Fracture networks in frozen ground

Fractures in frozen ground self-organize into networks through interactions between sequentially emplaced fractures, tensile stress and the developing fracture pattern. From this viewpoint we model the development of networks on a lattice representing the ground surface on which fractures initiate, propagate and arrest under a combination of uniform thermally induced tensi le stress, stress reduction near existing fractures and stochastic paramete rization of heterogeneity in frozen ground and in insulating snow, Tensile stress from cooling, tensile strength, propagation threshold, fracture dept h and elastic properties are chosen to approximate properties of frozen gro und. Using these parameters, model networks assemble with properties simila r to natural ice-wedge networks, including (1) individual fracture paths ha ve lengths ranging from tens to hundreds of meters; (2) fractures intersect to enclose regions with characteristic spacing between fractures of approx imately 22 m; (3) intersections between fractures are predominantly orthogo nal, with less common three-way approximately equiangular intersections. Jo int distributions of relative orientation and spacing between fractures fro m modeled networks and ice-wedge networks at Espenberg, Alaska, are compara ble at the level of variability in natural examples. This similarity is con sistent with the hypotheses that networks self-organize by stress-interacti ons between sequentially placed fractures in frozen ground and that network s are insensitive to the many details of fracture dynamics omitted from the model. Spacing between fractures in modeled networks is influenced by subo ptimal placement of fractures during network development and increases nonl inearly with the length scale of stress reduction around a fracture. Three- way approximately equiangular intersections form where modeled fractures ar rest on the outside of bends in earlier fractures.