Friction angle
The angle of friction or internal friction angle is the angle at which a solid or granular material can be loaded without slipping or failing. It is a measure of the frictional ability of their surfaces ( friction and roughness or smoothness ). The internal angle of friction of granular media is not identical to the "angle of repose" of bulk material or to the " angle of repose " of an embankment.
The angle of friction is given in degrees . The tangent of the angle of friction, which is dimensionless, is used in calculations . The tangent of the angle of friction is the ratio of friction force to normal force in the friction surface with which the body is loaded in the limit state of equilibrium. It indicates the inclination of the resulting force in the friction surface.
The angle of repose defines the slope of a heap or embankment. In nature, they are also found in cones of debris (see talus ).
Dry, pure sand consists of rounded grains of sand of almost the same size. As in a dense packing of balls , the mound of sand holds only because of the friction between the grains. As soon as the sides of the hill go beyond a critical angle, the sand begins to slide. A pile of sand cannot become steeper than 40 °. For this reason a dune top is never really pointed.
Friction of solids
If two solid bodies lie on top of one another and touch on a flat horizontal surface , the angle of friction is the angle of the force resulting from the horizontal force and the vertical force, which acts on the upper body in the “state of boundary equilibrium”. The limit state of equilibrium is reached with an increasing horizontal force when the upper body has just not started to slide.
If the horizontal force acting on the upper body in the direction of the flat surface is large enough, it can push it away. The vertical force N, which acts perpendicular ("normal") to the contact surface on the upper body, presses both bodies together and determines the size of the possible frictional resistance R, which prevents slipping (R = N * m; m is the coefficient of friction of two materials, which is determined experimentally). The smoother the surfaces, the smaller the coefficient of friction m and thus also the angle of friction and the possible friction force.
Alternatively, to determine the friction angle, the clamped lower body can be slowly inclined together with the loosely resting upper body. The angle of friction is then measured between the horizontal and the inclined surfaces when the upper body is not yet starting to slide.
Friction with granular material, angle of repose
A grainy, rolling pile (such as sand) has an internal angle of friction that depends , among other things, on the roughness of the grains . If the material is poured into a heap, a cone of heap is created (similar to the talus ). The angle of repose depends on the following properties:
- Roughness , the rougher the greater the angle.
- different grain size , the more different grain sizes there are, the larger the angle.
- Compaction , the more the bed is compacted, the greater the angle.
- Moisture content , the angle increases as the cohesion between the grains increases.
| cohesive soil ( clay , silt ) | 25 ° |
| narrow, round-grained soil, sand ( e.g. mudflat sand) | 27.5 ° -30 ° |
| Potatoes , sugar beets | 30 ° |
| Grain | 30 ° |
| angular, sharp-edged sand | 32 ° -35 ° |
| wide stepped (sandy) gravel | 32 ° -37 ° |
| Brown coal | 35 ° |
| sugar | 35 ° |
| salt | 40 ° |
| Road salt | 32 ° |
| cement | 40 ° |
| sharp-edged rubble (e.g. railway gravel ), ores | 40 ° |
| Hard coal , coke | 45 ° |
| Flour | 45 ° |
The influence of the high surface tension of the water in the capillary effective gaps between grains of fine sea sand becomes clear in the dripping wet construction of a sand castle . With a thin stream or a drop of sand-water slurry curdled from the hand from a small height, pointed turrets (angle of repose almost 90 °), almost vertical walls and even small, slightly protruding mushroom hoods can be built up, which overhang vertically in a small area without support, i.e. there form an angle of repose of over 90 °.
The strongest permanent, but only superficial binding force develops the water up to the capillary rise above the groundwater level - depending on the fineness of the material and the water - of about 0.5 meters. Above this, the water column in the sand matrix tears off and air penetrates the pores, water is cemented here also in the depths of the "mortar", but tends to run off under gravity inside and to evaporate on the surface - depending on the wind and weather. A further construction supplies water at the top, metastabilizes the structures, but increases the load on the base. Where the sand dries, it trickles down and forms its dry angle of repose of around 30 °.
Straight line of a floor
The internal angle of friction of a floor can be determined in the laboratory in a shear test with experimental devices. The soil sample is loaded vertically and horizontally (for example in a three-axis device or box shear device ) until it breaks. The parameters of the shear line of the two-dimensional stress state are determined with the aid of Mohr's stress circle . In the stress diagram, the vertical stress is plotted on the horizontal x-axis and the shear stress on the vertical y-axis. The shear line is characterized by its slope (the angle to the horizontal is the angle of friction) and by the distance at which the shear line intersects the vertical axis. This distance is the cohesion . Grainy (cohesive) soils have no cohesion, but only an angle of friction, that is, the shear line goes through the zero point of the stress diagram.
Coulomb fraction condition
A floor that is in a state of stress below the shear line can withstand the load. In the case of a stress state on the shear line, it fails (“limit stress state”), stress states above the shear line are not possible. The greater the angle of friction and / or the cohesion, the higher the load capacity. See also shear law and Mohr-Coulomb's fracture criterion .
Proof of sliding safety
The angle of friction is used together with the cohesion to calculate the resistance of a structure to horizontal displacement ( e.g. foundations , (angle) retaining walls , dams ). This proof is called slip safety proof or also shear strength proof .
Sand pouring on differently shaped surfaces
| Support format | support | Angle of calm |
|---|---|---|
| rectangle |  |
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| circle |  |
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| space |  |
 
|
| triangle |  |
|
| Double fork |  |
|
| oval |  |
|
| A pit |  |
 
|
| Double pit |  |
|
| Multiple pit |  |
|
| Random format |
|
Embankments
Cohesion and the angle of friction are responsible for the angle at which a slope made of soil material can be created without collapsing or slipping. In addition to the cohesion and the weight of the soil , the angle of friction is also an important influencing factor when verifying a slope against slope failure .
Web links
- Lueger: Lexicon of the entire technology: angle of friction
- Contact Mechanics and Friction, by Valentin L. Popov
- Technical mechanics statics - dynamics - fluid mechanics - strength theory ... by Alfred Böge
Individual evidence
- ↑ http://kaernten.orf.at/news/stories/2622702/ Unknown people let road salt run out, ORF.at of December 29, 2013.