### Project: Statics of drystone walls

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What is calculated

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EARTH PRESSURE

The retaining wall to be designed supports the soil behind it and possibly additional superimposed loads (buildings, traffic). Various calculation methods are used to calculate the earth pressure (https://de.wikipedia.org/wiki/Erddruck).

In the following interactive calculation example, the calculation method according to Coulomb is used. In this calculation method, it is assumed that a rigid earth wedge slides downwards on a straight sliding surface and presses on the retaining wall. The sliding movement is inhibited by friction in the sliding joint. The remaining force of the earth wedge acts on the retaining wall. The point of application of the force is at the point of the first third of the wall height from below. The force does not act horizontally on the back of the wall, but is inclined downwards due to the friction between the back of the wall and the soil. It is assumed that this inclination is equal to the internal friction angle of the soil (cf. point C.1.1 Merkblatt SIA 2053).

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RESULTING FORCE

The earth pressure and the dead weight of the wall together form the resulting force. The point of application of the** resulting force **is at the intersection of a vertical line through the centre of gravity of the trapezoidal cross-section and the straight line through the direction of force of the earth pressure.

Based on the position of the intersection between the **resulting force** and the foot line of the trapezoidal cross-section, two types of failure of the gravity wall can be checked:

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TILTING

In case of failure by tilting, the whole trapezoidal cross-section rotates forward around the front footpoint.

As long as the resulting force intersects the baseline of the trapezoidal cross-section, the wall is stable. The further the intersection point moves towards the outside, the smaller is the "safety reserve". As a rule the intersection point must therefore be in the middle third of the baseline.

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SLIDING

In the case of failure by sliding, the** resultant force** exceeds the frictional force of the stones lying on top of each other.

The friction angle of the rock is drawn from the point of intersection between a vertical line through the centre of gravity of the trapezoidal cross-section and the straight line through the direction of force of the earth pressure. The side of the friction angle facing the earth forms a right angle with the foot line of the trapezoidal cross-section. As long as the resulting force is within the angular range of the friction angle, no slippage of the stones occurs. Regarding this method of representation, see also the section on friction.

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TILTING & SLIDING

Common type of failure: In practice, a mixture of both types of failure is often found in defective dry stone walls. If too few long binder blocks are installed in the foundation area, the wall can rotate forward and slide forward at the same time. This creates a typical "fracture zone" running diagonally downwards.

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Disclaimer

The following interactive worksheet is for educational purposes only. It must not be used for dimensioning real retaining walls in dry stone masonry. Any dimensioning of a dry stone wall must be carried out by a civil engineer. Any use is at the user's own responsibility.

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Use of the interactive dimensioning example

The parameters of the earth pressure and the masonry can be adjusted with the various sliders. The geometry of the trapezoidal cross-section can be changed by pulling the corners of the cross-section into the appropriate position. The grid shown has a machine width of one metre.

The foot line is divided into three parts with** ****blue crosses**** ****X**. To prevent tipping, the intersection with the **resulting force** (orange) must be in the middle third. The **friction angle of the rock** is shown in red. If the resultant force (orange) lies within the red triangle, there is sufficient safety against slipping.

Interactive design of a gravity retaining wall of dry stone masonry

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Location of greatest stress in the wall section

If the resulting force is calculated at different heights of the trapezoidal cross-section, it can be observed that the resulting force intersects the base line of the trapezoidal cross-section further and further out, the closer to the base of the wall it is calculated. In the lower third of the wall height, the masonry is therefore exposed to a greater stress towards the outside than in the parts of the wall further up.

Use the **ORANGE SLIDER** in the interactive graphic below to see the resulting force at different heights of the wall cross-section.