Abstract: Breakage-induced evolution of particle size distribution (PSD) has a significant impact on the physical and mechanical properties of soil. It is therefore of great practical significance to study the evolution of particle breakage. The gradation transition matrix provides an effective approach to describing the detailed particle breakage of granular soils. This paper presents a series of  one-dimensional compression tests on carbonate sands with different initial conditions (i.e., PSD, relative density) to establish the gradation transition matrix of sample with more detailed information on particle breakage of each size group. The breakage of each single-sized particles of soil samples with multi-sized particles under different initial conditions is explored based on the dyeing and PCAS image recognition technologies. The results show that the presence of small-sized particles plays a negative effect on the breakage of the large-sized particles, while the presence of large-sized particles promotes the breakage of the small-sized particles. The PSD of each single-sized particles of a carbonate sand sample evolves towards the fractal distribution, and the relative breakage index  B_ri  of each single size group is linear with the input work per unit volume W_in . Finally, the breakage transition matrices of both uniformly and non-uniformly graded carbonate sands are established with consideration of interactions between particles with different sizes, which demonstrates its satisfactory performance. The proposed method provides a new insight into the evolution of particle breakage of granular soils with more detailed information of each size group.

Key words: particle breakage, fractal theory, dyed carbonate sand, compression, gradation transition matrix