﻿ 基于事故率的城市供水管网全寿命运行可靠性
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (9): 1286-1293.  DOI: 10.11908/j.issn.0253-374x.2019.09.008 0

### 引用本文

LIU Wei, SONG Zhaoyang. Accident Rate-Based Lifecycle Operational Reliability of Urban Water DistributionNetworks[J]. Journal of Tongji University (Natural Science), 2019, 47(9): 1286-1293. DOI: 10.11908/j.issn.0253-374x.2019.09.008

### 文章历史

1. 同济大学 土木工程学院，上海 200092;
2. 同济大学 土木工程防灾国家重点实验室，上海 200092

Accident Rate-Based Lifecycle Operational Reliability of Urban Water DistributionNetworks
LIU Wei 1,2, SONG Zhaoyang 1
1. College of Civil Engineering, Tongji University, Shanghai 200092, China;
2. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China
Abstract: An accident rate-based lifecycle operational reliability analysis approach of urban water distribution networks was proposed using the accident rate models for different pipe materials, the simulation models for different accidents, and the Langelier-based pipeline roughness model. The values of some key parameters were suggested by sensitivity analysis. Then, the operational reliability analysis of a case network was performed, by which the weak areas were determined and the network improvement measures were introduced.
Key words: water distribution networks    operational reliability    lifecycle    accident rate    pipe roughness

1 供水管网运行可靠性分析框架 1.1 运行可靠性定义及模拟方法

 ${R_i} = {P_{\rm{r}}}\left( {{H_i} \ge {H_{i,0}}} \right)$ (1)

 图 1 供水管网运行可靠性单次模拟流程 Fig.1 Single operational reliability simulation of water distribution networks

(1) 通过事故资料统计获得分析参数，包括事故类型和不同管材的事故率等，详见1.2节.

(2) 根据事故率随机生成管线状态，即是否发生事故和事故类型，并进行事故模拟，详见1.3节.

(3) 在单次模拟中，所有管线的状态构成一种事故情景，并采用水力分析方法对该情境下的供水管网进行分析，得到节点水压，若节点水压小于需求水压，则该节点失效.

(4) 对管网进行若干次模拟，最终节点运行可靠度等于1减失效次数与模拟次数相除.

1.2 管线事故率模型

1.2.1 灰口铸铁管

 $N(t) = N\left( {{t_0}} \right){{\rm{e}}^{\beta T}}$ (2)

1.2.2 钢管和球墨铸铁管

 图 2 钢管和球墨铸铁管事故率 Fig.2 Accident rate of steel pipe and ductile iron pipe

(1) 采用指数模型(图 3)，最终拟合结果为

 $N(t) = \left\{ {\begin{array}{*{20}{l}} {0.158{{\rm{e}}^{0.089T}}}&{钢管}\\ {0.167{{\rm{e}}^{0.155T}}}&{球墨铸铁管} \end{array}} \right.$ (3)
 图 3 增长率系数的指数拟合 Fig.3 Exponential fitting of growth rate coefficient

(2) 采用线性模型(图 4)，最终拟合结果为

 $N(t) = \left\{ {\begin{array}{*{20}{l}} {0.087T - 0.758}&{钢管}\\ {0.242T - 1.720}&{球墨铸铁管} \end{array}} \right.$ (4)
 图 4 增长率系数的线性拟合 Fig.4 Linear fitting of growth rate coefficient

1.3 事故模拟

1.3.1 渗漏

 $\mathit{\boldsymbol{A}}{\mathit{\boldsymbol{Q}}_{\rm{P}}} + {\mathit{\boldsymbol{Q}}_{\rm{N}}} + {\mathit{\boldsymbol{Q}}_{\rm{L}}} = {\bf{0}}$ (5)
 ${\mathit{\boldsymbol{Q}}_{\rm{L}}} = 0.6\varphi {\mathit{\boldsymbol{A}}_{\rm{L}}}\sqrt {2g{\mathit{\boldsymbol{H}}_{\rm{L}}}}$ (6)
 ${\mathit{\boldsymbol{Q}}_P} = 0.278\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{D}}^{2.63}}\Delta {\mathit{\boldsymbol{E}}^{0.54}}{\mathit{\boldsymbol{L}}^{ - 0.54}}$ (7)

1.3.2 爆管

(1) 事故位置两侧均存在阀门，如图 5中的管线7，此时，只需将事故管线两侧的2个阀门关闭即可达到隔离管线的目的.

 图 5 小型管网阀门布置 Fig.5 Valve layout of a small network

(2) 事故管线存在1个阀门，如图 5中的管线3，此时除了关闭管线3的阀门之外，还需要将管线6的阀门关闭.

(3) 事故管线不存在阀门，如图 5中的管线1，此时，需要关闭临近管线上的阀门，包括管线3、4和5.

1.4 基于Langelier的管线粗糙度时变模型

Sharp和Walski[19]根据大量调查和试验研究结果，将Hazen-Williams系数C与管壁绝对粗糙度e的关系表示为

 $C = 18.0 - 37.2\lg \frac{e}{D}$ (8)
 $e = {e_0} + aT$ (9)
 $a = {10^{ - \left( {4.08 + 0.38{L_{\rm{I}}}} \right)}}$ (10)

2 参数敏感性分析

 图 6 案例管网 Fig.6 Case network
2.1 管线粗糙度

 图 7 不同年份时的节点水压 Fig.7 Nodal heads in different years
2.2 灰口铸铁管事故率年增长率系数

 图 8 不同增长率系数时的节点运行可靠度 Fig.8 Nodal operational reliability at different growth rate coefficient

2.3 渗漏面积

 图 9 不同渗漏面积时各节点运行可靠度 Fig.9 Nodal operational reliability at different leak area

3 案例分析

(1) 需求水压20 m.

(2) 不同管材事故率为

 $N(t) = \left\{ {\begin{array}{*{20}{l}} {0.087T - 0.758}&{钢管}\\ {0.242T - 1.720}&{球墨铸铁管}\\ {0.574{{\rm{e}}^{0.11T}}}&{灰口铸铁管} \end{array}} \right.$ (11)

(3) 渗漏面积服从[0.1%S, 20%S]的均匀分布.

(4) 管道粗糙度系数考虑随运行时间的变化，根据1.4节确定.

(5) 对于一个具体事故而言，渗漏发生的概率为0.9，爆管概率为0.1.

(6) 模拟次数7 000次.

 图 10 案例管网各节点运行可靠度 Fig.10 Nodal operational reliability of the case network

4 结论

(1) 建立了基于事故率的供水管网全寿命运行可靠性分析方法，包括不同管材事故率模型的确定、渗漏和爆管事故的模拟以及管道粗糙度模型的建立.通过敏感性分析对参数取值进行了讨论，其中，灰口铸铁管事故率可采用指数模型、球墨铸铁管和钢管可采用线性模型，渗漏面积可取为[0.1%S, 20%S]内服从均匀分布的随机变量.

(2) 以某市供水管网为例对分析方法进行了可行性论证，结果表明，该市供水管网运行可靠性整体处于较高水平; 但从第30年开始，各节点运行可靠性均出现显著下降，薄弱区域位于管网南部，该区域管线成环性低，长距离管线较多，一旦管线失效，所连接的用户供水将受到严重影响.根据分析结果，建议了可提高管网运行可靠性的工程措施.

(3) 后续研究可针对以下几个问题展开：①综合考虑不同管材、管径、管龄、埋深等因素对管线事故率及运行可靠性的影响; ②考虑不同拓扑结构、源点数量、需求水压等对运行可靠性的影响; ③基于运行可靠性的最优阀门布置方案; ④考虑修复的运行可靠性(韧性)研究.

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