CELE Geotechnical Engineering — Soil Properties and Phase RelationshipsSummary

Soil consists of three distinct components: solid particles (Vs, Ws), water (Vw, Ww), and air voids (Va). The total volume V = Vs + Vv, where void volume Vv = Vw + Va. The total weight is W = Ws + Ww (air weight is negligible). A phase diagram shows these volumes and weights stacked vertically, providing a visual framework for all phase relationship calculations. Understanding this physical model is essential before attempting any calculation.

Void ratio e = Vv/Vs is the ratio of void volume to solid volume. Porosity n = Vv/V is the ratio of void volume to total volume. These parameters describe the same physical property (how 'loose' or 'dense' the soil is) but use different reference volumes. They are related by the identities: e = n/(1−n) and n = e/(1+e). For example, if e = 0.60, then n = 0.60/(1.60) = 0.375 or 37.5%. Conversely, if n = 0.40, then e = 0.40/(1−0.40) = 0.667. Both parameters always satisfy 0 ≤ n < 1 and e ≥ 0. Typical ranges: loose sand e ≈ 0.8–1.0, dense sand e ≈ 0.5–0.7, clay e ≈ 0.6–1.2.

Water content w = Ww/Ws is a weight ratio, defined as the mass of water divided by the mass of solid particles. It is expressed as a decimal or percentage (e.g., w = 0.15 or w = 15%). Critically, w can exceed 1.0 (100%) — for example, a soft clay or organic soil may have w = 1.50 (150%), meaning the water mass equals 1.5 times the solid mass. This is not a volume fraction; it is purely a weight ratio. Do NOT confuse w with S (degree of saturation). Water content is determined in the laboratory by drying a sample and measuring weight loss: w = (Ww)/(Ws) = (Wwet − Wdry)/(Wdry).

Degree of saturation S = Vw/Vv is the volume ratio of water to total voids. It ranges from 0 (dry soil, no water) to 1 (saturated, all voids filled with water). Values 0 < S < 1 describe partially saturated (moist) soil. For example, S = 0.6 means 60% of the voids contain water and 40% contain air. This is a volume-based parameter, not a weight-based one. In the field, S is related to e, w, and Gs by the master identity: Se = wGs. During the drying process in the laboratory, S decreases as water evaporates, eventually reaching S = 0 for fully dry soil.

Specific gravity Gs = γs/γw is the ratio of the density (or unit weight) of soil solids to the unit weight of water. It is a dimensionless number, typically 2.60–2.75 for mineral soils. Most commonly, Gs = 2.65 or 2.70 is assumed unless test data specify otherwise. For context: quartz (SiO₂) has Gs ≈ 2.65, feldspar ≈ 2.60, clay minerals ≈ 2.70–2.80, and organic soils may have Gs < 2.60. Gs is determined by pycnometer testing (ASTM D854 or PH Bureau of Soils equivalent). Note that Gs is a property of the mineral solids alone, independent of the soil's void ratio or saturation state.

This is the single most important relationship in soil phase relationships. Starting from Se = Vw/Vs × (V − Vs)/Vw = (Vw/Vv) × (Vv/Vs) and w = Ww/Ws, and using Gs = γs/γw = (Ws/Vs)/(Ww/Vw) × (ρw/ρw), the identity Se = wGs relates four fundamental parameters: saturation (S), void ratio (e), water content (w), and specific gravity (Gs). This relationship is dimensionally correct and holds for all soils, saturated or unsaturated. Use it to find any one parameter when the other three are known. For saturated soil (S = 1), this simplifies to e = wGs, which is extremely useful for quick calculations.

Dry unit weight γdry = Ws/V is the weight of solid particles per unit total volume. It represents the unit weight of the soil if all water and air were removed, and equals γdry = Gsγw/(1+e). As e increases (soil becomes looser), γdry decreases. For a given soil and Gs, γdry is inversely proportional to void ratio. Typical ranges: loose sand γdry ≈ 14–16 kN/m³, dense sand γdry ≈ 17–19 kN/m³, clay γdry ≈ 13–18 kN/m³. In the field, soil compaction (reducing e) increases γdry, which is why compaction specifications are often written as 'achieve 95% of maximum dry unit weight' as determined by the Standard Proctor test (ASTM D698).

Moist unit weight γ = W/V = (Ws + Ww)/V is the total weight (solids plus water) per unit total volume. It is the weight of soil 'as is' in the field, containing both solids and water at whatever saturation level exists. The simplest formula is γ = γdry(1+w), derived by expressing Ww = wWs and noting W = Ws(1+w), so γ = Ws(1+w)/V = (Ws/V)(1+w) = γdry(1+w). Alternatively, γ = (Gsγw + Seγw)/(1+e). Typical ranges: γ ≈ 18–22 kN/m³ for most natural soils. This is the unit weight you use for calculating weight of a fill or embankment at in-situ water content.

Saturated unit weight γsat = (Ws + Wwat)/V is the unit weight when all voids are filled with water (S = 1). It equals γsat = (Gs + e)γw/(1+e). Notice that γsat depends on both Gs and e: increasing e (looser soil) actually decreases γsat slightly because the 'extra' e is filled with water (γw ≈ 9.81 kN/m³) rather than solids (γs = Gsγw ≈ 26–27 kN/m³). For typical soils with Gs = 2.65–2.70 and e = 0.5–0.8, γsat ≈ 19–21 kN/m³. Below the water table (saturation line), use γsat for weight calculations. Above the water table (unsaturated zone), use γmoist or γdry. This distinction is crucial in effective stress calculations for multi-layer profiles.

Submerged unit weight γ′ = γsat − γw is the 'apparent' weight of saturated soil submerged in water (e.g., below the water table or in a reservoir). It represents the weight difference between solid and water phases. Derived by Archimedes' principle: the buoyant force equals the weight of displaced water (γw), so the net weight per unit volume is γsat − γw. Substituting γsat = (Gs + e)γw/(1+e), we get γ′ = [(Gs + e)/(1+e) − 1]γw = [(Gs − 1)/(1+e)]γw ≈ (0.65 to 1.0)γw for typical soils. For Gs = 2.65 and e = 0.65, γ′ ≈ (1.65/1.65)(9.81) ≈ 9.8 kN/m³, about equal to γw. This low value is why pore pressure (u) carries so much of the stress in saturated soil — the soil skeleton (γ′) is very light.

A phase diagram is a vertical stack diagram showing the three soil phases side by side: volumes on the left (Vs, Vw, Va) and weights on the right (Ws, Ww). The total height represents either V (total volume) or W (total weight). From this diagram, all phase ratios are visual: e = Vv/Vs appears as the ratio of (Vw + Va) to Vs; w = Ww/Ws appears as the ratio of Ww to Ws. The diagram reinforces that Wair ≈ 0 (negligible), so W ≈ Ws + Ww. A well-drawn phase diagram often solves half of a board exam problem because it immediately shows which unknowns are related and which ratios apply. Many students who draw the diagram before calculating find errors automatically.

Bearing capacity formulas (Terzaghi, Meyerhof, etc.) depend on γ (unit weight of soil) to calculate the self-weight contribution to bearing capacity. A saturated clay (S = 1, γsat) carries less bearing capacity than a partially saturated clay at higher γmoist because of pore pressure. The effective stress governing shear strength is σ′ = σ − u, where σ is calculated using γsat and u is the pore pressure. Designers must correctly identify whether soil is above or below the water table (use γmoist or γsat) and whether pore pressure development occurs during loading. Phase relationships determine these inputs.

Settlement of compressible soils (clays, silts) is governed by consolidation, which depends on the initial void ratio e₀ and the void ratio change Δe. The initial condition is characterized by the phase relationships: given γmoist and w, you solve for e₀ using γmoist = (Gsγw + Seγw)/(1+e) or γdry = Gsγw/(1+e). As consolidation occurs under applied load, e decreases, and the soil compresses. The final void ratio e_f is predicted by consolidation theory. Phase relationships provide the before-and-after 'snapshots' needed to calculate settlement ΔH = (Δe/(1+e₀))H.

Slope stability calculations (limit equilibrium or FEM) require accurate unit weights and pore pressures. A slope above the water table uses γmoist; below the water table, use γsat and include pore pressure u in the effective stress balance. The degree of saturation S (from Se = wGs if not directly measured) determines whether the soil is drained or undrained. In undrained analysis (rapid loading, no drainage), the shear strength is constant; in drained analysis (slow seepage, full drainage), shear strength increases with effective stress. Phase relationships determine the saturation profile and hence which analysis applies.

Standard Proctor and Modified Proctor tests establish the γd(max) and w(opt) for a soil (ASTM D698 or PH equivalent). Field compaction specifications (e.g., '98% Standard Proctor density') require achieving γdry ≥ 0.98 × γd(max) at field water content w. The contractor measures in-situ density (typically by sand cone or nuclear density gauge) as γmoist, then calculates γdry = γmoist/(1+w). If γdry ≥ 0.98 × γd(max), the specification is met. Phase relationships (specifically the formula γdry = γmoist/(1+w)) are applied on every construction inspection for embankments, road bases, and earth dams.

In multi-layered soil profiles, different layers have different saturation conditions. Above the water table (capillary zone or vadose zone), use γmoist or γdry; below the phreatic surface (water table), use γsat and include pore pressure u. The effective stress σ′ = σ − u is calculated by integrating γsat from depth and subtracting the pore pressure from the water table. Phase relationships allow you to estimate u if piezometers are not available: in a capillary zone, S < 1 but u may be negative (matric suction); below the water table, u > 0 and increases linearly with depth (u = γwz from the water table). Accurate phase relationships are essential for correct effective stress profiles and hence correct predictions of settlement and stability.

Earth dams are constructed in lifts (layers) with controlled compaction (high γdry to reduce permeability and increase strength). Designers calculate the weight of each lift using γmoist or γsat depending on in-situ conditions. Seepage analysis (through the dam and into the foundation) requires the permeability of the soil, which decreases with compaction (lower e). Phase relationships determine the void ratio after compaction: if target γdry is specified, then e = Gsγw/γdry − 1. The permeability coefficient k, in turn, is a function of e. Thus, phase relationships link compaction specifications (γdry) to seepage predictions (k). For operational (steady-seepage) analysis, phreatic lines (water table locations within the dam) are mapped, and γsat is applied in saturated zones while γmoist is used above the phreatic line.

Boring reports present soil descriptions and measured parameters: γ (field unit weight), w (laboratory water content), e (void ratio from laboratory tests or calculated), and S (degree of saturation if computed). All these parameters are related through phase relationships. When reading a boring log, cross-check consistency: if γmoist, w, and Gs are provided, verify that S = wGs/e is physically reasonable (0 ≤ S ≤ 1). If one parameter seems wrong, use phase relationships to back-calculate and flag it for quality control. This is a practical skill used by engineers during site investigation review.

As a clay dries (w decreases, S decreases), it shrinks (e and V decrease). Simultaneously, γdry may increase if the solid particles become more densely packed. The relationship Se = wGs shows that as w → 0, either S → 0 or e → 0 (or both). In practice, e decreases slightly due to capillary suction and matric stress, and S decreases significantly as water evaporates. The volume shrinkage is approximately ΔV/V ≈ Δw (a rule of thumb for clays). Conversely, if a dry clay is wetted, w increases, and if confined, pore pressure rises (swelling pressure). Phase relationships quantify these changes and are used in design of structures on expansive soils (e.g., in arid regions like parts of Central Luzon, Philippines).

Subgrades for pavements (roads, airfields) must achieve minimum compaction (minimum γdry) to provide adequate support. Field measurements provide γ (measured by sand cone or nuclear gauge) and w (oven drying of sample). The contractor then calculates γdry = γ/(1+w) and compares to specification (typically 95–100% of laboratory γd(max)). Phase relationships (specifically γ = γdry(1+w)) are applied daily in field quality assurance and quality control (QA/QC). Failure to meet compaction specifications results in pavement failure and project rejection.

Geotechnical FEM software (Plaxis, RS2, ABAQUS) requires input of soil unit weights (γdry, γsat, γ′), void ratio e, porosity n, and permeability k. These parameters are derived from phase relationships. For unsaturated soil analysis, the saturation S is required as an input or calculated from w and e. The FEM then solves equilibrium (forces), seepage (Darcy's law with k), and consolidation (governing pore pressure changes). Errors in phase relationships propagate through the entire analysis, leading to incorrect stresses, settlements, and factor of safety. Careful application of phase relationships at the pre-processing (input) stage ensures reliable FEM predictions.