Soil Dynamics, Liquefaction & Earthquake Geotechnics Notes

Last reviewed 16 Sept 2026 · 6 min read

Dynamic loading of soils

Soils are loaded dynamically by earthquakes, machine vibrations, blasting, pile driving, traffic and waves. Under rapid, cyclic loading:

strength and stiffness can degrade with cycles;
saturated loose soils can build up excess pore pressure and lose strength (liquefaction);
the ground can amplify earthquake shaking;
structures and slopes receive additional inertia forces.

Seismic waves

Wave	Type	Motion	Speed
P (primary)	Body wave	Compression–extension along propagation	Fastest
S (secondary)	Body wave	Shear, perpendicular to propagation (cannot travel in liquids)	Slower than P
Rayleigh	Surface wave	Elliptical retrograde motion	Slightly slower than S
Love	Surface wave	Horizontal shear	Between S and Rayleigh

Shear (S) waves cause most damage to structures and drive liquefaction.

Dynamic soil properties

Shear modulus $G$ — from shear wave velocity: $G = ρ V_{s}^{2}$ (small-strain value $G_{ma x}$ ).
Damping ratio $ξ$ — energy loss per cycle.
Poisson's ratio and Young's modulus $E = 2 G (1 + μ)$ .
$G$ decreases and damping increases with shear strain amplitude (modulus reduction and damping curves).

Field tests: seismic cross-hole and down-hole, seismic refraction, SASW/MASW, block vibration test (IS 5249), cyclic plate load test. Laboratory tests: resonant column, cyclic triaxial, cyclic simple shear, bender elements.

Site effects and IS 1893 soil types

Soft soil deposits amplify bedrock motion, especially when the site's natural period matches the dominant period of shaking (Mexico City 1985 is the classic example). IS 1893 (Part 1):2016 classifies founding strata for design spectra:

Soil type	Description
Type I — rock or hard soil	Well-graded gravels and sand–gravel mixtures, or poorly graded sands, with corrected SPT N > 30 (also stiff clays by strength)
Type II — medium soil	Sands with N between 10 and 30; stiff clays
Type III — soft soil	All soft soils other than SP with N < 10

Softer sites have response spectra with larger values at longer periods. Sites prone to liquefaction need special investigation.

Liquefaction

Liquefaction is the loss of shear strength of saturated, loose, cohesionless soil when cyclic loading causes excess pore water pressure to rise until effective stress approaches zero:

τ_{f} = (σ - u) tan ϕ^{'} \to 0 as u \to σ

The soil behaves like a heavy liquid.

Mechanism

Loose sand tends to contract under cyclic shear. During an earthquake, there is no time for water to drain, so the tendency to contract transfers load to the pore water; pore pressure rises cycle by cycle until the grains lose contact.

Effects

Sand boils; ground settlement and cracking; loss of bearing capacity (tilting and sinking of buildings — Niigata 1964); lateral spreading of gently sloping ground towards rivers and coasts; flotation of buried tanks and pipes; failure of embankments and quay walls; increased pressure on retaining walls.

Factors affecting liquefaction susceptibility

Soil type — fine to medium uniform sands and non-plastic silts are most susceptible; well-graded gravels drain quickly; clays generally resist (plasticity), though sensitive clays lose strength.
Relative density — loose soils liquefy; dense soils dilate and resist.
Saturation and water table — must be saturated; a shallow water table increases risk.
Confining pressure — higher effective stress (deeper layers) increases resistance; most liquefaction occurs within about 15–20 m of the surface.
Earthquake intensity and duration — larger peak acceleration and more cycles (larger magnitude) increase risk.
Age and cementation — older deposits resist better; recent fills and alluvium are vulnerable.
Drainage conditions — impervious caps trap pore pressure.

Simplified evaluation (Seed and Idriss)

FormulaCyclic stress ratio and factor of safety

Earthquake demand — cyclic stress ratio:

C S R = \frac{τ _{a v}}{σ _{v}^{'}} = 0.65 \frac{a _{ma x}}{g} \frac{σ _{v}}{σ _{v}^{'}} r_{d}

$a_{ma x}$ = peak horizontal ground acceleration; $σ_{v}$ , $σ_{v}^{'}$ = total and effective vertical stress at the depth; $r_{d}$ = stress reduction factor (≈ 1 at the surface, decreasing with depth; roughly $1 - 0.00765 z$ for $z \leq 9.15$ m).

Soil capacity — cyclic resistance ratio $C R R$ : from charts of corrected SPT $(N_{1})_{60}$ (or CPT $q_{c 1 N}$ , or $V_{s}$ ), for magnitude 7.5, adjusted by a magnitude scaling factor.

F S_{L} = \frac{C R R}{C S R}

Liquefaction is expected when $F S_{L} < 1$ (design commonly requires about 1.2–1.5).

Remedial measures

Densification: vibro-compaction, dynamic compaction, compaction piles, blasting.
Drainage: stone columns and gravel drains that dissipate pore pressure quickly.
Cementation / solidification: deep soil mixing, permeation or jet grouting.
Lowering the water table (dewatering).
Structural: deep foundations (piles) through liquefiable layers designed for loss of lateral support and downdrag; rafts; containment walls to prevent lateral spreading.
Replacement of liquefiable soil near the surface.

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Soil Dynamics, Liquefaction & Earthquake Geotechnics