# Optimization of Uplift Piles for a Base Plate Considering Local Anti-Floating Stability
## 4 Case Study
\begin{table}
\begin{tabular}{c c} \hline \hline
**Model Properties** & **Value** \\ \hline Length \(\times\) Width \(\times\) Height (m) & 500 \(\times\) 500 \(\times\) 80 \\ Young’s modulus of soil (GPa) & 0.13 \\ Poisson’s ratio of soil & 0.3 \\ Friction angle of the soil (\({}^{\circ}\)) & 20 \\ Cohesion of soil (kPa) & 30 \\ Hydraulic head (m) & 20 \\ Thickness of the base plate (m) & 1.5 \\ Bulk modulus of the base plate (GPa) & 13.9 \\ Shear modulus of the base plate (GPa) & 10.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of numerical model. * When the uplift piles for the base plate adopts large pile diameter and sparse spacing, the initial deformation degree of the base plate is large. The BESO process can greatly reduce the maximum differential deformation and total strain energy of the base plate. After optimization, the dispersion degree of pile lengths distribution is large. * When the uplift piles for the base plate adopts small pile diameter and dense spacing, the initial deformation degree of the base plate is small. During the optimization process, the maximum differential deformation and total strain energy are small and oscillated. After optimization, the pile lengths are close. * To consider the local anti-floating stability of the base plate, the uplift piles should be preferably designed with small pile diameters, dense spacing, and equal pile lengths. If only the design of large pile diameter and sparse spacing can be adopted, long piles should be arranged at the center area of the base plate; short piles should be arranged at the edge area and under the column loads. The length ratio of the short piles to the long piles should be about 0.4-0.6. * The deformation degree of the base plate of optimization design 1 (large pile diameter and sparse spacing, unequal pile lengths) and optimization design 2 (small pile diameter and dense spacing, equal pile lengths) are significantly lower than the original design. It proves that the two optimization designs can effectively increase the local anti-floating stability for the base plate. * In the numerical calculation related to the pile resistance, if the model has a large area of the base plate and a large number of piles, in order to improve the computational efficiency, the solid unit of the pile has to be replaced by the built-in pile unit in the numerical software, and it is still necessary to study and develop the topology optimization methods and procedures applicable to the pile unit, so as to promote the application in the actual engineering. Methodology, M.Y. ; writing--original draft, M.Y. ; funding acquisition, M.Y. and P.L. ; visualization, J.W. ; writing--review & editing, J.W. ; software, Q.L. ; formal analysis, Q.L. ; investigation, Q.L. ; data curation, J.W. ; supervision, P.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the Natural Science Foundation of China under Grant No. 51978018, Supported by Science and Technology Funding Scheme for the Third Construction Engineering Company LTD. of China Construction Second Engineering Bureau No. CSCEC2b3c-2021-K-65. Not applicable. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. The authors greatly appreciate the financial support from funding bodies and would be grateful to the reviewers for their valuable comments and suggestions to improve the quality of the paper. Author [PERSON] was employed by the company The Third Construction Engineering Company LTD. of China Construction Second Engineering Bureau. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. 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.