Buried Object Flotation in Liquefied Soil

Earthquake Shaking

Peak ground accel. a_max 0.30 g

Sand relative density D_r 45%

Buried Object

Density vs. saturated soil 0.55×

Live Readouts

r_u (excess pore pressure ratio)0%

Effective stress σ'/σ'₀

100%

Shaking cycles N

Object depth below surface

2.75 m

Soil intact — grains interlocked

How it works

Cyclic earthquake shear stress pumps up the water pressure trapped between saturated sand grains. The excess pore-pressure ratio after N shaking cycles follows the classic Seed–Booker / De Alba curve:

r_u = (2/π)·arcsin[ (N / N_liq)^(1/2θ) ],   θ ≈ 0.7
σ'(N) = σ'₀ · (1 − r_u)      (effective stress, Terzaghi)
N_liq ∝ (CRR / CSR)^c,  CSR ≈ 0.65·(a_max/g),  CRR grows with D_r

As r_u → 1 the effective stress σ' collapses toward zero. Since dry-friction shear strength τ_f = σ'·tanφ, the sand loses essentially all its ability to resist shear or hold anything in place — it behaves like a dense fluid. A buried object then obeys plain Archimedes buoyancy against the soil's residual strength:

Buoyant drive   B = (ρ_soil − ρ_object)·g
Residual lock   S(N) = S₀·(1 − r_u)
Object moves only once |B| > S(N)  →  net accel = (B − sign(B)·S(N)) / m_eff

This is exactly why light buried tanks, empty pipes and even manholes "pop up" out of the ground during real liquefaction (Niigata 1964, Christchurch 2011), while heavier, denser structures instead sink or tilt. Denser sand (higher D_r) resists longer before liquefying; stronger shaking (higher a_max) reaches r_u ≈ 1 sooner. Object drift is locked to zero until the residual strength S(N) drops below the buoyant drive |B| for the chosen density ratio — try dragging the density slider below and above 1.0× to see both flotation and sinking.

Sand grains Water table Buried object

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