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1Manuscript received, July 4, 1972. This paper serves only to introduce and update the paper, “Mechanics of Hydraulic Fracturing”, by M. King Hubbert and David G. Willis, which follows.
2U.S. Geological Survey.


Natural fractures in rocks comprise (1) joints, which are commonly closely spaced, are of limited linear extent, and have negligible tangential displacements, and (2) faults across which opposite blocks have tangential displacements ranging from millimeters to tens of kilometers. Induced fractures are principally those produced in surrounding rocks by fluid pressures applied within well bores.

The orientation of fractures with respect to applied stresses may vary widely, depending upon the amount of finite strain the rock has undergone after the fractures were formed. This discussion will be limited to fractures in rocks that have undergone only minor strain subsequent to the fracturing.

Because rocks are elastic solids, there exists in three-dimensional space beneath the surface of the ground a field of stress definable at each point by three mutually perpendicular, principal compressive stresses and by the space orientation of these stress axes. On the three planes perpendicular to the principal stresses, shear stresses are zero; on all other planes, if the principal stresses are unequal, nonzero shear stresses exist.

Parallel with the ground surface, the shear stresses must be zero. Hence, at each point of this surface, one of the three principal stress trajectories must terminate perpendicularly. Therefore, in regions of gentle topography and simple structure, the underground stress field is usually characterized by a system of principal stress trajectories, one of which is nearly vertical and the other two nearly horizontal.

When rocks are subjected to compression under unequal triaxial stresses, failure by fracture and tangential slippage occurs for certain stress combinations. Usually, conjugate sets of slip surfaces are formed whose lines of intersection are parallel with the intermediate axis of stress and whose acute angle (commonly about 60°) is bisected by the greatest principal stress. This phenomenon forms the basis for relating the orientation of common faults—normal, reverse, and transcurrent—to the associated stress fields.

Hydraulically induced fractures, whether by fluid pressure in wells or by the intrusion of igneous dikes, tend to follow surfaces parallel with the greatest and intermediate principal compressive stresses and per-pendicular to the least stress. Therefore, the orientations of hydraulic fractures, or of igneous dikes and sills, are greatly influenced by the prevailing stress state in the ambient rocks. In particular, in tectonically relaxed regions characterized by normal faulting, the greatest principal stress is nearly vertical and the intermediate and least principal stresses are nearly horizontal, the intermediate stress being in the strike direction of the local normal faults. In such a region, the preferred orientation of hydraulic fractures is vertical and perpendicular to the least principal stress and parallel with the strike of the local normal faults.

Hydraulic-fracture orientation may also be influenced by anisotropy or planar inhomogeneities in the rock such as bedding, schistose cleavage, or a system of parallel joints. If such a planar system does not depart too far from perpendicularity to the axis of least stress, hydraulic fractures may follow such a zone of weakness, across which the shear stress will not be zero. In this case, provided the rocks are also stressed tectonically, slippage along the fracture and possible resultant earthquakes are expectable consequences of increasing the fluid pore pressure in the rock.

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