# Seismic-Reliability-Based Optimal Layout of a Water Distribution Network

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Earthquake Intensity Attenuation

^{2}) based on the 90 earthquakes that have occurred in Japan as

#### 2.2. Determination of Pipe Failure Mode

Category | Correction Factor | |
---|---|---|

Pipe diameter (mm) (C1) | D < 100 | 1.6 |

100 ≤ D < 200 | 1.0 | |

200 ≤ D < 500 | 0.8 | |

500 ≤ D | 0.5 | |

Pipe material (C2) | Asbestos-Cement Pipe | 1.2 |

Poly-Vinyl Chloride Pipe, Vent Pipe | 1.0 | |

Cast Iron Pipe | 1.0 | |

Poly-Ethylene Pipe, High Impact (3-Layer) Pipe | 0.8 | |

Steel Pipe | 0.3 | |

Ductile Cast Iron Pipe | 0.3 | |

Topography (C3) | Narrow Valley | 3.2 |

Terrace | 1.5 | |

Disturbed Hill | 1.1 | |

Alluvial | 1.0 | |

Stiff Alluvial | 0.4 | |

Liquefaction (C4) | Total | 2.4 |

Partial | 2.0 | |

None | 1.0 |

_{i}, km) expressed as

_{fbreakage,i}= 0.1 and P

_{fleakage,i}= 0.5), the complementary probability is assigned for the normal condition (P

_{normal}= 0.4). However, if the cumulative probability of the leakage and breakage is greater than 1 (e.g., P

_{fbreakage,i}= 0.18 and P

_{fleakage,i}= 0.90), the model assumes that the normal condition (without any damage) is not available, and the two failure probabilities are normalized to make the sum of 1.0 (P

_{fbreakage,i}= 0.18/(0.18 + 0.90) = 0.17 and P

_{fleakage,i}= 0.90/(0.18 + 0.90) = 0.83).

#### 2.3. Pipe Failure Modeling

_{l}) are assigned to the closest node to the damaged pipe using the following equation:

**Figure 2.**A schematic diagram to describe pipe damage modeling: (

**a**) leakage condition and (

**b**) breakage condition.

#### 2.4. Negative Pressure Treatment

#### 2.5. Seismic Reliability Indicator

_{S}) is defined as the ratio of the total available system demand to the total required system demand:

_{given}= the available budget for pipe system.

_{i}determined for the ith pipe (USD/m); and L

_{i}= the length of the ith pipe.

#### 2.6. Resilience Indicator

^{3}/s); ${\mathrm{H}}_{\mathrm{k}}$ = head at reservoir k; ${\mathrm{Power}}_{\mathrm{i}}$ = power of the ith pump (Nm/s); $\mathsf{\gamma}$ = specific weight of water (N/m

^{3}); nr and np = number of reservoir and pumps, respectively. Note that this indicator was used only for a postoptimization analysis.

## 3. Study Network

## 4. Application Results

#### 4.1. Different Available Pipe Sizing Options

**Figure 4.**Maximum seismic reliability values of two case designs with different pipe sizing options.

**Figure 5.**Pipe layout comparison for the solutions obtained from Cases 1 and 2 (Figure 4); pipe diameters are in mm; the thicker and darker pipe is larger. (

**a**) Case 1; (

**b**) Case 2.

**Figure 7.**Trade-off relationship between total cost and seismic reliability in Case 1 where all pipes (152, 203, 254, 305, 356, 406, 457, 508, 610, and 762 mm) are available and without zero pipe option.

#### 4.2. Constant Layout with a Single Pipe Sizing Option

**Table 2.**Correction factors and discharge coefficients (Equation (6)) for the pipe sizes considered.

Pipe Sizes | Pipe’s Cross-Sectional Area (A) | Correction Factor (C1) | Discharge Coefficient | ||
---|---|---|---|---|---|

mm | inch | Breakage (100% of A) | Leakage (10% of A) | ||

152 | 6 | 28 | 1 | 1074 | 107 |

203 | 8 | 50 | 0.8 | 1910 | 191 |

254 | 10 | 79 | 0.8 | 2985 | 298 |

305 | 12 | 113 | 0.8 | 4298 | 430 |

356 | 14 | 154 | 0.8 | 5850 | 585 |

406 | 16 | 201 | 0.8 | 7640 | 764 |

457 | 18 | 254 | 0.8 | 9670 | 967 |

508 | 20 | 314 | 0.5 | 11,938 | 1194 |

610 | 24 | 452 | 0.5 | 17,191 | 1719 |

762 | 30 | 707 | 0.5 | 26,861 | 2686 |

#### 4.3. Random Designs

**Figure 9.**(

**a**) Seismic reliability of randomly generated solutions (

**black dot**) and Pareto solutions shown in Figure 7 (

**blue diamond**) and (

**b**) resilience of the same random designs.

## 5. Summary and Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Schaake, J.; Lai, D.D. Linear Programming and Dynamic Programming Applications to Water Distribution Network Design; Report No. 116; Department of Civil Engineering, Massachusetts Institute of Technology: Cambridge, MA, USA, 1969. [Google Scholar]
- Alperovits, E.; Shamir, U.U. Design of optimal water distribution systems. Water Resour. Res.
**1977**, 13, 885–900. [Google Scholar] [CrossRef] - Lansey, K.; Mays, L. Optimization model for water distribution system design. J. Hydraul. Eng.
**1989**, 115, 1401–1418. [Google Scholar] [CrossRef] - Simpson, A.; Dandy, G.; Murphy, L. Genetic algorithms compared to other techniques for pipe optimization. J. Water Resour. Plan. Manag.
**1994**, 120, 423–443. [Google Scholar] [CrossRef] - Savic, D.; Walters, G. Genetic algorithms for least-cost design of water distribution networks. J. Water Resour. Plan. Manag.
**1997**, 123, 67–77. [Google Scholar] [CrossRef] - Lansey, K.; Duan, N.; Mays, L.; Tung, Y. Water distribution system design under uncertainty. J. Water Resour. Plan. Manag.
**1989**, 115, 630–645. [Google Scholar] [CrossRef] - Xu, C.; Goulter, C. Reliability-based optimal design of water distribution networks. J. Water Resour. Plan. Manag.
**1999**, 125, 352–362. [Google Scholar] [CrossRef] - Babayan, A.; Kapelan, Z.; Savic, D.; Walters, G. Least cost design of robust water distribution networks under demand uncertainty. J. Water Resour. Plan. Manag.
**2005**, 131, 375–382. [Google Scholar] [CrossRef] - Kapelan, Z.; Savic, D.; Walters, G. Multiobjective design of water distribution systems under uncertainty. Water Resour. Res.
**2005**, 41, W11407-1–W11407-15. [Google Scholar] [CrossRef] - Giustolisi, O.; Laucelli, D.; Colombo, A. Deterministic versus stochastic design of water distribution networks. J. Water Resour. Plan. Manag.
**2009**, 135, 117–127. [Google Scholar] [CrossRef] - Jung, D.; Kang, D.; Kim, J.H.; Lansey, K. Robustness-based design of water distribution systems. J. Water Resour. Plan. Manag.
**2014**, 140. [Google Scholar] [CrossRef] - Su, Y.; Mays, L.; Duan, N.; Lansey, K. Reliability-based optimization model for water distribution systems. J. Hydraul. Eng.
**1987**, 113, 1539–1556. [Google Scholar] [CrossRef] - Federal Emergency Management Agency (FEMA). HAZUS97 Technical Manual; FEMA: Washington, DC, USA, 1997.
- Kim, Y.S.; Spencer, B.F.; Song, J.; Elnashai, A.S.; Stokes, T. Seismic Performance Assessment of Interdependent Lifeline Systems; MAE Center: Urbana, IL, USA, 2007. [Google Scholar]
- Hall, W.; Newmark, N. Seismic design criteria for pipelines and facilities. J. Tech. Counc. ASCE
**1978**, 104, 91–107. [Google Scholar] - Wright, J.P.; Takada, S. Earthquake Response Characteristics of Jointed and Continuous Buried Lifelines; Grant Report No. 15; National Science Foundation: New York, NY, USA, 1980.
- Hwang, R.N.; Lysmer, J. Response of buried structures to traveling waves. J. Geotech. Eng. Div.
**1981**, 107, 183–200. [Google Scholar] - Fragiadakis, M.; Christodoulou, S.E.; Vamvatsikos, D. Reliability assessment of urban water distribution networks under seismic loads. Water Resour. Manag.
**2013**, 27, 3739–3764. [Google Scholar] [CrossRef] - American Lifelines Alliance. Seismic Fragility Formulations for Water Systems Part 1 Guideline; American Lifeline Alliance: Washington, DC, USA, 2001. [Google Scholar]
- Eguchi, R.T.; Taylor, C.E.; Hasselman, T.K. Earthquake Vulnerability Models for Water Supply Components; Technical Report No. 83-1396-2c; J.H. Wiggins Company: Redondo Beach, CA, USA, 1983. [Google Scholar]
- Ballantyne, D.B.; Berg, E.; Kennedy, J.; Reneau, R.; Wu, D. Earthquake Loss Estimation Modeling of the Seattlewater System; Technical Report; Kennedy/Jenks/Chilton: Federal Way, WA, USA, 1990. [Google Scholar]
- Shinozuka, M.; Tan, R.Y.; Toike, T. Serviceability of Water Transmission Systems under Seismic Risk. In Lifeline Earthquake Engineering, the Current State of Knowledge; American Society of Civil Engineers: New York, NY, USA, 1981. [Google Scholar]
- Shinozuka, M.; Hwang, H.; Murata, M. Impact on water supply of a seismically damaged water delivery system. In Lifeline Earthquake Engineering in the Central and Eastern U.S.; American Society of Civil Engineers: New York, NY, USA, 1992; pp. 43–57. [Google Scholar]
- Shinozuka, M.; Rose, A.; Eguchi, R.T. Engineering and Socioeconomic Impacts of Earthquakes; Monograph Series 2; Multidisciplinary Center for Earthquake Engineering Research: Buffalo, NY, USA, 1998. [Google Scholar]
- Markov, I.; Mircea, G.; O’Rourke, T. An Evaluation of Seismic Serviceability of Water Supply Networks with Application to the San Francisco Auxiliary Water Supply System; Technical report NCEER 94-0001; National Center for Earthquake Engineering Research University of Buffalo, State University of New York: Buffalo, NY, USA, 1994. [Google Scholar]
- Hwang, H.; Lin, H.; Shinozuka, M. Seismic performance assessment of water delivery systems. J. Infrastruct. Syst.
**1998**, 4, 118–125. [Google Scholar] [CrossRef] - Shi, P. Seismic Response Modeling of Water Supply Systems. Ph.D. Thesis, Cornell University, Ithaca, NY, USA, 1 January 2006. [Google Scholar]
- Liu, G.Y.; Chung, L.L.; Yeh, C.H.; Wang, R.Z.; Chou, K.W.; Hung, H.Y.; Chen, S.A.; Chen, Z.H.; Yu, S.H. A Study on Pipeline Seismic Performance and System Post-Earthquake Response of Water Utilities (1/2); Technical Report MOEA-WRA-0990095; Water Resource Agency, MOEA: Taipei, Taiwan, 2010.
- Liu, G.Y.; Chung, L.L.; Huang, C.W.; Yeh, C.H.; Chou, K.W.; Hung, H.Y.; Chen, Z.H.; Chou, C.H.; Tsai, L.C. A Study on Pipeline Seismic Performance and System Post-Earthquake Response of Water Utilities (2/2); Technical Report MOEA-WRA-1000090; Water Resource Agency, MOEA: Taipei, Taiwan, 2011.
- GIRAFFE. GIRAFFE User’s Manual; School of Civil and Environmental Engineering, Cornell University: Ithaca, NY, USA, 2008. [Google Scholar]
- Rossman, L.A. EPANET 2 User’s Manual; U.S. Environmental Protection Agency (EPA): Cincinnati, OH, USA, 2000.
- Wang, Y. Seismic Performance Evaluation of Water Supply Systems. Ph.D. Thesis, Cornell University, Ithaca, NY, USA, 1 January 2006. [Google Scholar]
- Shi, P.; O’Rourke, T.D.; Wang, Y. Simulation of earthquake water supply performance. In Proceedings of the 8th National Conference on Earthquake Engineering, Paper No. 8NCEE-001295, EERI, Oakland, CA, USA, 18–22 April 2006.
- Wang, Y.; O’Rourke, T.D. Characterizations of seismic risk in Los Angeles water supply system. In Proceedings of the 5th China-Japan-US Symposium on Lifeline Earthquake Engineering, Haikou, China, 26–28 November 2007.
- Bonneau, A.L. Water Supply Performance during Earthquakes and Extreme Events. Ph.D. Thesis, Cornell University, Ithaca, NY, USA, 2008. [Google Scholar]
- Bonneau, A.L.; O’Rourke, T.D. Water Supply Performance during Earthquakes and Extreme Events; Technical Report MCEER-09-0003; University of Buffalo, State University of New York: Buffalo, NY, USA, 2009. [Google Scholar]
- Yoo, D.G.; Jung, D.; Kang, D.; Kim, J.H.; Lansey, K. Seismic hazard assessment model for urban water supply networks. J. Water Resour. Plan. Manag.
**2015**. [Google Scholar] [CrossRef] - Geem, Z.W.; Kim, J.H.; Loganathan, G.V. A New Heuristic Optimization Algorithm: Harmony Search. Simulation
**2001**, 76, 60–68. [Google Scholar] [CrossRef] - Kim, J.H.; Geem, Z.W.; Kim, E.S. Parameter Estimation of the Nonlinear Muskingum Model Using Harmony Search. J. Am. Water Resour. Assoc.
**2001**, 37, 1131–1138. [Google Scholar] [CrossRef] - Todini, E. Looped water distribution networks design using a resilience index based heuristic approach. Urban Water
**2000**, 2, 115–122. [Google Scholar] [CrossRef] - Kawashima, K.; Aizawa, K.; Takahashi, K. Attenuation of peak ground motion and absolute acceleration response spectra. In Proceedings of the 8th World Conference on Earthquake Engineering (WCEE), San Francisco, CA, USA, 24–28 July 1984; pp. 257–264.
- Lee, K.; Cho, K.H. Attenuation of peak horizontal acceleration in the Sino-Korea Craton. In Proceedings of the Annual Fall Conference of Earthquake Engineering Society of Korea, Cheonan, Korea, 27 September 2002; pp. 3–10.
- Baag, C.E.; Chang, S.J.; Jo, N.D.; Shin, J.S. Evaluation of seismic hazard in the southern part of Korea. In Proceedings of the International Symposium on Seismic Hazards and Ground Motion in the Region of Moderate Seismicity, Seoul, Korea, 1 November 1998; pp. 31–50.
- Isoyama, R.; Ishida, E.; Yune, K.; Shirozu, T. Seismic damage estimation procedure for water supply pipelines. In Proceedings of the 12th World Conference on Earthquake Engineering (WCEE), Auckland, New Zealand, 1–4 January 2000; p. 1762.
- Lambert, A. What do we know about pressure-leakage relationships in distribution systems? In Proceedings of the IWA Conference on Systems Approach to Leakage Control and Water Distribution System Management, Brno, Czech Republic, 16 May 2001.
- Puchovsky, M.T. Automatic Sprinkler Systems Handbook; National Fire Protection Association (NFPA): Quincy, MA, USA, 1999. [Google Scholar]
- Bentley Systems. WaterGEMS; Bentley Systems Incorporated: Exton, PA, USA, 2006. [Google Scholar]
- Giustolisi, O.; Savic, D.A.; Berardi, L.; Laucelli, D. An Excel-based Solution to Bring Water Distribution Network Analysis Closer to Users. In Proceedings of the Computer and Control in Water Industry, Exeter, UK, 5–7 September 2011; Volume 3, pp. 805–810.
- Muranho, J.; Ferreira, A.; Sousa, J.; Gomes, A.; Marques, A.S. Pressure-dependent Demand and Leakage Modeling with an EPANET Extension–WaterNetGen. Procedia Eng.
**2014**, 89, 632–639. [Google Scholar] [CrossRef] - Wood, D. KYPipe Reference Manual; Civil Engineering Software Center, University of Kentucky: Lexington, KY, USA, 1995. [Google Scholar]
- Cullinane, M.; Lansey, K.; Mays, L. Optimization-availability-based design of water-distribution networks. J. Hydraul. Eng.
**1991**, 118, 420–441. [Google Scholar] [CrossRef] - Bao, Y.; Mays, L. Model for water distribution system reliability. J. Hydraul. Eng.
**1990**, 116, 1119–1137. [Google Scholar] [CrossRef] - Farmani, R.; Walters, G.; Savic, D. Trade-off between total cost and reliability for Anytown water distribution network. J. Water Resour. Plan. Manag.
**2005**, 131, 161–171. [Google Scholar] [CrossRef] - Prasad, T.D.; Park, N. Multiobjective genetic algorithms for design of water distribution networks. J. Water Resour. Plan. Manag.
**2004**, 130, 73–82. [Google Scholar] [CrossRef] - Gheisi, A.; Naser, G. Multistate reliability of water-distribution systems: Comparison of surrogate measures. J. Water Resour. Plan. Manag.
**2015**, 141. [Google Scholar] [CrossRef] - Walski, T.; Brill, E.; Gessler, J., Jr.; Goulter, I.; Jeppson, R.; Lansey, K.; Lee, H.; Liebman, J.; Mays, L.; Morgan, D.; Ormsbee, L. Battle of the Network Models: Epilogue. J. Water Resour. Plan. Manag.
**1987**, 113, 191–203. [Google Scholar] [CrossRef] - Geem, Z.W. Harmony search in water pump switching problem. In Advances in Natural Computation; Springer: Berlin, Germany; Heidelberg, Germany, 2005; pp. 751–760. [Google Scholar]
- Geem, Z.W. Optimal cost design of water distribution networks using harmony search. Eng. Optim.
**2006**, 38, 259–277. [Google Scholar] [CrossRef] - Geem, Z.W. Harmony search optimisation to the pump-included water distribution network design. Civ. Eng. Environ. Syst.
**2009**, 26, 211–221. [Google Scholar] [CrossRef] - Lansey, K. Sustainable, robust, resilient, water distribution systems. In Proceedings of the 14th Water Distribution Systems Analysis Conference, Adelaide, South Australia, 24–27 September 2012; pp. 1–18.

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Yoo, D.G.; Jung, D.; Kang, D.; Kim, J.H. Seismic-Reliability-Based Optimal Layout of a Water Distribution Network. *Water* **2016**, *8*, 50.
https://doi.org/10.3390/w8020050

**AMA Style**

Yoo DG, Jung D, Kang D, Kim JH. Seismic-Reliability-Based Optimal Layout of a Water Distribution Network. *Water*. 2016; 8(2):50.
https://doi.org/10.3390/w8020050

**Chicago/Turabian Style**

Yoo, Do Guen, Donghwi Jung, Doosun Kang, and Joong Hoon Kim. 2016. "Seismic-Reliability-Based Optimal Layout of a Water Distribution Network" *Water* 8, no. 2: 50.
https://doi.org/10.3390/w8020050