Conjugate Joint Sets of Small Dihedral Angle
The Coulomb law of the Mohr theory of failure predicts a constant dihedral angle between conjugate failure planes regardless of the magnitude of the stress difference required for failure. The maximum principal stress bisects this angle. Experimental studies show that this angle actually becomes smaller as confining pressure is decreased. For low pressures, Nadai, enlarging on a suggestion by Leon, proposed a curved Mohr envelope which would intersect the normal stress axis at a right angle. If so, there could then be a critical stress circle tangent to the envelope only at the apex. The single plane of failure, lying parallel to the maximum principal stress, is a tension joint in the usual terminology (extension fracture). A slight increase in stress difference will move the critical circle off the apex, and it will then intersect the envelope at two points; the resulting conjugate fractures will enclose a small dihedral angle. Within a small range of increasing stress differences, the angle will increase to the usual angles for shear failure (about 60°). At least two field examples indicate that Nadai's proposals are correct. Parker's joint study in New York demonstrated a conjugate shear set with angles ranging from 0 to 20°. These joints have plumose surfaces that may be indicative of extension fractures. Similar jointing has been observed in western Pennsylvania and eastern Ohio, as studies by Nickelsen and Hough, and by Ver Steeg indicate. Duschatko's studies along the Lucero uplift, New Mexico, show a single joint set being replaced along strike by a conjugate joint set with dihedral angle increasing up to 65°. This type of fracturing appears to be present in the Bighorn and Bear-tooth Mountains as well.