Potential Dam Breach Flood Assessment with the 2D Diffusion and Full Dynamic Wave Equations Using a Hydrologic Engineering Center-River Analysis System

Abstract

Dam breaches have catastrophic consequences, causing severe property damage, life loss, and environmental impact. The potential dam breach downstream flooding of the Kulekhani reservoir, Nepal, was studied using a 2D Diffusion Wave Equation (DWE) and Full Dynamic Wave Equation (FDWE) through an open-source solver, Hydrologic Engineering Center-River Analysis System (HEC-RAS). The suitable dam breach model was identified based on the dam geometry and sixteen historical dam failure cases. The simulated downstream peak was tested with an empirical relation, considering reservoir volume and duration of failure. Model comparisons through the flood plain mapping of water depth, flow velocity, flood intensity as per guidelines of the American Society of Civil Engineers (ASCE), and arrival time were carried out for flood hazard assessment. FDWE was able to capture the physical flow phenomena in the river bend resulting in higher flow velocity at the outer bend, lower velocity at the inner bend, and formation of eddies due to the application of the turbulence model, considering possible momentum losses, whereas DWE was unable to capture these effects due to a simplified momentum equation. The total area of flood extension was found to be increased by 30% using FDWE than the DWE due to higher water surface elevation. Most of the towns along the Kulekhani River were classified as “Very High” intensity flood regions according to ASCE, due to the V-shape valley. The peak time difference at the Bagmati River confluence was evaluated between the models. This plays an important role in decision-making for the selection of the flood model to make a safe evacuation plan. The application of FDWE was found to be suitable for the rapidly varying unsteady flow in the steep meandering river.

1. Introduction

Over the last decades, multipurpose dams have been built for water supply, flood control, hydropower generation, irrigation, recreation, and tourism. Sadd el-Kafara Dam, Egypt [1], and Jawa Dam, Jordan [1,2], are some of the oldest dams in the world built over 2000 years ago. People have been living near the river for a long time, and the development of human civilizations is closely tied to the availability of water. Rivers are considered a consistent source of fresh water, providing fertile land for agriculture, and inland navigation for trades [3]. Living near a river might be hazardous due to recurring flooding events, bank erosion, and other natural hazards. Downstream flooding events due to the dam breach have a huge potential for widespread devastation, significant natural hazards, loss of property, and threaten human life [4]. Proper awareness and planning are essential for the people living riverfront to ensure safety and resilience against natural hazards. The Johnstown Flood (1889) [5,6] due to the South Fork Dam breach is considered one of the deadliest flood events due to dam breaches in U.S. history, where nearly two thousand people were killed and several villages were affected by the destruction of property. Similarly, the Vajont Dam Disaster (1963) [7], Teton Dam failure (1976) [8], Banqiao Dam failure (1975) [9], Taum Sauk Dam failure (2005) [10], and Malpasset Dam failure (1959) [11] are some of the dam breaks that have created serious threats to the people and property downstream of of the dam.

Vaskinn and Hassan [12] conducted a large-scale physical breach formation model test to identify different failure processes such as cracking, arching (pipe formation), head-cut formation, and progression of the breach. The downstream peak of the homogeneous dam was found to be higher than the zonal rockfill dam, as the breach duration was short for a homogeneous dam due to quick erosion. Ashraf [13] studied the large-scale physical model to establish the relationship between breach parameters, considering the breach opening, outflow peak, and breaching time through statistical methods using a regression model. The non-linear regression model resulted in a good arrangement with the physical model test. Sammen [14] described several existing regression equations for breach parameters including the well-known MacDonald and Langridge-Monopolis (1984), Froehlich (1995), Froehlich (2008), Von Thun and Gillette (1990), X and Zhang (2009) equations. The accuracy of the regression models was tested and identified with absolute relative error from 0.3 to 1.05 for breach width, and 0.6 to 0.8 for the duration of failure. Saberi et al. [15] established a new hydrograph approach to compute peak outflow with an empirical relationship between reservoir volume and time of the breach. The empirical relation was validated with past regression models and measured data sets. The accuracy of the downstream peak was improved with the simplification of the hydrograph shape.

Bellos [16] studied the uncertainty of the dam breach model parameters for maximum peak flood flow and inundation depth downstream using Monte Carlo simulation considering the Papadiana Dam failure, Greece. The uncertainty of peak flow was found to be higher than the water depth downstream. Albu [17] applied 2D DWE with HEC-RAS to evaluate the impact of dam breach size on flood downstream considering a case study of Dracsani Lake. Less effectiveness of breach size was emphasized for extremely unlikely catastrophic failure, and a 10% breach size simulation was found to be critical concerning depth and velocity. Mattas [18] applied FDWE to perform a dam breach flood hazard assessment of Papadia Dam, Greece. The breaching formation time was identified as a critical parameter for the downstream peak. The over-topping and piping scenarios were implemented, where over-topping was found to be vulnerable due to higher flood extension. Urzică [19] studied the impact of different recurring flood events with dam breach scenarios, for the assessment of flood control in multiple-reservoir systems. The 1000-year flood event was found to be vulnerable for all the 28 settlements downstream using DWE.

Yilmaz [20] modeled flood hazard assessment of the Dalaman Akköprü Dam breach using 2D FDWE and DWE to compare the change in water depth and flow velocity due to the influence of simplified and full momentum equation. Decreased flow velocity variation and higher water surface elevation were observed in some of the sections of the river due to the effect of local and convective acceleration using the FDWE. Pilotti et al. [21] estimated downstream hydrograph using a 2D FDWE with the application of open-source solver HEC-RAS and TELEMAC. A good match of downstream hydrograph results was obtained and compared with the experimental Cancano dam break test case. Psomiadis [22] performed the HEC-RAS 2D dam breach model of Bramianos Dam to compare the downstream potential flood hazard using the Digital Elevation Model and Digital Surface Model. The flood hydrographs using DWE and FDWE were compared and found to be more or less similar at the downstream side of the dam section. However, the effects of momentum loss were not studied due to computational cost. Costabile [23] compared the flow depths considering a case of flow interaction with the blocks using FDWE and DWE. The results have shown that the FDWE successfully captures the reflection of the wave and the wake effects due to the interaction of the block as expected. Costabile [23] also compared the simulated hydrograph results with the experimental data and concluded that the poor prediction was achieved with the DWE for all the gauges as it significantly underestimated the fluid–block interaction.

This paper studies the selection of an appropriate dam breach model and the possible dam break flood hazard assessment of the Kulekhani reservoir rockfill dam of Nepal. Two-dimensional FDWE and DWE have been applied on a steep meandering river to investigate the limitations and capabilities of the models, using open source solver HEC-RAS version 6.5 with the following objectives:

-

To define the appropriate dam breach model.

-

To study flood hazard assessment with FDWE and DWE considering:

(a)

Flow depth mapping;

(b)

Area of inundation;

(c)

Flood hazard classification based on flood intensity values;

(d)

Time of arrival mapping.

2. Materials and Methods

2.1. Area of Interest

The Kulekhani reservoir dam is the oldest rockfill dam in Nepal located at Dhorsing, Makwanpur. The impounded water of the reservoir has been used to generate electricity by three hydropower stations, Kulekhani I (60 MW) commissioned in 1982, Kulekhani II (32 MW) commissioned in 1986, and Kulekhani III (14 MW) commissioned in 2019 owned by Nepal Electricity Authority [24]. The designed Kulekhani reservoir capacity can withhold Probable Maximum Flood (PMF) up to 2540 m³/s considering a watershed area of 126 km² [25]. The zonal rock fill dam consists of an inclined clay core, coarse and fine filter materials, and boulder rip rap for slope protection as shown in Figure 1. The dam was constructed with an overall upstream slope of 1:2.35 and a downstream slope of 1:1.8. The clay core zone has been excavated until the bedrock, and provided with the grout curtain to prevent flow through seepage [25]. The 10 m crest-width dam has a central axis cross-sectional bottom length of 97 m and a top length of 397 m with a height of 114 m.

The meandering river of 16km reach length from the downstream of the dam to the confluence of the Bagmati River has been identified. The Kulekhani River has a steep overall slope of 1:42 and a narrow valley with a vertical side slope between 45 and 60°. The river bottom width varies from 50 to 250 m with less flood plain area due to the V-shape valley. The twelve possible towns identified as likely to be vulnerable due to dam breach are shown in Figure 2.

The existing total number of living households in the town was estimated based on the provided number of households on a 2785 05D Bhimphedi [27] topographic map and open street map from RAS-Mapper using HEC-RAS. The expected total number of households along the Kulekhani River until the Bagmati River confluence has been presented in

Table 1. Expected total number of households along the river to be flooded [27].

Town	Households
Thulchaur	13
Ranche, Nagmar, Khanikhet, and Debaltar	71
Lambagr and Sulikot	48
Tallogau, and Tinghare	10
Sano Tar	32
Simletar	20
Kuntar	18

.

2.2. Framework

All the pre-processing, solving, and post-processing works were carried out on the open-source solver HEC-RAS. The flow chart in Figure 3 shows the carried-out workflow model comparison, for dam breach flood hazard assessment using FDWE and DWE.

2.3. Data Acquisition

The geometrical data and hydraulic parameters are essential to setup the model. The geometrical data define land terrain and dam geometry, whereas hydraulic parameters are defined by Manning’s roughness, flow boundary conditions, initial water surface elevation in the dam considering the reservoir volume–elevation curve, downstream boundary conditions (ie. normal depth), and dam breach parameters (i.e., bottom width of breach and duration of the failure) with the appropriate breach model.

• Dam Geometry

The used dam geometry parameter during the simulation has been provided in

Table 2. Dam geometry.

Crest length	397 m
Crest width	10 m
Bottom width	97 m
Total height	114 m
Breach height	75 m
Upstream slope	1V:2.35H
Downstream slope	1V:1.18H

. The breach height of 75 m was adopted, considering the difference between the crest and downstream bed level.

• Digital Elevation Model (DEM) and Roughness Mapping

An available minimum 12.5 m resolution data set of DEM was adopted through the Alaska Satellite Facility (ASF) [28] and considered for defining the terrain up to the confluence of Bagmati River. The Esri Land Cover [29] map was also used to define varying Manning’s roughness using QGIS and RAS-Mapper. The expected river channel flow was drawn to represent the channel roughness precisely due to the poor resolution of the land cover map as shown in Figure 4. The roughness values listed in

Table 3. Model-defined Manning’s roughness.

Manning’s Roughness
Open water	0.035
Forest	0.14
Crops	0.05
Bare ground	0.04
River	0.037
No data	0.06

were assigned based on the work of Ven Te Chow (1959) [30] and Schneider (1989) [31]. The effective appropriate roughness in the river channel was defined considering the guideline for selecting Manning’s roughness coefficients by Schneider (1989) based on the river bed grain size distribution; further details can be found in the references [31].

• Volume–Elevation Curve

The reservoir volume elevation–area curve is an essential parameter for dam break that determines the change in volume with respect to change in elevation. The curve accurately represents the hydrodynamics of the dam breach to determine the dam release flow rate, often used in dam break simulation to calibrate and validate real case failure results as illustrated by Alcrudo [32]. The Kulekhani reservoir holds a volume of 85.285 million m³ with a surface area of 2.2 km² spread up to 7 km as illustrated in Figure 5. The volume–elevation curve of the Kulekhani reservoir was used during the simulation to determine the dam release flow rate.

2.4. Dam Breach Model

The dam breach modeling process is the mathematical and physical representation of the dam’s failure to release significant flow from the reservoir. The selection of an appropriate dam breach model is often considered a challenging task due to uncertainties of dam failure and resulting downstream peak, which is directly affected by the dam breach parameter [33]. Several validated regression equations have been established to determine the dam breach parameter, i.e., average breach width, side slope, volume of erosion, and time of breach based on the dam failure cases. HEC-RAS implements some well-known regression models such as Froehlich (1995), Froehlich (2008), MacDonald and Langridge-Monopolis (1984), Von Thun and Gillette (1990), and Xu and Zhang (2009) [34]. Figure 6 shows the typical trapezoidal breach section defined with side slope, widths, breach height, and water level. The implemented regression equations for defining the breach parameter have been formulated in

Table 4. Regression model equations for breach parameter [34].

Regression Equation	Average Breach Width (${\mathit{B}}_{\mathit{ave}}$)	Breach Formation Time (${\mathit{t}}_{\mathit{f}}$)
Froehlich (1995)	$B_{ave}=0.1803K_0{V}_w^{0.32}{h}_b^{0.19}$	$t_f\left(h\right)=0.00254V_w^{0.53}{h}_b^{-0.90}$
Froehlich (2008)	$B_{ave}=0.27K_0{V}_w^{0.32}{h}_b^{0.04}$	$t_f\left(s\right)=63.2\sqrt{\frac{V_w}{g{h}_b^2}}$
MacDonald and Langridge-Monopolis (1984)	$V_{\mathit{eroded}}=0.00348{\left(V_{\mathrm{out}}\times h_w\right)}^{0.852}$$W_b=\frac{V_{\mathit{eroded}}-h_b^2\left(C{Z}_b+h_b{Z}_b{Z}_3/3\right)}{h_b\left(C+h_b{Z}_3/2\right)}$	$t_f\left(h\right)=0.0179{\left(V_{\mathit{eroded}}\right)}^{0.364}$

.

Where; $W_b$ = Bottom width (m), $B_{ave}$ = Average width (m), $V_{eroded}$ = Volume eroded (m³), $t_f$ = Breach formation time ($s,h$), $K_o$ = constant (1.3 for over-topping), $V_w$ = Volume of the reservoir (m³), $V_{out}$ = Volume of the water passing through the breach (m³), g = acceleration due to gravity (m/s²), $h_b$ = breach height (m), $h_w$ = water depth (m), c = crest width (m), $Z_1$ = average slope-upstream face, $Z_2$ = average slope-downstream face, $Z_3$ = $Z_1$ + $Z_2$.

The regression models using Froehlich (1995), Froehlich (2008), and MacDonald and Langridge-Monopolis (1984) were tested using the over-topping scenario excluding Von Thun and Gillette (1990), and Xu and Zhang (2009) as they were providing higher breach bottom width than the existing bottom width geometry of the dam section, i.e., 97 m. The estimated dam breach parameters (ie. breach bottom width, side slope, and duration of breach) considering the breaching depth of 75 m (1459 m.a.s.l) and reservoir volume of 85.285 million m³ are presented in Figure 7.

2.5. Model Mesh

The river channel and flood plains experience spatial water depth and velocity variation. These detail variations due to the complexity of flow patterns are adequately captured by a 2D mesh as compared to the 1D model. Therefore, the 2D mesh was adopted to enhance the modeling capabilities in the complex flow behavior. In order to accurately capture the hydrodynamic behavior in the river channel, the central line and banks were assigned to refine and construct an aligned mesh along the direction of flow using HEC-RAS as shown in Figure 8. The refining of mesh helps to precisely evaluate the hydraulic parameters like velocity gradient and water surface elevation.

2.6. Breach Model Selection

The initial model was run with Froehlich (1995), Froehlich (2008), and MacDonald and Langridge-Monopolis (1984) to estimate the downstream peak. The peak discharge of 61,389 m³/s using Froehlich (2008) with 0.69 h duration of failure, 49,066 m³/s implementing Froehlich (1995) with 0.83 h duration of failure, and 17,594 m³/s considering a 2.51 h duration of failure with MacDonald and Langridge (1984) were evaluated at downstream of the dam as shown in Figure 9.

A significant difference in peak discharge was observed as the time of breach highly dominates the downstream flow peaks. Therefore, sixteen historical earth-fill dam break events were studied based upon the duration of failure to select the appropriate dam break model, as illustrated in

Table 5. Sixteen dam break cases with observed and estimated peaks using the hydrograph method [35,36].

Name	Height (m)	Reservoir Volume (Million m3)	Duration of Failure (h)	Observed Peak (m3/s)	Estimated Peak (m3/s)
Teton Dam (1976)	94	356	4	46,817	44,949
Baldwin Hills Dam (1963)	70.7	1.1	4.5	141	123
Euclides Da Cunha Dam (1977)	53.07	13.56	7.25	1004	945
Mammoth Dam (1943)	21.3	13.56	3	2521	2283
Hatchtown Dam (1914)	19.8	14.8	4	1973	1869
Whitewater Brook Upper Dam (1972)	18.8	0.51	3	70	86
Horse Creek Earth Dam (1914)	16.7	20.96	3	3885	3529
Puddingstone Dam (1926)	15.24	0.61	3	283	103
Wheatland Reservoir No. 1 Dam (1969)	13.7	11.55	1.5	4285	3889
Lake Latonka Dam (1966)	13.1	1.58	3	294	266
Frenchman Dam (1952)	12.1	8.6	3	1603	1448
Frankfurt Dam (1975)	9.75	0.35	2.5	79	71
Elk City Dam (1963)	9.14	0.9	0.83	607	545
Kelly Barnes Lake Dam (1977)	7.92	1.62	1.5	549	545
Hemet Dam (1927)	6.1	28.22	3	1602	4751
Goose Creek Dam (1916)	6.1	68.79	3	3880	11,581

.

Although breaching time and breach width are uncertain, Table 5 shows the breaching time for most of the observed real cases, which was found to be above 2.51 h for large dams. The duration of the breach with Froehlich (1995) was 0.83 h and Froehlich (2008) was 0.69 h which significantly increased the downstream peaks. Therefore, MacDonald and Langridge’s (1984) regression equation with a breach duration of 2.51 h was implemented to obtain the breach parameters with the expected peak discharge of 17,594 m³/s.

2.7. Evaluation with Empirical Equation

Sixteen dam breaks observed downstream peaks were tested against the hydrograph method as shown in Figure 10, suggested by Saberi et al. [15]. Downstream peaks ($Q_p,$ m³/s) were estimated considering the reservoir volume ($V_w$, m³) and time of the breach ($t_f,s$), as represented in Table 5.

$$Q_p=\frac{2V_w}{t_f(2\alpha +\beta -\alpha \beta )}$$

(1)

where

• Height of rectangle = $\left(Q_p\right)$;
• Height of triangular shape $=\beta \times Q_p$;
• Width of rectangular shape $=\alpha \times t_f$;
• Width of triangular shape $=t_f-\left(\propto \times t_f\right)/2$.

The regression model of Figure 11 shows a good correlation (R${}^2$ = 0.96) between historical events’ observed and estimated values from the hydrograph method. Thus, the empirical relation was used to evaluate the simulated results considering 2.51 h of breach time with 85.285 million m³ volume. The model produces more or less similar peak flow results with an absolute error of 2.5% as presented in

Table 6. Simulated and estimated peak values at section 0 (reference Figure 14), downstream of dam.

Simulated Peak (m3/s)	Estimated Peak (m3/s)
17,594	17,160

.

2.8. HEC-RAS Modelling

The HEC-RAS has a wide range of applications in an open channel flow with 1D and 2D model approaches for steady and unsteady state conditions. The 1D model is generally used for simplified flow problems, considering unidirectional flow in a straight channel where lateral flow variations are limited. A 2D model is more suitable for complex topography and meandering river channels with prone flood plains. To adequately capture the spatial flow velocity and water surface elevation variation across the section and the entire flood plain, a 2D model was adopted during the simulation. The reliability of the flow parameters (i.e., flow depth, velocity) depends upon the model input parameters: some of the influencing parameters are Manning’s roughness, DEM resolution, meshing size, and dam breach duration time in the case of breach flood assessment which highly influences the downstream peak discharge.

The Shallow Water Equation is widely used for solving rapidly varying unsteady flow problems such as dam break scenarios, change in channel geometry with contraction and expansion, and steep mountain terrain meandering rivers [37]. HEC-RAS uses the Finite Volume Method to solve the Shallow Water Equations by discretizing the computational domain to the grid cells and integrating the conservation equations with an implicit time integration scheme.

A hyperbolic partial differential equation is derived from the depth average integration of the Navier–Stokes equation, assuming the horizontal length scale larger than the vertical length scale. The vertical pressure gradient is nearly hydrostatic, with a vertical velocity much smaller than the horizontal velocity. Therefore, vertical velocity variation is not explicitly resolved by the shallow water equation and can be considered as a limitation. The 2D full momentum equations with conservative turbulence viscosity model in the differential form are [34]:

$$\frac{𝜕u}{𝜕t}+u\frac{𝜕u}{𝜕x}+v\frac{𝜕u}{𝜕y}-f_{c}v=-g\frac{𝜕z_s}{𝜕x}+\frac{1}{h}\frac{𝜕}{𝜕x}\left({\nu }_{t,xx}h\frac{𝜕u}{𝜕x}\right)+\frac{1}{h}\frac{𝜕}{𝜕y}\left({\nu }_{t,yy}h\frac{𝜕u}{𝜕y}\right)-\frac{{\tau }_{b,x}}{\rho R}+\frac{{\tau }_{s,x}}{\rho h}-\frac{1}{\rho }\frac{𝜕p_a}{𝜕x}$$

(2)

$$\frac{𝜕v}{𝜕t}+u\frac{𝜕v}{𝜕x}+v\frac{𝜕v}{𝜕y}+f_{c}u=-g\frac{𝜕z_s}{𝜕y}+\frac{1}{h}\frac{𝜕}{𝜕x}\left({\nu }_{t,xx}h\frac{𝜕v}{𝜕x}\right)+\frac{1}{h}\frac{𝜕}{𝜕y}\left({\nu }_{t,yy}h\frac{𝜕v}{𝜕y}\right)-\frac{{\tau }_{b,y}}{\rho R}+\frac{{\tau }_{s,y}}{\rho h}-\frac{1}{\rho }\frac{𝜕p_a}{𝜕y}$$

(3)

where

u = velocity in the x direction (m/s), v = velocity in the y direction (m/s), t = time (s), g = acceleration due to gravity (m/s²), $z_s$ = water surface elevation (m), ${\nu }_{t,xx}$, ${\nu }_{t,yy}$ = eddy viscosity in the x and y directions (m²/s), ${\tau }_{b,x},{\tau }_{b,y}$ = bottom shear stress in x and y direction (N/m²), ${\tau }_{s,x},{\tau }_{s,y}$ = surface wind stress in x and y direction (N/m²), R = hydraulic radius (m), h = water depth (m), $p_a$ = atmospheric pressure (N/m²)

In order to capture the Coriolis effect in the Kulekhani River, the latitude ($\varphi$) of 27.5° was defined in the model. The conservative turbulence model was applied to adequately capture the lateral flow velocity distribution, considering the Smagorinsky coefficient of 0.05, the transverse mixing coefficient of 0.1, and the longitudinal mixing coefficient of 0.3; a detailed discussion of the parameters has been made in the HEC-RAS reference manual [34].

The applied DWE is a simplified version of the momentum equation, primarily developed to solve 1D problems where lateral flow variations are neglected. The momentum equation has been simplified neglecting local acceleration, convective acceleration, turbulence effects, and Coriolis effects in Equations (2) and (3).

• Mesh Sensitivity and Stability Analysis

The mesh sensitivity and stability analyses were carried out with the FDWE as the DWE model was found to have high stability. The fixed time steps of $\Delta t$ = 0.2 s with varying spatial steps of $\Delta x$ = 30 m, $\Delta x$ = 20 m, $\Delta x$ = 10 m, $\Delta x$ = 5 m, and $\Delta x$ = 4 m were considered to evaluated hydrograph at cross-section II (reference Figure 14), as represented in Figure 12. The spatial step of $\Delta x$ = 5 m was selected for the model run as the result starts to converge with the decreasing spatial steps below $\Delta x$ = 5 m as illustrated in

Table 7. Mesh sensitivity analysis.

$\mathbf{\Delta }\mathit{x}$ (m)	Peak Flow (m3/s)
30	17,455.25
20	17,319.44
10	17,256.97
5	17,086.11
4	17,085.94

. The courant criterion was satisfied using the fixed time step method to ensure the model’s stability and robustness considering $\Delta x$ = 5 m and $\Delta t$ = 0.2 s.

$$\mathrm{Courant}\mathrm{Number}\left(\mathrm{CFL}\right)=\frac{\Delta t·V}{\Delta x}\le 1$$

(4)

where

• $\Delta t$ = Time step
• $\Delta x$ = Spatial step or computational grid cell length
• V = Flow velocity

3. Result and Discussion

3.1. Flow Characteristic

The flow behaviors, lateral flow velocity, and water surface elevation variation over the cross-section were evaluated as shown in Figure 13.

The meandering effects in the river often exhibit complex flow behavior due to influences of different types of forces. Centrifugal forces acting on the outer bend of the river result in higher flow velocity, leading to bank erosion, whereas centripetal forces acting in the inner bend result in less flow velocity leading to deposition, forming a point bar. The helical flow within the meandering due to the combined force effect of centripetal and Coriolis often affects sediment transport and river morphology. Numerical modeling of the nonlinear interaction of these types of forces is hard to achieve with simplified models. The model comparison was made using FDWE and DWE.

The FDWE was applied with the conservative turbulent model, and the Coriolis force (defined by 27.5° of latitude). The model was able to capture the effects of centrifugal and centripetal force, leading to higher flow velocity towards the outer bend and less flow velocity in the inner bend of the river as shown in Figure 13a. The result indicated that there is a higher chance of bank erosion at the outer bend and sediment deposition in the inner bend during the dam break as expected. The turbulent model was able to capture the formation of eddies in the meandering of rivers, especially in areas of flow separation as shown in Figure 13a. The velocity and water surface elevation variation across the cross-section were evaluated, as shown in Figure 13c. Constant vertical flow velocity was obtained due to the limitation of the model. The momentum equation of the Shallow Water Equation assumes vertical velocity much smaller than the horizontal velocity. Therefore, detailed effects of secondary flow due to meandering effects are not captured in the model.

The simplified DWE was applied neglecting local acceleration, convective acceleration, turbulence, and the Coriolis effect. The model was not able to capture the effects of centrifugal and centripetal forces, leading to higher central flow velocity as shown in Figure 13b,d. The model was also not able to capture the formation of eddies due to the absence of a turbulence model. The velocity and water surface elevation variation across the cross-section was not adequately obtained due to different flow behavior than expected, as shown in Figure 13b,d. Therefore, simulated results might lead to false velocity and water surface elevation.

Overall, the FDWE was able to capture the dynamic flow behavior in the meandering river than the DWE. Therefore, DWE was found to be unsuitable in meandering rivers where the flow velocity and water surface elevation variation across the cross-section behaved completely differently than the actual physical flow.

3.2. Flow Variation

To evaluate the flow variation in the river due to the application of FDWE and DWE, flow hydrographs from different cross-sections were obtained. The four cross-sections (i.e., I, II, III, IV) were specified at the downstream side of the river until the Bagmati confluence as shown in Figure 14. The flow hydrograph from the different sections was plotted and compared as shown in Figure 15, Figure 16, Figure 17 and Figure 18. The flow hydrograph of section I as represented by Figure 15 follows more or less the same distribution of discharge between the models due to fewer momentum losses, whereas the flow hydrograph of section IV as shown in Figure 18 near the confluence of Bagmati River experiences a noticeable variation in flow hydrograph between the models due to considerable momentum loss. This significantly affects the peak time and flow rate during the flood event. Peak time and flow rates are tabulated in

Table 8. Peak flow attenuation and time lag.

Section	Diffusion Peak (m3/s)	Peak Time (h)	Dynamic Peak (m3/s)	Peak Time (h)
Section I	17,588.76	1.73	17,582.21	1.75
Section II	17,522.24	1.78	17,086.11	1.90
Section III	17,469.44	1.87	16,832.48	2.12
Section IV	17,354.52	1.92	16,683.82	2.20

. The peak time difference at the confluence between the models was found to be 0.28 h, which is almost 17 min.

All four sections’ flow hydrographs were plotted for both models to evaluate the flood attenuation, as shown in Figure 19 and Figure 20. The flow hydrograph clearly indicated less flood peak attenuation and less flattening in the recession limb for both models, as river reach was steep with less floodplain area due to the V-shaped valley river. The river has a steep overall slope of 1:42 until the confluence of the Bagmati, where the bottom width varies from 50 to 250 m with a vertical side slope between 45 and 60°. Less attenuation with less time of lag was observed using the DWE than the FDWE model, as illustrated in summary Table 8. This implies FDWE captured all the possible momentum losses in the river reach. The momentum losses in the Kulekhani River were mainly due to friction loss, channel expansion–contraction loss, bend-induced energy loss, and dynamic loss due to turbulent mixing and eddy formation. The applied conservative momentum equation adequately captures these effects in the meandering river as shown in Figure 13a. Therefore, it is essential to select the appropriate FDWE flood model for precise early warning flood forecasts to safely evacuate the place.

3.3. Flood Hazard Assessment

The flood hazard assessment was carried out to identify the affected settlement downstream of Bagmati River confluence. Flow depth, time of arrival, and flood intensity mapping were carried out to identify the flood-prone area. The model comparison was carried out to evaluate the flood extension on settlements as shown in Figure 21.

• Flood Depth Mapping

The affected settlements were evaluated considering with and without floods using an open street map through RAS-Mapper as shown in Figure 21. The obtained flow depth mapping has shown that all twelve towns will be affected by both models due to dam breaches. The summary of the affected households has been presented in

Table 9. Flooded households along the river.

Town	$\begin{array}{c}\mathbf{Expected}\\ \mathbf{to}\mathbf{be}\mathbf{flooded}\end{array}$	$\begin{array}{c}\mathbf{Flooded}\\ \left(\mathbf{FDWE}\right)\end{array}$	$\begin{array}{c}\mathbf{Flooded}\\ \left(\mathbf{DWE}\right)\end{array}$
Thulchaur	13	7	4
$\begin{array}{c}\mathrm{Ranche},\mathrm{Nagmar},\\ \mathrm{Khanikhet},\mathrm{and}\\ \mathrm{Debaltar}\end{array}$	71	47	21
$\begin{array}{c}\mathrm{Lambagr}\mathrm{and}\\ \mathrm{Sulikot}\end{array}$	48	15	11
$\begin{array}{c}\mathrm{Tallogau},\mathrm{and}\\ \mathrm{Tinghare}\end{array}$	10	8	5
Sano Tar	32	14	12
Simletar	20	16	10
Kuntar	18	13	9

.

Comparatively, most households are affected using FDWE rather than a DWE, which is reasonable as the dynamic wave induces momentum loss capturing the effects of inertial forces. The spatial flow velocity and water surface elevation variation are accurately captured, according to the physical flow behavior as shown in Figure 13a,c. The water surface elevation was found to be higher due to spatial flow velocity variation which can be clearly visualized from Figure 13c,d. The increased water depth increases the flood extension, as shown in flood flow depth mapping in Figure 21, whereas the DWE results in higher central flow velocity due to the use of a simplified momentum equation. As a result, water surface elevation was found to be lower than the application of the FDWE as shown in Figure 13d. Both models predict that most of the households of Ranche, Nagmar, Khanikhet, and Debalta are vulnerable due to dam breach flooding, as shown in Figure 21 and Table 9.

• Flood Area

The flow extension area was calculated for both the models as represented in

Table 10. Total inundation area until the confluence of Bagmati River.

Area of Inundation (km2)
FDWE	DWE
2.92	2.25

until the Bagmati River confluence. The calculated total extension of the flow area has also shown that the flow is likely to be extended using FDWE. The flow extension increases up to 30%, which can be considered higher and cannot be underestimated. This also implies chances of flood flow over the towns are higher in the FDWE than in the DWE. Therefore, the appropriate flood model of the FDWE is required to adequately identify the flood-prone zones for the safe evacuation of places.

• Flood Intensity Mapping

The intensity of flood flow due to the dam breach was classified as per the American Society of Civil Engineers (ASCE) [39] flood intensity classification guideline as shown in Figure 22 to identify vulnerable places. Flood hazard was classified based on the intensity values as per the guideline of ASCE, which is tabulated in

Table 11. Flood hazard classification (ASCE).

Flood Hazard Classification	Flood Intensity (Depth × Velocity, m2/s)
Low–Medium	<2.1
High	2.1–3
Very High	>3

.

The flood is classified as “Low–Medium”, “High”, and “Very High” regions. The “Low–Medium” region is associated with a slight water level rise above the normal water level causing minimal damage. The “High” region indicates a slightly higher water level than the flood stage, which can cause structure and road damage and require evacuation. “Very High” represents a water level that is significantly higher than the flood stage, indicating potential threats to life and property and that places should be evacuated immediately.

The flood intensity map of Figure 22 clearly indicates that flood hazard lies in the “Very High” region in almost all of the towns with flood intensity above 3 m²/s, using both models. DWE model result has shown some flow area in the towns of Ranche, Nagmar, Khanikhet, and Debaltar lies in the “Low–Medium” region, due to less flow depth as a result of higher central flow velocity in the main channel, which can be visualized through Figure 13b,d. On the other hand, FDWE results in higher flow depth as shown in Figure 13c, likely to be spread in the towns. Most of the towns of Ranche, Nagmar, Khanikhet, and Debaltar were found to be flooded with “Low–Medium”, “High”, and “Very High” regions, due to the application of FDWE.

• Time of Arrival Mapping

The time of arrival mapping was compared between the models, as shown in Figure 23. The flood arrival time using the FDWE was slower than the DWE until the Bagmati River confluence. The central flow velocity was found to be higher in the DWE as it neglects the momentum loss in the river reach as shown in Figure 13b,d. The DWE result has shown that the flood quickly reaches the confluence of the Bagmati River. This indicates the importance of the actual arrival of flood time in flood-prone areas. The peak flood time difference at section IV (reference Figure 14), near the confluence of Bagmati River, was found to be almost 17 min between the models. This implies the necessity of precise time for making a safe evacuation plan which includes identifying safe routes to higher ground elevation, protecting personal belongings, etc. The safe evacuation of individuals and the protection of property is important to achieve less loss within the appropriate time. Therefore, FDWE must be applied for making a safe evacuation plan to achieve less loss for individuals as well as for the property.

4. Conclusions

A potential dam break flood hazard assessment was carried out using FDWE and DWE in the Kulekhani River, with an appropriate dam break model. The limitations and capabilities of the models were studied in the case of a dam break, and the following conclusions were drawn during the present study:

• The suitable regression breach model of MacDonald and Langridge (1984) with a downstream peak discharge of 17,594 m³/s was identified and adopted based on the sixteen historical dam break cases. The downstream peak flow was tested with the hydrograph method based on the duration of failure and volume of the reservoir. A more or less similar peak was obtained with an absolute error of 2.5%.
• The flow behavior/characteristics comparison between the models was carried out. The FDWE was able to capture the flow behavior in the meandering river accounting for higher flow velocity at the outer bend, lower velocity at the inner bend, and effects of the turbulent model with the formation of eddies, whereas the DWE was not able to capture these effects resulting in higher central flow velocity. The DWE model was found to be unsuitable in the steep meandering river of Kulekhani River, where momentum losses due to rapidly varying unsteady flow cannot be neglected as flow behavior was completely different than its physical flow.
• The flow variation at four different cross-sections was studied, and less attenuation was observed in both models due to the V-shaped valley with steep and less floodplain river. The attenuation of the peak flow was found to be more using FDWE than the DWE due to momentum loss. FDWE has the capability to capture the effects of momentum loss in the model. Almost 17 min of peak flow time difference was identified between the models in section IV, near the confluence of the Bagmati River.
• Flood hazard assessment was carried out using both models; the towns of Ranche, Nagmar, Khanikhet, and Debaltar were found to be highly affected. The total flood flow extension was found to be 30% higher with FDWE, as the flow depth was observed relatively higher than the DWE. The flood intensity mapping with the guideline of ASCE resulted in “Very High” regions for almost all of the towns along the river due to the V-shape valley river with fewer flood plains. Time of arrival mapping has shown that the flood reaches faster with the DWE as momentum loss was neglected with the simplified equation. Therefore, an appropriate model of FDWE should be implemented to have a better evacuation plan.
• To ensure a safe flood-prone area by enhancing the evacuation plan, a suitable model must be applied based on the hydraulic problems. The FDWE was found to be more suitable for rapidly varying unsteady flow problems due to dam breaches, in the case of the steep meandering river of Kulekhani.