Angle of repose

The friction angle, or angle of internal friction is the angle at which a solid state or a granular material may be charged, without slipping off or fail. It is a measure of the friction talent of their surfaces (friction and roughness or smoothness). The internal friction angle of granular media is not identical to the " angle of repose " of bulk or with the " angle of repose " of a landfill.

The friction angle is specified in degrees. In calculations we used the tangent of the friction angle, which is dimensionless. 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 border state of equilibrium. It indicates the slope of the resultant force in the friction surface.

The angle of repose defines the slope of a heap or a poured batter. In nature, they are also found in debris cones ( see talus ).

Dry, pure sand consists of nearly equal size, rounded sand grains. As in a dense packing of spheres holds the sand hills only because of the friction between the grains. Once the sides of the hill exceed a critical angle, the sand begins to slip. Steeper than 40 ° can not become a heap of sand. For this reason, a dune top is never really sharp.

• 4.1 embankments

Friction of solids

If two solid bodies on a flat horizontal surface on each other, so is the friction angle, the angle of the resultant force from the horizontal force and vertical force acting between the two bodies, in the "border state of equilibrium ", ie without being already start to slip. A horizontal force acting in the direction of the planar surface on the upper body, trying push him. The vertical component of force N in the contact area ( "normal") is perpendicular to this surface, both bodies are pressed against each other, it determines the size of the possible frictional resistance R, which prevents slipping; R = N * m (with m: coefficient of friction of two materials; determine experimentally ). The smoother the surface, the smaller the m, and thus the angle of friction and possible friction force.

Friction in granular material, angle of repose

A granular wheeled aggregate ( such as sand ) has an internal friction angle which depends, inter alia, on the roughness of the grains. Pour the material is in a pile, then a conical heap. Depending on the angle of repose of the following characteristics:

• Roughness, the rougher, the greater the angle.
• Different particle size, the more different particle sizes are present, the greater the angle.
• Compression, the more the bulk material is compressed, the greater the angle.
• Moisture content, the angle increases with increase in the cohesion between the grains.

The influence of the high surface tension of the water in the capillary effective gaps between grains of fine sea sand is clearly dripping wet when building a sand castle. With a thin stream or drops of sand -water slurry from a low height congealed out of hand, pointy turrets let ( angle of repose nearly 90 ° ) constituting nearly vertical walls and even small, slightly protruding mushroom caps, the small-scale vertically hanging unsupported, so there forming an angle of repose of about 90 °.

The strongest permanent, but only superficially acting binding force developed the water up to the capillary rise above the water table - depending on material fineness and water - about 0.5 meters. In tears the water column in the sand matrix above from and air penetrates into the pores, water cements thus also in the depth of the " mortar ", but tends to under gravity inside abzurinnen and superficially - to evaporate - depending on the wind and weather. A further construction delivers above water after, metastabilisiert the superstructure, but increases the load on the base. Where the sand dries it trickles and forms its dry bulk angle of about 30 ° here.

Just a soil shear

The internal friction angle of a soil can be determined in the laboratory shear test with test equipment. The soil sample is (for example, in the case Dreiaxialgerät or shear device) vertically and horizontally loaded to failure. It can be found from the Mohr 's circle parameters of the shear line of the two-dimensional stress state. In the voltage graph, the vertical stress is applied to the horizontal x - axis and the shear stress on the vertical y-axis. The shear line is characterized by its pitch ( the angle to the horizontal, the angle of friction ), and. By the distance in which the shear line intersects the vertical axis This distance is cohesion. Granular ( non-cohesive ) soils have no cohesion, but only a friction angle, that is, the shear straight line passes through the zero point of the voltage chart.

Coulomb failure criterion

A bottom which is in a state of tension below the shear line, the load withstands. In a state of stress on the shear line it fails ("intrinsic state of tension " ), stress states above the shear line are not possible. The greater the angle of friction, and / or cohesion, the higher is the strength. See also Mohr- Coulomb failure criterion.

Gleitsicherheitsnachweis

The friction angle is used together with the cohesion to calculate the resistance of a structure against horizontal displacement (for example, foundations, (angle) retaining walls, dams ). This proof is called Gleitsicherheitsnachweis or shear strength test.

Embankments

Cohesion and friction angle are responsible for the angle at which an embankment of earth material may be applied without collapsing. Also the detection of an embankment against slope failure of the friction angle is in addition to cohesion and the weight of the soil is an important factor.