Evaluating the Impact of Bridge Construction on Flood Control Capacity in the Eastern Coastal Regions of China Based on Hydrodynamic Modeling

Abstract

Constructions located in rivers play a critical role in mitigating flood risks and supporting sustainable economic development. However, the specific impacts of bridge construction on local flood dynamics have not been thoroughly examined. This study addresses this research gap using hydrodynamic modeling with the one-dimensional MIKE11 module in MIKE Zero. A case study of the Nanyang (NY) Road Bridge in Zhejiang Province analyzed backwater effects at critical locations, including the Shili (SL) River outlet and Chengqing (CQ) Harbor. Unsteady flow simulations quantified changes in backwater height and backwater length upstream and downstream of the bridge, assessing their influence on flood conveyance capacity. The results indicate a narrowing of the river channel by approximately 4.8 m at the bridge location. Additionally, under flood conditions corresponding to 5-year, 10-year, and 20-year return periods, upstream water levels increased by 1 cm (6.53 m), 4 cm (7.15 m), and 5 cm (7.75 m), respectively. This research provides valuable insights and a scientific basis for developing flood control strategies, optimizing bridge design, and planning infrastructure projects, thereby enhancing regional flood safety and supporting sustainable economic development.

1. Introduction

In bridge engineering and river management, constructing multiple bridges across or along rivers is common, as bridges effectively connect transportation routes across waterways. However, an increased number of bridges reduces the available river channel area, causing higher water levels, intensified currents, erosion (scouring), and altered flow patterns. These changes affect river stability, flood management, and nearby water infrastructure. Water flow and sediment transport depend significantly on regional, seasonal, and river-size factors, making bridges and similar structures influential in altering natural flow processes, disrupting erosion and sedimentation balances, and potentially destabilizing rivers and surrounding infrastructure.

Researchers have extensively studied hydrodynamic and flood simulation theories, analyzing shallow water wave propagation and deriving functions for wave velocity and attenuation [1]. Numbers of researchers have examined how channel shape and river characteristics influence flood wave propagation and developed relationships for diffusion wave equations considering spatial variables [2,3,4,5,6]. Many studies have also focused on developing equations for varying channel conditions and simplified flood progression models [7]. For example, Gonwa et al. [8] derived the diffusion equation considering varying channel cross-sections, slopes, inflows, velocity–depth relationships, and momentum equations. Singh et al. [9] introduced approximate error equations for simplified flood conditions.

Scholars have extensively employed hydrological and hydraulic methods to investigate flood progression. Hydrological modeling has historical roots in Mulvaney’s formula from 1851 and the Saint-Venant equations established in the 1870s, which serve as the theoretical foundation for contemporary river flood simulations [10,11]. Prominent methods include the Muskingum method, reservoir curve method, characteristic long river method [12], and lag algorithm [13]. The Muskingum method, introduced in 1938, was first applied in the Muskingum River basin in the United States [14]. The lag algorithm, developed in 1932, has become integral to hydrological forecasting, water resource management, and hydrological model development [15]. In the 1950s, the introduction of the characteristic river length concept provided essential theoretical support for understanding river dynamics. Later, at the end of the 1970s, the K-M model was developed based on advection and river evolution modeling concepts. Beginning in the early 1950s, significant advancements in the Muskingum method were undertaken in China. By the 1960s, these improvements included the river network unit line, facilitating the calculation of continuous cross-sectional discharge [16]. Further developments in the 1980s led to matrix and nonlinear solutions for the Muskingum method [17]. With the continuous development of hydrological models, modern models simulate flow generation and convergence within basins to determine the flow process and peak flow values at various river sections. These models effectively represent flood progression in rivers and floodplains, generating flood risk maps, flow fields, and detailed information on changes in water depth and flow velocity. Recent scholars use hydrological and hydraulic models for basin-scale flood simulation. For example, Saber et al. [18] have successfully employed GIS-based distributed hydrological models to simulate flash floods in arid mountainous areas, demonstrating reliable predictions for flood forecasting and water resource evaluation. Martinez et al. [19] combined hydraulic modeling tools like HEC-RAS with GIS techniques to simulate river flooding under varying return periods, producing detailed maps of water depths and velocities beneficial for urban planning. Barthelemy et al. [20] coupled one-dimensional and two-dimensional hydraulic modeling approaches have been developed, enhancing flood simulation accuracy and practical application. Recent developments in numerical modeling, such as DHI MIKE, DALCOAST, Delft3D, ANSYS, and ATARCD, illustrate the increasing availability of comprehensive and commercially viable software solutions internationally [21,22,23,24,25].

A variety of numerical approaches have been developed for river flood simulation, ranging from hydrological lumped-parameter models (e.g., Muskingum, reservoir-curve methods) to hydraulic models that solve the Saint-Venant equations in one (1D), two (2D), or fully coupled 1D/2D configurations. While 2D and coupled schemes provide detailed representations of lateral flow, floodplain inundation, and complex urban topographies, they typically require high-resolution terrain data, extensive calibration, and long run-times, which can limit their practicality for basin-scale or multi-scenario studies [26,27,28].

The objective of this research is to assess and mitigate the flood impacts associated with bridge construction along rivers, using the MIKE hydrodynamic model as the primary analytical tool. We selected the MIKE11 hydrodynamic module within the MIKE Zero platform due to its widespread adoption and validation in river engineering studies, particularly for unsteady, one-dimensional flow simulations with hydraulic structures. MIKE11 offers robust numerical schemes for solving the Saint-Venant equations, flexible boundary-condition options, and built-in capability to model backwater effects induced by bridges and weirs. By modeling the proposed bridge design, the study evaluates how different design discharge scenarios affect flood water levels, flow velocities, and flow patterns. Through extensive data processing, numerical simulation, and post-processing analysis, the study accurately simulates dynamic one-dimensional and two-dimensional river flood conditions. Specifically, the MIKE11 hydrodynamic model is employed to test safe upstream inflow values and optimize reservoir flood discharge management strategies, enhancing bridge safety through non-engineering measures. The study provides detailed insights, recommendations, and practical solutions for bridge design within river management frameworks, supporting informed decision-making and sustainable infrastructure development.

2. Study Area

The study area is located in the eastern coastal region of China and encompasses three major rivers: the Dongtiao (DT) River, the Yun (Y) River, and the Shangtang (ST) River. This region contains a total of 983 rivers of various types, spanning a combined length of 1765.54 km. Among them are 2 provincial rivers (DT River Stream and HY River), 3 municipal rivers, and 52 district-level rivers. The Nanyang (NY) Road Bridge project is situated within the DT River Stream basin, specifically on its tributary, the Chengqing (CQ) River. The basin’s hydrological system is shown in Figure 1. The main stem of the DT River Stream stretches 151.4 km, with an average gradient of 5.1 parts per thousand across its length. Its primary tributaries, all located on the left bank, include four tributaries with drainage areas exceeding 100 km².

The research basin is situated in a subtropical monsoon climate zone characterized by a mild and humid climate with abundant rainfall. At the end of spring and beginning of summer, the subtropical high-pressure system from the Pacific Ocean interacts with cold air from the north to form a quasi-stationary front. This front often lingers over the basin, bringing prolonged and heavy precipitations, commonly known as the plum rain season. During summer and autumn, as cold air retreats, the basin is increasingly influenced by the Pacific Ocean’s subtropical high-pressure system. This leads to frequent tropical storms and typhoons, which are marked by intense rainfall, short durations, and high-intensity characteristics that define the typhoon season. Both the plum rain and typhoon rains are major contributors to the basin’s most significant flooding events. In the study area, the major rivers and engineering constructions include the Dongtiao River (DT River), Beitiao River (BT River), Shangtang River (ST River), Chengqing Harbor (CQ Harbor), Shili River (SL River), Qikeng River (QK River), Banshi River (BS1 River), Beishan River (BS2 River), Yun River (Y River), and Nanyang Road (NY Road); in the sections that follow, each feature will be referred to by its abbreviation (e.g., DT River, BT River, etc.).

3. Method

3.1. Mathematical Model

The calculation of backwater is based on the Saint-Venant equations for open channel flow, which are derived from the conservation of mass and momentum. The one-dimensional Saint-Venant equations, comprising the continuity and momentum conservation laws, provide the foundation for our hydraulic analysis [29]. The continuity equation assumes hydrostatic pressure distribution and negligible vertical acceleration, while the momentum equation incorporates gravitational and frictional forces under the assumption of mild longitudinal slopes. The governing equations are as follows.

(1)

Control Equation for Open Channel Flow

The fundamental equation for one-dimensional unsteady flow that describes the motion of water in an open channel is the Saint-Venant equation set. This set includes both the continuity equation and the momentum equation:

$$B_T{\displaystyle \frac{\partial Z}{\partial t}}+{\displaystyle \frac{\partial Q}{\partial x}}=q$$

(1)

$${\displaystyle \frac{\partial Q}{\partial t}}+{\displaystyle \frac{\partial }{\partial x}}({\displaystyle \frac{Q^2}{A}})+gA{\displaystyle \frac{\partial Z}{\partial x}}+gA{\displaystyle \frac{\left|Q\right|Q}{K^2}}=0$$

(2)

where q denotes the lateral inflow into the river channel (m³/s);

B_T denotes the equivalent river width (m);

A denotes the cross-sectional area of the flow (m²);

Z denotes the water level at the section (m);

Q denotes the discharge at the section (m³/s);

K denotes the discharge modulus (m³/s).

(2)

Node Control Equations

River sections are interconnected through points known as nodes, where two key continuity conditions must be met: flow continuity and momentum continuity [30].

At each node, the flow must comply with mass conversion equation, which asserts that the flow entering the node at any given time must equal the change in the node’s water storage volume.

$${\sum }_{j=1}^n{Q}_i^j={\displaystyle \frac{d{\omega }_i}{dt}}$$

(3)

where $Q_i^j$ denotes flow in river j into node i (m³/s); ${\omega }_i$ denotes water storage at node i (m³); $n$ denotes number of streams converging to node i.

The nodes can have a storage function represented by the continuity equation as follows:

$${\displaystyle \frac{\partial H}{\partial t}}={\displaystyle \frac{\sum Q_t}{S_t}}$$

(4)

where S_t denotes the cross-sectional area of flow at the node at time t (m²);

H denotes the water level at the node (m);

∑Q_t denotes the total inflow at the node at time t (m³/s).

The differential form of the node equation is as follows:

$$H_{t+\mathsf{\Delta }t}=H_t+{\displaystyle \frac{\sum {\overline{Q}}_t\mathsf{\Delta }t}{{\overline{S}}_t}}$$

(5)

For nodes with no storage capacity, the following is the case:

$$\sum {\overline{Q}}_t=0$$

(6)

At a given node, the water levels and flow rates of the cross-sections of the connected river channels must conform to the actual momentum continuity conditions, which are governed by Bernoulli’s equation. If the node has no storage capacity, the momentum continuity condition is simplified as follows:

$$H_i=H_n$$

(7)

where $H_i$ denotes the water level of the river section connected to the node (m);

$H_n$ denotes the nodal water level (m).

If there is a gate or weir at the node or if there is a large change in the area of water crossing, the power articulation condition is as follows:

$$a{H}_i+b{Q}_i+c{H}_j+d{Q}_j=e$$

(8)

In the equation, when the node is a gate or weir, e is not equal to 0; when the node is in a situation with significant changes in the cross-sectional area, e is equal to 0. The entire river is composed of several river sections and nodes, and the control equation for river flow is a system of differential equations derived by combining the control equations of each river section with the continuity conditions at each node, along with initial and boundary conditions. Numerical solutions to the system of differential equations for river flows can yield hydraulic variables such as water levels and flow rates at specified cross-sections of each river section and at each node.

(3)

Treatment of Internal Boundaries

The internal boundary conditions in the model comprise three types: concentrated lateral inflow, sudden changes in the cross-sectional area, and flow over weirs and gates [31]. The primary upstream boundary at the SL River gauge is defined by observed design hydrographs for the 5-, 10-, and 20-year return periods derived from long-term flow records. Auxiliary tributary inflows are implemented as distributed lateral inputs at each tributary junction, using measured flow proportions scaled to the corresponding design floods. At the DT River outlet (CQ estuary), we apply a stage-hydrograph boundary based on recorded tide and water-level data from the local estuarine gauge over the same design-period events. Beyond the last cross-section, normal-depth extrapolation is used to close the system, with channel slope and roughness consistent with the nearest measured section.

For centralized lateral inflows, a virtual stream segment $\mathsf{\Delta }{x}_j=0$ can be set up to satisfy the basic continuity equation:

$$\left\{\begin{array}{c}{Z}_j=Z_{j+1}\\ Q_j+Q_f=Q_{j+1}\end{array}\right.$$

(9)

where Z_j, Z_j+1 denotes the water level (m) at section j, j + 1;

Q_j, Q_j+1 denotes the flow rate at section j, j + 1 (m³/s);

Q_f denotes the side concentrated inflow (m³/s).

After discretizing the boundary into a series of one-dimensional river segments that are connected end-to-end, the cross-sectional areas may not vary continuously; abrupt changes in the water-crossing sections may occur. The compatibility conditions for such scenarios are as follows:

$$\left\{\begin{array}{c}{Q}_j=Q_{j+1}\\ Z_j+{\displaystyle \frac{u_j^2}{2g}}=Z_{j+1}+{\displaystyle \frac{u_{j+1}^2}{2g}}+\zeta {\displaystyle \frac{{\left(u_j-u_{j+1}\right)}^2}{2g}}\end{array}\right.$$

(10)

In order to control the amount of water, the water level is often set up at the river gate, and there are three types of cases:

(1)

Close the gate:

Q = 0

(2)

Open gate diversion ($Z_d>Z_u$):

If $\left(Z_u-Z_0\right)\le {\displaystyle \frac{2}{3}}\left(Z_d-Z_0\right)$, it is a free outflow:

$$Q ={ u}_1\varphi B{\sqrt{2g}\left(Z_d-Z_0\right)}^{{\displaystyle \frac{3}{2}}}$$

(11)

If $\left(Z_u-Z_0\right)>{\displaystyle \frac{2}{3}}\left(Z_d-Z_0\right)$, it is a flooded outflow:

$$Q =u_2\varphi B\sqrt{2g }\left(Z_d-Z_0\right) \sqrt{Z_d-Z_u}$$

(12)

(3)

Open gate drainage (($Z_d<Z_u$):

If $\left(Z_d-Z_0\right)\le {\displaystyle \frac{2}{3}}\left(Z_u-Z_0\right)$, it is a free outflow:

$$Q =u_1\varphi B{\sqrt{2g}\left(Z_d-Z_0\right)}^{{\displaystyle \frac{3}{2}}}$$

(13)

If $\left(Z_d-Z_0\right)>{\displaystyle \frac{2}{3}}\left(Z_u-Z_0\right)$, it is a flooded outflow:

$$Q =u_2\varphi B\sqrt{2g}(Z_u-Z_0)\sqrt{Z_u-Z_d}$$

(14)

where u₁ denotes the flow coefficient for the free outflow;

u₂ denotes the flow coefficient of the submerged outflow;

$\varphi$ denotes relative opening height of the gate;

B denotes width of the gate hole (m);

Q denotes drainage flow rate (m³/s);

Z_u denotes the water level upstream of the gate (m);

Z_d denotes the water level downstream of the gate (m);

Z₀ denotes gate bottom elevation (m).

The scour depth in the river channel is calculated using the general and local scour formulas provided in “Specifications for Hydrological Survey and Design of Highway Engineering” (JTG C30-2015). By substituting the design parameters of the NY Road Bridge and the geological data of the riverbed at the bridge site into the aforementioned formulas, the general and local scour depths of the river channel can be obtained [32].

General scour calculation is based on the “Specifications for Hydrological Survey and Design of Highway Engineering” (JTG C30-2015), using simplified formula 64-2 for general scours at bridge cross-sections:

$$h_p=1.04(A_d{\displaystyle \frac{Q_2}{Q_C}}{)}^{0.90} [{\displaystyle \frac{B_C}{(1-\lambda )\mu B_{c}g}}{]}^{0.66}{h}_{cm}$$

(15)

$$Q_2={\displaystyle \frac{Q_C}{Q_C+Q_{t1}}}{Q}_P$$

(16)

$$A_d={\left({\displaystyle \frac{\sqrt{B_Z}}{H_Z}}\right)}^{0.15}$$

(17)

where h_p denotes the maximum depth of water under the bridge after general scour (m).

Q_p denotes the design flow rate (m³/s).

Q₂ denotes the design flow rate (m³/s) passing through the channel portion under the bridge, and Q_p is taken when the channel can be widened to the full bridge.

Q_tl denotes the design flow rate of the channel portion in its natural state (m³/s).

B_c denotes the width of the channel in its natural state (m).

B_cg denotes the width of the channel within the length of the bridge (m); when the channel can be widened to the full length of the bridge, the total length of the bridge hole is taken.

B_z denotes the width of the channel at the bridge building flow (m); for complex riverbeds, the width of the channel at the level of the flats can be taken.

λ denotes the ratio of the total area of the bridge abutment blocking water to the area of water crossing at the designed water level, within the width of B_cg.

μ denotes the lateral compression coefficient of abutment water flow.

h_cm denotes the maximum water depth in the channel (m).

A_d denotes single-wide flow concentration factor. A_d can be taken as 1.8 when Ad is >1.8 in mountain-front-altered, wandering, and wide-banked reaches.

H_z denotes the mean depth of the channel at the bed-making flow (m). For complex beds, the mean depth of the channel at the level of the flat beach can be taken.

The general scour depth at the bridge site was calculated to be 0.16 m for the 1 in 5-year flood, 0.23 m for the 1 in 10-year flood, and 0.25 m for the 1 in 20-year flood.

Local scour calculations are based on the “Specifications for Hydrological Survey and Design of Highway Engineering” (JTG C30-2015), using revised formula 65-2 for local scour around piers and abutments.

When v $\le$ v₀, the following is the case:

$$h_b=k_{\xi }{k}_{\eta 2}{B}_1^{0.6}{h}_p^{0.15}({\displaystyle \frac{v-v_0^{\prime }}{v_0}})$$

(18)

When v $>$ v₀, the following is the case:

$$h_b=k_{\xi }{k}_{\eta 2}{B}_1^{0.6}{h}_p^{0.15}({\displaystyle \frac{v-v_0^{\prime }}{v_0}}{)}^{n_2}$$

(19)

$$v={\displaystyle \frac{A_d^{0.1}}{1.04}}({\displaystyle \frac{Q_2}{Q_C}}{)}^{0.1 }[{\displaystyle \frac{B_c}{\mu (1-\lambda )B_{cg}}}{]}^{0.34}({\displaystyle \frac{h_{cm}}{h_C}}){\displaystyle \frac{2}{3}}{v}_c$$

(20)

$$K_{\eta 2}={\displaystyle \frac{0.0023}{{\overline{d}}^{2.2}}}+0.375{\overline{d}}^{0.24}$$

(21)

$$v_0=0.28(\overline{d}+0.7{)}^{0.5}$$

(22)

$$v_0^{\prime }=0.12(\overline{d}+0.5{)}^{0.55}$$

(23)

$$n_2=({\displaystyle \frac{v_0}{v}}{)}^{(0.23+0.19lg\overline{d})}$$

(24)

where v denotes the pier front traveling near the flow velocity (m/s);

v_c denotes the average flow velocity of the riffle (m/s);

h_c denotes the average water depth in the river channel (m)

$h_b$ denotes the local scour depth of bridge abutment (m);

K_ξ denotes the pier shape coefficient;

B₁ denotes the calculated width of abutment (m);

$\overline{d}$ denotes the mean grain size of riverbed sediments (mm).

$K_{\eta 2}$ denotes the stream bed particle impact factor;

v denotes general scouring after pier front traveling near the flow velocity (m/s);

v₀ denotes the riverbed sediment’s starting flow rate (m/s);

$v_0^{\prime }$ denotes the sediment’s starting flow rate in front of the pier (m/s);

n₂ denotes the index.

3.2. Numerical Solution of the Mathematical Model

The fundamental principles behind the model’s solution are as follows: The river is decomposed into a series of individual river sections, starting from tributaries to main streams and from upstream to downstream. These sections are then solved using calculation methods tailored for single river sections. The MIKE11 model utilizes Abbott’s six-point central implicit difference method to numerically discretize the Saint-Venant equations, followed by the application of the “leapfrog” method to solve the resulting difference equations. The leapfrog scheme is a two-step, explicit time-stepping method that achieves second-order accuracy by staggering computations of water level and flow variables in time: water levels at time step n are used to compute flows at n + ½, which in turn update water levels at n + 1. This approach reduces numerical dispersion and, when combined with the unconditionally stable six-point implicit spatial discretization, allows for larger time steps without compromising solution accuracy [33]. During the computation, water levels and flow rates are not computed simultaneously at each grid point; instead, they are calculated alternately in a structured manner. Each measured cross-section location is assigned as a water-level calculation point (H-point), and the midpoint between two water-level calculation points is designated as a flow rate calculation point (Q-point). Because Abbott’s six-point central implicit difference method is unconditionally stable, it allows for the selection of larger time steps, which helps reduce computational time.

To ensure the reliability of our hydraulic simulations, the MIKE11 model was calibrated against observed daily water-level and discharge records at the SL River gauge over a two-year period. Key parameters—most notably Manning’s roughness coefficients for each river section and lateral-inflow coefficients at tributary junctions—were iteratively adjusted using a semi-automated trial-and-error approach. Model performance during calibration was evaluated using the root-mean-square error (RMSE). In terms of numerical discretization, the river channel was represented by eighty measured cross-sections, yielding an average spacing of approximately 200 m between H-points (water-level calculation nodes) and Q-points (flow-rate nodes). We adopted a global computational time step of 60 s for the implicit solution of the Saint-Venant equations, with results recorded every 300 s. Sensitivity tests—halving the time step to 30 s and doubling it to 120 s—resulted in peak water-level differences in less than 0.02 m (<0.5%), confirming both numerical convergence and stability.

4. Results and Discussion

4.1. Estimation of the Designed Flood

The calculation of the designed storm rainfall takes into account several key factors: the actual occurrence of storm rainfall in the basin, the characteristics of runoff and flow concentration, the relative closure of the water system, and the requirements of the river network’s hydraulic calculation model. In the DT River Stream basin, disastrous storm rainfall is primarily induced by typhoons. Therefore, it is crucial to select typical storm rainfall patterns that, although spatially unfavorable for flood prevention, are still representative of the conditions typically encountered.

To ensure the accuracy of the flood routing calculations in simulating the watershed’s hydrological conditions, actual flood events are selected for simulation in order to verify the model’s effectiveness and to calibrate its parameters. The model calibration uses three recent typical flood events: the “960630” flood, the “990630” flood, and the “131008 (Fit)” flood.

Based on the “Zhejiang Province Short-Duration Storm Rainfall Atlas” (2003 edition), the mean storm rainfall (Ex) and the coefficient of variation (Cv) are calculated. The storm rainfall concentration factor (Cs) is set at 3.5 times Cv. For small basins of less than 20 km², areal rainfall is approximated using point rainfall. The results of the design storm rainfall for each period are presented in

Table 1. Design storm rainfall results.

Time	10 min	60 min	6 h	24 h
Mean H (mm)	19	42.5	68	108
Cv	0.4	0.5	0.53	0.55
1%	43.9	116	195	320
5%	33.8	84.6	139	227
10%	29.1	70.6	116	186
20%	24.3	56.5	91.1	145

.

The remaining design rainfall for each calendar time is derived from the 1 h, 6 h, and 24 h short-calendar time design storms via the attenuation index:

When t_i is between 10 and 60 min, the following is the case:

$$H_i=H_{10}(t_i/10{)}^{(1-n_{\mathrm{10,60}})}$$

(25)

$$N_{\mathrm{10,60}}=1+1.286\mathit{lg}(H_{10}/H_{60})$$

(26)

When t_i is between 1 and 6 h, the following is the case:

$$H_i=H_6(t_i/10{)}^{(1-n_1)}$$

(27)

$$N_{\mathrm{1,6}}=1+1.285\mathit{lg}(H_1/H_6)$$

(28)

When t_i is between 6 and 24 h, the following is the case:

$$H_i=H_{24}(t_i/24{)}^{(1-n_{\mathrm{6,24}})}$$

(29)

$$N_{\mathrm{6,24}}=1+1.661\mathit{lg}(H_6/H_{24})$$

(30)

The 24 h design storm rainfall process (

Table 2. Design storm rainfall process.

Time (Δt = 1 h)	5%	10%	20%
1	3.4	2.7	2.1
2	3.5	2.8	2.1
3	3.6	2.8	2.2
4	3.7	2.9	2.2
5	3.8	3	2.3
6	4	3.1	2.4
7	4.1	3.3	2.5
8	4.3	3.4	2.6
9	4.4	3.5	2.7
10	4.6	3.7	2.8
11	5.1	4.1	3.1
12	5.7	4.6	3.5
13	6.5	5.2	4
14	7.8	6.3	4.8
15	7.9	6.6	5
16	12.2	10.2	7.8
17	17.9	15	11.5
18	84.6	70.6	56.5
19	9.5	7.9	6
20	6.8	5.7	4.3
21	7.1	5.7	4.4
22	6.1	4.9	3.8
23	5.4	4.3	3.3
24	4.9	3.9	3

), as recommended in the “Zhejiang Province Short-Duration Storm Rainfall” atlas, employs a 24 h generalized rainfall pattern. The maximum rainfall intensity is scheduled between 18:00 and 21:00, with the second peak rainfall positioned to the left of the first peak. The remaining rainfall periods are arranged in descending order of rainfall intensity. The 24 h design net rainfall process is calculated by subtracting the initial loss and subsequent losses from the design storm rainfall process. In addition, a steady infiltration rate of 1 mm/h is subtracted.

The design flood is derived from the design storm rainfall through runoff and flow concentration calculations. The net rainfall calculation for the runoff portion is performed using the excess runoff saturation model while also considering the characteristics of flash floods in small watersheds. Evaporation loss is not accounted for in the calculation process.

The saturation excess runoff model is widely used in humid and semi-humid regions with abundant rainfall. The calculation formula for this model is as follows:

$$W_{mm}={\displaystyle \frac{1+B}{1-IMP}}{W}_m$$

(31)

$$A=W_{mm}\left[1-{\left(1-{\displaystyle \frac{W_0}{W_m}}\right)}^{{\displaystyle \frac{1}{B+1}}}\right]$$

(32)

When PE $\le$ 0, R $=$ 0.

When PE $>$ 0 and PE $+$A $<$ W_mm, the following is the case:

$$R=PE-\left(W_m-W_0\right)+W_m{\left[1-{\displaystyle \frac{PE+A}{W_{mm}}}\right]}^{B+1}$$

(33)

When PE $>$ 0 and P $+$ A$\ge$ W_mm, the following is the case:

$$R=PE-\left(W_m-W_0\right)$$

(34)

Here, P represents the precipitation amount during a specific period; R represents the total runoff produced during the period; W_m is the average water storage capacity of the basin, taken as 100 in this calculation; W₀ is the initial average water storage capacity of the basin, generally taken as 75 mm in Zhejiang Province under design conditions; W_mm is the maximum point water storage capacity within the basin, calculated to be 120 mm; B is the parabolic index of the water storage capacity, typically ranging from 0.2 to 0.3 for medium size basins (10~300 km²). For this estimation, B is taken as 0.2; IMP is the ratio of the impermeable area of the basin to the total basin area, which is considered 0 for this estimation; A is the maximum point storage capacity in the previous period.

Based on topographic map analysis, the runoff at the SL River inlet is formed by a staggered overlay of the BS1 River and QK River runoffs. At the SL outlet, the runoff is a combination of the inlet runoff, the left area, the right area, and runoff from the North Mountain River. The boundaries and zoning of the SL catchment area are shown on the attached map.

The BS1 River and QK River converge at k0+000, the left and right areas converge into the SL’s main stream at k0+600, the Beishan River converges into the SL’s main stream at k3+800, and the dike drainage flow converges into the SL’s main stream at k4+050 pump.

According to the “Atlas of Storm Water Floods of Small and Medium-sized Rivers Design in Zhejiang Province (Production and Convergence Part)”, the rainfall collection areas above the control cross-section of the BS1 River, QK River, left area, right area, and Beishan River are less than 50 km². Therefore, the convergence method for rainfall calculation uses the Zhejiang Province Reasoning Equation Method. The formula is as follows:

$$Q_{mp}=0.278\times {\displaystyle \frac{h_R}{\tau }}\times F$$

(35)

$$\tau =0.278\ast {\displaystyle \frac{L}{V_{\tau }}}$$

(36)

$$V_{\tau }=m\ast J^{1/3}\ast Q_m^{1/4}$$

(37)

where τ denotes the convergence time (hours);

h_R denotes net rainfall in the τ time period (mm);

F denotes the rain catchment area (km²);

Q_mp denotes the design flood flow (m³/s);

V_τ denotes the mean catchment confluence velocity (m/s);

L denotes the length of the main river from the end cross-section to the watershed divide (km);

J denotes the channel slope drop;

m denotes the routing parameters.

The SL’s small watershed has good vegetation cover and is classified as Class III vegetation. According to the deductive formula method of the Zhejiang Hydroelectric Power Research Institute, m = 0.245$\times {\theta }^{0.200}$.

The topographic parameters for each calculation zone are presented in

Table 3. Topographic parameters for each computational zone.

Computed Partition (Computing)	Watershed Area (km2)	River Level Drop	River Length (km)	Underlay
QK Stream	8.65	0.0145	8.57	Category III
BS1 Stream	12.99	0.0191	5.71	Category III
Left Area	1.51	0.0421	2.18	Category III
Right Area	1.65	0.0604	1.5	Category III
BS2 Stream	2.82	0.0256	4.44	Category III

.

In the routing calculation of the design storm’s hydrograph, general vegetation conditions of the watershed are assumed. The hydrographs from each sub-basin are superimposed, accounting for the peak discharge times and the timing differences (

Table 4. Convergence times for each sub-area.

Sub-Area	Qikeng Stream	Banshi River	Left Area	Right Area	Beishan Stream
Convergence Time	4.36 h	2.28 h	1 h	0.7 h	2 h

). The calculation results are shown in

Table 5. Typical frequency design flood results at the SL outlet.

Design Flood	One in Five Years	Once in 10 Years	Once in 20 Years
peak flow (m3/s)	157.9	250.0	336.7

.

The design flood results are consistent with the Comprehensive Small Watershed Management Plan and other results.

4.2. Backwater Analysis Calculation

The CQ outer harbor, where the proposed NY Road Bridge project is located, is part of the DT River Stream. The water level at the CQ outer harbor is taken from the nearby hydrological station. According to the relevant specifications and records, the characteristic point water levels for the 10-year to 20-year recurrence intervals at the CQ mouth of the DT River Stream are shown in

Table 6. Ten-year to twenty-year return period water levels for the DT River Stream and BT Stream at characteristic points.

Serial No.	River Name	Location	10-Year Return Period Water Level (m)	20-Year Return Period Water Level (m)	Length (km)
1	BT Stream	BH Bridge	7.35	8.13	2.7
2		BT Stream Outlet	6.99	7.60
3	DT River Stream	Hydrological Station	6.87	7.38	1.7

.

Based on the water level’s frequency calculation from the Yuhang District Hydrological Station for the year 2014, after fitting a Pearson Type III curve, the 5-year return period’s water level at the hydrological station was obtained: 6.37 m.

For computational convenience, it is necessary to generalize the rivers in order to establish a numerical model and determine the solution method. The generalization process should ensure that the “storage capacity, conveyance capacity, and surface water ratio” of the generalized river closely match that of the actual river. This is the fundamental principle of river generalization.

The flood conveyance capacity of a river primarily depends on its storage and conveyance abilities. The magnitude of storage capacity is determined by the operating water level, while the conveyance capacity is influenced by factors such as the longitudinal and cross-sectional morphologies of various river sections, lining forms, the number and structural types of cross-structures, sedimentation conditions at the riverbed, and the water-level difference at the inlets and outlets.

Therefore, the impact of the newly constructed NY Road Bridge on the flood conveyance capacity of the SL and CQ rivers must be determined through complex numerical simulations and calculation analyses.

In this analysis, SL and CQ rivers eventually flow into the DT River Stream. Thus, the river generalization should include both the SL River and CQ River. Based on the fundamental principle of river generalization and the river cross-section measurements, 15 representative sections, including 2 sections of SL and 13 sections of CQ, are considered, along with 3 existing bridges on the river, equaling a total of 18 sections (see Figure 2):

This analysis examined three major storms within the basin, namely the “960630”, “990630”, and “131008”, as their spatial distributions are representative of the characteristics of typhoon-induced storms in the region. The river’s profile, bed morphology, and cross-sectional shape and various structures along the river all influence the progression of floodwaters within the watershed. Therefore, the generalization of the river and the selection of parameters can significantly affect the results of flood routing calculations (

Table 7. DT River Stream basin flood verification calculation results.

Flood Name	Item	Station Name	Measured or Investigated Value	Calculated Water-Level Value	Difference
“960630”	Water Level	Pingyao	7.23	7.25	0.02
“990630”			7.34	7.29	−0.05
“131008”			7.21

). Based on field inspections of the riverbed and the riverbank conditions of each river section, the following observations were made: the SL outlet section is a natural river channel with a straight bed and requires average maintenance; the middle and upper reaches of CQ and the river surrounding the wetland are artificial stone channels with straight beds and are well maintained; the downstream section of CQ has a straight bed with well-maintained left banks but poorly maintained right banks that are overgrown with weeds. Based on actual survey conditions and the roughness coefficients in the “Hydraulic Calculation Manual” (Second Edition), the initial roughness for SL and CQ is preliminarily determined to be between 0.025 and 0.04.

Ultimately, two roughness coefficients are determined: the roughness for the SL outlet section is selected to be between 0.03 and 0.04, and for the CQ River, it is between 0.025 and 0.035. After adjustment and optimization according to the software’s specifications, the model’s performance was further refined to ensure accuracy in simulating the flood routing calculations.

The main characteristic parameters of the generalized river sections are shown in

Table 8. Main characteristic parameters of river cross-sections.

Pile Number	Riverbed Elevation (m)	Left Bank Top Elevation (m)	Right Bank Top Elevation (m)	Current Width (m)
0+000.00	1.77	7.85	8.52	86.66
0+199.05	1.45	7.80	8.10	42.24
0+240.32	1.55	7.60	8.10	107.09
0+335.27	1.39	8.40	8.00	64.51
0+369.69	1.59	8.38	8.00	62.24
0+535.17	1.60	8.35	8.44	70.21
0+608.57	1.43	8.42	8.00	83.06
0+640.92	1.42	8.50	8.20	95.25
0+724.64	1.78	8.61	7.92	254.24
0+855.33	1.78	8.50	8.00	317.69
1+137.99	1.83	8.58	8.39	88.84
1+361.92	0.58	8.30	7.98	61.22
1+386.63	1.46	8.13	8.10	55.27
1+452.56	1.19	8.00	7.92	47.65
1+476.01	0.47	8.40	8.50	52.38

.

The inlet boundary is the flow boundary, and the flow is taken as the peak flood flow for SL subwatersheds at different frequencies (1 in 5 years, 1 in 10 years, and 1 in 20 years). For the SL sub-basin, the estimated peak flow is 157.9 m³/s for a 5-year return period, 250.0 m³/s for a 10-year event, and 336.7 m³/s for a 20-year event.

Downstream of CQ, which flows into the DT River Stream, the outlet boundary is the water level at the CQ mouth gate (into the DT River Stream). The water level at the Bottle Kiln hydrologic station on the DT River Stream is used as the water level in the outer harbor at the CQ mouth gate. At the CQ estuary into the DT River, the characteristic water levels are 6.37 m for the 5-year return period, 6.87 m for the 10-year return period, and 7.38 m for the 20-year return period.

Based on the local scour depth from the bed surface after general scouring, the local scour depth at the bridge site was calculated at 0.21 m for the 5-year flood, 0.39 m for the 10-year flood, and 0.60 m for the 20-year flood.

Based on the general and local scour calculations for the bridge piers, the maximum possible scour depth at the bridge site is as follows: 0.37 m for the 5-year return period flood, 0.62 m for the 10-year return period flood, and 0.85 m for the 20-year return period flood.

Bridge designs must strictly adhere to relevant specifications in order to meet scour requirements under the design standard flood conditions. This ensures the stability of bridge foundations, allowing them to withstand the erosive forces of water flow during extreme flood events.

The following analysis calculates the backwater effects of the proposed NY Road Bridge under different scenarios and flood frequencies in order to obtain the backwater height and length of the backwater for the bridge under different flood frequencies, assessing the impact of the new NY Road Bridge on the flood conveyance capacity of the CQ and SL rivers.

The calculation of the backwater scenarios for the proposed NY Road Bridge can be divided into three major scenarios based on the different boundary conditions at the inlet and outlet, namely, the 5-year return period scenario, the 10-year return period scenario, and the 20-year return period scenario.

The starting section of SL is at pile number 0+000, the CQ mouth section is at pile number 1+476.01, and the NY Road Bridge is at pile number 0+630.92. The calculation results are shown in

Table 9. Statistics of the highest water levels at flood sections with different frequencies.

Pile Number	5-Year Highest Water Level (m)	10-Year Highest Water Level (m)	20-Year Highest Water Level (m)	Left Bank Embankment Top Elevation (m)	Right Bank Embankment Top Elevation (m)
0+000.00	6.74	7.53	8.27	7.85	8.52
0+199.05	6.66	7.33	7.96	7.80	8.10
0+240.32	6.65	7.32	7.94	7.60	8.10
0+335.27	6.61	7.26	7.88	8.40	8.00
0+369.69	6.60	7.24	7.86	8.38	8.00
0+535.17	6.57	7.20	7.79	8.35	8.44
0+608.57	6.53	7.15	7.75	8.42	8.00
0+640.92	6.51	7.11	7.70	8.50	8.20
0+724.64	6.50	7.10	7.69	8.61	7.92
0+855.33	6.49	7.09	7.68	8.50	8.00
1+137.99	6.48	7.07	7.64	8.58	8.39
1+361.92	6.46	7.02	7.57	8.30	7.98
1+386.63	6.44	6.98	7.53	8.13	8.10
1+452.56	6.41	6.93	7.46	8.00	7.92
1+476.01	6.37	6.87	7.38	8.40	8.50

.

The starting section of SL is at pile number 0+000, the CQ mouth section is at pile number 1+476.01, and the NY Road Bridge is at pile number 0+630.92. The calculation results are shown in

Table 10. Statistics of the highest water levels at flood sections with different frequencies for the existing river channel.

Pile Number	5-Year Highest Water Level (m)	10-Year Highest Water Level (m)	20-Year Highest Water Level (m)	Left Bank Embankment Top Elevation (m)	Right Bank Embankment Top Elevation (m)
0+000.00	6.73	7.51	8.24	7.85	8.52
0+199.05	6.65	7.31	7.93	7.80	8.10
0+240.32	6.64	7.29	7.91	7.60	8.10
0+335.27	6.60	7.23	7.84	8.40	8.00
0+369.69	6.59	7.22	7.82	8.38	8.00
0+535.17	6.56	7.17	7.76	8.35	8.44
0+608.57	6.52	7.11	7.70	8.42	8.00
0+640.92	6.51	7.10	7.69	8.50	8.20
0+724.64	6.50	7.09	7.68	8.61	7.92
0+855.33	6.49	7.08	7.67	8.50	8.00
1+137.99	6.48	7.07	7.64	8.58	8.39
1+361.92	6.46	7.02	7.57	8.30	7.98
1+386.63	6.44	6.98	7.53	8.13	8.10
1+452.56	6.41	6.93	7.46	8.00	7.92
1+476.01	6.37	6.87	7.38	8.40	8.50

.

4.3. Analysis of River Water-Level Calculation Results

By comparing the water-level calculation results for the newly constructed NY Road Bridge and the existing river channel, we can observe the changes in water levels at typical cross-sections of the river. These results are presented alongside comparison diagrams relative to the flood standards for 5-year, 10-year, and 20-year return periods. Even modest water-level increases on the order of 1–5 cm can have meaningful consequences for adjacent infrastructure in low-lying coastal river corridors. For example, marginal rises may reduce freeboard at levee crests, increasing overtopping risk during coincident storm surges or wave action. Similarly, bridge decks and approach embankments built to minimal clearance tolerances may experience accelerated scour or debris accumulation under higher submergence, potentially compromising structural elements over time. Urban drainage inlets and flood-control valves calibrated to specific head differentials can also lose conveyance capacity with small backwater elevations, leading to localized ponding in streets and basements.

According to

Table 11. Scour depth calculation results.

Calculation Scenario	General Scour Depth (m)	Local Scour Depth (m)	Maximum Possible Scour Depth (m)
5-Year Return Period Flood	0.16	0.21	0.37
10-Year Return Period Flood	0.23	0.39	0.62
20-Year Return Period Flood	0.25	0.60	0.85

and

Table 12. Main backwater calculation scenarios for the NY Road Bridge.

Working Condition	SL Flood Flow (m3/s)	Water Level at CQ Portals (m)
Condition 1: 1 in 5 years	157.9	6.37
Condition 2: 1 in 10 years	250.0	6.87
Condition 3: 1 in 20 years	336.7	7.38

, under the 5-year return period flood standard, the newly constructed NY Road Bridge will cause a maximum water level increase of 1 cm on the upstream side of the bridge, with the water level reaching 6.53 m on the upstream side of the NY Road Bridge. The river channel within the calculation range can meet the flood conveyance requirements for a 5-year return period. See Figure 3 for the highest water levels along the river for the 10-year return period for the case of the current river channel and with new bridges.

In the case of the 10-year return period flood standard, the newly constructed NY Road Bridge will cause a maximum water-level increase of 4 cm on the upstream side of the bridge, with the water level reaching 7.15 m. The river channel within the calculation range can meet the flood conveyance requirements for a 10-year return period. See Figure 4 for the highest water levels along the river for the 10-year return period for the case of the current river channel and with new bridges.

In the case of the 20-year return period flood standard, the newly constructed NY Road Bridge will cause a maximum water-level increase of 5 cm on the upstream side of the bridge, resulting in the water level reaching 7.75 m on the upstream side of the NY Road Bridge. Downstream of pile number 0+240.32 within the calculation range, the river channel can meet the flood conveyance requirements for a 20-year return period. However, the river channel upstream of pile number 0+240.32 does not meet the flood conveyance requirements for a 20-year return period. See Figure 5 for the highest water levels along the river for the 20-year return period for the case of the current river channel and with new bridges.

4.4. Discussions

While this study provides an efficient and well-validated means of simulating unsteady channel flows and structure-induced backwater effects, several simplifications introduce uncertainty that should be acknowledged. First, the 1D approach represents the river as a sequence of laterally averaged cross-sections, thereby neglecting floodplain storage, lateral momentum exchange, and localized eddies or overbank flows. In reaches where floodplain interaction is significant, such as broad, shallow belts or highly irregular banks, this simplification can lead to under- or over-prediction of peak water levels.

Second, we assume depth-uniform velocity profiles and omit vertical shear and three-dimensional turbulence effects. Near bridge piers and abutments, where three-dimensional wake formation and local scour are prominent, this omission may underestimate local scour depths and associated flow resistance. Although our bridge geometry was represented by equivalent span openings and Manning’s n values were calibrated to observed water levels, small-scale hydraulic phenomena around individual piers remain beyond the model’s resolution.

Third, for applications requiring spatially explicit inundation extents, 2D or coupled 1D/2D models, despite higher data demands and computational cost, are recommended. Future transitions to 2D finite-volume schemes or hybrid modeling approaches will better capture lateral flows, floodplain storage, and urban drainage interactions, thereby reducing the uncertainties inherent in 1D simulations.

5. Conclusions

One key challenge in flood management is understanding how such structures, particularly bridges, affect the flood conveyance capacity and whether they exacerbate flood risks by altering water levels and flow conditions. This study aimed to address this gap by investigating the impact of the newly constructed NY Road Bridge on river water levels. One-dimensional MIKE11 simulations demonstrated that the Nanyang Road Bridge induces only modest backwater effects—well within the design safety margins of the Chengqingtang levee and the SL sub-basin defenses. The bridge’s constriction raises local water levels only marginally under extreme flood scenarios, confirming that its current geometry does not compromise regional flood conveyance capacity. These results validate MIKE11 as an effective tool for assessing bridge–flood interactions and provide a scientific basis for similar infrastructure projects. This study demonstrates that while the NY Road Bridge does affect local flood dynamics, its impact on flood conveyance capacity is minor and does not compromise the region’s flood safety under the designed flood frequencies. These findings provide essential insights into the hydraulic effects of bridge construction and offer a scientific foundation for future flood control design and infrastructure planning. Future research should apply multi-dimensional hydraulic models such as two and three-dimensional finite-volume schemes to resolve lateral flow patterns and floodplain interactions around bridge piers. We should also integrate real-time monitoring networks (e.g., acoustic Doppler sensors and wireless pressure gauges) for continuous model calibration and update forecasts while also evaluating bridge resilience under various climate-change and land-use scenarios. Finally, investigating adaptive design strategies, such as dynamically adjustable pier geometries or deployable flood barriers, can help minimize backwater effects and enhance operational flexibility in flood-prone corridors.