ANALYSIS OF THE WIDTH OF PROTECTION ZONE NEAR A WATER SUPPLY NETWORK

A protection zone along water distribution network is one of the proposals to limit the negative effects of potential breakages of buried water pipes, connected with the creation of swallow holes, hollows or depressions [1, 2]. Water flowing out from a leaking pipe can wash out fine soil particles from a solid matrix and move them through soil pores causing suffosion. The phenomena of this kind are dangerous especially in urban areas with developed infrastructure. Empty spaces created incrementally under the soil surface can be hazardous for human health or property – accidents of cars falling in holes created after a water pipe failure are reported several times a year all over the world. The problem still exists because of two reasons.

The first is that water supply pipes are usually located along roads, which are used by vehicles at all times, and also where the density of infrastructure is often the highest. The second reason is connected with the fact that water pipes failures and breakages occur randomly during the whole maintenance period of every water supply system in the world [3, 4]. Plenty of methods for leakage detection, evaluating the technical conditions of operating water pipes and risk management in water distribution systems have been reported in the literature in recent years [e.g. 5–11]. Modelling and computer simulations have become common tools for the analysis of pipe failures and leakages [12–17]. Moreover, mathematical approaches, such as fuzzy sets, artificial neural networks or k-nearest neighbours algorithm have been developed lately for predicting water pipes failures or evaluating leakage potential [18–22]. These activities are very important in the aspect of water distribution quality and reliability, but they are not the only way to limit problems connected with pipes failures. Even the best high-tech systems do not protect against randomly-occurring failures. Thus, we propose to support the existing methods and activities by establishing a protection zone on the soil surface over a buried water network, where the outflow of water is possible after a potential failure of the pipe. Infrastructure and settlement in this zone should be carefully planned in order to exclude the possibility of diminishing stability of objects as well as to limit the social, economic and environmental costs in the case of leakage from a water pipe.

The presented investigations include the laboratory tests of a buried water pipe breakage for different cases of leak areas and values of hydraulic pressure head in the pipe and analysis of a distance between the place of water outflow on the soil surface and the location of the water failure, in the aspect of protection zone determination.

The first part of investigations involved physical simulations of a water pipe breakage, conducted in a laboratory on the setup reflecting the actual conditions scaled 1:10. The main part of the setup was an intentionally damaged water pipe buried in sand, supplied with water from a container located on the assumed height. The tests were conducted for four different values of leak areas (4.71, 9.42, 15.07 and 18.84 cm²) and hydraulic pressure head in a pipe varied in the range from 3.0 to 6.0 m H₂O, each 0.5 m. Detailed descriptions of the laboratory setup and realisation of the tests are given in the papers [2, 23, 24]. The statistical analysis, including the normality evaluation of measurements results obtained during physical simulations of a water pipe breakage in a laboratory, is presented in the article [25].

The subject of investigations in the range of the presented paper is a horizontal distance (y) between a leaking pipe and a location of water outflow on the soil surface (called “suffosion hole” in this paper) in the aspect of a protection zone determination. The analysis was based on tolerance intervals calculations with two assumptions. At first, it was assumed that the occurrence of water on the soil surface right above a leak is always possible and this assumption imposed the value of the lower tolerance limit as equal to 0 for all calculation cases. The second assumption – that all suffosion holes occur on one side of the leaking pipe, enabled to treat the upper tolerance limit as a half of protection zone width (Fig. 1).

Figure 1.

Upper limit (UTL) calculations were conducted for a tolerance level of 70%, 80% and 90%, and a confidence level of 95%, in Statistica 13 software (StatSoft, Inc.). Depending on the kind of data distribution (normal or non-normal – Tab. 1), a mean or a median was taken as a nominal specification, as well as the way of tolerance intervals determination was selected. The results of calculations for different cases corresponding to the test variants were analysed considering the influence of operating pressure in a pipe on a protection zone width and selection of an optimal value of tolerance level in calculations. The results of the analysis enabled to propose the width of a protection zone for the conditions of the investigations.

The results of the summarizing data set obtained during laboratory investigations are given in Table 2. The values of standard deviation indicate a high dispersion of data y, which is caused by the complexity of the problem of water leakage from a damaged pipe to the soil, as well as the wide variety of the parameters influencing the phenomenon. In the cases of leak area of 4.71 and 15.07 cm², an increasing tendency of data y is observed. Any dependence between a distance y and hydraulic pressure head H in a pipe is not visible for the remaining two cases.

The main part of investigations was to determine the upper tolerance limits UTL for data y selected according to pressure head in a pipe and leak area. The mean of all obtained values for tolerance level of 70% (UTL ₇₀), without any selection, equals 29.68 cm, i.e. the zone of the width of 2 · 29.68 cm = 59.36 cm under laboratory conditions (5.94 m under the actual conditions) will cover 70% of the water outflow points with a 95% confidence level. The mean of all obtained tolerance limits for 80% and 90% tolerance level (UTL ₈₀ and UTL ₉₀) equals 32.85 cm and 37.56 cm, respectively, and interpretation of these values is analogical to the UTL ₇₀.

The mean of data obtained for different H, as well as extreme values and a difference between them (a range) are given in Tab. 3. The lowest value – 11.85 cm – was obtained for the leak area of 15.07 cm² and tolerance level of 70%, whereas the highest (75.92 cm) for the leak area of 9.42 cm² and tolerance level of 90%. The values of range increase as a tolerance level rises and are higher than the values of mean for all but one case (leak area of 4.71 cm²). Minimal values are less diversified than the maximal ones for different leak areas, for all values of the tolerance level.

More detailed information about an upper tolerance limit for data y selected according to pressure head in a pipe and leak area is shown in Figures 2–5. Similarly to the average values (a median and a mean) of data y, values of upper tolerance limit increase as the pressure head in a pipe rises for the cases of leak area of 4.71 and 15.07 cm². For the other two cases, the correlation between the upper tolerance limit for data y and the pressure head in a pipe is not clear.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Obviously, higher tolerance level results in higher UTL. The analysis of Figures 2–5 indicates that the absolute value of the increases UTL (the difference between the values of the upper tolerance limit for 90% and 70% tolerance level – ΔUTL _90-70 and the difference between the values of the upper tolerance limit for 80% and 70% tolerance level – ΔUTL _80-70) rises for higher values of UTL. It is visible as linear trends in Fig. 6. The coefficient of determination (R ²) is the same for both lines because the proportion of the explained variance is also the same. Assuming that the most appropriable ΔUTL does not exceed 5 cm (additional 0.5 m of the zone width on each side of a water pipe under the actual conditions), the tolerance level of 90% can be taken in calculations only for the cases with UTL ₈₀ < 22.5 cm (29% of the cases in our investigation), whereas 80% tolerance level should be taken for 22.5 cm < UTL ₈₀ < 49.2 cm (57% of the cases). For UTL ₈₀ > 49.2 cm (14% of the cases), 70% tolerance level is recommended.

Figure 6.

A leak area is impossible to foresee under the actual conditions of water network maintenance before breakage occurs, whereas a range of operating pressure is always known. Thus, it seems to be sensible to examine the dependence between UTL and pressure in a pipe without selection on leak area (Fig. 7). The chart given in Fig. 7 does not indicate a clear correlation between UTL and H, however, the values for H = 3.0 m H₂O and 3.5 m H₂O are notably lower than for the H = 4.0–6.0 m H₂O. Taking into account the values of UTL according to Fig. 7 and the foregoing discussion about choosing a value of tolerance level in UTL calculation, we have proposed the width of protection zones according to Table 4. For all cases of pressure head, 80% tolerance level was taken in calculations, because of 22.5 cm < UTL ₈₀ < 49.2 cm. The proposed values are results of rounding the calculated values to integer numbers. The zone occurred wide, mainly because of the high dispersion of laboratory data, often characterizing phenomena influenced by diverse parameters. Such a wide zone is rather impractical for application, but as an initial proposition, it provides information on the possible range of water outflow on the soil surface.

Figure 7.

The protection zone width should be such adjusted to ensure the adequate security of infrastructure on the one hand, and on the other hand, not to hinder a land development. An excessively wide zone can create problems connected with the location of a water pipe or other infrastructure. The increase of UTL means a wider zone along a water pipe. Two main factors influence the value of UTL: dispersion of data y and statistical assumptions. The values of standard deviation of data y obtained during laboratory investigations occurred high for all cases in question, indicating a high dispersion of data y, and in consequence causing a high UTL range. The reason for the high dispersion is the complexity of the problem of water leak from a damaged pipe to the soil, connected with the fact that many various factors influence the phenomenon. The second of the above-mentioned factors – statistical assumptions – depends on the needed accuracy of calculations. Assumed higher tolerance and confidence levels results in higher UTL value. On the other hand, to practical purposes, the UTL value should be as low as possible. Thus, after the analysis, we recommend calculations for 90% tolerance level if UTL ₈₀ < 22.5 cm, 80% if 22.5 cm < UTL ₈₀ < 49.2 cm and 70% if UTL ₈₀ > 49.2 cm.

The proposed width of a protection zone along a water pipe is an approximation and pertains to specific laboratory conditions, so it cannot be treated as a general guideline for water network designing. However, the obtained results encourage the continuation of this research direction, drawing particular attention to the parameters influencing the phenomenon of water leaking from a damaged pipe to the soil medium.