The effective stress principle
Terzaghi effective stresstotal stress vs effective stresspore water pressuresigma prime
Total vertical stress, pore water pressure and Terzaghi's σ′ = σ − u — the single idea the whole of soil mechanics rests on.
Total Vertical Stress (σ = γz)
Total vertical stress at depth in a uniform soil layer, the weight of the overburden column standing on one unit of area.
Pore Water Pressure (u = γw zw)
Hydrostatic pore water pressure at a point below a static water table, from the depth of water standing above it.
Effective Stress (Terzaghi, σ′ = σ − u)
Terzaghi's effective stress principle: the grain-to-grain stress that controls soil strength equals total stress minus pore water pressure.
Submerged (Buoyant) Unit Weight
Effective or buoyant unit weight of soil below the water table, the saturated unit weight less the uplift of the water it displaces.
How they fit together
Terzaghi's insight was that soil grains do not feel the total weight above them — they feel what is left after the water in the pores carries its share. Strength and compression respond to that difference, σ′ = σ − u, and to nothing else. Compute total stress by summing unit weight times thickness down through the layers, compute pore pressure from the height of water above the point, subtract. Using submerged unit weight below the water table is the same subtraction done in one step rather than two.
The decision that matters is which stress the problem is asking about. Anything to do with strength, settlement or bearing capacity is governed by effective stress; total stress is only an intermediate. The consequences are counter-intuitive and worth internalising: raising the water table does not change the total weight of soil above a point by much, but it raises u sharply, drops σ′, and can drop the soil's shear strength enough to trigger a slope failure — which is why landslides follow heavy rain. Push it further and u equals σ, σ′ reaches zero, and the soil has no frictional strength at all: that is quicksand and that is a liquefaction failure. The subtlety is that u is not always hydrostatic — under seepage or rapid loading of a clay it is not, and reading it off the water table depth alone will mislead you.