Phase Relations of Soils - Soil Mechanics - Civil Engineering (CE)
Introduction
Soil is a particulate material, not a homogeneous solid like steel or concrete. Natural soil deposits consist of solid particles (mineral grains and rock fragments) with water and air occupying the voids between particles. The quantities of water and air may change with ambient conditions and location. To analyse soil behaviour for engineering purposes it is useful to represent soil as a three-phase system and to quantify the amount of each phase using weights and volumes.
Three-phase system (solids, water and air)
The three phases are:
- Solids - mineral particles which occupy a volume Vs and have weight Ws.
- Water - liquid occupying volume Vw and having weight Ww.
- Air - gaseous phase occupying volume Va; the weight of air is negligible and often ignored in weight relations.
The total volume of a soil sample is the sum of the volumes of the three phases:
V = Vs + Vw + Va
Depending on the amounts of water and air the soil may be:
- Dry (no water, Vw = 0),
- Partially saturated (both water and air present),
- Fully saturated (no air, Va = 0).
For engineering analysis we derive relations between weights and volumes of these phases. These relations are grouped as:
- Volume relations
- Weight relations
- Inter-relations
Volume relations
The volume of solids Vs is taken as the reference. The basic volumetric quantities are defined below.
- Void ratio (e)- the ratio of the volume of voids to the volume of solids:
e = Vv / Vs, where Vv = Vw + Va.
- Porosity (n)- the ratio of the volume of voids to the total volume of soil:
n = Vv / V. Porosity is often expressed as a decimal or percentage.
- Relation between void ratio and porosity:
From V = Vs + Vv we obtain
n = e / (1 + e) and equivalently e = n / (1 - n).
- Degree of saturation (S)- the ratio of the volume of water to the volume of voids, expressed as a fraction or percentage:
S = Vw / Vv. Thus 0 ≤ S ≤ 1 (or 0% ≤ S ≤ 100%).
- Air content (ac) - the ratio of the volume of air to the volume of voids: ac = Va / Vv and therefore ac = 1 - S.
- Percentage air voids (na)- the ratio of the volume of air to the total volume:
na = Va / V = n · ac = n · (1 - S).
Weight (mass) relations and definitions
In soil mechanics the following weight and density related quantities are used:
- Weight of solids (Ws) - true weight of mineral particles in the sample.
- Weight of water (Ww) - weight of water contained in voids.
- Total weight (W) - W = Ws + Ww (weight of air neglected).
- Water content (w)- the ratio of weight of water to weight of solids:
w = Ww / Ws. This is often expressed as a percentage.
- Specific gravity of solids (Gs) - the ratio of the density of soil solids ρs to the density of water ρw:
Gs = ρs / ρw. Using weights and volumes, Ws = Gs · ρw · Vs.
- Unit weight (γ) - weight per unit volume: γ = W / V.
- Dry unit weight (γd) - unit weight of soil after removal of all moisture: γd = Ws / V.
- Saturated unit weight (γsat) - unit weight when S = 1 (no air present).
- Unit weight of water (γw) - commonly taken as 9.81 kN/m³ (or 9810 N/m³) in SI units.
Inter-relations between volume and weight quantities
Using the definitions above one can derive standard relations used frequently in design and calculations.
Relation between water content, degree of saturation, void ratio and Gs:
Start from w = Ww / Ws.
Ww = γw · Vw.
Ws = Gs · γw · Vs.
Therefore w = Vw / (Gs · Vs).
But Vw / Vs = S · e.
Hence w = (S · e) / Gs.
Unit weight relations (useful forms):
Express total unit weight γ in terms of Gs, e and w:
Ws = Gs · γw · Vs.
Ww = w · Ws = w · Gs · γw · Vs.
W = Ws + Ww = Gs · γw · Vs · (1 + w).
V = Vs · (1 + e).
Therefore γ = γw · Gs · (1 + w) / (1 + e).
From this:
γd = γw · Gs / (1 + e) (dry unit weight).
At full saturation (S = 1), w = e / Gs and
γsat = γw · (Gs + e) / (1 + e).
Effective (buoyant) unit weight of saturated soil:
γ' = γsat - γw.
Other useful relationships
- Porosity and void ratio: n = e / (1 + e) and e = n / (1 - n).
- Degree of saturation and water content: w = (S · e) / Gs.
- Air content and degree of saturation: ac = 1 - S.
- Percentage air voids: na = n · (1 - S).
Typical values and remarks
- Specific gravity Gs for most mineral soils lies between about 2.60 and 2.80; a commonly used value for quartz-rich soils is 2.65.
- Void ratio e for compacted sands may be around 0.4-0.8; for loose sands e may exceed 1.0; clays often have higher e values depending on structure and consolidation.
- Porosity n ranges from a few percent in dense rock fragments to >50% in very loose, organic or peat soils.
- Degree of saturation S controls many engineering properties (e.g., shear strength, compressibility, permeability); small changes in S can change behaviour significantly.
Worked example
Calculate the water content w for a soil sample with void ratio e = 0.75, degree of saturation S = 60% and specific gravity Gs = 2.65.
Begin with the relation w = (S · e) / Gs.
Substitute the given values. Use S as a decimal (0.60).
w = (0.60 × 0.75) / 2.65
w = 0.45 / 2.65
w ≈ 0.1698 (decimal) or 16.98%.
Applications and importance
Phase relations and index properties (e, n, S, w, Gs) are fundamental to geotechnical engineering. They are used to:
- Relate field measurements to in-situ stresses and densities.
- Compute unit weights, which are needed for stability and settlement analysis.
- Estimate permeability and consolidation properties since these depend on void spaces and degree of saturation.
- Assess susceptibility to volumetric changes (swelling, shrinkage) and to evaluate bearing capacity of foundations.
Summary
Modelling soil as a three-phase system (solids, water and air) provides a consistent framework to quantify soil state and to derive useful relations between volume and weight quantities. Key relations include e = Vv/Vs, n = e/(1+e), S = Vw/Vv, and w = (S·e)/Gs. From these, unit weights and other engineering parameters are obtained and applied in design and analysis of geotechnical problems.
- Percentage air voids (na)- the ratio of the volume of air to the total volume:
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