Study on the Factors Affecting the Drainage Efficiency of New Integrated Irrigation and Drainage Networks and Network Optimization Based on Annual Cost System

Abstract

With the frequent occurrence of extreme weather events worldwide, the compound frequency of drought and flood events has significantly increased, imposing multidimensional pressures on agricultural water resource management. Agricultural water consumption accounts for approximately 70%, with severe waste, as a large amount of water is lost during transmission and distribution. Faced with increasingly severe and frequent extreme weather, traditional drainage systems may become unsustainable. Identifying the factors influencing drainage time is crucial for efficient drainage. The MIKE URBAN model has significant potential in farmland waterlogging simulation and drainage network optimization. This study validated the model’s accuracy based on infiltration well overflow capacity experiments, with Average Relative Error (ARE) values of 2.29%, 6.52%, 4.41%, 3.17%, 4.37%, and 5.69%, demonstrating good simulation accuracy. The MIKE URBAN model was used to simulate drainage networks, explore factors affecting drainage time, establish an annual cost system for the drainage network, and optimize the network using a genetic algorithm with the objective of minimizing annual costs. Research findings: There is a clear negative correlation between the maximum inflow of infiltration wells and drainage time. As inflow increases, drainage becomes faster, but beyond 0.0075 m³/s (27 m³/h), the efficiency gains level off. This indicates that selecting infiltration wells with at least a 20% opening ratio is essential. Similarly, increasing the collector’s diameter enhances drainage efficiency significantly, though the effect follows a diminishing return pattern. While smaller lateral spacing improves local water collection, it may lead to flow congestion if the collector is undersized; conversely, larger spacing increases drainage paths and delays, even if the collector is large. An optimal spacing range of 100–150 m is suggested alongside the collector diameter. Lateral diameter also affects performance: increasing it reduces drainage time, but the benefit plateaus around 200 mm, making further enlargement cost-ineffective. The genetic algorithm helped to optimize the drainage network design. Utilizing the genetic algorithm, the drainage network was optimized in just 15 iterations. The fitness function value rapidly decreased from 351,000 CNY to 55,000 CNY and then stabilized, reducing the annual cost from 59,640.67 CNY to 45,337.86 CNY—a 24% savings—highlighting the approach’s effectiveness in designing efficient and economical farmland drainage systems. This study has shown that the simulation-based optimization of drainage networks provides a more rational and cost-effective approach to planning drainage infrastructure.

1. Introduction

Against the backdrop of increasing extreme weather events globally, the frequency of compound drought and flooding events has significantly risen [1], and the problem of waterlogging is becoming more severe. Without effective drainage measures, crops under flooding stress are directly threatened by yield reduction [2], and agricultural water resources management is facing multidimensional pressures. Groundwater is generated from large paleolake deposits controlled by multiple tectonic movements [3]. However, due to excessive groundwater extraction, many areas have experienced phenomena such as land subsidence and surface cracks, leading to severe consequences. With the acceleration of urban modernization, natural ground surfaces are gradually being destroyed and replaced by hard, impermeable surfaces. This severely hinders precipitation infiltration, increases surface runoff, and consequently leads to flooding [4]. According to the Food and Agriculture Organization (FAO) of the United Nations, about 33% of irrigated farmland globally faces the dual threat of seasonal water scarcity and inadequate drainage capacity due to climate change [5], while only 25–30% of existing irrigation facilities are resilient enough to adapt to enhanced rainfall variability [6]. Studies have shown that traditional irrigation and drainage systems exhibit significant flaws in extreme hydrological events. For instance, during the 2015 drought in the Ganges Plain of India, the irrigation network had a 37% water supply gap [7]. In China’s North China Plain, the lack of drainage infrastructure led to crop yield losses. Additionally, the separation of irrigation and drainage functions can lead to soil salinization [8]. These challenges urgently require systematic optimization to enhance the resilience of water infrastructure. As early as the mid-19th century, European countries used tiles to build irrigation and drainage systems, and with the improvement in research and technology, the area of drained farmland nationwide steadily increased [9]. In India, the over-extraction of groundwater has become a serious issue, and to address the land–water–salt balance, research into underground drainage systems was initiated relatively early. Some studies show that although farmers need to invest in drainage system construction upfront to address waterlogging issues, once the system is built, it can effectively mitigate the yield and production losses caused by internal flooding and ensure economic benefits [10]. However, faced with increasingly severe and frequent extreme weather events, traditional irrigation and drainage systems may no longer be safe.

Traditional drainage methods occupy a large amount of arable land, significantly increase conveyance losses, result in a low irrigation water utilization coefficient, and fail to adequately guarantee drainage performance—potentially even affecting crop yields. As research progressed, the concept of dual-purpose irrigation and drainage channels emerged, which saved some farmland areas and reduced water head loss. Some scholars have pointed out that the height of dual-purpose channels should be between that of irrigation and drainage channels, but the drop is minimal, making it suitable only for flat areas; it is not suitable for hilly regions [11].

Due to the limitations of dual-purpose irrigation and drainage channels, such as occupying a large area of farmland and having poor compatibility with new water-saving irrigation methods, scholars began researching irrigation and drainage pipelines. Pipeline irrigation and drainage involves irrigation and drainage through pipelines, which operates quite differently from surface open channel irrigation and drainage. By studying the soil moisture movement mechanism, researchers have explored the differences between pipeline irrigation and drainage models and traditional open channel systems. For example, in the salinized farmland of Wuyuan County, the migration and distribution of soil salts were compared under two models: “drip irrigation + open drainage” and “flood irrigation + buried pipe drainage”. The study showed that both models resulted in salt removal from the soil, with the “flood irrigation + buried pipe drainage” model having a relatively better desalting effect [12]. Using the HYDRUS-1D model, a one-dimensional numerical simulation was conducted to evaluate the salinity improvement effect on saline–alkali land under water-saving irrigation, conventional irrigation, buried pipe drainage, and no drainage. The results indicated that buried pipe drainage improved leaching efficiency and effectively suppressed the process of soil salinization [13]. Furthermore, simulations using the Vedernikov infiltration equation and the Van der Molen leaching desalination equation studied the improvement process of coastal saline soil irrigation and drainage. The study pointed out that uniform flooding and leaching across the entire region could result in excessive leaching near the buried pipes, wasting water resources, while areas farther from the pipes experienced insufficient leaching, thus reducing leaching efficiency [14]. A double-layer buried pipe drainage experiment with alternating shallow and deep pipes was conducted, and the results showed that double-layer buried pipe drainage was more effective in flood control and salinity reduction than single-layer buried pipe drainage [15]. A comparison of surface drip irrigation and underground straw composite pipeline irrigation indicated that the latter helped promote winter wheat growth after the jointing stage, improving yield and water use efficiency. It also showed higher economic benefits and promising prospects for field crops with high planting density in supplemental irrigation areas [16].

In addressing the optimization of pressurized water distribution networks, several scholars have proposed various methods. One proposed an optimal path identification method based on genetic algorithms [17]; another utilized a GIS system to optimize the irrigation network in eastern Arkansas, USA [18]. A three-stage optimization model was introduced, where the first stage determines the lowest cost layout and pipe diameter, the second stage identifies the annual investment in pump stations and energy costs to meet crop water demand, and the third stage minimizes the total cost [19]. Some scholars introduced reliability as a constraint in the optimization model for the first time, integrating it with cost considerations and analyzing the relationship between the two [20]. An optimized pipe diameter model for agricultural irrigation systems was designed and applied in the Sinwankim area of Korea, saving 11% of costs compared to the original plan [21]. A three-level irrigation network planning was proposed for an irrigation district in India, aiming to determine the optimal pipe diameter at the lowest cost. The study showed that compared to traditional distribution methods, this approach significantly reduced losses and saved costs [22]. Genetic algorithms were used to optimize the network layout in agricultural irrigation systems, reducing construction and operational costs while ensuring water supply demands [23]. The PHSM algorithm was proposed to improve the efficiency of evolutionary algorithms in optimizing distribution systems [24]. For pressurized irrigation networks, an optimization program was written using Excel VBA, revealing that even minor changes in the network could lead to significant changes in optimization outcomes [25]. Complex network theory (CNT)was applied to replace traditional methods, reducing uncertainties in the distribution network [26]. These studies primarily focus on water distribution networks, but the optimization of complex networks remains a challenging problem that still needs to be addressed.

Integrated irrigation and drainage networks provide a technical solution to address the aforementioned contradictions by combining water delivery and drainage functions. The core design concept lies in using a modular network structure to dynamically switch between irrigation and drainage modes. Systematic studies have shown that such systems can significantly improve water resource utilization efficiency and reduce the impact of groundwater level fluctuations on crop growth by integrating both irrigation and drainage functions [27]. The integrated irrigation and drainage pipeline, designed for dual use, is especially crucial in low-lying, flood-prone areas, playing a vital role in ensuring crop safety during floods and supporting normal growth. This technology is of great significance for reforming the old canal systems and management models in farmland [28]. However, existing research primarily focuses on optimizing hydraulic performance or the cost optimization of single-function networks, and there is still a lack of universal models for the quantitative assessment of annual costs for complex networks (including construction investment, maintenance costs, etc.).

In the field of agricultural water management, models like DRAINMOD, SWAP, HYDRUS-1D/2D/3D are widely used [29], along with other open-source software [30,31]. Some scholars have simulated the dynamic water and nitrogen balance in paddy fields under traditional irrigation and drainage modes versus controlled irrigation and drainage modes using the DRAINMOD model. The results showed that the controlled irrigation and drainage mode achieved better water-saving and emission–reduction effects in paddy fields [32]. Other scholars have introduced the latest research and application progress of the HYDRUS model in China within the field of hydrological and hydraulic modeling, demonstrating its widespread application in soil moisture, salinity, heat, and nutrient transport [33]. Compared to other models, the MIKE URBAN model has the advantage of multi-module coupling capability, an easy-to-use operating system, and excellent visualization. However, it is primarily used for simulation analysis in municipal and river network systems, with relatively few applications in agricultural water management (DHI, 2021).

In a drainage network, infiltration wells serve as critical nodes, and their overflow capacity directly impacts both the drainage efficiency and the uniformity of irrigation. Physical experiments that measure the overflow capacity of infiltration wells are conducted to establish a hydraulic parameter database applicable to the MIKE URBAN model. This database is then used to validate the MIKE URBAN model’s simulation accuracy in farmland drainage and to develop a hydraulic network model that simulates drainage performance under different topological configurations and pipe diameter selections, thereby exploring the factors affecting drainage speed. Finally, a genetic algorithm is employed—with the objective of minimizing annual construction and annual operation and maintenance (O and M) costs—to optimize the network design. Specifically, our goals are the following:

(1) Study on infiltration well overflow capacity:

Drainage experiments were conducted to investigate the practical overflow capacity (i.e., drainage speed) of infiltration wells. The experiments considered four factors: infiltration well diameter, connection pipe diameter, water depth, and opening rate. A total of 10 experimental schemes were designed, with each scheme repeated 24 times (resulting in 240 tests covering all variable combinations), to analyze the effects of these factors on the drainage efficiency of the wells.

(2) Simulation of drainage network layout based on the MIKE URBAN model:

An experimental field in Yanggu County, Shandong, was selected as the simulation area to study the drainage performance and marginal effects of different network layouts. Multiple simulations using the MIKE URBAN model were performed for various drainage network layouts. Each layout was evaluated based on drainage speed, and the study investigated the factors influencing drainage speed as well as the marginal impact of different network configurations.

(3) Optimization of the drainage network:

In designing and optimizing the drainage network, annual cost is a key indicator of the system’s economic efficiency. With the objective of minimizing annual cost—and under constraints such as pipe diameter, pipe length, and pipe spacing—a fitness function was constructed. The algorithm structure was then optimized using tournament selection to enhance convergence and identify the optimal network layout.

2. Materials and Methods

2.1. Experimental Background and Objectives

In the integrated irrigation and drainage network, infiltration wells, as key nodes, directly affect the drainage efficiency of the system. This experiment quantifies the flow capacity of infiltration wells through physical testing, thereby establishing a hydraulic parameter database suitable for the MIKE model.

The experimental area is located in Yanggu County, Liaocheng City, Shandong Province, at 36°11′ N and 115°79′ E, with an elevation of 39.62 m. The long-term average annual rainfall is 560.2 mm, and the average temperature is 13.6 °C, falling within a semi-humid continental temperate monsoon climate. Yanggu County is situated on the north bank of the Yellow River in the western Shandong Plain, with a gently sloping terrain from southwest to northeast. It borders Dong’a County to the east, Xin County to the west, Taixian County of Henan Province to the south, and Dongchangfu District to the north; across the Yellow River to the southeast, it faces Dongping County.

2.2. Experimental Design

This experiment focuses on the flow capacity of infiltration wells. Through controlled head, variable head, and float valve comparative tests on infiltration wells of different specifications, the study observes their drainage performance under various flooding scenarios. The objective is to identify the factors influencing drainage efficiency, quantify the infiltration wells’ flow capacity, and provide data support for subsequent model simulations.

The experimental site is a 7.1 m × 6.1 m test pool, as shown in Figure 1, designed to simulate field irrigation and drainage processes effectively. The perimeter of the site has been treated with anti-infiltration measures or enclosures to ensure that test water does not leak or overflow, thereby ensuring the accuracy of measurement data. The core components include the following:

(1) Infiltration Well System: The infiltration wells are installed within the test pool to simulate the function of field drainage wells or irrigation–drainage piles. When the water level in the test pool reaches a certain height, water flows into the well through perforations in the well cover and is then discharged or collected through pipes connected to the drainage network.

Infiltration wells with diameters of dn200, dn250, and dn315 are used, all with a uniform height of 51 cm. The variation in well diameter is intended to investigate its effect on drainage capacity and provide reference parameters for subsequent drainage network optimization.

The well cover, as shown in Figure 2, is made of PVC material and features 10 mm diameter perforations with a 16 mm spacing. The perforation rates are 5%, 10%, 15%, 20%, 25%, and 30%. By adjusting the number of perforations, the experiment explores the flow capacity of infiltration wells under different perforation rates. Since the perforation rate significantly influences water inflow and drainage efficiency, comparative analysis of different rates helps determine an optimal perforation configuration.

(2) Connecting Pipes: The connecting pipes are attached to the infiltration wells using sealed joints to prevent leakage while allowing easy assembly and adjustment. These pipes simulate the water transport function of various levels of field drainage networks (e.g., collectors, laterals). By testing different pipe diameter combinations, the impact of pipe diameter on drainage efficiency can be analyzed.

The connecting pipes are made of PVC material with diameters of 160 mm, 110 mm, and 90 mm, each corresponding to different drainage capacities and hydraulic conditions.

(3) Float Valve: Made of PVC material, the float valve is used in comparative experiments by installing it on the connecting pipes. It automatically opens or closes based on water levels, controlling inflow and outflow speeds. This setup allows observation of the float valve’s buffering effect in response to water level fluctuations and sudden flow changes.

(4) Triangular Weir: The triangular weir is positioned at the drainage outlet of the test pool. By recording the height of the water level, it is possible to obtain the flow rate through the triangular weir. The drainage flow and process can be accurately monitored, providing essential data for subsequent analysis and model validation.

As shown in Figure 3, the triangular weir is constructed from welded steel plates, approximately 6 m in length and 0.6 m in width, with a relatively smooth inner surface. The overflow notch is designed according to ISO 1438 [34] standards to ensure accurate flow measurement under different discharge conditions. When water flows through the triangular weir, a high-precision liquid level sensor (sampling frequency: 10 Hz) continuously records water level variations in real time. The collected water level data are then converted using the corresponding weir height-flow rate reference table.

(5) Water Level Control System: Water supply valves are installed in the test pool, allowing manual or automatic water flow control to simulate rainfall or irrigation-induced ponding. Based on experimental requirements, different target water levels (e.g., 5 cm, 10 cm, 20 cm) can be set to observe drainage performance under varying ponding depths.

For constant water head tests, the inflow is finely adjusted using a manual valve to maintain a stable water level in the test pool (accuracy: ±1 cm). The experiment monitors flow rate variations at the triangular weir, the infiltration capacity of the wells, and the efficiency of water transport through the connecting pipes under stable water level conditions.

A measuring scale is placed inside the test pool to monitor water levels in real time. The water level in the test pool is manually recorded by reading the scale measurements at regular intervals.

The experiment was designed with the following four factors (

Table 1. Experimental Schemes.

Scheme Serial Number	Main Observed Content	Infiltration Well Diameter (mm)	Connecting Pipe Diameter (mm)	Water Depth (cm)	Hole Ratio and Hole Position	Number of Trials
1	Triangular Weir Water Surface Elevation	200	160	20, 10, 5, and 20 cm Variable Water Head	Top Cover Hole Ratios: 30%, 25%, 20%, 15%, 10%, 5%	24
2		200	110			24
3		200	90			24
4		250	160			24
5		250	110			24
6		250	90			24
7		315	160			24
8		315	110			24
9		315	90			24
10		200	160 (with Float Valve)			24

):

(1) Infiltration well diameter: 200 mm, 250 mm, 315 mm.

(2) Connecting pipe diameter: 160 mm, 110 mm, 90 mm.

(3) Ponding depth: Constant water head (5 cm, 10 cm, 20 cm) and variable water head (initial depth of 20 cm).

(4) Perforation ratio: 5% to 30% (adjusted by the number of perforations on the well cover).

These four factors (infiltration well diameter, connecting pipe diameter, ponding depth, and perforation ratio) are mutually independent. Each factor is assigned different values, forming distinct experimental schemes through their combinations. Each infiltration well diameter, connecting pipe diameter, ponding depth, and perforation ratio combination results in a unique experimental setup.

A special control scheme (Scheme 10) was included, where a float valve was installed in the connecting pipe to analyze its buffering effect during sudden water level changes or high-flow impact. This control scheme also covered 4 ponding depths × 6 perforation ratios, totaling 24 tests.

In summary, the experiment consisted of 240 tests in total.

The experimental procedure is divided into the following steps:

(1)

Constant head test:

Water is added to reach the target depth, maintaining the water level at 5 cm, 10 cm, and 20 cm within the test pool using dynamic valve adjustments. The flow rate over the triangular weir and water level changes in the test pool are recorded. Once the flow over the triangular weir stabilizes, a high-precision liquid level sensor (accuracy ±0.1 mm) is used to record the water surface height.

(2)

Variable head test:

The test pool is filled to an initial ponding depth of 20 cm via an irrigation–drainage pile, and then inflow is stopped. Water drains naturally through the infiltration well, causing the water level to drop. Once the triangular weir flow stabilizes, the water level decline rate and triangular weir flow rate are monitored in real time, and the water surface height is recorded.

(3)

Float valve control test:

A float valve is installed in the connecting pipe of the infiltration well system as a control mechanism to analyze its buffering effect on sudden flow fluctuations.

2.3. Experimental Measurement Items and Methods

2.3.1. Water Level Measurement

The measurement of water levels in the experiment is mainly divided into two parts: the water level in the test tank and the upstream water level of the triangular weir.

(1) Test Tank Water Level: The dynamic changes in the water level within the test tank are recorded in real time using a graduated scale inside the tank. The measurements include both constant water head conditions (5 cm, 10 cm, 20 cm) and variable water head conditions (initial depth of 20 cm).

(2) Upstream Water Level of the Triangular Weir: The water level changes are continuously collected in real time using a high-precision liquid level sensor (sampling frequency 10 Hz), whose measuring range is 0~500 mm; the resolution is 0.1 mm; accuracy ±0.1 mm; supply voltage is 12 V, with the data transmitted to the computer for analysis.

2.3.2. Drainage Time Measurement

For the determination of drainage time, a high-precision liquid level sensor is used, with a time step set to 3 s. The sensor continuously collects the triangular weir water level data for each time step and records them in the computer. In the non-fixed head test, after stopping the water inflow, the duration is recorded for the water level to drop from the initial value (20 cm) to the point where there is no obvious water accumulation. The recording stops when the water level in the experimental pool reaches the point where no significant accumulation remains. In the fixed head test, the time from the start of water inflow to the stabilization of flow is recorded as an indicator of the system’s response time.

2.3.3. Triangular Weir Flow Calculation Method

The triangular weir water level height is measured in real time using a high-precision liquid level sensor. The calculation formula for the flow rate of the ISO standard triangular weir is as follows:

$$Q=C\times {\displaystyle \frac{8}{15}}\sqrt{2g}\times H^{{\displaystyle \frac{5}{2}}}$$

(1)

In the formula:

Q—Flow rate, m³/h;

C—Flow coefficient (related to the weir angle and weir characteristics);

H—Water depth in front of the weir, m.

Based on the above formula, the flow rate of the infiltration well can be calculated according to the water depth in front of the weir.

3. MIKE URBAN Model Data Processing

3.1. Infiltration Well (Manhole) Parameters

In the MIKE URBAN model, the infiltration well (manhole) is a key node that connects adjacent pipes and serves as the infiltration point for rainwater during drainage. Through the infiltration well flow capacity test conducted in Yanggu County, the flow capacity of the infiltration well was quantified as the drainage flow rate per hour, as shown in

Table 2. Overflow capacity (drainage flow rate) of infiltration wells of different specifications.

Serial Number	Diameter of Infiltration Well (mm)	Connecting Pipe Diameter (mm)	Drainage Flow (m3/h)
			5%	10%	15%	20%	25%	30%
1	200	160	6	30	33	35	37	40
2		110	6	17	25	30	36	38
3		90	6	16	20	27	31	33
4	250	160	26	35	42	43	44	45
5		110	20	26	35	38	41	42
6		90	16	18	34	36	40	41
7	315	160	26	38	43	44	45	48
8		110	23	36	41	42	43	46
9		90	20	30	38	40	41	43
10	200 (with Float Valve)	160	6	16	28	31	35	37

.

Based on the experimental results, the flow capacity of infiltration wells with various specifications, composed of different components, can be simplified into a single value, greatly reducing the difficulty of parameter settings in the MIKE URBAN model. Additionally, based on these results, the influence of various factors on the drainage rate of infiltration wells can be analyzed:

(1) Effect of opening rate on drainage flow: As the opening rate increases, the drainage flow increases. In all combinations, as the opening rate increases from 5% to 30%, the drainage flow shows an upward trend. There is a diminishing marginal benefit, with some combinations showing a slowdown in the flow rate increase when the opening rate exceeds 20%. In most cases, the flow rate approaches its maximum when the opening rate is between 20% and 25%, and further increasing the opening rate has a limited impact on the flow rate. Therefore, the optimal range for the opening rate is 20% to 25%.

(2) Effect of infiltration well diameter on drainage flow: The larger the diameter of the infiltration well, the higher the drainage flow. A 315 mm infiltration well shows a 20% higher flow rate than a 200 mm infiltration well, and this growth trend follows the principle of increased overflow area in fluid dynamics.

(3) Effect of connection pipe diameter on drainage flow: As the pipe diameter increases, the drainage flow increases significantly.

(4) Effect of float ball device on drainage flow: The float ball causes a decrease in flow because it increases local resistance and limits the flow rate. However, the float ball can prevent backflow, and its use can be considered depending on the actual situation.

3.2. Pipe Diameter and Length Parameters

3.2.1. Drainage Parameter Design

In farmland drainage, the main hydraulic parameters affecting the pipeline are the drainage modulus or drainage flow rate.

The design drainage modulus (drainage flow per unit area) is typically calculated based on the design runoff depth R, and the calculation formula is as follows:

$$q={\displaystyle \frac{R}{86.4t}}$$

(2)

In the formula, $q$ is the design drainage modulus in m³/(s⋅km²); $R$ is the regional design runoff depth in mm; and $t$ is the drainage duration, taken as the crop’s allowable waterlogging duration in days.

The surface runoff coefficient of Yanggu County is higher than the average value of other counties in Liaocheng City by 0.18–0.32. The western and northwestern counties have values lower than the city’s average by 0.14–0.44. Based on this, the surface runoff in Yanggu County ranges from 0.32 to 0.44, with an average value of 0.38. Therefore, the design runoff depth is 46.70 mm.

Most of the experimental area is under dryland farming. According to the China High-Standard Farmland Construction Plan (2021–2030) [35] and the Technical Specifications for Farmland Drainage Engineering [36], the drainage standard for dryland farming is to drain the rainfall within 1 to 3 days, starting from the moment crops are submerged until there is no water accumulation on the field. In this study, the drainage standard used is to drain the 1-day rainfall within 1 day until there is no water accumulation on the field. Using Formula (2), the design drainage modulus is calculated to be 0.54 m³/(s·km²).

The design of the water conveyance pipeline should be based on the drainage capacity it is intended to carry. The design cross-section is calculated using the following formula:

$$Q_{dr}={\displaystyle \frac{1}{n}}{R_h}^{2/3}{i}^{1/2}\times \pi r^2$$

(3)

In the formula, $Q_{dr}$ represents the drainage capacity to be carried by the pipe; $i$ is the longitudinal slope of the pipe; $n$ is the pipe’s roughness coefficient; $R_h$ is the hydraulic radius of the pipe; and $r$ is the radius of the pipe.

For full pipe flow, $R_h=r/2$; hence, Formula (3) can be rewritten as follows:

$$r=({\displaystyle \frac{Q_{dr}n}{\pi i^{1/2}}}\times 2^{2/3}{)}^{3/8}$$

(4)

3.2.2. Impact Mechanism of Drainage Pipe Diameter and Length

The drainage pipe diameter is calculated based on the drainage modulus, which is 0.54 m³/(s·km²). The analysis of the main drainage influencing parameters is conducted based on the basic parameter settings, with additional analysis for 25%, 50%, 100%, and 200% variations.

The basic parameters are set as follows (

Table 3. Basic values of parameters affecting pipe diameter.

Parameter	Unit	Numerical Value
Lateral length	m	60
Collector length	m	150

):

(1) Impact of lateral length:

Figure 4 shows the effect of lateral length on both the lateral and collector diameters under drainage conditions. It can be observed that lateral length significantly affects the drainage pipe diameters, exhibiting a quadratic parabolic increase. When the lateral length is between 20 m and 180 m, the required diameter for the lateral ranges from 100 mm to 250 mm, while the collector diameter ranges from 200 mm to 450 mm. It is evident that the influence of lateral length on the main drainage pipe diameter is greater than the influence on the lateral diameter. The primary factor is that the area controlled by the collector is more significantly impacted by the lateral length, leading to a greater influence on the pipe diameter.

(2) Impact of collector length:

Figure 5 illustrates the effect of collector length on both the lateral and collector diameters under drainage conditions. It can be observed that the collector length still has a significant impact on the drainage pipe diameters, exhibiting a quadratic parabolic increase. When the collector length is between 50 m and 450 m, the required lateral diameter ranges from 100 mm to 230 mm, while the collector diameter ranges from 200 mm to 450 mm. The trend of its influence is quite similar to that of the lateral length.

3.2.3. Selection of Pipe Diameter and Length

In conclusion, under the drainage modulus of 0.54 m³/(s·km²), it is recommended to control the collector diameter between 200 mm and 450 mm and the lateral diameter between 100 mm and 250 mm. The collector length should be between 50 m and 450 m, while the lateral length should be between 20 m and 180 m.

3.3. Rainfall Boundary Condition Data

In the MIKE URBAN model, rainfall boundary data are one of the necessary input parameters. Rainfall pattern design typically refers to the setting or selection of the time-based rainfall distribution process for a design storm in drainage, flood control, or water resources planning in order to simulate or evaluate the rainfall intensity variation over time.

Using the rainfall data from the Cha Cheng meteorological monitoring station near the test area as the basis for the design rainfall, rainfall data from 1957 to 2013 were collected. The results yielded a 10-year return period rainfall of 122.92 mm, a 5-year return period rainfall of 102.29 mm, and a 20-year return period rainfall of 142.11 mm.

According to the “Design Standard for Irrigation and Drainage Engineering" (GB50288-2018) [37], the general drainage standard is typically based on a return period of 5 to 10 years. The “National High-Standard Farmland Construction Plan (2021-2030) [35]” specifies that the drainage design for dryland farming areas should have a storm recurrence period of 5–10 years. In Shandong province, a 10-year recurrence period is used. Therefore, in accordance with the above construction requirements, the preliminary drainage standard is set to a 10-year recurrence period, with the design rainfall of 122.92 mm.

The Chicago rainfall pattern is selected as the synthetic rainfall boundary data, with the rainfall design process curve shown in Figure 6.

3.4. Subdivision of Sub-Catchment Areas

A sub-catchment area refers to a smaller unit within a larger watershed or catchment area that is divided for hydrological or drainage system analysis. In each unit, precipitation or surface runoff is collected into a specific outflow point, and these smaller areas are collectively referred to as sub-catchment areas.

In the MIKE URBAN model, sub-catchment areas can be automatically delineated based on factors such as the layout of the pipeline network, topography, and rainfall conditions.

3.5. Model Accuracy Validation

To verify the application effectiveness of the MIKE URBAN model in drainage systems, this study uses the infiltration well overflow capacity test as a basis. The MIKE URBAN model is used to simulate the same conditions as the experiment, and a comparative analysis is conducted between the simulated and measured values to test the model’s accuracy. The drainage process of the experimental pool provides real hydraulic conditions, and by comparing the simulation results with the actual measured data, the reliability of the model in practical operation can be evaluated.

This study verifies the model’s accuracy using the experimental data from infiltration wells with three different diameters and six different opening rates in the unsteady head and 5 cm steady head tests. The model simulation accuracy is evaluated using the Average Relative Error (ARE). ARE < 10%, 10% < ARE < 20%, and 20% < ARE < 30% represent very good, average, and poor simulation performance, respectively.

The model verification results are shown in Figure 7 and Figure 8. Under the unsteady head condition, the ARE between the simulated and measured values for the dn200 infiltration well is 2.29%, for the dn250 infiltration well is 6.52%, and for the dn315 infiltration well is 4.41%. Under the 5 cm steady head condition, the ARE for the dn200 infiltration well is 3.17%, for the dn250 infiltration well is 4.37%, and for the dn315 infiltration well is 5.69%. The verification results indicate that the model performs well in simulating flooding and pipe drainage, with good agreement with the measured values. It can accurately simulate farmland drainage.

4. Flooding Simulation of Farmland Based on the MIKE URBAN Model

Farmland flooding refers to the phenomenon where excess water in the field cannot be drained in a timely manner, leading to excessively high soil moisture content, which in turn affects crop growth and may even result in reduced yield or crop failure. It is usually caused by multiple factors, including both natural and human factors. From a natural perspective, intense and concentrated rainfall generates a large amount of runoff in a short period of time. If the area is low-lying or the soil has poor permeability (such as clay layers or high groundwater levels), the excess rainwater will be difficult to infiltrate and drain quickly. From a human perspective, if the agricultural water infrastructure is incomplete or in poor condition, such as insufficient cross-sections of drainage ditches, inadequate pump station capacity, or lack of drainage pipe systems, and coupled with irrational land planning and blind reclamation that leads to the disappearance of natural water storage areas, these factors significantly increase the risk of flooding. Additionally, excessive groundwater extraction causes land subsidence, soil compaction, and crop root sensitivity to excess water, which further raises the probability of flooding.

In agricultural water projects, flooding not only leads to crop yield loss but can also cause a series of problems, such as soil degradation and infrastructure damage. With the increasing frequency of extreme weather events and the growing complexity of hydrological conditions, how to accurately simulate farmland flooding processes and optimize irrigation and drainage systems based on this has become an important issue to improve agricultural water resource utilization and ensure food security.

MIKE URBAN is characterized by its multi-module coupling ability, excellent visualization, and user-friendly operation. In this chapter, the MIKE URBAN model is used to simulate flooding in an experimental field in Yanggu County, Liaocheng City, Shandong Province. To consider the worst-case drainage scenario, soil infiltration was ignored in this simulation to ensure that the drainage system design can handle the maximum possible water accumulation. By simulating the drainage process in detail, we assess the drainage effectiveness of different pipeline layouts and analyze the factors influencing drainage speed. By adjusting key parameters and observing the simulation results, we further explore the “boundary effects” of these parameters, that is, the impact on drainage efficiency and system stability when parameters approach or exceed certain critical values. The above content will provide the necessary data support and theoretical basis for subsequent network economic analysis and comprehensive optimization.

4.1. Overview of the Simulation Area

In order to study the drainage performance of the irrigation and drainage network, this study selected an experimental field in Yanggu County, Liaocheng City, Shandong Province, as the simulation area, with the layout diagram shown in Figure 9. The area of the simulation block is approximately 550 m × 550 m, representing a typical farmland drainage area. The recurrence period for heavy rainfall is chosen as 10 years. The drainage requirements in this area are high. Therefore, a reasonable pipeline layout is needed to ensure that the drainage system can discharge water in a timely and effective manner to meet the farmland drainage needs.

The original layout of the area was as follows: a total of 66 infiltration wells, with a central vertical collector diameter of 315 mm, a horizontal lateral diameter of 200 mm, a lateral spacing of 100 m, a horizontal layout spacing of infiltration wells of 50 m, and a slope of 1‰.

4.2. Simulation Objectives and Parameter Settings

The main purpose of this simulation is to assess whether the original layout meets the drainage standards and to analyze the differences in drainage speed across different pipeline layouts. It aims to explore the factors affecting drainage time and their marginal effects, providing a theoretical basis for subsequent pipeline optimization. To achieve this, the simulation considers the following key variable parameters:

Collector diameter: The diameter of the collector directly affects the water flow capacity. Therefore, different collector diameters are simulated to evaluate their impact on drainage speed. The collector diameter is selected within the range of 200 mm to 450 mm.

Maximum inflow rate of the infiltration wells: The inflow rate of the infiltration wells determines the upper limit of the drainage capacity. Thus, it is adjusted to simulate the drainage effect under different maximum inflow rates. The hole opening rate is selected at 20% and above (with an infiltration well discharge flow > 27 m³/h).

Lateral spacing: The spacing of laterals affects the distribution of water flow. Appropriate lateral spacing can improve drainage efficiency. By adjusting the lateral spacing, its impact on drainage speed is explored.

Lateral diameter: The diameter of the lateral affects the flow velocity within the lateral, thus influencing the overall flow distribution of the drainage system. By adjusting the lateral diameter, the impact on water flow and drainage efficiency is further evaluated. The lateral diameter is selected within the range of 100 mm to 250 mm.

4.3. Simulation Results

By using the MIKE URBAN model, simulations were conducted for multiple different pipeline layout configurations, and each configuration was evaluated based on drainage speed. The simulation results are presented in tabular form, which lists the drainage speed under different parameter settings.

According to the Irrigation and Drainage Engineering Design Standard (GB 50288-2018) [37], the drainage system is considered adequate if floodwater is removed from the field surface within 24 h after crop submersion.

The original layout of the block included 66 infiltration wells, while the hydrological module of MIKE URBAN automatically divided the catchment area into 56 sub-catchments, resulting in the use of 56 infiltration wells.

4.4. Results Analysis

Based on the simulation results (

Table 4. Simulation results.

Serial Number	Diameter of Infiltration Well (mm)	Collector Diameter (mm)	Porosity (%)	Lateral Spacing (m)	Lateral Diameter (mm)	Whether it Meets the Requirements of Drainage	Maximum Drainage Time (h)
1	200	315	20	100 (66)	100	No	48.74
2					125	No	32.87
3					150	No	26.85
4					180	No	25.61
5					200	No	25.31
6					225	No	25.11
7					250	No	25
8					400	No	24.59
9			25	50 (56)	180	No	27.5
10					200	No	27.4
11					225	No	27.26
12					250	No	27.13
13				100 (56)	180	No	25.61
14					200	No	25.31
15					225	No	25.11
16					250	No	25
17				100 (56)	180	No	27.88
18					200	No	27.74
19					225	No	27.62
20					250	No	27.56
21	200	315	25	150 (56)	180	No	26.14
22					200	No	25.94
23					225	No	25.83
24					250	No	25.76
25				200 (56)	180	No	26.46
26					200	No	25.99
27					225	No	25.93
28					250	No	25.85
29			30	100 (66)	200	No	25.31
30		400	25	50 (56)	180	Yes	18.23
31					200	Yes	18.19
32					225	Yes	18.17
33					250	Yes	18.15
34				100 (66)	180	Yes	15.04
35					200	Yes	14.82
36					225	Yes	14.61
37					250	Yes	14.49
38				100 (56)	180	Yes	19.04
39					200	Yes	18.87
40					225	Yes	18.73
41					250	Yes	18.60
42				150 (56)	180	Yes	20.31
43					200	Yes	20.01
44					225	Yes	19.63
45					250	Yes	19.51
46				200 (56)	180	Yes	21
47					200	Yes	20.14
48					225	Yes	19.75
49					250	Yes	19.65

Note: The numbers in parentheses in the table represent the number of infiltration wells. “66” refers to the simulation based on the original layout of the block, while “56” corresponds to the simulation where the catchment areas were automatically divided by the MIKE URBAN model.

), we can analyze the drainage performance of each layout. The following is the main analysis of the results.

(1) Impact of maximum inflow of infiltration wells:

The simulation results indicate that when blocking is not considered, the maximum inflow of the infiltration well seems to have little effect on the drainage speed. Instead of using the inflow values obtained from previous experiments, a set of values increasing from small to large was artificially set for further simulation. The study found that the maximum inflow of the infiltration well has a negative correlation with the drainage time (Figure 10). Specifically, as the maximum inflow increases, the drainage time gradually decreases. However, when the maximum inflow exceeds 0.0075 m³/s (27 m³/h), the drainage speed stabilizes, and further increases in inflow no longer have a significant impact on the drainage speed. This suggests that when selecting the specifications for the infiltration well, an opening rate of at least 20% should be chosen.

(2) Impact of collector diameter:

To investigate the effect of collector diameter on drainage time, a strategy was adopted to modify the collector diameter based on the original layout, with the addition of both a larger diameter and a smaller diameter control group, as shown in

Table 5. Comparison of collector diameter.

Diameter of Infiltration Well (mm)	Collector Diameter (mm)	Porosity (%)	Lateral Spacing (m)	Lateral Diameter (mm)	Whether It Meets the Requirements of Drainage	Maximum Drainage Time (h)
200	250	20	100	200	No	44.83
	315				Yes	25.31
	400				Yes	14.82
	450				Yes	12.22
	500				Yes	8.43

.

As illustrated in Figure 11, the impact of collector diameter on drainage time follows a quadratic decreasing trend. As the collector diameter increases, the drainage speed significantly improves. This is because a larger collector diameter can better accommodate and transport water flow, thereby enhancing the overall drainage efficiency of the system.

In the simulation, with the lateral diameter and spacing kept constant, the collector diameter exhibited a negative correlation with drainage time. Therefore, the selection of the collector diameter directly influences the overall drainage capacity of the system.

(3) Impact of lateral spacing:

As shown in Figure 12 and Figure 13, the effect of lateral spacing on drainage performance is relatively complex and exhibits a synergistic interaction with the collector diameter.

When the lateral spacing is small, the high coverage density allows water to be quickly diverted into the drainage network. However, if the collector diameter is small, the inflow from multiple laterals can cause uneven flow distribution, which slows down the drainage process. Increasing the collector diameter can effectively mitigate this issue, thereby improving drainage speed.

Conversely, when the lateral spacing is large, each lateral covers a significantly larger area. Although the localized runoff can still enter the collector, the accumulation and transport distance of water at the lateral ends increases, leading to longer local drainage paths and a slower overall drainage process. Even with a larger collector diameter, this adverse effect cannot be completely offset.

Therefore, an optimal lateral spacing should be within the range of 100 m to 150 m, and its selection should be considered in conjunction with the collector diameter.

(4) Impact of lateral diameter:

To investigate the impact of lateral diameter on drainage time, a strategy was implemented to adjust the lateral diameter while maintaining a collector diameter of 315 mm and a lateral spacing of 100 m.

Drainage time decreases significantly as the lateral diameter increases. However, once the pipe diameter reaches a certain threshold, the rate of improvement gradually slows down. When the lateral diameter increases from 100 mm to 150 mm, the drainage time is drastically reduced from 48.74 h to 26.85 h, indicating that increasing the pipe diameter within the smaller size range has a substantial effect on improving drainage capacity. Primarily, this is because smaller pipe diameters often become a “bottleneck” in the system, and enlarging them can significantly alleviate drainage inefficiencies.

However, when the pipe diameter exceeds 180 mm, the reduction in drainage time becomes much less pronounced. For example, increasing the lateral diameter from 200 mm (25.31 h) to 250 mm (25.00 h) only shortens the drainage time by 0.31 h. This suggests that once the pipe diameter reaches a certain level, the water conveyance capacity is already sufficient to meet drainage demands. Further increasing the diameter yields only marginal efficiency gains, demonstrating a classic case of diminishing marginal returns.

Simulation data indicate that when the lateral diameter reaches approximately 200 mm, the reduction in drainage time levels off. In this range, the relationship between drainage efficiency and pipe diameter enters a “plateau phase”, where further increasing the pipe diameter offers little benefit but leads to higher investment and maintenance costs for the drainage network.

4.5. Summary

This chapter conducted a simulation study on the drainage network layout of the irrigation area in Yanggu County, Shandong Province, using the MIKE URBAN model. The study explored the impact of different network parameters (collector diameter, maximum infiltration capacity of the infiltration wells, lateral spacing, and lateral diameter) on drainage efficiency. Based on the analysis of the results, the following key findings regarding factors influencing drainage time were obtained:

(1) Impact of maximum infiltration capacity of infiltration wells:

As the maximum inflow capacity of infiltration wells increases, drainage time gradually decreases. However, when the inflow capacity exceeds 0.0075 m³/s (27 m³/h), the drainage speed stabilizes, and further increasing the inflow capacity no longer significantly improves the drainage rate. This indicates that a minimum perforation rate of 20% or higher should be considered when selecting infiltration well specifications.

(2) Impact of collector diameter:

The effect of collector diameter on drainage time follows a parabolic decreasing trend—as the collector diameter increases, the drainage speed significantly improves. This is because larger collectors can better accommodate and transport water flow, thereby enhancing the overall drainage efficiency. In the simulations, given constant lateral diameters and spacing, collector diameter was negatively correlated with drainage time. Therefore, the selection of an appropriate collector diameter is crucial for optimizing the overall system’s drainage capacity.

(3) Synergistic effect between lateral spacing and collector diameter:

The interaction between lateral spacing and collector diameter plays a complex role in determining drainage efficiency. Excessively small lateral spacing allows for rapid water diversion, but if the collector diameter is insufficient, multiple laterals discharging simultaneously may cause flow congestion. When collector diameter increases, congestion can be alleviated, resulting in faster drainage. Conversely, excessively large lateral spacing significantly increases the drainage area per lateral and extends the water transmission path at the lateral ends. In such cases, even if the collector diameter is expanded, it may not fully offset the inefficiencies caused by the prolonged drainage pathway. Considering both drainage efficiency and collector diameter, the optimal lateral spacing should be controlled within the range of 100 m to 150 m.

(4) Impact of lateral diameter:

As the lateral diameter increases, drainage time significantly decreases. However, after reaching a certain diameter threshold, the rate of improvement slows down. When the pipe diameter exceeds a certain level, the water conveyance capacity is already sufficient, and further enlarging the diameter only provides marginal efficiency improvements, exhibiting a typical “diminishing marginal returns” effect. Simulation results indicate that when the lateral diameter reaches approximately 200 mm, the reduction in drainage time flattens out, and in this range, the relationship between drainage efficiency and pipe diameter enters a “plateau phase”.

5. Optimization of Drainage Networks

This study is based on a 550 m × 550 m experimental field in Yanggu County, Liaocheng City, Shandong Province, where five key variables—collector diameter, lateral diameter, collector length, lateral length, and the number of infiltration wells—were set. Using a genetic algorithm, the drainage network was simulated and optimized, employing tournament selection to retain the best-performing individuals. The optimal network layout was determined with the objective of minimizing the annual cost of the drainage system.

5.1. The Composition of the Annual Cost System

In the process of pipeline network design and optimization, the annual cost system is an important indicator for evaluating the system’s economic efficiency. The annual cost is mainly composed of two parts: annual construction costs and annual operation and maintenance (O and M) costs. These two components cover various investments during the pipeline network construction process and various maintenance and operational expenditures during the network operation.

5.1.1. Annual Construction Costs (C₁)

The annual construction cost refers to the various expenditures incurred during the pipeline network construction process, including pipe laying, equipment installation, and all related construction costs. The formula for calculating the annual construction cost is as follows:

$$C_1=\xi \left(B+A\right)$$

(5)

where:

ξ—capital recovery factor, $\xi$ = ${\displaystyle \frac{{\left(1+r\right)}^y}{{\left(1+r\right)}^y-1}}$, where y is the depreciation period, taken as 30 years; r is the annual interest rate, taken as 6%.

B—Construction and installation costs, which include the following subitems:

(1)

Drainage well costs (drainage well unit price $\times$ number of drainage wells: C_m $\times$ n₂);

(2)

Pipe material cost (price per meter of pipe $\times$ length: Σ C_i$\times$l_i, i = 1, 2……);

(3)

Pipe installation cost (typically 10% of the material cost) (installation price per meter of pipe * length: Σ C_k $\times$ l_i, k = 1, 2……);

(4)

Trench excavation cost: w = $\sum \left(2dh+D_{i}h+{\displaystyle \frac{h^2}{p}}\right)\times l_i\times y_w$;

and backfilling costs: t =$\left(\sum \left(2dh+D_{i}h+{\displaystyle \frac{h^2}{p}}-{\displaystyle \frac{\pi D_i^2}{4}}\right)\times l_i\times y_t\right)$, where:

D_i is the pipe diameter in meters, i = 1, 2……; y_w is the excavation unit price in yuan; y_t is the backfilling unit price in yuan; d is the excavation width on both sides of the pipeline; h is the pipeline burial depth; p is the excavation side slope.

(5)

Other expenses x (e.g., road crossing facilities, anti-freeze facilities, etc.).

A—Independent fee, which can be calculated as A = (B + E) $\times \beta$, where β is the proportion of the total engineering investment cost and can be taken as 8%.

5.1.2. Annual Operation and Maintenance Costs (C₂)

The annual operation and maintenance costs mainly include pipeline maintenance and pipeline dredging costs (M). The calculation formula for annual operation and maintenance costs is as follows:

$$C_2=M$$

(6)

where:

M—Annual pipeline maintenance and dredging costs, M (per meter pipeline maintenance and dredging cost C_p $\times$ required maintenance and dredging pipeline length l_p), which can be taken as 0.5% of the material cost.

5.2. Objective Function

The minimization of annual costs is the core objective of this system. The annual cost F is the sum of the annual construction cost C₁ and the annual operation and maintenance cost C₂. By optimizing the network layout, equipment configuration, and system parameters. The annual cost can be minimized while meeting the drainage standards, thus achieving the most economically optimal network layout.

The objective function is as follows:

$$\min F=\xi \times (C_m\times n_2+\sum C_i\times l_i+w+t+\sum C_k\times l_i+x)+C_p\times l_p$$

(7)

5.3. Constraint Condition

5.3.1. Pipe Diameter Constraints

Due to the requirements of engineering construction, the pipe diameter should follow standard specifications. Additionally, based on the simulation results above, the constrained range for the collector diameter is determined as follows:

$$200\le D_i\le 450$$

(8)

In the equation:

$D_i$—Diameter of the i-th collector, mm.

The constraint for the lateral diameter is as follows:

$$100\le d_i\le 250$$

(9)

$d_i$—Diameter of the i-th lateral, mm.

5.3.2. Pipe Length Constraints

In practical engineering, the length of pipelines cannot be increased or decreased without limitations. Therefore, constraints should be applied to pipeline length. Within the set of pipe diameters, the constraint for the collector length is as follows:

$$50\le L_i\le 450$$

(10)

In the equation:

$L_i$—The length of the i-th collector, mm.

The constraint for the lateral length is as follows:

$$20\le l_i\le 180$$

(11)

$l_i$—The length of the i-th lateral, mm.

5.3.3. Time Constraints of Drainage

According to the “Irrigation and Drainage Engineering Design Standard” (GB 50288-2018) [37], to meet the drainage requirements, the drainage time should ensure that the water is drained to the field surface within 24 h after the crop is flooded. Therefore, the drainage time must be constrained. The constraint on drainage time is as follows:

$$0<t\le 24$$

(12)

In the equation:

$t$—Drainage time, h.

5.3.4. Constraints on Lateral Spacing

If the lateral spacing is too large, the coverage area of the infiltration wells will increase, leading to poor drainage in localized areas, which may cause water accumulation problems and fail to meet drainage requirements. When the lateral spacing is smaller, although the lateral coverage density is higher, water can be diverted more quickly into the network. However, if the collector diameter is too small, multiple laterals will merge into the collector, causing flow blockages or uneven flow distribution, which slows down the drainage speed. Additionally, the construction cost of the pipes will increase significantly, reducing the economic feasibility. Based on the above, the constraint on lateral spacing is as follows:

$$100\le p\le 150$$

(13)

In the equation:

$p$—Lateral spacing, m.

5.3.5. Flow Velocity Constraint

When the flow velocity is too low, it may result in a low drainage efficiency of the system, causing water to remain in the field for more than 24 h, failing to meet the design requirements. Additionally, sediments, suspended particles, and impurities carried by the water may accumulate at the bottom of the pipes, gradually forming sedimentation, leading to blockages and increased maintenance costs. On the other hand, when the flow velocity is too high, the fast-moving water increases the scouring force on the pipes, leading to pipe erosion. Therefore, the constraint on flow velocity is as follows:

$$0.6\le v\le 2.5$$

(14)

In the equation:

$v$—Flow velocity, m/s.

5.4. Fitness Function

In the genetic algorithm, the fitness function is used to measure the performance of an individual in the population, with the goal of evaluating and ranking individuals to ensure that better individuals can be selected and evolved. To achieve the objective of transforming the constraints into a part of the objective function during the optimization process, penalty terms are introduced in the construction of the fitness function. This means that if a solution violates the pre-set constraints, an additional penalty is added to its objective function value, which worsens its “fitness” and makes it less likely to be selected during the selection operation. The fitness function in this study can be expressed as follows:

$$F=C+P$$

(15)

In the equation:

$C$—Annual cost.

$P$—Penalty term.

5.5. Optimization Analysis of Pipeline Network

5.5.1. Algorithm Analysis

The optimization control has many parameters, with a population size of 500, a maximum of 400 iterations, and crossover and mutation probabilities set at 70% and 50%, respectively. A higher level of mandatory constraint is applied to the pipe diameter classification, with its penalty coefficient set to 10⁵ to quickly eliminate invalid individuals, while the penalty coefficient for other constraints is set to 10⁴.

In the previous iteration, the minimum fitness value significantly decreased, fully demonstrating the advantages of tournament selection. At the same time, the convergence curve showed a monotonic decrease, indicating that the offspring retained the advantages of the parents during the genetic process.

5.5.2. Annual Cost Analysis of Pipeline Network

Through the iteration of this population, as shown in Figure 14, the optimal solution for the network’s annual cost objective function is obtained after 15 genetic iterations. The fitness function rapidly decreased from an initial value of 351,000 yuan to 55,000 yuan and stabilized at convergence.

From the simulation results in the previous and current chapters, it can be seen that compared to the original layout (Scheme 35), although the number of infiltration wells, lateral diameter, and total lateral length have been reduced, the drainage time condition can still be met. According to

Table 6. Comparison between simulation results and original layout.

	Number of Infiltration Wells	Collector Diameter (mm)	Lateral Diameter (mm)	Collector Total Length (m)	Lateral Total Length (m)	Annual Cost (CNY)
Original layout	66	400	200	500	3000	59,640.67
Simulated layout	56	400	160	500	2120	45,337.86

, after optimization by the genetic algorithm, the new layout consists of 56 infiltration wells, a collector diameter of 400 mm, a lateral diameter of 160 mm, a total collector length of 500 m, and a total lateral length of 2120 m. Under this layout, the drainage time still meets the requirements, and the annual cost is 45,337.86 yuan. Compared to the original layout of the plot, not only has the layout been optimized, but the annual cost has also been reduced by 24%.

5.6. Summary

This section systematically analyzes the two main components of annual costs for irrigation and drainage networks, annual construction costs and annual operation and maintenance costs, and provides an economic evaluation basis for network optimization. During the network design process, annual construction costs include pipeline installation, equipment installation, and related construction expenses, while annual operation and maintenance costs cover pipeline maintenance, dredging costs, and other expenses. By quantifying these costs, the contribution of each cost component to the total annual cost can be clarified, providing a scientific basis for optimizing the network layout. In this chapter, the genetic algorithm is applied to the case study of the experimental fields in Yanggu County, Liaocheng City, Shandong Province. The objective is to minimize the annual network cost, subject to constraints on pipe diameter, pipe length, lateral spacing, drainage time, and flow velocity. Penalty terms are introduced, and the fitness function for the genetic algorithm is constructed. With a population size of 500, a maximum of 400 iterations, and crossover and mutation probabilities of 70% and 50%, respectively, the algorithm is iterated, and after 15 iterations, the results converge. The optimized layout results in an annual cost of 45,337.86 yuan, compared to the original layout’s cost of 59,640.67 yuan, a 24% savings in annual costs, demonstrating that network simulation and optimization can provide more rational and economical guidance for actual agricultural field layouts.

6. Conclusions

This study, based on the infiltration well overflow capacity test, quantifies the overflow capacity of infiltration wells, enabling the validation of the MIKE URBAN model. The validation results show that the Average Relative Errors (ARE) for different scenarios were 2.29%, 6.52%, 4.41%, 3.17%, 4.37%, and 5.69%, demonstrating the good simulation accuracy of the model. Furthermore, a hydraulic database for MIKE URBAN was constructed. The MIKE URBAN model was used to simulate different drainage network layouts and analyze the influence of different network parameters (e.g., maximum inflow of infiltration wells, collector diameter, lateral spacing, and lateral diameter) on drainage time. The simulation results indicate that the maximum inflow of infiltration wells, collector diameter, lateral spacing, and lateral diameter significantly affect drainage time.

The maximum inflow of infiltration wells shows a negative correlation with drainage time. As the maximum inflow increases, the drainage time decreases. However, when the maximum inflow exceeds 0.0075 m³/s (27 m³/h), the drainage speed stabilizes, and further increases in inflow have no significant impact. This suggests that when selecting the specifications for infiltration wells, an opening ratio of at least 20% should be chosen.

The influence of collector diameter on drainage time follows a quadratic decreasing pattern. As the diameter of the collector increases, the drainage speed significantly improves. This is because larger collectors can better carry and transmit water, improving the overall drainage efficiency of the system. In the simulations, with lateral diameter and spacing remaining the same, there was a negative correlation between the collector diameter and drainage time. Therefore, the choice of collector diameter directly impacts the overall drainage capacity of the system.

The effect of lateral spacing on drainage efficiency is more complex and shows a synergistic effect with the collector diameter. When the lateral spacing is small, the coverage density of the laterals is high, enabling faster diversion of water. However, when the collector diameter is small, multiple laterals converging into the collector lead to uneven flow distribution, slowing down the drainage speed. As the collector diameter increases, this congestion is alleviated, improving drainage speed. On the other hand, larger lateral spacing significantly increases the coverage area of each lateral. While the water collected from these larger areas may flow smoothly into the collector, the water flow accumulates, and its transmission distance increases, leading to longer drainage paths and slower drainage. Even if the collector diameter increases, this negative effect cannot be fully offset. Therefore, lateral spacing should be between 100 m and 150 m and should be considered in conjunction with the collector diameter.

As the lateral diameter increases, the drainage time decreases significantly, but after the diameter reaches a certain level, the rate of improvement in drainage time slows down. When the lateral diameter increases from 100 mm to 150 mm, the drainage time is reduced significantly from 48.74 h to 26.85 h. This shows that in the smaller pipe diameter range, increasing the diameter greatly improves the drainage capacity, as small diameters tend to create a “bottleneck” in the system. Expanding the diameter alleviates drainage issues significantly. When the diameter exceeds 180 mm, the reduction in drainage time continues but at a much slower rate (from 25.31 h with 200 mm to 25 h with 250 mm, only a 0.31 h decrease), suggesting that after a certain pipe diameter is reached, the water flow capacity is sufficient to meet drainage requirements. Further increases in pipe diameter only result in minimal improvements, showing typical “diminishing marginal returns.” Simulation data show that when the lateral diameter reaches about 200 mm, the drainage time reduction stabilizes. Within this range, the relationship between drainage efficiency and pipe diameter enters a “plateau phase,” and further increases in pipe diameter yield negligible benefits while increasing investment and maintenance costs.

This study, based on the 550 m × 550 m experimental field in Yanggu County, Liaocheng City, Shandong Province, sets five variables for the optimization of the irrigation and drainage network layout: collector diameter, lateral diameter, collector length, lateral length, and the number of infiltration wells. The study sets five constraints: pipe diameter, pipe length, drainage time, lateral spacing, and flow velocity, and uses a genetic algorithm to optimize the network layout. Different penalty coefficients were applied for each constraint, with a population size of 500, a maximum of 400 iterations, and crossover and mutation probabilities of 70% and 50%, respectively. After 15 iterations, the results stabilized. The optimized layout was determined with 56 infiltration wells, a collector diameter of 400 mm, a lateral diameter of 200 mm, a total collector length of 500 m, and a total lateral length of 2120 m, resulting in an annual cost of 45,337.86 yuan. This layout saved 24% in annual costs compared to the original design, demonstrating that the simulation optimization of the network can provide more rational and cost-effective guidance for actual agricultural field layouts.