Question 1 of 7: Dewatering a Trench with a Line of Sand-Point Wells

Question 1: Dewatering a Trench with a Line of Sand-Point Wells (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

a) Reasonable estimates of the essential soil properties. The problem gives the geometry but not the aquifer's hydraulic properties, so a candidate must supply defensible design values before any discharge can be computed. A "gravely sand" is a coarse, well-drained alluvial material; textbook ranges for such soils (Das, Schwab) place the saturated hydraulic conductivity at roughly K ≈ 10^-3–10^-2 m/s and the drainable (specific) porosity at roughly n ≈ 0.25–0.35. For this design, take the representative point estimate K = 4×10^-3 m/s — consistent, as it turns out, with the K ≈ 4.4×10^-3 m/s later measured directly on this same soil in the Question 4 permeameter test — and treat the aquifer as unconfined, homogeneous, and isotropic, with its saturated thickness fixed by the till at 10 m depth.

Approach. Model the closely spaced line of well points as a continuous line sink (an "equivalent slot") running parallel to the trench, and apply the Dupuit–Forchheimer equation for steady unconfined radial flow to a fully penetrating ditch, with the empirical Sichardt formula supplying the radius of influence.

1. Radius of influence (Sichardt). With required drawdown at the well line s = 6 − 1 = 5 m and K = 4×10^-3 m/s, $$R = 3000\,s\sqrt{K} = 3000(5)\sqrt{0.004} = \boxed{949\text{ m}}$$
2. Flow per unit trench length, one side (Dupuit). With H = 9 m and h = 4 m, $$q' = \frac{K\left(H^2-h^2\right)}{2R} = \frac{0.004\,(9^2-4^2)}{2(949)} = \frac{0.004(65)}{1898} = 1.37\times10^{-4}\ \text{m}^3/\text{s per m}$$
3. Discharge per well. Each well point serves a 10 m length of trench on its own side. Substituting the well spacing, $$Q_{\text{well}} = q' \times 10\text{ m} = \left(1.37\times10^{-4}\right)(10) = \boxed{1.37\times10^{-3}\ \text{m}^3/\text{s} \approx 1.4\ \text{L/s per well}}$$ This is a typical single well-point capacity (well points are usually sized for 0.5–3 L/s), which supports the assumed K as a reasonable order of magnitude.

c) Assumptions. The Dupuit–Forchheimer approximation (flow is essentially horizontal, equipotentials vertical, so vertical flow components near the wells are ignored); the closely spaced well points behave as one continuous line sink rather than as discrete radial wells; the aquifer is homogeneous, isotropic and unconfined, bounded below by the impermeable till with no leakage through it; steady state has been reached (no further time-lag drawdown); the aquifer extends to at least the computed radius of influence with an undisturbed head boundary there; and there is no significant recharge (rainfall, adjacent surface water) during the dewatering period. The single biggest source of uncertainty is K itself — because Q_well scales with K^1.5 through R, a K that is off by a factor of 2 changes the required well discharge by roughly √2× through the (H²−h²)/R term alone, which is why Question 4's direct measurement on the same soil is such a valuable check.