## 범람으로 인한 비점착성 흙댐 붕괴에 대한 테일워터 깊이의 영향

ShaimaaAman^{a}MohamedAbdelrazek Rezk^{b}RabieaNasr^{c}

## Abstract

본 연구에서는 범람으로 인한 토사댐 붕괴에 대한 테일워터 깊이의 영향을 실험적으로 조사하였다. 테일워터 깊이의 네 가지 다른 값을 검사합니다. 각 실험에 대해 댐 수심 측량 프로파일의 진화, 고장 기간, 침식 체적 및 유출 수위곡선을 관찰하고 기록합니다.

결과는 tailwater 깊이를 늘리면 고장 시간이 최대 57% 감소하고 상대적으로 침식된 마루 높이가 최대 77.6% 감소한다는 것을 보여줍니다. 또한 상대 배수 깊이가 3, 4, 5인 경우 누적 침식 체적의 감소는 각각 23, 36.5 및 75%인 반면 최대 유출량의 감소는 각각 7, 14 및 17.35%입니다.

실험 결과는 침식 과정을 복제할 때 Flow 3D 소프트웨어의 성능을 평가하는 데 활용됩니다. 수치 모델은 비응집성 흙댐의 침식 과정을 성공적으로 시뮬레이션합니다.

The influence of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. Four different values of tailwater depths are examined. For each experiment, the evolution of the dam bathymetry profile, the duration of failure, the eroded volume, and the outflow hydrograph are observed and recorded. The results reveal that increasing the tailwater depth reduces the time of failure by up to 57% and decreases the relative eroded crest height by up to 77.6%. In addition, for relative tailwater depths equal to 3, 4, and 5, the reduction in the cumulative eroded volume is 23, 36.5, and 75%, while the reduction in peak discharge is 7, 14, and 17.35%, respectively. The experimental results are utilized to evaluate the performance of the Flow 3D software in replicating the erosion process. The numerical model successfully simulates the erosion process of non-cohesive earth dams.

## Keywords

Earth dam, Eroded volume, Flow 3D model, Non-cohesive soil, Overtopping failure, Tailwater depth

## Notation

d_{50}

Mean partical diameterW_{c}

Optimum water contentZ_{o}

Dam height (cm)d_{o}

Tailwater depth (cm)Z_{eroded}

Eroded height of the dam measured at distance of 0.7 m from the dam heel (cm)t

Total time of failure (*sec*)t_{1}

Time of crest width erosion (*sec*)Z_{crest}

The crest height (cm)V_{total}

Total volume of the dam (m^{3})V_{eroded}

Cumulative eroded volume (m^{3})RMSE

The statistical variable root- mean- square errord

Degree of agreement indexy_{u.s.}

The upstream water depth (cm)y_{d.s}

The downstream water depth (cm)H

Water surface elevation over sharp crested weir (cm)Q

Outflow discharge (liter/*sec*)Q_{peak}

Peak discharge (liter/*sec*)

## 1. Introduction

Earth dams are compacted structures composed of natural materials that are usually mined or quarried from local locations. The failures of the earth dams have proven to be deadly, destructive, and costly. According to People’s Daily, two earthen dams, Yong’an Dam and Xinfa Dam located in Hulun Buir City in North China’s Inner Mongolia failed on 2021, due to a surge in the water level of the Nuomin River caused by heavy rain. The dam breach affected 16,660 people, flooded 325,622 mu of farmland (21708.1 ha), and destroyed 22 bridges, 124 culverts, and 15.6 km of roadways. Also, the failure of south fork dam (earth and rock fill dam) near Johnstown on 1889 is considered the worst U.S dam disaster in terms of loss of life. The dam was overtopped and washed away due to unexpected heavy rains, releasing 20 million tons of water which destroyed Johnstown and resulted in 2209 deaths, [1], [2]. Piping or shear sliding, failure due to natural factors, and failure due to overtopping are all possible causes of earth dam failure. However, overtopping failure is the most frequent cause of dam failure. According to The International Committee on Large Dams (ICOLD, 1995), and [3], more than one-third of the total known dam failures were caused by dam overtopping.

Overtopping occurs as the result of insufficient flood design or freeboard in some cases. Extreme rainstorms can cause floods which can overtop the dam and cause it to fail. The size and geometry of the reservoir or the dam (side slopes, top width, height, etc.), the homogeneity of the material used in the construction of the dam, overtopping depth, and the presence or absence of tailwater are all elements that influence this type of failure which will be illustrated in the following literature. Overtopping failures of earth dams may be divided into several failure mechanisms based on the material composition and the inner structure of the dam. For cohesive earth dams because of low permeability, no seepage exists on the slopes. Erosion often begins at the earth dam toe during turbulent erosion and moves upstream, undercutting the slope, causing the removal of large chunks of materials. While for non-cohesive earth dams the downstream face of the dam flattens progressively and is often said to rotate around a point near the downstream toe [4], [5], [6] In the last few decades, the study of failures due to overtopping has gained popularity among researchers. The overtopping failure, in fact, has been widely investigated in coastal and river hydraulics and morpho dynamic. In addition, several laboratory experimental studies have been conducted in this field in order to better understand different involved factors. Also, many numerical types of research have been conducted to investigate the process of overtopping failure as well as the elements that influence this type of failure.

Tabrizi et al. [5] conducted a series of embankment overtopping tests to find the effect of compaction on the failure of a homogenous sand embankment. A plane breach process occurred across the flume width due to the narrow flume width. They measured the downstream hydrographs and embankment surface profile for every case. They concluded that the peak discharge decreased with a high compaction level, while the time to peak increased. Kansoh et al. [6] studied experimentally the failure of compacted homogeneous non-cohesive earthen embankment due to overtopping. They investigated the influence of different shape parameters including the downstream slope, the crest width, and the height of the embankment on the erosion process. The erosion process was initiated by carving a pilot channel into the embankment crest. They evaluated the time of embankment failure for different shape parameters. They concluded that the failure time increases with increasing the downstream slope and the crest width. Zhu et al. [7] investigated experimentally the breaching of five embankments, one constructed with pure sand, and four with different sand-silt–clay mixtures. The erosion pattern was similar across the flume width. They stated that for cohesive soil mixtures the head cut erosion was the most important factor that affected the breach growth, while for non-cohesive soil the breach erosion was affected by shear erosion.

Amaral et al. [8] studied experimentally the failure by overtopping for two embankments built from silt sand material. They studied the effect of the degree of compaction of the embankment and the geometry of the pilot channel carved at the centre of the dam crest. They studied two shapes of pilot channel a rectangular shape and triangular shape. They stated that the breach development is influenced by a higher degree of compaction, however, the pilot channel geometry did not influence the breach’s final form. Bereta et al. [9] studied experimentally the breach formation of five dam models, three of them were homogenous clay soil while two were sandy-clay mixtures. The erosion process was initiated by cutting a pilot channel at the centre of the dam crest. They observed the initiation of erosion, flow shear erosion, sidewall bottom erosion, and distinguished the soil mechanical slope mass failure from the head cut vertically and laterally during these tests. Verma et al. [10] investigated experimentally a two-dimensional erosion phenomenon due to overtopping by using a wooden fuse plug model and five different soils. They concluded that the erosion process was affected mostly by cohesiveness and degree of compaction. For cohesive soils, a head cut erosion was observed, while for non-cohesive soils surface erosion occurred gradually. Also, the dimensions of fuse plug, type of fill material, reservoir capacity, and inflow were found to affect the behaviour of the overall breaching process.

Wu and Qin [11] studied the effect of adding coarse grains to the downstream face of a non-cohesive dam as a result of tailings deposition. The process of overtopping during tailings dam failures is analyzed and its effect on delaying the dam-break process and disaster mitigation are investigated. They found that the tested protective measures decreased the breach area, the maximum breaching flow discharge and flow velocity, and the downstream inundated area. Khankandi et al. [12] studied experimentally the effect of reservoir geometry on dam break flow in case of dry and wet bed conditions. They considered four different reservoir shapes, a long reservoir, a wide, a trapezoidal shaped and one with a 90◦ bend all with identical water volume and horizontal bed. The dam break is simulated by the sudden gate removal using a pneumatic jack. They measured the variation of water level over time with ultrasonic sensors and flow velocity component with an acoustic Doppler velocimeter. Also, the experimental results of water level variation are compared with Ritters solution (1892) [13]. They stated that for dry bed condition the long and 90 bend reservoirs results are close to the analytical solution by ritter also in these two shapes a 1D flow is noticed. However, for wide and trapezoidal reservoirs a 2D effect is significant due to flow contraction at channel entrance.

Rifai et al. [14] conducted a series of experiments to investigate the effect of tailwater depth on the outflow discharge and breach geometry during non-cohesive homogenous fluvial dikes overtopping failure. They cut an initial notch in the crest at 0.8 m from the upstream end of the dike to initiate overtopping. They compared their results to previous experiments under different main channel inflow discharges combined with a free floodplain. They divided the dike breaching process into three stages: gradual start of overtopping flow resulting in slow initiation of dike erosion, deepening and widening breach due to large flow depth and velocity, finally the flow depth starts stabilizing at its minimal level with or without sustained breach expansion. They stated that breach discharge has lower values than in free floodplain tests. Jiang [15] studied the effect of bed slope on breach parameters and peak discharge in non-cohesive embankment failure. An initial triangular breach with a depth and width of 4 cm was pre-set on one side of the dam. He stated that peak discharge increases with the increase of bed slope and then decreases.

Ozmen-cagatay et al. [16] studied experimentally flood wave propagation resulted from a sudden dam break event. For dam-break modelling, they used a mechanism that permitted the rapid removal of a vertical plate with a thickness of 4 mm and made of rigid plastic. They conducted three tests, one with dry bed condition and two tests with tailwater depths equal 0.025 m and 0.1 m respectively. They recorded the free surface profile during initial stages of dam break by using digital image processing. Finally, they compared the experimental results with the with a commercially available VOF-based CFD program solving the Reynolds-averaged Navier –Stokes equations (RANS) with the k– Ɛ turbulence model and the shallow water equations (SWEs). They concluded that Wave breaking was delayed with increasing the tailwater depth to initial reservoir depth ratio. They also stated that the SWE approach is sufficient more to represent dam break flows for wet bed condition. Evangelista [17] investigated experimentally and numerically using a depth-integrated two-phase model, the erosion of sand dike caused by the impact of a dam break wave. The dam break is simulated by a sudden opening of an upstream reservoir gate resulting in the overtopping of a downstream trapezoidal sand dike. The evolution of the water wave caused from the gate opening and dike erosion process are recorded by using a computer-controlled camera. The experimental results demonstrated that the progression of the wave front and dike erosion have a considerable influence on each other during the process. In addition, the dike constructed from fine sands was more resistant to erosion than the one built with coarse sand. They also stated that the numerical model can is capable of accurately predicting wave front position and dike erosion. Also, Di Cristo et al. [18] studied the effect of dam break wave propagation on a sand embankment both experimentally and numerically using a two-phase shallow-water model. The evolution of free surface and of the embankment bottom are recorded and used in numerical model assessment. They stated that the model allows reasonable simulation of the experimental trends of the free surface elevation regardeless of the geofailure operator.

Lots of numerical models have been developed over the past few years to simulate the dam break flooding problem. A one-dimensional model, such as Hec-Ras, DAMBRK and MIKE 11, ect. A two-dimensional model such as iRIC Nay2DH is used in earth embankment breach simulation. Other researchers studied the failure process numerically using (3D) computational fluid dynamics (CFD) models, such as FLOW-3D, and FLUENT. Goharnejad et al. [19] determined the outflow hydrograph which results from the embankment dam break due to overtopping. Hu et al. [20] performed a comparison between Flow-3D and MIKE3 FM numerical models in simulating a dam break event under dry and wet bed conditions with different tailwater depths. Kaurav et al. [21] simulated a planar dam breach process due to overtopping. They conducted a sensitivity analysis to find the effect of dam material, dam height, downstream slope, crest width, and inlet discharge on the erosion process and peak discharge through breach. They concluded that downstream slope has a significant influence on breaching process. Yusof et al. [22] studied the effect of embankment sediment sizes and inflow rates on breaching geometric and hydrodynamic parameters. They stated that the peak outflow hydrograph increases with increasing sediment size and inflow rates while time of failure decreases.

In the present work, the effect of tailwater depth on earth dam failure during overtopping is studied experimentally. The relation between the eroded volume of the dam and the tailwater depth is presented. Also, the percentage of reduction in peak discharge due to tailwater existence is calculated. An assessment of Flow 3D software performance in simulating the erosion process during earth dam failure is introduced. The statistical variable root- mean- square error, *RMSE*, and the agreement degree index, *d*, are used in model assessment.

## 2. Material and methods

The tests are conducted in a straight rectangular flume in the laboratory of Irrigation Engineering and Hydraulics Department, Faculty of Engineering, Alexandria University, Egypt. The flume dimensions are 10 m long, 0.86 m wide, and 0.5 m deep. The front part of the flume is connected to a storage basin 1 m long by 0.86 m wide. The storage basin is connected to a collecting tank for water recirculation during the experiments as shown in Fig. 1, Fig. 2. A sharp-crested weir is placed at a distance of 4 m downstream the constructed dam to keep a constant tailwater depth in each experiment and to measure the outflow discharge.

To measure the eroded volume with time a rods technique is used. This technique consists of two parallel wooden plates with 10 cm distance in between and five rows of stainless-steel rods passing vertically through the wooden plates at a spacing of 20 cm distributed across flume width. Each row consists of four rods with 15 cm spacing between them. Also, a graph board is provided to measure the drop in each rod with time as shown in Fig. 3, Fig. 4. After dam construction the rods are carefully rested on the dam, with the first line of rods resting in the middle of the dam crest and then a constant distance of 15 cm between rods lines is maintained.

A soil sample is taken and tested in the laboratory of the soil mechanics to find the soil geotechnical parameters. The soil particle size distribution is also determined by sieve analysis as shown in Fig. 5. The soil mean diameter *d _{50}*,equals 0.38 mm and internal friction angle equals 32.6°.

### 2.1. Experimental procedures

To investigate the effect of the tailwater depth (*d _{o}*), the tailwater depth is changed four times 5, 15, 20, and 25 cm on the sand dam model. The dam profile is 35 cm height, with crest width = 15 cm, the dam base width is 155 cm, and the upstream and downstream slopes are 2:1 as shown in Fig. 6. The dam dimensions are set as the flume permitted to allow observation of the dam erosion process under the available flume dimensions and conditions. All of the conducted experiments have the same dimensions and configurations.

The optimum water content, *W _{c}*, from the standard proctor test is found to be 8 % and the maximum dry unit weight is 19.42 kN/m

^{3}. The soil and water are mixed thoroughly to ensure consistency and then placed on three horizontal layers. Each layer is compacted according to ASTM standard with 25 blows by using a rammer (27 cm × 20.5 cm) weighing 4 kg. Special attention is paid to the compaction of the soil to guarantee the repeatability of the tests.

After placing and compacting the three layers, the dam slopes are trimmed carefully to form the trapezoidal shape of the dam. A small triangular pilot channel with 1 cm height and 1:1 side slopes is cut into the dam crest to initiate the erosion process. The position of triangular pilot channel is presented in Fig. 1. Three digital video cameras with a resolution of 1920 × 1080 pixels and a frame rate of 60 fps are placed in three different locations. One camera on one side of the flume to record the progress of the dam profile during erosion. Another to track the water level over the sharp-crested rectangular weir placed at the downstream end of the flume. And the third camera is placed above the flume at the downstream side of the dam and in front of the rods to record the drop of the tip of the rods with time as shown previously in Fig. 1.

Before starting the experiment, the water is pumped into the storage basin by using pump with capacity 360 m^{3}/hr, and then into the upstream section of the flume. The upstream boundary is an inflow condition. The flow discharge provided to the storage basin is kept at a constant rate of 6 L/*sec* for all experiments, while the downstream boundary is an outflow boundary condition.

Also, the required tailwater depth for each experiment is filled to the desired depth. A dye container valve is opened to color the water upstream of the dam to make it easy to distinguish the dam profile from the water profile. A wooden board is placed just upstream of the dam to prevent water from overtopping the dam until the water level rises to a certain level above the dam crest and then the wooden board is removed slowly to start the experiment.

### 2.2. Repeatability

To verify the accuracy of the results, each experiment is repeated two times under the same conditions. Fig. 7 shows the relative eroded crest height, *Z _{eroded} / Z_{o}*, with time for 5 cm tailwater depth. From the Figure, it can be noticed that results for all runs are consistent, and accuracy is achieved.

## 3. Numerical model

The commercially available numerical model, Flow 3D is used to simulate the dam failure due to overtopping for the cases of 15 cm, 20 cm and 25 cm tailwater depths. For numerical model calibration, experimental results for dam surface evolution are used. The numerical model is calibrated for selection of the optimal turbulence model (*RNG, K-e, and k-w*) and sediment scour equations (*Van Rin, Meyer- peter and Muller, and Nielsen*) that produce the best results. In this, the flow field is solved by the *RNG* turbulence model, and the *van Rijn* equation is used for the sediment scour model. A geometry file is imported before applying the mesh.

A Mesh sensitivity is analyzed and checked for various cell sizes, and it is found that decreasing the cell size significantly increases the simulation time with insignificant differences in the result. It is noticed that the most important factor influencing cell size selection is the value of the dam’s upstream and downstream slopes. For example, the slopes in the dam model are 2:1, thus the cell size ratio in X and Z directions should be 2:1 as well. The cell size in a mesh block is set to be 0.02 m, 0.025 m, and 0.01 m in X, Y and Z directions respectively.

In the numerical computations, the boundary conditions employed are the walls for sidewalls and the channel bottom. The pressure boundary condition is applied at the top, at the air–water interface, to account for atmospheric pressure on the free surface. The upstream boundary is volume flow rate while the downstream boundary is outflow discharge.

The initial condition is a fluid region, which is used to define fluid areas both upstream and downstream of the dam. To assess the model accuracy, the statistical variable root- mean- square error, *RMSE*, and the agreement degree index, *d*, are calculated as(1)RMSE=1N∑i=1N(Pi-Mi)2(2)d=1-∑Mi-Pi2∑Mi-M¯+Pi-P¯2

where *N* is the number of samples, *P _{i}* and

*M*are the models and experimental values,

_{i}*P*and

*M*are the means of the model and experimental values. The best fit between the experimental and model results would have an

*RMSE*= 0 and degree of agreement,

*d*= 1.

## 4. Results of experimental work

The results of the total time of failure, *t* (defined as the time from when the water begins to overtop the dam crest until the erosion reaches a steady state, when no erosion occurs), time of crest width erosion *t _{1}*, cumulative eroded volume

*V*, and peak discharge

_{eroded}*Q*for each experiment are listed in Table 1. The case of 5 cm tailwater depth is considered as a reference case in this work.

_{peak}Table 1. Results of experimental work.

Tailwater depth, d (cm)_{o} | Total time of failure, t (sec) | Time of crest width erosion, t (_{1}sec) | cumulative eroded volume, V (m_{eroded}^{3}) | Peak discharge, Q (liter/_{peak}sec) |
---|---|---|---|---|

5 | 255 | 22 | 0.21 | 13.12 |

15 | 165 | 30 | 0.16 | 12.19 |

20 | 140 | 34 | 0.13 | 11.29 |

25 | 110 | 39 | 0.05 | 10.84 |

## 5. Discussion

### 5.1. Side erosion

The evolution of the bathymetry of the erosion line recorded by the video camera1. The videos are split into frames (60 frames/*sec*) by the Free Video to JPG Converter v.5.063 build and then converted into an excel spreadsheet using MATLAB code as shown in Fig. 8.

Fig. 9 shows a sample of numerical model output. Fig. 10, Fig. 11, Fig. 12 show a dam profile development for different time steps from both experimental and numerical model, for tailwater depths equal 15 cm, 20 cm and 25 cm. Also, the values of *RMSE* and *d* for each figure are presented. The comparison shows that the Flow 3D software can simulate the erosion process of non-cohesive earth dam during overtopping with an *RMSE* value equals 0.023, 0.0218, and 0.0167 and degree of agreement, *d*, equals 0.95, 0.968, and 0.988 for relative tailwater depths, *d _{o}/(d_{o})_{ref},* = 3, 4 and 5, respectively. The low values of

*RMSE*and high values of

*d*show that the Flow 3D can effectively simulate the erosion process. From Fig. 10, Fig. 11, Fig. 12, it can be noticed that the model is not capable of reproducing the head cut, while it can simulate well the degradation of the crest height with a minor difference from experimental work. The reason of this could be due to inability of simulation of all physical conditions which exists in the experimental work, such as channel friction and the grain size distribution of the dam soil which is surely has a great effect on the erosion process and breach development. In the experimental work the grain size distribution is shown in Fig. 5, while the numerical model considers that the soil is uniform and exactly 50 % of the dam particles diameter are equal to the

*d*value. Another reason is that the model is not considering the increased resistance of the dam due to the apparent cohesion which happens due to dam saturation [23].

_{50}It is clear from both the experimental and numerical results that for a 5 cm tailwater depth, *d _{o}/(d_{o})_{ref}* = 1.0, erosion begins near the dam toe and continues upward on the downstream slope until it reaches the crest. After eroding the crest width, the crest is lowered, resulting in increased flow rates and the speeding up of the erosion process. While for relative tailwater depths,

*d*= 3, 4, and 5 erosion starts at the point of intersection between the downstream slope and tailwater. The existence of tailwater works as an energy dissipater for the falling water which reduces the erosion process and prevents the dam from failure as shown in Fig. 13. It is found that the time of the failure decreases with increasing the tailwater depth because most of the dam height is being submerged with water which decreases the erosion process. The reduction in time of failure from the referenced case is found to be 35.3, 45, and 57 % for relative tailwater depth,

_{o}/(d_{o})_{ref}*d*equals 3, 4, and 5, respectively.

_{o}/(d_{o})_{ref}The relation between the relative eroded crest height, *Z _{eroded} /Z_{o}*, with time is drawn as shown in Fig. 14. It is found that the relative eroded crest height decreases with increasing tailwater depth by 10, 41, and 77.6 % for relative tailwater depth,

*d*equals 3, 4, and 5, respectively. The time required for the erosion of the crest width,

_{o}/(d_{o})_{ref}*t*, is calculated for each experiment. The relation between relative tailwater depth and relative time of crest width erosion is shown in Fig. 15. It is found that the time of crest width erosion increases linearly with increasing,

_{1}*d*. The percent of increase is 36.4, 54.5 and 77.3 % for relative tailwater depth,

_{o}/Z_{o}*d*= 3, 4 and 5, respectively.

_{o}/(d_{o})_{ref}Crest height, *Z _{crest}* is calculated from the experimental results and the Flow 3D results for relative tailwater depths,

*d*, = 3, 4, and 5. A relation between relative crest height,

_{o}/(d_{o})_{ref}*Z*with time from experimental and numerical results is presented in Fig. 16. From Fig. 16, it is seen that there is a good consistency between the results of numerical model and the experimental results in the case of tracking the erosion of the crest height with time.

_{crest}/Z_{o}### 5.2. Upstream and downstream water depths

It is noticed that at the beginning of the erosion process, both upstream and downstream water depths increase linearly with time as long as erosion of the crest height did not take place. However, when the crest height starts to lower the upstream water depth decreases with time while the downstream water depth increases. At the end of the experiment, the two depths are nearly equal. A relation between relative downstream and upstream water depths with time is drawn for each experiment as shown in Fig. 17.

### 5.3. Eroded volume

A MATLAB code is used to calculate the cumulative eroded volume every time interval for each experiment. The total volume of the dam, *V _{total}* is 0.256 m

^{3}. The cumulative eroded volume,

*V*is 0.21, 0.16, 0.13, and 0.05 m

_{eroded}^{3}for tailwater depths,

*d*= 5, 15, 20, and 25 cm, respectively. Fig. 18 presents the relation between cumulative eroded volume,

_{o}*V*and time. From Fig. 18, it is observed that the cumulative eroded volume decreases with increasing the tailwater depth. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth,

_{eroded}*d*= 3, 4, and 5, respectively. The relative remained volume of the dam equals 0.18, 0.375, 0.492, and 0.8 for tailwater depths = 5, 15, 20, and 25 cm, respectively. Fig. 19 shows a relation between relative tailwater depth and relative cumulative eroded volume from experimental results. From that figure, it is noticed that the eroded volume decreases exponentially with increasing relative tailwater depth.

_{o}/(d_{o})_{ref}### 5.4. The outflow discharge

The inflow discharge provided to the storage tank is maintained constant for all experiments. The water surface elevation, *H*, over the sharp-crested weir placed at the downstream side is recorded by the video camera 2. For each experiment, the outflow discharge is then calculated by using the sharp-crested rectangular weir equation every 10 *sec*.

The outflow discharge is found to increase rapidly until it reaches its peak then it decreases until it is constant. For high values of tailwater depths, the peak discharge becomes less than that in the case of small tailwater depth as shown in Fig. 20 which agrees well with the results of Rifai et al. [14] The reduction in peak discharge is 7, 14, and 17.35 % for relative tailwater depth, *d _{o} /(d_{o})_{ref}* = 3, 4, and 5, respectively.

The scenario presented in this article in which the tailwater depth rises due to unexpected heavy rainfall, is investigated to find the effect of rising tailwater depth on earth dam failure. The results revealed that rising tailwater depth positively affects the process of dam failure in terms of preventing the dam from complete failure and reducing the outflow discharge.

## 6. Conclusions

The effect of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. The study focuses on the effect of tailwater depth on side erosion, upstream and downstream water depths, eroded volume, outflow hydrograph, and duration of the failure process. The Flow 3D numerical software is used to simulate the dam failure, and a comparison is made between the experimental and numerical results to find the ability of this software to simulate the erosion process. The following are the results of the investigation:

The existence of tailwater with high depths prevents the dam from completely collapsing thereby turning it into a broad crested weir. The failure time decreases with increasing the tailwater depth and the reduction from the reference case is found to be 35.3, 45, and 57 % for relative tailwater depth, *d _{o} /(d_{o})_{ref} =* 3, 4, and 5, respectively. The difference between the upstream and downstream water depths decreases with time till it became almost negligible at the end of the experiment. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth,

*d*= 3, 4, and 5, respectively. The peak discharge decreases by 7, 14, and 17.35 % for relative tailwater depth,

_{o}/(d_{o})_{ref}*d*= 3, 4, and 5, respectively. The relative eroded crest height decreases linearly with increasing the tailwater depth by 10, 41, and 77.6 % for relative tailwater depth,

_{o}/(d_{o})_{ref}*d*= 3, 4, and 5, respectively. The numerical model can reproduce the erosion process with a minor deviation from the experimental results, particularly in terms of tracking the degradation of the crest height with time.

_{o}/(d_{o})_{ref}## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Reference

D. McCullough

**The Johnstown Flood**

Simon and Schuster, NY (1968)

Google Scholar[2]Rose AT. The influence of dam failures on dam safety laws in Pennsylvania. Association of State Dam Safety Officials Annual Conference 2013, Dam Safety 2013. 2013;1:738–56.

M. Foster, R. Fell, M. Spannagle

**The statistics of embankment dam failures and accidents**

Can Geotech J, 37 (5) (2000), pp. 1000-1024, 10.1139/t00-030 View PDF

View Record in ScopusGoogle Scholar[4]Pickert, G., Jirka, G., Bieberstein, A., Brauns, J. Soil/water interaction during the breaching process of overtopped embankments. In: Greco, M., Carravetta, A., Morte, R.D. (Eds.), Proceedings of the Conference River-Flow 2004, Balkema.

A. Asghari Tabrizi, E. Elalfy, M. Elkholy, M.H. Chaudhry, J. Imran

**Effects of compaction on embankment breach due to overtopping**

J Hydraul Res, 55 (2) (2017), pp. 236-247, 10.1080/00221686.2016.1238014 View PDF

View Record in ScopusGoogle Scholar[6]

R.M. Kansoh, M. Elkholy, G. Abo-Zaid

**Effect of Shape Parameters on Failure of Earthen Embankment due to Overtopping**

KSCE J Civ Eng, 24 (5) (2020), pp. 1476-1485, 10.1007/s12205-020-1107-x View PDF

View Record in ScopusGoogle Scholar[7]

YongHui Zhu, P.J. Visser, J.K. Vrijling, GuangQian Wang

**Experimental investigation on breaching of embankments**

Experimental investigation on breaching of embankments, 54 (1) (2011), pp. 148-155 View PDF

CrossRefView Record in ScopusGoogle Scholar[8]Amaral S, Jónatas R, Bento AM, Palma J, Viseu T, Cardoso R, et al. Failure by overtopping of earth dams. Quantification of the discharge hydrograph. Proceedings of the 3rd IAHR Europe Congress: 14-15 April 2014, Portugal. 2014;(1):182–93.

G. Bereta, P. Hui, H. Kai, L. Guang, P. Kefan, Y.Z. Zhao

**Experimental study of cohesive embankment dam breach formation due to overtopping**

Periodica Polytechnica Civil Engineering, 64 (1) (2020), pp. 198-211, 10.3311/PPci.14565 View PDF

View Record in ScopusGoogle Scholar[10]

D.K. Verma, B. Setia, V.K. Arora

**Experimental study of breaching of an earthen dam using a fuse plug model**

Int J Eng Trans A, 30 (4) (2017), pp. 479-485, 10.5829/idosi.ije.2017.30.04a.04 View PDF

View Record in ScopusGoogle Scholar[11]Wu T, Qin J. Experimental Study of a Tailings Impoundment Dam Failure Due to Overtopping. Mine Water and the Environment [Internet]. 2018;37(2):272–80. Available from: doi: 10.1007/s10230-018-0529-x.

A. Feizi Khankandi, A. Tahershamsi, S. Soares-Frazo

**Experimental investigation of reservoir geometry effect on dam-break flow**

J Hydraul Res, 50 (4) (2012), pp. 376-387 View PDF

CrossRefView Record in ScopusGoogle Scholar[13]

A. Ritter

**Die Fortpflanzung der Wasserwellen (The propagation of water waves)**

Zeitschrift Verein Deutscher Ingenieure, 36 (33) (1892), pp. 947-954

[in German]

View Record in ScopusGoogle Scholar[14]

I. Rifai, K. El Kadi Abderrezzak, S. Erpicum, P. Archambeau, D. Violeau, M. Pirotton, *et al.*

**Floodplain Backwater Effect on Overtopping Induced Fluvial Dike Failure**

Water Resour Res, 54 (11) (2018), pp. 9060-9073 View PDF

This article is free to access.

CrossRefView Record in ScopusGoogle Scholar[15]

X. Jiang

**Laboratory Experiments on Breaching Characteristics of Natural Dams on Sloping Beds**

Advances in Civil Engineering, 2019 (2019), pp. 1-14

View Record in ScopusGoogle Scholar[16]

H. Ozmen-Cagatay, S. Kocaman

**Dam-break flows during initial stage using SWE and RANS approaches**

J Hydraul Res, 48 (5) (2010), pp. 603-611 View PDF

CrossRefView Record in ScopusGoogle Scholar[17]

S. Evangelista

**Experiments and numerical simulations of dike erosion due to a wave impact**

Water (Switzerland), 7 (10) (2015), pp. 5831-5848 View PDF

CrossRefView Record in ScopusGoogle Scholar[18]

C. Di Cristo, S. Evangelista, M. Greco, M. Iervolino, A. Leopardi, A. Vacca

**Dam-break waves over an erodible embankment: experiments and simulations**

J Hydraul Res, 56 (2) (2018), pp. 196-210 View PDF

CrossRefView Record in ScopusGoogle Scholar[19]Goharnejad H, Sm M, Zn M, Sadeghi L, Abadi K. Numerical Modeling and Evaluation of Embankment Dam Break Phenomenon (Case Study : Taleghan Dam) ISSN : 2319-9873. 2016;5(3):104–11.

Google Scholar[20]Hu H, Zhang J, Li T. Dam-Break Flows : Comparison between Flow-3D , MIKE 3 FM , and Analytical Solutions with Experimental Data. 2018;1–24. doi: 10.3390/app8122456.

R. Kaurav, P.K. Mohapatra, D. Ph

Studying the Peak Discharge through a Planar Dam Breach, 145 (6) (2019), pp. 1-8 View PDF

Z.M. Yusof, Z.A.L. Shirling, A.K.A. Wahab, Z. Ismail, S. Amerudin

**A hydrodynamic model of an embankment breaching due to overtopping flow using FLOW-3D**

IOP Conference Series: Earth and Environmental Science, 920 (1) (2021)

G. Pickert, V. Weitbrecht, A. Bieberstein

**Breaching of overtopped river embankments controlled by apparent cohesion**

J Hydraul Res, 49 (2) (Apr. 2011), pp. 143-156, 10.1080/00221686.2011.552468 View PDF

View Record in ScopusGoogle Scholar

## Cited by (0)

My name is Shaimaa Ibrahim Mohamed Aman and I am a teaching assistant in Irrigation and Hydraulics department, Faculty of Engineering, Alexandria University. I graduated from the Faculty of Engineering, Alexandria University in 2013. I had my MSc in Irrigation and Hydraulic Engineering in 2017. My research interests lie in the area of earth dam Failures.

Peer review under responsibility of Ain Shams University.

© 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University.