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Granulometry | |
---|---|
Basic concepts | |
Particle size, Grain size, Size distribution, Morphology | |
Methods and techniques | |
Mesh scale, Optical granulometry, Sieve analysis, Soil gradation | |
Related concepts | |
Granulation, Granular material, Mineral dust, Pattern recognition, Dynamic light scattering | |
Grain size (or particle size) is the diameter of individual grains of sediment, or the lithified particles in clastic rocks. The term may also be applied to other granular materials. This is different from the crystallite size, which refers to the size of a single crystal inside a particle or grain. A single grain can be composed of several crystals. Granular material can range from very small colloidal particles, through clay, silt, sand, gravel, and cobbles, to boulders.
Size ranges define limits of classes that are given names in the Wentworth scale (or Udden–Wentworth scale) used in the United States. The Krumbein phi (φ) scale, a modification of the Wentworth scale created by W. C. Krumbein [1] in 1934, is a logarithmic scale computed by the equation
where
This equation can be rearranged to find diameter using φ:
φ scale | Size range (metric) | Size range (approx. inches) | Aggregate name (Wentworth class) | Other names |
---|---|---|---|---|
<−8 | >256 mm | >10.1 in | Boulder | |
−6 to −8 | 64–256 mm | 2.5–10.1 in | Cobble | |
−5 to −6 | 32–64 mm | 1.26–2.5 in | Very coarse gravel | Pebble |
−4 to −5 | 16–32 mm | 0.63–1.26 in | Coarse gravel | Pebble |
−3 to −4 | 8–16 mm | 0.31–0.63 in | Medium gravel | Pebble |
−2 to −3 | 4–8 mm | 0.157–0.31 in | Fine gravel | Pebble |
−1 to −2 | 2–4 mm | 0.079–0.157 in | Very fine gravel | Granule |
0 to −1 | 1–2 mm | 0.039–0.079 in | Very coarse sand | |
1 to 0 | 0.5–1 mm | 0.020–0.039 in | Coarse sand | |
2 to 1 | 0.25–0.5 mm | 0.010–0.020 in | Medium sand | |
3 to 2 | 125–250 μm | 0.0049–0.010 in | Fine sand | |
4 to 3 | 62.5–125 μm | 0.0025–0.0049 in | Very fine sand | |
8 to 4 | 3.9–62.5 μm | 0.00015–0.0025 in | Silt | Mud |
10 to 8 | 0.98–3.9 μm | 3.8×10−5–0.00015 in | Clay | Mud |
20 to 10 | 0.95–977 nm | 3.8×10−8–3.8×10−5 in | Colloid | Mud |
In some schemes, gravel is anything larger than sand (comprising granule, pebble, cobble, and boulder in the table above).
ISO 14688-1:2017, establishes the basic principles for the identification and classification of soils on the basis of those material and mass characteristics most commonly used for soils for engineering purposes. ISO 14688-1 is applicable to natural soils in situ, similar man-made materials in situ and soils redeposited by people. [3]
Name | Size range (mm) | Size range (approx. in) | |||
---|---|---|---|---|---|
Very coarse soil | Large boulder | lBo | >630 | >24.8031 | |
Boulder | Bo | 200–630 | 7.8740–24.803 | ||
Cobble | Co | 63–200 | 2.4803–7.8740 | ||
Coarse soil | Gravel | Coarse gravel | cGr | 20–63 | 0.78740–2.4803 |
Medium gravel | mGr | 6.3–20 | 0.24803–0.78740 | ||
Fine gravel | fGr | 2.0–6.3 | 0.078740–0.24803 | ||
Sand | Coarse sand | cSa | 0.63–2.0 | 0.024803–0.078740 | |
Medium sand | mSa | 0.2–0.63 | 0.0078740–0.024803 | ||
Fine sand | fSa | 0.063–0.2 | 0.0024803–0.0078740 | ||
Fine soil | Silt | Coarse silt | cSi | 0.02–0.063 | 0.00078740–0.0024803 |
Medium silt | mSi | 0.0063–0.02 | 0.00024803–0.00078740 | ||
Fine silt | fSi | 0.002–0.0063 | 0.000078740–0.00024803 | ||
Clay | Cl | ≤0.002 | ≤0.000078740 |
An accumulation of sediment can also be characterized by the grain size distribution. A sediment deposit can undergo sorting when a particle size range is removed by an agency such as a river or the wind. The sorting can be quantified using the Inclusive Graphic Standard Deviation: [4]
where
The result of this can be described using the following terms:
Diameter (phi units) | Description |
---|---|
< 0.35 | very well sorted |
0.35 < < 0.50 | well sorted |
0.50 < < 1.00 | moderately sorted |
1.00 < < 2.00 | poorly sorted |
2.00 < < 4.00 | very poorly sorted |
4.00 < | extremely poorly sorted |
Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, D. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation.
In fluid dynamics, potential flow or irrotational flow refers to a description of a fluid flow with no vorticity in it. Such a description typically arises in the limit of vanishing viscosity, i.e., for an inviscid fluid and with no vorticity present in the flow.
Sediment is a naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of wind, water, or ice or by the force of gravity acting on the particles. For example, sand and silt can be carried in suspension in river water and on reaching the sea bed deposited by sedimentation; if buried, they may eventually become sandstone and siltstone through lithification.
Phi is the twenty-first letter of the Greek alphabet.
Gravel is a loose aggregation of rock fragments. Gravel occurs naturally on Earth as a result of sedimentary and erosive geological processes; it is also produced in large quantities commercially as crushed stone.
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. The effect is named after the British physicist Brian Josephson, who predicted in 1962 the mathematical relationships for the current and voltage across the weak link. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mechanics are observable at ordinary, rather than atomic, scale. The Josephson effect has many practical applications because it exhibits a precise relationship between different physical measures, such as voltage and frequency, facilitating highly accurate measurements.
Siltstone, also known as aleurolite, is a clastic sedimentary rock that is composed mostly of silt. It is a form of mudrock with a low clay mineral content, which can be distinguished from shale by its lack of fissility.
In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality.
In quantum field theory, a quartic interaction is a type of self-interaction in a scalar field. Other types of quartic interactions may be found under the topic of four-fermion interactions. A classical free scalar field satisfies the Klein–Gordon equation. If a scalar field is denoted , a quartic interaction is represented by adding a potential energy term to the Lagrangian density. The coupling constant is dimensionless in 4-dimensional spacetime.
In general relativity, Schwarzschild geodesics describe the motion of test particles in the gravitational field of a central fixed mass that is, motion in the Schwarzschild metric. Schwarzschild geodesics have been pivotal in the validation of Einstein's theory of general relativity. For example, they provide accurate predictions of the anomalous precession of the planets in the Solar System and of the deflection of light by gravity.
The chemists Peter Debye and Erich Hückel noticed that solutions that contain ionic solutes do not behave ideally even at very low concentrations. So, while the concentration of the solutes is fundamental to the calculation of the dynamics of a solution, they theorized that an extra factor that they termed gamma is necessary to the calculation of the activities of the solution. Hence they developed the Debye–Hückel equation and Debye–Hückel limiting law. The activity is only proportional to the concentration and is altered by a factor known as the activity coefficient . This factor takes into account the interaction energy of ions in solution.
Clastic rocks are composed of fragments, or clasts, of pre-existing minerals and rock. A clast is a fragment of geological detritus, chunks, and smaller grains of rock broken off other rocks by physical weathering. Geologists use the term clastic to refer to sedimentary rocks and particles in sediment transport, whether in suspension or as bed load, and in sediment deposits.
Prolate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the focal axis of the ellipse, i.e., the symmetry axis on which the foci are located. Rotation about the other axis produces oblate spheroidal coordinates. Prolate spheroidal coordinates can also be considered as a limiting case of ellipsoidal coordinates in which the two smallest principal axes are equal in length.
Sediment transport is the movement of solid particles (sediment), typically due to a combination of gravity acting on the sediment, and the movement of the fluid in which the sediment is entrained. Sediment transport occurs in natural systems where the particles are clastic rocks, mud, or clay; the fluid is air, water, or ice; and the force of gravity acts to move the particles along the sloping surface on which they are resting. Sediment transport due to fluid motion occurs in rivers, oceans, lakes, seas, and other bodies of water due to currents and tides. Transport is also caused by glaciers as they flow, and on terrestrial surfaces under the influence of wind. Sediment transport due only to gravity can occur on sloping surfaces in general, including hillslopes, scarps, cliffs, and the continental shelf—continental slope boundary.
Gyrokinetics is a theoretical framework to study plasma behavior on perpendicular spatial scales comparable to the gyroradius and frequencies much lower than the particle cyclotron frequencies. These particular scales have been experimentally shown to be appropriate for modeling plasma turbulence. The trajectory of charged particles in a magnetic field is a helix that winds around the field line. This trajectory can be decomposed into a relatively slow motion of the guiding center along the field line and a fast circular motion, called gyromotion. For most plasma behavior, this gyromotion is irrelevant. Averaging over this gyromotion reduces the equations to six dimensions rather than the seven. Because of this simplification, gyrokinetics governs the evolution of charged rings with a guiding center position, instead of gyrating charged particles.
Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure the "accessible void", the total amount of void space accessible from the surface.
In fluid dynamics, the Reynolds number is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow. These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation.
A cobble is a clast of rock defined on the Udden–Wentworth scale as having a particle size of 64–256 millimeters (2.5–10.1 in), larger than a pebble and smaller than a boulder. Other scales define a cobble's size differently. A rock made predominantly of cobbles is termed a conglomerate. Cobblestone is a building material based on cobbles.
Lagrangian field theory is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used to analyze the motion of a system of discrete particles each with a finite number of degrees of freedom. Lagrangian field theory applies to continua and fields, which have an infinite number of degrees of freedom.
In applied mathematics, the central differencing scheme is a finite difference method that optimizes the approximation for the differential operator in the central node of the considered patch and provides numerical solutions to differential equations. It is one of the schemes used to solve the integrated convection–diffusion equation and to calculate the transported property Φ at the e and w faces, where e and w are short for east and west. The method's advantages are that it is easy to understand and implement, at least for simple material relations; and that its convergence rate is faster than some other finite differencing methods, such as forward and backward differencing. The right side of the convection-diffusion equation, which basically highlights the diffusion terms, can be represented using central difference approximation. To simplify the solution and analysis, linear interpolation can be used logically to compute the cell face values for the left side of this equation, which is nothing but the convective terms. Therefore, cell face values of property for a uniform grid can be written as: