WATER DISTRIBUTION NETWORK REHABILITATION: Selection and Scheduling of Pipe Rehabilitation Alternatives Yehuda Kleiner A thesis subrnitted in conformity rith the requirernents for the degree of Doctor of Philosophy Graduate Department of Civil Engineering University of Toronto @ copyright by Yehuda Kleiner 199 7 National Library Bibliothèque nationale 1*1 .canada du Canada Acquisitions and Acquisitions et Bibliographie Services seMces bibliographiques 395 Wellington Street 335, rue Wellington Ottawa ON KiA ON4 Ottawa ON KIA ON4 Canada Canada The author has granted a non- L'auteur a accordé une Licence non exclusive licence allowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distribute or sell reproduire, prêter, distribuer ou copies of this thesis in microfoxm, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/fïIm, de reproduction sur papier ou sur fonnat électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts f?om it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être Unprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. ABSTRACT Kleiner, Yehuda, 199 7. Water distribution nehvork rehabilitation: srlection and scliedding of pipe rehabilitation afrernatives.A thesis subrnitted in conformity with the requirements for the degree cf Doctor of Philosophy. Graduate Department of Civil engineering. University of Toronto. The most expensive cornponent of a water supply system is the distribution network. Aging water supply infrastructure, coupled with the continuous stress placed on the pipes by operational and environmental conditions, have led to system deterioration which manifests itself in increased operation and maintenance costs. water losses, reduction in the quality of senrice and reduction in the quality of water supplied. In this thesis. a methodology is proposed to select. for each pipe in an existing network. the rehabilitation alternative and the time of its implementation, so as to minirnize the cost of the rehabilitation investment and al1 maintenance costs over a pre-defined time horizon and subject to certain consuaints. The methodology explicitly considers the detenoration over tirne of both the structural integrity and the hydraulic capacity of every pipe in the system. The cost associated with eüch pipe in the network is calculated ÿs the present value of an infinite Stream of costs. The proposed method. nmed the multistage network rehabilitation aridysis procedure (MNRAP) is based on a dynamic programming approach combined with partial and (sometimes) impiicit enumention schemes. A compu ter propm was developed to implement the methodology . Subsequently, the vrilidity of the MYRAP was established in two ways: 1. Sorne simple systems were exhaustively enumerated for al1 possible combinations of rehabiliiiiiion alternatives selection and scheduling, and their minimum cost sequences were compared to those obtained by applying MNRAP. An excellent agreement was demonstrated between the two sets of results. 2. A study was conducted in which six water utility managers from the Greater Toronto Area and the Region of Waterloo (the participants) were presented with a sample water distribution system inciuding al1 pertinent data kat would typically be available when preparing a long-terrn rehabilitation program. The participants were required to implement their best engineering judgrnent and anaiysis tools in determinhg an optimal rehabilitation policy, subject to stated consuaints. These policies were then compared to that obtained by the MNRAP. The cornparison demonstrated the advantages of MNRAP over existins analysis practices; (a) in its comprehensiveness and (b) in the explicit, robust manner with which the economics and the hydraulics of the water distribution system are simultaneously considered over a planning time horizon. In conclusion, the LMNRAPpromises to provide a valuable decision support system for engineen and decision makers in devising long-term network rehabilitation plans. ACKNOWLEDGEMENTS My sincerest thmh to rny supervisor Professor B. J. Adams. who graciously allowed me to take my time in exploring various ideas and to hit some brick walls in the process. Professor Adams was always there for me with good advice. extra insight and constructive comments when needed. His ability to inspire acadernic excellence in his students is much appreciated. I wish to thank Professor J. S. Rogers. rny CO-supervisorfrom the Mechanical and Industrial Engineering Department. By illuminating some aspects of rny thesis from a different perspective, Prof. Rogers enabled me to gain further insight into the network optirnization aspects of my thesis. My sincere thanks to professors B. W. Karney and P. H. Byer for their constant support throughout my years at the University of Toronto. and for their valuable comments and suggestions. I would also like to thank the graduate students of the Environmental Engineering Section of the Civil Engineering Department whose camaraderie has made my time there enjoyable. especially James Mcleod. without whose help 1would still be wrestling with some of the finer aspects of C prograrnrning. 1 feel pnvileged to have worked with an excellent group of people. Finally. 1 thank my family, without whose support al1 of this would not have ken possible. TABLE OF CONTENTS 1 . Introduction ................................................................................................ 1 1.1. General .............................. ... .............................................................. 1 1.2. Problem Scope and Thesis Scope ........................................................ -3 1.3. Thesis Outline ..................................................................................... 6 2 . Literature Review ..................... ............................................................... 8 2.1 Introduction ..................................................................................... 8 2.2 Existing Rehabilitation Models ............................................................ 9 1.3 Pipe Age as a Decision Variable ........................................................ 15 2.3 Distribution System Reliability .......................................................... 17 2.5 Water Qudity in the Distribution System ......................................... 23 2.6 Proposed .M ethodology and How It Advances Knowledge ................ 25 3 . Mode1 Formulation ............................................................................... 26 Pr~blernStatement ........................................................................... 26 Cost of Capital Investment............................................................... 27 Cost of Maintenance ......................................................................... 28 Total Cost ....................................................................................... 29 3-41 Total Cost for Replacement Alternatives ............................... 29 3.4.2 Total Cosr for Relining Alternatives ...................................... 36 Total Cost and Time Horizon ....................................................... 37 Deterioration of Pipe Friction Coefficient ................................... 38 Additional Constraints ................................................................ 41 Cost of Energy ................................................................................. 42 Mathematical Statement of the Problem ............................................ 43 4 . The Optimization Procedure ...................................................................... 45 4.1 Introduction ..................................................................................... 45 4.2 Conceptual Approach ....................................................................... 46 4.3 Rehtiw Timing of Rehabilitation Measures ...................................... 53 4.4 The Dynamic Prograrnming Approach .............................................. 60 4.5 An Illustration of the DP Approach ................................................... 63 4.6 Summq of the DP Process ............................................................. 65 3.7 Additionai State Reduction ............................................................... 67 6 . Discussion .............................................................................................. 75 6.1 General ................... .. ................................................................... 75 6.2 Minimum Residual Pressure ..................................l... ........................ 75 6.3 The Size of the Analysis Timestep .................................................... 77 6.4 Time Horizon . Infinite Cost Stream and Residual Capacity ............... 78 6.5 The Discount Rate ........................................................................... 79 6.6 Systern Hydraulic Capacity ............................................................... 82 6.7 Using MNRAP ................................................................................. 84 7 . Mode1 Vdidation ...................................................................................... 87 7.1 Introduction ....................................................................................