Geostatistical analyses of exfoliation and tectonic joint set spacing in alpine granites (Aar Valley, Switzerland)

Joint set spacing is a fundamental parameter in the determination of rock mass quality and can be measured in situ by means of, e.g., scanline surveys and/or by remote sensing techniques, such as photogrammetric analyses. In many Alpine areas, rock mass outcrops are not easily accessible, and geomechanical propexrties can be measured only in a few unevenly distributed locations, which are often separated by large distances (in the order of hundreds of meters). Geostatistical techniques have been explored to achieve a reliable estimate of rock mass properties in unreachable zones. This work aims to estimate joint set spacing of outcropping rock masses and the associated uncertainty, using photogrammetric models and geostatistical modeling, in an area of about 30 km2, located in the Aar Massif of the Swiss Central Alps. Since the joint set spacing is strongly related to fracture genesis, joints were subdivided according to their type and age into three younger exfoliation joint sets and older tectonic joint sets. Each fracture set spacing was analyzed by variography and its spatial distribution was estimated using Sequential Gaussian Simulations. The present research proves that photogrammetric techniques combined with geostatistical modeling can be satisfactorily applied to develop predictive maps of joint spacing, providing that the geological processes governing the formation of joints are taken into account. Moreover, predictive maps must be associated with the corresponding uncertainty maps. Finally, in mountainous area, whenever a full three-dimensional approach is not feasible due to the absence of subsurface data, at least the ground altitude, besides latitude and longitude, has to be included in the geostatistical modeling.