General effective-stress rules are derived for various physical properties of inhomogeneous porous rocks. Some rigorous relations arising in the analysis show that the fluid (pore) pressure p{sub f} is least effective at counteracting the changes caused by confining pressure for the solid (grain) volume; p{sub f} is more effective for the total (solid plus pore) volume; p{sub f} is still more effective for the pore volume; and p{sub f} is most effective at maintaining the fluid content of the pores. Although these results are expected intuitively, this analysis provides the first rigorous demonstration. During analysis of coefficients, care is taken to distinguish between rigorous inequalities (following from thermodynamics) and empirical inequalities (commonly observed, but not required by thermodynamics). For microscopically inhomogeneous rocks (the Gassmann limit), it is shown that the confining pressure is always at least as effective as the fluid pressure at changing the fluid permeability; therefore, it is impossible to use any {open_quotes}equivalent homogeneous rock{close_quotes} to explain experimental results of Zoback and Byerlee and others (wherein it has been shown experimentally that the permeability sometimes is more strongly influenced by fluid pressure than confining pressure). The authors show that the equivalent homogeneous rock paradigm may be successfully replacedmore » by the {open_quotes}two-constituent porous medium{close_quotes} paradigm. In principle, the new paradigm can explain the data, but new measurements of pore compressibilities are required before quantitative comparisons can be made. 103 refs., 7 figs., 2 tabs.« less

Effective stress for transport properties of inhomogeneous porous rock

The velocity V sub p of compressional waves has been measured in rock samples of low porosity to confining pressures P sub c of 2 kb for a number of different constant pore pressures P sub p. An effective pressure defined by P sub e = P sub c-nP sub p, n less than or equal to 1, is found to be the determining factor in the behavior of V sub p rather than an effective pressure defined simply by the differential pressure Delta P = P sub c-P sub p. As pore pressure increases at constant effective pressure, the value of n increases and approaches 1, but as effective pressure increases at constant pore pressure, the value of n decreases. These observations are consistent with Biot's theory of the propagation of elastic waves in a fluid-saturated porous solid.

Effect of pore pressure on the velocity of compressional waves in low‐porosity rocks

The effective pressure law for permeability in Chelmsford granite and Barre granite

Transmission Electron Microscopy of Experimentally Deformed Olivine Crystals

Summary

Marine refraction studies during the past decade have found considerable lateral variability in the seismic properties of the upper basaltic regions of the oceanic crust. In many localities, compressional and shear-wave velocities are quite low at the top of the basalt section and velocities increase rapidly with depth. It is concluded that pore pressure may be at least in part responsible for the low upper crustal velocities and contribute significantly to the lateral variability. This is supported by compressional and shear-wave velocity measurements as functions of confining pressure and pore pressure for basalt from the Juan de Fuca ridge and dolerite from the Samail ophiolite, Oman. Within the oceanic crust, regions of overpressure and underpressure will possess anomalous velocities, the magnitude of which will depend upon the porosity and the deviation of the pore pressure from hydrostatic. The influence of pore pressure on velocities is expected to diminish with depth and is unlikely to be significant at lower crustal depths where porosity is extremely low. Of significance, Poisson's ratio is shown to be dependent on pore pressure as well as confining pressure. At constant confining pressure, Poisson's ratio increases with increasing pore pressure. Thus, overpressured regions within the upper oceanic crust are likely to have relatively high Poisson's ratios as well as low compressional- and shear-wave velocities.

/pdf/pore-pressure-and-oceanic-crustal-seismic-structure-e9dankzo57.pdf

Pore pressure and oceanic crustal seismic structure

Change in shear‐wave velocity for four dry sedimentary rocks has been studied as a function of the variation of both external hydrostatic pressure and internal pore pressure in the range 0 to 2,500 psi. The experimental method employs a beam of ultrasonic energy passing through a liquid in which a copper‐jacketed parallel‐sided slab of rock is rotated. The shear‐wave velocity is calculated from the laws of refraction and reflection of waves at a liquid‐solid boundary applied to the angle at which minimum energy is transmitted. The variation of shear‐wave velocity with pressure has been found to be a function of net overburden pressure, Pe-nPi, where Pe=external hydrostatic pressure on the jacketed sample, Pi=internal pore pressure and n = a pressure‐dependent factor less than unity. The values of n at several differential pressures were chosen to yield a smooth curve passing through the displaced data points when the shear‐wave velocities were plotted as a function of net overburden pressure. Using the n ...

Ultrasonic Shear-Wave Velocities in Rocks Subjected to Simulated Overburden Pressure and Internal Pore Pressure

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Ultrasonic Shear-Wave Velocities in Rocks Subjected to Simulated Overburden Pressure and Internal Pore Pressure