基于分形理论的堆石料级配优化研究

Optimization of gradation of rockfill materials based on the fractal theory

建立颗粒粒径的质量分布分形模型,收集不同堆石坝工程32条堆石料级配曲线,统计分形维数D的分布特性。各堆石坝工程堆石料级配具有良好的分形特性,可考虑将D作为反映和描述堆石料级配特性的新指标,D在2.348~2.699之间,大多数堆石料的分形维数在2.6左右。以古水垫层料为研究对象,设计了6组不同分形维数的级配曲线,采用随机颗粒不连续变形方法（SGDD）研究不同分形维数对堆石料压实性能和宏细观力学特性的影响。分形维数从2.0到2.8,孔隙比呈先减后增趋势,在D=2.7时压实性能最优,而力链的非均匀程度随分形维数的增大而增大。综合考虑试样压实性和力链的非均匀程度,确定D=2.7时的级配为优化级配。

A fractal model for the rockfill particle-size distribution is employed and the range of fractal dimension is estimated through fitting the gradation curves of 32 rockfill materials from different rockfill dams. The gradation of rock materials possesses good fractal behavior, so that the fractaI dimension D can be used as a new index to describe the gradation characteristics ofrockfill materials. Based on the analysis of statistics, it is shown that fractal dimension D varies from 2.348 to 2.699, and it is about 2.6 for most dam materials. Six sets of gradation curves for cushion layer of Gushui rockfill dam are designed based on the fractal model. By employing the stochastic granular discontinuous deformation method （SGDD）, the effects of fractal dimension on compaction capacity and the macroscopic and mesoscopic mechanical properties of rockfill materials are analyzed. As fractal dimension varies from 2 to 2.8, the void ratio decreases first and then increases, the material achieves its maximum compaction at D = 2.7. The degree of heterogeneity of force chains increases with the increasing of fractal dimension, and attains the maximum at D = 2.8. By considering both the compaction capacity and the force chain heterogeneity, it is found that the gradation at D = 2.7 is the optimum gradation.