Assessing long-term rock stability is an important aspect in the analysis of slopes, dam and bridge foundations, and other infrastructure. At such long time scales, rock failure occurs through time-dependent methods such as subcriticai crack growth. Natural analogs, such as caves, where rock breakdown has occurred undisturbed over tens to hundreds of thousands of years, can be used to study such failure. An on-going project is reconstructing the process of natural cave breakdown at Kartchner Caverns through LIDAR scanning of the cave geometry and rockfall accumulation and 3D damage modeling of the resulting point clouds. Two modeling methods are compared in order to examine the importance of including time-dependence when analyzing rock behavior over long time scales. The first method is implemented as a fracture mechanics model through user subroutines in Abaqus. Damage occurs through calculation of decreasing rock bridge size from subcriticai crack growth. The second method is implemented as a bonded particle model in PFC3D, using the flat-joint contact model for intact rock and the smooth-joint contact model for joints. Damage occurs through strength reduction of the material properties. The trade-offs in the two models (relative computational simplicity vs. more direct inclusion of time dependence) are discussed.