Geometry and Physical-Mechanical Properties of Rock Massifs with Underground Structures

The geometry of underground structures has a profound impact on the metric properties of rock massifs, leading to local metric and dimensional changes that influence both local and macroscopic characteristics in the surrounding area. By incorporating fractal structures and functions, more realistic models for rocks and underground structures are developed. These fractal elements significantly affect effective physical-mechanical properties, particularly elastic modules, through the percolation effect, linked to the presence of scattered or concentrated fractures within the assessed volume. Understanding the fractal dimension and percolation threshold allows the derivation of analytical relationships describing elastic modules concerning damage concentration near this critical threshold. The study introduces the Weierstrass fractal model, designed to analyze horizontal underground excavations while accounting for surface roughness. This model facilitates stress distribution evaluation and stress concentration estimation near excavation profiles. Utilizing statistical mechanics to calculate fractal parameters provides continuum estimates for various aspects, including fractal density distribution and dimensions characterizing excavation contour roughness. It also identifies shear microstresses where fractal functions lack differentiability. Factoring in non-differentiability in fractal models offers insight into the complex changes in metric properties compared to traditional smooth models for underground excavations. Considering fractal properties when calculating effective physical-mechanical properties reveals their dependency on the fractal dimension across material concentrations. The fractal model aids in describing the process of microcrack aggregation into a through-crack as a percolation phenomenon, pinpointing the percolation threshold and its influence on effective elastic properties in the vicinity.