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 {ital l} of a fracture as a function of the area {ital l}{approximately}{ital A}{sup {beta}}, with the same exponent {beta}=0.68{plus_minus}0.03 for many deformation types. A consequence of this scaling relation is that the width of a fracture scales with the length as {ital w}{approximately}{ital l}{sup (1{minus}{beta})/{beta}}. A spring network model is shown to reproduce the pattern, both visually and statistically, with the same scaling exponents. {copyright} {ital 1996 The American Physical Society.}