Hubbert and Rubey's theory (1959) that overthrust faults are facilitated by abnormal fluid pressures is extended to include the effect of the “toe” of the thrust plate. Three types of toes are considered: an eroding toe, a noneroding toe or “riser,” and a composite thrust sheet with a riser and toe as exemplified by Rich's model of the Pine Mountain thrust. Equations are derived for each type of toe in three cases: gravity sliding, horizontal overthrusting, and tectonic thrusting down a slope.
In the absence of a toe, a thrust sheet of any length will slide down the slope of critical angle according to Hubbert and Rubey. The presence of an eroding toe sets a minimum length-to-thickness ratio for a thrust sheet which will slide down a given slope with a given fluid-to-overburden pressure ratio. Typical geological examples with an eroding toe require roughly twice the slope derived without consideration of the toe. A riser demands twice the slope again. A Pine Mountain type thrust is intermediate between thrusts having an eroding toe and thrusts with a riser.
The maximum length of a horizontal thrust with an eroding toe is a little more than half that derived without the toe for typical geological cases. The riser again doubles the effect of the toe, and the Pine Mountain thrust is intermediate. Similar effects are found for thrusts tectonically pushed down a slope.
While consideration of the toe requires either greater slopes or higher fluid pressures than those derived by Hubbert and Rubey, these increases are not such as to invalidate their hypothesis except in certain instances. For example, a very thick thrust plate with a noneroding toe seems impossible. For the most part, however, these considerations serve as a refinement, or second approximation to their very attractive theory.