Dams are important structures that provide various benefits, such as hydroelectric power generation, irrigation, and flood control. However, dam failures can lead to catastrophic consequences, causing significant economic and human losses. Therefore, predicting the potential impact of a dam break is crucial for ensuring the safety of people and property downstream. The width of the breach is a critical factor in estimating the flooded area downstream of an earth-rock dam during a dam break. Traditional empirical formulas developed by the Scientific Research Institute of the Ministry of Railways and the Yellow River Water Conservancy Commission are used to estimate the width of the breach, taking into account the storage capacity, length, and height of the dam. However, these formulas have been found to have significant errors when compared to actual breach widths observed in dam break cases at home and abroad. To improve the accuracy of these formulas, this paper uses an allometric model to fit the data from seven dam break cases, resulting in an optimization formula for calculating the width of the breach. The new formula takes into account the length, height, and storage capacity of the dam, as well as the degree of compaction of the soil in the dam body. The optimized formula has been found to have a maximum error of only 4.5% when compared to actual breach widths, indicating that it is more accurate than the traditional empirical formulas. The optimization formula proposed in this study provides a more accurate method for estimating the width of the breach in earth-rock dam breaks, and can be used to improve the accuracy of calculations for maximum flow rate. The results of this study can also have significant implications for dam safety engineering, as well as for the development of effective emergency response plans in the event of a dam break. In addition, the DBFL-IWHR model is used to simulate the downstream flood evolution and compared with the traditional empirical formula. The DBFL-IWHR model is a two-dimensional hydrodynamic model that takes into account the complex interactions between the water flow and the topography of the river channel. The results show that the maximum flow rate calculated by the traditional formula is lower than that of the DBFL-IWHR model, and that the arrival time of the maximum flow rate in the downstream section is delayed compared to that of the DBFL-IWHR model. This highlights the importance of using accurate models in predicting the potential impact of dam breaks on downstream areas. In conclusion, the optimization formula proposed in this study provides a more accurate method for estimating the width of the breach in earth-rock dam breaks, and can be used to improve the accuracy of calculations for maximum flow rate. Furthermore, the use of accurate hydrodynamic models, such as the DBFL-IWHR model, is recommended for simulating the downstream flood evolution and predicting the potential impact of dam breaks. These findings may have significant implications for dam safety engineering, emergency response planning, and the protection of people and property downstream of earth-rock dams. [ABSTRACT FROM AUTHOR]