On the use of Effective Stress in Granular Media

Effective stress, typically defined as the difference between lithostatic and hydrostatic pressures, has long been used to help explain deformation in experimental and subsurface environments. The correction factors to account for finite grain-to-grain contact areas have been defined (cf. Terzaghi's boundary porosity, as well as Bishop and Eldin 1950-51 and Skempton 1960-61). However, the relationships among finite grain contacts, gravity, and buoyancy have often been poorly explained and the finite contact area corrections are often ignored even when contact areas are large. Force balance on a grain scale can help clarify these issues. For small grain-to-grain contact areas the usual effective stress captures the average stress on a reference plane exerted by the grains, but this is far from the value of the stress between grains. As contact areas increase, there is a shielding of buoyancy forces that normally arise from the vertical gradient of fluid pressure. New correction factors are derived for average grain- to-grain contact area stresses which should be employed when analyzing data from experimental piston/cylinder devices when grain contact areas within the sample differ from grain contact areas with the piston surfaces. The role of fluid and grain densities, as well as the role of pore pressure and its gradient are self consistent. Although force balance arguments are based on static conditions, implications for dynamics with compaction, pressure solution, and fluid flow modeling in a porous media will also be presented.