Precise Calculation for Characteristic Parameters of Valley-type Debris Flow Using a Methed of Recursive Equivalent Area Substitution
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摘要:
为解决“沟谷型”泥石流在不规则断面处特征参数的精细求解问题，笔者以曼宁公式为基础，建立“等代”面积递归逼近的数学模型，实现了最深泥位、流体速度、威胁范围的求解计算，其结果比较符合实际。利用该模型在豫西某泥石流受威胁对象段任取10个断面进行研究分析：①计算出10年一遇、20年一遇、50年一遇、100年一遇等降水概率工况下最深泥位、流速、行洪断面大小，研究其随雨强大小的演变规律。②定量分析了各断面泄洪能力强弱。③结合泥石流强度判定标准对所选区域进行危险度分区，划分了极高危险区、高危险区、中危险区、低危险区。该模型不仅可以为预测泥石流各项指标提供基本参数，而且可为灾害防治提供科学依据。研究成果对泥石流的精细化防治方面具有重要支撑作用。
Abstract:In order to solve the problem of key parameters in predicting "valley-type" debris flow at irregular profiles, based on Manning's formula, this paper establishes an approaching mathematical model of "equivalent area substitution method", which completed calculation for the deepest mud level, the flow rate and the threat range. The result is close to reality. This paper select 10 profiles randomly in the affected area by debris flow in western Henan, by this model: ① the deepest mud level was calculated, the flow velocity, and the area size of the cross-flood profiles under the probability of rainfall once in 10 years, and in 20 years, 50 years, in 100 years. ② Moreover, this paper has done some research for the law of evolution with different rain intensity, and quantitatively analyzed the flood discharge capacity of each profile. ③ Combined with the judgment standard of debris flow intensity, the selected areas were classified into extermely high-risk areas, high-risk areas, medium-risk areas, and low-risk areas. Furthermore, the model can not only provide basic parameters for predicting various indicators of debris flow, but also provide scientific basis for preventing and controlling disaster of debris flow. Finally, the results of this research have a certain significance in the refined prevention and control of debris flow.
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图 1 研究区位置及地质背景图
（a）.康山村地质背景图；（b）.栾川县地形地貌图
Figure 1. The map of Geological condition and the locationfor study area
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图 2 泥石流发育形态特征图和量测断面位置图
（a）.研究区测量断面位置示意图；（b）.康山村泥石流隐患沟发育特征示意图
Figure 2. The map of characteristics for debris flow developmental features and the location of the measurement profiles
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图 3 AA`断面数学模型构建示意图
Figure 3. Schematic diagram of mathematical model construction for AA` profiles
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图 4 数学模型中角度和断面面积函数关系图
Figure 4. The relationship between the angle and crossing profiles area function in the mathematical mode
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图 6 行洪断面和雨强关系图
Figure 6. The diagram for relationship of water crossing profiles under different rain intensity conditions
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图 7 流速、最深泥位和雨强关系图
Figure 7. The diagram for relationship of flow velocity,deepest mud level under different rain intensity conditions
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图 8 AA`断面100年一遇降水工况下泥位深度分区示意图
（a）.最深泥位、淹没区、未淹没区、总行洪宽度示意图 ；（b）.泥石流低强度区划分标准及其宽度示意图；（c）.泥石流中强度区划分标准及其宽度 ；（d）.泥石流高强度区划分标准及其宽度示意图
Figure 8. Schematic diagram of the mud level depth division under the 100-year rainfall on the AA` profiles
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图 9 各降水强度下测量断面区域危险度分区图
（a）.100年一遇雨强条件下承灾体危险度分区图；（b）.50年一遇雨强条件下承灾体危险度分区图；（c）.20年一遇雨强条件下承灾体危险度分区图；（d）.10年一遇雨强条件下承灾体危险度分区图
Figure 9. Hazard zoning map of the measurement profiles area under various rainfall intensities
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图 10 各断面淹没区、高位区淹没宽度占压其行洪总宽度比例
（a）.各断面淹没区宽度占压其行洪总宽度比例图；（b）.各断面高危险区淹没宽度占压其行洪总宽度比例图
Figure 10. The ratio of the submerged area and high-level area width to the total flood width of each profiles
表 1 AA`断面测量数据表
Table 1 The table of measurement data for AA` profiles
点号 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 X 3770586 3770593 3770601 3770608 3770629 3770635 3770638 3770669 3770715 3770735 Y 533751 533752 533754 533755 533758 533759 533759 533765 533772 533776 H 1069 1069 1068 1062 1063 1063 1064 1067 1068 1071 
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表 2 不同雨强条件下各断面的泥位、流速计算表
Table 2 Calculation table for mud level and flow velocity of each profiles under various rain conditions
降水概率 断面名称 A-A` B-B` C-C` D-D` E-E` F-F` G-G` H-H` I-I` J-J` 100年一遇 最深泥位（m） 3.95 6.03 6.11 8.48 6.45 4.45 7.05 4.97 5.28 5.38 流速（m/s） 1.68 1.39 1.54 1.37 1.37 1.44 1.34 1.48 1.42 1.46 断面面积（m2） 189 224 229 195 246 249 287 395 460 481 50年一遇 最深泥位（m） 3.62 5.54 5.61 8.06 6.17 4.57 6.72 4.56 4.56 4.94 流速（m/s） 1.35 1.30 1.41 1.20 1.25 1.26 1.30 1.37 1.21 1.38 断面面积（m2） 117 190 194 160 218 284 236 333 402 406 20年一遇 最深泥位（m） 3.23 5.25 4.99 7.51 5.51 3.99 5.98 4.06 4.06 4.39 流速（m/s） 1.30 1.25 1.23 1.20 1.20 1.10 1.18 1.25 1.05 1.26 断面面积（m2） 93 145 153 124 159 228 188 264 319 320 10年一遇 最深泥位（m） 2.97 4.83 4.60 6.91 5.07 3.67 5.50 3.74 3.74 4.04 流速（m/s） 1.26 1.18 1.11 1.76 1.13 0.99 1.10 1.15 0.93 1.18 断面面积（m2） 78 123 130 105 135 193 159 224 271 271
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表 3 泥石流强度判定准则
Table 3 Judgment criteria for debris flow intensity
泥石流强度 泥深H（m） 关系 泥深H与最大流速V的乘积（m2/s） 高 H≥2.5 或 V*H≥2.5 中 0.5<H≤2.5 且 0.5<V*H≤2.5 低 0<H≤0.5 且 0<V*H≤0.5
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表 4 模型递归的最终角度以及面积误差表
Table 4 Final angle and area error table for model iterations
断面名称 A-A` B-B` C-C` D-D` E-E` F-F` G-G` H-H` I-I` J-J` 100年一遇 α1（°） 86.57 84.97 37 53 83 83 70.88 88.14 88.24 87.7 α2（°） 47.96 45.23 85.05 74.44 74 87 85.51 51 27 83.17 CAD测量实际面积（m2） 175 214 237 202 244 278 279 380 501 468 模型求解的理论面积（m2） 189 224 229 195 246 249 287 395 460 481 面积误差（%） 6 4.7 3.5 3.5 6.1 2.1 3 4.1 8 3 断面名称 A-A` B-B` C-C` D-D` E-E` F-F` G-G` H-H` I-I` J-J` 50年一遇 α1（°） 86.57 84.97 37 53 82 83 67 88.14 88.5 87.7 α2（°） 47.96 45.23 85.05 74.44 74 87 83 51 27 83.17 CAD测量实际面积（m2） 116 175 199 157 202 265 251 332 392 409 模型求解的理论面积（m2） 117 190 194 160 218 284 236 333 402 406 面积误差（%） 0.90 8.42 2.61 2.00 8.02 7.30 5.66 0.22 2.64 0.77 断面名称 A-A` B-B` C-C` D-D` E-E` F-F` G-G` H-H` I-I` J-J` 20年一遇 α1（°） 86.57 84 37 53 82 84 67 88.14 88.5 87.7 α2（°） 47.96 45.23 85.05 72 73.53 87 83 51 27 83.17 CAD测量实际面积（m2） 96 154 153 119 162 215 184 282 312 338 模型求解的理论面积（m2） 93 145 153 124 159 228 188 264 319 320 面积误差（%） 3.52 5.60 0.28 4.21 1.98 5.66 2.04 6.39 2.13 5.10 断面名称 A-A` B-B` C-C` D-D` E-E` F-F` G-G` H-H` I-I` J-J` 10年一遇 α1（°） 86.57 84 37 53 82 84 67 88.14 88.5 87.7 α2（°） 47.96 45.23 85.05 72 73.53 87 83 51 27 83.17 CAD测量实际面积（m2） 85 125 125 99 130 179 146 246 262 294 模型求解的理论面积（m2） 78 123 130 105 135 193 159 224 271 271 面积误差（%） 7.22 2.07 4.03 6.16 3.78 7.40 8.71 9.04 3.48 7.86
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