Abstract: The delayed crushing of rockfill particles is specifically referring to the crushing of particles after loading for a certain period time, which is the basis for the rheological deformation calculation using the discrete element method (DEM). Based on the fracture mechanics, the internal defects of particles are generalized into a coin-shaped crack, and the relationship between the instantaneous crushing strength of particles and the half-length of the crack is developed. The Logistic function is used to describe the distribution of particle strength as a random variable, and the probability distribution of half-length of crack is obtained by using the method of solving the probability distribution of random variable function. The rockfill particle is processed into a plate specimen, and its sub-critical crack propagation velocity is measured using a bi-torsional relaxation test. On this basis, the formula for crack propagation of particles is integrated to obtain the time expression for crack penetration (i.e. delayed particle crushing). The probability distribution of delayed crushing time of particles can be calculated using the half-length of the crack as a random variable. The results of dolomite particles in Hongshiyan landslide dam in Yunnan Province show that under the same stress level, large particles have long delayed crushing time and large standard deviation, while small particles have short delayed crushing time and small standard deviation. This is consistent with the macro-phenomenon that the rheological deformation of rockfill materials converges quickly in laboratory tests, while the rheological deformation of rockfill dam lasts a long time in field. The development of delayed crushing time of particles provides conditions for simulating the rheological behaviors of rockfill using the DEM, improving the rheological constitutive model for rockfill materials, and solving the time size-effects of rockfill rheology for laboratory tests.