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Assessment of life risk due to flood overtopping of concrete dam
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摘要: 对混凝土大坝洪水漫顶的生命风险评价方法进行研究，以改进传统的评价方法。提出基于Copula函数和三点式变倍比放大法来随机生成年最大入库洪水过程线概率序列的峰量双变量分析方法，同时进行生命风险的评估；并对溃坝生命风险评价标准进行研究，以得出更符合我国大坝现状的生命风险评估标准。以贵州某水电站为例，对其加固后的洪水漫顶生命损失进行评估，依据风险标准进行生命损失风险评价，结果显示加固后该水电站拱坝洪水漫顶对下游村镇造成生命损失的风险较小，属于社会可接受范围。混凝土坝洪水漫顶生命风险评价的方法考虑了洪水特征量间的相互关系，所得洪水发生概率更加贴合实际。Abstract: The life risk assessment method for flood overtopping of concrete dam is studied and the traditional assessment method is improved in this paper. Based on the Copula function and the three-point variable-ratio amplification method, a bivariate analysis method of peak-volume is proposed to generate the random sequence of annual maximum flood hydrograph, and then the life risk is assessed. The life risk assessment criteria for dam break are studied and a proper one is proposed to suit the current situation of dams in China. Taking a hydropower station in Guizhou province as an example, the life loss due to flood overtopping is evaluated for the retaining dam after reinforcement, and the life loss risk is assessed according to the risk criterion. Results show that the life risk due to flood overflow in the downstream area of the hydropower station is small and within the socially acceptable range. In conclusion, considering the relationship among flood characteristics, the flood occurrence probability calculated by the proposed risk assessment method is more consistent with the reality.
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图 1 大中型及小型水库社会生命风险标准
Figure 1. Social life risk criteria for large and medium-sized reservoirs and small reservoirs
图 4 随机生成的洪量w的P-III分布
Figure 4. P-III distribution of the randomly generated flood volume w
图 6 坝前最高水位累积频率曲线
Figure 6. Cumulative frequency curve of highest water levels in front of the dam
图 7 概率10−5的洪水漫顶工况的下游最大淹没水深示意（2050-06-10T15:43）（单位: m）
Figure 7. Schematic diagram of the downstream maximum submerged depth under flood overtopping condition with probability of 10−5 (2050-06-10T15:43) (unit: m)
表 1 Archimedean Copula函数参数
$ \theta $ 与Kendall相关系数$ \tau $ 的关系Table 1. Relationship between Archimedean Copula function parameter and Kendall rank correlation coefficient
Copula类型 Copula函数表达式 θ τ Gumbel-Hougaard $ \exp \left\{ { - {{\left[ {{{\left( { - \ln u} \right)}^\theta } + {{\left( { - \ln v} \right)}^\theta }} \right]}^{1/\theta }}} \right\} $ $ \left[ {1,\infty } \right] $ $ 1 - {\theta ^{ - 1}} $ Clayton $ {\left( {{u^{ - \theta }} + {v^{ - \theta }} - 1} \right)^{ - 1/\theta }} $ $ \left( {0,\infty } \right) $ $ \theta /\left( {\theta + 2} \right) $ Frank $- \dfrac{1}{\theta }\ln \left[ {1 + \dfrac{ {\left( { {\text{exp(} } - \theta u) - 1} \right)\left( { {\text{exp(} } - \theta v) - 1} \right)} }{ { {\text{exp(} } - \theta ) - 1} } } \right]$ $ R\backslash \left\{ 0 \right\} $ $1 + \dfrac{4}{\theta }\left[ {\dfrac{1}{\theta }\displaystyle\int\limits_0^\theta {\dfrac{t}{ {\exp \left( t \right) - 1} }{\text{d} }t - 1} } \right]$ 
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表 2 各村镇信息
Table 2. Information of villages and towns
村镇 平均海拔高程/m 人口/人 SJ村 240 1 148 SZ村 240 1 709 ZG村 250 1 248
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表 3 SJ村受灾严重性
Table 3. Severity of the disaster in SJ village
各年最大入库洪水
过程线概率洪水严重性/ (m2·s−1) 生命损失/人 总死亡
人数/人死亡率 测点S1 测点S2 测点S3 测点S4 测点S5 测点S1 测点S2 测点S3 测点S4 测点S5 1.0×10−5 0.83 0.89 0.19 0.34 0 0.017 0.150 0.058 0.058 0 0.283 2.47×10−4 2.0×10−5 0.11 0.07 0.01 0 0 0.017 0.150 0.058 0 0 0.225 1.96×10−4 3.0×10−5 0.17 0.07 0.05 0 0 0.017 0.150 0.058 0 0 0.225 1.96×10−4 4.0×10−5 0.05 0.02 0 0 0 0.017 0.150 0 0 0 0.167 1.45×10−4 5.0×10−5 0.08 0.07 0 0 0 0.017 0.150 0 0 0 0.167 1.45×10−4 7.0×10−5 0 0 0 0 0 0 0 0 0 0 0 0 8.0×10−5 0 0 0 0 0 0 0 0 0 0 0 0
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