Experimental study of model dikes in gelatin

An accepted experimental method for modeling dikes involves injecting fluids into translucent gelatin. Previous studies explored gelatin dikes in two-dimensions. This study examines dikes in three-dimensions, in the context of linear elastic fracture mechanics, for two different model dike fluids: water and air. Based on buoyancy tests, the density of the gelatin is approximately the same as water. Dikes with only water have circular faces and do not propagate upward after water injection ceased. Dikes with only air have faces shaped like a slice of bread, and they rise to the surface spontaneously and erupt after air injection ceased. The different geometries and different propagation behaviors appear to reflect how different driving pressure distributions affect the stress intensity factor (K_I) around the dikes. For a uniform driving pressure, K_I is uniform around a circular dike, and the dike should stay circular. A dike would be unable to propagate in any direction if the fracture toughness (K_Ic) exceeds K_I. These findings account for the circular water-filled dikes. For a driving pressure that increases linearly from the bottom to the top of a circular crack, K_I is highest at the top of a circular dike, and decreases monotonically around the crack circumference to a minimum at the bottom of the dike. If K_I exceeds the fracture toughness along the upper part of the dike and approaches zero at the dike bottom, then the propagation pattern around the air-filled dikes can be accounted for. Consequently, the three-dimensional propagation patterns of model dikes containing air or water in gelatin experiments can be accounted for using linear elastic fracture mechanics theory if the driving pressure for the dike and the fracture toughness of the gelatin fall within particular ranges.