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## Calculation of the wall displacement |

To calculate the wall displacement due to the earthquake, DReW Seismic compares the ground acceleration time-history with the critical threshold at any time of the simulation.

When the ground acceleration exceeds the critical threshold, the motion equation is solved to calculate the angular acceleration of the wall. Once this latter is known, angular velocity and rotation (θ) of the wall are calculated by successive integration. All the equations employed can be found in the paper by Conte, Pugliese and Troncone (2022).

Finally, the displacement of the top of the wall (u) is calculated under the reasonable assumption that the wall rotates rigidly around a point located at a distance Y from its base, as shown from the following figure.

Movement undergone by the wall during the earthquake

A schematic representation of the integration procedure is shown in the following figure.

Schematic representation of the integration procedure of the differential equation of motion