Ultimate state and probability of particle breakage for rockfill materials based on fractal theory
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摘要: 为了研究具有分形级配的堆石料颗粒破碎规律与初始分形维数和围压的关系,采用粗粒土大型三轴试验仪,针对不同初始级配的缩尺堆石料,展开不同围压下的颗粒破碎试验,通过计算颗粒破碎前后分形维数的变化,建立围压与颗粒分形维数D的关系式,对现有的颗粒破碎度指标Br的上限值进行修正,利用分形颗粒集合体的概念对颗粒破碎概率进行计算。研究结果表明,堆石料的初始分形维数D0影响其应力应变特征；堆石料颗粒破碎存在极限值,分形维数和破碎度指标与破碎前后分形维数和围压相关；颗粒集合体可以用来计算分形级配堆石料分形维数变化规律,颗粒集合体中颗粒破碎概率与粒径无关,不同粒径颗粒具有相同的破碎概率,随着围压增加破碎概率增加,且存在上下限值,破碎概率与初始分形维数D0相关。Abstract: In order to study the particle breakage rules of rockfill with fractal gradation, a large-scale triaxial test equipment for coarse soil is used to carry out particle breakage experiments under different confining pressures for scaled rockfill materials with different initial gradations. By calculating the change of fractal dimension before and after particle breakage, the effects of stress on the fractal dimension are studied, and the existing particle breakage index Br is modified. The probability of particle breakage is calculated by using the concept of fractal particle aggregation. The results show that the initial fractal dimensions affect the stress and strain characteristics of the rockfill materials. The fractal dimension and the index of breakage degree are related to the fractal dimension and confining pressure before and after breakage. The particle aggregation can be used to explain the increase of the fractal dimension in fractal gradation. The probability of particle breakage of particle aggregation is independent of the particle size, and the probability of particle breakage increases with the increase of the confining pressure. The probability of particle breakage has upper and lower limits, and the crushing probability is related to the initial fractal dimension D0.
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Keywords:
- rockfill material /
- fractal dimension /
- particle breakage /
- breakage probability /
- gradation
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图 3 应力应变曲线
Figure 3. Curves of deviatoric stress and volumetric strain vs. axial strain
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图 4 不同围压下颗粒破碎后分形维数增量D-D0
Figure 4. Relationship between increase of fractal dimension and confining pressure
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图 5 分形维数极限值与初始分形维数关系图
Figure 5. Relationship between ultimate and initial fractal dimensions
表 1 堆石料干密度试验结果
Table 1 Dry density test results of rockfill materials
初始分形维数D0 最大干密度/(g·cm-3) 最小干密度/(g·cm-3) 2.3 2.20 1.60 2.5 2.23 1.69 2.6 2.25 1.74 2.7 2.24 1.77 
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表 2 堆石料破碎后颗分结果及分形维数D
Table 2 Grain-size distributions and fractal dimension before and after tests
初始分形维数D0 围压/kPa 各粒组颗粒质量分数/% 分形维数D 拟合度 <60 mm <40 mm <20 mm <10 mm <5 mm 2.7 — 100 88.5 71.9 58.4 47.5 — — 500 100 88.7 73.0 60.3 49.0 2.714 0.999 1000 100 89.0 74.3 61.3 49.2 2.720 0.998 2000 100 92.9 75.4 62.6 51.5 2.737 0.995 3000 100 93.1 76.6 63.3 52.5 2.745 0.995 2.6 — 100 85.0 64.4 48.8 37.0 — — 500 100 87.7 67.4 51.6 40.2 2.634 0.999 1000 100 87.7 68.3 53.4 42.1 2.652 0.999 2000 100 91.0 69.8 55.3 44.0 2.676 0.996 3000 100 91.1 70.9 56.3 44.0 2.686 0.996 2.5 — 100 81.6 57.7 40.8 28.9 — — 500 100 83.3 62.5 45.5 33.7 2.563 0.999 1000 100 85.3 62.9 47.5 35.7 2.585 0.999 2000 100 87.7 65.4 49.1 37.5 2.607 0.998 3000 100 90.4 67.0 51.4 39.4 2.629 0.996 2.3 — 100 75.3 46.3 28.5 17.6 — — 500 100 81.7 52.3 35.4 24.3 2.426 0.999 1000 100 82.8 55.4 38.2 27.0 2.470 0.999 2000 100 87.5 58.7 41.6 30.7 2.522 0.996 3000 100 87.7 60.0 42.9 31.7 2.537 0.996
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