Question 4 of 7: Constant-Head Permeameter Test on the Soil Cylinder

Question 4: Constant-Head Permeameter Test on the Soil Cylinder (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.

Approach. Get the Darcy (superficial) velocity from the measured flow rate and the cylinder's cross-section, divide by porosity for the true seepage velocity, then apply Darcy's law with the hydraulic gradient set by the total head drop from the constant supply level down to the tailwater level in the base bath.

1. Flow rate and Darcy (superficial) velocity. The cylinder's cross-section is the same as in Question 2, A = 0.1964 m²: $$Q = \frac{865\ \text{L}}{10\ \text{min}} = 1.442\times10^{-3}\ \text{m}^3/\text{s}, \qquad v = \frac{Q}{A} = \frac{1.442\times10^{-3}}{0.1964} = 7.34\times10^{-3}\ \text{m/s}$$
2. a) Seepage velocity. Flow actually occurs only through the void space, so the true (seepage) velocity is the Darcy velocity scaled up by 1/n, using the porosity found in Question 2: $$v_s = \frac{v}{n} = \frac{7.34\times10^{-3}}{0.334} = \boxed{0.0220\ \text{m/s}\ (22.0\ \text{mm/s})}$$
3. b) Hydraulic gradient and conductivity. Head is measured from the constant supply surface (soil top + 76 cm column = 1.0 + 0.76 = 1.76 m above the cylinder base) down to the tailwater surface where flow discharges into the bath (0.10 m above the base); resistance to flow occurs only inside the soil, so the full head loss acts across the L = 1.0 m sample: $$i = \frac{\Delta h}{L} = \frac{1.76 - 0.10}{1.0} = 1.66$$ $$K = \frac{v}{i} = \frac{7.34\times10^{-3}}{1.66} = \boxed{4.42\times10^{-3}\ \text{m/s}}$$ This matches the order of magnitude assumed for this same gravelly-sand aquifer in Question 1.

c) Other methods for in-situ K. Laboratory: falling-head permeameter (better suited to finer, lower-K soils than the constant-head test used here), and back-calculation of k from a consolidation (oedometer) test's coefficient of consolidation c_v. Field: pumping (aquifer) tests with observation wells, single-well slug or bail tests, the auger-hole method, borehole packer (falling/constant-head) tests, piezometer (Hvorslev) tests, and the Guelph permeameter for near-surface unsaturated/vadose-zone conductivity.

d) Soil characteristics affecting K. Grain-size distribution and effective particle size (D₁₀), void ratio/porosity and pore connectivity, soil fabric and structure (macropores, fissures, layering/anisotropy), degree of saturation, particle shape and packing, clay mineralogy and dispersion, and permeant fluid properties (viscosity, temperature).