Chapter 5 — Permeability¶
5.1 Darcy's law¶
Water flows through soil under a hydraulic gradient \(i = \Delta h / L\). Darcy's law states:
\[v = k i\]
where \(v\) is the discharge velocity and \(k\) is the coefficient of permeability. The seepage velocity (through the voids) is \(v / n\), where \(n\) is porosity.
5.2 What controls permeability¶
Permeability depends on:
- particle size and grading — coarser, well-graded soils are more permeable;
- void ratio — more voids, more flow;
- saturation — unsaturated soils have much lower permeability;
- soil structure — fissures and layers can dominate.
Typical ranges span ten orders of magnitude: gravel (\(10^{-2}\) m/s) down to clay (\(10^{-10}\) m/s). This enormous range is why permeability is the hardest parameter to estimate reliably.
5.3 Measuring permeability¶
- Constant-head test — for coarse, permeable soils.
- Falling-head test — for fine soils.
- Field tests — pumping tests, borehole tests, and piezometer response tests measure the in-situ value, which may differ greatly from the laboratory value because of structure and layering.
5.4 Layered soils¶
Where the soil is layered, flow is anisotropic:
- Horizontal flow is dominated by the most permeable layers (weighted by thickness).
- Vertical flow is dominated by the least permeable layers (weighted by reciprocal).
The result is usually \(k_h > k_v\), sometimes by an order of magnitude, which matters for consolidation rates and seepage.
5.5 Key takeaways¶
- Darcy's law: \(v = ki\) — flow is proportional to gradient.
- Permeability spans ten orders of magnitude — the hardest parameter to pin down.
- Measure it in the field where structure and layering matter.
- Layered soils are anisotropic: \(k_h > k_v\).
- Permeability controls seepage, consolidation rate, and drainage design.