Dam Overtopping Research Articles

Risk assessment of a glacial lake with abruptly slowing expansion, Jiongpu, Southeastern Tibet

The expansion of potentially hazardous glacial lakes is a symptom of global warming during this interglacial period. A pertinent example is the Jiongpu glacial lake in southeastern Tibet, the area of which has expanded approximately fivefold in the last half-century. However, recently, the glacier tongue has retreated to a high steep slope, and the rate of retreat of the glacier and expansion of the lake have temporarily slowed. The risk of a glacier tongue landslide after glacier detachment and subsequent glacial lake outburst flood (GLOF) needs to be assessed. In this study, we employed a combination of unmanned aerial vehicle (UAV), sonar, geological radar, remote sensing, field investigation, sampling, drilling, and dating techniques to determine the critical parameters of potential GLOFs, including glacier tongue geometry, lake bathymetry, and moraine dam geometry and composition. Utilizing empirical models and multiphase flow models, we identified the most hazardous triggers and simulated the processes of a glacier tongue landslide into the lake, moraine dam overtopping by a displacement wave, and subsequent flood evolution. The results showed that the most hazardous trigger in volume is a glacier tongue landslide, accounting for 58.29 % of all triggers associated with potential GLOFs. Lapped by the largest glacier tongue landslide impulse wave, the moraine dam would not fail because the minimum safety factor is approximately 1.66 ± 0.7 according to empirical methods and geological slope simulation. However, overtopping would occur, resulting in a peak discharge of approximately 9740 ± 4137 m3/s at the moraine dam based on r.avaflow calculations. The flood would reach the densely populated Jinling township and inundate approximately 46 ± 4.55 % of the houses according to HEC-RAS. Reducing the water level of the glacial lake represents an effective strategy for mitigating potential losses. This concise, physics-based method effectively assesses GLOF triggers and processes and can be applied to risk assessments of other expanding glacial lakes.

Simulation of landslide dam failure due to overtopping considering vertical soil particles distribution

Accurate prediction of potential landslide dam breaches is crucial for timely and effective emergency responses to the resulting flood. Although many models for landslide dam overtopping have been proposed in past studies, most of these models did not consider the heterogeneity of dam materials, which is important in reflecting the erodibility of soil. In this study, a new mathematical model for landslide dam breaches due to overtopping was proposed based on a constructed vertical distribution model of dam particle size. Two real-world dams, the Tangjiashan landslide dam and Baige landslide dam, were used to evaluate the performance of the proposed model. In addition, the proposed model was compared with four existing dam failure models, and sensitivity analysis was conducted on the median particle size and particle size distribution. The results demonstrate that the computational outcomes of the proposed model align more closely with the actual results, indicating that the proposed model outperforms the four existing models in accurately simulating the landslide dam failure process. It also suggests that ignoring the variation of dam material particle size along the vertical direction inside the dam body would increase the prediction relative errors of key breach outcomes.

Potential effects of internal dam-break in Stare Miasto Reservoir in Poland

Study regionThe research object is located in Wielkopolska province (Poland), which is well-known for its rural character and scarcity of water. To prevent droughts, small reservoirs are installed in local watersheds. It enables control of water conditions for agriculture and improvement of local climate. The main challenge is prevention from the deposition of sediments in a reservoir. To minimize this threat, the specific constructions of the reservoir are applied, e.g. internal dams. Study focusThe Stare Miasto reservoir consists of an internal dam with the upper zone separated. The highway bridge split the main part. In 2014 a flood wave propagated through the reservoir. The crest of the internal dam was shifted generating a potential risk of internal dam failure. The consequences of such an event were analyzed using a two-dimensional hydrodynamic numerical tool that solves the shallow water equations with finite volume method on unstructured mesh. New hydrological insight for the regionThe results obtained prove that the dam break increases the risk of bridge instability. The shear stresses generated during break of internal dam may exceed 50 N/m2, what cause danger of deep scour generation under and below the construction. Unexpectedly, the existence of the bridge decreased the threat of the main dam overtopping. The study may be a valuable inspiration for the design of new reservoirs inevitable in controlling water resource conditions in the region.

Scraping Effect of Dam-Overtopping Debris Flow—A Case Study of Chutou Gully ‘8.20’ in Miansi Town, Wenchuan County

ABSTRACT After the May 12 earthquake in Wenchuan, numerous debris flow disasters occurred due to heavy rainfall. After the earthquake, disaster prevention and mitigation projects, such as the sand dam, played an essential role in safety. However, when the outflow of solid material exceeds the designed storage capacity of the sand dam, the debris flow overtopping the dam intensifies the scraping effect on the source material of the gully channel. This paper takes the ”8.20” debris flow in the Chutou gully as the research object. A transport mode of the debris flow after dam overtopping is studied through comprehensive field investigation, theoretical analysis, and indoor model tests. A quantitative evaluation model is established for the scraping depth and scraping volume of dam-overtopping debris flow. The study results showed that once the debris flow overtops a dam, the loose source carried by the channel is involved in the entire migration process, enlarging the fluid scale and intensifying the damage along the channel. The results agree with the measurements and observations, with maximum relative errors of 5.81% and 14.70%, respectively. This shows model validity. Furthermore, the test results show that the debris flow scarping phenomenon in the γ=[1.4 t/m3, 1.6 t/m3] interval is the most significant. Overall, this study will help improve future engineering decisions, design strategies, and finding the best design solutions to minimize the risk of dam-overtopping debris flow disasters.

Analysis of Uncertainty in Internal Erosion Simulations for DLBreach and WinDAM C

The work detailed here is part of an international initiative on the evaluation of dam safety simulation software for internal erosion performance and best practices. The primary experiments involve simulating uncertainty in the failure events of two dams with two different models: DLBreach and WinDAM C. DLBreach is a physically-based dam/levee breach model developed by Wu. WinDAM C is also a physically based dam breach model capable of analyzing both dam overtopping and internal erosion. The dams selected for the analysis include a 1.3 m high dam tested in the lab and a larger 15.56 m high dam, which suffered a failure in the field. The findings from these experiments are extended with a further analysis on variance, sensitivity, and optimization. Finally, a regression model is trained using the results of these simulators as an inquiry into how well such a system can be captured using machine learning techniques. The results of these experiments, together with the results of the other members of the initiative, improve our understanding of the influences that users bring to using these tools.

The Impacts of River Channel Blockages Caused by Sliding Embankment Collapses during Earthquakes

New Japanese regulations governing earth embankment construction were introduced after a debris flow in Atami City, Shizuoka Prefecture, caused significant damage. Slope failures block river channels during earthquakes, triggering flooding, inundation, and debris flows. Appropriate risk assessments are crucial for residential areas potentially impacted by earthen embankment landslides during seismic events. This study evaluates the methods used to assess the potential damage caused by such landslides and previous research on the harm caused by embankment failures during earthquakes. We derived predictive equations based on statistical analyses of historical dam landslides that triggered river channel blockages when residential earth embankments failed in the Nigawa Yurino area. The equations describe the morphologies of landslide dams in river channels. The results indicated that the predictive equations were reasonably accurate. We built and validated a two-dimensional model of landslide dam overtopping and breaching using experimental data on a gently sloping dam. We derived the outflow volumes associated with residential earth embankment failures when full reservoirs breached in the Nigawa Yurino area. Our findings suggest that the peak outflow volumes after such embankments breach are generally lower than those associated with dam landslides or deep-seated dam failures, but higher than those of glacial lake outburst floods.

Uncertainty analysis on flood routing of embankment dam breach due to overtopping failure

The breach risk of reservoir dam exists objectively while exerting benefits. There is great uncertainty in the overtopping breach process of embankment dam and the dam break flood routing which affects the accuracy of dam risk analysis and may cause unnecessary waste in emergency scheduling. However, the uncertainty analysis of the breach process and its consequence is currently inadequate. Therefore, a stratified sampling Monte Carlo method is proposed to simulate uncertain overtopping breach flood of embankment dams. The main sources of uncertainty are analyzed and determined as uncertain dam breach and flood routing processes. The uncertain breach process of dam is studied by presenting a sensitive study between 3 mechanism breach models and 5 parametric breach models. The random dam breach process is restored using HEC-RAS semi-empirical breach model by estimating breach characteristics through multiple common breach models. The random flood routing is carried out through 1D–2D coupled unsteady flow analysis in which the random breach process is adopted as an upper inflow boundary condition. According to the case study results, though parameters have been controlled in a limited range, the flood routing results in the early stage of dam overtopping failure present greater uncertainty. As the flood progresses further downstream, the uncertainty will gradually decrease. This study could serve as a reference for dam breach risk map making.

A 2D Hydraulic Simulation Model Including Dynamic Piping and Overtopping Dambreach

Numerical simulation of unsteady free surface flows using depth averaged equations that consider the presence of initial discontinuities has been often reported for situations dealing with dam break flow. The usual approach is to assume a sudden removal of the gate at the dam location. Additionally, in order to prevent any kind of dam risk in earthen dams, it is very interesting to include the possibility of a progressive dam breach leading to dam overtopping or dam piping so that predictive hydraulic models benefit the global analysis of the water flow. On the other hand, when considering a realistic large domain with complex topography, a fine spatial discretization is mandatory. Hence, the number of grid cells is usually very large and, therefore, it is necessary to use parallelization techniques for the calculation, with the use of Graphic Processing Units (GPU) being one of the most efficient, due to the leveraging of thousands of processors within a single device. The aim of the present work is to describe an efficient GPU-based 2D shallow water flow solver (RiverFlow2D-GPU) supplied with the formulation of internal boundary conditions to represent dynamic dam failure processes. The results obtained indicate that it is able to develop a transient flow analysis taking into account several scenarios. The efficiency of the model is proven in two complex domains, leading to >76× faster simulations compared with the traditional CPU computation.

Introducing a probabilistic framework to measure dam overtopping risk for dams benefiting from dual spillways

Introducing a probabilistic framework to measure dam overtopping risk for dams benefiting from dual spillways

Experimental investigation of sediment movement as a result of homogeneous earth-fill dam overtopping break over a simplified urban area

When an earth-fill dam breaks, dam body sediment and water flow simultaneously move to downstream area causing devastation. Dam break studies in the literature have concentrated mostly on the water flow part while ignoring the sediment movement by designing the dam body as a movable metal gate. This study, however, is the first one experimentally investigating flow and sediment transport due to an earth-fill dam break by constructing the dam body from sediment. Sediment propagation as a result of homogenous earth-fill dam overtopping break was experimentally studied in a laboratory flume of 18.4 m long and 2.0 m wide, and 0.88 m in height in the Hydraulics Laboratory of Izmir Katip Celebi University, Izmir, Turkey. Downstream section right after the dam body was designed as a smooth bed and rough bed. The rough bed, resembling a simplified urban area, was created by using thirteen 10 × 10 × 10 cm sized concrete blocks. The dam body was constructed as homogenous with uniform material having D50 = 0.441 mm. The earth-fill dam body was built using the standard compression methods; each layer of sediment with a thickness of 10 cm was laid in layers, and the body was prepared with a crest width of 10 cm, a transverse base width of 200 cm, a longitudinal base width of 202 cm and height of 60 cm with upstream and downstream slopes of 1:1.6. The water level behind the dam was gradually raised until it overtopped the crest level. A pre-breach was formed at the top of the dam to trigger the break. During each dam break event, water depths were measured by three ULS-40D level meter sensors at different locations, and the final sediment bathymetry map was generated using the ULS-40D Probes at 10 × 10 cm grids. The results showed that, in both smooth and rough downstream bed cases, the dam body eventually collapsed while a great portion of it was carried away by the flood flow. The sediment spreading occurred all over the downstream area, showing significant non-uniform variation in thickness both longitudinally and transversely, especially in the simulated urban area. All the residential areas, while breaking in motion, were submerged under the muddy flow. Some blocks were almost submerged while sediment heights reached half level of some blocks at the end of the experiment. Sediment heights were higher in the urban area.

Experimental Study on Failure Model of Tailing Dam Overtopping under Heavy Rainfall

Abstract Unusual rainfall is the primary cause of the failure of the tailing dams, and overtopping is the most representative model of the tailing dam failure. The upstream tailing dam was selected as the research object to study the whole process of breach extension and the overtopping dam-failure mechanism under the full-scale rainfall condition. The results showed that the significant size grading phenomenon in the front, middle, and end of the tailing pond was obvious due to the flow separation effect, and its average particle diameter was D50. At different moments of rainfall, the height of the infiltration line at different positions of the dam body was different; at the rainfall of 3600 s, the height of the infiltration line lagged behind the height of the tailing pond, and this phenomenon from the tail of pond to the outside of the dam slope became more obvious. After the rainfall of 3600 s, the height of the infiltration line lagging behind the water level in the pond basically disappeared, and the rate of infiltration line rise kept pace with the rate of water level. The process of overtopping dam-failure experienced dam overtopping (gully erosion), formation of a multistepped small “scarp,” breach rapid expansion, formation of large “scarp,” and burst (fan-shaped formation). The width and depth of the breach showed a positive correlation, and the widening rate of the breach was 3 to 8 times of the deepening rate, especially in the middle of the dam break, widening behavior occupied the dominant factor. The shape of the dam body after failure was parabolic, and the dam body had obvious elevation changes. These results provide the theoretical guidance and engineering application value for improving the theory and early warning model of the upstream tailing dam.

Multiscale Investigations of Overtopping Erosion in Reinforced Tailings Dam Induced by Mud-Water Mixture Overflow

The overtopping failure that occurred to the reinforced tailings dam has led to devastating catastrophes, including severe environmental disasters as well as tragedy in terms of any loss of properties and life. To study the feature of overtopping erosion for the reinforced fine-grained tailings dam induced by mud-water mixture overflow, the red mud concentration of overflow, the erosion depths and erosion rate have been consistently detected and recorded by a series of physical model tests. This investigation conclusively showed that the red mud concentration for flooding over the dam slope had a nonlinear trend of first becoming larger, subsequently decreasing with the time going on in the process of tailing dam overtopping; the maximum red mud concentration achieved 19.0%. The erosion on the dam slope was shaped like a trumpet. The red mud concentration of the mud-water mixture flow affected the erosion depth significantly. The hydraulic tests simulating erosion behaviour in the reinforced fine-grained tailings were carried out with different red mud concentrations (0%, 10%, and 20%). For the mud-water mixture flow in a red mud concentration of 20%, the final erosion depth exhibited a ladder shape from the front to the trailing end (dam toe) of the tailings sample. The final erosion depths were 1.56 cm, 0.9 cm, and 0.55 cm at the front, middle, and trailing end, respectively. With the red mud concentration decreasing, the final erosion depth at the front of the tailings sample reduced significantly while increasing at the trailing end. This study brought more scientific insights into the overtopping erosion process to the reinforced fine-grained tailings dam triggered by the mud-water mixture flow at multiscale.

Numerical simulation of dam-breach flood waves

Dam breach due to the earthquake, Land sliding inside the dam reservoir, dam overtopping as a result of intense precipitation in a watershed are examples of dangerous risks which flood caused by any of them should be predicted by suitable hydraulic or numerical models in the framework of a risk management plan. In the present research, 2DHec-Ras model has been applied in order to flood modeling of Sattarkhan dam. This dam is in the North West of Iran, located 15 km from the west of Ahar city, in the East Azerbaijan province, Iran. The downstream part of the dam to Ahar city has been studied considering the population and infrastructures in this district according to two different scenarios of dam failure. The first scenario includes piping of flow and dam failure profile with steep side walls while the second scenario consists of inclined sidewalls in the dam breach profile and overtopping of flow as the main cause of breaching. The population centers have been selected in the downstream area of dam according to the field facts. The maximum flood depth reaches up to 9.1 m for the first scenario and 7.1 m for the second scenario at the Islamic Azad University and Tabriz-Ahar road, respectively. The results show the notable risk for some of the population centers in the downstream of the dam. Furthermore, the arrival time of flood, recession time, and maximum velocities in the targeted areas for preparing emergency action plans has been calculated.

Dam break analysis using 1D geometry at Jatigede Dam, Sumedang

Dam breaks can result in flash floods which have enormous destructive power. This destructive force becomes even more significant when the dam break occurs in a dam with a large capacity. An example is the Jatigede Dam, which has a capacity of 1,060 million m3. To determine the flash flood characteristics and potential impact of the collapse of the Jatigede Dam, an analysis of the dam break was carried out using HEC-RAS software. The dam break scenario uses a Probable Maximum Flood (PMF) inflow with the partial opening of two spillway gates in the middle, which causes the dam overtopping. The Froehlich and Von Thun, and Gillette regression methods were used to defining the breach parameters. Based on the dam break analysis, the simulated flash flood of the Von Thun-Gillette method resulted in a higher velocity and lower water surface elevation than the Froehlich method. The difference in the velocity, dimension of the breach shape, water surface elevation, and discharge is caused by the breaching shape and breach formation time.

Overtopping and flood routing process of landslide dams consisted of ice-soil mixtures: A preliminary study

With global warming, glacial collapse chain disasters have frequently occurred in high-mountain areas. In particular, the ice avalanche-glacial debris flow/landslide-barrier lake-flood burst chain disaster caused the most serious consequences. Different from the general landslide dam consisted of rocks and soils, the landslide dam initiated by ice avalanches contains a considerable amount of ice. The appearance of ice will influence the overall performance of the landslide dam by melting, which may cause differential settlements, local weak zones, a more porous structure, and a lower erosion resistance of the landslide dam. Such changes in the erodibility and geometry of the landslide dam will further affect the dam overtopping and flood routing process, which have not been investigated yet and urgently require further study. Therefore, in this study, a preliminary study of the effects of different ice fractions of the landslide dam is conducted, which mainly involves changes in the dam erodibility, the dam geometry, the overtopping development, the final breach size, the process of downstream flood routing, etc. Results show that with the increasing amount of ice melting, the coefficient of soil erodibility and the soil void ratio increase significantly, implying a more erodible dam material and a looser dam structure. The melting of ice can also induce obvious dam settlement, which further results in an earlier dam burst and a shorter rescue time. With the increasing initial ice amount in the landslide dam, the overtopping process develops more rapidly, the breach expands greater both horizontally and vertically, the subsequent flood becomes larger, and the peak arrival time comes earlier.

2D-HEC-RAS Modeling of Flood Wave Propagation in a Semi-Arid Area Due to Dam Overtopping Failure

Dam overtopping failure and the resulting floods are hazardous events that highly impact the inundated areas and are less predictable. The simulation of the dam breach failure and the flood wave propagation is necessary for assessing flood hazards to provide precautions. In the present study, a two-dimensional HEC-RAS model was used to simulate the flood wave resulting from the hypothetical failure of Al-Udhaim Dam on Al-Udhaim River, Iraq, and the propagation of the resulting dam-break wave along 100 km downstream the dam site for the overtopping scenario. The main objective is to analyze the propagation of the flood wave so that the failure risk on dam downstream areas can be assessed and emergency plans may be provided. The methodology consisted of two sub-models: the first is the dam breach failure model for deriving the breach hydrograph, and the second is the hydrodynamic model for propagating the flood wave downstream of the dam. The breach hydrograph is used as an upstream boundary condition to derive the flood impact in the downstream reach of Al- Udhaim River. The flood inundation maps were visualized in RAS-Mapper in terms of water surface elevation, water depth, flow velocity, and flood arrival time. The maximum recorded values were: 105 m (a.m.s.l.), 18 m, 5.5 m/s, and, respectively. The flow velocity decreased from upstream to downstream of the terrain, which means less risk of erosion in the far reaches downstream of the study area. The inundation maps indicated that the water depth and flow velocity were categorized as Catastrophic limits on the terrain's area. The results offer a way to predict flood extent and showed that the impact of a potential dam break at Al-Udhiam Dam will be serious, therefore, suitable management is needed to overcome this risk. Moreover, the maps produced by this study are useful for developing plans for sustainable flood management. Doi: 10.28991/cej-2021-03091739 Full Text: PDF

Influence of a low-head dam on water quality of an urban river system

Dam removal in the United States is becoming a common practice for stream restoration as these structures age, climate driven precipitation patterns change, and ecological uplift becomes desirable. Yet in highly urbanized watersheds, these dams may operate as retention basins removing pollutants and mitigating hydrological change. While elimination may be ecologically and economically advantageous, sediment and pollutant removal processes may be better protective of water quality and damaging flooding. In Central Virginia, we compared a watershed split between an urbanized subwatershed (>20% impervious surface encompassing 37.8% of the total watershed land surface) flowing through a 18 Ha reservoir with a rural subwatershed (<5% impervious encompassing 63.2% of the total watershed land surface) located in the James River and Chesapeake Bay watersheds. This reservoir is scheduled for removal in the near future. Comparisons of data suggest that while portions of the urbanized watershed are degraded, this condition is not reflected at the confluence where water quality more closely resembles the rural and minimally impervious subwatershed. This conclusion was further strengthened from data collected following an unexpected dam overtopping in August 2018 where the reservoir was temporarily drained because of safety concerns. After the draining, water quality reversed with the confluence resembling the urbanized rather than the rural subwatershed. Most significantly, water quality flowing into the James River quickly and significantly shifted from a good to a degraded condition. This case study suggests reservoirs in highly urbanized watersheds may serve as critical water quality improvement structures and removal as part of a stream restoration strategy must be carefully considered.

Analysis of Dam Overtopping Failure Risks Caused by Landslide-Induced Surges Considering Spatial Variability of Material Parameters

Many of the existing reservoir dams are constructed in alpine and gorge regions, where the topography and geological conditions are complicated, bank slopes are steep, and landslides have a high potential to occur. Surges triggered by landslides in the reservoir are one of the major causes of dam overtopping failures. Many factors affect the slope stability of reservoir banks and the height of surges triggered by landslides, such as spatial variability of material properties, speed of landslides, etc. To reasonably evaluate dam overtopping risk caused by landslide-induced surges is a key technology in engineering that is urgent to be solved. Therefore, a novel risk analysis method for overtopping failures caused by waves triggered by landslides induced by bank instability considering the spatial variability of material parameters is proposed in this study. Based on the random field theory, the simulation method for the spatial variability of material parameters is proposed, and the most dangerous slip surface of the reservoir bank slope is determined with the minimum value of the safety factors. The proxy risk analysis models for both the slope instability and dam overtopping are constructed with the consideration of spatial variability of material parameters, and then the dam overtopping failure risk caused by landslide-induced surges is calculated using the Monte-Carlo sampling. The proposed models are applied to a practical engineering project. Results show that the spatial variability of material properties significantly affects the instability risk of slopes, without considering which the risks of slope instability and dam overtopping may be overestimated. This study gives a more reasonable and realistic risk assessment of dam overtopping failures, which can provide technical support for the safety evaluation and risk control of reservoir dams.

Numerical simulation of landslide dam overtopping failure considering headward erosion

Landslide dams often fail shortly after the formation, resulting in huge risks to the downstream residents and properties. Fast and accurate forecasting of the breaching process and discharge hydrograph is important for a decision making to mitigate the damages. Morphological data indicate that the longitudinal length of most landslide dams is much larger than their transverse length. Additionally, headward erosion is more intense in landslide dams than manmade dams during the overtopping failure process. However, most existing models neglect this phenomenon. The objective of this study is to build up a dam-break model considering the headward erosion process, assuming that the change rate of downstream slope-angle is consistent with the rate of breach vertical erosion. And a dam-break numerical model to simulate the overtopping failure process of landslide dams considering the headward erosion was developed based on the theories of hydraulics, hydrology, soil mechanics, sediment dynamics, and etc. Nevertheless, the breach final bottom elevation, which can only be measured after the dam failure, is directly applied in currently available dam break models. To overcome this problem and for the prediction purpose of a newly formed landslide dam, we proposed an empirical model to estimate the breach final bottom elevations of high, medium and low erodibility landslide dams based on the statistical analysis of worldwide landslide dam failure cases collected recently. To verify the effectiveness of proposed dam-break numerical model, the ‘11.03′ Baige landslide dam which locates at the border of Tibet Autonomous Region and Sichuan province was selected as a case study. Results of this study show that the relative errors in the simulated peak discharge, time to the peak, and the total flood volume are 1.59%, 3.50% and 0.53%, respectively, which meet the accuracy requirements of hydrological forecasting. The relative error in the prediction of breach final bottom elevation is 4.28%, which indicates that the accuracy of the simulation is satisfactory. Finally, a sensitivity analysis indicates that the downstream slope affects the prediction of the breach and flood hydrograph significantly, and the excavation of diversion channel is an effective measure to reduce the peak discharge of dam overtopping failure.

Experiments on the characteristics of breach variations due to natural dam overtopping

Natural dams are a common geological disaster that can threaten the safety of people and buildings for several hundreds of kilometres downstream. However, the failure characteristics of natural dams are still unclear, especially the variation characteristics of breaches. In this paper, 20 groups of flume experiments are conducted. Based on the experimental results, the longitudinal and lateral variations of breaches during overtopping are studied. In addition, the relationship between the width and depth of breaches is quantitatively analysed. The results are as follows: during the process of a natural dam overtopping failure, the relationship between the breach depth and time is controlled by the slope of the flume. It is demonstrated that there is an “S” shape when the slope is small and a straight line when the slope is large. In terms of the rate of lateral expansion of the breach, it is demonstrated that the rate of lateral expansion of the breach is smaller in the earlier stage and later stage and is larger in the middle stage. The relationship between width and time is S-shaped. The slope at the bottom of the breach fluctuates during the entire process. The main reason is that the dam break is accompanied by backward erosion, but the slope remains below the underwater angle of repose of the material. Based on the experimental data, the quantitative relationship between the width and depth of breach is investigated. On the basis of the quantitative relationships, a mathematical model of dam breaks is established. The rationality of the model is verified by comparison with actual cases, and the relationship between the width and depth of breaches is proved to be reasonable.