Gravitational Stresses in Natural Rock Arches: Implications for Subcritical Crack Growth

Abstract:

Sandstone arches of southern Utah are actively evolving landforms, created and sculpted by erosion, and field inspections show widespread evidence of macroscopic cracks in areas of predicted static tension and compression. However, the relatively small scale of these landforms suggests that these static stresses, generated by self-weight of the lintel, are well below reported laboratory rock strength measurements, indicating that subcritical crack growth may play in an important role in arch evolution. We compiled a set of nineteen 3D models of arches, generated from ground- and drone-based photogrammetry, and used these to assess the static stress field in each feature. Results highlight the spatial distribution and magnitude of both tensile and compressive stresses, and how these vary with arch geometry. Inverted catenary forms reduce tensile stresses, while beam-like arches have nearly symmetrical tensile and compressive stress distributions. Tensile cracks observed in the field frequently correspond to areas of predicted tension in our models, sometimes at relatively low stress magnitudes. Cracks in areas of compression are similar. Recent arch collapses events (partial and total), as well as limited observations of fresh and changing crack geometries, suggest macroscopic fractures can propagate under subcritical stresses, setting the stage for new analyses of arch structural evolution.