Aquitard Consolidation: Spatial Diffusion Solver (2D)

Pumping

Extraction rate (drawdown) 4.0 m/yr

Aquitard Compressibility

Inelastic / elastic storage ratio 60×

Live Readouts

Boundary head decline

0.0 m

Effective stress Δσ'

0.0 kPa

Land subsidence (now)

0.00 m

Simulated time

0.0 yr

Committed future subsidence (if pumping holds steady, once diffusion catches up)

0.00 m

Boundary: elastic — fully recoverable

How this differs from the 3D version

The 3D simulator treats the whole clay aquitard as one lumped block: the instant head drops by ΔH, the entire layer feels the full effective-stress change at once and compacts by Δb = −S_sk·b₀·ΔH. That is exact only when the clay drains instantly — real clay does not.

This 2D version instead solves Terzaghi's actual 1D consolidation diffusion equation across depth z through the clay, independently at each of 41 depth nodes:

∂s/∂t = c_v(z,t)·∂²s/∂z²      (s = local head decline / effective stress)
c_v = K_clay / S_sk(z,t)      (S_sk switches per node: elastic ↔ inelastic)

The two sand aquifers on either side are far more permeable, so their head follows the pump instantly — that becomes the boundary condition driving diffusion inward from both faces. Because inelastic storage S_skv is many times larger than elastic S_ske, the diffusivity c_v collapses once a node goes virgin — so the interior of a thick clay bed can lag the boundary by years to decades. Total compaction is the exact integral of the local elastic/inelastic law over the resolved profile, not one number for the whole layer.

Profile panel (top) — the live head-decline profile across the aquitard's depth (bright line), with faded "isochrones" from earlier moments so you can watch the diffusion front creep inward. Node color marks elastic (green) vs inelastic/virgin (red) at that depth.
History panel (bottom) — boundary head decline (reacts instantly) vs. actual land subsidence (lags behind it) over simulated time.
Committed future subsidence — the compaction that will still happen even if you freeze the pumping rate right now, because the aquitard's interior hasn't caught up to the boundary yet. This delayed/residual compaction is a well-documented real phenomenon (San Joaquin Valley, Jakarta) that a lumped 0-D model can't represent at all — verified numerically to converge to the 3D model's own formula in the no-delay limit, and to reproduce Terzaghi's classic analytical consolidation curve for a fixed diffusivity.

Elastic node — fully recoverable Inelastic node — virgin loading

Boundary head decline (instant) Land subsidence (lagged)