INTERACTIVE COMPANION · FIELD NOTES · GEOLOGY

The Sinking Sand Bench

A live model accompanying “Younger Rock Beneath Older Rock”

The law of superposition says the older layer is the one underneath. It holds for a dull reason. Sediment normally gets denser as it packs down, so the stack sits the stable way up and stays there. Now invert the densities. Put heavy young sand on light old ooze and the column turns into a very slow lava lamp, which is what a 2025 study says happened across a whole basin under the North Sea. Everything on this page is the club's own arithmetic, the same model that produced the numbers in the article, and it is not the published analysis. Set the two porosities and watch the densities cross. Then liquefy the sand and time its fall.

Model 1 · Weigh the two materials

Saturated bulk density is a weighted average of grain and pore fluid: \(\rho_{\text{bulk}} = \phi\rho_{\text{fluid}} + (1-\phi)\rho_{\text{grain}}\). Quartz sand grains are heavy, 2650 kg/m³. Opal-A microfossil shells come in lighter, around 2100, because the silica is hydrated, and their skeletons stack into an open framework that holds far more water. So the ooze loses twice over. Your job with the sliders below is to build a stack in which the older ooze outweighs the younger sand. It is harder than it sounds.

Sand porosity φ 0.40 Real shallow marine sand sits near 0.40. Loosen it and watch the sand bar shrink. The crossover reading tells you how loose the sand would have to get before the stack turns the right way up. Ooze porosity φ 0.65 Diatom ooze holds an open framework, so 0.65 is ordinary. Drag it down towards 0.35 and watch Δρ collapse. This is the one slider here that can flip the verdict on its own. Opal-A grain density 2100 kg/m³ Nobody pins this down closer than a couple of hundred kg/m³. Sweep the full range and watch Δρ travel between 650 and 563. It never changes sign, which is the whole finding. Pore fluid 1030 kg/m³ North Sea formation brine is about 1030 and fresh water is 1000. Heavier brine lifts both materials at once, so watch how little the gap between them cares.

sand: – ooze: – Δρ: – crossover at sand φ = – unstable

Club values from the article: sand φ = 0.40 → 2002 kg/m³, ooze φ = 0.65 → 1404.5 kg/m³, Δρ = 597.5 kg/m³, crossover at 0.769.

Model 2 · Liquefy it and start the clock

Density contrast on its own does nothing at all. Sand is a solid because its grains press against one another, and a solid will sit there being heavy for ever. Terzaghi's effective stress is total stress minus pore pressure, and strength follows the grain-borne part alone. Raise the pore pressure until the water is carrying the whole overburden. The grains stop touching, the strength goes to zero, and the sand becomes a liquid in the only sense that matters mechanically. What happens next is buoyancy against viscous drag, \(v = 2\Delta\rho\,g R^2 / 9\mu\), and the one quantity in that expression nobody on Earth has measured is the viscosity.

Pore-pressure ratio 0.60 Slide it up and watch the strength reading fall in a perfectly straight line. Nothing else moves until you reach 1.00 exactly. Watch for what that means: no threshold to beat, only a load to hand to the water. Effective viscosity μ = 10^18 Pa·s Drag this one from end to end. Sink time crosses fourteen orders of magnitude while every other reading barely twitches. Watch the marker leave the shaded window at both ends. Body radius 500 m Velocity goes as R², so a body twice as wide falls four times faster. Take it down to 100 m and watch a plausible descent turn into one that never finishes. Sink distance 200 m 200 m is the vertical relief reported for the real mounds. Time scales straight with distance, so this is the tame slider. Compare how little it does against the viscosity one.

state: locked (solid) strength left at 50 m: – velocity: – time to sink: – Reynolds: – verdict: –

Reference viscosities: water 10⁻³, honey 10¹, pitch 10⁸, rock salt 10¹⁷ to 10¹⁸, window glass 10¹⁸, upper mantle 10²¹ Pa·s. Press Run descent once the sand is liquefied. The animation runs at a fixed speed so you can see it; the real clock is the sink time in the readout.

Why this is the weak joint

Sweep the viscosity slider and watch the asymmetry. Sink time moves across fourteen orders of magnitude. Nothing else on the page moves at all. The density contrast is settled arithmetic, because grain densities and porosities are quantities somebody has actually measured, and the inversion survives the full plausible range of both. The viscosity of liquefied ooze under burial conditions has never been measured by anybody. Our model needs it to sit between hot pitch and rock salt. That is a reasonable thing to ask for, and salt diapirs do exactly this kind of rise through denser sediment on exactly these timescales, so the request has precedent. It remains an assumption wearing the costume of a result.

Which points straight at the experiment somebody should run. Put ooze in a rheometer under burial pressure and find out.