Seismic Reliability and Rehabilitation Decision of Water Distribution System

Trans. Tianjin Univ. 2010, 16: 223-228DOL 10.1007/s12209-01 0-0039-9Seismic Reliability and Rehabilitation Decisionof Water Distribution System"LIU Chunguang (柳春光) 1,2，HE Shuanghua (何双华)2(1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University ofTechnology, Dalian 116024,China; 2. Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 1 16024, China)◎Tianjin University and Springer-Verlag Berlin Heidelberg 2010Abstract: In order to evaluate the seismic reliability of water distribution system and make rehabilitation decisionscorrespondingly, it is necessary to assess pipelines damage states and conduct functional analysis based on pipe leak-age model. When an earthquake ocurred, the water distribution system kept serving with leakage. By adding a virtualnode at the centre of the pipeline with leakage, an efficient approach to pressure-driven analysis was developed forsimulating a variety of low relative scenarios, and a hydraulic leakage model was also built to perform hydraulic analy-sis of the water supply network with seismic damage. Then the mean-first-order-second-moment method was used toanalyse the seismic serviceability of the water distribution system. According to the assessment analysis, pipes thatwere destroyed or in heavy leakage were isolated and repaired emergently, which improved the water supply capabilityof the network and would constitute the basis for enhancing seismic reliability of the system. The proposed approachto seismic reliability and rehabilitation decision analysis on water distribution system is demonstrated effectivethrough a case study.Keywords: water distribution system; hydraulic analysis; leakage model; seismic reliability; rehabilitation decisionW ater distribution system is an important part of ur- pressure is not sufficient for supplying the required de-ban lifeline systems. Due to severe earthquakes occurred mand'. In this paper, pressure-driven demand analysis isin recent years, there were many structure damages and developed for simulating pressure deficient conditions,function failures in the water distribution system, which and the mean-first-order-second-moment method is in-brought great inconvenience to people's life and huge troduced to analyse the seismic serviceability of the watereconomic losses. Thus, it is important to analyse and es- distribution system, which can be applied to further studytimate the serviceability of the water distribution system on seismic performance control analysis and enhance-properly before and after the earthquake.ment of seismic resistance of water distribution system.Seismic performance of the water distribution system refers to the ability that the water supply network 1 Damage states simulation of pipe networkmeets the post-earthquake special demands for waterquantity and pressure under the seismic damage". As 1.1 Damage behaviour and anti-seismic measuresburied pipelines are numerous and geographically dis-of buried pipelinetributed, the locations of slight or moderate damage areThe main damage types of water supply pipelinesvery difficult to discover and repair after the earthquake. under earthquake in China arel4 as follows.Therefore, the water supply network often served with(1) Joint damage: mortar fller falls off in joint,leakage after the earthquakel-, and leakage models spigot pulls out or bell breaks for segmented pipeline; theneeded to be built to perform hydraulic analysis.weld crack or the bolts of pipe-flanges loosen for steelConventional demand-driven models of water sys- pipeline.tem are formulated under the assumption that water con-(2) Longitudinal and oblique crevices appear insumption or demand defined at nodes is statistically con- pipe bodies of reinforced concrete, asbestos concrete andstant, which is not suitable for the cases in which nodal cast iron. Small diameter steel and cast-iron pipe bodyAccepted date: 209-11-13.中国煤化工*Supported by National Natural Science Foundation of China (No. 50478094).CNMH GLIU Chunguang, born in 1964, male, Dr, Prof.MHCorrespondence to LIU Chunguang, E-mail: liucg@dlut.edu.cn.Transactions of Tianjin University Vol. 16 No.32010break when corrosion is severe.ence of a single pipeline on the local water network can(3) Tee joint, elbow, valves and the linking points be obtained through the hydraulic analysis of the dam-of pipelines with structures were broken because of stress aged water distribution systeml1,o.concentration and motion phase difference.2.1 Mass conservation equationFlexible joints show better anti-seismic performanceAfter an earthquake, the leaking water networkthan rigid ones under the same condition, because the should still satisfy the mass balance equation at eachformer absorb more site strain. Also, the pipes with larger node. A network including actual nodes and virtual nodesdiameter are destroyed less than those with smaller di- is formed through the damage simulation of the postameter, indicating that the stiffiness of the pipeline may earthquake network. For the actual node i , the mass con-restrain the deformation of the surrounding soil. More- servationequation can be witten as follows:over, tubes and pipes with good ductility, such as highQ+Zq, =0(-1.,2,..,N)(1)density polyethylene and high quality steel pipes, shouldbe applied to water supply network for anti-seismic pur- For the virtual node i, the mass conservation equationpose.can also be expressed as1.2 Damage states of buried pipelineQu+Zqy=0(i= ,2,.,N,.)(2Based on the past earthquake experiences and ex-periments on pipe joints in China, three damage states of where q;j is the flow in the link connecting iand j , m/s;buried pipeline under earthquake are defined as follows.Q is the outflow at the actual node i, m'/s; Qu; is the(1) Undamaged or slight damage: no damage on leak flow at the virtual node i, m2/s; m is the number ofpipe body, deformation of the joint is smaller than the links; N is the number of actual nodes; and NL is theultimate cracking displacement R, there might be lttle number of virtual nodes.leakage at joints, and pipes can work normally without 2.1.1 Pressure driven demand simulationrepairs.When an outage occurs, nodal pressures are affected.(2) Moderate damage: there is slippage between Pressure may drop below a reference level, the so-calledrubber ring and pipe body at flexible joints, deformation pressure for supplying 100% of desired demand or refer-of the joint is greater than the ultimate cracking dis- ence demand. Whenever the level is below the referenceplacement R，and less than ultimate leakage displace- level, nodal demand is a function of pressure in pressure-ment R, , pipes serve with leakage.dependent demand')](3) Serious damage: deformation of the joint isHowever, it is believed that a junction demand is notgreater than the ultimate leakage displacement R，the afected by pressure, in other words, water consumptionpipe joints are damaged, or pipes cannot supply water will be maxed out (keep constant) if the pressure isunless being replaced.above a threshold. In general, the threshold above whichThe connectivity analysis of the pipe network is per- demand is no longer sensitive to pressure must be greaterformed under the assumption that the disconnected nodes than or equal to the reference pressure at which all de-are deleted and pipes connected with the disconnected mands are met. The junction demand is reduced from thenodes are out of service. Pipelines with moderate damage normal reference demand when the pressure drops beloware in leakage, but it is dificult to locate the leakage po- the reference pressure and increases above the referencesitions due to the randomness of earthquake motions, the demand when the pressure is greater than the referencediversity of site conditions and the complexity of buried pressure but less than the threshold(7. Pressure-dependentpipelines5l. Therefore, the Chinese point leakage model demand is then defined as fllows:(C model for short) is adopted in this paper.0H;≤H"in2 Hydraulic analysis of leakage networkQ,={Q."H,-H Y”2HGu(4)H;≤H"imH≤GHimG,m; s is the deformation at the joint, m; and R is the ulti-M(i,i)= .(14)HL≤Gmate cracking displacement of the pipe, m.2.2 Energy conservation equationBy solving the linear system of equations, we can obtainThe pipe network should also satisfy the energy 0H() , and thenconservation around hydraulic loops, that is, each nodeH(+)=H(*)+AH()(15)can only have one value of water headl0. For each linkThrough repeated iterations, the value of H, con-in the network, the flow and the water head loss in it haveverges to the true value.the following relationship:9; =s,(H,-H,)"(6) 3 Seismic reliability analysis of the networkwhere Sg anda are coefficients related to the material,diameter and length of the pipe. In this paper, Hazen-As the nodal pressure of the network after the earth-Williams expression is adoptedl8,9):quake is the basis for evaluating the network's service-s; =0.27853Crw; D202_,0547)ability and working performance, it could be consideredas the index to assess the network' s seismic reliability.x= 0.548)By introducing random hydraulic model of water supplywhere CHwy is the Hazen-Williams friction factor forsystem，we present a mean-first-order-second-momentpipeij; D，is the diameter of pipe ij, m; and Ly is themethod to evaluate the system's seismic reliability underlength of pipe ij , m.pressure deficient conditions.2.3 Solution methodology for the hydraulic model3.1 Limit state equationsThe hydraulic equation of the network with leak-Each node's limit state equations of the network af-age is a nonlinear equation set on the unknown waterter earthquake can be written ashnheads as follows:Z;=H;- H"n (i=1,2,,n)(16)F(H)=AQ -Q、=(f(H),f(H,., f。(H))"=0 (9)If Z denotes normal distribution, the failure probabilitywhere A is the adjacency matrix of the network; 2, de- of node i can be expressed by rliability index as fllowsnotes the flow vector of the pipes; 0、is the calculateddemand vector of the nodes; H represents the calculatedp=P(H