# 6.2.2: Grain size, density and bulk properties

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Two important parameters for sediment transport are the median particle diameter \(D_{50}\) and the grading, for example, \(D_{90}/D_{10}\). \(D_x\) is defined as the sediment particle diameter (in metres) for which \(x\)% by weight is finer. In American literature, a \(\phi\)-scale is often used to identify the particle dimensions:

\[\phi = -\log_2 D\]

where

\(D\) | sand grain diameter | \(mm\) |

Sediment is called well-sorted if \(D_{90}/D_{10}\) is small (say < 1.5, although there is no formal classification); for large values of \(D_{90}/D_{10}\) (for instance > 3) we speak of poorly sorted or well-graded sediment.

Besides grain size, other properties of either the grains or the bulk material are important for sand transport, such as: grain shape (the grains are not perfect spheres), grain density, fall velocity, angle of repose, porosity and sediment concentration:

- The grain density \(\rho_s\) depends on the mineral composition of the sand. Most of the world’s beach sands consist of quartz (feldspar is the second most common mineral), with a mass density of 2650 \(kg/m^3\). Other minerals are often referred to as heavy minerals since their mass density is usually greater than 27 000 \(kg/m^3\);
- Relative density \(s\) is defined as the ratio of sediment density over water density \(\rho_s/\rho\). For natural sediments \(s\) will be normally around 2.65;
- The fall velocity depends on the grain characteristics as well as on the fluid characteristics (such as water density and viscosity). This is further discussed in Sect. 6.2.3. Roughly speaking, the fall velocity of medium-sized sand particles (\(0.1\ mm < D < 0.5\ mm\)) in water varies from \(0.01\ m/s\) to \(0.05\ m/s\);
- When (dry) sand is poured onto a flat surface, it will form a mound. The surface of the mound has a slope tan \(\varphi_r\) (with \(\varphi_r\) is the angle of repose) which depends mainly on the grain size;
- The porosity \(p\) is defined as the ratio of pore space (voids) to the whole sediment volume. Natural sands have porosities in the range of 0.25 to 0.50; a frequently applied figure is 0.40 (or 40%);
- The sediment concentration \(c\) can be defined in two ways: mass concentration and volume concentration. The mass concentration is the mass of the solid particles per volume (\(c\) in \(kg/m^3\) or equivalently \(g/L\)) and is often used when measuring sediment concentrations. Volume concentration is defined as the ratio of the volume of solid particles to the whole volume (\(c\) in \(m^3/m^3\) or in %). Sediment in a sediment bed has a volume concentration of \(n = 1 - p\). For sediment in suspension, the volume concentration \(c\) indicates the volume of sediment per volume of the mixture. If the sediment in such a mixture settles to the bed, \(1\ m^3\) of solid particles will occupy \(1/(1 − p)\) (\(p\): porosity) \(m^3\) at the bed. Volume concentrations are obtained from mass concentrations by multiplication with \(1/\rho_s\);
- Contrary to the grain density (\(\rho_s\)) as mentioned above, bulk density is the mass of a unit volume of e.g. a mixture of particles and air or water. The dry bulk density is defined as \(n \rho_s\). If the whole pore volume is filled with water (density \(\rho\)), then we obtain the saturated bulk density, which is defined as: \(n \rho_s + p \rho\). A typical figure for the dry bulk density is 1600 \(kg/m^3\), and for the saturated bulk density 2000 \(kg/m^3\).