Total Vertical Stress (σ = γz)

Every geotechnical calculation starts here: the ground is heavy, and the deeper you go the more of it is sitting on your head. Total vertical stress is simply the weight of a column of soil one unit in area, so γ multiplied by z. A typical moist sand at γ = 18 kN/m³ produces 18 kPa for every metre of depth, so at 5 m the total vertical stress is 18 × 5 = 90 kPa: roughly nine tonnes pressing on every square metre. In imperial practice a 120 pcf fill at 20 ft gives 120 × 20 = 2400 lbf/ft², which is 2400 ÷ 144 = 16.7 psi.

The trap is layering. This one-line form is only valid inside a single uniform stratum; a real profile is a running sum, $\sigma_v$ = Σ γᵢ hᵢ, taken layer by layer from the surface down. Use the moist unit weight above the water table and the saturated unit weight below it, and never reach for an "average γ" across a boundary: a 2 m crust of stiff fill over soft clay will give you the right answer at 2 m and a badly wrong one at 10 m. Karl Terzaghi built the whole discipline on this bookkeeping in his 1925 Erdbaumechanik, the first book to treat soil as a material with calculable stresses rather than as an obstacle to be guessed at.