# GIS-Based Identification of Locations in Water Distribution Networks Vulnerable to Leakage
## 3 Materials and Methods
### Parameters Used in Vulnerability Analysis of the WDN
For instance, a 50% increase in pressure in high-density polyethylene (HDPE) pipes had a 22.67% leakage rate compared to unplasticized polyvinyl chloride (uPVC) (34.23%) and galvanized steel at a 42.93% leakage rate [44]. Pipelines in Sharjah's WDN mainly consist of asbestos cement (AC), then medium-density polyethylene (MDPE), high-density polyethylene (HDPE), and glass-reinforced polymer (GRP). Pipe diameters are also not consistent in any WDN. Pipes with small diameters usually experience significantly more damage regardless of the pipe materials, due to variation in water pressure, compared to pipes with large diameters [23]. Diameter is therefore considered a crucial parameter in leakage vulnerability analysis. In the 13 studied DMAs in this project, pipe diameters vary from 1200 mm to 19 mm. Pipes with large diameters greater than 600 mm usually branch out from the transmission pipeline to supply WDN in the DMA. Medium pipe diameters between 400 mm to 100 mm are used to distribute and circulate water in the WDNs. Small pipe diameters of 63 mm and lower are usually used for customer connection and service points. To represent pipe diameter and material in this study, the Nikuradse friction factor equation was used, assuming all pipes in the WDN are rough pipes. The friction factor (_f_), as in Equation (5), was only affected by relative roughness. The analysis used the Nikuradse equation to compute the friction factor in all the pipe segments in the 13 DMAs. \[\frac{1}{\sqrt{f}}-2 log\left(\frac{d}{\varepsilon}\right)=1.14 \tag{5}\]  
where \(f\) is the friction factor (dimensionless), \(d\) is the pipe diameter (mm), _\(\varepsilon\)_ is the roughness height (mm), and _\(\varepsilon/d\)_ is the relative roughness. The analysis showed that the maximum \(f\) value for each area was around 0.016. \begin{table}
\begin{tabular}{c c c c c c} \hline
**DMA** & **Area Name** & **Length (m)** & **Fitting** & **CC** & **Fitting/L** \\ \hline
1 & Rahmaniya 1 & 22,492 & 38 & 132 & 0.008 \\
2 & Rahmaniya 3 & 23,501 & 23 & 151 & 0.007 \\
3 & Ind. Area 4 & 30,701 & 84 & 130 & 0.007 \\
4 & Barashi & 57,819 & 72 & 153 & 0.004 \\
5 & Mayasloon & 13,651 & 27 & 36 & 0.005 \\
6 & Al Faya & 16,800 & 9 & 30 & 0.002 \\
7 & Al Gutwair & 11,002 & 56 & 44 & 0.009 \\
8 & Butina & 17,585 & 86 & 45 & 0.007 \\
9 & Al Sabkha & 33,467 & 20 & 42 & 0.002 \\
10 & Al Ghafia & 35,667 & 46 & 42 & 0.002 \\
11 & Al Nasserya & 17,786 & 29 & 71 & 0.006 \\
12 & Al Qadisiya & 25,041 & 41 & 29 & 0.003 \\
13 & Ind. Area 6 & 29,720 & 84 & 120 & 0.007 \\ \hline \end{tabular}
\end{table} 
Table 4: Number of fittings. The weights in Table 5 were assigned to each of the six parameters (or leakage conditioning factors) based on their contribution to leakage using the Analytic Hierarchy Process (AHP) [45]. This method has proven to be successful in determining the weights of the conditioning factors of many processes that are known to have some risk, such as landslides, earthquakes, flooding, and coastal inundation [46; 47; 48; 49]. The AHP method was chosen because it has many advantages, including its simplicity, consideration of objective or subjective, or either quantitative or qualitative information in the decision process, and it can be used with any level of detail when representing the problem at hand. The logistic regression model, which combines the six parameters, can be represented as shown in Equation (6) below. \[Z=\text{a}_{1}\text{Q}+\text{a}_{2}\text{P}+\text{a}_{3}\text{Chl}+\text{a}_{4 }\text{FL}+\text{a}_{5}\text{ LJ}+\text{a}_{6}\text{f} \tag{6}\]  
where \(Z\) is the dependent variable based on the independent parameters in Table 5, and \(\text{a}_{1}\), \(\text{a}_{2}\),..., \(\text{a}_{n}\) are the model coefficients depending on the weight values for the corresponding parameters. Then, the logistic regression function, which helps to determine the probability of the occurrence of \(Z\) with values ranging from 0 to 1, can be written as follows [50]:  
\[f(Z)=\frac{1}{1+e^{-Z}} \tag{7}\]