Failure in laboratory fault models in triaxial tests

A model of a fault in the Earth is a sand-filled saw cut in a granite cylinder subjected to a triaxial test. The saw cut is inclined at an angle a to the cylinder axis, and the sand filling is intended to represent gouge. The triaxial test subjects the granite cylinder to a constant confining pressure and increasing axial stress to maintain a constant rate of shortening of the cylinder. The required axial stress increases at a decreasing rate to a maximum, beyond which a roughly constant axial stress is sufficient to maintain the constant rate of shortening: Such triaxial tests were run for saw cuts inclined at angles ?? of 20??, 25??, 30??, 35??, 40??, 45??, and 50?? to the cylinder axis, and the apparent coefficient of friction ??a (ratio of the shear stress to the normal stress, both stresses resolved onto the saw cut) at failure was determined. Subject to the assumption that the observed failure involves slip on Coulomb shears (orientation unspecified), the orientation of the principal compression axis within the gouge can be calculated as a function of ??a for a given value of the coefficient of internal friction ??i. The rotation of the principal stress axes within the gouge in a triaxial test can then be followed as the shear strain across the gouge layer increases. For ??i ??? 0.8, an appropriate value for highly sheared sand, the observed values ??a imply that the principal-axis of compression within the gouge rotates so as to approach being parallel to the cylinder axis for all saw cut angles (20?? < ?? < 50??). In the limiting state (principal compression axis parallel to cylinder axis) the stress state in the gouge layer would be the same as that in the granite cylinder, and the failure criterion would be independent of the saw cut angle.