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Topic: problem solver

Paper details:

In less than one page (could be one paragraph), explain
a) the significance of p; and
b) the derivation of ? (lambda) and its relationship to hydrostatic and lithostatic stress in the upper 5
km of the earth.
c) Referring to the Hubbert and Rubey article, what is the significant of Figure 7, and why did the authors choose to illustrate their argument with this figure? One paragraph will be sufficient.
D) Using words, diagrams, and equations, develop the low-angle thrust fault paradox. Your answer need only be one very concise paragraph, in addition to any diagrams and equations that you utilize.
need C in different paragraph please

ROLE OF FLUID PRESSURE IN MECHANICS OF OVERTHRUST FAULTING
I. MECHANICS OF FLUID-FILLED POROUS SOLIDS AND ITS APPLICATION TO OVERTHRUST FAULTING
M KING HUBBERT and WILLIAM W RUBEY

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 s is the normal stress across the plane of slippage, t0 the shear strength of the material when s is zero, and ? the angle of internal friction. However, once a fracture is started t 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 ?, 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 Szz is jointly supported by the fluid pressure p and the residual solid stress szz; as p is increased, szz is correspondingly diminished until, as p approaches the limit Szz, or ? approaches 1, szz approaches 0.
For the case of gravitational sliding, on a subaerial slope of angle ?

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 ? down which the block will slide can be made to approach 0 as ? 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 0.9Szz are being observed in deep oil wells in various parts of the world.

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