Effective stress

Effective stress is a force that keeps a collection of particles rigid. Usually this applies to sand, soil, or gravel.

If you pinch a stack of coins between your fingers, the stack stays together. If you then loosen the pressure between your fingers, the coin stack falls apart. Similarly, a pile of sand keeps from spreading out like a liquid because the weight of the sand keeps the grains stuck together in their current arrangement, mostly out of static friction. This weight and pressure is the effective stress.

Effective stress is easy to disrupt by the application of additional forces; every footstep on a sand pile demonstrates this. It is an important factor in the study of slope stability and soil liquefaction, especially from earthquakes.

Karl von Terzaghi first proposed the relationship for effective stress in 1925. For him, the term "effective" meant the calculated stress that was effective in moving soil, or causing displacements. It represents the average stress carried by the soil skeleton.

Effective stress (σ') acting on a soil is calculated from two parameters, total stress (σ) and pore water pressure (u) according to:

Typically, for simple examples

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.

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