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 l of a fracture as a function of the area l~A^β, with the same exponent β0ex0ex=0ex0ex0.68±0.03 for many deformation types. A consequence of this scaling relation is that the width of a fracture scales with the length as w~l^(1-β)/β. A spring network model is shown to reproduce the pattern, both visually and statistically, with the same scaling exponents.