Study on fractal feature and settling velocity of tailings floc
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摘要: 絮凝沉降广泛存在于尾矿处置的各个工艺环节，实现尾矿絮凝沉降速度的精确测算对于指导尾矿充填及地表堆存等工程问题具有重要的现实意义。本文借助分形理论研究了尾矿絮凝体的结构特征，建立了絮凝体几何尺寸与颗粒粒径、分形维数之间的数学关系，综合分析了浮力效应、回流效应以及黏滞效应对絮凝体沉降的影响作用，最终构建了沉降速度的测算模型。开展尾矿絮凝沉降试验，同时利用聚焦光束反射测量(FBRM)技术对絮凝体几何形态的变化进行观测，并根据实测数据对沉降速度测算模型进行了验证分析。结果显示：絮凝体沉降速度随其等效粒径增大而增大，可划分为加速沉降、匀速沉降、压密沉降3个阶段；试验尾矿絮凝体的粒径为140~350 μm，当分形维数取2.25时，沉降速度为1.3~2.0 mm/s，模型计算值与实测值存在较好的相关性，具有一定的实际应用价值。Abstract: Flocculent settling widely exists in various processes of tailings disposal.It bears significance for the accurate calculation of the flocculent settling velocity in engineering, such as tailings backfilling and surface disposal.This paper studied the structural characteristics of tailings flocs from the perspective of the fractal theory, and established the mathematical relationship between tailings particle size, geometry size of floc and fractal dimension.It analyzed the influence of buoyancy effect, reflux effect and viscosity effect on floc settling, and deduced a calculation formula of tailings flocculent settling velocity.This study carried out a tailings flocculent settling test observed the changes in geometric morphology of flocs by focused beam reflectance measurement technology(FBRM), and carried out validation analysis between testing data and model calculation value.The results showed that the settling velocity increased with the equivalent grain size of flocs, which could be divided into three stages, namely accelerated settling, uniform settling and compaction settling.The equivalent grain size of flocs of test tailings were 140~350 μm, and the settling velocity calculated by the formula were 1.3~2.0 mm/s when the fractal dimension was 2.25, which demonstrates significant correlation with the testing value, and had certain practical application value.
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Key words:
- tailings /
- flocculent settling /
- floc /
- fractal dimension /
- settling velocity
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图 1 尾矿颗粒组成及分类
ψ—固体颗粒占比；φ—体积分数；n—孔隙率；上标cl、si、sa、m分别代表黏粒、粉粒、砂粒和细颗粒；下标s表示固相；ψsa、ψsi、ψcl之和为1；φssa、φssi、φscl及n的和为1
Figure 1. Particle composition and classification of tailings sample
图 6 絮体沉降速度与等效粒径的变化曲线
Figure 6. Variation of the settling velocity with the equivalent diameter of floc
图 7 干涉沉降系数与絮体等效粒径的变化
Figure 7. Variation of the hindered settling coefficient with the equivalent diameter of floc
图 8 粗颗粒沉降速度与絮体特征粒径的变化
Figure 8. Variation of the the settling velocity of sand with the equivalent diameter of floc
表 1 模型参数取值
Table 1. Model parameter value
序号 物理量 单位 取值 1 cm kg/m3 145.6 2 csa kg/m3 17.0 3 φsm % 5.23% 4 φssa % 0.61% 5 d50m μm 30.67 6 d50sa μm 115 7 μw Pa·s 1.01×10-3 8 φf % φf=f(df，DF) 
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