粗粒土的分数阶应变率及其与分形维度的关系

Fractional strain rate and its relation with fractal dimension of granular soils

在波浪荷载、潮汐作用下砂土等粗粒土常常经受长期动力变形。运用分数阶微积分理论,分析了5种不同粗粒土在不同加载条件下的累积变形特性及粗粒土的分数阶应变率,传统的整数阶应变率随着加载次数的变化而变化,而粗粒土的分数阶应变率在同一加载条件下保持为常数。通过粗粒土颗粒破碎的分形理论,尝试建立分数阶应变率与土颗粒分布的分形维度之间的关系,分析土体分形维度对分数阶应变率大小的影响,发现随着分形维度的增加,分数阶应变率的数值降低。

Due to the wave-load and tidal load, granular soils, such as sand, often suffers from long-term cyclic deformation. Cumulative strains of five different granular soils under different loading conditions are analyzed by using the fractional calculus, and its there exists a fractional strain rate for granular soils subjected to repeated loads. Unlike the traditional integral strain rate which is varying with the load cycles, the fractional strain rate remains constant for a given loading condition. To investigate the physical origin of the fractional approach, fractal breakage theory of granular soils is used. It is found that the fractional strain rate has a strong connection with the corresponding fractal dimension of a given granular soil. It decreases with the increase of the fractal dimension.