The pore pressure must be included in any discussion of the state of stress within a rock. Rock cylinders at elevated stress levels, loaded uniaxially to a stress less than the yield strength, can be fractured by holding the constraints constant and increasing the pore fluid pressure. This can be described in terms of the Mohr envelopes using effective stresses.
The effective stress concept can simplify data with various confining and pore pressures. When the pore and confining pressures are equal, the pore pressure appears to be totally effective in reducing the confining pressure effects. The area over which the pore pressure acts has been the subject of some prior discussions.
Terzaghi1 defined boundary porosity as "... the ratio of that part of the area of the potential surface which is in contact with the interstitial liquid and the total area of this surface." His method of calculation included a discussion of splitting failure which was objected to by Mr. Kessler, National Bureau of Standards. The values calculated by Terzaghi were close to unity. Leliavsky,2 using unjacketed cement cores, reported that the interstitial fluid pressure appeared to' act upon about 92% of the surface of failure. He concluded: "The fraction of the area of cross-section over which the internal pressure acts can therefore have nothing to do with ordinary porosity, and the results of the experiments tend to support Professor Terzaghi's views."
In 1947 Balmer3 determined the boundary porosity of concrete when the confining and pore pressures were equal. He also found values close to unity. In 1948 McHenry4 published some of the results from the same equipment and included the first data in which the pore pressure was controlled at some value less than the confining pressure. In those tests he also concluded that the boundary porosity of concrete was close to unity.
In general, the boundary porosity of 100% satisfactorily described the failure of sandstone and limestone in the experiments by Handin et al. 5 Three conditions were found necessary to use the "effective stress" concept (i.e., a 100% boundary porosity;
"The interstitial fluid is inert relative to the mineral constituents of the rock so that the pore pressure effects are purely mechanical.
The permeability is sufficient to allow pervasion of the fluid and, furthermore, to permit the interstitial fluid to flow freely in and out of the rock during the deformation so that the pore pressure remains constant.
The rock is a sandlike aggregate with connected pore space
Thus it appears that boundary porosity values should be close to unity. The primary purpose of this chapter is to develop an expression for boundary porosity through a force analysis, using Mohr's condition of failure. This equation will then be tested using published failure data.
Octahedral stresses provide a convenient vehicle in discussing plasticity or yielding phenomena. The octahedral normal, s, and shearing stresses, t, are expressed (mathematical Equation)(Available in full paper) where s1, s2, and s3 are the three principal stresses. These stresses have been used to describe the state of stress in solid materials.
