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 tensile stress, stress reduction near existing fractures and stochastic parameterization of heterogeneity in frozen ground and in insulating snow. Tensile stress from cooling, tensile strength, propagation threshold, fracture depth and elastic properties are chosen to approximate properties of frozen ground. Using these parameters, model networks assemble with properties similar to natural icewedge networks, including (1) individual fracture paths have lengths ranging from tens to hundreds of meters; (2) fractures intersect to enclose regions with characteristic spacing between fractures of approximately 22 m; (3) intersections between fractures are predominantly orthogonal, with less common three‐way approximately equiangular intersections. Joint distributions of relative orientation and spacing between fractures from modeled networks and ice‐wedge networks at Espenberg, Alaska, are comparable at the level of variability in natural examples. This similarity is consistent with the hypotheses that networks self‐organize by stress‐interactions between sequentially placed fractures in frozen ground and that networks are insensitive to the many details of fracture dynamics omitted from the model. Spacing between fractures in modeled networks is influenced by suboptimal placement of fractures during network development and increases nonlinearly with the length scale of stress reduction around a fracture. Three‐way approximately equiangular intersections form where modeled fractures arrest on the outside of bends in earlier fractures.