Multi-Scale Simulation of Urban Underpass Inundation During Extreme Rainfalls: A 2.8 km Long Tunnel in Shanghai

Abstract

Urban underpasses are critical flood-prone hotspots during extreme rainfall, posing significant threats to urban resilience and infrastructure safety. However, a scale gap persists between catchment-scale hydrological models, which often oversimplify local geometry, and high-fidelity hydrodynamic models, which typically lack realistic boundary conditions. To bridge this gap, this study develops a multi-scale framework that integrates the Storm Water Management Model (SWMM) with 3D Computational Fluid Dynamics (CFD). The framework employs a unidirectional integration (one-way forcing), utilizing SWMM-simulated runoff hydrographs as dynamic inlet boundaries for a detailed CFD model of a 2.8 km underpass in Shanghai. Simulations across six design rainfall events (2- to 50-year return periods) revealed two distinct flooding mechanisms: a systemic response at the hydraulic low point, governed by cumulative inflow; and a localized response at entrance concavities, where water depth is rapidly capped by micro-topography. Informed by these mechanisms, an intensity-graded drainage strategy was developed. Simulation results show significant differences between different drainage strategies. Through this framework and optimized drainage system design, significant water accumulation within the underpass can be prevented, enhancing its flood resistance and reducing the severity of disasters. This integrated framework provides a robust tool for enhancing the flood resilience of urban underpasses and offers a basis for the design of proactive disaster mitigation systems.

1. Introduction

The increasing frequency of extreme rainfall events, compounded by extensive impermeable surfaces in urban areas, has exacerbated urban flooding risks [1,2]. Among vulnerable assets, road underpasses and tunnels are particularly hazardous due to their topographically low-lying nature, often leading to rapid inundation, traffic disruption, and safety threats [2,3]. Therefore, the flood resistance of underpasses is much lower than that of other urban infrastructures, and they are often the most severely affected by heavy rain [4]. In order to improve the overall urban resilience and ensure the sustainable development of the city, it is necessary to explore a method to effectively improve the flood resistance of underpasses.

The conventional hydrological analysis for urban road tunnels primarily involves a runoff risk assessment method, which typically begins by defining the tunnel’s geometry, allowable water depth, and design storm characteristics [3]. The runoff from each portal is routed to create inflow hydrographs, and the system’s hydraulic capacity (gravity and pump drainage) is subsequently evaluated to confirm pumps can handle the design flow [5]. Data such as high-resolution Digital Elevation Models (DEMs), rainfall or radar data, land use/imperviousness maps, soil conditions, and existing drainage infrastructure are integrated within a Geographic Information System (GIS) framework [6].

Computational Fluid Dynamics (CFD) offers a technically feasible approach for high-resolution simulation of flow within tunnels, providing indispensable insights into critical zones, pump intake design, and local flood damage mitigation [7]. However, applying CFD to long, confined tunnels presents multiple challenges: high computational cost, the dependence on accurate time-varying inlet conditions from catchment models, the difficulty in reliably capturing free-surface and turbulent flow features, and a general lack of field measurement data for validation [8]. Current research on urban flooding heavily relies on the simulation and calibration of rainfall-runoff models. Numerous studies have employed commonly used models, such as MIKE (Modeling Environment for Water Resources), SWMM (Storm Water Management Model), and InfoWorks (Innovyze InfoWorks), to effectively simulate both surface waterlogging and sewer drainage processes triggered by heavy rainfall in urban areas [9,10,11]. Specifically, the SWMM has found widespread application in assessing the effects of different return periods, drainage conditions, and the effectiveness of sponge city measures [8,9,10,11].

To extend the applicability scale of such models, many studies have integrated SWMM with other modeling frameworks. For instance, SWMM has been coupled with LISFLOOD-FP for 2D modeling of urban flash floods [8], and with TELEMAC-2D in the STUFMS model to simulate water exchange between surface and subsurface systems [12]. Similarly, coupled models such as WRF-SWMM have been developed for urban flood forecasting [13]. The reliability of SWMM has been validated by its consistency with observed urban flood data [14], and real-time calibration methods have been proposed to enhance its accuracy during flood events [15]. Collectively, these studies demonstrate that existing rainfall–runoff models are capable of addressing a broad spectrum of urban flood simulation needs, and multi-scale information simulation can be achieved by integrating other platforms or models.

For fine-scale hydrodynamic analysis, CFD has been widely utilized to investigate fluid motion in simulated flow fields, including air-water two-phase flows in hydrological contexts [16]. CFD is frequently applied to analyze water-related structures and equipment [17,18,19,20,21], identify urban flood risk zones and drainage bottlenecks [22,23], and simulate flows within drainage networks and stormwater facilities [24,25,26,27,28,29]. These applications demonstrate CFD’s capability to realistically simulate the complex water-air interactions and to accurately capture the development of water accumulation in localized areas such as underpasses.

While catchment-scale rainfall–runoff models are well-suited for city- or watershed-scale simulations, they often oversimplify complex geometries and internal flow paths, thus lacking the resolution to accurately simulate localized inundation dynamics inside specific underpasses. Conversely, although CFD can resolve such details, it cannot independently generate accurate upstream inflow boundary conditions.

To address this gap, this paper proposes a novel integrated methodology that integrates catchment-scale runoff generation with high-fidelity 3D CFD simulation to comprehensively model the flooding process in urban underpasses. The specific objectives are as follows: (1) To develop an integrated SWMM-CFD framework that directly uses SWMM-simulated runoff hydrographs as dynamic boundary conditions for the CFD model; (2) to apply this framework to identify inundation hotspots in a real-world underpass under various design rainfall events; and (3) to demonstrate the utility of the framework for evaluating and optimizing the design of drainage systems inside the underpass.

2. Methods

2.1. Overall Research Framework

This paper proposes a method for analyzing water accumulation in urban underpasses during heavy rainfall events. The method consists of two modules: a rainfall-runoff simulation module and a water accumulation process simulation module. Due to the accessibility, user-friendly operation, comprehensive functionality, and support for complex network systems, SWMM was selected for the rainfall–runoff simulation to effectively visualize areas affected by urban waterlogging, and CFD software 2020 was employed for simulating water accumulation at a small scale (tunnels/underpasses).

The specific workflow is illustrated in Figure 1. First, a rainfall–runoff model of the study area is established based on geographic information. This model simulates and obtains the inflow volume at the underpass entrances under specified rainfall intensity conditions, from which runoff velocity data at the entrances are derived. Second, a detailed 3D model of the underpass is constructed. The runoff velocity data are applied as boundary conditions to simulate the inflow into the underpass under actual heavy rainfall. Subsequently, the CFD simulation is performed to capture the movement of stormwater runoff inside the underpass, thereby achieving a full-process simulation of water accumulation. This process allows for the determination of waterlogging characteristics and the generation of a water level hydrograph (the variation in water depth over time).

The simulation parameters were established in accordance with the Standard for Design of Outdoor Wastewater Engineering (GB 50014, Standard for design of outdoor wastewater engineering, China Planning Press Co., Ltd.: Beijing, China, 2021.). Two primary criteria define the hydraulic performance assessment: (1) A water depth exceeding 0.15 m in any travel lane is classified as a ponding event, so this value serves as the critical failure threshold for the underpass analysis; (2) for critical arterial roads in central urban zones, the standard mandates that accumulated water must be cleared within 0.5 to 2 h following the cessation of rainfall.

2.2. Catchment Runoff Simulation (SWMM)

2.2.1. Case Overview

This study focuses on an urban underpass tunnel in Shanghai, simulating and analyzing its internal water accumulation under heavy rainfall conditions. This tunnel area has been significantly affected by thunderstorms and typhoons during the summer. Coupled with its flat terrain and inadequate surface drainage capacity, the region faces a high risk of urban waterlogging. The total length of the underpass tunnel is 2800 m, with a height difference of 40 m between its lowest point and the ground surface. A photograph of the tunnel entrance is shown in Figure 2, while its layout plan and standard cross-section are presented in Figure 3 and Figure 4, respectively.

2.2.2. Pipe Network Skeletonization and Sub Catchment Delineation

Based on the planned stormwater trunk network and existing pipe/manhole data, the drainage system was skeletonized in ArcGIS 10.8. Pipe layouts were replaced with line features, and manholes were represented as point features (nodes). In total, 242 nodes and 246 pipe sections were defined, including 5 grounding points for the underpass tunnel and the rest as stormwater inlets. Among these, five sections represent the open rectangular slopes of the underpass, while the remaining circular pipes convey stormwater toward the outlets. Six outlets were identified: five correspond to tunnel entrances, and one serves as the system outlet. After skeletonization, all nodal and pipe attributes were assigned. A simplified drainage network is shown in Figure 5. Sub-catchments were delineated using the Thiessen polygon method in ArcGIS, which assigns each area to the nearest node, ensuring boundaries are equidistant between adjacent nodes. The automated delineation created one sub-catchment per node (Figure 6).

Key parameters were calculated and assigned to each sub-catchment to build the stormwater model, including average slope, flow length, and area. Slope data is derived from elevation points on drawings and converted into slope using ArcGIS’s built-in tools; flow length and area data are derived from pre-defined sub-catchment results. For parameters that could not be directly derived, values recommended in the SWMM manual [30] were adopted, as follows.

For the various Manning coefficients, the SWMM manual recommends a Manning coefficient of 0.011 for concrete or asphalt, and 0.2 for turf and soil. The roughness coefficient for pipes is taken as a smooth steel pipe surface. For depression water storage parameters, the American Society of Civil Engineers recommends a water storage of 1.6 mm for impermeable areas and 6.4 mm for permeable areas. For permeability parameters, the most suitable permeability parameters for Carnegie sandy loam soil in Shanghai were selected from the SWMM manual. User-input units of measurement are automatically converted to SI units within the program. The SWMM manual provides specific explanations regarding parameter sensitivity, with area parameters and impermeability showing the most significant sensitivity. Area parameters are calculated using ArcGIS software; impermeability is determined according to the Shanghai Urban Drainage Design Manual, with 0.8 for residential land and 0.9 for roads. The sensitivity of the remaining parameters decreases as rainfall intensity increases. In the high-intensity rainfall data generated in this paper, the influence of the remaining parameters on the results can be ignored, as shown in

Table 1. Parameter values for the stormwater model of the underpass tunnel.

Parameter	Meaning	Value
N-Imperv	Manning’s n for impervious areas	0.011
N-Perv	Manning’s n for permeable areas	0.2
N-Conduit	Pipe roughness coefficient	0.01
Dstore-Imperv	Depression storage for impervious areas (mm)	1.6
Dstore-Perv	Depression storage for permeable areas (mm)	6.4
Zero-Imperv	Imperviousness of areas without depression storage (%)	25
MaxRate	Maximum infiltration rate (in/hr)	14.77
MinRate	Minimum infiltration rate (in/hr)	1.77
Decay	Infiltration decay coefficient (hr-1)	19.64
Imperv	Imperviousness (%)	80

.

2.2.3. Rainfall Generation

The study area experiences rainfall characterized by high intensity, short duration, and spatial concentration. To represent these features, intense, short-duration events were simulated using the Chicago rainfall pattern, which effectively captures peaked storm profiles. Rainfall intensity was input into the SWMM based on the local standard intensity formula (Equation (1)), with the area classified as a major urban center.

$$q={\displaystyle \frac{9.58(1+0.846\mathit{lg} P)}{(t+7{)}^{0.656}}}$$

(1)

where q denotes design rainfall intensity, mm/min; P denotes design return period, in years; t denotes rainfall duration time, in min.

Six design rainfall events were defined with exceedance probabilities of 50%, 20%, 10%, 5%, 3.3%, and 2% (corresponding to return periods of 2, 5, 10, 20, 30, and 50 years, respectively). Each event had a duration time of 180 min, with a peak intensity location coefficient r of 0.405.

2.2.4. Runoff Data Extraction at Tunnel Entrances/Exits

The generated rainfall time series was input to the SWMM as precipitation data. To extract runoff hydrographs at the tunnel portals, the road sections at each entrance and exit were conceptualized within the SWMM as open-channel pipe segments. These simplified segments were assigned an open rectangular cross-section, with their widths matching the dimensions from the engineering drawings, as shown in Figure 7.

2.3. Underpass Inundation Simulation (CFD Model)

2.3.1. Geometric Model Construction

A detailed 3D geometric model of the underpass was developed based on the construction design drawings. In plan view, the tunnel exhibits a roughly “7”-shaped alignment, oriented north–south. The northern end incorporates a 90° bend connecting to an east–west highway, while the southern end adjoins a north–south main road. The total tunnel length is approximately 2.8 km, with a maximum elevation difference of 40 m between its highest and lowest points, resulting in a longitudinal profile that descends and then ascends.

To balance computational efficiency and simulation accuracy, the model was selectively refined. Key geometric parameters that critically influence inundation depth were preserved faithfully, including tunnel floor elevation, centerline axis, and bottom cross-sectional shape. Given the higher flooding risk, only the lower level of the underpass was modeled. Its original cross-section (Figure 8a) was simplified by approximating curved elements with straight-line segments. The longitudinal ditches on both sides of the road are omitted, and the road surface is directly connected to the crash barrier. Because the cross-sectional area of the ditch is very small, its impact on water accumulation is minimal. Furthermore, calculations show that the area of the lower half of the original cross-section is 15.065 m², while the area of the lower half of the simplified cross-section is 15.108²; the difference between the two is less than three-thousandths, which can be considered as simplification based on the principle of equivalent area (Figure 8b). The final 3D model was generated by ArcGIS 10.8extruding this simplified cross-section along the derived centerline axis, as shown in Figure 9.

2.3.2. Mesh Generation and Numerical Setup

A structured hexahedral mesh was generated for the computational domain. To capture free-surface dynamics and flow gradients accurately, the mesh was refined in regions of high curvature and near the bottom boundary. The meshing strategy prioritized vertical resolution near the ground, with progressive coarsening toward the top and along the longitudinal axis to optimize computational efficiency. The base mesh size was 5 m. To resolve the near-ground flow, an inflation layer (expansion layer) was implemented, consisting of 20 layers originating from the ground surface. These layers utilized a growth rate of 1.2, with the thickest layer capped at 3 m. This vertical refinement was applied independently of the longitudinal and transverse densities to maintain a manageable total element count. The final mesh consists of 59,602 elements and 36,024 nodes.

To properly resolve wall-bounded flows, a boundary-layer mesh was implemented with a y⁺ value maintained between 30 and 60. This range is critical for the realizable k-ε turbulence model used in the simulation, which requires y⁺ > 30 for the application of standard wall functions. Because the y⁺ values align with the structural requirements of the turbulent boundary layer, the mesh is considered suitable for this study (Figure 10).

2.3.3. Water Level Identification and Data Processing Method

The water surface within the computational domain was captured using the Volume-of-Fluid (VOF) method. The CFX module in ANSYS2025R1 automatically maintains interface clarity by using its built-in high-resolution numerical format, thus eliminating the need for a separate interface compression scheme. The numerical framework employed the Realizable k-ε turbulence model with standard wall functions and the Pressure-Implicit with Splitting of Operators (PISO) scheme for pressure–velocity coupling, utilizing a second-order implicit temporal discretization. To ensure numerical stability while maintaining computational efficiency, a constant time step of 10 s is used. The convergence criteria for each time step are ensuring that the residuals of continuity, momentum, and turbulence equations decrease to below 1 × 10⁻⁴, and that the calculated Courant number is less than 0.5, meeting the requirements of the turbulence model. Regarding boundary conditions, the tunnel’s end faces were defined as inflow boundaries, where water enters at a specified velocity, and air is permitted to flow freely in and out, except at water-covered interfaces. The channel locations within the tunnel were designated as outflow boundaries, with water exiting the domain based on a prescribed mass flow rate. To verify the physical integrity of the simulation, multiple monitoring points were placed at the inflow and outflow boundaries to ensure the absence of non-physical reflections or numerical instabilities.

In the VOF formulation, the volume fraction of water (α) in each computational cell defines the phase: α = 0 for a cell full of air, α = 1 for full water, and the α = 0.5 iso-surface represents the air–water interface (Figure 11). To accurately resolve the water surface elevation, the mesh was refined in the vertical direction. The instantaneous water level at a given cross-section was determined by an averaging algorithm: extracting the elevations of all grid nodes within the section with α values between 0.25 and 0.75 and computing their arithmetic mean. This processed data was then used to generate water-depth hydrographs at specified locations over time.

3. Results and Discussion

3.1. Rainfall–Runoff Simulation Results (SWMM Output)

The design rainfall hyetographs for different return periods are presented in Figure 12, and the corresponding simulated runoff at the tunnel portals is summarized in

Table 2. Simulation results for underpass tunnel inlet/outlet under different rainfall return periods.

Return Period (Year)	Tunnel Inlet/Outlet Location	Maximum Flow Velocity (m/s)	Maximum Depth (m)	Maximum Flow Rate (m3/s)
2	North	1.90	0.05	0.66
	South	1.81	0.05	0.62
5	North	2.10	0.05	0.85
	South	2.01	0.05	0.81
10	North	2.24	0.06	0.99
	South	2.14	0.06	0.95
20	North	2.36	0.06	1.14
	South	2.26	0.06	1.08
30	North	2.43	0.07	1.22
	South	2.32	0.07	1.17
50	North	2.51	0.07	1.33
	South	2.40	0.07	1.27

. Since the CFD simulation requires runoff velocity as the inflow boundary condition, two methods were evaluated to derive this velocity: (1) direct use of the velocity output from SWMM, and (2) calculation by dividing the SWMM-simulated flow rate by the cross-sectional area of the tunnel entrance. A comparison of the velocity and flow rate time series used in both approaches is provided in Figure 13.

The results shown in Table 2 and Figure 12 and Figure 13 reveal several key patterns. First, both flow rate and velocity peaks are slightly higher at the north entrance than at the south entrance. Second, their temporal trends correspond closely to the rainfall hyetograph, showing a single-peak shape whose magnitude scales with the return period. Critically, runoff continues to enter the underpass well after rainfall ceases, as evidenced by the prolonged recession of the flow curves compared to the rainfall hyetograph. The CFD simulation must therefore extend beyond the 180 min rainfall duration to capture this effect. Third, comparing the two velocity sources shows that velocities calculated from flow rate are more accurate than those output directly by SWMM. Therefore, the derived velocity data were selected as the dynamic inflow boundary condition for all subsequent CFD simulations.

3.2. Inundation Dynamics Under Undrained Conditions (CFD Simulation Results)

3.2.1. Identification of Critical Inundation Hotspots

Based on the observation images from the on-site cameras, three relatively obvious water accumulation points were observed in the underpass under heavy rain conditions, as illustrated in Figure 14. These three primary water accumulation points were identified: Point A, at the north-end bend; Point B, at the mid-section lowest point; and Point C, within the southern horizontal concavity. The 90° bend at Point A locally obstructs flow, but the continuing downward slope limits ponding depth below the 0.15 m regulatory threshold, thus excluding it from further analysis. Point B, as the tunnel’s lowest elevation, receives converging flow from both entrances, leading to significant accumulation. Point C, characterized by a long, near-flat concave profile, traps most of the runoff entering from the south, also resulting in substantial ponding.

To establish a baseline for hydraulic behavior, initial CFD simulations were conducted under undrained (free-flow) conditions. By disregarding outflow mechanisms, the model ensures all incoming runoff is retained, allowing for a rigorous analysis of maximum accumulation and flow trajectories. Based on calculated velocity data, the runoff generated by a 180 min rainfall event reaches the underpass over a total duration of 190 min. The active inflow boundary was maintained until the 190 min mark to account for the cessation of runoff. The total simulation time was set to 210 min. This includes a 20 min redundancy period post-runoff to ensure complete hydraulic stabilization and ponding formation. This duration was selected to balance model accuracy with computational efficiency.

3.2.2. Temporal Evolution of Water Accumulation

Based on the identified critical points, the temporal evolution of water accumulation was analyzed in detail at Points B and C, excluding Point A due to its relatively low depth. Time-series curves of water depth under six different rainfall return periods were extracted for each point, illustrated in Figure 15 and Figure 16.

At Point B (Figure 15), water accumulation began approximately 30 min after the onset of rainfall and continued to increase throughout the 210 min simulation. The slope of the depth–time curve changed around the 60 min mark, indicating a shift in the accumulation rate. The most pronounced depth increase occurred under the 50-year return period, while the 2-year event showed the gentlest rise. For return periods between 2 and 50 years, the depth curves exhibited oscillatory increases and intersected with one another. Except for the 2-year event, which reached the 0.15 m threshold at 60 min, all other return periods exceeded this level within 45 min. As Point B is positioned at the lowest elevation of the tunnel profile, it acts as a hydraulic sink. It receives and concentrates runoff from both northern and southern entrances. Consequently, the onset of ponding (after ~30 min) is governed by the upstream concentration time. Its water depth and growth rate are highly dependent on the total inflow volume and intensity. Thus, it exhibits pronounced variability across different return periods: greater rainfall intensity leads to faster concentration and larger inflow, resulting in a more rapid rise and a higher peak depth. The entire process reflects a system-scale hydrological response.

At Point C (Figure 16), water accumulation began rapidly at approximately t = 15 min. For all return periods except the 2-year event (which reached the mark at 40 min), water levels surpassed the 0.15 m threshold within the first 30 min. The subsequent water depth profile exhibited an oscillatory trend, which can be categorized into four distinct phases:

Phase I (0–30 min): Initial Accumulation. Despite relatively low initial rainfall intensity, the water level rose sharply. This is attributed to the V-shaped or trapezoidal geometry of the tunnel; the narrow base causes even low runoff volumes to result in significant depth increases.

Phase II (30–120 min): Geometric Buffering. As rainfall intensity and runoff volume increased during the early-to-mid stage of the storm, the rate of depth increase slowed. This deceleration is due to the increasing horizontal cross-section of the tunnel at higher elevations, which requires a larger volume of water to achieve the same incremental rise in depth.

Phase III (120–150 min): Volume Dominance. During the mid-to-late stage, although rainfall intensity began to decline from its peak, the cumulative runoff volume increased drastically. This surge overwhelmed the geometric expansion of the tunnel, triggering a second rapid rise in water depth.

Phase IV (Post-150 min): Peak and Stabilization. In the final stage and the period following the cessation of rainfall, runoff subsided. The water depth at Point C reached a maximum of 0.9 m, where it subsequently stabilized and fluctuated due to residual flow dynamics.

The contrasting ponding behaviors at Points B and C are fundamentally rooted in their distinct topographical features and spatial positions within the tunnel.

Located near the southern entrance within a local depression (concave section), Point C acts as a localized storage zone. Its inundation is driven by unilateral inflow from the southern portal. Due to the short flow path and the local concavity, Point C exhibits an extremely rapid response (~15 min). The process is dominated by local micro-topography: the concave cross-section provides significant storage capacity, while the minimal longitudinal slope severely restricts gravitational drainage. Consequently, the water level rises rapidly to a topographically defined equilibrium (~0.9 m). Once this threshold is met, Point C transitions from a storage buffer to an overflow source, where subsequent fluctuations reflect the balance between variable inlet flow and spillage dynamics.

In contrast, Point B serves as the primary hydraulic sink, situated at the lowest point of the tunnel’s longitudinal profile. Its behavior is governed by catchment convergence, receiving runoff from both the northern and southern entrances. This results in a slower, more cumulative response compared to Point C. The water depth at Point B shows a strong positive correlation with rainfall intensity, reflecting the inherent bottleneck effect of the tunnel’s overall drainage system. Point C significantly modulates the flood progression toward the tunnel’s center. Until the 150 min mark, Point B is primarily affected by inflow from the north, as Point C captures and stores the southern inflow. Once Point C reaches its 0.9 m capacity, it begins to overflow toward Point B. Interestingly, this overflow introduces a velocity buffering effect: water entering Point C at a specific velocity loses its kinetic energy as it is integrated into the standing pool; when it eventually overflows, it must re-accelerate under gravity toward Point B. This energy dissipation and storage delay effectively slow the accumulation rate at Point B, highlighting the decisive role of entrance-area micro-topography in mitigating or staggering flash inundation within the tunnel.

In summary, location dictates the core mechanism of the ponding pattern. Point B represents a systemic hydrological response, requiring mitigation focused on managing the integrated catchment runoff. Point C represents a localized hydraulic obstruction, where mitigation hinges on improving local drainage conditions. This clear contrast provides direct theoretical justification for subsequent targeted and differentiated drainage design strategies.

3.2.3. Key Inundation Characteristics Comparison

Both locations exhibit water-depth curves with a fluctuating, upward trend, which results from the complex interaction between time-varying inflow, turbulent flow structures, and the geometric constraints of the tunnel. To quantify the inundation behavior, two key metrics were extracted from the water-depth time series at Points B and C: (1) the time required to reach the 0.15 m warning threshold, and (2) the maximum (peak) ponding depth. These are summarized in Figure 17 and Figure 18, respectively.

Figure 17 implies that the time for water depth at Point B to reach 0.15 m decreases systematically as the rainfall return period increases, which is attributed to the higher rainfall intensities associated with longer return periods. In contrast, the time-to-threshold at Point C shows little sensitivity to the return period, remaining under 30 min for most events.

The peak depth also responds differently to different return periods between points (Figure 18). The peak water depth at Point B scales with the return period, reflecting increased cumulative inflow to this low point. Conversely, the depth at Point C plateaus at ~0.9 m for all return periods. This upper limit is determined by the geometry of Point C, because the minimum height difference between Point C and the two ends is 0.9 m. When the water depth reaches 0.9 m, the excess water will overflow and flow to Point B, thus limiting further water accumulation at Point C.

3.3. Performance Evaluation and Optimization of Drainage Designs

3.3.1. Drainage Schemes Design and Setup

Building upon the inundation characteristics identified under undrained conditions, a targeted drainage strategy was developed for the critical accumulation Points B and C. The primary objective was to ensure that post-mitigation water depths align with the safety thresholds specified in the “Standard for Design of Outdoor Wastewater Engineering” (GB 50014). For the conceptual design of the drainage outlets at both locations, the dimensions were maintained at a width of 0.6 m and a length of 7.5 m, consistent with the engineering specifications. Given the relatively large gaps in the drainage grates, the CFD simulation assumed that discharge occurs uniformly across the entire ditch area. Consequently, the entire top surface of the ditch was modeled as a boundary condition for the drainage outlet (Figure 19 and Figure 20).

To evaluate whether the drainage system satisfies these regulatory requirements, the simulation timeframe was structured as follows: (1) The inflow boundary remains active until t = 190 min, which accounts for the 180 min rainfall duration plus an additional 10 min to capture residual surface runoff entering the underpass; (2) the simulation continues for a post-rainfall window of 110 min (approximately 1.83 h), as a recession and compliance phase. The model is executed for a total of 300 min (5 h). This 300 min window provides sufficient duration to verify if the water depth recedes below the 0.15 m threshold within the mandated 2 h post-rainfall limit. This timeframe optimizes computational efficiency while ensuring a rigorous verification of regulatory compliance.

Since the variation in hydraulic head during the drainage phase is relatively small compared to the total pump head, a constant rated discharge (1.38 m³/s) provides a conservative and computationally efficient estimate. The head at Points B and C remains relatively constant during the operation, as routine maintenance minimizes the impact of mechanical aging, and the rainwater is assumed to be clean with negligible density variations. Based on the total theoretical inflow volumes derived from the SWMM simulation, two distinct drainage strategies were formulated: (1) Standard Design Scheme—This approach utilizes a capacity-matching strategy. The combined drainage capacity at Points B and C is dynamically configured for each return period to ensure it exceeds the total simulated inflow. The specific pump configurations for each return period are detailed in

Table 3. Pump configuration for the Standard Design Scheme.

Return-Period (Years)	Theoretical Inflow (m3)	Designed Drainage Capacity at Point B (m3)	Designed Drainage Capacity at Point C (m3)
2	1948.05	828 (2 pumps)	1242 (3 pumps)
5	2444.45	1242 (3 pumps)	1242 (3 pumps)
10	2838.69	1242 (3 pumps)	1656 (4 pumps)
20	3224.07	1656 (4 pumps)	1656 (4 pumps)
30	3494.16	1656 (4 pumps)	2070 (5 pumps)
50	3808.26	2070 (5 pumps)	2070 (5 pumps)

. (2) Maximum Drainage Scheme—To evaluate the upper limit of the site’s mitigation potential, this scheme allocates the maximum feasible installation of five pumps per point. The drainage capacity remains constant and at its maximum across all return periods (

Table 4. Pump configuration for the Maximum Drainage Scheme.

Return-Period (Years)	Theoretical Inflow (m3)	Designed Drainage Capacity at Point B (m3)	Designed Drainage Capacity at Point C (m3)
2	1948.05	2070 (5 pumps)	2070 (5 pumps)
5	2444.45	2070 (5 pumps)	2070 (5 pumps)
10	2838.69	2070 (5 pumps)	2070 (5 pumps)
20	3224.07	2070 (5 pumps)	2070 (5 pumps)
30	3494.16	2070 (5 pumps)	2070 (5 pumps)
50	3808.26	2070 (5 pumps)	2070 (5 pumps)

).

3.3.2. Effectiveness of Standard and Maximum Drainage Schemes

CFD simulations were performed to evaluate the performance of the Standard and Maximum Drainage schemes. The resulting time-series water depths at Points B and C under the Standard Drainage scheme are presented in Figure 21 and Figure 22, with the corresponding peak depths across return periods summarized in Figure 23. The time-series water accumulation depths for the Maximum Drainage scheme are shown in Figure 24 and Figure 25.

Compared to the undrained scenario (Figure 15, Figure 16 and Figure 17), the water accumulation results in Figure 21, Figure 22 and Figure 23 based on standard drainage design show significant time delays at which the 0.15 m threshold is reached, and substantial reductions in the peak water depths at both locations B and C. This confirms that drainage implementation effectively mitigates flood risk. Notably, the peak depth at Point C was reduced by approximately 67% (from about 0.9 m to 0.3 m). However, for all return periods, the water depth at both points remained above 0.15 m at the end of the 300 min drainage window, indicating that this design does not fully meet the regulatory requirement for timely drainage.

As can be seen from Figure 24 and Figure 25, the Maximum Drainage scheme demonstrated a significantly higher drainage capacity. At Point B, among six different intensities of rainfall over a 2–50 year period, the five least intense rainfall events resulted in water depths below 0.15 m within 300 min, while the most intense event still resulted in water depths above 0.15 m. This suggests its effective capacity is capped at approximately the 30-year rainfall level. At Point C, among six different intensities of rainfall over a 2–50 year period, the four least intense rainfall events resulted in water depths below 0.15 m within 300 min, while the two most intense events still resulted in water depths above 0.15 m, indicating a functional capacity threshold at the 20-year level.

3.3.3. Proposed Optimized Drainage Scheme

Since the Standard Drainage scheme failed to meet drainage timelines for extreme events, and the Maximum Drainage scheme resulted in excessive redundant capacity for low-intensity events, an Optimized Drainage scheme was developed. The core principle of this scheme is dynamic capacity matching, where pump configurations are iteratively refined based on the performance gaps identified in the previous two simulations.

The optimization process utilized the residual water volume from the Standard Drainage scheme results as a primary metric for capacity adjustment. To account for the discrepancies between theoretical and actual drainage efficiency caused by factors such as fluctuating hydraulic pressure, air entrainment, and mechanical losses, the optimization favored results where the residual volume was minimal, as these provided a more reliable baseline. For return periods where the Standard Drainage scheme left significant flooding, the Maximum Drainage scheme was used as the reference for scaling up capacity, as detailed in

Table 5. Configuration design of pumps for Optimized Drainage scheme.

Return-Period (Years)	Theoretical Inflow (m3)	Designed Drainage Capacity at Point B (m3)	Designed Drainage Capacity at Point C (m3)
2	1948.05	1242 (3 pumps)	1656 (4 pumps)
5	2444.45	1656 (4 pumps)	1656 (4 pumps)
10	2838.69	1656 (4 pumps)	2070 (5 pumps)
20	3224.07	2070 (5 pumps)	2070 (5 pumps)
30	3494.16	2070 (5 pumps)	2484 (6 pumps, 1 extra included)
50	3808.26	2898 (7 pumps)	2484 (6 pumps, 1 extra included)

.

The extra pump specified in Table 5 represents redundant reserve capacity. These units are intended for permanent installation but are designed for dynamic activation: they remain idle during low-intensity storms and are triggered only when rainfall intensity threatens to exceed the base drainage capacity. This strategy provides a dynamic capacity-matched drainage response, ensuring the 0.15 m depth threshold is consistently achieved within the 300 min mandate across all design scenarios.

CFD simulations validated the effectiveness of the optimized design, as illustrated in Figure 26 and Figure 27. When compared to the maximum-capacity scenario, the optimized approach maintained a peak water depth of 4 m at Point B, while the peak depth at Point C was successfully reduced from 0.35 m to 0.25 m. Crucially, the water depths at both locations subsided below the 0.15 m regulatory threshold within the mandated 300 min timeframe across all return periods, confirming full compliance with the GB 50014 standard.

The optimized strategy offers distinct operational advantages for return periods ranging from 2 to 50 years. The reduction in active pump units slightly extends the duration during which water depth exceeds 0.15 m for higher-frequency events (2, 5, and 10-year return periods). In these cases, the maximum ponding depths are kept below 0.3 m at Point B and 0.25 m at Point C, with the exceedance window limited to a brief 20–30 min interval. This demonstrates that the optimized scheme effectively balances computational and energy efficiency with public safety, providing a robust defense against flash flooding while avoiding the unnecessary operational costs of a maximum-capacity deployment.

4. Conclusions

This study developed and implemented a novel multi-scale modeling framework that hybridizes catchment-scale hydrological simulation with high-fidelity 3D Computational Fluid Dynamics (CFD). The analysis demonstrates that the proposed SWMM-CFD framework effectively bridges the scale gap in urban flood modeling, providing a transition from macro-level runoff to micro-level fluid dynamics. The principal conclusions are as follows:

• The SWMM-CFD framework proved to be a robust tool for simulating the complete inundation life cycle in urban underpasses. It successfully captures the transition from rainfall–runoff generation to complex internal accumulation, effectively accounting for intricate architectural features that traditional 1D or 2D models often overlook.
• Two distinct flooding patterns were identified: a systemic response at the tunnel’s lowest point (Point B) and a localized response at the entrance concavity (Point C). While water depth at Point B is strongly correlated with total inflow volume, the accumulation at Point C is governed and eventually capped by local micro-topography.
• A graded drainage strategy, which matches pump capacity to the expected inflow intensity across varying return periods, demonstrated superior performance. This approach significantly improves economic and operational efficiency compared to under-designed (Standard) or over-designed (Maximum) schemes.
• By enabling precise predictions of underpass responses to varying rainfall intensities, this framework allows for the implementation of proactive mitigation measures, such as automated flood barriers. This contributes to the overall flood control capacity and long-term sustainability of urban infrastructure.

Future research can extend this work in several promising directions: (1) further research on various emergency flood prevention measures, such as flood barriers; (2) seeking opportunities for validation against high-resolution sensor data from actual flood events remains a priority; (3) the framework could be adapted for real-time flood forecasting and smart pump control by integrating live rainfall radar data and implementing faster, reduced-order CFD models or pre-simulated scenario libraries.