Scaling relations for the lengths and widths of fractures

Fault-fracture patterns have been studied in slabs of clay during extensional deformations. Fractures nucleate and grow on many scales. A new scaling relation is proposed for the length I of a fracture as a function of the area l similar to A(beta), with the same exponent beta = 0.68 +/- 0.03 for many deformation types. A consequence of this scaling relation is that the width of a fracture scales with the length as Mi similar to l((1-beta)/beta). A spring network model is shown to reproduce the pattern, both visually and statistically, with the same scaling exponents.