After this chapter, you should be able to
- Relate void ratio, porosity, degree of saturation and water content.
- Calculate dry, bulk and saturated unit weights from a phase model.
- Explain why compaction response depends on material and effort.
- Apply Darcy's law within its laminar-flow domain.
- Distinguish discharge velocity from seepage velocity.
Engineering context and evidenceSource §Lesson 03 · Engineering context and evidence · NHI-06-088 Chapters 2, 4 and 5
The three-phase model provides a disciplined accounting system for solids, water and air. It underpins interpretation of density, compaction, saturation and hydraulic behaviour. Compaction changes fabric and void ratio by mechanical effort; consolidation is a time-dependent volume response to stress and drainage and must not be used as a synonym.
Core principles and terminologySource §Lesson 03 · Core principles and terminology · NHI-06-088 Chapters 2, 4 and 5
Water content can initially help particles rearrange under compactive effort, while excess water occupies space and limits dry density for a given method. Hydraulic conductivity depends on pore geometry, fluid properties, fabric and saturation. Darcy flow is a continuum approximation for laminar conditions; fissures and preferential paths can dominate field behaviour.
- Void ratio, e
- Volume of voids divided by volume of solids.
- Porosity, n
- Volume of voids divided by total volume.
- Degree of saturation, S
- Volume of water divided by volume of voids.
- Hydraulic conductivity, k
- Coefficient relating hydraulic gradient to Darcy discharge velocity for stated material and fluid conditions.
Equations, conventions and valid useSource §Lesson 03 · Equations, conventions and valid use · NHI-06-088 Chapters 2, 4 and 5
Use S as a decimal in the equation and a consistent specific gravity Gs. The relation assumes the water and solid mass definitions used in the phase model.
The second expression gives bulk unit weight at the stated degree of saturation. Set S = 1 for saturated unit weight.
Q is volumetric discharge through gross area A. Darcy velocity is Q/A; average seepage velocity is approximately Q/(nA) when the continuum assumptions apply.
Engineering workflowSource §Lesson 03 · Engineering workflow · NHI-06-088 Chapters 2, 4 and 5
- Declare SI units and whether saturation is entered as a fraction or percentage.
- Check that e > 0, 0 ≤ S ≤ 1, Gs > 0 and the water unit weight matches the unit system.
- Calculate porosity and water content before unit weights as an internal consistency check.
- For compaction, name the laboratory or field method and compare like-for-like moisture-density data.
- For flow, define total-head points, gradient direction, specimen length and gross area.
- Check for laminar conditions, anisotropy, side leakage, cracking and scale effects.
- Report values with test condition and uncertainty rather than as universal soil constants.
| Quantity | Definition | Frequent confusion |
|---|---|---|
| Water content w | Water mass / dry-solid mass | Degree of saturation |
| Porosity n | Void volume / total volume | Void ratio e |
| Dry unit weight γd | Dry-solid weight / total volume | Bulk unit weight γ |
| Darcy velocity | Q / gross area | Average pore-water velocity |
Verified teaching exampleSource §Lesson 03 · Verified teaching example · NHI-06-088 Chapters 2, 4 and 5
Phase-state and flow consistency check
For Gs = 2.65, e = 0.65, S = 75% and γw = 9.81 kN/m3, find n, w, γd and bulk γ. Separately, find Q for k = 2.0×10−6 m/s, Δh = 1.5 m, L = 4.0 m and A = 3.0 m2.
- Phase fractions
n = 0.65/1.65; w = 0.75×0.65/2.65
n = 0.394; w = 18.4% - Unit weights
γd = 2.65×9.81/1.65; γ = (2.65+0.75×0.65)×9.81/1.65
γd = 15.76; γ = 18.65 kN/m3 - Darcy flow
i = 1.5/4 = 0.375; Q = 2×10−6×0.375×3
Q = 2.25×10−6 m3/s = 0.194 m3/day
Result. The phase quantities are internally consistent and the laminar-flow teaching calculation gives Q = 2.25×10−6 m3/s.
Phase relationships and Darcy flow
Reproduce the teaching equations with explicit saturation and SI-unit conventions.
- Inputs
- Gs, e, S and γw · k, Δh, L and gross area A · Porosity for seepage velocity
- Outputs
- n, w, γd, γbulk and γsat · Gradient, discharge and average seepage velocity
- Status states
- Complete teaching case · Invalid or non-finite input · Outside stated method domain
- Validation
- Implemented against the supplied worked example; independent technical approval pending
Phase Relationships and Darcy Flow
A transparent SI-unit teaching check for phase identities and one-dimensional laminar Darcy flow.
Porosity is 0.394 and Darcy discharge is 2.250e-6 m³/s.
- Porosity n
- 0.3939
- Water content w
- 18.40%
- Dry unit weight γd
- 15.755 kN/m³
- Bulk unit weight γ
- 18.654 kN/m³
- Saturated unit weight γsat
- 19.620 kN/m³
- Hydraulic gradient i
- 0.3750
- Discharge Q
- 2.250e-6 m³/s
- Average seepage velocity
- 1.904e-6 m/s
Show calculation trail
n = e/(1+e) = 0.3939w = Se/Gs = 18.40%γd = Gsγw/(1+e) = 15.755 kN/m3γ = (Gs+Se)γw/(1+e) = 18.654 kN/m3i = Δh/L = 0.3750; Q = kiA = 2.250e-6 m3/s
Failure modes and engineering judgementSource §Lesson 03 · Failure modes and engineering judgement · NHI-06-088 Chapters 2, 4 and 5
- Entering 75 instead of 0.75 for saturation in an equation.
- Mixing density in kg/m³ with unit weight in kN/m³.
- Equating laboratory optimum moisture content with a universal field target.
- Applying Darcy's law to an open fissure without checking the flow regime.
- Calling Q/A the actual velocity through pores.
Key points
- Phase relationships are accounting identities with strict definitions.
- Compaction and consolidation describe different mechanisms.
- Hydraulic conductivity is condition-, direction- and scale-dependent.
- Darcy calculations need a defined head gradient, area and applicability check.
Source references recorded by the supplied chapter
- FHWA NHI-06-088, Soils and Foundations Reference Manual, Volume I, Chapters 2, 4 and 5.