Optimizing the geometry of hunchbacked block-type gravity quay walls using non-linear dynamic analyses and supervised machine learning technique

In the present study, the seismic behavior of hunchbacked block-type gravity quay walls rested on non-liquefiable dense seabed soil layer is investigated and the optimal geometries for these wall types are proposed by performing non-linear time history dynamic analyses using Lagrangian explicit finite difference method. For this purpose, first, a reference numerical model of the hunchbacked quay wall is developed and its seismic response is validated against the well-documented physical model tests. Then, the optimal hunch angles corresponding to the minimum horizontal displacement and zero rotation of the hunchbacked quay wall are estimated through the sensitivity analyses on the hunch angle of the wall, the friction angle of the backfill, and the ratio of hunch height to wall height. Subsequently, the statistical relationships are presented to predict the optimal hunch angle of the walls using the multiple non-linear regression based on the supervised machine learning technique. The results of non-linear dynamic analyses show that the deformation pattern, the movement mechanism, and consequently the seismic response of the hunchbacked quay wall change considerably with the variation of the hunch angle of the wall. In this regard, the rotation angle of the wall towards the seaside due to seismic loading decreases, and the deformation pattern and the movement mechanism of the hunchbacked quay wall alter from overturning towards the seaside to overturning towards the landside with an increase of the hunch angle. For all considered values of the ratio of hunch height to wall height and the backfill friction angle, increasing the hunch angle in the range of 25 to 35 degrees leads to a significant decrease in wall deformation. While increasing the hunch angle in the range of 35 to 50 degrees has less influence on reducing the wall deformation. For hunch angle values greater than 50 degrees, increasing the hunch angle has the opposite effect on improving the seismic performance of the hunchbacked quay wall and its seismic-induced deformations increase. Additionally, in the ratio of hunch height to wall height equal to 0.7, the optimal hunch angles corresponding to the zero wall rotation and the maximum reduction in the horizontal displacement of the wall decrease from 42.7 to 9. 23 degrees and from 53 to 34.5 degrees, respectively, with an increase of the friction angle of the backfill soil from 15 to 45 degrees.