Abstract: 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.

Key words: granular soil, particle breakage, multifractal characteristic, boundary cluster, size-fractal curve