Assessment of Life Loss and Early Warning Strategies under Cascading Failures of Cascade Dams
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摘要:
梯级坝级联溃决引发的洪水放大效应显著提升下游生命风险，亟需系统化的风险评估与预警决策方法.构建了融合“洪水演进模拟-生命损失评估-预警决策”的分析框架.基于不同类型坝体的溃口参数与地形数据，采用二维水动力模型模拟级联溃决过程，引入HURAM模型量化不同风险区域生命损失率，并构建预警疏散时间与总疏散损失的响应关系，确定“最优”预警决策.以清江流域为例，模拟假设发生千年一遇洪水并诱发三座梯级坝级联溃决场景.结果表明，该方法框架能系统性评估级联溃决的生命损失风险与制定合理的预警决策，级联溃决显著放大洪峰流量，隔河岩（8.29%），高坝洲（47.05%），同时受上游坝体结构与“U”型河谷地形影响，坝前水位提升而溃决洪水流量削弱；级联溃决二维模型较一维模型更精细刻画风险区，生命损失风险提高约5.3%；在高坝洲溃坝前3.4 h启动预警，可使疏散总损失降至最低（约8.70亿元）.级联溃决放大效应受地形与坝体结构共同调控，生命损失率受水深等致灾因子的非线性影响显著增强，相应成果为梯级坝级联溃决灾害的风险评估与应急管理提供了可行路径与理论支撑.
Abstract:Cascading failures of cascade dams significantly amplify downstream life risk due to the flood magnification effect, highlighting the urgent need for a systematic framework for risk assessment and early warning decision-making. This study proposes an integrated analytical framework that couples flood evolution simulation, life loss estimation, and early warning optimization. A two-dimensional hydrodynamic model is employed to simulate cascading dam-break scenarios based on breach parameters of different dam types and high-resolution terrain data. The HURAM model is used to quantify life loss rates across varying risk zones. Furthermore, a response relationship between early warning lead time and total evacuation loss is established to identify the optimal warning strategy. Using the Qingjiang River Basin as a case study, a hypothetical scenario involving three sequential dam failures triggered by a 1-in-1 000-year flood is simulated. The results demonstrate that the proposed framework enables comprehensive life loss risk assessment and informed early warning decisions under cascading failure conditions. Compared to single dam failure, cascading breaches increase peak flood discharges by 8.29% at Geheyan and 47.05% at Gaobazhou. However, due to the influence of upstream dam structures and U-shaped valley topography, local flood attenuation occurs despite upstream water level rise. The two-dimensional model captures terrain and velocity distribution more accurately, resulting in an approximately 5.3% increase in estimated life loss risk relative to the one-dimensional model. To minimize evacuation loss, the optimal early warning time is determined as 3.4 hours before Gaobazhou dam failure, reducing total economic loss to approximately 870 million CNY. The results highlight that the flood amplification effect is constrained by both terrain and dam structure, while life loss is highly sensitive to non-linear interactions with hazard parameters such as water depth. This study provides a practical approach and theoretical foundation for cascading dam failure risk management.
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图 4 模型试验与数值模型对比
a.水槽试验；b.2D数值模型
Fig. 4. Comparison between physical experiment and numerical model
图 5 上下游坝前流量过程曲线
a.上游坝；b.下游坝
Fig. 5. Flow process curves before upstream and downstream dams
图 8 清江干流梯级水库及其影像图
Fig. 8. Cascade reservoirs along the mainstream of the Qingjiang River and their satellite images
图 11 一维模型下级联溃决洪水淹没区演进过程
a.高坝洲溃决前水位分布；b.高坝洲溃决11 h后下游淹没阶段；c.高坝洲溃决40 h退水阶段
Fig. 11. Evolution of flood inundation area under one-dimensional model of cascade failure
图 12 二维模型下级联溃决洪水淹没区演进过程
a.高坝洲溃决前水位分布；b.高坝洲溃决11 h后下游淹没阶段；c.高坝洲溃决40 h后退水阶段
Fig. 12. Evolution of flood inundation area under two-dimensional model of cascade failure
图 13 一维模型城镇中心典型河道断面简化图
Fig. 13. Simplified cross-section of a typical river channel at the town center in the one-dimensional model
图 14 一维模型下危险区R7生命损失率评估示意图
Fig. 14. Schematic diagram of fatality rate assessment in high-risk zone R7 under one-dimensional model
图 15 淹没区的洪水特征参数占比
a.水深；b.疏散距离；c.流速
Fig. 15. Distribution proportions of key hydraulic parameters in inundated zones
图 16 二维模型下危险区生命损失率评估示意图
Fig. 16. Estimated fatality rates in high-risk zones based on the two-dimensional model
图 18 梯级坝溃口峰值流量分布
a.水布垭；b.隔河岩；c.高坝洲
Fig. 18. Distribution of peak discharges at cascade dam breaches
图 19 洪水特征对生命损失的敏感图
a.洪水深度；b.疏散距离；c.洪水流速
Fig. 19. Sensitivity of life loss to flood characteristics
图 20 不同时间对生命损失的敏感图
a.溃坝持续时间；b.预警时间
Fig. 20. Sensitivity of life loss to different time factors
表 1 溃坝参数经验公式
Table 1. Empirical formulas for dam failure parameters
参数 公式 溃口深度Hb
溃口顶部宽度Bt
平均溃口宽度Bave
溃口峰值流量Qp
溃决失效时间Tf$ {Y}_{1}={H}_{\mathrm{b}}/{H}_{\mathrm{d}} $
$ {Y}_{2}={B}_{\mathrm{t}}/{H}_{\mathrm{b}} $
$ {Y}_{3}={B}_{\mathrm{a}\mathrm{v}\mathrm{e}}/{H}_{\mathrm{b}} $
$ {Y}_{4}={Q}_{\mathrm{p}}/\sqrt{g{{V}_{\mathrm{w}}}^{5/3}} $
$ {Y}_{5}={T}_{\mathrm{f}}/{T}_{\mathrm{r}} $注：Vw为库容，Hd为原始坝高，Tr单位时间，g为重力加速度. 
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表 2 清江梯级坝体参数
Table 2. Parameters of cascade dams in the Qingjiang River
坝高(m) 坝长(m) 水位
(m)库容
(亿m3)类型 水布垭 233 660 400 43.1 面板
堆石坝高坝洲 151 653 200 34.5 混凝土重力坝 隔河岩 57 419 80 4.3 重力
拱坝
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表 3 梯级坝溃口参数计算表
Table 3. Parameters of the breach models
溃口参数 Hb (m) Qp (m3/s) Bt (m) Bave (m) Tf (h) 水布垭
隔河岩
高坝洲143
151
47115 930
289 389
72 816696
188
410584
188
2003.5
0.3
0.05
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表 4 级联溃决洪水危险区间划分
Table 4. Classification of hazard zones for cascade failure floods
区间 水深(m) 疏散距离(m) R0 0 0 R1 0~1.0 0~100 R2 1.0~1.5 100~153 R3 1.5~3.0 153~311 R4 3.0~4.5 311~462 R5 4.5~4.8 462~500 R6 4.8~6.0 500~631 R7 > 6.0 > 631
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表 5 洪水风险区间生命损失率
Table 5. Fatality rates in flood risk zones
区域 R0 R1 R2 R3 R4 R5 R6 R7 总计 人口数 202 965 23 935 12 781 37 721 36 141 9 095 31 354 4 308 35.83万 损失(%)
死亡人数0
00
00
00
00.06
220.15
140.24
751.35
58-
169
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表 6 预警时间与损失价值关系表
Table 6. Relationship between warning time and loss value
时间(h) 基本疏散(106) 生命损失(106) 可移动损失(106) 总疏散(106) 0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10379.0
570.0
690.7
807.6
924.5
1 041.4
1 158.3
1 275.2
1 392.1
1 509.0
1 625.9133 119
28 787
4 002
60
6
0
0
0
0
0
01 932
603
100
10
2
0
0
0
0
0
0135 430.0
29 960.0
4 792.7
877.6
932.5
1 041.4
1 158.3
1 275.2
1 392.1
1 509.0
1 625.9
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表 7 梯级坝峰值流量对比
Table 7. Comparison of peak discharge among cascade dams
类型 模拟值
(m3/s)计算值
(m3/s)放大效应
(%)水布垭 145 590 115 930 - 隔河岩
高坝洲313 385
107 079289 389
72 8168.29
47.05
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