Dynamic reserves of evaluation model for materials source in the channel based on fractal theory and model test
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摘要:
汶川地震后，大量松散固体物源堆积在沟道中，使沟道泥石流发生的概率激增。准确的计算泥石流沟道物源的动储量一直是泥石流物源统计的难点。文章以七盘沟下游主沟段沟道物源为研究对象，在实地勘查、资料收集的基础上，以室内模型试验为研究手段，引入分形理论将复杂的土体粒度成分用分维值定量描述，研究不同沟道堆积体在不同降雨作用下的侵蚀规律，建立以降雨强度和分维度为双影响因子的动储量评价模型。研究表明：粗粒土不易起动，但在充足的水动力条件下，侵蚀作用会成倍放大；上细下粗土发生泥石流时侵蚀变化和总的侵蚀规模较小，这种粒序分布形式有益于沟道的稳定；上粗下细土与粗粒土的侵蚀现象类似，但发生大规模泥石流的降雨阈值低于粗粒土；沟道物源中，侵蚀作用效应的排序为：溯源侵蚀>下切侵蚀>侧缘侵蚀>潜蚀；文章所拟合的公式适用于宽缓型沟道泥石流，对于窄陡型沟道泥石流存在一定的局限性。
Abstract:After the Wenchuan earthquake, many loose solid sources accumulated in the channel, which increased the probability of debris flow. It was difficult to calculate the dynamic reserves of debris flow sediment source accurately. Based on field investigation, data collection and laboratory model test, this paper introduced the fractal theory to quantitatively describe the complex soil particle size composition with fractal dimension, and studied the erosion regular of different deposits in channels under different rainfall effects. A dynamic reserve evaluation model with rainfall intensity and fractal dimension as double influencing factors was established. The results show: Coarse-grained soil is not easy to start, but under sufficient hydrodynamic conditions, erosion will be multiplied; When debris flow occurs, the erosion change and total erosion scale of "fine-grained on coarse-grained soil" are small, and which is beneficial to the stability of channel; The erosion phenomenon of "coarse-grained on fine-grained soil" is similar to that of coarse-grained soil, but the rainfall threshold of large-scale debris flow is lower than coarse-grained soil; For materials source in the channel, the order of erosion effect is headward erosion > shear erosion > lateral erosion > subsurface erosion; The formula fitted in this paper is suitable for the wide and slow channel of debris flow, but it has some limitations for the narrow and steep channel.
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Key words:
- debris flow /
- the materials source in channel /
- dynamic reserves /
- model test /
- fractal theory
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表 1 模型试验降雨条件
Table 1. Rainfall conditions of the model test
雨频/% 雨强/（mm∙h−1） 前期降雨用时/s 径流/（L∙h−1） 10 33.2 359 406.8 5 38.1 341 511.4 2 44.4 320 648.2 1 49.1 306 752.4 
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表 2 “7·10”后沟道物源颗粒累积百分含量
Table 2. Cumulative percentage of particles in the channel after “7·10”
编号 颗粒累积/% 200 60 20 5 2 0.5 0.25 0.075 ZG1 100 21.7 7.2 1.3 1.0 0.9 0.4 0.2 ZG2 100 16.9 5.9 1.4 1.7 1.4 0.5 0.2 ZG3 100 22.9 6.9 1.4 0.9 0.8 0.4 0.10 平均 100 20.8 7.0 1.7 1.2 1.1 0.4 0.2
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表 3 “8·20”后沟道物源颗粒累积百分含量
Table 3. Cumulative percentage of particles in the channel after “8·20”
编号 颗粒累积/% 200 60 20 5 2 0.5 0.25 0.075 ZG1 100 81.3 43.7 32.9 22.6 9.5 5.2 1.1 ZG2 100 79.9 53.0 40.6 33.3 17.0 7.3 4.1 ZG3 100 86.7 50.9 39.3 26.7 17.8 11.2 3.9 平均 100 82.6 49.2 37.6 27.5 14.8 7.9 3.0
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表 4 试验土分维值
Table 4. Fractal dimension of test soil
试验堆积体 分维值D 范围 类型 “7·10”粗粒土 2.250 <2.60 块碎石土 “8·20”细粒土 2.639 2.60≤D<2.82 碎石土 双层上细下粗 2.522 <2.60 块碎石土 双层上粗下细 2.596 <2.60 块碎石土 注：其中分维D越小，粒度越粗，分维D越大，粒度越细。
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表 5 单因素对照试验设计方案
Table 5. Single factor-controlled trial design scheme
编号 堆积体
分维D降雨强度
/（mm∙h-1）编号 堆积体
分维D降雨强度
/（mm∙h-1）1-1 2.639 33.2 3-1 2.522 33.2 1-2 38.1 3-2 38.1 1-3 44.4 3-3 44.4 1-4 49.1 3-4 49.1 2-1 2.250 33.2 4-1 2.596 33.2 2-2 38.1 4-2 38.1 2-3 44.4 4-3 44.4 2-4 49.1 4-4 49.1
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表 6 沟道侵蚀数据统计
Table 6. Data statistics of the channel erosion
D q/（mm∙h−1） V侵/m3 D q/（mm∙h−1) V侵/m3 2.639 33.2 0.015 90 2.522 33.2 0.003 11 38.1 0.033 10 38.1 0.020 63 44.4 0.066 21 44.4 0.045 94 49.1 0.145 78 49.1 0.062 91 2.250 33.2 0.002 95 2.596 33.2 0.001 90 38.1 0.019 07 38.1 0.020 91 44.4 0.039 63 44.4 0.116 03 49.1 0.131 33 49.1 0.132 82
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表 7 雨强计算
Table 7. Calculation of rain intensity
频率 暴雨均值
H/（mm∙h−1）变差系数
CV模比系数
Kp暴雨设计值
Hp/（mm∙h−1）2% 22 0.35 1.92 42.2 5% 1.67 36.7 10% 1.47 32.3 20% 1.26 27.7
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表 8 锄头沟“8·20”后沟道物源颗粒累积百分含量
Table 8. Cumulative percentage of particles in Chutougou after “8·20”
取样 颗粒累积/% 200 50 20 5 2 0.5 0.25 0.075 S1 100 40.1 32.8 28.3 21.7 12.6 9.2 1.4 S2 100 59.4 38.5 32.9 21.3 9.5 6.2 1.1 S3 100 65.2 46.4 41.4 31.7 16.6 11.7 2.1 平均 100 54.8 39.0 34.2 24.9 12.9 9.0 1.5
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表 9 本文拟合计算结果
Table 9. The results of the fitting calculations in this paper
沟道 D 雨频 降雨强度
/（mm∙h-1）流通堆积区
/km侵蚀量
/（104 m3）锄头沟 2.572 20% 27.7 4.3 12.75 10% 32.3 24.46 5% 36.7 45.58 2% 42.2 99.23 七盘沟 2.250 20% 28.0 3.9 10.56 10% 33.2 22.03 5% 38.1 44.09 2% 44.4 107.49
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表 10 动储量计算
Table 10. Dynamic reserve calculation
沟道 设防标准 动储量/（104 m3） 均值/（104 m3） 锄头沟 V5%+2V10%+3V20% 132.75 122.91 3V5% 136.74 V2% 99.23 七盘沟 V5%+2V10%+3V20% 119.83 119.86 3V5% 132.27 V2% 107.49
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