## 5 Summary and Conclusions  
This study employed a unique approach of cyclic loading (via simple shear testing) to evaluate the effects of particle shape (in terms of roundness, sphericity and regularity) on the damping ratio of dry sand, which has practical implications for geotechnical engineering applications. Moreover, two AI-based models (ANN and SVM) were developed that can effectively predict the effects of sand particle shape on the damping ratio. Based on the experimental results and AI-based modeling results, the following conclusions can be drawn:  
* The shape of the sand particles changes during cyclic loading, becoming progressively more rounded and spherical with an increasing number of loading cycles, resulting in an increase in the damping ratio.
* The damping ratio was found to decrease as the number of loading cycles increased. This can be attributed to the fact that cyclic loading rearranges the sand particles, prompting an increase in the packing capability (and hence a decrease in the volume of voids) of the samples. This is followed by an increase in the number of contact points between the particles, thereby leading to higher energy dissipation during cyclic loading.
* Compared to the SVM, the proposed ANN model, trained using LM algorithms, was found to produce more promising results in predicting the damping ratio of the dry sand as a function of the particle shape parameters, vertical stress, number of loading cycles and CSR. This was supported by the model's high \(R^{2}\) value of 0.962 for both the training and testing datasets.
* Based on the sensitivity analysis results, vertical stress was found to be the most important parameter affecting the damping ratio, while the effects/importance of the CSR were relatively small. That is, increasing the vertical stress resulted in an increase in the damping ratio, while the effects of increasing the CSR on the damping ratio were fairly small. This is because vertical stress plays a major role in controlling the contact forces between the sand particles (and hence the energy dissipation) during cyclic loading.  
Further research is recommended to validate the results of the proposed AI-based model and to investigate the impacts of other factors on the damping ratio, such as particle size, particle sorting and loading rate. Moreover, the study could be expanded to include other soil types and to investigate the effects of particle shape on other relevant geotechnical properties, such as shear strength and compressibility.  
Conceptualization, A.B.; methodology, A.B.; software, A.B., R.S and H.B.; validation, A.B., S.C. and A.S.; formal analysis, A.S.; investigation, A.B.; resources, A.B.; data curation, A.B. and R.S.F.; writing--original draft preparation, A.B. and A.S.; writing--review and editing, A.B., A.S. and R.S.F.; visualization, A.B., A.S. and H.B.; supervision, S.C.; project administration, A.B.; funding acquisition, A.B. and S.C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The first author gratefully acknowledges Deakin University for making this research possible through the provision of the Australian Government Research Training Program (RTP) Scholarship.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.