Abstract: The delayed crushing of rockfill particles is specifically referring to the crushing of particles after loading for a certain time. It is a prerequisite for quantitative analysis of rockfill rheology by using discrete element method to give the particle delay breaking time. In this paper, from the point of view of fracture mechanics, the internal defects of particles are generalized into a one-dollar crack, and the relationship between the instantaneous crushing strength of particles and the half-length of the crack is given. Logistic function was used to describe the distribution of particle strength as random variable, and the probability distribution of crack half-length was obtained by using the method of solving the probability distribution of random variable function. The bi-torsional relaxation test of granular rock was carried out to measure the sub-critical crack propagation velocity parameter, and the time expression of crack penetration (i.e., particle delayed crushing) was obtained by integrating. The probability distribution function of particle delay breaking time can be obtained by taking the crack half-length as random variable. The calculation results of dolomite particles in redstone project in Yunnan province show that, under the same stress conditions, large particles have long delay time and large standard deviation, while small particles have short delay time and small standard deviation. This is consistent with the macro phenomenon that rheological deformation of rockfill materials converges quickly in laboratory test, while rheological deformation of rockfill dam lasts a long time in field. The calculation results of particle delay breaking time provides basic conditions for using discrete element to simulate rockfill rheology, improving the rockfill rheological constitutive model, and solving the time-size effect of rockfill rheology for laboratory test.