基于分形理论的人工骨料比表面积计算方法——以白鹤滩水电站为例

分形理论目前已经越来越广泛地应用于岩石力学问题中。骨料比表面积常可通过图像处理技术计算得到，但操作步骤繁琐，存在一定误差，且无法将骨料比表面积和骨料级配联系起来。基于分形理论，对骨料的粒径分布、级配、体积、表面积进行相关分析，推导出了一种骨料比表面积计算方法。结合白鹤滩水电站旱谷地料场人工骨料，计算了不同级配粒径成品料的比表面积。结果表明：80~150，40～80,20～40,5～20 mm级配成品料比表面积分别为22.57,30.75,60.44,15006，计算值与实测值较为吻合;骨料粒径对骨料分形维数和比表面积都有较大的影响，级配骨料越细，其比表面积越大，两者呈幂函数相关；计算结果与软件处理结果误差为10%左右，说明利用分形理论可准确计算人工骨料的比表面积。

Calculation method on specific surface area of artificial aggregate based on fractal theory: a case study of Baihetan Hydropower Station

Fractal theory has been increasingly used in rock mechanics problems. The specific surface area of the aggregate is often calculated by image processing technology, however the operation is cumbersome and easy to produce error, and the specific surface area of aggregate and the aggregate gradation cannot be linked. Based on the fractal theory, the particle size distribution, gradation, volume and surface area of the aggregate were correlated and a calculation method of aggregate specific surface area was derived. Combined with the gradation curve of artificial aggregates in the dry land of the Baihetan Hydropower Station, the specific surface area of the finished materials with different grades was calculated. The results show that the specific surface area of the 80~150, 40~80, 20~40, 5~20 mm graded product are 22.57, 30.75, 60.44, 150.06, respectively. The calculated values are consistent with the measured value. The aggregate particle size has a great influence on the fractal dimension and specific surface area of the aggregate. The finer the graded aggregate, the larger the specific surface area, and they have power function correlation. The error between the calculation result and the software processing result is about 10%, showing that the fractal surface theory can accurately calculate the specific surface area of the artificial aggregate.