Question 3 of 7: Hydrogeology – Terms & Groundwater Calculations

Question 3: Hydrogeology – Terms & Groundwater Calculations (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) (i) Influent stream – a stream whose bed lies above the local water table, so it continuously loses water downward, recharging the underlying aquifer (typical of arid/semi-arid regions, opposite of an effluent/gaining stream). (ii) Perched water table – a local, discontinuous zone of saturation held up above the regional water table by a lens of low-permeability material (an aquiclude) within the unsaturated zone. (iii) Drawdown – the difference in elevation between the original (static) water table or potentiometric surface and its lowered level around a pumping well, forming the "cone of depression." (iv) Subsidence – sinking or settling of the ground surface, commonly caused by compaction of aquifer material after groundwater (or oil/gas) withdrawal lowers pore pressure, or by dissolution of soluble bedrock at depth. (v) Speleothems – secondary mineral deposits (usually calcite) precipitated from dripping or flowing groundwater inside caves, forming features such as stalactites, stalagmites, and flowstone.

Given. (i) freshwater lens with the water table 2 m above sea level in a coastal aquifer; (ii) Point A at 12 m and Point B at 58 m elevation, 360 m apart, both on the water table; (iii) seepage velocity X→Y = 2.1×10⁻⁶ m/s, effective porosity n_e = 0.45, K = 0.6×10⁻⁵ m/s, distance X–Y = 87 m, elevation of Y = 28 m above sea level.

Find. (i) depth of the freshwater lens below sea level; (ii) hydraulic gradient A→B; (iii) elevation of Point X.

Approach. (i) uses the Ghyben–Herzberg relation for a floating coastal freshwater lens; (ii) is the definition of hydraulic gradient (head drop over flow-path length); (iii) inverts the Darcy seepage-velocity equation to back out the head loss between X and Y, then adds it to Y's known elevation (flow moves from higher to lower head, so X, upgradient, sits higher).

1. (i) Ghyben–Herzberg freshwater lens depth. For a floating lens of fresh water (ρ_fresh ≈ 1000 kg/m³) on denser seawater (ρ_sea ≈ 1025 kg/m³) in hydrostatic equilibrium, the classic teaching ratio is $$\frac{\text{depth below sea level}}{\text{height above sea level}} \approx \frac{\rho_{sea}}{\rho_{sea}-\rho_{fresh}} \approx 40.$$ With the water table $h=2\text{ m}$ above sea level: $$\boxed{\text{depth} \approx 40 \times 2\text{ m} = 80\text{ m below sea level}}.$$
2. (ii) Hydraulic gradient A→B. Gradient is head difference over flow-path distance: $$i=\frac{\Delta h}{L}=\frac{58-12}{360}=\frac{46}{360}=0.1278.$$ $$\boxed{i \approx 0.128\ (12.8\%)}.$$
3. (iii) Elevation of Point X. Darcy's law gives the seepage (average linear) velocity as $v=\dfrac{Ki}{n_e}$, so the gradient between X and Y is $$i=\frac{v\,n_e}{K}=\frac{(2.1\times10^{-6})(0.45)}{0.6\times10^{-5}}=0.1575.$$ The head drop over the 87 m path is $\Delta h = i\,L = 0.1575\times87 = 13.70\text{ m}$. Groundwater flows from X to Y, so X is upgradient (higher head) than Y: $$\boxed{\text{elev}_X = \text{elev}_Y + \Delta h = 28 + 13.70 = 41.7\text{ m above sea level}}.$$

(c) A heavily pumped well draws down the water table around it, creating an expanding cone of depression whose radius of influence grows the longer/harder the well is pumped. If that cone of influence extends far enough to reach the neighbouring property, it locally steepens and can even reverse the natural hydraulic gradient in that direction, pulling groundwater — and anything dissolved or suspended in it (e.g. leachate from a septic system, fuel tank, or saline water in a coastal aquifer) — toward the pumping well from areas (including the neighbour's land) that were previously outside its capture zone. In effect, the pumping well "reaches out" hydraulically and can draw contamination that would otherwise have stayed put, or bypassed the well entirely, into its own capture zone and, along the way, through the neighbouring property's soil and well.