Relative Density of a Granular Soil

Void ratio on its own says nothing about how dense a sand is, because a well-graded gravel at e = 0.35 may be loose while a uniform fine sand at e = 0.60 is dense. Relative density fixes that by measuring against the material's own extremes, determined in the lab by pouring it in as loosely as possible and then vibrating it as tight as it will go. A field void ratio of 0.60 in a sand with $e_{\text{max}}$ = 0.85 and $e_{\text{min}}$ = 0.42 gives $D_r$ = 0.25 ÷ 0.43 × 100 = 58%, which the standard descriptive scale calls medium dense (0–15% very loose, 15–35% loose, 35–65% medium, 65–85% dense, 85–100% very dense).

The trap is that $D_r$ is defined only for cohesionless soils — quoting a relative density for a clay is meaningless, because clays have no reproducible loosest and densest states. The second trap is precision: $e_{\text{max}}$ and $e_{\text{min}}$ are themselves test results with a few percent of scatter, and because they appear in a difference, that scatter is magnified. A $D_r$ reported to the nearest whole percent is pretending to an accuracy nobody has. It still matters enormously: liquefaction susceptibility, pile driving resistance and settlement all key off $D_r$, and the 1964 Niigata liquefaction happened in sands that would have plotted around 40%.