Current status and prospects of calculation methods for dam and dike failures (Ⅱ)：Two-dimensional and three-dimensional mathematical models
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摘要:
堤坝溃决作为国内外频发的灾害事故之一，对人类的生产生活产生巨大影响，溃决计算方法研究对堤坝溃决洪水的评估、预测与风险防范至关重要。从数学计算角度出发，重点对溃口发展二维、三维数学计算模型梳理总结，概要汇总了常见二维、三维数学计算模型的特点，并列表对比分析了常见溃口计算方法，简要介绍了3种典型的二维数学计算模型，为相关学者开展不同模型的比对研究提供参考，更好把握堤坝溃决数学计算模型的发展现状。对常用数值计算方法与相关通用商业软件和开源软件进行了汇总与对比，梳理了机器学习方法在溃决计算中的应用现状与前景，并给出了未来研究方向与研究重点相关建议。总的来说，溃口发展机理研究与数学模拟中仍存在较多简化与假设，二维和三维数值计算方法朝着精细化描述溃口发展过程的方向发展，但算力需求大，计算耗时长，对溃口发展全过程的精准快速模拟计算将可能是持续的研究热点。机器学习方法已逐渐应用于溃口发展预测分析，未来将在溃口发展分析研究中有更加广泛深入的应用。
Abstract:Significance Dam and dike failure, as one of the most frequent disaster events worldwide, exerts a profound impact on human production and daily life. Research on breach calculation methods is crucial for the assessment, prediction, and risk prevention of dam-break and dike-break floods.
Progress From a mathematical modeling perspective, this paper reviews and summarizes two-dimensional (2D) and three-dimensional (3D) computational models for breach development. The characteristics of common 2D and 3D mathematical models are summarized, and a comparative table of typical breach calculation methods is presented. Three representative 2D mathematical models are briefly introduced to facilitate comparative studies among researchers and to better understand the current development of dam-breach mathematical models. Furthermore, commonly used numerical computation techniques, commercial software, and open-source tools are summarized and compared. The current applications and future prospects of machine learning methods in breach calculation are also discussed, along with suggestions for future research directions and key priorities.
Conclusion and Prospect Overall, existing studies on breach development mechanisms and numerical simulations still involve many simplifications and assumptions. Both 2D and 3D numerical methods are evolving toward more refined descriptions of breach development processes, but they require significant computational resources and time. Accurate and efficient full-process simulation of breach evolution is expected to remain an active research topic. Machine learning methods have gradually been applied to the prediction and analysis of breach development, and they are expected to extensively and in-depth applied in future relevant research.
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图 1 溃决计算过程示意图
x，y，z. 空间三维坐标系方向；O. 原点；h. 水深；zb. 溃口底部高程
Figure 1. Schematic diagram of breach calculation process
Table 1. Summary of commonly used two-dimensional computational models worldwide
来源 溃口形态 溃口水流 堤坝料冲蚀 输沙模型 力学机制 数值模拟方法 WANG等[10] 清水冲刷 浅水方程 冲蚀率公式 — 溃口侧向坍塌 FDM FAEH[11] 二维Exner方程 浅水方程 推移质与悬疑质公式 平衡输沙模型 溃口侧向坍塌 FVM 王光谦等[12] 二维质量守恒和
动量守恒方程考虑河床变形的
二维浅水方程推移质输沙率公式 非平衡输沙模型 溃口侧向坍塌 FVM SWARTENBROEKX等[13] 二维Exner方程 浅水方程 推移质公式 平衡输沙模型 溃口侧向坍塌 FVM CAO等[14] 二维非平衡全沙输移方程 广义浅水方程 推移质公式 非平衡输沙模型 溃口侧向坍塌 FVM WU等[15] 二维非平衡全沙输移方程 广义浅水方程 全沙输移公式 非平衡输沙模型 溃口侧向坍塌 FVM JUEZ等[16] 二维Exner方程 圣维南方程与浅水方程 10种不同的冲蚀公式 平衡输沙模型 溃口无侧向坍塌 FVM ROSATTI等[17] 二维质量守恒和动量守恒
方程（固相）浅水方程（液相） 水流浓度公式 两相流模型 溃口无侧向坍塌 FVM SWARTENBROEKX等[18] 二维质量守恒和动量守恒
（推移质）浅水方程（清水） 冲蚀率公式 两层流模型 溃口无侧向坍塌 FVM LI等[19] 二维非平衡输沙方程
（悬移质）浅水方程 挟砂率和沉积率
经验公式两层流模型 溃口无侧向坍塌 FVM RAZAVITOOSI等[20] N-S方程（固相非牛顿流体） N-S方程（液相，
非牛顿流体）— 两相流模型 溃口无侧向坍塌 SPH GUAN等[21] 二维非平衡输沙方程
（推移质）浅水方程（清水） 推移质公式 非平衡输沙模型 溃口侧向坍塌 FVM KESSERWANI等[22] 二维非平衡输沙方程
（悬移质）浅水方程 悬移质公式 非平衡输沙模型 溃口无侧向坍塌 FDM（间断
Galerkin方法）DI CRISTO等[23] 二维质量守恒和动量守恒
方程（固相）浅水方程（液相） 推移质公式 两相流模型 底床崩塌算法 FVM EL KADI ABDERREZZAK 等[24] 二维Exner方程 浅水方程 推移质公式 平衡输沙模型 溃口侧向坍塌 FVM 陆灵威等[25] 矩形 浅水方程 — — 溃口无侧向坍塌 FDM 吴泽艳等[26] 固定形状 浅水方程 — — 溃口侧向无坍塌 FDM（间断
Galerkin方法）DAZZI等[27] 二维Exner方程 浅水方程 推移质公式 平衡输沙模型 溃口侧向坍塌 FVM 马利平等[28] DB-IWHR模型 浅水方程 — — 溃口侧向坍塌 FVM 刘嘉欣等[29] 二维非平衡输沙方程 含源项浅水方程 悬移质和推移质公式 非平衡输沙模型 溃口侧向坍塌 FVM 张大伟[30] Exner方程 浅水方程 de Vries输沙率公式 平衡输沙模型 溃口无侧向坍塌 FVM 王春正等[31] 动量方程（固相） N-S方程（液相） — 流固耦合模型 — FVM与FEM 注：FDM. 有限差分法； FVM. 有限体积法；SPH. 光滑粒子流体动力学方法；FEM. 有限元法；下同 
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Table 2. Summary of selected three-dimensional computational models worldwide
模型 溃口形态确定方法 溃口水流 冲蚀方式 力学分析 计算方法 王晓玲等[35] — N-S方程 — 溃口无侧向坍塌 FVM和VOF LAROCQUE等[38] — N-S方程 — 溃口无侧向坍塌 FVM和VOF（Fluent软件） MARSOOLI[36] 三维非平衡输沙方程 N-S方程 推移质与悬移质公式 溃口无侧向坍塌 FVM和VOF 罗诗怡等[39] 梯形或经验冲蚀率公式 N-S方程 推移质经验公式 溃口侧向坍塌 FVM（Fluent软件） 牟迪等[42]和丁伟业等[43] 矩形 N-S方程 — 溃口无侧向坍塌 FVM（OpenFOAM软件） ZHANG等[48] 固定形状 N-S方程 — 溃口侧向无坍塌 FEM 刘青泉等[46] 土体弹塑性理论（固相） N-S方程（液相） 基于临界剪应力的线性侵蚀模型 溃口侧向坍塌 SPH MUNOZ等[37] 固定形状 RANS方程 — 溃口无侧向坍塌 FVM和VOF 杨柳等[44] 动量方程（固相） N-S方程（液相） 流固耦合作用 溃口无侧向坍塌 CFD-DEM（SDEM软件） 李炎隆等[40] 三维非平衡输沙方程 N-S方程 Meyer-Peter & Muller推移质
与悬移质公式溃口侧向坍塌 FVM（FLOW-3D软件） 朱远乐等[45] 质量守恒与动量守恒 质量守恒与动量守恒 — 溃口无侧向坍塌 PFC（PFC3D软件） SU等[47] 动量方程（固相） N-S方程（液相） 水土耦合作用 溃口侧向坍塌 SPH-DEM 王娇等[41] 三维输沙方程 N-S方程 沉积模型（Meyer-Peter推移质输沙
公式和悬移质泥沙扩散方程）溃口侧向坍塌 FVM（FLOW-3D软件） 注：VOF. 流体体积法；CFD-DEM. 计算流体力学-离散元方法；PFC. 颗粒流程序；SPH-DEM. 光滑粒子流体动力学−离散元方法
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[1] Centre for Research on the Epidemiology of Disasters: UN Office for Disaster Risk Reduction(CRED-UNDRR). The human cost of disasters: An overview of the last 20 years(2000–2019)[R]. Brussels, Belgium: CRED-UNDRR, 2020. [2] International Commission on Large Dams(ICOLD). Dam failures statistical analysis[R]. Paris, France: ICOLD, 1995. [3] 陈生水, 钟启明. 土石坝溃坝数学模型及应用[M]. 北京: 中国水利水电出版社, 2019.CHEN S S, ZHONG Q M. Numerical models for earth-rock dam breaching and their applications[M]. Beijing: China Water & Power Press, 2019. (in Chinese) [4] 陈生水, 陈祖煜, 钟启明. 土石坝和堰塞坝溃决机理与溃坝数学模型研究进展[J]. 水利水电技术, 2019, 50(8): 27-36. doi: 10.13928/j.cnki.wrahe.2019.08.004CHEN S S, CHEN Z Y, ZHONG Q M. Progresses of studies on failure mechanism and numerical dam failure model of earth-rockfill dam and landslide dam[J]. Water Resources and Hydropower Engineering, 2019, 50(8): 27-36. (in Chinese with English abstract doi: 10.13928/j.cnki.wrahe.2019.08.004 [5] PERAMUNA P D P O, NELUWALA N G P B, WIJESUNDARA K K, et al. Review on model development techniques for dam break flood wave propagation[J]. WIREs Water, 2024, 11(2): e1688. doi: 10.1002/wat2.1688 [6] SREEKUMAR U, GILDEH H K, MOHAMMADIAN A, et al. Tailings dam breach outflow modelling: A review[J]. Mine Water and the Environment, 2024, 43(4): 563-587. doi: 10.1007/s10230-024-01015-y [7] MARANZONI A, TOMIROTTI M. Three-dimensional numerical modelling of real-field dam-break flows: Review and recent advances[J]. Water, 2023, 15(17): 3130. doi: 10.3390/w15173130 [8] 刘嘉欣, 钟启明, 陈亮, 等. 堰塞坝溃决机理与溃决过程模拟技术研究综述[J]. 防灾减灾工程学报, 2022, 42(3): 638-652. doi: 10.13409/j.cnki.jdpme.20210726001LIU J X, ZHONG Q M, CHEN L, et al. Review on the simulation technologies of breach mechanism and breaching process of landslide dam[J]. Journal of Disaster Prevention and Mitigation Engineering, 2022, 42(3): 638-652. (in Chinese with English abstract doi: 10.13409/j.cnki.jdpme.20210726001 [9] BAO H, LIU L, LAN H X, et al. Progressive hydraulic failure mechanism and multi-stage instability risk early warning for loess check dams[J]. Journal of Hydrology, 2025, 663: 134226. doi: 10.1016/j.jhydrol.2025.134226 [10] WANG Z G, BOWLES D S. Three-dimensional non-cohesive earthen dam breach model. Part 1: Theory and methodology[J]. Advances in Water Resources, 2006, 29(10): 1528-1545. doi: 10.1016/j.advwatres.2005.11.009 [11] FAEH R. Numerical modeling of breach erosion of river embankments[J]. Journal of Hydraulic Engineering, 2007, 133(9): 1000-1009. doi: 10.1061/(ASCE)0733-9429(2007)133:9(1000) [12] 王光谦, 钟德钰, 张红武, 等. 汶川地震唐家山堰塞湖泄流过程的数值模拟[J]. 科学通报, 2008, 53(24): 3130-3136. doi: 10.3321/j.issn:0023-074X.2008.24.022WANG G Q, ZHONG D Y, ZHANG H W, et al. Numerical simulation of discharge process of Tangjiashan dammed lake in Wenchuan earthquake[J]. Chinese Science Bulletin, 2008, 53(24): 3130-3136. (in Chinese with English abstract doi: 10.3321/j.issn:0023-074X.2008.24.022 [13] SWARTENBROEKX C, SOARES-FRAZÃO S, STAQUET R, et al. Two-dimensional operator for bank failures induced by water-level rise in dam-break flows[J]. Journal of Hydraulic Research, 2010, 48(3): 302-314. doi: 10.1080/00221686.2010.481856 [14] CAO Z X, YUE Z Y, PENDER G. Landslide dam failure and flood hydraulics. Part Ⅱ: Coupled mathematical modelling[J]. Natural Hazards, 2011, 59(2): 1021-1045. doi: 10.1007/s11069-011-9815-7 [15] WU W M, MARSOOLI R, HE Z G. Depth-averaged two-dimensional model of unsteady flow and sediment transport due to noncohesive embankment break/breaching[J]. Journal of Hydraulic Engineering, 2012, 138(6): 503-516. doi: 10.1061/(ASCE)HY.1943-7900.0000546 [16] JUEZ C, MURILLO J, GARCÍA-NAVARRO P. Numerical assessment of bed-load discharge formulations for transient flow in 1D and 2D situations[J]. Journal of Hydroinformatics, 2013, 15(4): 1234-1257. doi: 10.2166/hydro.2013.153 [17] ROSATTI G, BEGNUDELLI L. Two-dimensional simulation of debris flows over mobile bed: Enhancing the TRENT2D model by using a well-balanced Generalized Roe-type solver[J]. Computers & Fluids, 2013, 71: 179-195. doi: 10.1016/j.compfluid.2012.10.006 [18] SWARTENBROEKX C, ZECH Y, SOARES-FRAZÃO S. Two-dimensional two-layer shallow water model for dam break flows with significant bed load transport[J]. International Journal for Numerical Methods in Fluids, 2013, 73(5): 477-508. doi: 10.1002/fld.3809 [19] LI J, CAO PROFESSOR Z, PENDER, et al. A double layer-averaged model for dam-break flows over mobile bed[J]. Journal of Hydraulic Research, 2013, 51(5): 518-534. doi: 10.1080/00221686.2013.812047 [20] RAZAVITOOSI S L, ALI AYYOUBZADEH S, VALIZADEH A. Two-phase SPH modelling of waves caused by dam break over a movable bed[J]. International Journal of Sediment Research, 2014, 29(3): 344-356. doi: 10.1016/S1001-6279(14)60049-4 [21] GUAN M F, WRIGHT N G, SLEIGH P A. 2D process-based morphodynamic model for flooding by noncohesive dyke breach[J]. Journal of Hydraulic Engineering, 2014, 140(7): 04014022. doi: 10.1061/(ASCE)HY.1943-7900.0000861 [22] KESSERWANI G, SHAMKHALCHIAN A, ZADEH M J. Fully coupled discontinuous Galerkin modeling of dam-break flows over movable bed with sediment transport[J]. Journal of Hydraulic Engineering, 2014, 140(4): 06014006. doi: 10.1061/(ASCE)HY.1943-7900.0000860 [23] DI CRISTO C, GRECO M, IERVOLINO M, et al. Two-dimensional two-phase depth-integrated model for transients over mobile bed[J]. Journal of Hydraulic Engineering, 2016, 142(2): 04015043. doi: 10.1061/(ASCE)HY.1943-7900.0001024 [24] EL KADI ABDERREZZAK K, DIE MORAN A, TASSI P, et al. Modelling river bank erosion using a 2D depth-averaged numerical model of flow and non-cohesive, non-uniform sediment transport[J]. Advances in Water Resources, 2016, 93: 75-88. doi: 10.1016/j.advwatres.2015.11.004 [25] 陆灵威, 林斌良, 孙健, 等. 河道溃堤水波的物理模型实验研究[J]. 水力发电学报, 2016, 35(11): 25-34. doi: 10.11660/slfdxb.20161104LU L W, LIN B L, SUN J, et al. An experimental study of propagation of dike-break waves[J]. Journal of Hydroelectric Engineering, 2016, 35(11): 25-34. (in Chinese with English abstract doi: 10.11660/slfdxb.20161104 [26] 吴泽艳, 杨忠勇. 基于简单WENO-RKDG的溃坝问题数值模拟[J]. 应用力学学报, 2017, 34(6): 1126-1133.WU Z Y, YANG Z Y. Numerical simulation of two-dimensional dam-break flow based on the simple WENO Limiter-Runge-Kutta discontinuous Galerkin method[J]. Chinese Journal of Applied Mechanics, 2017, 34(6): 1126-1133. (in Chinese with English abstract [27] DAZZI S, VACONDIO R, MIGNOSA P. Integration of a levee breach erosion model in a GPU-accelerated 2D shallow water equations code[J]. Water Resources Research, 2019, 55(1): 682-702. doi: 10.1029/2018WR023826 [28] 马利平, 侯精明, 张大伟, 等. 耦合溃口演变的二维洪水演进数值模型研究[J]. 水利学报, 2019, 50(10): 1253-1267.MA L P, HOU J M, ZHANG D W, et al. Study on 2-D numerical simulation coupling with breach evolution in flood propagation[J]. Journal of Hydraulic Engineering, 2019, 50(10): 1253-1267. (in Chinese with English abstract [29] 刘嘉欣, 阎志坤, 钟启明, 等. 尾矿库漫顶溃坝机理与溃坝过程数值模拟[J]. 中南大学学报(自然科学版), 2022, 53(7): 2694-2708. doi: 10.11817/j.issn.1672-7207.2022.07.027LIU J X, YAN Z K, ZHONG Q M, et al. Breach mechanism of tailings dam due to overtopping failure and numerical simulation of breach process[J]. Journal of Central South University (Science and Technology), 2022, 53(7): 2694-2708. (in Chinese with English abstract doi: 10.11817/j.issn.1672-7207.2022.07.027 [30] 张大伟. 土石坝漫顶溃决过程模拟[J]. 中国防汛抗旱, 2022, 32(1): 80-83. doi: 10.16867/j.issn.1673-9264.2021248ZHANG D W. Simulation of overtopping breach process of embankment dam[J]. China Flood & Drought Management, 2022, 32(1): 80-83. (in Chinese with English abstract doi: 10.16867/j.issn.1673-9264.2021248 [31] 王春正, 孙亮, 黄玲玲, 等. 基于双向流固耦合模型的溃坝水流数值模拟[J]. 科学技术与工程, 2023, 23(26): 11090-11097.WANG C Z, SUN L, HUANG L L, et al. Numerical simulations of dam break flow based on two-way coupling model for fluid-structure interactions[J]. Science Technology and Engineering, 2023, 23(26): 11090-11097. (in Chinese with English abstract [32] 杨啸铭. 基于PFC2D的邱山铁矿尾矿库坝体稳定性和溃坝模拟分析研究[D]. 昆明: 昆明理工大学, 2015.YANG X M. Simulation analysis of dam stability and dam break of Qiushan iron mine tailings based on PFC2D[D]. Kunming: Kunming University of Science and Technology, 2015. (in Chinese with English abstract [33] 张红武, 张俊华, 卜海磊, 等. 试论推移质输沙率公式[J]. 南水北调与水利科技, 2011, 9(6): 140-145. doi: 10.3724/SP.J.1201.2011.06140ZHANG H W, ZHANG J H, BU H L, et al. Discussion of bed-load transport equations[J]. South-to-North Water Transfers and Water Science & Technology, 2011, 9(6): 140-145. (in Chinese with English abstract doi: 10.3724/SP.J.1201.2011.06140 [34] AKGUN C, NAS S S, USLU A. 2D and 3D numerical simulation of dam-break flooding: A case study of the Tuzluca dam, Turkey[J]. Water, 2023, 15(20): 3622. doi: 10.3390/w15203622 [35] 王晓玲, 张爱丽, 陈华鸿, 等. 三维溃坝洪水在复杂淹没区域演进的数值模拟[J]. 水利学报, 2012, 43(9): 1025-1033.WANG X L, ZHANG A L, CHEN H H, et al. Three-dimensional numerical simulation of dam-break flood routing in the complex inundation areas[J]. Journal of Hydraulic Engineering, 2012, 43(9): 1025-1033. (in Chinese with English abstract [36] MARSOOLI R, WU W M. Three-dimensional numerical modeling of dam-break flows with sediment transport over movable beds[J]. Journal of Hydraulic Engineering, 2015, 141: 04014066. doi: 10.1061/(ASCE)HY.1943-7900.0000947 [37] MUNOZ D H, CONSTANTINESCU G. 3-D dam break flow simulations in simplified and complex domains[J]. Advances in Water Resources, 2020, 137: 103510. doi: 10.1016/j.advwatres.2020.103510 [38] LAROCQUE L A, IMRAN J, CHAUDHRY M H. 3D numerical simulation of partial breach dam-break flow using the LES and k-ε turbulence models[J]. Journal of Hydraulic Research, 2013, 51(2): 145-157. doi: 10.1080/00221686.2012.734862 [39] 罗诗怡, 谢新生, 刘路, 等. 大桥水库大坝逐渐溃决的数值模拟[J]. 人民黄河, 2017, 39(5): 45-50. doi: 10.3969/j.issn.1000-1379.2017.05.012LUO S Y, XIE X S, LIU L, et al. Numerical simulation of Daqiao reservoir gradual dam break[J]. Yellow River, 2017, 39(5): 45-50. (in Chinese with English abstract doi: 10.3969/j.issn.1000-1379.2017.05.012 [40] 李炎隆, 邱文, 王琳, 等. 混凝土面板砂砾石坝漫顶溃坝数值模拟[J]. 应用力学学报, 2023, 40(1): 96-106.LI Y L, QIU W, WANG L, et al. Numerical simulation for concrete-face sand-gravel dam breaching due to overtopping[J]. Chinese Journal of Applied Mechanics, 2023, 40(1): 96-106. (in Chinese with English abstract [41] 王姣, 吴泽亮, 熊威, 等. 堤防弯道决口逐渐溃决三维数值模拟[J]. 水利水运工程学报, 2024(1): 27-34.WANG J, WU Z L, XIONG W, et al. Analysis of gradual dike bend breach through 3D numerical simulation[J]. Hydro-Science and Engineering, 2024(1): 27-34. (in Chinese with English abstract [42] 牟迪, 陈丽芬, 宁德志. 溃坝及其对结构物作用的三维数值模拟研究[J]. 中国造船, 2020, 61(增刊2): 231-239. doi: 10.3969/j.issn.1000-4882.2020.z2.025MU D, CHEN L F, NING D Z. Three-D numerical study of interaction between dam-break wave and circular cylinder[J]. Shipbuilding of China, 2020, 61(S2): 231-239. (in Chinese with English abstract doi: 10.3969/j.issn.1000-4882.2020.z2.025 [43] 丁伟业, 金生, 艾丛芳. 耦合VOF的非线性k-ε模型三维溃坝数值模拟[J]. 水道港口, 2017, 38(5): 489-494.DING W Y, JIN S, AI C F. 3-D numerical simulation of dam-break flow based on VOF method with nonlinear k-ε turbulent model[J]. Journal of Waterway and Harbor, 2017, 38(5): 489-494. (in Chinese with English abstract [44] 杨柳, 王金安, 黎伟佳. 基于CFD-DEM耦合的尾矿库溃坝数值模拟[J]. 金属矿山, 2022(8): 219-227. doi: 10.19614/j.cnki.jsks.202208030YANG L, WANG J A, LI W J. Numerical simulation of tailings pond dam break based on CFD-DEM method[J]. Metal Mine, 2022(8): 219-227. (in Chinese with English abstract doi: 10.19614/j.cnki.jsks.202208030 [45] 朱远乐, 赵新勇, 王淇萱, 等. 基于PFC3D的灰岭尾矿库溃坝三维数值模拟研究[J]. 水电能源科学, 2023, 41(8): 94-97. doi: 10.20040/j.cnki.1000-7709.2023.20221577ZHU Y L, ZHAO X Y, WANG Q X, et al. Research on three-dimensional numerical simulation of dam break of Huiling tailings pond based on PFC3D[J]. Water Resources and Power, 2023, 41(8): 94-97. (in Chinese with English abstract doi: 10.20040/j.cnki.1000-7709.2023.20221577 [46] 刘青泉, 安翼. 漫顶溃坝过程的水土耦合数值模型研究[J]. 泥沙研究, 2019, 44(3): 13-18. doi: 10.16239/j.cnki.0468-155x.2019.03.003LIU Q Q, AN Y. Soil-water coupling numerical model for overtopping failure process of earth dam[J]. Journal of Sediment Research, 2019, 44(3): 13-18. (in Chinese with English abstract doi: 10.16239/j.cnki.0468-155x.2019.03.003 [47] SU Z Y, WANG S, LI D Q, et al. SPH-DEM modeling overtopping failure of earthfill dams[J]. Acta Geotechnica, 2024, 19(2): 953-970. doi: 10.1007/s11440-024-02258-3 [48] ZHANG T, PENG L, FENG P. Evaluation of a 3D unstructured-mesh finite element model for dam-break floods[J]. Computers & Fluids, 2018, 160: 64-77. doi: 10.1016/j.compfluid.2017.10.013 [49] LIU Z K, FEI J B, JIE Y X. Including μ(Ⅰ) rheology in three-dimensional Navier-Stokes-governed dynamic model for natural avalanches[J]. Powder Technology, 2022, 396: 406-432. doi: 10.1016/j.powtec.2021.11.003 [50] 马洪福, 孙东坡, 刘明潇, 等. 基于聚类分析的堤防溃口水力边界特征值研究[J]. 水力发电学报, 2019, 38(4): 75-86. doi: 10.11660/slfdxb.20190408MA H F, SUN D P, LIU M X, et al. Characteristic parameters of hydraulic boundary at embankment breaches based on cluster analysis[J]. Journal of Hydroelectric Engineering, 2019, 38(4): 75-86. (in Chinese with English abstract doi: 10.11660/slfdxb.20190408 [51] KHOSRAVI K, SHEIKH KHOZANI Z, HATAMIAFKOUEIEH J. Prediction of embankments dam break peak outflow: A comparison between empirical equations and ensemble-based machine learning algorithms[J]. Natural Hazards, 2023, 118(3): 1989-2018. doi: 10.1007/s11069-023-06060-4 [52] 王琳, 张润宇, 苑鹏飞, 等. 基于径向基网络的堰塞体溃决峰值流量预测研究[J]. 水力发电学报, 2024, 43(5): 68-79.WANG L, ZHANG R Y, YUAN P F, et al. Radial basis function model for predicting peak outflow caused by landslide dam failure[J]. Journal of Hydroelectric Engineering, 2024, 43(5): 68-79. (in Chinese with English abstract [53] SEYEDASHRAF O, MEHRABI M, AKHTARI A A. Novel approach for dam break flow modeling using computational intelligence[J]. Journal of Hydrology, 2018, 559: 1028-1038. doi: 10.1016/j.jhydrol.2018.03.001 [54] YAN X H, AO R G, MOHAMMADIAN A, et al. Fast mathematical modeling of partial-breach dam-break flow using a time-series field-reconstruction deep learning approach[J]. Physics of Fluids, 2023, 35(4): 043306. doi: 10.1063/5.0142335 [55] LI C L, HAN Z, LI Y G, et al. Physical information-fused deep learning model ensembled with a subregion-specific sampling method for predicting flood dynamics[J]. Journal of Hydrology, 2023, 620: 129465. doi: 10.1016/j.jhydrol.2023.129465 [56] 张强. 基于分区异步元胞自动机的土坝漫顶溃坝模拟[J]. 南昌工程学院学报, 2020, 39(1): 20-24.ZHANG Q. Simulation on dam-break of earth dam due to overtopping based on partition asynchronous cellular automata[J]. Journal of Nanchang Institute of Technology, 2020, 39(1): 20-24. (in Chinese with English abstract [57] 蔡木良, 支欢乐, 李文欢, 等. 基于元胞自动机的实时降雨下流域洪水淹没过程分析[J]. 中国农村水利水电, 2023(7): 35-40.CAI M L, ZHI H L, LI W H, et al. Inundation process analysis of watershed flood under real-time rainfall data using cellular automata[J]. China Rural Water and Hydropower, 2023(7): 35-40. (in Chinese with English abstract [58] 白冰, 董飞, 李传奇, 等. 基于元胞自动机和深度学习的城市洪涝预报[J]. 水利水电技术(中英文), 2024, 55(12): 17-28.BAI B, DONG F, LI C Q, et al. Rapid urban flood forecasting based on cellular automata and deep learning[J]. Water Resources and Hydropower Engineering, 2024, 55(12): 17-28. (in Chinese with English abstract [59] 张宝森, 栗铭阳, 刘占奎, 等. 河流水深测量方法综述及研究进展[J]. 水利学报, 2025, 56(1): 32-41.ZHANG B S, LI M Y, LIU Z K, et al. Overview and research progress on river depth measurement techniques[J]. Journal of Hydraulic Engineering, 2025, 56(1): 32-41. (in Chinese with English abstract [60] GARSOLE P A, BOKIL S, KUMAR V, et al. A review of artificial intelligence methods for predicting gravity dam seepage, challenges and way-out[J]. AQUA: Water Infrastructure, Ecosystems and Society, 2023, 72(7): 1228-1248. doi: 10.2166/aqua.2023.042 [61] DARJI K, PATEL D, PRAKASH I, et al. Hydrodynamic modeling of dam breach floods for predicting downstream inundation scenarios using integrated approach of satellite data, unmanned aerial vehicles (UAVs), and Google Earth Engine (GEE)[J]. Applied Water Science, 2024, 14(9): 187. doi: 10.1007/s13201-024-02253-9 [62] 陈兰, 范宣梅, 熊俊麟, 等. 藏东南多依弄巴流域冰湖溃决危险性评价[J]. 地质科技通报, 2023, 42(2): 258-266. doi: 10.19509/j.cnki.dzkq.tb20220235CHEN L, FAN X M, XIONG J L, et al. Hazard assessment of glacial lake outbursts in the Doyinongba basin, southeastern Tibetan Plateau[J]. Bulletin of Geological Science and Technology, 2023, 42(2): 258-266. (in Chinese with English abstract doi: 10.19509/j.cnki.dzkq.tb20220235 [63] PIANFORINI M, DAZZI S, PILZER A, et al. Real-time flood maps forecasting for dam-break scenarios with a transformer-based deep learning model[J]. Journal of Hydrology, 2024, 635: 131169. doi: 10.1016/j.jhydrol.2024.131169 [64] 宋宜祥, 张晓波, 黄达. 基于SSA-Adam-BP神经网络模型的堰塞坝稳定性预测[J]. 地质科技通报, 2022, 41(2): 130-138. doi: 10.19509/j.cnki.dzkq.2022.0040SONG Y X, ZHANG X B, HUANG D. Stability prediction of landslide dams based on SSA-Adam-BP neural network model[J]. Bulletin of Geological Science and Technology, 2022, 41(2): 130-138. (in Chinese with English abstract doi: 10.19509/j.cnki.dzkq.2022.0040 [65] 黄艳, 喻杉, 罗斌, 等. 面向流域水工程防灾联合智能调度的数字孪生长江探索[J]. 水利学报, 2022, 53(3): 253-269. doi: 10.13243/j.cnki.slxb.20210865HUANG Y, YU S, LUO B, et al. Development of the digital twin Changjiang River with the pilot system of joint and intelligent regulation of water projects for flood management[J]. Journal of Hydraulic Engineering, 2022, 53(3): 253-269. (in Chinese with English abstract doi: 10.13243/j.cnki.slxb.20210865 -
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