### Project: Statics of drystone walls

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Statics / Friction

Friction is a force that impedes the sliding of bodies in contact with each other. If the bodies lie on top of each other without moving, the friction is called static friction; if they move against each other, it is called ** sliding friction**.

The friction between two objects depends on the weight of the material and the surface condition of the contact surface (rough, smooth, dry, wet, etc). The force that has to be applied to move two objects lying on top of each other against each other is called the __frictional force f__.

The friction coefficient μ and the friction angle θ are used as measures of friction.

A simple way to measure the coefficient of friction μ is to place two objects on top of each other and then tilt them until the top object slides. The angle at which one object starts to slide on the other is called the friction angle θ.

The coefficient of friction μ is defined as the tangent of the angle of friction θ and, conversely, the angle of friction θ corresponds to the arctan of the coefficient of friction μ.

If two stones lie horizontally on top of each other, there is no frictional force f. If, on the other hand, the stones are tilted slowly, the frictional force increases. The frictional force counteracts the force of gravity, which pulls the stone on top downwards. As the angle increases, the component of gravity eventually exceeds the maximum value of the frictional force f, and the object slides off. The angle at which the stone slips is called the angle of friction.

The friction values (friction coefficient, friction angle) change depending on the surface condition of the stones (broken, sawn, etc). In dry masonry we work with broken / rough pointed stone surfaces. The following friction values for such surfaces can be found in the technical literature:

Friction is reduced if the contact surface is wet or if there is an additional fine material in the joint ( sand, earth, clay).

Explanation of the interactive graphic below:

The parameters for inclination, weight and coefficient of friction can be set on the sliders.

The graph shows the components of gravity (Bx) and the counteracting friction force (A). If the force of gravity exceeds the friction force, the stone slides away.

Typical values of friction coefficients for different types of rock:

__Class / Coefficient of friction / Associated rock types__

Low friction / 0.36 -0.51 / slate (high mica content), slate, marl

Medium friction / 0.51 - 0.67 / sandstone, siltstone, chalk, gneiss, slate

High friction / 0.67 - 0.84 / basalt, granite, limestone, conglomerate

If an additional force acts on the stone (for example, another stone that pushes, or the soil of the slope behind it), the conditions change.

If the additional force pushes upwards, it counteracts the force of gravity. In order for the stone to slide, an additional force must be applied that exceeds the component of gravity AND the frictional force.

If the additional force pushes downwards, it acts together with gravity. For the stone to slide, the added forces (gravity and additional force) must be greater than the frictional force. In this case, it takes much less force to make the stone slide.

In masonry, this experiment corresponds to the inclination of the bearing surfaces of the bricks. If they are inclined towards the slope, much more force is needed to make the bricks slide. If the bearing surfaces are inclined towards the outside, a small additional force is sufficient to cause the bricks to slide.

In another representation of the interactive graphic of our stone, the resulting force (X) is formed from "additional force" and gravity.

The angle of friction RWI (shown in grey) is plotted from the centre of gravity against the foot line of the stone, with the left limit of the angle forming a right angle with the foot line (point N).

If the resulting force (X) is inside (or outside to the left) of the triangle of the angle of friction RWI, the stone remains stable. If the resulting force (X) is outside the triangle of friction angle RWI on the right, the stone slides away.

Typical values of friction coefficients for different rock types:

Class / Friction angle (dry) / Associated rock types

Low friction / 20° - 27° / slate (high mica content), slate, marl.

Medium friction / 27° - 34° / sandstone, siltstone, chalk, gneiss, slate

High friction / 34° - 40° / basalt, granite, limestone, conglomerate

We encounter this representation again in the interactive graphic for retaining wall dimensioning.