Abstract: In order to study the failure characteristics of hard rock with nonlinear velocity variety in unloading phase， three unloading rate variety modes of cosine， linear and exponent were used to study the damage and failure of the hard rock by using the indoor triaxial compression tests and particle flow numerical simulation. The results show that the hard rock with exponential unloading rate first fails to stabilize， while the hard rock with cosine unloading rate is less likely to fail. The faster unloading rate in the early stage has a greater impact on the damage accumulation in the whole unloading process. The bearing strength of hard rock in unloading process is affected by both initial confining pressures and unloading modes， and the higher the confining pressure is， the more significant the influence of unloading mode is. According to the Mogi-Coulomb strength criterion， exponential unloading affects hard rock strength through internal friction angle， while the strength of hard rock under linear and cosine unloading mode is mainly affected by cohesion. Exponential unloading is easy to cause partial breakage at the end due to rapid unloading at the early stage. With the increase of confining pressure， linear unloading leads to multiple "V-shaped" shear failures from the steep dip shear fracture zone. Cosine unloading presents a plastic failure characteristic trend with the increase of confining pressure.

Key words: hard rock; nonlinear unloading rates; failure characteristics; crack evolutions; particle flow