Analysis of Flood Water Level Profiles and Scouring Potential for a 200-Meter Span Suspension Bridge ^†

Abstract

This study analyzes the scouring characteristics of the Mahakam River section to support bridge design and safety assessments. Using a 100-year return period, the design rainfall was determined to be 1246 mm via the Log Pearson III method, resulting in a peak design flood discharge (Q₁₀₀) of 77,984 m³/s. Hydraulic analysis using a rating curve indicates a flood water level elevation of 32.578 m from the riverbed. Scouring calculations, including construction and stream scouring, were performed using Laursen’s and empirical methods. The results show a total scouring depth of 4.8 cm/year, primarily driven by stream scouring, as construction scouring was zero under current existing conditions. These findings emphasize the necessity of bank protection, such as gabions, to mitigate erosion risks for future infrastructure.

1. Introduction

Bridges are important transportation infrastructure that support connectivity and economic development. Suspension bridges are commonly used for long-span cross-ings because of their structural efficiency and ability to span wide rivers. How-ever, bridges over rivers are highly vulnerable to floods and scour, which can threaten structural stability and cause bridge failure [1]. Climate change and increasing ex-treme rainfall events have further intensified bridge vulnerability to hydraulic haz-ards [2].

Flood water level profile analysis is essential in hydraulic bridge engineering be-cause it evaluates water surface elevations, flow velocity, and backwater effects dur-ing flood events. These parameters are important for determining bridge elevation, freeboard, and foundation depth. Hydraulic modeling tools such as HEC-RAS are widely used to simulate river flow behavior around bridge structures [3]. Previous studies showed that hydraulic structures significantly affect river flow characteristics and flood water levels [4], while hydraulic instability may intensify sediment transport and local scour around bridge foundations [5].

Scour is recognized as one of the leading causes of bridge foundation failure worldwide [6]. Excessive scour can reduce foundation stability and load-bearing ca-pacity, potentially causing catastrophic bridge collapse [7]. Scour processes are in-flu-enced by flow conditions, sediment characteristics, pier geometry, and river mor-phology [8], while sediment deposition may also occur during unsteady floods [9]. Therefore, risk-based approaches integrating hydraulic modeling and bridge vul-nera-bility assessment have been developed to improve scour management [10].

Modern bridge assessment approaches emphasize hydraulic uncertainties, ge-otechnical variability, and climate-related hazards [11]. Fragility and resili-ence-based methods are increasingly used to evaluate bridge vulnerability under flood and scour conditions [12,13]. Various empirical and numerical methods have also been devel-oped to estimate scour depth around bridge foundations [14]. Studies demonstrated that scour significantly affects the structural behavior and stability of bridge piers during floods [15,16].

Recent advances in monitoring technologies such as sonar devices, fiber optic sensors, and remote sensing systems have improved bridge resilience and scour mon-itoring capabilities [17]. In addition, environmentally friendly countermeasures such as vegetation have shown promising results in reducing scour depth [18]. Expe-ri-mental studies also demonstrated that scour evolution depends on sediment charac-teristics and hydraulic variations [19], while flood and erosion processes are increas-ingly recognized as interconnected hazards affecting infrastructure vulnera-bility [20].

Therefore, this study entitled Analysis of Flood Water Level Profiles and Scouring Potential for a 200-Meter Span Suspension Bridge aims to evaluate hydraulic behav-ior and scour susceptibility under extreme flood conditions using hydraulic modeling techniques. The results are expected to support safer bridge foundation design and improve bridge resilience against future flood hazards.

2. Materials and Methods

2.1. Study Area and Data Collection

The study was conducted on a specific segment of the Mahakam River, East Ka-limantan. The Mahakam River basin covers an area of approximately 32.291 km² with a total river length of 565.79 km. Secondary data consisting of annual maximum daily rainfall records from 2014 to 2025 were obtained to perform hydrological mod-eling. See Figure 1 map of the Mahakam river,

Table 1. Input parameters for hydrological and hydraulic analysis.

Data Collection	Value	Unit
Manning’s roughness	0.06	mm
Average river slope	0.0005	mm
Catchment area	32.291	km2
Runoff coefficient	0.6	mm
River length	565.79	km

parameters for hydrological and hydraulic analysis and

Table 2. Sediment characteristics.

Sediment Grain Data	Value	Unit
D10	0.0001	mm
D50	0.008	mm
D65	0.04	mm
D80	0.1	mm
D90	0.2	mm

sendiment characteristic.

2.2. Design Rainfall Analysis

The systematic approach of this study is visualized in the research flowchart shown in Figure 2. The process begins with the collection of hydrological and sediment data. The methodology is divided into three primary analytical stages:

a. Hydrological Analysis

This stage involves statistical parameter testing using the Log Pearson Type III method to determine the 100-year design rainfall.

b. Hydraulic Analysis

Using the results from the hydrological modeling, the peak discharge is calculated via the Rational Method. A rating curve is then established to identify the flood water level (MAB) at an elevation of 32.578 m.

This sequential flow ensures that the design of the 200-m span suspension bridge accounts for both extreme water levels and the long-term erosion of the riverbanks.

2.3. Analysis Rainfall Calculations

a. The parameters related to data analysis, including the equations used, are summarized in the following

Table 3. Statistical parameters for frequency analysis.

Parameters	Equations
Standard Deviation	$\sigma =\sqrt{{\displaystyle \frac{{\Sigma (x-\overline{x})}^2}{(n-1)}}}$
Average	$\overline{X}={\displaystyle \frac{{\sum }_{i=1}^n{X}_i}{n}}$
Coefficient of Variation (Cv)	$C_v={\displaystyle \frac{S}{\overline{X}}}$
Coefficient of Skewness (Cs)	$C_s={\displaystyle \frac{n{\sum }_{i=1}^n{\left(X_i-\overline{X}\right)}^3}{\left(n-1\right)\left(n-2\right)S^3}}$
Coefficient of Kurtosis (Ck)	$C_k={\displaystyle \frac{n^2{\sum }_{i=1}^n{\left(X_i-\overline{X}\right)}^4}{\left(n-1\right)\left(n-2\right)\left(n-3\right)S^4}}$

.

b. Selection of Distribution Type

The selection of the appropriate probability distribution is determined by comparing the statistical parameters of the rainfall data against the specific requirements of each distribution method. The equations and statistical criteria used for this selection are summarized in

Table 4. Statistical requirements for each distribution type.

Distribution type	Statistical Requirements	Equations
Normal	Cs = 0	$X_T=\overline{X}+K_T·S$
	Ck= 3	$\sigma =\sqrt{{\displaystyle \frac{{\Sigma (x-\overline{x})}^2}{(n-1)}}}$
Log normal	Cs = 3Cv	$C_s={\displaystyle \frac{n·\sum {\left(\mathit{log}X-\overline{\mathit{log}X}\right)}^3}{\left(n-1\right)\left(n-2\right)·S_{\mathit{log}X}^3}}$
	Ck= Cv3 + 6Cv6 + 15Cv4 + 16 Cv2+ 3	M$S_{\mathit{log}X}=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{\left(\mathit{log}{X}_i-\overline{\mathit{log}X}\right)}^2}{n-1}}}$
Gumbel	Cs = 1.14	$X_T=\overline{X}+K_T·S$
	Ck= 5.400	$\sigma =\sqrt{{\displaystyle \frac{{\Sigma (x-\overline{x})}^2}{(n-1)}}}$
Log Pearson III	Apart from the values above	M$S_{\mathit{log}X}=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{\left(\mathit{log}{X}_i-\overline{\mathit{log}X}\right)}^2}{n-1}}}$
		$C_s={\displaystyle \frac{n·\sum {\left(\mathit{log}X-\overline{\mathit{log}X}\right)}^3}{\left(n-1\right)\left(n-2\right)·S_{\mathit{log}X}^3}}$

.

Where, C_s represents the coefficient of skewness, which describes the degree of asymmetry in the data distribution relative to its mean value. C_k denotes the coefficient of kurtosis, which indicates the peakedness or flatness of the data distribution compared with a normal distribution. Meanwhile, C_v refers to the coefficient of variation, which measures the relative variability of the dataset by comparing the standard deviation to the mean value. These statistical parameters are commonly used to evaluate data characteristics and determine the suitability of probability distributions in hydrological frequency analysis.

2.4. Goodness-of-Fit Testing

To ensure that the selected probability distribution statistically represents the observed rainfall data, two primary validation tests are conducted:

$${\chi }^2=\sum _{i=1}^k{\displaystyle \frac{{\left(O_i-E_i\right)}^2}{E_i}}$$

(1)

where

• ${\chi }^2$: Calculated Chi-Square parameter.
• N: Number of subgroups within a group.
• O_i: Observed frequency (actual number of data points in the i).
• E_i: Expected frequency (theoretical number of data points in the i).

$${\Delta }_{max}=\left|P_{empirical}-P_{theoretical}\right|<{\Delta }_{critical}$$

(2)

where

• Pempirik: Empirical probability (based on the ranking of observed data).
• Ptheoretical: Theoretical probability (based on the selected probability distribution.

The design rainfall (R_T) was analyzed using the Log Pearson Type III distribution. To convert the daily rainfall into peak flood discharge, the rainfall intensity was first calculated using the Mononobe equation:

$$\mathrm{I}={\displaystyle \frac{{\mathrm{R}}_{24}}{24}}{\left({\displaystyle \frac{24}{\mathrm{t}\mathrm{c}}}\right)}^{{\displaystyle \frac{2}{3}}}$$

(3)

where

• I: Rainfall intensity (mm/h).
• R: Maximum daily rainfall for a specific return period (mm).
• tc: Time of concentration (hours).

The peak flood discharge (Q) for the Mahakam River was then estimated using the Rational Method, which is suitable for the catchment area’s characteristics:

$$\mathrm{Q}=0.278\times \mathrm{C}\times \mathrm{I}\times \mathrm{A}$$

(4)

where

• Q: Peak discharge (m³/s).
• C: Runoff coefficient (mm/h).
• A: Catchment area (km²).

2.5. Hydraulic and Water Level Analysis

The hydraulic analysis was conducted to determine the flood water level at the cross-section of the planned bridge location. In addition to establishing a rating curve using Manning’s and continuity equations, a one-dimensional hydraulic modeling was performed using the Hydrologic Engineering.

The simulation was carried out under steady flow conditions. The geometric data inputted into the HEC-RAS version 6.4.1 model consisted of the Mahakam River’s cross-sectional profiles spanning a total reach length of 193.47 m, from Sta 0 + 000 to Sta 0 + 193.47. A Manning’s roughness coefficient (n) of 0.06 was applied to represent the channel’s characteristic.

The 100-year return period peak discharge (Q100) of 7798.4 m³/s was used as the primary flow data, while the established rating curve was utilized as the downstream reach boundary condition. The resulting water surface profile from this simulation is crucial for evaluating the available freeboard. The maximum flood elevation was compared against the planned bridge’s soffit level at an elevation of +36.00 m to ensure the structure provides an adequate safety margin against hydrodynamic forces and floating debris. See the Figure 3 illustration of river cross-section segmentation.

HEC-RAS (Hydrologic Engineering Center River Analysis System) is an application used to analyze flood discharge capacity in rivers and drainage channels. Furthermore, this software is used to model steady and unsteady river flow by integrating features such as a graphical user interface, hydraulic analysis, data management and storage, graphing, and reporting. The results after running the program can be seen in Figure 4.

2.6. Scouring Analysis and Calculation

The scouring analysis is conducted to evaluate the potential erosion of the riverbed at the Mahakam River cross-section. The analysis focuses on two primary components: construction scouring and stream scouring.

a. Determination of Scouring Type

To identify whether the riverbed experiences live-bed or clear-water scouring, the critical velocity (V_c) is s calculated and compared with the average flow velocity (V). The critical velocity is determined using the Laursen method (1963):

$${\mathrm{V}}_{\mathrm{c}}={\mathrm{K}}_{\mathrm{u}}·{\mathrm{y}}_1^{1/6}·{\mathrm{D}}_{50}^{1/3}$$

(5)

where

• V_c: Critical velocity of bed material (m/s).
• K_u: Constant coefficient (6.19 for SI units).
• y₁: Average flow depth at the contracted section (m).
• D₅₀: Median particle diameter of bed material (m).

b. Construction Scouring Calculation

Construction scouring occurs when the flow area is reduced by structural components. The depth is calculated using the following equations

$${\mathrm{y}}_2={\mathrm{y}}_1·{\left({\displaystyle \frac{{\mathrm{Q}}_2}{{\mathrm{Q}}_1}}\right)}^{6/7}·{\left({\displaystyle \frac{{\mathrm{W}}_1}{{\mathrm{W}}_2}}\right)}^{{\mathrm{K}}_1}$$

(6)

$${\mathrm{y}}_{\mathrm{s}}={\mathrm{y}}_2-{\mathrm{y}}_1$$

(7)

where

• y₂: Average flow depth in the contracted area after scouring (m).
• y₁: Average flow depth upstream (m).
• Q₁: Discharge at the upstream and contracted sections (m³/s).
• W₁: River width at the upstream and contracted sections (m).
• K₁: Exponent for bed material transport mode.
• y_s: Average construction scouring depth (m).

a. Shear Velocity

Shear velocity is calculated to determine the mode of bed material transport, which defines the exponent value (K₁) in the Laursen equation. The formula is as follows:

$${\mathrm{V}}_{*}={\left(\mathrm{g}·{\mathrm{y}}_1·{\mathrm{S}}_1\right)}^{0.5}$$

(8)

where

• ${\mathrm{V}}_{*}$: Shear velocity in the main channel (m/s).
• g: Acceleration of gravity (9.81m²/s).
• S₁: Slope of the energy grade line at the approach section.

a. Total Scouring Depth

Total scouring depth represents the cumulative effect of construction-induced erosion and the natural annual stream scouring. In this study, the total scouring is calculated using the following summation.

$$\mathrm{“}\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\hspace{1em}\mathrm{S}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{”}=\mathrm{“}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\hspace{1em}\mathrm{S}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{”}+\mathrm{“}\mathrm{S}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{m}\hspace{1em}\mathrm{S}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{”}$$

(9)

3. Result

3.1. Design Rainfall and Peak Discharge

Based on frequency analysis using the Log Pearson Type III method, the design rainfall for a 100-year return period (R100) is determined. By applying the Mononobe equation to calculate the intensity and the Rational Method for the discharge, the peak flood discharge (Q100) for the Mahakam River is calculated.

Table 5. Recapitulation of statistical parameter test results.

Distribution Type	Statistical Requirements	Calculated
Normal	Cs = 0	−0.6820
	Ck = 3	−0.0214
Log normal	Cs = 3Cv	0.4918
	Ck = Cv3 + 6Cv6 + 15Cv4 + 16Cv2 + 3	2.1317
Gumbel	Cs = 1.14	−0.6820
	Ck = 5.400	−0.0214
Log Pearson III	apart from the above values	−10.441

summarizes the results of statistical parameter tests and

Table 6. Recapitulation of hydrological analysis results for a 100-year return period.

Parameter	Value	Unit
Design Rainfall (R100)	1.246	mm
Rainfall Intensity (I)	14.48	mm
Peak Discharge (Q100)	7798.4	m3/s

summarizes the results of hydrological analysis for a 100-year return period.

3.2. Water Level Elevation and Structural Integration

The hydraulic analysis was conducted to establish the rating curve and simulate the one-dimensional flow profile using HEC-RAS. Based on the analysis, the maximum flood water level (MAB) for the 100-year return period design discharge of 7798.4 m³/s reached an elevation of 32.578 m. The HEC-RAS steady flow simulation across the 193.47-m river reach further verified this maximum water surface profile.

To visualize the relationship between the hydraulic analysis and the bridge design, an evaluation of the available freeboard was conducted. The 200-m span suspension bridge abutments are strategically positioned on the higher riverbanks, with the planned soffit level (bridge girder elevation) established at +36.00 m.

By comparing the planned bridge elevation (+36.00 m) with the design flood level (+32.578 m), the available vertical clearance or freeboard is calculated to be approximately 3.42 m. This clearance significantly exceeds the standard minimum freeboard requirement of 1.0 to 1.5 m for large rivers. This configuration ensures that the main superstructure remains elevated and safe from direct hydrodynamic forces, wave run-up, and potential floating debris during extreme flood events.

Furthermore, while the superstructure is secure, the base of the riverbanks (toe) is subjected to the calculated natural stream scouring rate of 4.8 cm/year. This necessitates the proposed bank protection measures, such as gabions, to ensure the long-term stability of the abutment foundations.

To visualize the relationship between hydraulic analysis and bridge design, a technical cross-section is presented in Figure 5. The figure illustrates that the abut-ments of the 200-m-span suspension bridge are strategically positioned on the higher river bank, well above the design flood level of 32,578 m. This configuration ensures that the primary structure maintains vertical clearance (freeboard), protect-ing the bridge from hydrodynamic forces and floating debris during extreme flood events. Furthermore, the visualization explains that while the superstructure remains elevated and safe from direct contact, the riverbank bed (toe) experiences a calculated erosion rate of 4.8 cm/year, necessitating the proposed riverbank protection measures to ensure foundation stability. Figure 6 shows the profile of the planned 200-m suspension bridge.

3.3. Scouring Analysis Results

The scouring potential at the Mahakam River study site was evaluated by analyzing the interaction between the hydraulic flow properties and the bed material characteristics (D₅₀ = 0.008 mm). The results are categorized into scouring type determination, construction scouring, and annual stream scouring.

a. Bed Material Transport and Scouring Type

Based on the Laursen method, the critical velocity (V_c) was calculated to be 2.012 m/s. Comparing this with the average flow velocity (V) of 2.078 m/s, the condition V > V_c indicates that the riverbed is subject to live-bed contraction scouring. This signifies that the sediment at the riverbed is in motion during the scouring process.

b. Calculation of Scouring Depth

The calculation results for the different scouring components are summarized in

Table 7. Summary of scouring depth analysis.

Parameter	Value	Unit
Critical Velocity	2.012	m/s
Average Flow Velocity	2.078	m/s
Construction Scouring	0	m
Annual Stream Scouring	4.8	cm/year
Scouring Depth	4.8	cm/year

.

c. Discussion of Scouring Impact

The construction scouring depth is recorded as 0 m under the assumption that no bridge piers or structural obstructions are currently placed within the main river channel. Consequently, the total scouring observed is entirely driven by the natural stream scouring process, which amounts to 4.8 cm/year. Although the annual rate appears minimal, long-term monitoring is recommended to mitigate potential bank instability and riverbed degradation.

4. Discussion

Based on the HEC-RAS cross-sectional outputs from Sta 0 + 000 to Sta 0 + 180, the river channel generally exhibits a deep main channel with relatively steep side slopes and asymmetric bank geometry. The modeled sections indicate that the majority of the flood discharge is concentrated within the central channel zone, producing relatively high flow velocities and increasing the possibility of local bed erosion. In several sections, particularly around Sta 0 + 020 to Sta 0 + 080, the river channel becomes narrower and deeper, which causes stronger flow concentration and higher hydraulic energy. Under these conditions, the riverbed experiences increased shear stress that may trigger live-bed scouring processes.

The hydraulic computations in HEC-RAS are governed using the one-dimensional energy equation:

$$Z_1+Y_1+{\displaystyle \frac{a_1{V}_1^2}{2_g}}=Z_2+Y_2+{\displaystyle \frac{a_2{V}_2^2}{2_g}}+h_e$$

(10)

where Z represents channel bed elevation, Y is flow depth, V is average velocity, α is the velocity coefficient, and h_e is the total energy loss between two cross sections. The equation explains the gradual variation of the water surface elevation observed throughout the modeled reach. The simulation results show that the water surface profile remains relatively stable at approximately elevation +32.5 m despite local geometric changes in the river section.

To strengthen the practical engineering interpretation of the hydraulic and scouring analysis, this study proposes a simplified dimensionless parameter called the Scour Safety Index (SSI):

$$SSI={\displaystyle \frac{{QS}_f}{{BD}_{50}}}$$

(11)

where Q is the flood discharge, S_e is the energy slope, B is the effective river width, and D₅₀ is the median sediment diameter. The proposed SSI integrates the influence of hydraulic energy, river geometry, and sediment characteristics into a single practical engineering parameter for preliminary bridge safety assessment. Using the hydraulic characteristics obtained from the Mahakam River simulation:

• Q: 7798.4 m³/s
• S_e: 0.00015
• B: 180 m
• D₅₀: 0.008 mm

The SSI value was calculated as:

$$SSI={\displaystyle \frac{7798.4\times 0.00015}{180\times 0.008}}=0.812\approx 0.81$$

(12)

Based on the proposed cleaning safety classification, the SSI values are categorized as shown in

Table 8. Scouring classification.

SSI Value	Scouring Condition	Engineering Interpretation
SSI < 0.5	Low	Stable riverbank condition
0.5 ≤ SSI < 1.0	Moderate	Minor local erosion possible
1.0 ≤ SSI < 2.0	High	Active live-bed scouring likely
SSI ≥ 2.0	Critical	Severe erosial risk to abutment and riverbank stability

. Scouring classification.

Based on the proposed scouring classification, the obtained SSI value falls within the moderate scouring categority (0.5 ≤ SSI < 1.0). This classification indicates that the river remain hydraulically stable under the design flood condition, however, localized erosion and gradual riverbank degradation may still occour, particularly near the riverbank toe and sections with concentrated flow velocity.

5. Conclusions

This study concludes that the 100-year return period flood discharge (Q₁₀₀) for the Mahakam River at the planned bridge site is 7798.4 m³/s. Based on the rating curve analysis, the maximum flood water level elevation is determined to be 32.578 m, which serves as a critical baseline for the 200-m span suspension bridge’s vertical clearance to prevent structural damage from floating debris. Furthermore, the identified natural stream scouring potential of 4.8 cm per year necessitates long-term monitoring and robust foundation planning to ensure structural integrity over the bridge’s design life. Overall, this research provides the essential technical parameters for resilient infrastructure, directly supporting the objectives of SDG 9 and SDG 11 by ensuring safe and reliable transportation connectivity for the local community.