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Mechanics of fluid-filled porous solids and its application to overthrust faulting, [Part] 1 of Role of fluid pressure in mechanics of overthrust faulting

Marion King Hubbert and William Walden Rubey
Mechanics of fluid-filled porous solids and its application to overthrust faulting, [Part] 1 of Role of fluid pressure in mechanics of overthrust faulting
Bulletin of the Geological Society of America (February 1959) 70 (2): 115-166

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, sigma = S - p (1); tau = T (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 tau crit = tau + sigma tan phi (3); where sigma is the normal stress across the plane of slippage, tau sigma the shear strength of the material when sigma is zero, and phi the angle of internal friction. However, once a fracture is started tau sigma is eliminated, and further slippage results when tau crit = sigma tan phi = (S - p) tan phi (4). This can be further simplified by expressing p in terms of S by means of the equation: p = lambda S (5), which, when introduced into equation (4), gives tau crit = sigma tan phi = (1 - lambda ) S tan phi (6). From equations (4) and (6) it follows that, without changing the coefficient of friction tan phi , 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 (sub zz) is jointly supported by the fluid pressure p and the residual solid stress sigma (sub zz) ; as p is increased, sigma (sub zz) is correspondingly diminished until, as p approach s the limit S (sub zz) , or lambda approaches 1, , sigma (sub zz) approaches O. For the case of gravitational sliding, on a sub-aerial slope of angle theta : T = S tan theta (7), where T is the total shear stress, and S the total normal stress on the inclined plane. However, from equations (2) and (6): T = tau (sub crit) = (1 - )S tan phi (8). Then, equating the right-hand terms of equations (7) and (8), we obtain: tan theta = (1 - lambda ) tan phi (9), which indicates that the angle of slope theta down which the block will slide can be made to approach 0 as lambda 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 greater 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 (sub zz) are being observed in deep oil wells in various parts of the world.


ISSN: 1050-9747
Coden: BUGMAF
Serial Title: Bulletin of the Geological Society of America
Serial Volume: 70
Serial Issue: 2
Title: Mechanics of fluid-filled porous solids and its application to overthrust faulting, [Part] 1 of Role of fluid pressure in mechanics of overthrust faulting
Pages: 115-166
Published: 195902
Text Language: English
Publisher: Geological Society of America (GSA), Boulder, CO, United States
Accession Number: 1959-014863
Categories: Economic geology of energy sources
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus.
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute. Reference includes data from Bibliography and Index of North American Geology, U. S. Geological Survey, Reston, VA, United States
Update Code: 1959
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