= Soil-particle density
{title2=$\rho_s=M_s/V_s$}
<Soil-particle density> compares dry particle <mass> with the <volume> assigned to the particles themselves:
$$
\rho_s=\frac{M_s}{V_s}.
$$
Spaces between particles are excluded from $V_s$. By contrast, the denominator of <soil bulk density> includes those spaces. A measurement must specify how particle volume is determined, especially when the particles themselves contain pores.<ISO 11508:2017 Soil quality: Determination of particle density>[Scope; section 3.1, definition and volume convention]{ref}
One measurement principle uses a <pycnometer>: determine the dry sample mass, then infer its volume from the displaced liquid mass and the liquid's <density>. Trapped gas, access to internal pores and the chosen volume convention matter when interpreting the displacement. The standard distinguishes fine soil from gravel and stones, and its stated particle-volume convention includes internal particle pores while excluding spaces between particles.<ISO 11508:2017 Soil quality: Determination of particle density>[Sections 3.1 and 4.1.1, definition and fine-soil measurement principle]{ref}
A constructed mixture shows why particle composition matters. Assume additive volumes, no internal pore complication, and two kinds of particles with densities $2.60$ and $1.30\,\mathrm{g\,cm^{-3}}$. Equal masses of $13\,\mathrm g$ occupy $5$ and $10\,\mathrm{cm^3}$, respectively. The combined <soil-particle density> is
$$
\rho_s=\frac{26}{15}\,\mathrm{g\,cm^{-3}}\approx1.73\,\mathrm{g\,cm^{-3}},
$$
rather than the arithmetic mean $1.95\,\mathrm{g\,cm^{-3}}$. For <mass fractions> $w_i$ and constituent densities $\rho_i$, the same additive-volume model gives $\rho_s^{-1}=\sum_i w_i/\rho_i$.
For compatible volume conventions, a particle-and-pore model relates the two densities to <porosity>:
$$
\varepsilon=1-\frac{V_s}{V}=1-\frac{\rho_b}{\rho_s}.
$$
This identity requires the same dry mass in both density definitions. An assumed <soil-particle density> therefore makes the derived <porosity> an estimate under that assumption, rather than an independent measurement of pore volume.<ISO 11508:2017 Soil quality: Determination of particle density>[Scope, particle density used with bulk-density measurements to calculate porosity]{ref}
Back to article page
