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1Manuscript received, July 4, 1972. Published, in revised form, with permission of Society of Petroleum Engineers of AIME; originally published in Transactions of Society of Petroleum Engineers of AIME, 1957, v. 210, p. 153-168.
2U.S. Geological Survey.


A theoretical examination of the fracturing of rocks by means of pressure applied in boreholes leads to the conclusion that, regardless of whether the fracturing fluid is of the penetrating or nonpenetrating type, the fractures produced should be approximately perpendicular to the axis of least stress. The general state of stress underground is that in which the three principal stresses are unequal. For tectonically relaxed areas characterized by normal faulting, the least stress should be horizontal; the fractures produced should be vertical, and the injection pressure should be less than that of the overburden. In areas of active tectonic compression, the least stress should be vertical and equal to the pressure of the overburden; the fractures should be horizontal, and injection pressures should be equal to, or greater than, the pressure of the overburden.

Horizontal fractures cannot be produced by hydraulic pressures less than the total pressure of the overburden.

These conclusions are compatible with field experience in fracturing and with the results of laboratory ex-perimentation.

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