The
effective stress (\sigma') acting on a soil is calculated from the total normal stress (\sigma) and
pore water pressure (u) according to: : \sigma' = \sigma - u\, This equation is fundamental in understanding the strength of soils under drained conditions, which applies to coarse-grained soils (sand, silt) and fine-grained soils (clay) over the long-term. This is because soil strength is due primarily to interparticle friction, which - similar to the concept of a block sliding on a table - is proportional to the normal stress. The pore water pressure reduces the normal stress and thus reduces the soil strength. Much like the concept of stress itself, the formula is a construct, for the easier visualization of forces acting on a soil mass, especially simple analysis models for
slope stability, involving a slip plane. With these models, it is important to know the total weight of the soil above (including water), and the pore water pressure within the slip plane, assuming it is acting as a confined layer. However, the formula becomes confusing when considering the true behaviour of the soil particles under different measurable conditions, since none of the parameters are actually independent actors on the particles. Consider a grouping of round
quartz sand grains, piled loosely, in a classic "cannonball" arrangement. As can be seen, there is a contact stress where the spheres actually touch. Pile on more spheres and the contact stresses increase, to the point of causing frictional instability (dynamic
friction), and perhaps failure. The independent parameter affecting the contacts (both normal and shear) is the force of the spheres above. This can be calculated by using the overall average
density of the spheres and the height of spheres above. If we then have these spheres in a
beaker and add some water, they will begin to float a little depending on their density (
buoyancy). With natural soil materials, the effect can be significant, as anyone who has lifted a large rock out of a lake can attest. The contact stress on the spheres decreases as the beaker is filled to the top of the spheres, but then nothing changes if more water is added. Although the water pressure between the spheres (pore water pressure) is increasing, the effective stress remains the same, because the concept of "total stress" includes the weight of all the water above. This is where the equation can become confusing, and the effective stress can be calculated using the buoyant density of the spheres (soil), and the height of the soil above. The concept of effective stress truly becomes interesting when dealing with non-
hydrostatic pore water pressure. Under the conditions of a pore pressure gradient, the ground water flows, according to the permeability equation (
Darcy's law). Using our spheres as a model, this is the same as injecting (or withdrawing) water between the spheres. If water is being injected, the seepage force acts to separate the spheres and reduces the effective stress. Thus, the soil mass becomes weaker. If water is being withdrawn, the spheres are forced together and the effective stress increases. Two extremes of this effect are
quicksand, where the groundwater gradient and seepage force act against
gravity; and the "sandcastle effect", where the water drainage and capillary action act to strengthen the sand. As well, effective stress plays an important role in
slope stability, and other
geotechnical engineering and
engineering geology problems, such as
groundwater-related subsidence. == References ==