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Application of fractal theory in rockfill rheology
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摘要: 流变过程中堆石颗粒不断破碎，分形维数在流变过程中随时间发生变化。基于流变过程基本规律，将分形理论应用于堆石料流变过程，构造了两类随时间变化的流变过程分形维数，并建立了颗粒破碎率与分形维数的关系。通过分析过程流变试验颗粒破碎率的变化规律，验证了流变过程中双曲线型分形维数假定的合理性。在此基础上，考虑流变过程中的能量关系并结合颗粒破碎耗能的相关研究，进一步推导了堆石料流变过程中体变随时间的变化规律，从而建立堆石料特定荷载情况下的流变本构模型。与试验结果对比表明：该模型可以从分形的角度反映堆石料流变规律。Abstract: The rockfill material crushes during the process of rheology and the fractal dimension of rockfill material varies with time. Based on the basic rule of rheological process of coarse-grained soils, the fractal theory is applied into the analysis of rheological process, and two typical expressions of fractal dimension that varies with time are given. The reationship between the particle breakage index and the fractal dimension is also described. By analysing the particle breakage index of incomplete rheological test, the reasonability of the expression of hyperbola fractal dimension during rheological process is confirmed. On this basis, the volumetric strain is derived considering the energy balance of coarse granular aggregates and the related research of the particle breakage energy. Thus a rheological constitutive model for rockfill materials is proposed. Compared with experimental data, the proposed model can reflect the rheological properties of rockfill material based on fractal theory.
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Key words:
- rockfill material /
- rheology /
- fractal dimension /
- particle breakage index /
- constitutive model
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图 6 模型计算值与试验值对比
Figure 6. Comparison between model predictions and experimental results
表 1 试样颗粒级配
Table 1. Particle size distribution of sample
粒径/mm 60~50 50~40 40~30 30~20 20~10 10~5 < 5 质量百分比/% 8.52 8.22 9.79 16.68 20.21 15.20 21.38 
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表 2 过程流变试验结束后的级配
Table 2. Particle size distribution after test
不同粒径颗粒含量/% 粒径区间/mm 制样前 剪切结束 1 h 4 h 8 h 24 h 60~50 8.52 8.06 5.96 6.65 6.81 7.36 50~40 8.22 7.35 9.55 8.72 8.46 6.72 40~30 9.79 11.02 8.62 8.60 9.23 11.39 30~20 16.68 14.48 17.78 17.19 17.38 13.51 20~10 20.21 19.53 19.40 20.15 20.21 20.06 10~5 15.20 15.77 14.90 15.47 13.92 16.64 < 5 21.38 23.79 23.81 23.22 13.92 24.33
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表 3 模型参数取值
Table 3. Values of model parameters
参数 M α β γ s1 s2 s3 a 数值 1.58 7.7×10-4 0.478 0.041 -0.64 1.32 1.20 1.02
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