石英砂砾破碎过程中粒径分布的分形行为研究

荷载作用下粒状土的颗粒破碎改变土的粒径分布,从而影响其力学特性。试验证据显示随着颗粒破碎的增加,任何初始分布的土粒都将趋向一种自相似的分形分布。为了揭示土的粒径分布的分形转变机制,利用侧限压缩试验研究高压应力下石英砂砾的粒径分布演化规律和颗粒破碎特性,基于分形模型和粒径分布实测数据研究破碎过程中粒径分布的分形行为。研究发现:颗粒破碎增长导致粒状土趋向分形分布的过程与颗粒破碎量密切相关,并可以通过增大的分形维数来描述。尽管石英砂砾的初始分布和粒径有所不同,分形维数大于2.2的粒径分布实测数据均展示了较为严格的自相似性,因而该数值可作为分形分布的分形维数下限值。研究还发现:相同破碎状态下Hardin相对破碎率小于Einav相对破碎率,但二者对应力和体应变的响应规律是一致的。颗粒破碎发展至粒径分布成为分形分布时,体应变与相对破碎率的比值将保持恒定,并且受初始分布的均匀性和颗粒大小的影响很小。这一特点可用于分形分布的识别,并意味着试验中如果粒径分布是分形的,则无须为了粒径分析而终止试验,只需测量到体应变就可估计相对破碎率。

Fractal behavior of particle-size distribution during particle crushing of quartz sand and gravel

The particle breakage of granular soil under loading alters the particle-size distribution (PSD) and further affects its mechanical properties. The experimental evidence shows that any initial distribution of soil particles will tend to be fractal with the development of particle breakage. In order to reveal the transformation mechanism of fractal PSD of soil, a series of confined compression tests on a quartz sand and gravel are conducted to investigate the evolution of PSD and the behavior of particle breakage under even larger compressive stress. The fractal behavior of PSD is studied during particle crushing based on a fractal model and the measured PSD data. It is found that a fractal distribution of granular soil is caused by the growth of particle breakage, which is related to the amount of particle breakage and characterized by the increase of the values of fractal dimension. Despite the different initial distributions and particle sizes of the quartz sand and gravel, the measured PSD data that the values of fractal dimension exceed to 2.2 are shown to be strictly self-similar. Therefore the value of 2.2 can be considered as the lower limit of the fractal dimension of a fractal distribution. The Hardin’s relative breakage is larger than the Einav’s relative breakage in the same breakage state, but the rule of two indexes in response to the stress and volumetric strain is consistent. Once the PSD becomes fractal during particle crushing, the ratio of volumetric strain to relative breakage remains constant and is not much affected by either the uniformity of the initial distribution or the initial particle size. This constant ratio is a useful index for the identification of a fractal distribution, and implies that the relative breakage may be estimated from the measured volumetric strain in a test if the PSD is fractal, without having to terminate the test to analyze the particle size.