William W. Rubey

Bio: William W. Rubey is an academic researcher from United States Geological Survey. The author has contributed to research in topics: Hydrosphere & Atmosphere. The author has an hindex of 15, co-authored 24 publications receiving 4924 citations. Previous affiliations of William W. Rubey include University of California, Los Angeles.

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.

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

Geologic History of Sea Water

Abstract: Paleontology and biochemistry together may yield fairly definite information, eventually, about the paleochemistry of sea water and atmosphere. Several less conclusive lines of evidence now available suggest that the composition of both sea water and atmosphere may have varied somewhat during the past; but the geologic record indicates that these variations have probably been within relatively narrow limits. A primary problem is how conditions could have remained so nearly constant for so long. It is clear, even from inadequate data on the quantities and compositions of ancient sediments, that the more volatile materials—H 2 O, CO 2 , Cl, N, and S— are much too abundant in the present atmosphere, hydrosphere, and biosphere and in ancient sediments to be explained, like the commoner rock-forming oxides, as the products of rock weathering alone. If the earth were once entirely gaseous or molten, these “excess” volatiles may be residual from a primitive atmosphere. But if so, certain corollaries should follow about the quantity of water dissolved in the molten earth and the expected chemical effects of a highly acid, primitive ocean. These corollaries appear to be contradicted by the geologic record, and doubt is therefore cast on this hypothesis of a dense primitive atmosphere. It seems more probable that only a small fraction of the total “excess” volatiles was ever present at one time in the early atmosphere and ocean. Carbon plays a significant part in the chemistry of sea water and in the realm of living matter. The amount now buried as carbonates and organic carbon in sedimentary rocks is about 600 times as great as that in today9s atmosphere, hydrosphere, and biosphere. If only 1/100 of this buried carbon were suddenly added to the present atmosphere and ocean, many species of marine organisms would probably be exterminated. Furthermore, unless CO 2 is being added continuously to the atmosphere-ocean system from some source other than rock weathering, the present rate of its subtraction by sedimentation would, in only a few million years, cause brucite to take the place of calcite as a common marine sediment. Apparently, the geologic record shows no evidence of such simultaneous extinctions of many species nor such deposits of brucite. Evidently the amount of CO 2 in the atmosphere and ocean has remained relatively constant throughout much of the geologic past. This calls for some source of gradual and continuous supply, over and above that from rock weathering and from the metamorphism of older sedimentary rocks. A clue to this source is afforded by the relative amounts of the different “excess” volatiles. These are similar to the relative amounts of the same materials in gases escaping from volcanoes, fumaroles, and hot springs and in gases occluded in igneous rocks. Conceivably, therefore, the hydrosphere and atmosphere may have come almost entirely from such plutonic gases. During the crystallization of magmas, volatiles such as H 2 O and CO 2 accumulate in the remaining melt and are largely expelled as part of the final fractions. Volcanic eruptions and lava flows have brought volatiles to the earth9s surface throughout the geologic past; but intrusive rocks are probably a much more adequate source of the constituents of the atmosphere and hydrosphere. Judged by the thermal springs of the United States, hot springs (carrying only 1 per cent or less of juvenile matter) may be the principal channels by which the “excess” volatiles have escaped from cooling magmas below. This mechanism fails to account for a continuous supply of volatiles unless it also provides for a continuous generation of new, volatile-rich magmas. Possibly such local magmas form by a continuous process of selective fusion of subcrustal rocks, to a depth of several hundred kilometers below the more mobile areas of the crust. This would imply that the volume of the ocean has grown with time. On this point, geologic evidence permits differences of interpretation; the record admittedly does not prove, but it seems consistent with, an increasing growth of the continental masses and a progressive sinking of oceanic basins. Perhaps something like the following mechanism could account for a continuous escape of volatiles to the earth9s surface and a relatively uniform composition of sea water through much of geologic time: (1) selective fusion of lower-melting fractions from deep-seated, nearly anhydrous rocks beneath the unstable continental margins and geosynclines; (2) rise of these selected fractions (as granitic and hydrous magmas) and their slow crystallization nearer the surface; (3) essentially continuous isostatic readjustment between the differentiating continental masses and adjacent ocean basins; and (4) renewed erosion and sedimentation, with resulting instability of continental margins and mountainous areas and a new round of selective fusion below.

Role of fluid pressure in mechanics of overthrust faulting ii. overthrust belt in geosynclinal area of western wyoming in light of fluid-pressure hypothesis

Abstract: Pressures of interstitial fluids significantly greater than the normal hydrostatic pressure are known in many parts of the world. Many occurrences are in thick sections of relatively young sediments; some are in areas that have been intensely deformed. Abnormal fluid pressures in the Gulf Coast region are associated with thick bodies of shale or mudstone, and with high hydraulic gradients across bedding. The rocks there have been buried rather rapidly and are evidently not yet fully compacted. The mechanism by which clay consolidates under pressure affords a quantitative relationship among the variables—depth, strength of clay, and fluid pressure—and this relationship indicates that the Gulf Coast examples agree fairly well with observations on depth and porosity in Paleozoic shales of Oklahoma and Tertiary shales of Venezuela. Critical data are lacking, but permeability clearly decreases tremendously as clay rocks are compacted. This decrease in permeability provides a self-sealing mechanism that greatly retards the escape of pore water from deeply buried clay rocks. The relationship between rate of compaction and the development of abnormal fluid pressures probably applies not only to clay rocks but also to carbonates and possibly to micaceous and chloritic metamorphic rocks. Conditions of geosynclinal deposition are, in general, those most favorable to the development of abnormal fluid pressures. The hypothesis that large-scale overthrusting is facilitated by abnormal fluid pressures which, in turn, are associated with geosynclinal deposition is applied to the overthrust belt of western Wyoming and adjacent States. This is a long curving belt of several bedding-plane faults which have an aggregate horizontal displacement across the belt of 50 miles or more. The sedimentary rocks that make up the belt were evidently deposited in a major geosyncline bordered by uplands not far to the west. At any given locality, the rate of deposition of the sediments increased continuously until the beginning of intense deformation and overthrusting. The geosynclinal axis and the bordering uplands probably migrated slowly eastward across the belt. Several lines of indirect evidence suggest that abnormal fluid pressures developed in this region during final stages of rapid geosynclinal sinking and that thick plates of Paleozoic and Mesozoic sedimentary rocks sheared off from the underlying rocks and moved slowly eastward. Rate of movement probably was controlled by erosion of upfolds that arose at the front of each moving plate. The fundamental cause of the lateral stresses that propelled the overthrusts is not known, but it may be examined instructively in the light of the fluid-pressure hypothesis. The thrust sheets might, for example, have slid by simple gravitation down the western limb of the geosyncline on reasonable slopes and not improbable fluid pressure-overburden ratios. Such large-scale slumping of thrust sheets, however, seems to require gaps at the rear of the thrust sheets. The long intermontane valleys of Idaho and Utah may possibly have originated as such gaps or rifts, but no proof has yet been recognized that they were formed in this manner. An alternative possibility, regional compression, requires concentration of the lateral stresses within the upper few miles of the earth9s crust; in this general region emplacement of the Idaho batholith seems the most likely source of such superficially concentrated stresses. However, this batholith is so far from the front edge of the overthrust belt that it would require extremely high fluid pressure-overburden ratios over a wide area. Perhaps some combination of the two forces—pushing wide thrust plates down a gentle slope—is the most likely explanation.

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.

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.

The hydraulic geometry of stream channels and some physiographic implications

Abstract: Some hydraulic characteristics of stream channels — depth, width, velocity, and suspended load — are measured quantitatively and vary with discharge as simple power functions at a given river cross section. Similar variations in relation to discharge exist among the cross sections along the length of a river under the condition that discharge at all points is equal in frequency of occurrence. The functions derived for a given cross section and among various cross sections along the river differ only in numerical values of coefficients and exponents. These functions are:

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.

Continental stretching: An explanation of the Post-Mid-Cretaceous subsidence of the central North Sea Basin

Abstract: The North Sea is a major continental basin filled with early Paleozoic to Recent sediments. Though graben formation started in the Triassic, the last major period of extension occurred between the Middle Jurassic and the mid-Cretaceous. Following the faulting and graben formation associated with this extension, subsidence within the central North Sea was widespread and uniform and has created a saucershaped sedimentary basin. This was filled successively by chalks, sandstones, and finally, during most of the Tertiary, by shales and mudstones. We examined the subsidence of six wells down the middle and two on the flanks of the Central Graben. In the period of widespread steady subsidence the water-loaded basement depth in the middle increased by 1100–1400 m. On the flanks the basement subsided 600–700 m. We suggest that most of this subsidence results from the thermal relaxation of the lithosphere which was thinned during a Middle Jurassic to mid-Cretaceous stretching of the crust. Assuming a crustal stretching and associated lithospheric thinning of between 50 and 100% in the middle and decreasing on either side, we obtained a good match to the observed amplitude and rate of subsidence. The Middle Jurassic to mid-Cretaceous subsidence which is found within the graben proper we relate to the fault-controlled initial subsidence which occurred during the actual stretching. The measured heat flow is compatible with such a stretching model. Though there is no seismic refraction data across the Central Graben, this model is strongly supported by evidence of a thinner crust under the Viking Graben to the north and the Witchground/Buchan Graben complex to the east. Using the above observations as the basis for a geological interpretation, we examined the thermal maturity and hydrocarbon potential of certain sedimentary horizons in the northern section of the Central Graben. In analyzing the various wells we extended previous work on the compaction correction to handle overpressuring and mixed lithologies in backstripping studies. Further, we expanded these methods to include the variation of thermal conductivity, and calculations of the degree of thermal maturation of the deposited sediments, through time.