Impact of Different Water Supply Modes on the Hydraulic Reliability of Large-Scale Irrigation Pipeline Network

Abstract

This study investigates the impact of various water supply modes on the hydraulic reliability of large-scale irrigation networks. An EPANET hydraulic model was developed to simulate the performance of the irrigation network under three supply modes: segmented, uniform, and random water supply. Three key indicators were selected to evaluate the hydraulic reliability of the pipeline network under each mode: Water Supply Uniformity C_u, Pressure Reliability H_k, and Velocity Reliability $\left|v\right|$. These parameters were standardized using the min-max normalization method, and the resulting reliability scores were scaled to a unified range of 0–5, where higher values indicate greater system reliability. The results demonstrate that the EPANET model effectively simulates the hydraulic performance of large-scale irrigation networks. Specifically, under the segmented water supply mode, the reliability values for water supply uniformity, node pressure head, and flow velocity are 4.04, 0.84, and 0.64, respectively. Under this mode, significant flow deviations and pressure head fluctuations occur between the branches, with flow velocities typically exceeding the optimal range. Furthermore, the node pressure head at the branch inlets fails to meet the required minimum pressure head (H_min), indicating potential operational inefficiencies. In the uniform water supply mode, the highest reliability values are observed for water supply uniformity (4.76) and flow rate (4.49), with node pressure head reliability (0.94) slightly surpassing that of the segmented mode. Pressure head fluctuations and flow deviations are significantly reduced, with flow velocities generally aligning with the economic flow rates of the pipeline. However, despite these improvements, many nodes still fail to meet the required minimum pressure head, indicating limitations in meeting demand under peak conditions. In the random water supply mode, node pressure head reliability reaches its highest value (1.54), while water supply uniformity and flow rate reliabilities are 3.99 and 2.50, respectively. Flow deviations and pressure head fluctuations are comparable to those observed in the uniform supply mode. Notably, a higher proportion of nodes meet the minimum pressure head requirement compared to the uniform mode. Overall, the hydraulic reliability of the pipeline network is highest under the uniform water supply mode (2.83), followed by the random water supply mode (2.49), with the segmented water supply mode exhibiting the lowest hydraulic reliability (1.79). These findings provide valuable insights for the selection of optimal water supply modes and the assessment of hydraulic reliability in large-scale irrigation systems.

1. Introduction

The water supply and distribution network plays a pivotal role in urban water management, agricultural irrigation, and various other sectors. In recent years, the development of irrigation pipelines has substantially enhanced water distribution efficiency and facilitated more precise water metering in irrigation areas [1,2], thereby contributing to the establishment of large-scale pipeline networks [3]. In Xinjiang, China, inland irrigation areas have capitalized on terrain elevation differences to implement self-pressurized irrigation systems, constructing multiple large-scale automated self-pressurized pipeline networks for water transmission and distribution. These networks offer a range of advantages, including improved water use efficiency, conservation of water resources, reduced energy consumption, and simplified operational management [4].

The reliability of the water transmission and distribution pipeline network is essential for ensuring the network’s integrity and maintaining a consistent water supply [5,6]. In addition, the hydraulic reliability of irrigation networks differs from that of urban water networks. It is influenced by topographic elevation, crop water demand patterns, supply flow rates during the irrigation season, and the alternating cycle of pipe filling and draining during non-irrigation periods [7].

Current research methods for evaluating pipeline network reliability include analytical methods, simulation approaches, and proxy index techniques [8,9]. Wang et al. [10,11] developed a reliability evaluation system for mine water supply pipeline networks using the Analytic Hierarchy Process (AHP), while Wang et al. [12] applied the AHP-fuzzy comprehensive evaluation method to assess the drainage pipeline network in Huai’an City. Shi et al. [13] evaluated the hydraulic reliability of urban water supply networks using indicators such as the ratio of node pressure head to minimum pressure head, the ratio of node flow to total flow, and flow velocity. Liu et al. [14] identified key hydraulic performance indicators for urban water supply networks, including node pressure head, node pressure head qualification rate, pressure head uniformity, and pipe section flow velocity. Zhang et al. [15] proposed five indicators to evaluate the hydraulic reliability of urban water supply networks: water supply guarantee rate, node water pressure head ratio, water pressure head distribution uniformity, node water volume reliability, and remaining water supply capacity. Yan et al. [16] suggested that the hydraulic reliability of urban drainage networks can be assessed using indicators such as pipeline water depth, pipeline flow velocity, pipeline filling degree, and pipeline bearing capacity. Shi [17] emphasized that key hydraulic reliability indicators for urban water supply networks include flow rate, node hydraulic availability, and the number of pipe sections. These evaluation indicators are primarily derived from the reliability assessment of urban water supply systems, which are typically large-scale, structurally complex, and operate under high water supply pressure head [18]. Such systems generally provide 24-h uninterrupted water supply, often include regulatory structures, and require high operational and maintenance standards, with evaluation metrics that are easily quantifiable [19].

The reliability assessment standards for irrigation networks differ from those established for urban water supply systems. Research on the hydraulic reliability of irrigation networks remains limited. With the advancement of large-scale agriculture, these irrigation systems are expanding in size and increasing in complexity, incorporating various water supply modes such as segmented, uniform pressure head reduction, and random water supply [20,21]. However, a comprehensive methodology for evaluating the reliability of large-scale irrigation pipeline networks has yet to be established.

Field research on large-scale irrigation pipelines presents significant challenges. However, hydraulic models provide an effective tool for simulating network performance under different operational scenarios [22,23]. EPANET, an open-source software tool, supports pipeline network design, operational simulation, information management, and other tasks for pressurized pipelines [24]. Liu et al. [25] applied EPANET to perform hydraulic analysis of urban water supply networks, Wang et al. [26] used EPANET to simulate the operational conditions of sprinkler irrigation systems, and Ma et al. [27] employed EPANET to develop a main-pipe network model for micro-irrigation systems under random water use conditions.

To simulate the hydraulic performance of large-scale irrigation pipelines under various water supply modes and evaluate their hydraulic reliability, a study was conducted on a large-scale self-pressurized micro-irrigation system in Xinjiang. Using EPANET, a hydraulic simulation model for the irrigation pipeline network was developed, and an evaluation index system for the network’s hydraulic reliability was established. The hydraulic reliability of the irrigation pipeline network under different water supply modes was analyzed, with the objective of providing valuable insights to ensure the safe and efficient operation of large-scale irrigation pipelines.

2. Materials and Methods

2.1. Overview of the Research Area

The study area is located in a city in Xinjiang, China, covering a controlled irrigation area of 12,600 hm². This project features a self-pressurized micro-irrigation system supplied by a single water source. The terrain exhibits a higher elevation in the south and west, gradually descending towards the north and east, with a maximum elevation difference of 70 m. The soil type is sandy loam, predominantly used for the cultivation of cotton, corn, and red dates. The trunk pipeline of the irrigation network is constructed from PPCP (Polypropylene Composite) pipes, with a diameter of 2400 mm and a length of 207 m. The system comprises three main pipelines made from sand-filled fiberglass, with diameters ranging from 600 mm to 1800 mm. These pipelines are oriented in a north-south direction, with a total length of 53,610 m. The sub-main pipelines, with diameters ranging from 300 mm to 600 mm, are arranged perpendicular to the main pipelines. The sub-main pipeline on the west side of the main pipelines is 750 m in length and equipped with 2 branch valves, while the sub-main pipeline on the east side extends 1750 m and includes 4 branch valves. Each branch pipe is equipped with a branch valve at its head, with the flow rate controlled by the branch valve. A total of 144 branch valves are installed, and the water supply mode is controlled through the branch valve numbers. The branch pipelines are arranged perpendicular to the sub-main pipelines, oriented in a north-south direction. The ‘a’ and ‘b’ sub-main pipelines, located at the southern end of the system, provide unidirectional water supply to the north, with each branch pipe serving an irrigation area of 25 hm². The ‘c’ and ‘d’ sub-main pipelines supply water bidirectionally to both the north and south, with each branch pipe managing an irrigation area of 75 hm². The remaining sub-main pipelines also provide bidirectional water supply, with each branch pipe controlling an irrigation area of 100 hm². Main Pipe I is equipped with 16 sub-main pipelines and 48 branch valves, covering an irrigation area of 4200 hm². Main Pipe II has 18 sub-main pipelines and 54 branch valves, irrigating 4800 hm². Main Pipe III consists of 15 sub-main pipelines and 42 branch valves, serving an irrigation area of 3600 hm². The pipeline layout is illustrated in Figure 1.

2.2. Water Supply Mode

The urban water supply network includes both intermittent and continuous supply, while agricultural water supply encompasses rotation irrigation, supplementary irrigation, and random supply. By combining urban and agricultural water supply systems, three irrigation water supply modes for agricultural pipeline networks are proposed [28].

• Segmented water supply

In this mode, the pipeline network is divided into multiple independent sub-regions, each supplied with centralized water from separate pump stations or water sources. This mode is suitable for areas with significant elevation differences that require zoned water distribution. Each group is supplied with centralized water at designated time intervals. During the irrigation season, the entire pipeline network is operated with continuous water supply through the main pipelines, while water supply to the sub-main pipelines and branch pipes alternates, with control managed by the branch valves. The corresponding flow calculation formula for the branch valves is as follows:

$$Q_i={\displaystyle \frac{10mA}{3600\eta Tt}},$$

(1)

where Q_i is the design flow rate of the i-th branch pipe, m³/s; m is the irrigation quota, mm; A is the irrigation area of the i-th branch pipe, ha; T is the irrigation cycle, d; t is the daily working time, h; η is the irrigation water utilization coefficient.

• Uniform water supply.

During peak water usage periods, when the originally designed segmented water supply system fails to meet production demands, a uniform water supply mode is implemented to address issues such as water and time competition. In this mode, the water distribution is evenly allocated to each node based on demand through a balanced network design. This mode is suitable for areas with stable demand distribution and flat terrain. The design flow rate of the branch valve in the uniform water supply mode is still calculated according to Formula (1).

• Random water supply.

In the random water supply mode, water distribution is adjusted in real-time or on an unplanned basis, lacking systematic planning. This mode is suitable for emergency situations or scenarios with significant demand fluctuations (e.g., disaster relief). In the irrigation network, the opening and closing of each outlet in the pipeline system are independent of the operational status of other outlets and are not constrained by time or location. The design flow rate Q at each branch pipe is calculated using the First Clément formula [29,30].

$$Q=p_i{\sum }_{k=1}^n{Q}_i+U\sqrt{p_i\left(1-p_i\right)}\sqrt{{\sum }_{k=1}^n{\left(Q_i\right)}^2},$$

(2)

where Q_i is the water flow rate of the i-th branch valve; N is the number of nodes downstream of the pipeline; and U is the percentile related to the normal distribution function. When the number of nodes n > 100, the guarantee rate of irrigation water during peak periods is 90%, and U is taken as 1.282; p_i is the probability of opening the i-th water intake.

2.3. Evaluation Indicators

2.3.1. Indicator Construction

Based on the current technical specifications for pipeline water delivery engineering “GB/T 20203-2017”, water-saving irrigation engineering standards “GB/T 50536-2018”, irrigation and drainage engineering design standards “GB50288-2018”, and micro-irrigation engineering standards “GB/T 50485-2020”, the four standards identify Water Supply Uniformity C_u as a key indicator, with C_u serving as the primary metric. Both the first and fourth standards specify the minimum pressure for emitters, and in conjunction with urban pressure reliability, this has been utilized to define the pressure reliability for the irrigation pipeline network. Additionally, in pipeline system design, the concept of economic flow velocity is introduced, with flow velocity deviation employed as an indicator. These core indicators were then used to develop a hydraulic reliability evaluation index system for irrigation pipeline networks.

• Uniformity of water supply.

This indicator assesses the uniformity of outflow at each node within a specific research area. A higher value indicates greater uniformity in water supply across the pipeline network. The calculation is performed using the following formula:

$$C_u=1-{\displaystyle \frac{\sum _{i=1}^n\left|q_i-\overline{q}\right|}{n\overline{q}}},$$

(3)

where C_u represents the water supply uniformity, $\overline{q}$ denotes the average flow rate of the branch valve, and segmented calculations are applied when the lengths (or control areas) of branch pipes differ. In this case, the calculation is performed for sections of equal length (or control area); Q_i represents the water flow rate of the i-th branch valve.

• Pressure head reliability.

The ratio of the actual pressure head at each node in the pipeline network to the minimum required pressure head is calculated using the following formula:

$$H_k={\displaystyle \frac{H_i}{H_{\mathrm{m}\mathrm{i}\mathrm{n}}}},$$

(4)

where H_k represents the pressure head reliability and H_min [31] denotes the minimum node head that the pipeline network must maintain. Referring to the minimum pressure head requirements for urban water supply pipelines, H_min is calculated as the sum of the design working pressure head of the emitters, the maximum head difference in the community (Δh), and the safety factor. Specifically, the design working pressure head of the emitters is 10 m, Δh is 7.5 m, and the safety factor is set to 5 m, in accordance with the Irrigation and Drainage Engineering Design Standards “GB50288-2018”.

• Flow velocity deviation.

This indicator evaluates whether the flow velocity in each section of the pipeline network falls within the appropriate range. The calculation is performed using the following formula:

$$\left|v\right|={\displaystyle \frac{\left|v-v_i\right|}{v_i}},$$

(5)

where $\left|v\right|$ represents the flow velocity deviation, v denotes the flow velocity of the i-th branch pipe, and v_i is the economic flow velocity of the i-th branch pipe.

2.3.2. Indicator Grading

Each indicator is categorized into five levels based on its impact on the water supply performance of the pipeline network. Scores are assigned to each level, with a maximum score of 5. A higher score indicates better water supply performance of the pipeline network. The scoring criteria for different indicators are presented in

Table 1. Indicator Rating.

Grade	Score	${\mathit{C}}_{\mathit{u}}$	${\mathit{H}}_{\mathit{k}}$	$\left|\mathit{v}\right|$
1	4–5	[0.95,1.0]	[1.3,1.4]	[0,0.05)
2	3–4	[0.90,0.95)	[1.2,1.3)	[0.05,0.15)
3	2–3	[0.85~0.90)	[1.1,1.2)	[0.15,0.25)
4	1–2	[0.80~0.85)	[1.0,1.1)	[0.25,0.35)
5	0–1	[0~0.80)	<1.0,>1.4	[0.35,1]

.

The hydraulic reliability index values of the pipeline network are subjected to dimensionless processing using Equations (6) and (7).

For indicators where larger values indicate better performance, the dimensionless processing is conducted as follows:

$$r(i,j)={\displaystyle \frac{C(i,j)}{C_{\mathrm{m}\mathrm{a}\mathrm{x}}\left(i\right)+C_{\mathrm{m}\mathrm{i}\mathrm{n}}\left(i\right)}},$$

(6)

For indicators where smaller values indicate better performance, the processing is conducted as follows:

$$r(i,j)={\displaystyle \frac{C_{\mathrm{m}\mathrm{a}\mathrm{x}}\left(i\right)+C_{\mathrm{m}\mathrm{i}\mathrm{n}}\left(i\right)-C(i,j)}{C_{\mathrm{m}\mathrm{a}\mathrm{x}}\left(i\right)+C_{\mathrm{m}\mathrm{i}\mathrm{n}}\left(i\right)}},$$

(7)

where C_max(i) and C_min(i) represent the maximum and minimum values of the i-th indicator, respectively, and r(i, j) is the standardized evaluation index value for the i-th indicator and j-th value. The normalized indicators are presented in

Table 2. Normalized indicator.

Grade	Score	${\mathit{C}}_{\mathit{u}}$	${\mathit{H}}_{\mathit{k}}$	$\left|\mathit{v}\right|$
1	4–5	[0.95,1]	[0.54,0.58]	(0.95,1]
2	3–4	[0.90,0.95)	[0.5,0.54)	(0.85,0.95]
3	2–3	[0.85~0.90)	[0.46,0.5)	(0.75,0.85]
4	1–2	[0.80~0.85)	[0.42,0.46)	(0.65,0.75]
5	0–1	[0~0.80)	<0.42,>0.58	[0,0.65]

.

2.3.3. Calculation of Indicator Weights

The relative importance of the three indicators, C_u, H_k, and $\left|v\right|$, was determined using the Analytic Hierarchy Process (AHP) [32,33]. A judgment matrix, denoted as R_c, was constructed as follows:

$$R_c=\left|\begin{array}{ccc}1& 0.5& 2\\ 2& 1& 2\\ 0.5& 0.5& 1\end{array}\right|,$$

(8)

The weights of each indicator were calculated using the root mean square method. A higher weight indicates a greater degree of influence. The calculated results are presented in

Table 3. Weight Values of Indicators.

Indicator	${\mathit{C}}_{\mathit{u}}$	${\mathit{H}}_{\mathit{k}}$	$\left|\mathit{v}\right|$
weight	0.31	0.49	0.20

.

The consistency ratio was calculated using the following formula to verify whether the weights assigned above are reasonable.

$$CR={\displaystyle \frac{CI}{RI}}={\displaystyle \frac{\frac{{\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}-n}{n-1}}{RI}}={\displaystyle \frac{\frac{\left(\frac{1}{n}\sum _{i=1}^n\frac{{\left(R_c\mathrm{W}\right)}_i}{W_i}\right)-n}{n-1}}{RI}},$$

(9)

where n represents the number of dimensions, where n = 3; CI is the consistency index; IR is the random consistency index, with n = 3, RI = 0.58; ${\lambda }_{max}$ is the maximum eigenvalue; W denotes the weight of the indicator; and Rc is the judgment matrix.

According to Formula (9), CR = 0.084 < 0.1, indicating that the results of the judgment matrix meet the consistency requirements, and the weight assignment of the indicators is reasonable.

2.4. Hydraulic Reliability Assessment Method for Pipelines Network

2.4.1. Reliability of Water Supply Uniformity

The formula for calculating the reliability of water supply uniformity is as follows:

$$S_1={\sum }_{i=1}^k{\displaystyle \frac{Q_i{S}_{C_u}^i}{Q_s}},$$

(10)

where Q_i is the flow rate at the i-th node; Q_s is the total flow rate of the corresponding main pipe; k is the total number of nodes; and $S_{C_u}^i$ represents the C_u score of the i-th branch valve. This score is obtained by interpolation based on the calculated water supply uniformity index and the C_u scores provided in Table 1.

2.4.2. Reliability of Node Pressure Head

The formula for calculating pressure head reliability is expressed as follows:

$$S_2={\sum }_{i=1}^k{\displaystyle \frac{Q_i{S}_{H_k}^i}{Q_s}},$$

(11)

where $S_{H_k}^i$ is the H_k score of node i, obtained by interpolation based on the pressure head reliability index score provided in Table 1.

2.4.3. Flow Velocity Reliability

The formula for calculating flow velocity reliability is expressed as follows:

$$S_3={\sum }_{i=1}^k{\displaystyle \frac{Q_i{S}_{\left|v\right|}^i}{Q_s}},$$

(12)

where $S_{\left|v\right|}^i$ represents the score of node i, determined by interpolation based on the calculated flow velocity reliability and the values in Table 1.

2.4.4. Hydraulic Reliability of Pipeline Network

Based on the “Pipeline Water Delivery Engineering Technical Specifications” (GB/T 20203-2017), the “Micro-Irrigation Engineering Standards” (GB/T 50485-2020), and the calculation formula for urban water supply reliability [14], the hydraulic reliability Equation (13) is derived.

$$S={\sum }_{i=1}^3{W}_i{\mathrm{S}}_i,$$

(13)

where S denotes the hydraulic reliability of the pipeline network, W_i represents the reliability weight of the i-th indicator (as shown in Table 3), and S_i refers to the reliability of the i-th indicator.

2.5. Models and Verification

2.5.1. Model Construction

The model construction process is outlined in the following four steps.

Step 1: Pipe network drawing. Relevant data for the irrigation pipeline network are collected, including parameters such as pipe material, diameter, length, and valve locations. The actual pipeline network is simplified into a CAD format, with key nodes identified, including locations, lengths, intersection points, and outlet positions of the main pipelines.

Step 2: Model import. The CAD file of the pipeline network is imported into EPANET. The basic information of the pipeline network is modified and refined based on actual data, and the model is discretized. Due to the large scale and length of the pipeline network, the node spacing along the pipeline is set to 50 m to ensure model accuracy, particularly with respect to the elevation data of the pipeline network.

Step 3: Input parameters. The necessary parameters for the pipeline network, such as geographical coordinates, elevations, and topology structure, are input. Roughness coefficients for the pipelines are set, and the water source is configured, along with the status of each inlet and outlet. The actual water supply flow required by the branch pipes is used as the initial data to populate the calculation model.

Step 4: Model solving. Hydraulic calculations are performed using EPANET to determine parameters such as pressure head and flow rate at various nodes in the pipeline network, employing the Hazen–Williams (H-W) head loss formula for hydraulic modeling. Once the calculations are completed, the model construction is finalized [34].

2.5.2. Model Verification

Install pressure head and flow monitoring equipment at key locations in the pipeline network, such as the main pipe, branch pipe, and branch pipe inlet, to monitor real-time pressure head and flow data at each node. The pressure head and flow errors at each node are calculated by comparing the measured data from 5 May 2023, with the results generated by the EPANET hydraulic model. The model was validated using the hydraulic model verification standards proposed by the UK Water Research Centre (WRC). The results are presented in

Table 4. Error of Flow and Pressure head at Each Node.

Node	Error (%)		Node	Error (%)		Node	Error (%)
	Pressure Head	Flow		Pressure Head	Flow		Pressure Head	Flow
Ⅰ-a	3.73	0.40	Ⅱ-a	2.94	0.51	Ⅲ-a	4.44	0.14
Ⅰ-b	3.05	0.59	Ⅱ-b	3.29	0.08	Ⅲ-b	2.50	1.52
Ⅰ-c	4.28	0.98	Ⅱ-c	4.48	0.00	Ⅲ-c	0.57	0.00
Ⅰ-d	3.43	0.46	Ⅱ-d	/	0.78	Ⅲ-d	4.66	0.54
Ⅰ-e	4.76	0.00	Ⅱ-e	4.00	0.42	Ⅲ-e	3.95	0.27
Ⅰ-f	1.07	0.37	Ⅱ-f	4.42	0.33	Ⅲ-f	1.81	0.87
Ⅰ-g	6.52	0.25	Ⅱ-g	5.00	0.72	Ⅲ-g	3.92	0.55
Ⅰ-h	4.34	0.30	Ⅱ-h	7.27	0.24	Ⅲ-h	7.45	0.37
Ⅰ-i	4.88	0.21	Ⅱ-i	2.08	0.12	Ⅲ-i	3.92	0.00
Ⅰ-j	/	/	Ⅱ-j	6.12	0.39	Ⅲ-j	/	1.64
Ⅰ-k	1.80	0.21	Ⅱ-k	/	/	Ⅲ-k	4.08	0.26
Ⅰ-l	3.25	0.50	Ⅱ-l	4.60	0.26	Ⅲ-l	1.88	1.66
Ⅰ-m	2.78	0.68	Ⅱ-m	1.56	1.24	Ⅲ-m	1.36	0.91
Ⅰ-n	4.17	0.26	Ⅱ-n	1.90	0.46	Ⅲ-o	/	1.21
Ⅰ-o	1.47	0.01	Ⅱ-o	7.45	0.15	Ⅲ-q	4.58	0.26
Ⅰ-p	4.00	0.00	Ⅱ-p	1.81	0.01
			Ⅱ-s	0.65	0.12

. The / in the table indicates that the measured data at this node are missing.

The results of Table 4 indicate that the pressure head and flow rate errors of the pipeline network are controlled within 7.5% and 5%, respectively, demonstrating that the hydraulic model meets the simulation requirements.

3. Results

3.1. Hydraulic Analysis of Pipeline Network Under Different Water Supply Modes

3.1.1. Segmented Water Supply

An irrigation cycle should be maintained within 5 to 7 days to meet the water demand of the entire pipeline network during peak usage periods. When designing the rotational irrigation groups, it is essential to consider the average water consumption of each branch pipe. For efficiency, a configuration of four rotational irrigation groups is used as an example. Each group comprises 12 branch pipes and 36 branch valves operating simultaneously, with a water supply duration of 1.5 days per cycle, resulting in a 6-day rotational irrigation cycle. The specific grouping is presented in

Table 5. Grouping of fragmented water supply.

Group	Main Pipe-Sub Main Pipe
1	Ⅰ-a	Ⅰ-b	Ⅰ-o	Ⅰ-p	Ⅱ-a	Ⅱ-b	Ⅱ-i	Ⅱ-j	Ⅱ-m	Ⅱ-n	Ⅲ-a	Ⅲ-b
2	Ⅰ-c	Ⅰ-d	Ⅰ-i	Ⅰ-j	Ⅱ-c	Ⅱ-d	Ⅱ-o	Ⅱ-p	Ⅲ-c	Ⅲ-4	Ⅲ-i	Ⅲ-j
3	Ⅰ-e	Ⅰ-f	Ⅰ-k	Ⅰ-l	Ⅱ-e	Ⅱ-f	Ⅱ-r	Ⅱ-s	Ⅲ-e	Ⅲ-f	Ⅲ-m, Ⅲ-o, Ⅲ-q
4	Ⅰ-g	Ⅰ-h	Ⅰ-m	Ⅰ-n	Ⅱ-g	Ⅱ-h	Ⅱ-k	Ⅱ-l	Ⅲ-g	Ⅲ-h	Ⅲ-k	Ⅲ-l

Note: In Table 5, the Roman numerals before the hyphen represent the main pipeline (trunk), while the lowercase letters after the hyphen correspond to the sub-main pipeline.

.

Taking the second group as an example, the designed water supply flow rate for the system was calculated to be 13,700 L/s using Formula (1). According to the principles of rotational irrigation grouping, if the flow rate is evenly distributed among the branch pipes, the average design flow rate for each branch pipe is 380.96 L/s.

This design flow rate was used as the initial value for node water output in EPANET; however, a warning message appeared, stating “Negative pressure head occurred at 00:00:00 h, analysis terminated.” The results showed that negative pressure head occurred at multiple nodes within the pipeline network, as illustrated in Figure 2a–c. The maximum negative pressure head approached −200 m, indicating that the pipeline network could not function as intended. In practice, the network was unable to achieve the desired water flow rate. To resolve this, the water supply flow rate to the branch pipes was reduced. Through iterative calculations, the flow rate was adjusted until the pressure head at each node became positive, allowing EPANET to run successfully. The pressure head and flow distribution at each branch valve are presented in Figure 2d–f.

As shown in Figure 2, in the segmented water supply mode, when the system is divided into 4 groups, each group simultaneously operates 72 branch pipes, causing the network to malfunction. After reducing the water flow rate to the branch pipes, the pipeline network can operate normally; however, the pressure head at the inlet of the water supply branch pipe decreases significantly, resulting in considerable pressure head fluctuations and flow discrepancies between the branch pipes. Field test results indicate that the working pressure head of the emitters ranges from 0.3 to 12 m, leading to uneven irrigation.

According to the Technical Standard for Micro Irrigation Engineering (GB/T 50485-2020), the flow deviation rate for branch pipes should be less than 20%. The proportion of flow rates in the branches of main pipes I, II, and III that meet the required standards is 16.66%, 50.00%, and 50.00%, respectively. The proportion of branch pipe inlets that meet the minimum required pressure head (H_min) is 0.00%, 25.00%, and 25.00%, respectively. Throughout the pipeline network, the working pressure head at the inlet of the branch pipes ranges from 1.32 to 36.45 m, exhibiting a large variation. Notably, in the regions adjacent to the water supply and non-water supply branches, the pressure head fluctuation values range from 13.46 to 46.93 m.

The flow velocity at the inlet of the branch pipe in main pipe II-a is 1.8 m/s, while the flow velocities of the other branch pipes range from 2.2 to 4.5 m/s, significantly exceeding the economic flow velocity of 1.2 m/s. The considerable fluctuations in pressure head and flow rate, along with the elevated flow velocities, can pose safety risks to the pipeline and compromise the reliability of the network. These findings suggest that, for large-scale pipeline networks, the use of a rotational irrigation system may not effectively meet the water supply demands.

3.1.2. Uniform Water Supply

Under the uniform water supply mode, the flow rate is distributed according to the control area. The total flow rate of the designed pipeline network is 13,700 L/s. The flow rate for each branch pipe in the six sub-main pipes (I-a, I-b, II-a, II-b, III-a, and III-b) is 27.2 L/s. The flow rate for each branch pipe in the remaining sub-main pipes (I-c, I-d, II-c, II-d, III-c, and III-d) is 81.6 L/s, while the flow rate for each of the remaining branch pipes is 108.8 L/s. Based on the allocated flow rates, EPANET operates normally. The pressure head and flow results at the inlet of each branch pipe are presented in Figure 3.

As shown in Figure 3, under the uniform water supply mode, all 144 branch valves are open, and the flow deviation rate for all branch pipes is 1.1%, which complies with the “Technical Standard for Micro Irrigation Engineering” (GB/T 50485-2020). The pressure head at each branch valve within the pipeline network ranges from 3.11 to 46.87 m, with pressure head fluctuations between adjacent branches varying from 0.57 to 16.81 m. These fluctuations are considerably lower than those observed under the segmented water supply mode. The distribution of extreme pressure head values does not follow a clear pattern, primarily due to terrain elevation differences. The proportion of branch pipe valves reaching the minimum required pressure head (H_min) in main pipes I, II, and III are 2.08%, 25.00%, and 100.00%, respectively. The higher pressure head at the inlet of branch pipes in main pipe III is attributed to two factors: first, the elevation within the control area of main pipe III is lower than that of main pipes I and II; second, main pipe III is shorter in length and utilizes pipes of the same diameter as those in main pipes I and II, despite the higher flow rate.

The flow velocity across the pipeline network ranges from 0.59 to 1.19 m/s, which is close to the economic flow velocity and supports the safe operation of the system. This suggests that the uniform water supply mode is more suitable for large-scale irrigation pipeline networks.

The flow velocity across the pipeline network ranges from 0.59 to 1.19 m/s, which is close to the economic flow velocity. This indicates that the uniform water supply mode is more suitable for large-scale irrigation pipeline networks.

3.1.3. Random Water Supply

In the random water supply mode, the probability of opening each branch valve is determined by a random function. When the irrigation guarantee rate of the pipeline network is 90%, 110 branch valves are randomly opened, accounting for 76.4% of the total number of branch valves. At this point, the system can meet the water supply demand for the opened branch pipes. Figure 4 presents the flow rate and pressure head at the inlet of each branch pipe under one of the random water supply configurations.

According to Figure 4, under the random water supply mode, the flow deviation rate for all branch pipes is 1.1%, which satisfies the requirements specified in the “Technical Standard for Micro Irrigation Engineering” (GB/T 50485-2020). The proportion of branch pipe inlets where the pressure head reaches H_min in main pipes I, II, and III is 30.34%, 72.50%, and 97.22%, respectively. The pressure head in main pipe I is relatively low, likely due to the higher elevation of most of the opened branch pipes. The pressure head at each branch valve ranges from 2.96 to 46.96 m, with pressure head fluctuations between adjacent branches ranging from 0.19 to 18.72 m. These fluctuations are comparable to those observed in the uniform water supply mode and are significantly lower than those in the segmented water supply mode.

The flow velocity within the pipeline network ranges from 0.53 to 2.00 m/s, with some pipelines exhibiting minor deviations from their economic flow velocity. However, these deviations are not significant. Thus, the random water supply mode can be considered a flexible and effective solution for meeting the demands of large-scale irrigation pipeline networks.

3.2. Comparison of Hydraulic Reliability of Pipeline Network Under Different Water Supply Modes

The hydraulic reliability of the pipeline network under different water supply modes was calculated using Formulas (3)–(13), based on the flow rate, pressure head, and velocity values at the nodes simulated by EPANET. The calculated hydraulic reliability values for various regions and pipeline systems are presented in

Table 6. Hydraulic reliability of pipeline network under different water supply modes.

Water Supply Mode	Region	Reliability
		${\mathit{S}}_1$	${\mathit{S}}_2$	${\mathit{S}}_3$	S
Segmented	Ⅰ main pipe	4.04 b	0.46 d	2.04 b	1.88 c
	Ⅱ main pipe	3.79 b	1.00 c	0.36 c	1.74 c
	Ⅲ main pipe	4.29 ab	1.11 c	0.20 c	1.91 c
	The entire network	4.04 b	0.84 cd	0.64 c	1.79 c
Uniform	Ⅰ main pipe	4.8 a	0.61 d	4.33 a	2.65 b
	Ⅱ main pipe	4.75 a	1.62 b	4.39 a	3.14 a
	Ⅲ main pipe	4.80 a	0.89 c	4.26 a	2.78 a
	The entire network	4.76 a	0.94 c	4.49 a	2.83 a
Random	Ⅰ main pipe	3.73 b	2.04 a	2.67 b	2.69 ab
	Ⅱ main pipe	4.16 a	1.95 a	2.53 b	2.75 a
	Ⅲ main pipe	4.10 b	0.71 d	2.41 b	2.41 b
	The entire network	3.99 a	1.54 bc	2.50 b	2.49 b

Note: Different lowercase letters in the vertical columns of the table indicate that there are significant differences in reliability between different regions and water supply modes (p < 0.05).

.

The results presented in Table 6 indicate a clear pattern in the hydraulic reliability of different water supply modes and individual branch pipes. Except for the areas controlled by the II and III main pipes in the segmented water supply mode, the reliability follows the order from high to low: water supply uniformity reliability, flow velocity reliability, and node pressure head reliability. This pattern primarily arises because the calculation is based on flow distribution, while the pressure head values are derived from the model. Among the different water supply modes, the hydraulic reliability of the uniform water supply mode is generally the highest, followed by the random water supply mode, with the segmented water supply mode exhibiting the lowest hydraulic reliability.

In the segmented water supply mode, the water supply uniformity reliability and node pressure head reliability in the area controlled by the III main pipe are the highest, while its flow velocity reliability is the lowest. This is attributed to the low elevation of the III main pipe, which increases the pressure head difference within this area of the self-pressurized system. Additionally, the weight assigned to node pressure head reliability is relatively high, such that higher pressure head results in greater flow velocity. In all areas, except for that controlled by the I main pipe, the reliability of water supply uniformity is the highest, the reliability of flow rate is the lowest, and the reliability of pressure head is intermediate. Therefore, in a self-pressurized water supply system, if the segmented water supply mode is adopted, the impact of terrain elevation differences should be prioritized, and attention should be given to controlling the water flow velocity in the pipeline to improve the hydraulic reliability of the pipeline network.

Under the uniform water supply mode, the hydraulic reliability of the pipeline network in each region is generally higher than that in the segmented water supply mode. The difference in hydraulic reliability between the main pipes is minimal, with the reliability of water supply uniformity being comparable to that of flow velocity, both of which are higher than those observed in the segmented water supply mode. However, the reliability of node pressure head is the lowest, particularly in the III main pipe. The main issue in the uniform water supply mode lies in whether the pressure head at each node of the pipeline network can meet the design requirements.

Under the condition of a 90% water supply guarantee rate, adopting a random water supply mode can also satisfy the water supply demands of each branch pipe, with the corresponding network reliability value falling between those of the first two modes. Unlike the first two modes, the reliability of node pressure head in the area controlled by the III main pipe is significantly lower in this mode, indicating that in the random water supply mode, particular attention should be given to node pressure head in low-lying areas.

Under the three water supply modes, the reliability of uniform water supply in the entire pipeline network is ranked from high to low as uniform water supply, segmented water supply, and random water supply. The reliability of node pressure head in the pipeline network is ranked from high to low as random water supply, uniform water supply, and segmented water supply. The reliability of pipeline flow rate is ranked from high to low as uniform water supply, random water supply, and segmented water supply. The hydraulic reliability of the pipeline network is highest under the uniform water supply mode, followed by the random water supply mode, and is lowest under the segmented water supply mode.

4. Discussion

In regions with limited irrigation water resources, irrigation projects commonly implement a system in which the main pipelines are supplied continuously with water, while the branch pipelines operate under a rotational supply system. This approach aims to reduce project costs, optimize equipment utilization, and expand the irrigated area [35,36]. For large-scale irrigation systems, the typical operational mode during the irrigation season involves continuous water supply to the main pipelines and rotational water supply to the branch pipelines. This water supply configuration is also the dominant approach used in large-scale drip irrigation projects in Xinjiang, China [37,38].

The water supply mode significantly affects the hydraulic reliability of the pipeline network. Research has shown that the traditional rotational irrigation method for branch pipes, commonly employed in design, is not fully suitable for large-scale pipeline networks. In the segmented water supply mode, based on the rotational irrigation system, the designed flow rates for branch pipes are excessively high, resulting in negative pressure head in various sections of the pipeline network during operation. This is a primary cause of frequent pipe bursts during the initial operation phase of the local pipeline network. Upon transitioning to a uniform water supply mode, the flow rates to the branch pipes were reduced. Although this adjustment enables the pipeline network to fulfill its water distribution function, only a limited number of branch pipes achieve the required minimum inlet head (H_min), and pressure head fluctuations between adjacent branch pipes increase. Furthermore, the flow rate generally exceeds the economic flow velocity, and the total flow in the pipeline network fails to meet the design specifications, leading to increased flow deviation between branch pipes. As a result, the reliability of the pipeline network is compromised. To ensure proper field irrigation performance, it is often necessary to install pressure head or flow regulation equipment downstream of the control valves in the field irrigation system. Additionally, when planning rotational irrigation groupings, not only the number of rotational irrigation groups but also the positioning of open branch pipes within the pipeline network should be considered to optimize the rotational irrigation scheme. It is also recommended to install automatic intake and exhaust valves, along with other control devices, at the inlets of the branch pipes [39].

With the development of large-scale agriculture, the scale and complexity of irrigation pipeline networks have significantly increased. Failure to optimize the water supply mode in a timely manner can render the original rotational irrigation system ineffective, negatively impacting the water supply efficiency of the pipeline network [40,41]. To maximize project benefits, a pressure head reduction and uniform water supply mode has been adopted. Research indicates that, compared to the segmented water supply mode, the uniform water supply mode, based on the continuous irrigation system, significantly reduces pressure head fluctuations in the pipeline network. Additionally, the flow velocity in the branch pipes approaches the economic flow velocity, which reduces the flow deviation rate and enhances the hydraulic reliability of the network. However, the pressure head at the inlet of most branch pipes still fails to reach the required minimum node head (H_min). To further improve the safety and reliability of the water supply, effective monitoring and timely adjustment of the water supply flow are recommended.

With the diversification of local cropping patterns, there has been an emerging demand for a certain degree of random water supply to meet the water requirements of various sectors [42,43], which has led to increased complexity in system scheduling. Research indicates that under a random water use system, the random water supply mode can effectively distribute the flow across branch pipes, provided that the total flow of the pipeline network meets the overall water demand. The number of nodes with a pressure head of H_min at the inlets of branch pipes exceeds that of the uniform water supply mode. The pressure head fluctuations between branch pipes are comparable to those in the uniform water supply mode, with extreme pressure head variations mostly occurring between adjacent branch pipes that experience significant flow changes. The reliability of node pressure head in the pipeline network surpasses that of the first two modes. Although the actual flow velocity of some branch pipes deviates from the economic flow velocity, the deviation is minimal; overall, the hydraulic reliability of the pipeline network lies between that of the first two modes. To ensure system stability, it is essential to monitor pipeline sections with significant fluctuations in water supply flow, particularly at nodes located in lower terrain areas. Gradual operation of valves should be implemented to avoid sudden pressure head changes. Furthermore, the installation of pressure head sensors at nodes prone to fluctuations is recommended to enable real-time monitoring of system pressure head and flow, allowing for prompt adjustments to the number of open branch pipes.

The design of the pipeline network must account for water distribution uniformity, system operability, and safety. Determining the appropriate hydraulic evaluation indicators for assessing the safety of the pipeline network is crucial [44]. The hydraulic reliability of large-scale irrigation pipe networks is influenced by factors such as water supply uniformity, pressure head reliability, and flow velocity deviation. These indicators often serve as key constraints in the optimization of pipeline network design [45]. This study demonstrates that, among these three indicators, pressure head reliability carries the greatest weight, followed by water supply uniformity, with flow velocity deviation having the lowest weight. Under the uniform water supply mode, the pipeline network system exhibits the highest hydraulic reliability, along with the best performance in water supply uniformity and minimal flow velocity deviation. In the random water supply mode, the hydraulic reliability of the pipeline network is intermediate, falling between the segmented and uniform water supply modes, with the highest node being pressure head reliability. In contrast, the hydraulic reliability of the pipeline network is the lowest under the segmented water supply mode.

In summary, for large-scale irrigation pipeline networks, the traditional centralized water supply model reduces the hydraulic reliability of the system. Adopting a pressure head-reducing uniform water supply mode improves hydraulic reliability, although it does not fully ensure pressure head stability across the network. By implementing a random water supply mode, node pressure head reliability is enhanced. In practical applications, it is crucial to carefully control the proportion and location of open branch pipes. Additionally, in areas with uneven terrain, special attention must be given to managing the pressure head at nodes located at lower elevations.

5. Conclusions

A hydraulic model of a large-scale irrigation pipeline network was developed using EPANET, and the hydraulic reliability of the network was analyzed under three water supply modes: segmented, uniform, and random water supply. The key findings are as follows:

(1) In the large-scale irrigation pipeline network, the traditional segmented water supply mode leads to significant pressure head fluctuations and flow deviations among branch pipes, with flow velocities generally exceeding the economic flow rate. Additionally, the pressure head node fails to meet the minimum required node head (H_min). In the uniform water supply mode, pressure head fluctuations and flow deviations among branch pipes are reduced, and flow rates generally align with their economic flow rate. However, many nodes still do not reach H_min. In the random water supply mode, the proportion of nodes meeting H_min is higher than that in the uniform water supply mode. Pressure head fluctuations and flow deviations in the pipeline network are not significantly different from those in the uniform water supply mode, although the actual flow rates of some branch pipes slightly deviate from their economic flow rate.

(2) In the segmented water supply mode, the reliability of water supply uniformity, node pressure head, and flow velocity in the pipeline network are 4.04, 0.84, and 0.64, respectively. In the uniform water supply mode, the reliability of water supply uniformity and flow rate is the highest, with values of 4.76 and 4.49, respectively. However, the reliability of node pressure head is lower than in the segmented water supply mode, at 0.94. In the random water supply mode, the node pressure head reliability is the highest, at 1.54, while the reliabilities of water supply uniformity and flow rate are 3.99 and 2.50, respectively. Overall, the hydraulic reliability of the pipeline network is highest in the uniform water supply mode (2.83), followed by the random water supply mode (2.49), with the segmented water supply mode exhibiting the lowest reliability (1.79).

The innovations of this study lie in the following aspects: First, while previous research has primarily focused on small-scale pipeline systems, this study addresses large-scale irrigation pipeline networks characterized by longer pipe lengths and larger diameters. Second, conventional pipeline systems typically operate with a constant water supply and pressure. In contrast, this study introduces different water supply modes based on crop water requirements, dynamically adjusting water delivery according to varying demands. The results of this study provide valuable insights for the selection of water supply modes and the hydraulic reliability assessment of large-scale irrigation pipeline networks. This research represents an initial exploration of a large-scale self-pressure head drip irrigation pipeline network system in Xinjiang, China. In practical applications, it is essential to consider various pipeline network configurations, as well as factors such as water quality and economic considerations.

To enhance the hydraulic performance of water distribution networks, a comprehensive strategy integrating cutting-edge technologies can be implemented. Guided by methodologies such as artificial intelligence and recommendations from DeepSeek [46], the optimization process begins with intelligent network design and management. By synergizing Geographic Information Systems (GIS) and Supervisory Control and Data Acquisition (SCADA) systems, dynamic zoning adjustments can be achieved through real-time analysis of water consumption patterns. Hydraulic modeling tools like EPANET further enable precise simulation of pressure distribution and topology optimization. For intelligent control, variable-frequency pump stations can be deployed to adjust pump speeds based on real-time pressure feedback, balancing energy efficiency with stability, while pressure-reducing valves (PRVs) installed at critical nodes mitigate leakage risks and stabilize pressure. Economically, acoustic leak detection technologies offer targeted identification and repair of pipeline leaks, reducing water loss, while demand-side initiatives such as incentivizing off-peak water usage help flatten demand peaks. Additionally, machine learning algorithms can predict short-term water demand to minimize arbitrary scheduling, and pre-deployed rapid-response temporary pipelines enhance emergency adaptability. Collectively, these measures—spanning smart design, adaptive control, economic efficiency, and predictive operations—significantly improve hydraulic performance, ensuring a resilient, sustainable, and user-centric water distribution system.