Pumping a confined aquifer at a constant rate Q creates a spreading cone of depression. For small values of the well function's argument, the Theis solution reduces to the Cooper–Jacob approximation, evaluated here on a radial array from the well rather than a 2D mesh:
s(r,t) = (2.303 Q) / (4πT) · log10( 2.25 T t / (r² S) )
The top panel is a true radial cross-section: distance from the well on the x-axis, elevation on the y-axis — the water-table curve is s(r,t) plotted directly, not a camera view of a deforming grid.
A head decline s increases the effective stress carried by the clay aquitard by Δσ′ = γw·s (Terzaghi's principle). Below the clay's historical maximum stress the compaction is elastic and recovers on recharge; once s exceeds that maximum, the clay compacts inelastically and never fully rebounds:
Δb = Sske · Δs (elastic, reversible)
Δb = Sskv · Δs (virgin/inelastic, permanent, Sskv ≫ Sske)
The bottom panel is a stress–compaction diagram (the classic soil-mechanics e–log σ′ plot): the live trace shows the observation point's path through elastic segments and virgin-compaction excursions, exactly the same accounting used for the subsidence bowl above, now made visible as its own phase-space curve.
- Q — well discharge; higher Q deepens and widens the cone faster.
- T — aquifer transmissivity; a "tighter" aquifer (lower T) produces a steeper, more local cone for the same Q.
- S — storativity; lower S makes the cone propagate and deepen faster for the same pumping.
- r — moves the observation marker on both panels to any distance from the well.
- Pause pumping — stops drawdown growth; the elastic part of the compaction slowly rebounds while the permanent part stays.