Every page that follows rests on one equation from Karl Terzaghi: the total weight pressing down on the sediment skeleton is split between the pore water and the grains. Lower the water pressure, and the grains must carry more — so they compress.
At any depth, the total stress σ is the weight of everything above — sediment grains plus water — per unit area. That load is constant; it is set by geology and does not change when you pump. It is carried partly by the pore-water pressure u and partly by grain-to-grain contact, the effective stress σ′:
Only σ′ deforms the skeleton. Pore water carries pressure but provides no shear support between grains. So compaction is driven entirely by changes in effective stress — not by the absolute water level, but by how the load is shared.
Pumping lowers head, which lowers pore pressure u. Because total stress σ is unchanged, every pascal that u loses is a pascal that σ′ gains:
This is why a recoverable water-level change can cause an unrecoverable ground-surface change: the water comes back, but the rearranged grains do not.
| Total stress σ at readout depth | — psi |
| Pore pressure u (initial → now) | — psi |
| Effective stress σ′ (initial → now) | — psi |
| Increase in σ′ (Δσ′) | — psi |
The increase in effective stress is felt by every layer alike. But the resulting strain depends on compressibility, which differs by one to two orders of magnitude between sands and clays — a difference rooted in particle shape and how the grains were deposited.
Sand and coarser grains are roughly equant and rounded. As they settle they come to rest in a tight, mechanically stable framework of grain-to-grain contacts already close to its densest packing, so added stress causes little further rearrangement. Low compressibility — and high conductivity dissipates the pressure change almost instantly — so the deformation is small and essentially elastic.
Clay minerals are thin, plate-shaped particles. Deposited in quiet water they flocculate (edge-to-face attraction) into an open, high-porosity "card-house" fabric riddled with voids. That loose arrangement sits far from a stable packing, so rising effective stress collapses it — the platelets rotate and slide into a denser, face-to-face stack. The result is compaction that is large, slow to drain (page 06), and largely permanent (pages 04–05).
In a confined aquifer, lowering head reduces pore pressure but the sediment stays saturated and total stress barely changes — so \(\Delta\sigma' \approx \gamma_w\,\Delta h\) exactly, applied over the full thickness below. In a water-table aquifer, the dewatered interval also loses the buoyant support of water and shifts from saturated to moist unit weight, adding a smaller second term. Most large-magnitude subsidence is driven by head decline in confined systems.
Total stress is the integrated unit weight of overburden:
Lofgren (1968) worked out these stress balances for the San Joaquin Valley and showed that measured compaction tracked the computed change in effective stress — the field confirmation of Terzaghi's principle at basin scale.