This paper describes an experimental and analytical study that examined the effects of soil on leakage rate from defective water pipes. An experimental model was designed and constructed to simulate idealized cracks in defective water pipes discharging into a bed of granular materials. Tests were run on three different materials: LBS-B, LBS-A, and glass ballotini with different characteristics. The results reveal that the presence of bedding material surrounding a leaking pipe causes a significant change in the leakage rate versus free flow conditions. The bedding has a greater impact on larger defect openings. There was a significant drop in the values of the coefficient of discharge (Cd) when the pipe discharged into a soil bed versus free flow conditions; this value was 38% lower for coarse particles and 70% for finer particles. The results also showed that high leakage rates could flow from the defective pipe without fluidization of the bedding materials. An analytical model based on the method of fragments was presented to predict the leakage rate after which the predicted results were compared with values measured experimentally.
An analytical model has been presented to predict the leakage rate, in the presence of soil, that provides reasonable estimates of the leakage rate.
Soil with different characteristics (permeability, particle size, particle shape, and bed height) was tested.
Influence of the surrounding soil on the hydraulic behaviour of leakage was examined.
Leaks in water distribution systems (WDSs) are serious issues that occur on a global scale. A significant volume of water is lost annually from WDSs. This loss amounts to some 126 billion m3 per annum (expressed as non-revenue water) (Liemberger & Wyatt 2019). In some countries, this loss accounts for 40% to 50% of the water supplied compared to an estimated global average of 30% for most systems (Global Water Market 2017). Concurrently, water demand is rising due to population growth, while resources are diminishing (Adedeji et al. 2018). Consequently, understanding the mechanism of leakage and the factors controlling it can play a crucial role in minimizing water scarcity.
Here, q is the flow rate (m3/s), is the discharge coefficient, is the orifice area (m2), g is the acceleration due to gravity (m/s2), and h is the pipe head (m).
Experimental and field research has demonstrated that the leakage exponent may be much more than the 0.5 of the orifice flow equation and typically fluctuates between 0.35 and 2.95 (Farley & Trow 2003; Greyvenstein & van Zyl 2007), thus demonstrating that leaks in WDSs are more pressure sensitive than expected based on the orifice flow equation. The work of van Zyl & Clayton (2007) proposed a number of potential contributing factors to explain the range of leakage exponents found in the literature including pipe material behaviour, leak hydraulics, soil hydraulics, and water demand, but these are not yet fully understood. Changes in the geometry of the unconfined flow regime, piping, and hydraulic fracture have complicated the interactions between leaky pipes and the surrounding soil.
Several studies have attempted to assess the effect of the pipes' surrounding media on leakage rates (Walski et al. 2006; De Paola et al. 2014). Walski et al. (2006) studied orifice/soil interactions in pipe leaking utilizing narrow long tube equipment assuming one-dimensional flow. They studied the two components of head loss that were due to flow through an orifice (ho) and Darcy flow in soil (hs). They then developed a dimensionless ‘orifice/soil’ (OS) number to quantify their significance. Walski et al. (2006) found that ‘in most real-world scenarios, the OS number is large,’ suggesting that orifice head loss is dominant. De Paola et al. (2014) also reached a similar conclusion based on an experimental study in which it was acceptable to neglect the effects of the surrounding soil on the leakage rate. However, other studies indicate that seepage heads may dominate. For example, Burnell & Race (2000) found that leakage from their supply pipes correlated linearly with pipe internal pressure, thus indicating that soil head loss controlled leakage in that instance.
Noack & Ulanicki (2008) quantitatively investigated the influence of soil on leakage characteristics. Their major focus was on soil permeability, and they used 100 different types of soils with hydraulic permeabilities ranging from to m/s. Their findings reveal that the leaking characteristic for high permeability soil (such as sandy soil) is similar to that for discharge to air – namely a square root rule. For low-permeability soil, the exponent rises while the leakage discharge drops. Ćipranić & Sekulić (2015) concluded that the impact of water percolating through the soil cannot be ignored in low-permeability soils.
Fox et al. (2016) investigated the impact of an idealized porous medium on the leaking behaviour of longitudinal slits in viscoelastic tubing. Their results show that the existence of an idealized porous media around the pipe causes a significant increase in the pressure while leading to a reduction in the leakage flow rate versus a free discharge leak. They further highlight the limitations of current dynamic leakage modelling, which simplifies or ignores the impact of soil conditions.
Latifi et al. (2018) also investigated the impact of the soil surrounding the pipe on leakage flow from a 1 mm orifice diameter. They considered different soil types and found that the leakage varied as a function of soil parameters. However, they found no relevant correlation between leakage and certain parameters. They concluded that hydraulic permeability is an important variable in determining the leakage rate.
The soil surrounding the leaking water pipes might be removed as a result of the outlet jet of the leaks, thus resulting in fluidization of the soil bedding (van Zyl et al. 2013; He et al. 2017; Pike et al. 2018; Ghorbany et al. 2022; Latifi et al. 2022). van Zyl et al. (2013) investigated soil fluidization surrounding leaky water pipes and found that the head loss from a leaking pipe is composed of three components: (1) via the orifice, (2) in the fluidized zone, and (3) through static soil. They found that most of the head loss occurs within the fluidized zone. Significant (but lower) head loss occurs through the orifice, but only a small percentage of the loss occurs in the static soil. In another experimental study, Latifi et al. (2022) investigated the factors that influence the fluidized and mobile bed zone geometric parameters. They reported that water pressure and soil properties, mainly particle size, have the largest influence on the height, width, and cross-sectional area of the zones.
Ledwith et al. (1990) studied pipe pressures using two-dimensional (2D) fluidization experimental equipment. They studied the flow rate necessary for initial and complete fluidization. The experiments were conducted on sand at different depths. The results showed that although the bed of soil was only 42 cm high, it could withstand a pressure head of 33 m of water before becoming completely fluidized.
This prior work had significant value in understanding and controlling WDSs leakages. However, the effects of surrounding soil on the leakage mechanism remain unclear and require further study. The interaction of soil particles with the orifice is expected to alter the downstream jet behaviour and might obstruct a portion of the orifice itself.
Other models utilized for predicting water flow through porous media include the Kozeny–Carman and Poiseuille models. The Kozeny–Carman equation is commonly employed to estimate permeability (k) but necessitates additional input parameters such as porosity, tortuosity, and specific surface area (Kozeny 1927; Carman 1937). On the other hand, the Poiseuille equation is typically used as a starting point for developing predictive equations (Yong et al. 2012). It is often combined with the assumption of the validity of Darcy's law, and subsequently, relationships are derived (Taylor et al. 1990). Darcy's law serves as the foundation for the majority of models used to predict water flow through porous media (Lambe & Whitman 1979; Olson & Daniel 1981) and has been adopted by numerous researchers, including Harr (1962) and Madanayaka & Sivakugan (2016), in the analytical solutions of confined seepage flow when employing the method of fragments (see later, section 3.2).
This study illustrates the results of a series of experiments to investigate the impact of bedding materials surrounding leakage pipes on leakage behaviour. The experiments were conducted in a modified seepage tank with leakage flow from a model of a defective water pipe into a bed of granular sand. Three different sands with different characteristics were considered: sand-fraction B (LBS-B), sand-fraction A (LBS-A), and glass ballotini (GB). The leakage rate, applied pressure in the pipe, and pore-water pressure head downstream of the defect were measured. Our study also presents an analytical model based on the method of fragments to predict the leakage rate in the presence of soil. The predicted results were then compared with those measured experimentally.
MATERIALS AND METHODS
Specially constructed boxes measuring 100 × 100 × 132 mm and having narrow (typically fractions of a mm) defect openings spanning the full width of the boxes simulated fractured water distribution pipes. The engineered leak openings were manufactured using laser cutting machines with high-dimension precision. They were constructed of two square-edged stainless-steel plates 10 mm thick and butted above the machined boxes and then welded to the required aperture. The defect sizes were adjusted using flat feeler gags measuring between 0.33 and 0.92 mm. The form of the defects remained unchanged with square-edged orifices 10 mm thick and 132 mm long.
Measurements of flow and pressure upstream of the defect
The flow rate through the defect was measured initially using the volume-time method by intercepting the outflow and collecting it in a graduated cylinder to a given volume and timing the procedure. This was repeated three times for each flow rate, and an average value was obtained. Later, a flow meter (model Signet 2551) with a display unit was used to record the leakage rate. The meter has a feature for averaging the flow rate (i.e., setting a time over which the meter averages the flow signals). This feature was set to 25 s during each test run to smooth the display on the liquid crystal display (LCD). The flow meter's specifications achieve ±2% accuracy. Pressure measurements upstream of the engineered leak opening was obtained using a pressure indicator (Model-DPI 261) with a head range up to 351 m (3,441 kPa) and an accuracy of 0.04%.
Measurements of pore pressure head
The pore-water pressure head in the bedding material was measured using a sight tube. A 3-mm diameter hole was drilled through the rear wall of the tank and connected to the sight tube. This hole was constructed along the centreline of the defect at a height 10 mm above the defect. A needle with a 2 mm diameter was inserted into this hole. This needle was long enough to provide a good connection point for the sight tube and the inside of the tank. Prior to preparing the test sample in the tank, the needle was covered with a screen to prevent grains from entering the pressure tap, thus preventing the needles from being obstructed. This might have affected the measured pressure head in the bed. Pore-water pressure head readings were taken directly from a vertically positioned water manometer with a water column precision of 1 mm.
Materials tested and specimen preparation
All tests were performed using saturated materials. Soil specimens were made by pouring a known amount of sand from a funnel with a 14 mm diameter nozzle into the tank. The height for pouring was maintained in a fixed position at about 15 mm above the tank's water level. Raining the soil into water minimized the air between the grains, which might have occluded voids and decreased permeability, thus affecting the measured head. Following deposition, specimens were densified by tapping the tank's base in a symmetrical manner with a rammer. Table 1 lists the properties of the test specimens. The permeability coefficient of the tested materials is between 0.24 and 0.87 cm/s.
|Material .||Dry density (mg/m3) .||Specific gravity .||Void ratio .||Permeability (cm/s) .|
|Sand-fraction B (LBS-B)||1.73||2.65||0.53||0.24|
|Sand-fraction A (LBS-A)||1.70||2.66||0.56||0.87|
|Material .||Dry density (mg/m3) .||Specific gravity .||Void ratio .||Permeability (cm/s) .|
|Sand-fraction B (LBS-B)||1.73||2.65||0.53||0.24|
|Sand-fraction A (LBS-A)||1.70||2.66||0.56||0.87|
This research did not consider the impact of clay around the pipes. Clay is normally avoided as a bedding material because moisture changes can cause a significant volume increase or decrease. However, it is expected that materials with very low permeability, i.e., clay, will be resistant to fluidization, instead undergo hydraulic fracture.
Tests were performed at controlled pressures upstream of the defect. Some tests used controlled flow rates while monitoring the behaviour of the particulate bed. Water was allowed to flow vertically through the defect into the bed of particles. Initially, a small pressure was applied (such as 2 kPa) after which the leakage rate then increased incrementally. For each increment in pressure (thus indicating leakage rate), the pore pressure head in the particulate bed was recorded after being allowed to stabilize for some time (3 min). Pore-water pressure heads in the bed were obtained using the sight tube, whereas pressure upstream of the defect was read from the pressure indicator. The flow rate (i.e., leakage rate) was read from the flow meter. The same procedure was repeated with each increment in pressure and leakage rate. At least three tests were conducted under similar conditions to validate the test results for repeatability and reproducibility.
RESULTS AND DISCUSSION
Effects of bedding materials
The presence of bedding material surrounding a leaking pipe caused a significant change in the leakage rate versus free flow conditions. This material had a greater impact on larger defect widths.
Figure 4(a) shows that, in the case of discharge into the soil acting as a bedding material, the bedding materials significantly changed the leakage rate versus free flow conditions (without soil). A significant drop in the leakage rate occurred when discharges flowed into a bed of sand. This drop became larger for finer sand particles. Particle size and therefore permeability can be expected to have a large impact on leakage rate. For example, an applied pressure in the pipe of 15 kPa produced a leakage rate of about 1,200 L/h through a defect width of 0.62 mm under free flow conditions. When discharged into a bed of coarse particles (1.6 mm) LBS-A, this same applied pressure produced 540 L/h. The same conditions produced a leakage rate of about 300 L/h in a similar bed height containing finer particles of LBS-B (0.9 mm).
The effect of soil on leakage rate is more pronounced for larger defect widths. Figure 4(b) shows the pressure–leakage relationship for two different defect widths (0.33 and 0.92 mm) discharging into the same bed of materials (a 300-mm bed height of LBS-B). In comparison to the free flow condition (Figure 4(b)), we see that the soil impact on the leakage rate is greater for the larger defect size of 0.92 mm.
The change in discharge coefficient is simply a reflection of the energy lost by the fluid as it flows through the orifice. This coefficient can be affected by a number of factors such as pipe material, orifice shape and size, and the head upstream of the orifice. Brater et al. (1996) reported that the values for the discharge coefficients of short tubes – namely orifices with a large ratio of length (pipe thickness) to orifice size, which was the case in this study, were found to vary from approximately 0.72 to 0.83.
The presence of bedding material surrounding a leaking pipe produced significant changes in the coefficient of discharge and added dependence on the defect and particle sizes; thus, the permeability of the bedding material.
Leakage rate estimates using the method of fragments
Here, q is the flow (leakage) rate (m3/s), h is the head loss over the flow domain (m), k is the soil permeability (m/s), and Φ is dimensionless form factor; Φ is defined as the number of equipotential drops in ith fragment to number of flow channels . The head loss through the fragment is assumed to change linearly. Harr (1962) presented six types of fragments for confined flow systems. Fragment types I and IV are considered in the current study because they are relevant to the leakage model presented here. Harr (1962) provides details for fragments Types II, III, V, and VI.
This elemental section can be used to derive the form factor for fragment type IV, which represents the leakage model considered here.
Here, q is the leakage rate (m3/s), h is the head loss over the flow domain (m), K is the soil permeability (m/s), b is bed height (m), and a is the defect width (m).
Substituting the values of the experimental model (bed height b = 0.3 m and defect width a = 0.33 mm (0.00033 m)), in Equation (12), we find that the approximate solution gives a form factor Φ = 6.813. The leakage rate can be predicted using Equation (13) for a given soil permeability k, head loss over the flow domain, h, bed height b, and defect width a.
Fluidization of bedding materials
Bedding materials fluidization occurs when particles in the bed become free to move with the pore fluid (i.e., the particles become separated and in motion with the pore fluid) (van Zyl et al. 2013). The onset of this phenomenon can be predicted by examining the pressure–leakage relationship. Therefore, tests were performed at controlled pressures and in some tests at controlled flow rates while monitoring the behaviour of the particulate bed for fluidization. Other controlling parameters affecting fluidization and leakage rate were also considered in the study, such as particle size, particle shape, bed depth, and defect size (see Sections 3.4 and 3.5).
Figure 9(b) presents the data for a 300-mm bed of GB and a 0.62-mm defect width. The initial phase up to the leakage rate of approximately 600 L/h shows a linear relationship between the applied pressure and leakage rate. Fluidization was observed above this flow rate, and there was a significant increase in leakage rate associated with a slight drop in the applied pressure. However, in this instance, the flow remained below those of the orifice flow. Beyond a certain point of flow, namely 1,400 L/h, the leakage did not continue to increase as the pressure increased because of cavitation in the orifice.
Figure 9(c) shows similar data but for a 300-mm bed of coarse material (LBS-A) and a 0.62-mm defect size. The material did not fluidize even though there was a high leakage rate (1,400 L/h) during the test. The data also show a linear correlation between the applied pressure and leakage rate up to a rate of about 1,300 L/h (until cavitation) as is clear from the free flow conditions. Similar to the data in Figure 9(b), the flow remained below those for the orifice flow. In this test, the effect of soil was more pronounced on leakage than the orifice alone at all stages.
Effects of particle size and shape
Particle shape also has a substantial impact on leakage rate, and the pore-water pressure head downstream of the defect that initiates fluidization. In our experiments, the pore-water pressure head for the LBS-B (0.9 mm), which is sand-subrounded and slightly elongated and flattened – compared with those of GB with the same particle size; it had high sphericity. Fluidization of LBS-B was initiated at a leakage rate of about 632 L/h, whereas a leakage rate of about 1,500 L/h was required to fluidize a similar bed of GB. Higher spherical material fluidized at higher pressure and flow rates.
Effects of bed depth and defect size
The measured pressure upstream of the defect at which fluidization occurred varied with the defect size (Figure 12). A smaller defect width indicated a larger pressure upstream of the defect to fluidize the bed of granular materials. For example, an applied pressure of about 31 kPa was required to fluidize a 300 mm bed of LBS-B for the 0.33-mm orifice opening. The large defect width (0.92 mm) only required 16 kPa to fluidize the same bed of granular materials. This difference might be because the small defect widths required high upstream pressure to generate a sufficient leakage rate to fluidize the granular bed.
This study investigated the influence of soil bedding on the hydraulic behaviour of leakage from failed water pipes. Using a special experimental model, a series of experiments were performed on three different soils: (1) LBS-B, (2) LBS-A, and (3) GB with different characteristics. The impact of various parameters on leakage behaviour was considered: particle size, particle shape, bed height, defect width, and fluidization of the soil bedding. The experiments were performed at controlled pressures upstream of the defect. Some tests used controlled flow rates while monitoring the behaviour of the soil bed.
Based on this study, several conclusions can be drawn:
The presence of bedding material surrounding a leaking pipe causes a significant change in the leakage rate versus free flow conditions. This material has a greater impact on larger defect sizes.
A significant drop in the values of was observed when discharged into a soil bed versus free flow condition with a reduction in the value of by about 38% for the coarse particles and by 70% in the case of finer particles.
High leakage rates can flow from defective pipes without fluidization of the soil bed. This implies that leaks can occur in WDSs without breaking the soil surface. This makes it more difficult to detect leaks in these systems.
The characteristics of soil bedding including particle size, particle shape, bed height, and defect width have a significant impact on the leakage rate and fluidization of the bedding materials. Coarser soil particles, high spherical materials, and a higher bed height fluidized at higher leakage rates and pressure.
In the case of fluidization of the bedding materials, the pressure–leakage relationship obeys the orifice flow equation. However, a discrepancy from the orifice flow equation can occur at high applied pressure and leakage rates as a result of cavitation in the orifice.
An analytical model based on the method of fragments predicts the leakage rate in the presence of the surrounding soil. Here, the flow region is divided into a number of fragments with a defined dimensionless form factor. The leakage rate can be predicted for a given soil permeability k, head loss over the flow domain h, bed height b, and defect width a. Comparisons of the results show a good fit between predicted and measured values. The method of fragments provides sensible estimates of the leakage rate and is relatively fast.
The following points are suggested to reduce leakage rates from underground water pipes:
Applying pressure management techniques (e.g., using pressure-reducing valves (PRV)) to control the water pressure inside the pipeline is recommended.
Considering a backfill soil specification with finer particles instead of coarser particles.
Increasing the depth of embedment of water pipes to increase the soil resistance to fluidization and thus reduce the leakage rate. However, shallow depths may be preferred to allow quick flow of water to the surface so that leaks can be found and repaired quickly.
The author would like to thank Umm Al-Qura University, Saudi Arabia, for the support provided during the present work.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.