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# Numerical Analysis of Laterally Loaded Long Piles in Cohesionless Soil

Ayman Abd-Elhamed1,2,*, Mohamed Fathy3, Khaled M. Abdelgaber1

1 Physics and Engineering Mathematics Department, Faculty of Engineering-Mattaria, Helwan University, Cairo, 11718, Egypt
2 Faculty of Engineering, King Salman International University, South Sinai, Ras Sedr, Egypt
3 Basic and Applied Science Department, College of Engineering and Technology, Arab Academy for Science, Technology and Maritime Transport, Cairo, 11799, Egypt

* Corresponding Author: Ayman Abd-Elhamed. Email:

(This article belongs to this Special Issue: Artificial Intelligence and Machine Learning Algorithms in Real-World Applications and Theories)

Computers, Materials & Continua 2022, 71(2), 2175-2190. https://doi.org/10.32604/cmc.2022.021899

## Abstract

The capability of piles to withstand horizontal loads is a major design issue. The current research work aims to investigate numerically the responses of laterally loaded piles at working load employing the concept of a beam-on-Winkler-foundation model. The governing differential equation for a laterally loaded pile on elastic subgrade is derived. Based on Legendre-Galerkin method and Runge-Kutta formulas of order four and five, the flexural equation of long piles embedded in homogeneous sandy soils with modulus of subgrade reaction linearly variable with depth is solved for both free- and fixed-headed piles. Mathematica, as one of the world's leading computational software, was employed for the implementation of solutions. The proposed numerical techniques provide the responses for the entire pile length under the applied lateral load. The utilized numerical approaches are validated against experimental and analytical results of previously published works showing a more accurate estimation of the response of laterally loaded piles. Therefore, the proposed approaches can maintain both mathematical simplicity and comparable accuracy with the experimental results.

## Keywords

A. Abd-Elhamed, M. Fathy and K. M. Abdelgaber, "Numerical analysis of laterally loaded long piles in cohesionless soil," Computers, Materials & Continua, vol. 71, no.2, pp. 2175–2190, 2022.

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