2.4 Pumping from a Multi‑aquifer System

Let’s consider an example of a complex multi aquifer system composed by an unconfined and two confined aquifers (Figure 15). Denote by Δz₁, Δz₂, and Δz₃, the piezometric decline in the three pervious formations, respectively. Land settlement η₁ caused by the depressurization of the unconfined aquifer is computed as is described in Section 2.2. As far as the two confined aquifers are concerned, we have to take into account the decrease of the total geostatic stress equal to Δz₁γ(ϕ_f ‑ θ_w), with ϕ_f the porosity of the water table aquifer. As a result, σ_z increases for formations 2 and 3 (Figure 15), respectively:

Δσ₂ = Δz₂γ − Δz₁γ(ϕ_f − θ_w)

Δσ₃ = Δz₃γ − Δz₁γ(ϕ_f − θ_w)

The compactions η₂ and η₃ of the confined aquifers are obtained from Equation 4 and Figure 12 where the representative effective stress prior to pumping is calculated by the use of formulae similar to Equation 11. The subsidence η at the ground surface is then represented by Equation 13.

Figure 15 ‑ Sketch of a pumped multi‑aquifer system.