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
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, τ0
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 Szz 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 Szz, or λ approaches 1, σzz approaches 0.
For the case of gravitational sliding, on a subaerial slope of angle θ
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 0.9Szz are being observed in deep oil wells in various parts of the world.