Granulometric curve¶
Soils usually do not consist of grains with just one particle size, but of grains with a range of varying sizes. The distribution of the grain sizes in a soil has a significant effect on a number of its properties, such as its strength and load bearing capacity, its tendency to erode and its suitability as a filter. Commonly, the distribution of grain sizes in soils is expressed in the form of a curve, which is known as the particle size distribution (PSD), the granulometric curve or the gradation curve. The determination of the granulometric curve takes place via sieving or via hydrometer analysis, depending on the particle size.
Physical meaning¶
The granulometric curve is generally depicted as a percentage of weight on the vertical axis, which is linear, as a function of the grain diameter on the horizontal axis, which is logarithmic. It is common to include a header which helps the soil classification by size. An example is shown in the figure below.
It is attempted here to explain briefly the physical meaning of the curve. The point [0.7 , 70%] belongs to the granulometric curve. This means that 70% of the weight of the soil consists of grains with a diameter smaller than 0.7 mm. Then one can write that $$ d_{70} = 0.7 \;\;mm $$ In the same way for the depicted soil $d_{30}$ is equal to 0.4 mm. $d_{50}$, which here is equal to 0.52 mm, is referred to as the mean grain size.
To describe the general shape of the granulometric curve and to assist in soil characterization, two (unitless) shape parameters are commonly used, the uniformity coefficient $C_u$ and the curvature coefficient $C_c$. These are described below.
Uniformity coefficient $C_u$¶
The coefficient of uniformity is defined as: $$ C_u = \frac{d_{60}}{d_{10}} $$ To illustrate the meaning of this shape characteristic, in the following figure three examples of granulometric curves are shown, and the uniformity coefficients are calculated.
- Black curve: $d_{60}$= 0.5 mm, $d_{10}$= 0.052 mm, $C_u$= 9.6
- Blue curve: $d_{60}$= 0.026 mm, $d_{10}$= 0.013 mm, $C_u$= 2
- Red curve: $d_{60}$= 0.4 mm, $d_{10}$= 0.2 mm, $C_u$= 2
It can be observed that the uniformity coefficient does not depend on the mean size of the grains in the soil, but rather on how 'steep' the granulometric curve is. The flatter the curve, the larger the coefficient of uniformity. A soil consisting of one size of particles would have a vertical line as a granulometric curve and a coefficient of uniformity that is equal to one. Only such soils have a uniformity coefficient that is equal to one.
Curvature coefficient $C_c$¶
The coefficient of curvature is defined as: $$ C_c = \frac{d^2_{30}}{d_{60}\cdot d_{10}} $$ To illustrate the meaning of this shape characteristic, in the following figure three examples of granulometric curves are shown, and the uniformity coefficients are calculated.
- Black curve: $d_{60}$= 0.5 mm, $d_{30}$= 0.2 mm, $d_{10}$= 0.052 mm, $C_c$= 7.7
- Blue curve: $d_{60}$= 0.5 mm, $d_{30}$= 0.13 mm, $d_{10}$= 0.052 mm, $C_c$= 5.0
- Red curve: $d_{60}$= 0.5 mm, $d_{30}$= 0.28 mm, $d_{10}$=0.052 mm, $C_c$= 10.8
It can be observed that the curvature coefficient does not depend on the mean size of the grains in the soil, exactly like the uniformity coefficient. It rather describes the behavior of the curve between $d_{10}$ and $d_{60}$. If $d_{30}$ is closer to $d_{10}$ than it is to $d_{60}$, then the curvature coefficient is small. If on the other hand $d_{30}$ is closer to $d_{60}$ than it is to $d_{10}$, then the curvature coefficient is large. A soil consisting of one size of particles would have a vertical line as a granulometric curve and a curvature coefficient that is equal to one. However, other curves can also have a curvature coefficient that is equal to one, namely all granulometric curves that are linear between $d_{10}$ and $d_{60}$.
The widget below allows the user to modify the granulometric curve and illustrates how the coefficient of uniformity and the curvature coefficient change with its shape.
Programmed by Franck Andy Dzoupet Yimtchi
The Granulometric Curve, Eleni Gerolymatou & Franck Andy Dzoupet Yimtchi, CC-BY-SA (4.0) 