The Three-Phase System of Soil
Every soil, at any moment, is really three ingredients sharing one volume: solids, water, and air. This single idea is the foundation of nearly every numerical Loksewa asks you to solve.
V = Vs + Vw + Va | Vv = Va + Vw | W = Ws + Ww (weight of air is negligible)
- Understand the three-phase system
- Draw the phase diagram from memory
- Calculate e, n, w, Sr
- Mass-volume & weight-volume relations
- Specific gravity of soil (Gs)
- Lab & field density methods
- Solve Loksewa numericals
The Three Phases
Natural soil consists of three phases: Solids, Water, and Air.
Weight of air is negligible, so it never appears on the weight side of the diagram - only on the volume side.
Engineering Importance
The relative proportion of these three phases governs almost every soil property an engineer designs against.
| Property | Depends on |
|---|---|
| Settlement | Water + Air |
| Strength | Solids |
| Permeability | Voids |
| Compressibility | Air + Water |
| Bearing capacity | Void ratio |
The Three Components
Solid Phase
- Sand, silt, clay, gravel
- Organic matter
- Carries structural load
Water Phase
- Occupies voids
- Controls strength & compressibility
Air Phase
- Occupies remaining voids
- Present in unsaturated soils only
Important Symbols
| Quantity | Symbol |
|---|---|
| Volume of solids | Vs |
| Volume of water | Vw |
| Volume of air | Va |
| Volume of voids | Vv |
| Total volume | V |
| Weight of solids | Ws |
| Weight of water | Ww |
| Total weight | W |
Void Ratio (e)
Definition: ratio of volume of voids to volume of solids.
Higher e means more voids -> lower strength and higher compressibility. (No upper limit.)
| Soil | Typical void ratio |
|---|---|
| Dense sand | 0.3 - 0.5 |
| Loose sand | 0.6 - 0.9 |
| Clay | 0.8 - 1.5 |
| Organic soil | > 2 |
Porosity (n)
Definition: ratio of volume of voids to total volume.
Unlike void ratio, porosity is capped: its maximum possible value is 100%.
Void Ratio vs. Porosity
| Void ratio (e) | Porosity (n) |
|---|---|
| Voids / Solids | Voids / Total volume |
| No upper limit | Maximum = 100% |
Water Content (w)
Definition: ratio of weight of water to weight of solids.
| Soil | Typical water content |
|---|---|
| Dry sand | 2 - 10% |
| Moist sand | 10 - 20% |
| Clay | 20 - 70% |
| Organic soil | > 100% (possible) |
Degree of Saturation (Sr)
Definition: percentage of voids filled with water.
(w in decimal form.) Sr = 0% is bone-dry soil; Sr = 100% is fully saturated soil.
Mass-Volume RelationshipADDED
These are the "density" definitions - mass of each phase divided by a chosen volume. They describe how tightly packed a soil is, and how that changes with water content.
| Quantity | Formula | Meaning |
|---|---|---|
| Bulk density | rho = M / V | Mass of soil (solids + water) per total volume |
| Dry density | rho_d = Ms / V | Mass of solids only per total volume |
| Saturated density | rho_sat = (Ms + Mw,sat) / V | Bulk density when all voids are filled with water |
| Submerged density | rho' = rho_sat - rho_w | Effective density when soil is under water (buoyancy removed) |
Key relation: rho_d = rho / (1 + w)
Weight-Volume RelationshipADDED
The same idea, expressed in unit weights (gamma = rho x g) - the form most commonly used directly in Loksewa numericals.
| Quantity | Formula |
|---|---|
| Bulk unit weight | gamma = W / V |
| Dry unit weight | gamma_d = Ws / V = gamma / (1 + w) |
| Saturated unit weight | gamma_sat = [(Gs + e) / (1 + e)] x gamma_w |
| Submerged (buoyant) unit weight | gamma' = gamma_sat - gamma_w = [(Gs - 1) / (1 + e)] x gamma_w |
gamma_w (unit weight of water) = 9.81 kN/m3 (or 1 g/cm3) - memorize this constant, it appears in almost every numerical.
Specific Gravity of Soil (Gs)ADDED
Definition: ratio of the unit weight of soil solids to the unit weight of water at 4 deg C.
Gs is a property of the mineral itself - it does not depend on how loosely or densely the grains are packed, which is why it stays nearly constant for a given soil type.
| Soil type | Typical Gs |
|---|---|
| Sand | 2.65 - 2.67 |
| Silt | 2.67 - 2.70 |
| Clay | 2.70 - 2.80 |
| Organic soil | < 2.00 |
Laboratory Determination of Specific GravityADDED
The standard lab test uses a Pycnometer (specific gravity) bottle - a simple, favorite Loksewa numerical setup.
- Weigh the empty, dry pycnometer -> W1
- Add a dry soil sample and weigh -> W2
- Fill the remaining space with water, remove air bubbles, and weigh -> W3
- Empty and refill the pycnometer with water only, weigh -> W4
Other accepted methods: Density bottle method (fine-grained soil) and Gas jar / measuring flask method (used in some field labs).
Field Density MethodsADDED
Used to find the in-place bulk density of a compacted fill or natural ground - essential for quality control on embankments and road sub-grades.
Sand Replacement Method
- Dig a small hole, weigh the excavated soil
- Fill the hole with calibrated, known-density sand from a pouring cylinder
- Volume of hole = volume of sand poured in
Core Cutter Method
- A steel cylinder of known volume is driven into the soil
- Extracted, trimmed flush, and weighed
- Best suited to soft, cohesive soils (not gravelly ground)
Other field methods used in practice: rubber balloon method and nuclear density gauge (fast, non-destructive).
Memory Box
- V = Vs + Vv = Vs + Va + Vw
- W = Ws + Ww
- e = Vv / Vs
- n = Vv / V = e / (1+e)
- w = (Ww/Ws) x 100%
- Sr = (Vw/Vv) x 100%
- Sr = (w x Gs) / e
- Gs = Ws / (Vs x gamma_w)
- gamma_d = gamma / (1+w)
- gamma_sat = [(Gs+e)/(1+e)] x gamma_w
- gamma' = gamma_sat - gamma_w
- Air has negligible weight
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