Compaction, consolidation and shear strength

In short

Compaction, consolidation and shear strength are the three behavioural pillars of soil mechanics: compaction is the rapid densification of soil by mechanical energy that expels air, consolidation is the slow expulsion of water under sustained load, and shear strength is the soil's resistance to sliding failure. Together they decide how much an embankment settles, how long a clay foundation keeps settling, and whether a slope, footing or excavation stands up. Every quantitative design in geotechnical practice - allowable bearing pressure, settlement checks, embankment stability, pavement subgrade acceptance - draws on these parameters, obtained per IS 2720 laboratory tests. The topic carries the heaviest weight in GATE Civil (Geotech) and is standard ground in interviews at L&T, AFCONS, NHAI, Tata Projects, Gammon, AECOM, consultancies and all state PWD/irrigation departments.

Explained

Compaction: principles and laboratory tests

• Compaction is densification by expelling air using mechanical energy (rolling, ramming, vibration) at essentially unchanged water content; it is immediate and man-made. Dry density rises, void ratio falls, air voids fall; saturation rises but the soil never becomes fully saturated by compaction.
• Objectives: increase shear strength and bearing capacity, reduce compressibility and future settlement, reduce permeability, control swelling/shrinkage and frost susceptibility.
• Compaction curve: plot dry density γd against water content w. It rises to a peak - maximum dry density (MDD) at the optimum moisture content (OMC) - and then falls. Dry of OMC, capillary suction and grain friction resist packing and added water lubricates; beyond OMC, water occupies pore space that soil grains could have filled.
• Standard Proctor test (IS 2720 Part 7): 1,000 cm³ mould, 2.6 kg rammer, 310 mm drop, 3 layers × 25 blows → compactive energy ≈ 592-595 kJ/m³.
• Modified Proctor test (IS 2720 Part 8): same mould, 4.89 kg rammer, 450 mm drop, 5 layers × 25 blows → ≈ 2,700 kJ/m³, about 4.5 times standard energy. Higher energy gives higher MDD at lower OMC; the peak shifts up and to the left.
• Zero air voids (ZAV) line / saturation line: the theoretical γd if all voids were water-filled. The compaction curve always lies to its left and roughly parallel; a point on or right of it means a computational error.
• Effect of soil type: well-graded coarse soils give high MDD (≈ 20-22 kN/m³) at low OMC (≈ 7-12%); uniform fine sands and heavy clays give low MDD (≈ 14-17 kN/m³) at high OMC (≈ 20-30%).
• Compaction versus consolidation: compaction expels air, is quick, applies to partly saturated soil, and is produced by dynamic/impact energy; consolidation expels water, is slow, applies to saturated soil, and is produced by static sustained load.

Field compaction, control and compacted soil behaviour

• Equipment selection: smooth-wheeled rollers for gravel/sand and finishing; sheepsfoot (pad-foot) rollers for cohesive soils (kneading action); pneumatic tyred rollers for a wide range including sandy clay; vibratory rollers for cohesionless sands and gravels; rammers/plate compactors in confined trenches and backfill.
• Controlling variables: water content (compact near OMC, usually OMC ± 2%), layer thickness (loose lift typically 200-300 mm), number of passes (typically 4-8), roller weight and contact pressure, speed.
• Relative compaction (degree of compaction) = field γd / laboratory MDD × 100. Typical specifications: embankment body ≥ 95% of laboratory MDD by heavy compaction (IS 2720 Part 8), subgrade and top 500 mm of road ≥ 97% (MoRTH Specifications for Road and Bridge Works), earth dam shells and cores per project specification, usually 95-98%.
• Field density tests: core cutter (IS 2720 Part 29) for soft cohesive soil free of gravel; sand replacement (IS 2720 Part 28) general purpose; water/rubber balloon method; nuclear density gauge for rapid non-destructive checks. Water content by oven drying (105-110 °C), rapid moisture meter or infra-red.
• Relative density (density index) Id - for cohesionless soils, compares in-situ void ratio with the loosest and densest states (IS 2720 Part 14); do not confuse it with relative compaction.
• Dry side versus wet side of OMC: compaction dry of optimum gives a flocculated structure - higher strength and modulus at once, higher permeability, but high swell potential on wetting. Wet of optimum gives a dispersed structure - lower permeability, more ductile, less swell and less prone to cracking under differential settlement, though it shrinks more on drying; hence dam cores are placed slightly wet of OMC and pavement subgrades near or slightly dry of OMC.
• Over-compaction: compacting wet of OMC with heavy plant can cause heaving/"rubber" subgrade and loss of density.
• CBR (California Bearing Ratio, IS 2720 Part 16) is measured on specimens compacted to field density and moisture, soaked 96 hours; it feeds flexible pavement design under IRC 37.

Consolidation: theory, parameters and settlement

• Consolidation is the gradual reduction in volume of a saturated soil under sustained load caused by the expulsion of pore water; load transfers from pore water to the soil skeleton over time. Governed by effective stress: σ′ = σ − u.
• Total settlement = immediate (elastic distortion) + primary consolidation (pore-water expulsion) + secondary consolidation (creep at constant effective stress).
• Oedometer / consolidation test (IS 2720 Part 15): a 60-75 mm diameter, 20-25 mm thick specimen is confined in a ring between porous stones and loaded in increments (each held 24 h), typically 10, 25, 50, 100, 200, 400, 800 kPa, then unloaded. One-dimensional strain, two-way drainage.
• e-log σ′ plot: the virgin compression line is a straight line of slope compression index Cc; unload-reload gives the flatter recompression/swelling index Cr (Cs), typically Cc/5 to Cc/10.
• Preconsolidation pressure σ′c: the maximum past effective stress, found by Casagrande's construction (bisector of the angle between the horizontal through the point of maximum curvature and the tangent there, intersected with the virgin line extended).
• Overconsolidation ratio OCR = σ′c / σ′0. OCR = 1 normally consolidated (NC); OCR > 1 overconsolidated (OC) - less compressible, often from past erosion, desiccation or ice loading; OCR < 1 underconsolidated - still consolidating under its own weight (recent deltaic deposits, dredged fill).
• Terzaghi's 1-D theory - assumptions: fully saturated homogeneous soil; soil grains and water incompressible; Darcy's law valid; k and av constant; one-dimensional flow and compression; small strains; a unique linear e-σ′ relation; load applied instantaneously.
• Governing equation: ∂u/∂t = cv ∂²u/∂z², solved for the degree of consolidation U as a function of the time factor T = cv t / d², where d is the longest drainage path (= H/2 for double drainage, H for single drainage).
• cv from the test curve: Casagrande's logarithm-of-time fitting (t50, T50 = 0.197) and Taylor's square-root-of-time fitting (t90, T90 = 0.848). cv falls as plasticity rises - roughly 10⁻⁸ to 10⁻⁶ m²/s for clays.
• Secondary consolidation: Δe = Cα × log(t2/t1) per log cycle after primary consolidation ends; significant in organic soils, peat and highly plastic clays.
• Accelerating consolidation: preloading, surcharge, sand drains / prefabricated vertical drains (PVDs) which shorten the drainage path and allow radial flow, vacuum consolidation. (Detail of ground treatment belongs to ground improvement.)

Shear strength: Mohr-Coulomb and effective stress

• Shear strength is the maximum resistance to shear stress before failure; it comes from cohesion (electro-chemical bonding, cementation) and internal friction (interlocking and sliding of grains, proportional to normal effective stress).
• Mohr-Coulomb failure criterion: τf = c + σ tanφ (total stress) and the correct effective-stress form τf = c′ + σ′ tanφ′. Shear strength is fundamentally controlled by effective stress.
• Mohr circle: plot of stress state; failure occurs when the circle touches the failure envelope. Failure plane inclination α = 45° + φ/2 to the major principal plane.
• Typical values: loose sand φ′ ≈ 28-30°, dense sand/gravel φ′ ≈ 35-45°; NC clay c′ ≈ 0 with φ′ ≈ 20-28°; soft clay undrained strength cu ≈ 25-50 kPa, stiff clay cu > 100 kPa.
• Critical void ratio: dense sand dilates and loose sand contracts on shearing; at the critical void ratio there is no volume change. Dense sand shows a peak then a lower residual strength.
• Drainage conditions and test types (the single most examined comparison):
  • UU (unconsolidated-undrained), IS 2720 Part 11: no drainage at any stage; quick; gives cu (φu ≈ 0 for saturated clay). Used for short-term/end-of-construction stability on saturated clay.
  • CU (consolidated-undrained), IS 2720 Part 12: consolidate under cell pressure, then shear undrained, with pore pressure measurement to get c′, φ′. Used for sudden drawdown, rapid loading of a consolidated deposit.
  • CD (consolidated-drained), IS 2720 Part 12: drained throughout, very slow; gives c′, φ′ directly. Used for long-term stability, slow loading and sands.
• Laboratory and field tests:
  • Direct shear / box shear (IS 2720 Part 13): 60 × 60 mm box; simple, fast, suited to sands; drawbacks - failure plane forced, non-uniform stress, no pore-pressure control, drainage not controllable.
  • Triaxial compression (IS 2720 Parts 11 and 12): cylindrical specimen (38 mm or 100 mm) under cell pressure σ3 with deviator stress added; controlled drainage and pore pressure; the standard for parameters.
  • Unconfined compression (IS 2720 Part 10): σ3 = 0, cu = qu/2; only for saturated cohesive soil that stands unsupported.
  • Vane shear (IS 4434 / IS 2720 Part 30): in-situ cu for soft sensitive clay; gives sensitivity = undisturbed cu / remoulded cu.
  • SPT (IS 2131) and static cone penetration test (IS 4968) give correlated φ and relative density for sands; the SPT N value is corrected for overburden and dilatancy.
• Pore pressure parameters (Skempton): Δu = B[Δσ3 + A(Δσ1 − Δσ3)]; B ≈ 1 for fully saturated soil (B is also the saturation check in a triaxial test).
• Stress path and p-q plot: Kf line gives tanα = sinφ′ and the intercept a = c′ cosφ′ - a common numerical question.
• Thixotropy - regain of strength with time at constant water content after remoulding; important for driven piles in clay (set-up).
• Liquefaction: saturated loose sand under cyclic (seismic) loading builds pore pressure until σ′ → 0 and shear strength vanishes. Assessed per IS 1893 provisions with SPT/CPT-based procedures; relevant across the Indo-Gangetic plain, Kachchh and Assam.

Codes, standards and how the three interlock

• IS 2720 (Methods of test for soils) governs all laboratory work - Part 7 light compaction, Part 8 heavy compaction, Part 10 UCS, Parts 11-12 triaxial, Part 13 direct shear, Part 15 consolidation, Part 16 CBR, Parts 28-29 field density, Part 30 laboratory vane.
• IS 1498 classification; IS 6403 bearing capacity (uses c and φ); IS 8009 Part 1 settlement of shallow foundations (uses Cc, cv); IS 1904 general foundation design requirements; IS 2720 Part 40 free swell index for expansive soil; IS 1893 Part 1 seismic including liquefaction; IRC 37 flexible pavements (CBR); MoRTH Specifications earthwork compaction acceptance; IS 7894 earth dam stability. Code revisions occur periodically - verify the current amendment for design use.
• The chain in practice: compaction fixes the as-placed density and hence the strength and compressibility of fill; consolidation parameters fix how much and how fast a saturated clay below the fill settles; shear strength parameters fix bearing capacity and stability. Consolidation also raises shear strength - which is the basis of staged construction of embankments on soft clay.

Key points

• Compaction - expulsion of air by mechanical energy at near-constant water content; immediate densification.
• Consolidation - expulsion of pore water from saturated soil under sustained load; time-dependent.
• OMC/MDD - the water content giving the greatest dry density for a given compactive effort; both shift with energy.
• Compactive energy - standard Proctor ≈ 592 kJ/m³, modified Proctor ≈ 2,700 kJ/m³; more energy → higher MDD, lower OMC.
• ZAV line - theoretical fully saturated dry density; the compaction curve lies entirely to its left.
• Relative compaction - field dry density as a percentage of laboratory MDD; typically ≥ 95-97% in road and embankment works.
• Dry-of-optimum compaction - flocculated, stronger and more permeable but swells; wet-of-optimum - dispersed, less permeable, more ductile.
• Effective stress - σ′ = σ − u; it alone governs volume change and shear strength.
• Compression index Cc - slope of the virgin e-log σ′ line; Cr for recompression, about Cc/5 to Cc/10.
• Preconsolidation pressure - maximum past effective stress from Casagrande's construction; OCR = σ′c/σ′0.
• Coefficient of consolidation cv - rate parameter in T = cv t/d²; from t50 (T = 0.197) or t90 (T = 0.848).
• Drainage path d - half the layer thickness for double drainage, full thickness for single; settlement time varies as d².
• mv and av - coefficient of volume compressibility mv = av/(1+e0); av = Δe/Δσ′.
• Mohr-Coulomb - τf = c′ + σ′ tanφ′; failure plane at 45° + φ/2 to the major principal plane.
• UU, CU, CD - undrained short-term, consolidated-undrained for rapid loading on consolidated soil, drained long-term.
• φu ≈ 0 concept - for a saturated clay sheared undrained, all Mohr circles have the same diameter; strength = cu.
• Dilatancy and critical void ratio - dense sand expands and loose sand contracts on shearing; equal at critical state.
• Liquefaction - cyclic pore pressure build-up drives σ′ to zero in loose saturated sand; checked per IS 1893.

Formulas and examples

Example 1 - Compaction: dry density, voids and ZAV. A Proctor specimen of volume 1,000 cm³ weighs 1,950 g at w = 14%. G = 2.68.

• Bulk density = 1,950/1,000 = 1.95 g/cm³ → γd = 1.95/1.14 = 1.711 g/cm³ (16.78 kN/m³).
• Void ratio: e = (G γw/γd) − 1 = (2.68/1.711) − 1 = 1.566 − 1 = 0.566.
• Degree of saturation S = wG/e = (0.14 × 2.68)/0.566 = 0.3752/0.566 = 66.3% → air voids present, as expected.
• ZAV dry density at the same w = 2.68/(1 + 0.14 × 2.68) = 2.68/1.3752 = 1.949 g/cm³ - well above 1.711, confirming the curve lies left of the ZAV line.
• If MDD = 1.78 g/cm³ and field γd = 1.711 g/cm³, relative compaction = 1.711/1.78 = 96.1% - acceptable for a 95% specification.

Example 2 - Compactive energy comparison.

• Standard Proctor: (2.6 × 9.81 N × 0.310 m × 25 × 3)/(1,000 × 10⁻⁶ m³) = (25.51 × 0.310 × 75)/0.001 = 593.1/0.001 = 593 kJ/m³.
• Modified Proctor: (4.89 × 9.81 × 0.450 × 25 × 5)/0.001 = (47.97 × 0.450 × 125)/0.001 = 2,698/0.001 = 2,698 kJ/m³ → ratio 4.55.

Example 3 - Consolidation settlement and time. A 4 m thick NC clay layer lies between two sand layers. e0 = 0.90, Cc = 0.32, existing σ′0 = 120 kPa at mid-depth, added stress Δσ′ = 80 kPa, cv = 3.0 × 10⁻⁸ m²/s.

• ΔH = (0.32 × 4/1.90) × log10(200/120) = 0.6737 × log10(1.6667) = 0.6737 × 0.2218 = 0.1494 m ≈ 149 mm.
• Drainage is two-way → d = 4/2 = 2 m.
• Time for 90% consolidation: T90 = 0.848 → t = 0.848 × 4/(3.0 × 10⁻⁸) = 3.392/3.0×10⁻⁸ = 1.131 × 10⁸ s = 3.58 years.
• Time for 50%: T50 = 0.197 → t = 0.197 × 4/(3.0 × 10⁻⁸) = 2.627 × 10⁷ s = 0.83 years; settlement then = 0.5 × 149 = 75 mm.
• If the base were impervious (single drainage), d = 4 m, and t90 would be 4× larger = 14.3 years - the d² effect.

Example 4 - Triaxial test: c and φ from two specimens. CD tests on identical specimens: Specimen A, σ3 = 100 kPa, deviator stress at failure = 200 kPa; Specimen B, σ3 = 200 kPa, deviator = 330 kPa.

• A: σ1 = 300 kPa → centre 200, radius 100. B: σ1 = 530 kPa → centre 365, radius 165.
• Envelope slope: sinφ′ = (165 − 100)/(365 − 200) = 65/165 = 0.3939 → φ′ = 23.2°.
• Intercept: from radius = (centre) sinφ′ + c′ cosφ′ → 100 = 200 × 0.3939 + c′ cos23.2° → 100 = 78.79 + 0.9192 c′ → c′ = 21.21/0.9192 = 23.1 kPa.
• Failure plane inclination α = 45 + 23.2/2 = 56.6° to the horizontal (major principal plane).
• Check with σ1 = σ3 tan²(45+φ/2) + 2c tan(45+φ/2): tan(56.6°) = 1.516 → 100 × 2.298 + 2 × 23.1 × 1.516 = 229.8 + 70.0 = 299.8 ≈ 300 kPa. ✔

Example 5 - Vane shear and sensitivity. A 75 mm high, 50 mm diameter vane records a peak torque of 48 N·m; after remoulding, 12 N·m.

• cu = T/[π D²(H/2 + D/6)] = 48/[π × 0.05² × (0.0375 + 0.008333)] = 48/[π × 0.0025 × 0.045833] = 48/3.5995 × 10⁻⁴ = 133.4 kPa.
• Remoulded cu = 12/3.5995 × 10⁻⁴ = 33.3 kPa → sensitivity = 133.4/33.3 = 4.0 (medium sensitive clay).

Where it is used

• Highways and expressways: NHAI/MoRTH earthwork - OMC-controlled compaction of embankments and subgrade, field density acceptance by sand replacement or nuclear gauge, CBR for pavement thickness under IRC 37.
• Earth and rockfill dams and canal embankments: core placed wet of OMC for low permeability; shell shear strength governs slope stability; projects of CWC, state irrigation departments, NHPC.
• Buildings and industrial foundations on soft clay: Kolkata, Mumbai reclaimed areas, Chennai coastal clay, Kochi - consolidation settlement by oedometer parameters per IS 8009, bearing capacity from c and φ per IS 6403.
• Ports, reclamation and metro works: PVD plus surcharge preloading to pre-consolidate dredged fill (Mumbai Trans Harbour, JNPT, Kochi); staged embankment construction using strength gain from consolidation.
• Job roles: geotechnical engineer and soil-testing engineer in consultancies (AECOM, WSP, STUP, Tandon, L&T Geostructure), QA/QC earthwork engineer on highway packages, NABL-accredited soil laboratory technologist, site engineer signing compaction test records.
• Statutory and seismic work: liquefaction assessment for structures in seismic zones III-V per IS 1893, and geotechnical investigation reports mandated for high-rise approvals by municipal authorities.

Interview questions

• Q: What is the difference between compaction and consolidation? A: Compaction expels air from a partly saturated soil by mechanical energy and is instantaneous; consolidation expels pore water from a saturated soil under sustained load and takes months or years.
• Q: Why does dry density fall beyond the optimum moisture content? A: Beyond OMC the added water occupies pore volume that soil solids could otherwise have filled, and since it cannot be expelled by the compactive effort, the solids per unit volume reduce.
• Q: What happens to OMC and MDD if you use modified instead of standard Proctor? A: MDD increases and OMC decreases - the peak shifts up and to the left - because higher compactive energy needs less lubricating water to reach a denser packing.
• Q: Can a compaction test point ever lie on the zero air voids line? A: No - compaction cannot remove all air, so the curve always lies left of the ZAV line; a point on or beyond it indicates a measurement or calculation error.
• Q: Why is an earth dam core compacted slightly wet of optimum? A: A wet-of-optimum dispersed structure gives lower permeability, more ductile behaviour and less tendency to crack under differential settlement or swell on wetting, which matters more than the small strength loss.
• Q: State the effective stress principle and why it matters. A: σ′ = σ − u; volume change and shear strength depend only on effective stress, so raising pore pressure at constant total stress reduces strength - the mechanism behind liquefaction and rainfall-triggered slope failure.
• Q: How long will consolidation take if the clay layer thickness doubles? A: Four times as long, since t is proportional to the square of the drainage path for the same degree of consolidation.
• Q: What is overconsolidation ratio and how does it affect settlement? A: OCR = preconsolidation pressure / present effective overburden pressure; an overconsolidated clay recompresses along the flatter Cr line and settles far less than a normally consolidated clay for the same stress increase.
• Q: Which triaxial test would you specify for the stability of an embankment on soft clay immediately after construction? A: A UU test giving cu, because the clay has no time to drain during rapid construction; the long-term case uses CD or CU parameters.
• Q: Why is the direct shear test considered inferior to the triaxial test? A: The failure plane is pre-determined, stresses and strains are non-uniform, drainage cannot be properly controlled and pore pressure cannot be measured.
• Q: What does a saturated clay's φu = 0 mean physically? A: In an undrained test any increase in cell pressure is carried entirely by the pore water, so effective stress and hence strength do not change - all Mohr circles have the same diameter and the envelope is horizontal.
• Q: How do vertical drains speed up consolidation? A: They shorten the drainage path and allow predominantly radial flow to the drain, so the same degree of consolidation is reached in a fraction of the time without changing the final settlement.
• Q: Why does dense sand show a peak strength followed by a lower residual strength? A: Dense sand must dilate to shear, which mobilises extra resistance at peak; once it loosens to the critical void ratio, only frictional residual strength remains.

Common mistakes

• Using bulk density instead of dry density in compaction calculations, or forgetting to divide by (1 + w).
• Confusing relative compaction (percentage of laboratory MDD, for all soils) with relative density / density index (based on emax and emin, only for cohesionless soils).
• Taking d = full layer thickness when drainage is two-way (it should be H/2) - this makes the predicted time four times too long.
• Mixing logarithm bases: Cc and the settlement equation use log10, while T-U relations use natural logarithms internally - and using log σ′ ratios with wrong units of stress.
• Using total-stress c and φ where long-term effective-stress c′ and φ′ are required, or quoting cu for a free-draining sand.
• Forgetting that the e-log σ′ settlement formula with Cc applies only to normally consolidated clay - an overconsolidated clay needs the Cr branch up to σ′c and Cc beyond it.
• Ignoring secondary consolidation in organic/peaty soils and reporting only primary settlement as the total.
• Treating the Casagrande construction point of maximum curvature by eye without plotting on a proper semi-log scale, giving a badly wrong σ′c.

Related topics

Soil properties and classification · Foundations: shallow and deep · Earth pressure and slope stability · Ground improvement techniques · Site investigation and soil exploration · Pile foundation design