粗粒土的颗粒破碎影响其强度、刚度和变形,故引入分形理论量化破碎程度。依据粒度分形曲线存在折线性,阐释界限粒组含义,提出以界限粒径为限,分段概化土体多重分形特征,计算其多重分形维数D(r),总结D(r)增量变化规律,建立增量计算模型,量化颗粒破碎程度。理论及试验分析表明:等效替代缩尺方法减小D(r),对界限粒径影响不显著,缩尺前后颗粒分形特性保持一致;不同尺寸颗粒破碎概率不同,粗粒段破碎概率高于细粒段破碎概率。细粒段D(r)增量随干密度的增加先缓慢增大后急剧增大,随围压增大而减小,其增量与干密度及围压为指数函数关系;粗粒段D(r)增量随干密度增加先增大后减小,其增量与干密度及围压呈高次非线性规律。据此建立考虑干密度及围压影响的D(r)增量模型,用MatLab作多元非线性回归分析求解系数,对比模型值与试验值分布规律,分析其残差置信度。研究结果表明模型结构合理,可为评价粗粒土多重分形特性及量化颗粒破碎效应提供一种简便有效的方法,可提高粗粒土工程应用科学性及可靠程度。

The strength, stiffness and deformation of granular soil are affected by particle breakage. The fractal theory is employed to quantify the degree of particle breakage. According to the fold linearity of size-fractal curves, the definition of boundary cluster is expounded and proposed as a bound to generalize the multifractal feature of soil by subsections. In subsequence, D(r), the multifractal dimension, is calculated, and the incremental variation of D(r) is also summed up. Thereby, the calculation model for incremental D(r) is established to quantify the degree of particle breakage. Theoretical and experimental analysis reveals that reducing D(r) by scaling method with equivalent substitution has no significant impact on boundary particle size as the fractal characteristics of particles are consistent before and after the scaling. The breakage probability of particles varies with particle size, for example, the breakage probability of coarse grain segment is higher than that of fine grain segment. In fine grain segment, the increment of D(r) increases slowly at first and then intensifies sharply with the augment of dry density but reduces with the rising of confining pressure; the relations between D(r) and dry density and confining pressure can be described as an exponential function. In coarse grain segment, the increment of D(r) increases firstly and then declines with the rising of dry density; D(r) increment in coarse grain segment is in high-order nonlinear relation with dry density and confining pressure. On this basis, the model of D(r) increment in consideration of the influences of dry density and confining pressure is established, the coefficients of which are solved by MatLab with multivariate nonlinear regression analysis. In addition, the distributions of model values and test values are compared, the residual reliability of both values is analyzed, and the rationality of the established model structure is demonstrated. The research finding offers a simple and convenient approach to evaluating the multifractal characteristics of granular soil and quantifying the effect of the particle breakage.