability Plot for Timber Poles in Kelowna at 0 years (a) Deterministic (b) Probabilistic Illustration 3.16: Lognormal Probability Plot for Timber Poles in Kelowna at 25 years (a) Deterministic (b) Probabilistic  68              (a) (b) (a) (b) Illustration 3.17: Lognormal Probability Plot for Timber Poles in Kelowna at 50 years (a) Deterministic (b) Probabilistic Illustration 3.18: Lognormal Probability Plot for Timber Poles in Castlegar at 0 years (a) Deterministic (b) Probabilistic  69              (a) (b) (a) (b) Illustration 3.19: Lognormal Probability Plot for Timber Poles in Castlegar at 25 years (a) Deterministic (b) Probabilistic Illustration 3.20: Lognormal Probability Plot for Timber Poles in Castlegar at 50 years (a) Deterministic (b) Probabilistic  70 Table 3.6 shows the lognormal parameters for wind fragility curves for Vancouver, Victoria, Kelowna and Castlegar, for various pole ages. Table 3.6: Lognormal Parameters for Wind Fragility Location Service Life Ln(mR) ζR Vancouver 0 3.288 0.1506 25 3.1136 0.2236 50 2.7556 0.427 Victoria 0 3.265 0.165 25 3.1458 0.2045 50 2.8181 0.3954 Kelowna 0 3.2806 0.1533 25 3.2606 0.1544 50 3.1733 0.1889 Castlegar 0 3.2078 0.151 25 3.1015 0.1827 50 2.8706 0.319  The expected annual probability of failure can be estimated by using Eq. 3.17 which involves convolution of PDF for wind speed and CDF for wind fragility. Table 3.7 shows the annual probabilities of failure and corresponding reliability indices (Eq. 3.19) for timber poles in Vancouver, Victoria, Kelowna and Castlegar respectively for various ages, designed as per both deterministic and probabilistic wind loads.     71 Table 3.7: Annual Probability of Failure & Reliability Index values for Timber Poles Design Load Location Service Life Annual Probability of Failure (Pf) Annual Reliability (R%)  Annual Reliability Index (β) Deterministic  Vancouver 0 0.3212 67.88 0.4643 25 0.6072 39.28 -0.272 50 0.831 16.9 -0.9581 Victoria 0 0.2748 72.52 0.5984 25 0.4842 51.58 0.0396 50 0.7786 22.14 -0.7675 Kelowna 0 0.1297 87.03 1.1278 25 0.1504 84.96 1.0347 50 0.2859 71.41 0.5654 Castlegar 0 0.3593 64.07 0.3603 25 0.5402 45.98 -0.1009 50 0.7649 23.51 -0.7222 Probabilistic  Vancouver 0 0.0123 98.77 2.248 25 0.0705 92.95 1.472 50 0.3875 61.25 0.286 Victoria 0 0.0105 98.95 2.308 25 0.0529 94.71 1.617 50 0.3406 65.94 0.411 Kelowna 0 0.0135 98.65 2.212 25 0.0184 98.16 2.088 50 0.0477 95.23 1.668 Castlegar 0 0.0180 98.20 2.097 25 0.0482 95.18 1.663 50 0.2048 79.52 0.825  CSA 22.3 No. 60826 suggest reliability level for transmission lines based on return periods of 50, 150 and 500 years. The reliability level along with reliability indices corresponding to a particular return period is shown in Table 3.8. (CSA C22.3 No.60826 2006).   72 Table 3.8: Relationship between return period and reliability index (CSA C22.3 No.60826 2010)   Return period of load, T   50 150 500 Annual probability of failure Pf 0.02 to 0.01 0.0067 to 0.0033 0.002 to 0.001 Annual reliability, R 0.98 to 0.99 0.993 to 0.997 0.998 to 0.999 Annual reliability index, β 2.05 to 2.33 2.46 to 2.75 2.88 to 3.09 A return period 50 years was used for wind load in this research. It can be seen from Table 3.7, that the achieved reliabilities of timber poles in Vancouver, Victoria, Kelowna and Castlegar designed according to the deterministic design procedure are very low as compared to those suggested CSA 22.3 No. 60826 reliability based design code. On the contrary, timber poles design considering probabilistic wind loads showed a marked increase in the reliability index (β). The calculated reliability index values were in accordance with the target reliability values mentioned in Table 3.8. This indicates that the weather loading zones as stipulated in CSA 22.3 No.1 needs immediate revision. Sub-division can be added to maps, which may represent the weather loading conditions of a specific area in a realistic manner. Graphical comparison of reliability index (β) for Vancouver, Victoria, Kelowna and Castlegar are shown in Illustrations 3.21 and 3.22. Illustration 3.21 suggests that reliabilities of timber poles designed as per deterministic design loads are not uniform across all the selected locations. On the other hand, timber poles designed as per probabilistic wind loads depict uniform reliabilities across all selected locations. It may be noted that the trend of reliability of timber poles with time is different as compared to those at 0 years. This is basically due to inclusion of local climatic factors such as annual temperature and annual rainfall, which effect the reliability of timber poles variably. However, consequently it may be realized that timber poles designed as per probabilistic wind loads yield higher reliability as opposed to deterministic design loads.   73  Illustration 3.21: Reliability Index of Timber Poles designed according to deterministic wind loads  Illustration 3.22: Reliability Index of Timber Poles designed according to Probabilistic wind loads  74  Development of Fuzzy based Condition Assessment Tool for Timber Utility Poles 4.1. General Timber Poles have been used for decades to provide mechanical support for overhead transmission and distribution lines. Timber poles are widely available, naturally durable, and flexible and possess sufficient initial strength. These qualities render timber as the first choice by many utility companies to be used in their overhead electric supply network. Utility Timber poles are designed to withstand expected workloads as well as environmentally induced loads such as wind and ice.  Being a natural material, timber poles are prone to fungal and insecticide attacks which diminish their structural integrity over time. Degradation of timber poles is a complex process and is influenced by several factors, including type of preservative treatment, environmental exposure, loading conditions and nature of fungal attacks. Timber poles that support overhead lines are connected in series. The strength of any line is dictated by the strength of the weakest pole. Failure of any single pole can trigger a cascading effect and result in ultimate collapse of the whole line (Datla and Pandey 2006). This would not only cause disruption in electric supply, but also cause devastation to the reputation of the utility provider.  Reliability and structural integrity of timber poles are therefore eminent concerns for utility companies.  In order to ensure acceptable reliability and healthy operations of electric supply lines, utility service providers conduct regular inspection of their timber pole assets. The data collected during these regular inspections form the basis of maintenance and rehabilitation decisions. The basic aim of a condition assessment program is to identify and diagnose any defect in timber poles and rectify them appropriately to avoid catastrophic failures. Condition assessment of timber poles is usually performed by field inspectors and the efficacy of the assessments vary depending on the experience and personal judgement of the inspector. Due to the cognitive uncertainty associated with human decision making, the results of condition assessment can be highly subjective. Fuzzy logic provides an ideal approach to quantify subjectivity and present the results in an objective manner. In this research, a Fuzzy logic based Fuzzy synthetic evaluation (FSE) technique is used to develop the condition rating mechanism for timber utility poles.   75 4.2. Application of FSE technique to Condition Rating of Timber Utility Poles. Timber pole condition assessment is a key component of the asset management process and provides a perspective to facilitate decision making. Information regarding the current condition of timber poles is required to make informed decisions regarding maintenance or future optimization. Apart from condition of the pole, maintenance decisions are greatly influenced by the availability of funds and importance of the line. It is imperative for a condition assessment program to be able to prioritize the poles according to their condition, so that funds can be allocated for structures which require immediate maintenance and rehabilitation. In this research, FSE technique has been proposed to perform condition assessment of utility timber poles and subsequent prioritization. The term inspection used in this study refers to all methods of assessing the condition of wood poles by observing defect indicators including visual and non-destructive evaluation methods. Description of different inspection methods has been discussed in detail in section 2.5. Similarly, the terms criteria, defect criteria, defect indicators and performance indicators have been used interchangeably in this research. The step by step process of FSE methodology has been outlined in detail in section 2.6. 4.2.1. Description of defect criteria and development of membership functions The current condition of timber poles can be reflected through observed defect indicators which are obtained through inspections (visual or non-destructive evaluation). A defect indicator is a measurable entity that reflects the degradation of the timber pole up until the inspection. As discussed earlier, degradation of timber poles depend upon the type of wood, environmental conditions and operating loads. However, the role of operational and environmental condition have not been considered explicitly to determine condition rating in this research. Rather it is postulated that impact of all the external conditions (i.e. operational and environmental) will manifest itself in some form of observable defect, which would be subsequently identified during inspection. For example, poles installed in areas having hot and humid environment have a greater tendency to degrade due to decay as compared to poles in  76 temperate environment, even though both poles manufactured with similar quality standards. The effect of environment, however is not considered in the condition rating of timber poles.  The overall condition of a utility timber pole asset is a testament to the contribution of each defect indicator. Engineering judgment, expert knowledge and available literature on performance and behavior of timber poles help establish the contribution of each defect indicator. Depending upon the nature of the available data, contribution of each defect indicator on its respective universe of discourse can be expressed either numerically or linguistically.  In this research, four basic criteria have been identified for evaluating the condition of timber poles. These criteria include external decay, internal decay, wood pecker damage and mechanical damage. The basic criteria are then further divided into their respective sub-criteria. Fig. 4.1 shows the hierarchical structure for condition based assessment of timber poles.    Figure 4.1: Hierarchical Structure for Timber Pole Condition Assessment (WP refers to wood pecker) Shell RotCore RotWP Hole Width WP Hole Depth Vehicle DamageMechanical DamageInternal DecayWood Pecker DamageExternal DecayCondition of Timber poleLevel 3 Level 2 Level 1 (GOAL) 77 4.2.1.1. Bio-degradation (External and Internal Decay) Bio-degradation (decay) is a major factor responsible for strength loss in timber poles. Decay is not a condition, rather a process whereby timber poles undergoes degradation and significant amount of strength reduction. Fungi are considered to be the major cause of decay and failure in timber poles. Depending upon the type of fungi, decay can classified as External or internal. External decay is caused by soft rot fungi (Ascomycetes) which softens the external surface of pole by producing cavities within the cellulose layer of wood cells. As they require nitrogen and high moisture content, soft rot fungi are more active in areas close to soil and therefore results in reduced circumference of timber pole at or below the ground line. Internal decay is usually caused by brown/white rot fungi (Basidiomycetes) and proliferate internally through airborne spore rather than attacking externally near soil. Brown rot fungi decomposes cellulose within wood cells and leave lignin, whereas white rot fungi attack both cellulose and lignin.  Studies (Ezer 2001; Wareing 2005) have shown that decay mainly occurs at the ground line. This is due to the fact that decay fungi require specific amount of moisture and oxygen to survive. The area at and below the ground line provides a conducive environment for growth of decay fungi. This critical zone extends from 6 inch above to 18 inch below ground line. Sapwood of poles is highly susceptible to fungal attacks as compared to its heartwood and does not provide much resistance to decay fungi. Preservative treatments are applied to timber poles, which penetrate the venerable sapwood thus providing resistance against fungal attack. Reduction in toxicity of preservative treatment with time will result in propagation of decay.  Although external decay is potentially more serious in terms of its effects, it is not viewed as a greater threat than internal decay due to several reasons. Application of preservative treatment to timber poles provide sufficient resistance from external decay. It is only after a fairly long service life that the treatment loses its efficacy and external decay starts to develop. In addition, it can be visually detected and rectified. On the other hand, internal decay that generally occurs in the ground line zone, is not visible to naked eye and NDE methods may have to be used to identify it. Internal decay can occur early during the service life, in certain cases even before the erection of timber poles and can cause failure of pole well before external decay.   78 Similar to concrete and steel, certain codes have been developed , which specify degradation limits to facilitate utilities in making decision regarding rehab and replacement of timber poles. For instance, National Electric Safety Code (NSEC) provides a provision to replace or rehabilitate a timber pole structure subject to deterioration, if the strength is reduced to 2/3 or up to 67%, to that when it was installed. (Nelson and Sinclair 2005) A similar provision has been made in CSA 22.3 1-10 Overhead systems, however the strength threshold has been increased to 60% instead 67%. Utilities have devised “rule of thumb” criteria tables which are used to determine effective residual circumference or remaining sound shell thickness as a function of pole circumference or dimension. Maintenance decision are then made based upon comparison of results with the threshold values. Such practices however do not prove to be user friendly for inspectors and yield imprecise results.  Due to inherent amount of variability in timber properties such as stiffness, fibre strength, growth properties, moisture content etc., exact calculation of residual strength of timber poles has always remained a complex process. (Nelson and Sinclair 2005)  Although, new technologies in NDE methods have been developed over the years, utility companies are more inclined towards conventional methods of inspection. According to a survey (Mankowski et al. 2002) conducted on different utility practices, it was observed that bulk of the utility companies still rely on visual and sound & bore techniques to carry out inspection of timber poles. The section modulus method is a widely used method to calculate the residual strength of in service timber poles and proves to be more accurate than the rule of thumb criteria. The strength of poles is measured by determining the remaining section modulus of a decayed of damaged x-section. Inspection holes are drilled in the pole at ground line and depth of decay is measured. The section modulus is calculated by subtracting the decayed area from the sound wood area based on pole diameter. This gives a percentage remaining strength, which is then multiplied by the fibre strength of that particular timber species to get the average residual bending capacity.  In this research, the section modulus method has been utilized to evaluate the extent of internal and external decay on the sectional properties and also to establish their respective membership  79 functions. Decay at ground line can manifest itself in different patterns. The decay patterns considered in this research to evaluate the condition of the timber pole are shown in Fig. 4.2.  Figure 4.2  Possible decay patterns at ground line a) Internal decay (Core Rot);  b) External decay (shell rot) External decay can be considered as a potentially serious problem for timber poles. The strength of distribution poles is governed by their bending strength at ground line. The equation of bending resistance for timber poles is given by: M = Fb .S……………………………………………………………………………..(4.1) Where,  M  = Bending Moment (N-m) Fb = Fiber Strength of timber pole (N/m2) S  = Section Modulus (m3) It is clear from the above equation that moment capacity is directly proportional to section modulus. The section modulus is a function of pole circumference or diameter at a particular section.  The outer 2 to 3 inches of the shell of a typical distribution pole is theoretically known to retain 80% – 90% of the total bending strength (Ezer 2001; Wareing 2005). In case of external decay, the variation in strength can occur due to loss of outer shell thickness and reduced diameter can be estimated by Eq. 4.2: Decayed Portion(a) (b)  80 ………………………………………………….…... (4.3) ………………………….…. (4.4) Dm = Do – 2t    ………………………………………………………………….…… (4.2) Where,  Dm = Measured diameter of pole at ground line Do = original diameter of pole at ground line t = External decayed shell thickness  The section modulus obtained by the measured diameter is then subsequently divided by the original section modulus to get the % remaining strength:  Where Zm and Zo are the measured and original section modulus respectively. Calculation based on equation 4.3 reveal that a reduction of 15% in external shell thickness of a timber pole can cause a 40% reduction in the bending strength. On the contrary, the variation in strength due to internal decay can be estimated by comparing the reduced section from a hollow core or pocket, which can be estimated as:     The effect of internal decay on bending strength is very less as compared to external decay.  Around 80% of the central core has to be removed to get the same amount of reduction as in the case of external decay.  4.2.1.2. Wood Pecker Damage Wood pecker damage is not considered as a serious problems by utility companies because of its localized impact. Wood peckers are usually more profound in forest areas, however, they face little difficulty in developing habitat in most urban and suburban settings as well (Harness and Walters 2005). There are a variety of reasons for which wood peckers peck utility timber poles. These include drumming, searching for food source such as insects, and making holes  81 w for nesting purposes. Wood peckers drum on timber poles to establish their territorial boundaries and also to communicate with other wood peckers to perform mating rituals. Wood peckers also choose timber poles as they provide them with an unbarred view of the surrounding area and keep them vigilant from attacks by predators. Steenhof (2011) studied the effect of wood pecker damage on the strength of utility timber poles. Depending upon their severity, wood pecker damage was classified into three levels i.e. exploratory damage, feeding damage and nesting damage.  Severity of wood pecker damage is a function of the width of wood pecker hole opening and the respective depth to which it penetrates within the poles. In case of exploratory and feeding damage, wood peckers create openings of varying width in the exterior shell but penetrate to a limited depth. However, in case of nesting damage, wood peckers create small openings in the exterior shell but penetrate deep to produce hollow areas or pockets within the pole x-section. Fig. 4.5 shows a hypothetical representation of exploratory, feeding and nesting damage which can be manifested by wood peckers in timber poles (Steenhof 2011).   Figure 4.3: Hypothetical manifestation of Wood Pecker Damage (a) Exploratory (b) Feeding (c) Nesting. w and d are width and depth of Wood Pecker holes respectively (Adapted from Steenhof 2011) In this research, wood pecker damage is characterized by the width of opening and depth of hole. An increased width of wood pecker hole opening corresponds to a reduction in circumference resulting in loss of section and significant strength loss. The width of hole is measured and % reduction in diameter is calculated. Similarly, the penetration of wood pecker beyond the opening can create hollow portions within the pole x-section. The hollow area reduces the section modulus at that particular section and can have the same effect as that of (a) (b) (c) Dia. Of Pole Dia. Of Pole d  82 internal decay. The % age of hollow area compared to the original x-section at a particular location on the pole gives the value of % remaining strength. Hence both width and depth of wood pecker holes shall be considered respectively to evaluate wood damage to timber poles in this study.  Damage can occur in any direction along the circumference of the pole, however damage occurring either with extreme fibres i.e. tension and compression or with neutral axis are viewed to be more critical towards the determination the effect on strength. In addition to orientation, location of wood pecker holes is also important to identify stress points along the length of the pole. Steenhof (2011) conducted a series of experiments to evaluate the effect of these three damage levels on the bending and shear strength of timber poles. The results of experiments suggested the wood pecker damage oriented with extreme fibers i.e. either compression or tension fibers has a greater effect on strength reduction as compared to damage oriented with neutral axis.  4.2.1.3. Mechanical Damage Mechanical or physical damage caused by motor vehicle accident is also another important reason for utility timber pole failures. Depending upon the intensity of impact by the vehicle, the utility pole can receive considerable surface damage in the form of dent or bump. In certain cases, the impact of the collision is so intense that it can cause the timber pole to break altogether at the point of impact (Illustration 4.1). If the pole survives the impact of the accident, the extent of damage can be evaluated by measuring the depression or indentation and calculating the reduction in circumference. As mentioned previously, the outer 2 to 3 inches shell consists of 80% to 90% of the total bending strength possessed by a timber pole. Therefore, the loss of section should be measured carefully to determine the reduced circumference at that particular location. Similar to wood pecker damage, it is also very important to determine the orientation of damage with respect to neutral axis. The extent of damage caused by motor vehicles can be reflected as the loss of strength due to reduction in circumference.   83  Illustration 4.1: Examples of Damage caused by motor vehicle collisions (1. Dstar.org & 2. Via [Public domain], via Wikimedia Commons)) 4.2.1.4. Membership Functions for Defect Indicators Delphi method was used to convert opinion of engineers and professionals into a fuzzy set. For this reason, a survey questionnaire was developed and distributed amongst engineers and professionals related to the utility industry, in which they were asked to provide a subjective evaluation based on their professional judgment. The participants of the survey were asked to indicate the degree of membership μ, between 0 and 1, that a measured value x of a defect indicator belongs to a specific category in an evaluation set i.e. “Very Good”, “Good”, “Fair”, “Poor” and “Very Poor”. The survey participants were asked to provide the degree of membership for each category in the evaluation set and for each defect indicator i.e. External decay, internal decay, wood pecker damage and mechanical damage. A brief description of defect indicators along with figures were also provided along with the Delphi survey questionnaire to assist the participants in decision making. Each individual response of the participants in the survey constituted a sample grade of membership {x, μ(x)}. There are several methods to construct fuzzy membership functions including fuzzy clustering, statistical regression and pair wise comparison (Dubious and Parade 1980). In this study, statistical regression will be used to analyze the surveyed grade of membership {x, μ(x)} to develop membership functions. The membership functions corresponding to each of the four defect indicators are shown in Illustrations 4.2 to 4.6.  1 2  84  Illustration 4.2: Membership Function for External Decay  Illustration 4.3: Membership Function of Internal Decay  85  Illustration 4.4: Membership Function of Wood Pecker Hole Depth  Illustration 4.5: Membership Function of Width of Opening  86  Illustration 4.6: Membership Function of Mechanical Damage Figure. 4.4 presents the proposed hierarchical framework for development of Condition assessment tool using Fuzzy Synthetic Evaluation.  87  Figure 4.4: Proposed Hierarchical Framework of Fuzzy Synthetic Evaluation Identification and description of  defect/ Performance indicatorsDevelopment of Membership Functions for  defect/ Performance Define qualitative scales for evaluation of defect/ performance indicatorsn-tuple fuzzy sets for each defect/ performance indicatorsMappring of observed values of indicators on qualitative scalesEstimating weights for each defect/ performance indicators using Analytical Hierachy Process (AHP)n-tuple fuzzy comprehensive set Matrix Multiplication of weight vector and n-tuple fuzzy sets of Development of weight vector Centre of area, scoring method etc.Prioritization and ranking of timber poles FuzzificationAggregationDefuzzification 88 4.2.1.5. Determination of Neutral Axis (NA) The location of neutral axis depends upon the arrangement and configuration of a utility pole structure in any overhead line segment. Fig 4.5 shows the neutral axis line X - Y where timber fibers neither in compression nor under tension. It may be noted that the neutral axis is always perpendicular to the resultant load. (Ausgrid 2015)     Figure 4.5: Neutral Axis of a Timber Pole (Ausgrid 2014) A utility timber may experience extreme wind loads at right angle to conductors, which can be considered as a worst case scenario. Based on the worst case scenario, the location of neutral axis in different pole arrangements are shown in Figs 4.6 – 4.9.  89  Figure 4.6  Neutral Axis of an in-line Timber pole (Ausgrid 2014)  Figure 4.7  Neutral Axis of Timber Pole with services (Ausgrid 2014)  Figure 4.8  Neutral Axis for an Angle Timber Pole (Ausgrid 2014)  90   Figure 4.9  Neutral Axis for a Dead End Timber Pole (Ausgrid 2015) 4.3. Validation of Timber Pole Condition Rating Framework The main purpose of the proposed framework is to classify the timber poles in to an appropriate evaluation category based upon the established criteria and subsequently rank them according to the overall evaluation results. The basic criteria set chosen to perform condition based ranking of timber poles in this research is given as: A = {External Decay, Internal Decay, Wood Pecker Damage, Mechanical Damage}….…(4.5) The 5-tuple fuzzy evaluation set defined in this research to be assigned to each basic criteria is given by: B = {Very Good, Good, Fair, Poor, Very Poor}………………………………….…………….(4.6) The pole which receives the highest ranking in descending order, can be considered as most critical in terms of maintenance and rehabilitation decisions. The prioritization of timber poles is carried out purely based on the outcomes of the condition assessment. However, orientation and location of certain defects such as wood pecker damage should also need to be considered to obtain a realistic estimation of the remaining strength of timber pole. The influence of each criteria or defect indicator selected in this research, contributes towards the reduction in strength of timber poles in two ways i.e. external and internal loss of x-section.  For illustration purposes, in this research external decay is defined as % reduction in diameter due to loss of external shell. Internal decay is defined as the % remaining shell thickness due  91 to rotting of central area. Wood pecker damage is defined by two parameters; Width of opening and depth of opening. Both of these parameters are defined as the % of total diameter of the timber pole at that particular location. Similarly, the mechanical damage is defined as % reduction in diameter of the effective section due to loss of section by vehicle damage. In order to illustrate the proposed framework, a distribution line consisting of ten timber poles is considered to be assessed and prioritized. Let us suppose that condition inspection of one timber pole yields the following results as shown in Table 4.1. Table 4.1: Inspection Results of basic categories Inspection Categories Mode of Measurement Inspection Results External Decay (Shell Rot) % reduction in outer diameter 11 Internal Decay (Core Rot) % loss of internal core x-section 50 Wood Pecker Damage (Hole Width) % of total diameter 20 Wood Pecker Damage (Hole Depth) % of total diameter 60 Mechanical Damage %  reduction in outer diameter 4 4.3.1. Fuzzification of basic criteria into five tuple fuzzy sets After getting the result of defect indicators, the next step is to map the values on their respective fuzzy evaluations sets to get the grade of membership. The mapping of defect indicators on to their respective membership function yielded the following results given in Table 4.2.     92 …………………………………(4.7) Table 4.2: Fuzzy sets corresponding to results of basic criteria Inspection Categories Fuzzy Set Normalized Fuzzy set External Decay (Shell Rot) (0.00, 0.00, 0.00, 0.66, 0.34) (0.00, 0.00, 0.00, 0.66, 0.34) Internal Decay (Core Rot) (0.17, 0.83, 0.00, 0.00, 0.00) (0.17, 0.83, 0.00, 0.00, 0.00) Wood Pecker Damage (Hole Width) (0.00, 0.00, 0.50, 0.50, 0.00) (0.00, 0.00, 0.50, 0.50, 0.00) Wood Pecker Damage (Hole Depth) (0.00, 0.00, 0.00, 0.50, 0.50) (0.00, 0.00, 0.00, 0.50, 0.50) Mechanical Damage (0.00, 0.33, 0.33, 0.00, 0.00) (0.00, 0.50, 0.50, 0.00, 0.00) 4.3.2. Determination of weights for basic criteria The next step in the FSE is to determine the weight of each criteria. The AHP process has been used to establish weight matrix and the procedure is outlined in detail in section 2.6.2.1.2. The pair wise comparison matrix and the derived weight matrix for the basic criteria are given in Eqs. 4.7 and 4.8 respectively:   ED ID WP MDED 1.00 1.50 2.00 1.00ID 0.67 1.00 1.50 1.50WP 0.50 0.67 1.00 0.50MD 1.00 0.67 2.00 1.00I = 93 (15) …………………..…..……(4.8)  It is clear from the weight matrix, that external decay has the highest importance, whereas wood pecker damage has the least importance. Strictly speaking, the pair wise comparison developed is reflective of engineering judgement based on severity of each attribute and may not be applicable for universal application. The pair wise comparison can be adjusted based on location and site specific climatic conditions. According to the hierarchical structure, Wood pecker damage has been further divided into two sub categories i.e. opening width and depth of hole. For simplicity, both of them are assigned equal importance and hence both the sub categories carry a weight of 0.5 each.  4.3.3. Aggregation of Criteria After obtaining the fuzzy set and assigning weights to each criteria, the next step is to obtain the final generalized fuzzy set. The hierarchical structure is used to carry out the aggregation process. The weights estimated at each level using AHP are shown in Table 4-3. Table 4.3: Weights estimated using AHP Level 3 Categories Weights Level 2 Categories Weights Shell Rot 1.00 External Decay 0.32 Core Rot 1.00 Internal Decay 0.27 Opening Width 0.50 Wood Pecker Damage 0.15 Depth of hole 0.50   Vehicle Damage 1.00 Mechanical Damage 0.26  1.32 w 1 0.321.11 w 2 = 0.270.64 w 3 0.151.08 w 4 0.26W =J = => 94 Each basic criteria which consists of only one sub criteria was carried over to the next level without aggregation. The only criteria with sub criteria at level 3 is wood pecker damage, which would be aggregated using the weights assigned. Aggregation of at level 3 yielded the following results: Shell Rot = (0.00, 0.00, 0.00, 0.66, 0.34) Core Rot = (0.17, 0.83, 0.00, 0.00, 0.00) Opening width = (0.00, 0.00, 0.25, 0.25, 0.00) Depth of hole = (0.00, 0.00, 0.00, 0.25, 0.25) Vehicle damage = (0.00, 0.33, 0.33, 0.00, 0.00)   Similarly, the aggregation of criteria at level 2 yields the following results: External Decay = (0.00, 0.00, 0.00, 0.66, 0.34) Internal Decay = (0.17, 0.83, 0.00, 0.00, 0.00) Wood Pecker Damage = (0.00, 0.00, 0.125, 0.25, 0.125) Mechanical Damage = (0.00, 0.50, 0.50, 0.00, 0.00) The aggregation at the final level of the hierarchy gives the final fuzzy, as follows: Condition evaluation of timber pole (F) = (0.05, 0.35, 0.15, 0.25, 0.13)………….….(4.9) A graphical representation the final fuzzy set obtained by the Fuzzy synthetic evaluation is shown in Illustration 4.7.  95  Illustration 4.7: Condition rating results using FSE 4.3.4. Defuzzification The final fuzzy set obtained gives membership of each qualitative level according to evaluation set. The maximum operator principle is used in this study to evaluate the crisp value of a fuzzy set. The principle assigns the entry in the final set as the final outcome or crisp value, whose grade of membership is the largest. According to Eq. 4.9, the value of the largest entry is 0.35, which is the crisp outcome and corresponds to the overall evaluation of good. 4.4. Prioritization and ranking of poles In practice, line managers are not only concerned with the condition assessment of individual poles but are interested in prioritize different poles to get a snapshot of the overall condition. This also help the line managers to make informed decisions regarding the allocation of funds for poles in substandard condition. However, in certain situations, using the maximum operator principle would yield similar results. For example, consider the following fuzzy sets which have identical results according to the maximum operator principle.  96 ………………(4.11) ………………………(4.12) ………………………………………………………………..…(4.13) X = (0.15, 0.37, 0.35, 0.10, 0.03) Y = (0.18, 0.39, 0.20, 0.17, 0.06) It is clear from the above two sets that maximum operators are 0.37 and 0.39 respectively, which correspond to an overall evaluation of Good. However, it may be noted that value in fuzzy set X corresponding to the evaluation of Good is higher than that of fuzzy set Y. In order to deal with prioritization issues in situations, where fuzzy sets have identical evaluations, a defuzzified weighted cumulative index (DWCI) technique proposed by Sun and Gu (2011) is used. In this method, a monotone decreasing weight vector is associated with the evaluation set B to distinguish among these five linguistic assessments as shown below: B = {Very Good, Good, Fair, Poor, Very Poor}   Wv = ( 5, 4, 3, 2, 1 )………………………………………………………………………………(4.10) Normalization of the weight vector gives the following values (0.333, 0.267, 0.200, 0.133, 0.067). The DWCI of the timber pole can be calculated as:    μ F (Very Good)μ F (Good)DWCI = 0.333 0.267 0.200 0.133 0.067 μ F (Fair)μ F (Poor)μ F (Very Poor)0.050.35DWCI = 0.333 0.267 0.200 0.133 0.067 0.150.250.13DWCI = 0.182 97 The DWCI value is calculated for each pole and compared to rank them accordingly. Ranking of poles can also be done by comparing both the linguistic evaluation obtained from maximum operator principle and value of DWCI for each pole. In both the approaches i.e. using DWCI alone or using combination of MOP and DWCI, the priority ranking is made meaningful by assigning a single numerical score to each timber pole. Based on hypothetical condition assessment, the final evaluations results of ten timber poles using MOP and DWCI is given in Table 4.4.   Table 4.4: Fuzzy Synthetic Evaluation results of ten timber poles Pole Fuzzy Evaluation Set  MOP DWCI Ranking using MOP and DWCI Ranking using DWCI alone (μVG, μG, μF,μP,μVP) A (0.05, 0.35, 0.15, 0.25, 0.13) Good 0.182 7 8 B (0.30, 0.11, 0.41, 0.10, 0.08) Fair 0.230 8 7 C (0.18, 0.39, 0.20, 0.17, 0.06) Good 0.231 6 6 D (0.00, 0.13, 0.32, 0.33, 0.22) Poor 0.157 10 10 E (0.14, 0.16, 0.20, 0.26, 0.24) Poor 0.180 9 9 F (0.32, 0.30, 0.11, 0.17, 0.10) Very Good 0.240 4 4 G (0.37, 0.35, 0.15, 0.10, 0.03) Very Good 0.262 2 2 H (0.50, 0.24, 0.19, 0.07, 0.00) Very Good 0.278 1 1 I (0.27, 0.29, 0.24, 0.16, 0.04) Good 0.239 5 5 J (0.36, 0.23, 0.18, 0.14, 0.09) Very Good 0.242 3 3     98 4.5. Summary In this chapter, a fuzzy based condition rating tool was developed using fuzzy synthetic evaluation technique. The application of fuzzy logic not only provides an impetus to address uncertainty associated in defining scales for qualitative indicators but also provides the capability to handle subjective and imprecise information.  The condition rating tool facilitates engineers and line managers in ranking timber poles based on their level of deterioration and prioritizing maintenance and rehabilitation strategies. Four defect indicators, external decay, internal decay, wood pecker damage and mechanical damage were selected in this study to assess condition of timber poles.  A Delphi survey questionnaire was developed to obtain expert opinion of industry professionals. An evaluation set consisting of five qualitative categories was used to allow each rater to assign different degree of membership for different categories, in case of each defect indicator. The response of each participant was analyzed using statistical regression to construct membership functions corresponding to the four defect indicators. The weights for defect indicators was determined using Analytical Hierarchy Process (AHP). Defuzzification was performed using maximum operator principal. In order to prioritize timber poles based on their condition, a defuzzified weighted cumulative index (DWCI) technique was employed.    99  Conclusions & Recommendations 5.1. Conclusion The research conducted in this thesis provides a systematic approach encompassing both strength and quality evaluation of timber utility poles. In first part of the thesis, a study has been presented to estimate the structural reliability achieved for timber poles subject to wind loadings. Timber poles were designed according to the loading provisions outlined in the CSA 22.3 No.1 deterministic design standard as well as probabilistic weather loadings. The reliability analysis for the designed timber poles was performed using fragility analysis. Four locations in the Province of British Columbia, Canada were selected for analysis purposes. Extreme value analysis was used to estimate the probabilistic wind loading for the chosen locations for a return period of 50 years. In order to provide a holistic approach, age dependent degradation of timber poles with time was also considered in the analysis. The results of the reliability analysis showed that for the same grade of construction, the structural reliability of timber poles achieved using deterministic wind loadings was not uniform across the locations under consideration. On the other hand, timber poles designed according to probabilistic wind loading depicted almost uniform reliability across all location. This non-uniformity in estimated reliability was primarily due to the inconsistency between the deterministic design loads for a specific zone and the local weather statistics. Deterministic designs loads are assigned to various zones across Canada based on personal experience and subjective judgement. These specified zones usually cover substantially large areas and hence do not account for local weather conditions. It is therefore imperative to account for local weather statistics for design of timber poles. Division of weather zones into further sub division would provide a more realistic approach. Furthermore, the age dependent analysis suggested that presence of decay decreased the reliability of timber poles with time. However, the effect of decay on reliability is dictated by the weather conditions in any particular location.  In addition to reliability, this research also focused on the development of fuzzy synthetic evaluation (FSE) framework for condition rating of timber utility poles. Condition assessment of timber poles is an important aspect of asset management for any utility provider. The FSE technique is based on the concept of fuzzy logic and includes identification of criteria’s, fuzzification, weight estimation, aggregation and defuzzification. An evaluation set consisting  100 of five qualitative levels – very good, good, fair, poor, and very poor was used to fuzzify the basic. Four defect indicators - external decay, internal decay, wood pecker damage and mechanical damage were identified as basic criteria for FSE. Delphi method was employed to construct membership functions for each defect indicator. AHP was used to assign weights to each defect indicator for subsequent aggregation. Defuzzification was carried out using both maximum operator principal (MOP) and defuzzified cumulative weighted index (DCWI). The FSE framework condition rating was applied to a hypothetical case study of ten timber utility poles for validation purposes. The results obtained were compelling evidence of the versatility and practicality of the FSE technique for condition rating of timber poles. 5.2. Limitations & Future Recommendations Some limitations and recommendations for future work are as follows:  Reliability analysis was carried out for timber poles only in this research. In future, reliability analysis can be conducted to compare timber poles to alternate options such as composite or steel poles, designed according to Canadian standards.   Due to lack of data at some locations, effect of soil properties on reliability of timber poles was not accounted for in this research. Future studies can incorporate soil conditions for more comprehensive results.    In this research, wind load has been considered as an intensity measure to carry out reliability analysis for timber utility poles. In future studies, other hazards such as snow load, rain load, earthquake load etc. can be applied as intensity measure, either individually or in combination with each other.    Only Flexure failure of timber poles at ground level is assumed for reliability analysis in the current research. Timber poles, however have the tendency to depict other failure modes such as torsional or shear failures. These other failures modes, can also be investigated in future studies.  The age dependent degradation model used in this study was developed from an Australian perspective.  Research and analysis can be carried out on actual data from utility companies to develop a degradation model commensurate to Canadian  101 conditions. The data collected can also be used to study the effect of periodic maintenance on reliability of timber poles.  Although, FSE technique provided significant headway towards the proposed objective of this research, it has also opened doors for further exploration in this regard. A few recommendations for future work may include:  Development of a customizable condition rating tool on a programmable interface (e.g. Visual Basic) allowing the users to incorporate expert opinions or making adjustment to the tool according to their needs and requirements.  Integration of the condition rating tool with geographical software’s such as ArcGIS to provide spatial based evaluation of timber poles.   Broaden the capabilities of the condition rating tools beyond timber poles to accommodate evaluation of conductors, insulators, transformers etc.  Inclusion of additional indicators such as environmental and economic, apart from defect indicators, to make the evaluation more comprehensive.    102 References Ahluwalia, S. S. (2008). “A Framework for Efficient Condition Assessment of the Building Infrastructure.” Phd Dissertation, University of Waterloo.  Al-barqawi, H., and Zayed, T. (2006). “Condition Rating Model for Underground Infrastructure.” Journal of Performance of Constructed Facilities, 20(2), 126–135.  American Society of Civil Engineers (ASCE). (2006). Reliability-Based Design of Utility Pole Structures (No. 111). American Society of Civil Engineers, Reston, VA.  Ausgrid. (2015). Pole Inspection and Treatment Procedures NS145. Sydney, NSW.  Australian Standards (AS 5604). (2005). Timber - Natural Durability Ratings. Standards Australia, Sydney, NSW.  Ayyub, B. M., and Haldar, A. (1985). “Practical Structural Reliability Techniques.” Journal of Structural Engineering, 110(8), 1707–1724.  Bjarnadottir, S., Li, Y., Asce, M., and Stewart, M. G. (2013). “Hurricane Risk Assessment of Power Distribution Poles Considering Impacts of a Changing Climate.” Journal of Infrastructure Systems, 19(1), 12–24.  Brischke, C., and Rapp, A. O. (2008). “Influence of wood moisture content and wood observations in different micro-climates.” Wood Science and Technology, 42, 663–677.  Brown, R., and Willis, H. L. (2006). “The Economics of Aging Infrastructure.” IEEE power & energy magazine, (may/june), 36–43.  Buckley, J. J. (2012). “Fuzzy hierarchical analysis.” Fuzzy Sets and Systems, 17(3), 233–247.  Canadian Standards Association CSA C22.3 No.1. (2015). CAN/CSA C22.3 No.1 Overhead systems. Canadian Standards Association, Mississauga, ON.  Canadian Standards Association CSA C22.3 No.60826. (2010). CAN/CSA C22.3 No.60826 Design criteria of overhead transmission lines. Canadian Standards Association, Mississauga, ON.  Canadian Standards Association CSA O15. (2015). CAN/CSA-O15 series-15 Wood utility poles and reinforcing stubs. Canadian Standards Association, Mississauga, ON.  Canadian Standards Association CSA-O80. (2011). CAN/CSA-080 Wood preservation. Canadian Standards Association, Mississauga, ON.  Chang, D. Y. (2004). “Extent Analysis and synthetic decision.” Optimization Techniques and Applications, 1, 352–355.  103  Chen, S.-J., and Hwang, C.-L. (1992). Fuzzy Multiple Attribute Decision Making - Methods and Application. Springer-Verlag, Berlin Heidelberg.  Daigle, O. (2013). “The Effect of woodpecker damage on the reliability of wood utility poles by.” MASc Thesis, University of Waterloo.  Datla, S. V. (2007). “Probabilistic Models for Life Cycle Management of Energy Infrastructure Systems.” PhD Dissertation, University of Waterloo.  Datla, S. V., and Pandey, M. D. (2006). “Estimation of life expectancy of wood poles in electrical distribution networks.” Structural Safety, 28(3), 304–319.  Dubious, D., and Parade, H. (1980). Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, NY.  Ellingwood, B. R. (2004). “Performance-Based Design: Structural Reliability Considerations.” Advanced Technology in Structural Engineering, ASCE, 1–8.  Endrenyi, J., and Anders, G. J. (2006). “Aging, Maintenance and Reliability.” IEEE power & energy magazine, (may/june), 59–67.  Ezer, E. (2001). “Measurement of Wood Pole Strength Polux ® a New Non-Destructive Inspection Method.” IEEE Rural Electric Power Conference, 1–7.  Foschi, R. O. (2004). “Reliability theory and applications to risk analysis of power components and systems.” Electrical Power & Energy Systems, 26(2004), 249–256.  Foschi, R. O., Li, H., and Zhang, J. (2002). “Reliability and performance-based design : a computational approach and applications.” Structural Safety, 24, 205–218.  Fu, X., Li, H.-N., and Li, G. (2016). “Fragility analysis and estimation of collapse status for transmission tower subjected to wind and rain loads.” Structural Safety, Elsevier Ltd, 58(2016), 1–10.  Fwa, T. F., and Shanmugam, R. (1998). “Fuzzy Logic Technique for Pavement Condition Rating and Maintenance-Needs Assessment.” 4th International Conference on Managing Pavements.  Gaiotti, R., and Smith, B. S. (1989). “P-Delta Analysis of Building Structures.” Journal of Structural Engineering, 115(4), 755–770.  Goel, A. (2008). “Design of Transmission Lines for Atmospheric Icing.” Atmospheric Icing of Power Systems, Springer Science+Business Media B.V., 327–374.     104 Gustavsen, B., and Rolfseng, L. (2005). “Asset management of wood pole utility structures.” Electrical Power & Energy Systems, 27, 641–646.  Harness, R. E., and Walters, E. L. (2005). “Woodpeckers and utility pole damage.” IEEE Industry Applications Magazine, 68–73.  Institute of Elecrtrical and Electronic Engineers (IEEE). (1991). Trial-Use Design Guide for Wood Transmission Structures. Institute of Electrical and Electronic Engineers, New York, NY.  Kabir, G., and Hasin, M. A. A. (2012). “Multiple criteria inventory classification using fuzzy analytic hierarchy process.” International Journal of Industrial Engineering Computations, 3, 123–132.  Klir, G. J., and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic - Theory and Applications. Prentice Hall Inc., Englewood Cliffs, NJ.  Lassen, L. E., and Okkonen, E. A. (1969). Sapwood Thickness of douglas-fir and five other western softwoods. USDA Forest Service, Madison, WI.  Li, H., Zhang, J., and Bhuyan, G. (2006). “Reliability Assessment of Electrical Overhead Distribution Wood Poles.” 9th International Conference on Probabilistic Methods applied to power systems KTH, Stockholm, Sweden, 9–12.  Li, J., Dackermann, U., and Subhani, M. (2007). “R & D of NDTs for Timber Utility Poles in Service – Challenges and Applications ( Extension for Bridge Sub-Structures and Wharf Structures ).” Civil Structural Health Monitoring Workshop (CSHM-4), 8.  Li, W. (2005). Risk Assessment of Power Systems: Models, Methods and Applications. Wiley-IEEE, Hoboken, NJ.  Li, Y., and Ellingwood, B. R. (2006). “Hurricane damage to residential construction in the US : Importance of uncertainty modeling in risk assessment.” Engineering Structures, 28(2006), 1009–1018.  Lu, R., Lo, S., and Hu, J. (1999). “Analysis of reservoir water quality using fuzzy synthetic evaluation.” Stochastic Environmental Research and Risk Assessment, 13, 327–336.  Mankowski, M., Hansen, E., and Morrell, J. (2002). “Wood Pole Purchasing, Inspection, and Maintenance: A survey of Utility practices.” Forest Products Journal, 52(11/12), 43 –50.  Morrell, J. J. (2008). Estimated Service Life of Wood Poles. North American Wood Pole Council.     105 Morrell, J. J. (2012). Wood Pole Maintenance Manual : 2012 Edition. RC-51 Forest Research Laboratory, Oregan State University, Oregon, WA.  Morrell, J. J., Freitag, C., Chen, C., Love, C., and Leavengood, S. (2009). Oregon State University Utility Pole Research Cooperative. Department of Wood Science & Engineering, Oregan State University, Oregon, WA.  Najjaran, H., Sadiq, R., and Rajani, B. (2004). “Modeling Pipe Deterioration using Soil Properties – An Application of Fuzzy Logic Expert System.” Pipeline Engineering and Construction, 1–10.  Nelson, R. F. (1998). Reliability-Centered Power Line Management Inspection Process, Measurement Techniques and Data Management Considerations. The Institution of Electrical Engineers (IEE), London.  Nelson, R., and Sinclair, M. (2005). Evaluation of Wood Pole Condition Assessment Tools, 1010654. Electric Power Research Institute (EPRI), Palo Alto, CA.  Nguyen, M., Foliente, G., and Wang, X. (2004). “State-of-the-Practice & Challenges in Non-Destructive Evaluation of Utility Poles in Service.” Key Engineering Materials, 273, 1521–1528.  Rajani, B., Kleiner, Y., and Sadiq, R. (2006). “Translation of pipe inspection results into condition ratings using the fuzzy syntiietic evaluation technique.” Journal of Water Supply: Research and Technology -AQUA, 1(55), 11 –24.  Rosowsky, D. V, and Ellingwood, B. R. (2002). “Performance-Based Engineering of Wood Frame Housing : Fragility Analysis Methodology.” Journal of Structural Engineering, 128(1), 32–38.  Ryan, P. C., Stewart, M. G., Spencer, N., and Li, Y. (2014). “Reliability assessment of power pole infrastructure incorporating deterioration and network maintenance.” Reliability Engineering and System Safety, Elsevier, 132, 261–273.  Saaty, T. L. (1988). Muticriteria Decision Making: The Analytic Hierarchy Process. University of Pittsburgh, Pittsburgh PA.  Sadiq, R., Husain, T., Veitch, B., and Bose, N. (2004). “Risk-based decision-making for drilling waste discharges using a fuzzy synthetic evaluation technique.” Ocean Engineering, 31, 1929–1953.  Sadiq, R., and Rodriguez, M. J. (2004). “Fuzzy synthetic evaluation of disinfection by-products — a risk-based indexing system.” Journal of Environmental management, 73, 1–13.     106 Salman, A. M. (2014). “Age-Dependent Fragility and Life-Cycle Cost Analysis of Timber and Steel Distribution Poles Subjected to Hurricanes.” MASc Thesis, Michigan Technological University.  Sandoz, J. L., and Vanackere, O. (1997). “Wood Poles Ageing and Non Destructive Testing Tool.” CIRED 97, Institute of Electrical Engineers (IEE), 6.  Sasmal, S., and Ramanjaneyulu, K. (2008). “Condition evaluation of existing reinforced concrete bridges using fuzzy based analytic hierarchy approach.” Expert Systems with Applications, 35, 1430–1443.  Schultz, M. T., Gouldby, B. P., Simm, J. D., and Wibowo, J. L. (2010). Beyond the Factor of Safety : Developing Fragility Curves to Characterize System Reliability. Washington, DC.  Seavey, R., and Larson, T. (2002). Inspection of Timber Bridges. Office of Research Services, Department of Transporation, St Paul, Minnesota.  Sedjo, R. A. (2002). “Wood Materials used as a means to reduce Greenhouse Gases (GHGS): An Examination of Wooden Utility Poles.” Mitigation and Adaptation Strategies for Global Change, Kluwer Academic, Netherlands, 191–200.  Shafieezadeh, A., Onyewuchi, U. P., Begovic, M. M., and DesRoches, R. (2013). “Fragility Assessment of Wood Poles in Power Distribution Networks against Extreme Wind Hazards.” Advances in Hurricane Engineering, ASCE, 851–861.  Shafieezadeh, A., Onyewuchi, U. P., Begovic, M. M., and DesRoches, R. (2014). “Age-Dependent Fragility Models of Utility Wood Poles in Power Distribution Networks Against Extreme Wind Hazards.” IEEE Transactions on Power Supply Delivery, 29(1), 131–139.  Shahi, A. (2008). “Strengthening of Wooden Cross arms in 230 kV Transmission Structures using Glass Fibre Reinforced Polymer ( GFRP ) Wrap.” MASc Thesis, University of Waterloo.  Shupe, T., Lebow, S., and Ring, D. (2008). Causes and Control of Wood Decay, Degradation & Stain. Agricultural Center, Louisiana State University.  Steenhof, M. C. (2011). “Effect of Woodpecker Damage and Wood Decay on Wood Utility Pole Strength.” MASc Thesis, University of Waterloo.  Sun, L., and Gu, W. (2011). “Pavement Condition Assessment Using Fuzzy Logic Theory and Analytic Hierarchy Process.” Journal of Transportation Engineering, 137(9), 648–655.     107 Tallavo, F. J. (2009). “New Methodology for the Assessment of Decayed Utility Wood Poles Using Ultrasonic Testing.” PhD Dissertation, University of Waterloo.  Tesfameriam, S. (2008). “Siesmic Risk Assessment of Reinforced Concrete Buildings using Fuzzy based Techniques.” PhD Dissertation, University of Ottawa.  Tesfameriam, S., and Vanier, D. J. (2005). “The Analytical hierarchy process for eliciting decision preferences in asset management.” National Research Council of Canada, 1–34.  U.S. Department of Agriculture - Forest Products Laboratory (USDA-FPL). (2010). Wood Handbook - Wood as an Engineering Material. Madison, WI.  U.S. Department of Agriculture - Rural Utilities Services (USDA-RUS). (2009). Design Manual for High Voltage Transmission Lines.  U.S. Dept of Agriculture - Forest Products Laboratory (USDA-FPL). (2014). Wood and Timber Condition Assessment Manual Second Edition. (R. J. Ross and R. H. White, eds.), General Technical Report FPL-GTR-234, U.S. Department of Agriculture, Forest Service, Madison, WI.  Wang, C., Leicester, R. H., and Nguyen, M. (2008). “Probabilistic procedure for design of untreated timber poles in-ground under attack of decay fungi.” Reliability Engineering and System Safety, 93, 476–481.  Wang, C., and Wang, X. (2012). “Vulnerability of timber in ground contact to fungal decay under climate change.” Climate Change, 115, 777–794.  Wareing, B. (2005). Wood Pole Overhead Lines.  Wolfe, R. W., Bodig, J., and Lebow, P. K. (2001). Derivation of Nominal Strength for Wood Utility Poles. Madison, WI.  Xu, R. (2000). “Fuzzy Least square priority method in the analytic hierarchy process.” Fuzzy Sets and Systems, 112(3), 395–404.  Yan, J. M., and Vairavamoothy, K. (2004). “Fuzzy Approach for Pipe Condition Assessment.” New Pipeline Technologies, Security, and Safety Pipelines 2003, 466 – 476.  Zhai, X., and Stewart, M. G. (2010). “Structural reliability analysis of reinforced grouted concrete block masonry walls in compression.” Engineering Structures, Elsevier Ltd, 32(1), 106–114.     108 Appendix-A: Extreme Value Analysis a) Vancouver Year (Sorted) Max Wind Speed V (m/s) Ranking (L) No of Observations (N) Y=L/(N+1) X= -LN(-LN(Y)) 1966 18.333 1 56 0.0175439 -1.396999671 1988 19.167 2 56 0.0350877 -1.208931715 1986 19.444 3 56 0.0526316 -1.0799183 1970 20.000 4 56 0.0701754 -0.977106171 1976 20.000 5 56 0.0877193 -0.88937713 1983 20.000 6 56 0.1052632 -0.811504184 1969 20.556 7 56 0.122807 -0.740575045 1977 20.556 8 56 0.1403509 -0.674784476 1984 20.556 9 56 0.1578947 -0.612927248 1989 20.556 10 56 0.1754386 -0.554152994 1978 21.111 11 56 0.1929825 -0.49783521 1968 21.389 12 56 0.2105263 -0.443495766 1982 21.667 13 56 0.2280702 -0.390758772 1985 21.667 14 56 0.245614 -0.339320988 1987 21.667 15 56 0.2631579 -0.288932091 1990 21.667 16 56 0.2807018 -0.239381043 1965 21.944 17 56 0.2982456 -0.190486403 1973 22.222 18 56 0.3157895 -0.142089241 2005 22.222 19 56 0.3333333 -0.094047828 2009 22.778 20 56 0.3508772 -0.04623356 1996 23.056 21 56 0.3684211 0.001472253 2004 23.056 22 56 0.3859649 0.049180985 1979 23.611 23 56 0.4035088 0.096998848 1980 23.611 24 56 0.4210526 0.145028734 1981 23.611 25 56 0.4385965 0.193371856 1998 23.611 26 56 0.4561404 0.242129232 1971 24.167 27 56 0.4736842 0.291403118 1963 24.722 28 56 0.4912281 0.341298403 1974 24.722 29 56 0.5087719 0.391924047 1992 24.722 30 56 0.5263158 0.443394593 1994 24.722 31 56 0.5438596 0.495831822 2000 24.722 32 56 0.5614035 0.549366602 2008 24.722 33 56 0.5789474 0.604141 2012 24.722 34 56 0.5964912 0.660310759 1995 25.278 35 56 0.6140351 0.718048242 1999 25.278 36 56 0.6315789 0.777545982 2002 25.278 37 56 0.6491228 0.839021046  109 1958 25.833 38 56 0.6666667 0.902720456 1967 25.833 39 56 0.6842105 0.96892803 2010 25.833 40 56 0.7017544 1.037973134 1972 26.389 41 56 0.7192982 1.11024205 2003 26.389 42 56 0.7368421 1.186192975 2006 26.389 43 56 0.754386 1.266376177 2001 26.667 44 56 0.7719298 1.351461592 1964 26.944 45 56 0.7894737 1.442277465 1993 27.222 46 56 0.8070175 1.539865809 1959 27.778 47 56 0.8245614 1.645564354 1991 27.778 48 56 0.8421053 1.761131781 2011 27.778 49 56 0.8596491 1.88894701 1997 28.889 50 56 0.877193 2.032342235 1975 30.000 51 56 0.8947368 2.196194392 1960 31.389 52 56 0.9122807 2.388060749 2007 31.389 53 56 0.9298246 2.6205978 1961 33.056 54 56 0.9473684 2.917527168 1962 35.000 55 56 0.9649123 3.332098203 1957 35.833 56 56 0.9824561 4.034214532     110 b) Victoria Year (Sorted) Max Wind Speed V (m/s) Ranking (L) No of Observations (N) Y=L/(N+1) X= -LN(-LN(Y)) 1985 17.50 1 48 0.020408163 -1.358876991 1983 18.61 2 48 0.040816327 -1.162736073 1986 18.61 3 48 0.06122449 -1.027190759 1990 19.17 4 48 0.081632653 -0.918498667 1979 19.44 5 48 0.102040816 -0.825219803 1984 19.44 6 48 0.12244898 -0.74196631 1975 20.00 7 48 0.142857143 -0.665729811 1981 20.00 8 48 0.163265306 -0.594640213 1980 20.56 9 48 0.183673469 -0.5274442 1987 20.56 10 48 0.204081633 -0.463252897 2004 20.56 11 48 0.224489796 -0.401406902 1976 21.11 12 48 0.244897959 -0.341398403 2001 21.11 13 48 0.265306122 -0.282823494 2008 21.11 14 48 0.285714286 -0.225351487 2009 21.11 15 48 0.306122449 -0.168704343 1991 21.67 16 48 0.326530612 -0.112642357 1992 21.67 17 48 0.346938776 -0.05695385 1996 21.67 18 48 0.367346939 -0.001447492 2002 21.67 19 48 0.387755102 0.054053607 2011 21.67 20 48 0.408163265 0.109716629 1965 22.22 21 48 0.428571429 0.165702981 1978 22.22 22 48 0.448979592 0.222171718 1998 22.78 23 48 0.469387755 0.27928267 2000 22.78 24 48 0.489795918 0.337199446 2003 22.78 25 48 0.510204082 0.396092459 1966 23.33 26 48 0.530612245 0.456142129 1970 23.61 27 48 0.551020408 0.517542411 1982 23.61 28 48 0.571428571 0.580504824 1994 23.61 29 48 0.591836735 0.645263202 2005 23.61 30 48 0.612244898 0.712079437 1988 24.17 31 48 0.632653061 0.781250586 2007 24.72 32 48 0.653061224 0.853117841 1968 25.00 33 48 0.673469388 0.928078089 1977 25.28 34 48 0.693877551 1.006599065 1993 25.28 35 48 0.714285714 1.08923964 1997 25.28 36 48 0.734693878 1.176677534 2010 25.28 37 48 0.755102041 1.269748053  111 1973 25.83 38 48 0.775510204 1.369499632 1999 25.83 39 48 0.795918367 1.477275855 1974 26.39 40 48 0.816326531 1.594840751 2012 26.39 41 48 0.836734694 1.724578142 1971 27.22 42 48 0.857142857 1.869824714 1989 27.22 43 48 0.87755102 2.035461538 2006 27.22 44 48 0.897959184 2.229049689 1969 28.61 45 48 0.918367347 2.463249175 1995 28.89 46 48 0.93877551 2.761784869 1967 30.28 47 48 0.959183673 3.177909127 1972 30.28 48 48 0.979591837 3.881528369        112 c) Kelowna Year (Sorted) Max Wind Speed V (m/s) Ranking (L) No of Observations (N) Y=L/(N+1) X= -LN(-LN(Y)) 1992 16.39 1 25 0.04 -1.18 1995 16.39 2 25 0.08 -0.94 1996 16.39 3 25 0.12 -0.77 1978 18.61 4 25 0.15 -0.63 1983 18.61 5 25 0.19 -0.50 1986 18.61 6 25 0.23 -0.38 1987 18.61 7 25 0.27 -0.27 1977 20.56 8 25 0.31 -0.16 1982 20.56 9 25 0.35 -0.06 1984 20.56 10 25 0.38 0.05 1990 20.56 11 25 0.42 0.15 1994 20.56 12 25 0.46 0.26 1991 21.11 13 25 0.50 0.37 1988 21.67 14 25 0.54 0.48 1974 21.94 15 25 0.58 0.60 1976 21.94 16 25 0.62 0.72 1979 22.22 17 25 0.65 0.86 1985 22.22 18 25 0.69 1.00 1981 22.50 19 25 0.73 1.16 1997 22.78 20 25 0.77 1.34 1998 23.06 21 25 0.81 1.54 1989 24.17 22 25 0.85 1.79 1973 24.72 23 25 0.88 2.10 1975 24.72 24 25 0.92 2.53 1980 27.78 25 25 0.96 3.24   113   d) Castlegar Year (Sorted) Max Wind Speed V (m/s) Ranking (L) No of Observations (N) Y=L/(N+1) X= -LN(-LN(Y)) 1981 16.39 1 16 0.05882353 -1.041411525 1972 18.89 2 16 0.11764706 -0.760836746 1980 20.00 3 16 0.17647059 -0.550777448 1979 20.56 4 16 0.23529412 -0.369436456 1970 21.39 5 16 0.29411765 -0.201940696 1971 21.94 6 16 0.35294118 -0.040617693 1973 21.94 7 16 0.41176471 0.119568534 1974 21.94 8 16 0.47058824 0.282665606 1977 23.06 9 16 0.52941176 0.452574378 1969 23.33 10 16 0.58823529 0.633693595 1975 24.72 11 16 0.64705882 0.831678317 1976 26.39 12 16 0.70588235 1.054671882 1966 26.94 13 16 0.76470588 1.315783759 1967 26.94 14 16 0.82352941 1.639093245 1968 26.94 15 16 0.88235294 2.078137249 1978 27.78 16 16 0.94117647 2.803054168  114  

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