M. King Hubbert

Bio: M. King Hubbert is an academic researcher from Royal Dutch Shell. The author has contributed to research in topics: Darcy's law & Population. The author has an hindex of 16, co-authored 32 publications receiving 7507 citations. Previous affiliations of M. King Hubbert include International Union of Geological Sciences & United States Geological Survey.

Role of fluid pressure in mechanics of overthrust faulting: I. Mechanics of fluid-filled porous solids and its application to overthrust faulting

Abstract: Promise of resolving the paradox of overthrust faulting arises from a consideration of the influence of the pressure of interstitial fluids upon the effective stresses in rocks. If, in a porous rock filled with a fluid at pressure p, the normal and shear components of total stress across any given plane are S and T, then are the corresponding components of the effective stress in the solid alone. According to the Mohr-Coulomb law, slippage along any internal plane in the rock should occur when the shear stress along that plane reaches the critical value where σ is the normal stress across the plane of slippage, τ 0 the shear strength of the material when σ is zero, and ϕ the angle of internal friction. However, once a fracture is started τ 0 is eliminated, and further slippage results when This can be further simplified by expressing p in terms of S by means of the equation which, when introduced into equation (4), gives From equations (4) and (6) it follows that, without changing the coefficient of friction tan ϕ , the critical value of the shearing stress can be made arbitrarily small simply by increasing the fluid pressure p. In a horizontal block the total weight per unit area S zz is jointly supported by the fluid pressure p and the residual solid stress σ zz ; as p is increased, σ zz is correspondingly diminished until, as p approaches the limit S zz , or λ approaches 1, σ zz approaches 0. For the case of gravitational sliding, on a subaerial slope of angle θ where T is the total shear stress, and S the total normal stress on the inclined plane. However, from equations (2) and (6) Then, equating the right-hand terms of equations (7) and (8), we obtain which indicates that the angle of slope θ down which the block will slide can be made to approach 0 as λ approaches 1, corresponding to the approach of the fluid pressure p to the total normal stress S . Hence, given sufficiently high fluid pressures, very much longer fault blocks could be pushed over a nearly horizontal surface, or blocks under their own weight could slide down very much gentler slopes than otherwise would be possible. That the requisite pressures actually do exist is attested by the increasing frequency with which pressures as great as 0.9 S zz are being observed in deep oil wells in various parts of the world.

Mechanics of Hydraulic Fracturing

Abstract: 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 experimentation.

Theory of scale models as applied to the study of geologic structures

Abstract: INTRODUCTION Many of the phenomena of physical science are simple enough and well enough understood that they are amenable to complete mathematical analysis without recourse to auxiliary experimentation. There are other phenomena, however, which, though being made up of well-understood simple systems, are so complicated as a whole as to render complete mathematical analysis difficult or impossible. The distribution of stress in a complicated machine part, or the flow of water in an irregularly shaped vessel, would constitute examples of the latter kind. When something must be known about one of these more complicated problems it is usual, whenever possible, to obtain the desired information empirically by direct experimentation. Often, however, the thing studied is too large to be experimented with. Or, as in the case of large engineering structures, the information on a bridge, dam, or building is needed in advance of designing the structure. Under these conditions, where . . .

Role of Fluid Pressure in Mechanics of Overthrust Faulting: Reply

Abstract: Promise of resolving the paradox of overthrust faulting arises from a consideration of the influence of the pressure of interstitial fluids upon the effective stresses in rocks. If, in a porous rock filled with a fluid at pressure p, the normal and shear components of total stress across any given plane are S and T, then ![Formula][1] ![Formula][2] are the corresponding components of the effective stress in the solid alone. According to the Mohr-Coulomb law, slippage along any internal plane in the rock should occur when the shear stress along that plane reaches the critical value ![Formula][3] where σ is the normal stress across the plane of slippage, τ the shear strength of the material when σ is zero, and ϕ the angle of internal friction. However, once a fracture is started τ is eliminated, and further slippage results when ![Formula][4] This can be further simplified by expressing p in terms of S by means of the equation ![Formula][5] which, when introduced into equation (4), gives ![Formula][6] From equations (4) and (6) it follows that, without changing the coefficient of friction tan ϕ , the critical value of the shearing stress can be made arbitrarily small simply by increasing the fluid pressure p. In a horizontal block the total weight per unit area S zz is jointly supported by the fluid pressure p and the residual solid stress σzz; as p is increased, σzz is correspondingly diminished until, as p approaches the limit S zz, or λ approaches 1, σzz approaches 0. For the case of gravitational sliding, on a subaerial slope of angle θ ![Formula][7] where T is the total shear stress, and S the total normal stress on the inclined plane. However, from equations (2) and (6) ![Formula][8] Then, equating the right-hand terms of equations (7) and (8), we obtain ![Formula][9] which indicates that the angle of slope θ down which the block will slide can be made to approach 0 as λ approaches 1, corresponding to the approach of the fluid pressure p to the total normal stress S . Hence, given sufficiently high fluid pressures, very much longer fault blocks could be pushed over a nearly horizontal surface, or blocks under their own weight could slide down very much gentler slopes than otherwise would be possible. That the requisite pressures actually do exist is attested by the increasing frequency with which pressures as great as 0.9 S zz are being observed in deep oil wells in various parts of the world. [1]: /embed/graphic-1.gif [2]: /embed/graphic-2.gif [3]: /embed/graphic-3.gif [4]: /embed/graphic-4.gif [5]: /embed/graphic-5.gif [6]: /embed/graphic-6.gif [7]: /embed/graphic-7.gif [8]: /embed/graphic-8.gif [9]: /embed/graphic-9.gif

The Mechanics of Earthquakes and Faulting

Abstract: This essential reference for graduate students and researchers provides a unified treatment of earthquakes and faulting as two aspects of brittle tectonics at different timescales. The intimate connection between the two is manifested in their scaling laws and populations, which evolve from fracture growth and interactions between fractures. The connection between faults and the seismicity generated is governed by the rate and state dependent friction laws - producing distinctive seismic styles of faulting and a gamut of earthquake phenomena including aftershocks, afterslip, earthquake triggering, and slow slip events. The third edition of this classic treatise presents a wealth of new topics and new observations. These include slow earthquake phenomena; friction of phyllosilicates, and at high sliding velocities; fault structures; relative roles of strong and seismogenic versus weak and creeping faults; dynamic triggering of earthquakes; oceanic earthquakes; megathrust earthquakes in subduction zones; deep earthquakes; and new observations of earthquake precursory phenomena.

Weak elastic anisotropy

Abstract: Most bulk elastic media are weakly anisotropic. -The equations governing weak anisotropy are much simpler than those governing strong anisotropy, and they are much easier to grasp intuitively. These equations indicate that a certain anisotropic parameter (denoted 6) controls most anisotropic phenomena of importance in exploration geophysics. some of which are nonnegligible even when the anisotropy is weak. The critical parameter 6 is an awkward combination of elastic parameters, a combination which is totally independent of horizontal velocity and which may be either positive or negative in natural contexts.

Mechanics of deformation and acoustic propagation in porous media

Abstract: A unified treatment of the mechanics of deformation and acoustic propagation in porous media is presented, and some new results and generalizations are derived. The writer's earlier theory of deformation of porous media derived from general principles of nonequilibrium thermodynamics is applied. The fluid‐solid medium is treated as a complex physical‐chemical system with resultant relaxation and viscoelastic properties of a very general nature. Specific relaxation models are discussed, and the general applicability of a correspondence principle is further emphasized. The theory of acoustic propagation is extended to include anisotropic media, solid dissipation, and other relaxation effects. Some typical examples of sources of dissipation other than fluid viscosity are considered.

Mechanics of fold-and-thrust belts and accretionary wedges

Abstract: The overall mechanics of fold-and-thrust belts and accretionary wedges along compressive plate boundaries is considered to be analogous to that of a wedge of soil or snow in front of a moving bulldozer. The material within the wedge deforms until a critical taper is attained, after which it slides stably, continuing to grow at constant taper as additional material is encountered at the toe. The critical taper is the shape for which the wedge is on the verge of failure under horizontal compression everywhere, including the basal decollement. A wedge of less than critical taper will not slide when pushed but will deform internally, steepening its surface slope until the critical taper is attained. Common silicate sediments and rocks in the upper 10-15 km of the crust have pressure-dependent brittle compressive strengths which can be approximately represented by the empirical Coulomb failure criterion, modified to account for the weakening effects of pore fluid pressure. A simple analytical theory that predicts the critical tapers of subaerial and submarine Coulomb wedges is developed and tested quantitatively in three ways: First, laboratory model experiments with dry sand match the theory. Second, the known surface slope, basal dip, and pore fluid pressures in the active fold-and-thrust belt of western Taiwan are used to determine the effective coefficient of internal friction within the wedge,/x = 1.03, consistent with Byerlee's empirical law of sliding friction,/at, = 0.85, on the base. This excess of internal strength over basal friction suggests that although the Taiwan wedge is highly deformed by imbricate thrusting, it is not so pervasively fractured that frictional sliding is always possible on surfaces of optimum orientation. Instead, the overall internal strength apparently is controlled by frictional sliding along suboptimally oriented planes and by the need to fracture some parts of the observed geometrically complex structure for continued deformation. Third, using the above values of/at, and/x, we predict Hubbert-Rubey fluid pressure ratios X = Xt, for a number of other active subaerial and submarine accretionary wedges based on their observed tapers, finding values everywhere in excess of hydrostatic. These predicted overpressures are reasonable in light of petroleum drilling experience in general and agree with nearby fragmentary well data in specific wedges where they are available. The pressure-dependent Coulomb wedge theory developed here is expected to break down if the decollement exhibits pressure-independent plastic behavior because of either temperature or rock type. The effects of this breakdown are observed in the abrupt decrease in taper where wedge thicknesses exceed about 15 km, which is the predicted depth of the brittle-plastic transition in quartz-rich rocks for typical geothermal gradients. We conclude that fold-and-thrust belts and accretionary wedges have the mechanics of bulldozer wedges in compression and that normal laboratory fracture and frictional strengths are appropriate to mountain-building processes in the upper crust, above the brittle-plastic transition.