A better understanding of landslide dynamics is an important scientific goal, as it is a key factor in the process of improving risk assessment and mitigation. Some of the most interesting and fruitful frameworks for the study of this class of phenomena are provided by self-organized criticality theory. We explore this framework in connection to scale-invariant aspects of landslide processes using Cellular Automata models (CAms). In our CAms, real topographic surfaces acquired from digital elevation models are used to define the altitude values in the initial state of the system. other environmental features such as geology and land use are included in order to represent the spatial variability of local conditions. The landslide dynamics are defined by (i) a stability threshold, which is used to decide when a site of the area becomes unstable, (ii) a transition function, which defines how instabilities propagate within the system depending on slope gradients, and (iii) a driving rule, which describes the weakening of the material over time, thus driving the system toward instability. Changes in the generated landslide event size distributions and in topography characteristics are monitored over time. In order to explore the relation between weakening and the stationary state of the system, a sliding range of values for the weakening rate is applied. Results show that the proposed models display key features of self-organized criticality, thus offering a series of useful insights into the dynamics of landslide processes.