Gradation of coarse grained soil and fractal geometry character of particle breakage

Abstract

验证颗粒质量-粒径分布分形模型用于表示粗粒土级配的适用性,研究粗粒土在不同缩尺粒径的情况下,采用不同缩尺方法缩尺后土体分形维数的变化规律;基于分形维数建立缩尺级配与原始级配之间的联系,分析不同母岩材料、级配和颗粒形状粗粒土三轴试验资料,推算粗粒土的相对破碎率,并探讨分形维数与相对破碎率的关系。研究结果表明:分形维数能定量描述粗粒土的原始级配和缩尺级配,不同缩尺方法得到的粒度分形曲线形态有较大差别,与原始级配的粒度分形曲线有不同程度的偏离,缩尺粒径越小偏离程度越大。在所研究的4种缩尺方法中,分形维数与缩尺粒径的对数呈较好的线性关系;围压越大,破碎分形维数和相对破碎率越大,试验前粗粒土的分形维数越大,剪切试验后相对颗粒破碎率越小。不同母岩、级配和颗粒形状的破碎分形维数与相对破碎率呈幂函数关系,通过分形维数和拟合参数可估算不同围压下的相对破碎率。 The applicability of soil cumulative mass particle-size distribution for coarse grained soil was verified, and the change rule of fractal dimension was analyzed in the situation of different particle sizes and scale methods. The connection between scale gradation and original gradation was also established through fractal dimension. Relative breakage rate was calculated according to the triaxial tests with different parent rocks, gradations and particle shapes. The correlation between fractal dimension and relative breakage rate was also discussed. The results show that fractal dimension can quantitatively describe original gradation and scale gradations. There exist great differences between fractal dimension curves of particle size with different scale methods, and all of them deviate from original gradation's, the smaller scale size is, the bigger the deviation is. In the four scale methods, an excellent linear relationship between fractal dimension and the logarithm values of particle size has been found. The bigger the pressure is, the larger the broken fractal dimension and relative breakage rate is. The relative breakage rate decreases with the increase of fractal dimension before test. The broken fractal dimension and relative breakage rate displays a power functional relation under the condition of different parent rocks, gradations and particle shapes. Therefore, relative breakage rate of different pressure can be estimated through fractal dimension and fitting parameters.