Void ratio, porosity and saturation from one density test

Updated: 2026-08-13 · ISKRIT

Bulk density, water content and particle density are three measurements. Everything else in the index table is arithmetic on those three, which is why one bad weighing propagates into eight reported values.

The three phases

A soil sample is solids, water and air. Dry density strips the water out of the bulk density:

ρd = ρ / (1 + w)

The void ratio compares the volume of the voids to the volume of the solids, and porosity compares voids to the total. They carry the same information in two forms:

e = ρs / ρd − 1 and n = e / (1 + e)

Degree of saturation is the fraction of the voids that holds water:

Sr = w · ρs / (e · ρw)

Worked through

Take ρ = 1.94 g/cm³, w = 0.22 and ρs = 2.70 g/cm³. Dry density is 1.94 / 1.22 = 1.59 g/cm³. Void ratio is 2.70 / 1.59 − 1 = 0.698. Porosity is 0.698 / 1.698 = 0.411, so 41 percent of the sample volume is void. Saturation is 0.22 · 2.70 / 0.698 = 0.851, or 85 percent.

When saturation comes out above 100 percent

It cannot. Sr above unity means one of the three inputs is wrong, and the arithmetic has just told you so. The usual causes, in order of how often they turn out to be the culprit: particle density assumed rather than measured, the sample dried at the wrong temperature so the water content is overstated, or the cutting ring not full so the bulk density is understated.

This is the most useful check in the whole index table, because it is the only one that is self-validating. Treat a saturation of 104 percent as a laboratory finding, not as a rounding artefact to be quietly clipped to 100.

What the result is most sensitive to

Particle density is the one most often taken from a table rather than measured, and it is the one that moves the answer most. For a soil with organic content or heavy minerals, the tabulated 2.65 can be out by more than the whole measurement error of the other two inputs combined.

The soil index properties calculator computes the full three-phase set from the three measurements, flags a saturation above unity as an input error rather than clipping it, and returns the USCS group symbol from the same data.