Relation between vein length and aperture

Veins formed in a variety of rock types and tectonic environments were measured at seven field locations to determine a general scaling relationship between the length and opening displacement (aperture). For these naturally formed extension fractures displacement-length profiles for both single- and multiple-segment veins display centrally located maxima and gently tapered displacement gradients at the tips. This geometry is consistent with elastic-plastic crack growth models, which also predict linear scaling between length and displacement. The geometry is used to estimate stresses of formation for the veins. Length-maximum displacement plots for single-segment fractures show data clustered along linear trends. Similar plots for multiple-segment fractures show greater scatter and are marginally better fit by a square root function than by a line. The geometries of multiple-segment veins are consistent with elastic models for crack-tip stress interactions. Aspect ratios for single-segment fracture sets vary between 1 × 10−3 and 8 × 10−3, consistent with tensional fracture strengths roughly an order of magnitude lower than compressive shear strengths implied by shear displacement-length ratios recorded for faults, which are about 10−2.