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Hydraulic conductivity measures how readily a soil transmits water under a hydraulic gradient. In unsaturated soil it can fall sharply as large pores drain, so the saturated value cannot stand in for every field condition. The unit-gradient approximation can simplify free-drainage calculations, but it is an assumption about the total-head gradient—not a universal property of soil.
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Chapter contents
Choose the route closest to the decision, or read from Chapter 1. The chapters remain open; these grouped routes are a navigable index.
Route 1 · Define the decision
Route 2 · Work the ledgers
Route 3 · Transfer the method
Route 4 · Check limits and evidence
Route 5 · Ask and continue
CHAPTER 1 OF 12 · DEFINE THE DECISION
1. Separate conductivity from flux
In one-dimensional form, the Darcy–Buckingham relation can be written q=−K(h)dH/dz, with signs determined by the vertical-coordinate convention. K is hydraulic conductivity; dH/dz is the total-head gradient; q is water flux density.
A high K does not guarantee a high flux if the gradient is small. A strong gradient can still produce little flux when dry soil has a very low unsaturated K.
CHAPTER 2 OF 12 · DEFINE THE DECISION
2. Distinguish saturated and unsaturated K
At saturation, connected pores are water-filled and the conductivity is Ksat for the tested structure and fluid. Below saturation, air enters pores and the effective water pathways shrink; K becomes a steep function of water content or pressure head.
USDA NRCS guidance notes that unsaturated conductivity changes drastically with water content because larger, more conductive pores drain first. Texture alone is not enough: structure, bulk density, macropores, temperature and measurement direction also matter.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. Work a flux ledger
Suppose the unsaturated conductivity at the measured state is 12 mm/day. Under a downward total-head gradient magnitude of 1, the flux magnitude is 12 mm/day. Changing only the gradient changes the flux proportionally.
| K at the measured state | Gradient magnitude | Flux magnitude | Reading |
|---|---|---|---|
| 12 mm/day | 0.4 | 4.8 mm/day | Weak driving force |
| 12 mm/day | 1.0 | 12 mm/day | Unit-gradient case |
| 12 mm/day | 1.6 | 19.2 mm/day | Stronger driving force |
| 1.2 mm/day | 1.0 | 1.2 mm/day | Drier, less-conductive state |
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. State the unit-gradient approximation
During free drainage of a sufficiently deep, fairly uniform profile without a shallow water table, the matric-head gradient may be small relative to the gravitational term. The magnitude of the total-head gradient can then be approximated by one, giving q≈K at the local state.
This is a conditional approximation. A fluctuating water table, layered profile, root extraction, infiltration front or strong texture contrast can make the gradient differ greatly from one.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Change the boundary condition
Keep K=12 mm/day but place the profile above a shallow water table so the pressure-head gradient offsets part of gravity. If the total gradient magnitude is 0.2, the flux is 2.4 mm/day, not 12.
| Scenario | Assumed gradient | Predicted flux | Main check |
|---|---|---|---|
| Free drainage | 1.0 | 12 mm/day | Deep profile and head data |
| Shallow-water-table influence | 0.2 | 2.4 mm/day | Pressure-head profile |
| Infiltration front | 2.0 | 24 mm/day | Transient head gradient |
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. See how layers create resistance
For steady saturated flow through two equal-thickness layers in series with K1=10 and K2=1, the effective conductivity is the harmonic mean, 2/(1/10+1/1)≈1.82, not the arithmetic mean 5.5.
Unsaturated layered flow is more complicated because K changes with head and interfaces can create capillary barriers. The calculation is a bottleneck lesson, not a complete transient model.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Connect potential, bypass and chemistry routes
Use the soil-water potential guide to construct the total-head gradient and separate matric, osmotic, gravitational and pressure terms. Use preferential flow and matrix bypass when rapid macropore transport violates a single-domain reading.
The guides to saturation extracts and salinity, sodicity and dispersion and gypsum and leaching show how solution and structure can alter flow pathways.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Choose measurements that match the question
Ksat can be measured in the laboratory or field, but sample disturbance and scale matter. Unsaturated K can be inferred from transient profiles, tension infiltrometers or fitted retention–conductivity models; each method carries assumptions.
Pair conductivity evidence with pressure-head measurements by depth and time. A conductivity curve without the field head gradient cannot determine actual flux.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Know the limits and common misconceptions
Hydraulic conductivity is not an immutable texture label. It depends on water state, structure, direction, temperature and sometimes chemistry. Ksat is not the same as infiltration rate, which also responds to surface and transient storage conditions.
The unit-gradient approximation does not mean that matric potential is zero. It means the chosen total-head gradient is being approximated by the gravitational contribution under a restricted drainage setting.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Use an evidence and source routine
Record coordinate and sign convention, depth, water content, pressure head, total head, gradient, K function and method, saturation state, layering, anisotropy, temperature, boundary conditions, water table, roots, macropores and observation interval.
USDA NRCS Irrigation Soil–Plant–Water Relationships distinguishes saturated from sharply water-dependent unsaturated conductivity. NRCS Soil Survey Technical Note 6 reviews Darcy flow and saturated conductivity. USDA ARS’s free-drainage study states the field conditions under which a unit gradient may occur.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Is q equal to K?
Only in magnitude when the total-head gradient magnitude is one under the stated sign convention.
Why does K fall so much as soil dries?
Air empties larger conductive pores first and breaks water-path continuity.
Can Ksat predict drainage time?
Not alone. The unsaturated K relation, storage, profile geometry and boundary gradients are also needed.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Continue with a dry-layer check
Place a 10 cm layer with K=6 mm/day above a 10 cm layer with K=0.6 mm/day and assume steady series flow. Calculate the harmonic effective K≈1.09 mm/day, then explain why a transient unsaturated interface may depart from that fixed-K result.
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