Effective Stress (Terzaghi, σ′ = σ − u)

This single subtraction is the most important sentence in soil mechanics. Water in the pores carries pressure but cannot carry shear, so only the part of the load transmitted through grain contacts — the effective stress — controls strength, stiffness and volume change. Karl Terzaghi arrived at it in Istanbul in the early 1920s while measuring how clay consolidated, and published it in Erdbaumechanik in 1925; before that, soil "science" was a collection of contractors' rules of thumb. A point 5 m down with σ = 90 kPa and a water table 4 m above it has u = 39.2 kPa, so σ′ = 90 − 39.2 = 50.8 kPa, and it is that 50.8 kPa the shear strength is calculated from.

The trap is forgetting that σ′ can be driven to zero without removing any soil at all — just raise the pore pressure. That is liquefaction: a shaken loose sand generates excess pore pressure until u equals σ and the grains float apart, which is exactly what turned Niigata's apartment blocks over in 1964 while they stayed intact. The same arithmetic runs the other way in an excavation, where pumping the water down raises σ′ and settles every building for a block around. Draw down the water table and you have loaded the ground, even though you added nothing to it.