Refined Simulation of Old Urban Inundation and Assessment of Stormwater Storage Capacity Based on Surface–Pipe Network–Box Culvert–River Coupled Modeling

Abstract

Old urban districts, characterized by complex drainage networks, heterogeneous surfaces, and high imperviousness, are particularly susceptible to flooding during extreme rainfall. In this study, the moat drainage district of Xi’an was selected as the research area. A refined hydrologic–hydrodynamic simulation and an assessment of drainage and flood-retention capacities were conducted based on the coupled GAST–SWMM model. Results show that the model can accurately capture the rainfall–surface–pipe–river interactions and reproduce system responses under different rainfall intensities. The box culvert’s effective regulation capacity is limited to 1- to 2-year return periods, beyond which overflow rises sharply, with overflow nodes exceeding 80% during a 2-year event. The moat’s available storage capacity is 17.20 × 10⁴ m³, sufficient for rainfall events with 5- to 10-year return periods. In a 10-year return period event, the box culvert overflow volume (12.56 × 10⁴ m³) approaches the upper limit, resulting in overtopping. These findings provide a scientific basis for evaluating drainage efficiency and guiding flood control management in old urban districts.

1. Introduction

Driven by the dual pressures of global climate change and rapid urbanization, urban flood disasters have shown a concerning trend of increasing frequency and intensity [1,2,3,4]. According to data from the World Meteorological Organization (WMO), over the past 50 years, flood-related disasters have occurred almost daily over the past five decades, resulting in an average of 115 fatalities and approximately USD 202 million in economic losses per day [5]. This trend has been strongly evidenced in recent extreme rainfall events in several megacities: during the ‘7·20’ extreme rainstorm in Zhengzhou in 2021, the cumulative precipitation reached 449 mm, with a maximum hourly rainfall of 201.9 mm, setting a new record for hourly rainfall in mainland China. In 2016, a once-in-50-years rainstorm in Xi’an led to waterlogging depths of up to 2.5 m at Xiaozhai Crossroad, paralyzing the local transportation system [6,7,8]. These cases not only reveal the vulnerability of cities in the face of extreme rainfall but also highlight the inadequacy of traditional drainage systems under new climatic conditions, underscoring the urgent need for more precise and dynamic simulation and assessment of urban flood processes [9,10].

In response, urban flood modeling has evolved significantly over the past decades. Early studies primarily focused on either surface runoff simulations using two-dimensional (2D) models or sewer network hydraulics using one-dimensional (1D) models such as SWMM. However, these standalone applications were unable to fully capture the interactions between surface and subsurface flows, thereby limiting the accuracy of urban flood process representation [11]. With an improved understanding of the integrated nature of urban flooding, researchers have increasingly recognized the limitations of single models and turned to coupled modeling approaches to achieve more comprehensive and realistic simulations. For example, some studies have achieved coupling between open-source models such as SWMM and self-developed 2D surface flow modules [12], advancing the transition from single-model applications to multi-process and multi-dimensional coupled systems.

Currently, coupled simulations have become the mainstream in urban flood research. Common approaches include (1) coupling of hydrological models with 1D hydrodynamic models, (2) coupling of hydrological models with 2D surface flow models, (3) coupling of 1D pipe or river network models with 2D surface models, and (4) full-process coupling encompassing hydrology, surface flow, pipe networks, and river networks. Among these, 1D–2D coupled models are the most widely adopted [13], typically realized through the coupling of river networks or drainage systems with surface flow modules. Depending on spatial representation and computational complexity, these couplings can be classified as semi-distributed or fully distributed. The semi-distributed coupling is often driven by a hydrological model and activates 2D inundation calculations only when pipe overflow occurs, providing a balance between computational efficiency and accuracy. In contrast, the fully distributed coupling employs complete hydrodynamic equations to explicitly describe both surface and subsurface processes, thereby achieving higher physical realism at the cost of significantly increased computational demand.

Despite these advances, old urban districts present unique challenges. The complexity of drainage networks and the diversity of underlying surfaces often limit the effectiveness of conventional models under extreme rainfall conditions [14]. Accurate flood simulation in these areas requires consideration of multiple interacting components, including underground drainage pipelines, surface roads, and open channels, which collectively determine the spatiotemporal patterns of runoff generation, convergence, and discharge [15,16,17,18,19]. For example, Min et al. [20] developed a 1D–2D coupled model for downtown Yangon, Myanmar, integrating the open-channel “minor drain system” with the “major runoff system” of streets, sidewalks, and squares. Their results highlighted the difficulty of simulating complex hydraulic interactions in historic urban areas, emphasizing the need for both advanced coupling techniques and computational efficiency [21,22].

Moreover, constrained by spatial limitations and construction conditions, drainage system upgrades in many old urban districts can only be implemented locally, resulting in multi-level drainage systems composed of pipelines, box culverts, and river networks. The hydraulic processes within these systems are highly complex, with frequent water exchanges among pipelines, box culverts, open channels, and the surface, resulting in dynamic and heterogeneous drainage pathways. Box culverts, in particular, are large drainage structures commonly found in historic city centers. Their hydraulic behavior differs markedly from both conventional pipelines and natural river channels, exhibiting pronounced transient flow characteristics [23,24]. Nevertheless, many existing models simplify them as enlarged pipes, neglecting their unique storage capacity and flow dynamics, which can compromise simulation accuracy.

In summary, flood modeling in old urban areas faces three critical challenges: (1) Model Simplification: Conventional models typically simplify the drainage network into a single layer, neglecting the intricate hydraulic interplay between the multi-level drainage infrastructures specific to old urban areas; (2) Accuracy-Efficiency Balance: High-resolution simulation of complex systems requires capturing multi-scale processes, yet traditional models struggle to balance computational demand with physical fidelity [25,26]; and (3) Unclear System Performance: The operational principles of these unique drainage systems across different rainfall return periods are not well understood, requiring comprehensive modeling to delineate the efficacy of multi-level drainage networks.

This study employs a GPU-accelerated, high-resolution coupled modeling framework that integrates the Accelerated Surface Water Flow and Associated Transport (GAST) model with the Storm Water Management Model (SWMM). This approach enables precise and efficient simulation of water exchange processes among surface flows, sewer networks, box culverts, and open channels in old urban areas. Using detailed drainage pipeline data, high-resolution digital elevation models, land-use information, and hydrological observations, we constructed an urban rainfall–runoff model that captures surface and open-channel flows, conduit flows in underground networks, and their interactions. The framework further allows quantitative assessment of box culvert drainage capacity and urban moat flood attenuation performance, providing both scientific support for urban waterlogging mitigation and a technical foundation for high-performance simulation of complex, multi-level urban drainage systems.

2. Materials and Methods

The study area includes the urban drainage network, box culverts, and the Xi’an City Moat, forming a highly complex urban drainage system. Hydrological and hydraulic interactions are considered across multiple components, including surface runoff generation, pipe network conveyance, box culvert routing, and river network flow. To accurately represent these processes, a refined urban flood-inundation model was developed using the GAST–SWMM framework, comprising surface runoff generation, pipe network routing, and coupled 1D–2D hydrodynamic simulation modules.

2.1. Surface Runoff Generation

The conservative form of the 2D shallow water equations (SWEs) is employed to simulate flow dynamics within the 2D computational domain [27,28]. Surface runoff is computed using the dynamic wave approach, with spatial discretization implemented via a finite volume Godunov scheme. Mass and momentum fluxes are evaluated using the HLLC approximate Riemann solver, and friction source terms are treated with the bed-slope flux method. To enhance numerical accuracy, a second-order TVD-MUSCL scheme is applied, and stability is ensured under the CFL condition [29,30]. Time integration is performed using a two-stage Runge–Kutta method to maintain second-order temporal accuracy [31]. GPU-based parallel computing is further employed to accelerate the simulation.

$${\displaystyle \frac{\partial q}{\partial t}}+{\displaystyle \frac{\partial F}{\partial x}}+{\displaystyle \frac{\partial G}{\partial y}}=S$$

(1)

$$q=\left[\begin{array}{c}h\\ q_x\\ q_y\end{array}\right]·F=\left[\begin{array}{c}uh\\ u{q}_x+g{h}^2/2\\ u{q}_y\end{array}\right]·G=\left[\begin{array}{c}vh\\ v{q}_x\\ v{q}_y+g{h}^2/2\end{array}\right]$$

(2)

$$S=\left[\begin{array}{c}i\\ -\mathrm{g}h\partial z_b/\partial x-C_{f}u\sqrt{u^2+v^2}\\ -\mathrm{g}h\partial z_b/\partial y-C_{f}v\sqrt{u^2+v^2}\end{array}\right]$$

(3)

where t is the time, s; q is a variable vector including the water depth h, m; q_x and q_y are the single-width flows along the x and y directions, respectively, m²/s; F and G are the fluxes along the x and y directions, respectively; g is the gravitational acceleration, m³/s; u and v are the flow velocities along the x and y directions, respectively, m/s; S is the source term vector; i is the infiltration source term; z_b is the riverbed bottom elevation; and C_f is the Xie Cai coefficient, which can be expressed as C_f = gn²/h^1/3, where n is the Manning coefficient, s/m^1/3.

2.2. Pipe Network Flow Routing

The SWMM model, developed with support from the U.S. Environmental Protection Agency, is widely used for simulating urban 1D drainage networks [32]. It solves the Saint-Venant equations to simulate flow movement within pipe networks and provides three computational approaches: kinematic wave, diffusive wave, and dynamic wave [33]. Considering that the dynamic wave method can account for inlet and outlet losses in pipe segments and simulate pressurized flow as well as other complex and variable flow conditions in closed conduits, the present study employs the dynamic wave approach for drainage network routing. The governing equations are as follows:

$${\displaystyle \frac{\partial A}{\partial t}}+{\displaystyle \frac{\partial Q}{\partial x}}=0$$

(4)

$$gA{\displaystyle \frac{\partial H}{\partial x}}+{\displaystyle \frac{\partial \left(Q^2/A\right)}{\partial x}}+{\displaystyle \frac{\partial Q}{\partial x}}+\mathrm{g}A{S}_f=0$$

(5)

where A is the cross-sectional flow area of the pipe, m²; Q is the discharge in the pipe, m³/s; x is the longitudinal distance along the fixed cross-section, m; t is time, s; g is the gravitational acceleration, m/s²; and S_f is the friction slope, $S_f=\left(K/\left(gA{R}^{4/3}\right)\right)Q\left|V\right|$, K is the resistance coefficient, $K=g{n}^2$, where n is the Manning roughness coefficient of the pipe; R is the hydraulic radius of the flow cross-section, m; and V is the flow velocity, m/s.

The inflow of surface runoff into the stormwater inlet is calculated using the weir flow equation, as follows:

$$Q=mb\sqrt{2g}{h}^{3/2}$$

(6)

where Q is the inflow of surface runoff into the stormwater inlet, m³/s; m is the discharge coefficient; b is the width of the inlet, m; and h is the water depth in the inlet, m.

2.3. 1D–2D Coupled Model

The coupling of urban surface runoff and pipe network drainage primarily involves resolving the water exchange between the 2D surface model and the 1D pipe network model. In the model, stormwater inlets or grates are conceptualized as nodes, which serve as the sole conduits for water exchange between the 2D surface model and the 1D pipe network model [34,35]. Research on water exchange between 2D surface models and 1D pipe networks remains limited, with few validations from physical experiments. Computationally, overflow and inflow are typically calculated using weir flow or orifice flow equations [36]. Therefore, in this study, the same approach is adopted for calculating water exchange at the nodes.

When the node water level Z₁ is lower than the surface grid water level Z₂, which in turn is below the surface elevation Z (Figure 1a), the inflow is calculated using the weir flow equation, as follows:

$$Q_R=m_{1}b\sqrt{2g}{\left(Z_2-Z\right)}^{3/2}$$

(7)

where Q_R is the inflow to the node, m³/s; C₁ is the orifice coefficient, [0, 1]; b is the perimeter of the pipe network node, m; Z₂ is the water level of the surface grid, m; Z is the surface elevation, m.

When the node water level Z₁ is lower than the surface grid water level Z₂, which exceeds the surface elevation Z (Figure 1b), the inflow is calculated using the orifice flow equation, as follows:

$$Q_H=m_2{A}_1\sqrt{2g\left(Z_2-Z_1\right)}$$

(8)

where Q_H is the backflow into the node, m³/s; m₂ is the orifice coefficient, [0, 1]; A₁ is the node area, m²; and Z₁ is the node water level, m.

When the node water level Z₁ exceeds the surface grid water level Z₂ (Figure 1c), the inflow is calculated based on the difference between Z₂ and Z₁, as follows:

$$Q_Y=m_2{A}_1\sqrt{2g\left(Z_1-Z_2\right)}$$

(9)

where Q_Y is the overflow from the node, m³/s, and C₂ is the orifice coefficient, [0, 1].

3. Study Area and Model Construction

3.1. Study Area

Xi’an, one of China’s first designated historical and cultural cities, is a key central city in the western region. It is situated in the Guanzhong Basin in the middle reaches of the Weihe River Basin, with an average annual precipitation of 621 mm and an average annual temperature of 13.4 °C, between 107.40°–109.49° E and 33.42°–34.45° N [37]. This study focuses on the drainage catchment of the Xi’an Moat, with a total catchment area of 34.27 km². The urban drainage system was designed based on a 3-year return period storm. The location map is shown in Figure 2.

The moat, encircling the Ming Dynasty city wall, is an artificial channel constructed during the Ming Dynasty in 1370 AD. It has a total flood storage capacity of 14.47 × 10⁴ m³ and a landscape water storage capacity of approximately 12.75 × 10⁴ m³. The channel has a perimeter of 14.6 km and a trapezoidal cross-section, with a top width ranging from 14.5 m to 54.0 m, a bottom width from 7.0 m to 24.6 m, and a depth from 4.0 m to 15.5 m. The channel slopes from higher elevations in the southeast to lower elevations in the northwest, with a bottom elevation difference of 11.3 m. The outer bank exhibits significant topographic variation, with a height difference of up to 21.6 m. As a regulating reservoir, the moat receives stormwater runoff from within the urban area and adjacent external areas. During flood seasons, it plays a critical role in stormwater drainage and temporary storage for an area of approximately 34.27 km², significantly contributing to urban flood control in Xi’an.

Reinforced concrete box culverts are installed along one or both sides (inner and outer banks) of the moat bed (see Figure 2a,b). During non-flood seasons, stormwater is discharged directly through the box culverts into the outlet pipe downstream of the drainage outfall. During flood events, the limited drainage capacity of the box culverts and outlets causes stormwater to overflow into the moat through the culverts. The floodwater is temporarily stored in the moat and is then discharged through the sluice gate at the northwestern corner of the moat.

3.2. Model Construction

3.2.1. Surface Runoff Model Construction

A surface runoff and river network routing model for the drainage sub-catchments of the Xi’an Moat was developed based on the GAST model. The underlying surface data, including land use and high-resolution digital elevation model (DEM) data, were provided by the Xi’an Municipal Institute of Surveying and Mapping. The DEM has a spatial resolution of 5 m (Figure 3a), and land use is classified into eight categories (Figure 3b): water bodies, roads, woodland, cropland, buildings, bare land, mixed-use land, and roofs. The study area covers 34.27 km², and the model is discretized into 2.444 million grids with a resolution of 5 m.

Regarding model parameterization, we first conducted preliminary parameter selection. Infiltration rates were primarily referenced from studies in regions with similar conditions [38], while Manning’s coefficients were determined mainly based on urban drainage design standards and relevant literature [39,40]. Subsequently, a trial-and-error calibration approach was employed, adjusting key parameters according to the simulation outcomes and observed data to ensure that the model could reasonably reproduce surface runoff and sewer network hydraulic behavior. The final calibrated parameters are listed in

Table 1. Manning’s Roughness Coefficients and Steady Infiltration Rates for Different Land Use Types.

Land Use Type	Manning Value	Steady Infiltration Rate (mm/h)
Water Bodies	0.010	0
Roads	0.014	0
Woodland	0.200	37.55
Cropland	0.045	20
Buildings	0.014	0
Bare Land	0.030	19.43
Mixed-Use Land	0.025	5
Roofs	0.014	0

.

3.2.2. Drainage Network Routing Model Construction

An urban underground drainage network model was constructed based on SWMM, with pipe network data provided by the Xi’an Municipal Institute of Surveying and Mapping. The model consists of 5569 nodes, one outlet, and 5570 conduits, including 5452 circular pipes and 118 rectangular box culverts. Stormwater outside the moat is conveyed through the drainage system into the outer box culverts at 27 junctions, while stormwater inside the moat is discharged into the inner box culverts at 18 junctions. The layout of the drainage network is shown in Figure 4. Both circular pipes and box culverts are made of reinforced concrete.

For the parameterization of the sewer pipes’ Manning’s coefficient, an initial value was first selected based on relevant literature [41]. Subsequently, a trial-and-error calibration was conducted, adjusting key parameters according to the simulation results and observed data to ensure that the model could reasonably reproduce the hydraulic behavior of the sewer network. The final calibrated Manning’s coefficient was set to 0.012, which not only falls within the recommended range in the literature but also achieves a good balance between physical realism and modeling accuracy.

3.2.3. 1D-2D Coupled Model Construction

The rainfall-runoff processes in the study area consist of four components: surface runoff, river network routing, drainage network routing, and box culvert routing. In the model construction, the river network and surface runoff processes are represented by a 2D model, whereas the drainage network and box culvert routing processes are represented by a 1D model. During model coupling, water exchange between the 1D and 2D domains is achieved through vertical coupling. Spatially, the drainage network is coupled with the surface, and the box culverts are coupled with the river network to enable water exchange, as illustrated in Figure 5. In the constructed coupled model, a total of 5555 coupling nodes were defined between the surface and the drainage network, and 115 coupling nodes were defined between the box culverts and the river network.

3.3. Model Validation

Rainfall events on 29 July 2024, and 11 September 2023, were selected to validate the coupled model by comparing simulated inundation locations with observed waterlogging points. On 29 July 2024, the total rainfall was 37.9 mm, with a duration of 19 h and a maximum rainfall intensity of 26.7 mm/h. On 11 September 2023, the total rainfall was 74.2 mm, with a duration of 10 h and a maximum rainfall intensity of 61.8 mm/h. The rainfall events and inundation locations are shown in Figure 6, and the simulated water depths compared with observations are summarized in

Table 2. Comparison of simulated and observed water depths for the rainfall events on 29 July 2024, and 11 September 2023.

Rainfall Event	Location	Name	Observed Water Depth (m)	Simulated Water Depth (m)	Relative Error	Average Relative Error
11 September 2023	A	Taiyi Road Interchange	0.78	0.76	2.7%	4.7%
	B	Nanshaomen	0.60	0.56	6.7%
29 July 2024	A	Taiyi Road Interchange	0.70	0.63	10.0%	5.8%
	B	Nanshaomen	0.45	0.43	4.4%
	C	Youyi Road	0.10	0.103	3.0%

. For the 11 September 2023 rainfall event, the average relative error between simulated and observed water depths was 4.7%, with a maximum relative error of 6.7%. For the 29 July 2024 event, the average relative error was 5.8%, with a maximum relative error of 10.0%. It can be observed that, for the rainfall events considered, the 1D–2D coupled model developed in this study can reliably simulate rainfall–runoff and inundation processes. The simulated inundation locations closely match the observed waterlogging points, and the relative errors in water depth are all within 10.0%, indicating that the model is capable of effectively reproducing urban rainfall and flood processes.

3.4. Rainfall Scenario Design

This research used a design rainstorm formula from the local rainfall intensity frequency (IDF) curve, and the Chicago rainfall model is used to generate the rainfall pattern.

$$q={\displaystyle \frac{2210.84\times \left(1+2.915\times lgP\right)}{{\left(t+21.933\right)}^{0.974}}}$$

(10)

where q is the designed storm intensity, L/(s·hm²); P represents the designed return period, year; and t indicates the storm duration, minutes.

Rainfall events with 1-, 2-, 5-, 10-, 20-, and 50-year return periods and a duration of 3 h were designed, and the corresponding hyetographs are shown in Figure 7. The total rainfall depths corresponding to the 1-, 2-, 5-, 10-, 20-, and 50-year return periods (with a duration of 3 h) are 13.57, 25.49, 41.24, 53.16, 65.07, and 80.82 mm, respectively. The associated peak rainfall intensities are 39.24, 73.68, 119.20, 153.64, 188.07 and 233.59 mm/h, respectively.

4. Results and Discussion

4.1. Detailed Simulation of Complex Drainage System

For the detailed simulation of rainfall-induced flooding in the Moat area, design rainfall events with 1-, 2-, 5-, 10-, 20-, and 50-year return periods and a duration of 3 h were employed. The rainfall–runoff and surface flow processes under these scenarios were simulated to evaluate the drainage capacity of the pipe network, node overflow conditions, and the spatiotemporal evolution of surface waterlogging.

The drainage performance of the pipe network under different rainfall return periods is presented in

Table 3. Statistics of Pipe Network Performance under Different Rainfall Return Periods.

Return Period	Rainfall Volume (×104 m3)	Total Drainage (×104 m3)	Number of Pipes at Full Capacity	Proportion of Pipes at Full Capacity	Total Overflow Nodes	Proportion of Overflow Nodes	Total Overflow Volume (×104 m3)
1-year	46.5	14.99	493	8.85%	244	4.38%	0.57
2-year	87.35	24.69	1531	27.49%	1064	19.11%	9.95
5-year	141.33	28.41	2644	47.48%	2142	38.46%	28.16
10-year	182.18	30.47	3188	57.25%	2862	51.39%	58.66
20-year	222.99	31.72	3637	65.31%	3348	60.12%	86.35
50-year	276.97	33.18	4013	72.06%	3636	65.29%	93.29

. For the six design rainfall scenarios, the total drainage volumes in the study area were 14.99 × 10⁴, 24.69 × 10⁴, 28.41 × 10⁴, 30.47 × 10⁴, 31.72 × 10⁴, and 33.18 × 10⁴ m³, respectively. The proportions of pipes reaching full capacity (fill ratio = 1) increased with return period, being 8.85%, 27.49%, 47.48%, 57.25%, 65.31%, and 72.06%, respectively. Similarly, the percentages of nodes experiencing overflow were 4.38%, 19.11%, 38.46%, 51.39%, 60.12%, and 65.29%, with corresponding total overflow volumes of 0.57 × 10⁴, 9.95 × 10⁴, 28.16 × 10⁴, 58.66 × 10⁴, 86.35 × 10⁴, and 93.29 × 10⁴ m³. As shown in Figure 8, the spatial distribution of overflow nodes and fully loaded pipes varies significantly with rainfall return period. Under low return period events, most pipes have fill ratios below 0.5, and only a few nodes experience overflow, primarily concentrated in areas where the drainage system is heavily loaded, which reach the overflow threshold first. As the return period increases, the number of fully loaded pipes rises, overflow becomes more widespread, and total overflow volumes increase substantially.

The results indicate that both the number and proportion of overloaded pipes and overflow nodes increase continuously with the rainfall return period. Under the 1-year return period rainfall, the proportions of overloaded pipes and overflowing nodes are 8.8% and 4%, respectively, indicating that the system operates in a generally good condition. However, starting from the 2-year return period, the proportions of overloaded pipes and overflowing nodes increase significantly, reaching 27% and 19%, respectively. In this study, a 3 h design rainfall event was used for the simulations, whereas the drainage network is typically designed based on 24 h rainfall. Due to the shorter duration, the simulated rainfall has a relatively higher peak intensity, so even 1–2-year return period events may cause full-pipe flow or local overflows in the simulation. Therefore, for the same rainfall return period, different rainfall durations can result in substantially different hydraulic loads on the drainage network.

Under the 50-year return period, more than two-thirds of the pipes are at full capacity, and a similar proportion of nodes experience overflow. The trends of node overflow and pipe overloading under different return periods are illustrated in Figure 9. A noticeable inflection point is observed between the 2- and 50-year return periods, which can be considered as the critical resilience threshold of the drainage system. Rainfall events below this threshold can be effectively managed, and the risk of urban flooding remains controllable. Once the rainfall exceeds this threshold, the system quickly approaches saturation, the drainage capacity reaches its limit, and extensive severe flooding is likely to occur.

According to statistics, the maximum surface water ponding areas under different rainfall return periods are 1.23 × 10⁴, 7.50 × 10⁴, 26.54 × 10⁴, 33.29 × 10⁴, and 47.02 × 10⁴ m³, respectively. The surface flooding conditions are shown in Figure 10. Under the 1a return period, only slight ponding occurs in some areas. Starting from the 2-year return period, the flooded area increases significantly, which is consistent with the conclusions from the pipe network drainage capacity analysis.

Under different rainfall return periods, the spatial distribution of surface flooding points remains relatively consistent, mainly concentrated in low-lying urban areas, along roads, and around transportation hubs. A comparison between Figure 8 (pipe fill ratios) and Figure 10 (flood map) shows that the spatial extent of surface flooding closely corresponds to the locations of overflowing nodes in the pipe network, further confirming the close relationship between surface ponding and the performance of the drainage system.

4.2. Flood Storage Capacity Analysis of Box Culverts

Rainfall events with 1-, 2-, 5-, 10-, 20-, and 50-year return periods, each with a duration of 3 h, were applied to evaluate box culvert discharge and overflow under different scenarios. The operational status of box culverts under different rainfall return periods is presented in

Table 4. Operational Status of Box Culverts under Different Rainfall Return Periods.

Return Period	Box Culvert Discharge (104 m3)	Box Culvert Overflow (104 m3)	Number of Overflow Nodes	Proportion of Overflow Nodes
1-year	14.38	0.00	0	0.00%
2-year	23.52	2.99	23	19.49%
5-year	24.89	9.66	62	52.54%
10-year	25.47	12.56	74	62.71%
20-year	25.85	16.94	89	75.42%
50-year	26.21	19.91	96	81.36%

. The simulation results indicate that under the six rainfall return periods, the box culvert discharge volumes are 14.38 × 10⁴, 23.52 × 10⁴, 24.89 × 10⁴, 25.47 × 10⁴ 25.85 × 10⁴, and 25.85 × 10⁴ m³, respectively; the overflow volumes are 0.00, 2.99 × 10⁴, 9.66 × 10⁴, 12.56 × 10⁴, 16.94 × 10⁴, and 19.91 × 10⁴ m³; and the proportions of overflowing nodes are 0.00%, 19.49%, 52.54%, 62.71%, 75.42%, and 81.36%, respectively.

As shown in Figure 11, under the 1a rainfall scenario, the box culverts operate normally with no overflow. Starting from the 2-year return period, overflow begins to occur, and the proportion of overflow nodes increases significantly to 19.49%. Regarding the culvert discharge, the increase from the 2- to 50-year scenarios is limited (from 23.52 × 10⁴ m³ to 25.85 × 10⁴ m³), indicating that the culvert capacity is nearly saturated. As rainfall intensity further increases, the excess water beyond the culvert’s capacity is discharged as overflow, resulting in a continuous rise in both the number of overflow nodes and the total overflow volume, reaching 81.36% and 19.91 × 10⁴ m³, respectively, under the 50-year return period.

These results indicate that the self-regulation capacity of the box culvert system begins to become insufficient under the 2-year return period, and the system is approaching a state of failure. When the rainfall return period exceeds 5-year, more than half of the nodes experience overflow, and the drainage performance of the system is severely compromised. Therefore, the culvert’s capacity to regulate urban flooding in the study area is effectively limited to rainfall intensities of approximately 1- to 2-year return periods; once this critical threshold is exceeded, its regulatory effectiveness rapidly deteriorates, significantly increasing regional overflow and flood risk.

4.3. Dynamic Flood Storage Analysis of the Xi’an City Moat

The moat in the study area, functioning as a dynamic flood-regulating facility, was evaluated under design rainfall events with 1-, 2-, 5-, 10-, 20-, and 50-year return periods and a duration of 3 h, in order to assess its flood storage and regulation performance across different scenarios. As shown in Figure 12, the volume of water overflowing from the box culverts into the Moat increases steadily with rainfall intensity, reaching 0.00, 2.99 × 10⁴, 9.66 × 10⁴, 12.56 × 10⁴, 16.94 × 10⁴, and 19.91 × 10⁴ m³, respectively. Under normal conditions, the Moat maintains a landscape water level corresponding to a storage volume of approximately 127.5 × 10⁴ m³, while its total designed flood storage capacity is 144.7 × 10⁴ m³, leaving an available flood storage space of 17.2 × 10⁴ m³. Based on the overflow data, under the 5-year return period, the box culvert overflow is 9.66 × 10⁴ m³, which is below the Moat’s available storage capacity. For the 10-year return period, the overflow increases to 12.56 × 10⁴ m³, approaching but not exceeding the storage limit. Under the 20-year return period, the overflow reaches 16.94 × 10⁴ m³, nearly fully occupying the available storage. In the 50-year return period, the overflow rises to 19.91 × 10⁴ m³, clearly exceeding the Moat’s flood-regulating capacity.

Based on the surface water inundation simulation results (Figure 10 and Figure 13), the moat begins to overflow under the 10-year return period rainfall. This indicates that although the box culvert overflow under the 10-year rainfall does not exceed the moat’s flood storage capacity, the total inflow into the moat—including direct surface runoff and box culvert overflow—already surpasses its storage limit, leading to overtopping. As the rainfall return period increases, both the overtopping volume (at Points 1 and 2) and the inundated area increase significantly (Figure 14 and Figure 15), reaching 5.19 × 10⁴ m³, 7.00 × 10⁴ m³, and 8.59 × 10⁴ m³ in volume, and 8.44 × 10⁴ m², 11.4 × 10⁴ m², and 13.00 × 10⁴ m² in area, respectively.

In summary, the effective upper limit of the moat’s flood-regulation capacity corresponds to rainfall events with return periods of approximately 5–10 years. For events exceeding a 10-year return period, its storage and regulation capacity is markedly reduced, the system gradually fails, and the risk of surface water accumulation increases.

5. Conclusions

Based on high-resolution topography, land use, drainage system, and hydrological data of the Xi’an Moat catchment, a coupled GAST-SWMM model integrating surface, pipe network, box culverts, and river was developed. The model was designed to simulate surface rainfall–runoff generation and convergence, flow dynamics within the underground drainage system, and water exchanges between surface and subsurface domains. Furthermore, the model quantified the flood-retention capacities of the box culverts and the moat, as well as their critical thresholds. The main conclusions are as follows:

(1)

The GAST–SWMM coupled model, incorporating the Surface–Pipe Network–Box Culvert–River framework, effectively reproduced the complete process, including rainfall, surface runoff generation, pipe network transport, and river network flow and overflow. The model demonstrated high accuracy in simulating complex urban hydrological and hydraulic processes, providing a reliable technical tool for urban flood risk assessment and infrastructure performance evaluation.

(2)

The study performed a high-resolution simulation of the dynamic water exchange and hydrological–hydrodynamic response within the coupled “rainfall–surface–pipe–river network” system. The model captured the full hydrological and hydraulic processes under six design rainfall events with return periods from 1 to 50 years. Simulation results indicate that the total drainage volume in the study area increased from 14.99 × 10⁴ m³ (1 year) to 33.18 × 10⁴ m³ (50 years). The system load intensified continuously, with the proportion of fully filled pipes (fill ratio = 1) rising from 8.85% to 72.06%, and the percentage of overflow nodes increasing from 4.38% to 65.29%. The total overflow volume sharply increased from 0.57 × 10⁴ m³ to 93.29 × 10⁴ m³. The model accurately captured the spatiotemporal dynamics of surface runoff generation, convergence, infiltration, and surface–pipe water exchange, revealing the system’s dynamic response mechanisms under varying rainfall intensities.

(3)

The study revealed in detail the dynamic response and critical thresholds of the “rainfall–surface–pipe–river network” system. Simulation results indicate that the drainage capacity of the box culverts approaches saturation under the 2-year return period rainfall (23.52 × 10⁴ m³), with their effective regulatory capacity limited to approximately the 1- to 2-year return periods. Beyond this standard, the overflow volume increases sharply (reaching 19.91 × 10⁴ m³ under the 50-year return period), with the proportion of overflow nodes exceeding 80%. For the moat, when maintaining the landscape water level, the available storage capacity is 17.2 × 10⁴ m³, corresponding to an effective regulation capacity of roughly the 5- to 10-year return period. Under the 10-year return period, the culvert overflow (12.56 × 10⁴ m³) nearly reaches this regulation limit, and overtopping begins to occur.

6. Discussion and Outlook

This study developed and validated a high-performance, high-precision coupled model integrating surface flow, sewer networks, box culverts, and river networks, providing a powerful tool for understanding and simulating the dynamic response of complex drainage systems in old urban areas under extreme rainfall. However, the value of any model lies not only in its simulation capabilities but also in its contribution to scientific understanding and practical guidance for engineering applications. Accordingly, this section discusses the key findings of this study and outlines potential future applications and developments.

6.1. Discussion

(1)

Assessment and optimization of drainage system capacity

The model can accurately identify system bottlenecks, such as critical inundation areas and the corresponding rainfall thresholds. Based on these insights, engineers can use the model to test and compare various improvement measures (e.g., pipe diameter enlargement, construction of retention/detention basins, or distributed green infrastructure), enabling a fully quantitative design process from “problem diagnosis” to “solution optimization” and significantly improving investment efficiency.

(2)

Flood control scheduling and risk management for river channels

The model provides crucial technical support for optimizing real-time flood operations. Simulation results allow quantification of the flood mitigation effect of preemptive discharge from urban moats before heavy rainfall, effectively reducing the risk of overflow in critical sections. This analysis provides a quantitative basis for developing science-based, forecast-informed, dynamic river management strategies, shifting from passive emergency response toward proactive, adaptive risk management.

(3)

Enhancing overall system resilience

The true value of the model lies in its forward-looking capabilities. By inputting design storms under future climate scenarios, the model can “stress-test” existing infrastructure to assess its long-term reliability. This allows decision-makers to move from reactive responses to proactive planning, prioritizing reinforcement or redundancy for the most vulnerable components, thereby supporting climate-adaptive infrastructure development and long-term resilience strategies.

6.2. Outlook

The strengths of this study largely stem from the availability of refined datasets. However, its reliance on detailed underground drainage data-such as geometric configurations and topological connectivity-poses a major obstacle to its wider application in data-scarce areas. In addition, the model’s complexity and relatively high computational cost impose certain requirements on users’ expertise and computational resources. These are common challenges faced by physically based models in the pursuit of high fidelity. Recognizing such limitations is not an endpoint, but rather a new starting point toward broader applicability. The outcomes of this study have laid a crucial foundation for developing the next generation of versatile flood modeling toolkits. Future research can be deepened in the following directions:

(1)

Serving as a benchmark for simplified models

The validated high-precision model in this study can serve as a reliable “virtual reality.” The high-fidelity datasets it generates under various scenarios-such as surface water depth and sewer flow-can be used to calibrate, validate, and optimize key parameters of simplified or conceptual models designed for data-scarce regions, thereby substantially improving their physical soundness and predictive accuracy.

(2)

Developing a hierarchical and hybrid modeling strategy

For large cities or metropolitan regions, a flexible modeling paradigm can be established. In data-rich core or high-risk areas, the refined framework presented here can be used for detailed simulation and design evaluation, while in data-scarce peripheral or preliminary screening zones, the calibrated simplified models can be employed. The two components can be dynamically coupled with their boundaries, achieving an optimal balance between precision and efficiency.

In summary, this study not only provides specific technical solutions for flood mitigation in the case region but, more importantly, establishes a highly reliable benchmark that bridges the gap between “high-fidelity research” and “broad-scale application.”