2.3 Pumping from a Single Confined Aquifer
Let Δz be the piezometric decline in the confined aquifer (Figure 14). Since the weight of the overlying soil column does not change, that is, σc is constant, there is an equal, albeit of opposite sign, change in the effective intergranular stress and the pore pressure, that is, Δσz = p = γΔz. Computing σc at the mid‑point of the aquifer as the sum of the stress σc′ at the bottom of the overlying aquitard plus the weight of aquifer column down to the mid‑point results in:
σc = σc′ + 0.5s0[(1 – ϕ)γ′ + ϕγ]
thus, the intergranular stress is shown by Equation 11.
| σz0 = σc′ + 0.5s0[(1 – ϕ)γ′ + ϕγ] – p | (11) |
where:
| σc′ | = | geostatic stress at the bottom of the overlying impermeable layer (ML-1T-2) |
| p | = | pore pressure measured on the mid‑plane of the aquifer prior to the piezometric decline (ML-1T-2) |
Figure 14 ‑ Sketch of a pumped confined aquifer.
Land subsidence is equal to the aquifer compaction as calculated by the use of a graph as shown in Figure 12 and Equation 3. Again, if s0 is large, it can be split into sub‑intervals and σz0 computed for each sub‑interval (while Δσz is the same for each sub‑interval).
In summary, the compaction of a single confined aquifer amounts to (Equation 12):
| η = s0cbΔσz | (12) |
with s0 the aquifer thickness, cb is the uniaxial vertical soil compressibility, and Δσz is the change in the effective intergranular stress.