Rock mass classification and geomechanical models have a particular importance for carbonate rocks, due to their peculiar fabric, variability of the main features, and scarce availability of experimental data. Carbonates are particularly sensitive to syn-depositional and post-depositional diagenesis, including dissolution and karstification processes, cementation, recrystallisation, dolomitisation and replacement by other minerals. At the same time, as most of sedimentary rocks, they are typically stratified, laminated, folded, faulted and fractured. The strength and deformability of carbonate rock masses are, therefore, significantly affected by the discontinuities, as well as by their pattern and orientation with respect to the in situ stresses. Further, discontinuities generally cause a distribution of stresses in the rock mass remarkably different from those determined by the classical elastic or elasto-plastic theories for homogeneous continua. Goal of this work is the description of the difficulties in elaborating geomechanical models to depict the stress–strain behavior of karstified carbonate rock masses. Due to such difficulties, a high degree of uncertainty is also present in the selection of the most proper approach, the discontinuum one or the equivalent continuum, and in the numerical model to be used within a specific engineering application as well. The high uncertainty might cause wrong assessments as concerns the geological hazards, the design costs, and the most proper remediation works. Even though recent developments in the application of numerical modeling methods allow to simulate quite well several types of jointed rock masses, as concerns carbonate rock masses many problems in representing their complex geometry in the simulation models still remain, due to peculiarity of the structural elements, and the presence of karst features. In the common practice, the improper use of the geomechanical models comes from a superficial geological study, or from the lack of reliable geological and structural data that, as a consequence, bring to erroneous evaluations of the influence of the geological-structural features on the in situ stress state and the stress–strain rock mass behavior.

Hydraulic erosion that takes place underground leads to the formation of complex channel networks whose morphology emerges from the dynamic behavior of each channel, based on the presence of other channels nearby. Our approach to the problem of modeling such channel networks for computer graphics application involves a self-organized model of channel development and a two-stage simulation for constructing the geometry of the channels. By emphasizing self-organization of flow and pressure, our simulation is able to reproduce several types of channel behavior known from hydrogeomorphology, such as tributary capture.