Adiscrete element numerical model forLac du Bonnet graniteis built for time-dependent fracture simulations. The heterogeneity is consideredbydifferentmineral components randomly distributed inside the rock. The minerals are representedby elastic Voronoi cellsconnected by elasto-plastic contacts. The Hillig-Charles equationis implanted in thenumericalmodel for analyzingtime-dependent damage due tosubcritical crack growth. The damageprocesses duringuniaxial compressive creep tests are investigated. The numericalsimulations reveal not only reasonable lifetime of the specimens under different loads, but also show primary, secondary and tertiary creepstagesuntil final failure characterized by macroscopic fracturing.The simulationresultsof crack growth and damage index evolution deliver adeeperinsight into the microscopic damage process.