# The Open Civil Engineering Journal

ISSN: 1874-1495 ― Volume 13, 2019
RESEARCH ARTICLE

# An Integral Equation Model for a Pile in a Layered Transversely Isotropic Saturated Soil

Uwiduhaye Fabrice, Jian-Fei Lu*, Dan-Dan Jin
Department of Civil Engineering, Jiangsu University, Zhenjiang, Jiangsu, 212013, P.R. China

## Abstract

### Objective:

In this paper, an integral equation model is established to predict the time-dependent response of a vertically loaded pile embedded in a layered Transversely Isotropic Saturated Soil (TISS).

### Methods:

Based on the fictitious pile method, the pile-soil system is decomposed into an extended saturated half-space and a fictitious pile. The extended half-space is treated as a layered TISS, while the fictitious pile is considered as a 1D bar. The pile-soil compatibility is accomplished by requiring that the axial strain of the fictitious pile be equal to the vertical strain of the extended layered TISS along the axis of the pile. The second kind Fredholm integral equation of the pile is then derived by using the aforementioned compatibility condition and the fundamental solution of the layered TISS, which is equivalent to the solution of the layered TISS subjected to a uniformly-distributed load acting vertically over a circular area with the radius equal to that of the pile. The fundamental solution of the layered TISS is obtained via the Reflection-Transmission Matrix (RTM) method for the layered TISS. Applying the Laplace transform to the Fredholm integral equation, and solving the resulting integral equation, the transformed solution is obtained. The time domain solution of the pile-soil system is retrieved via the inverse Laplace transform.

### Results and Conclusion:

Numerical results of this paper agree with existing solutions very well, validating the proposed pile-soil interaction model. A parametric study is carried out to examine the influence of some parameters on the response of the pile-soil system.

Keywords: Pile, Layered Transversely Isotropic Saturated Soil (TISS), Consolidation, Fredholm integral equation, Fictitious pile method, RTM.

### Article Information

#### Identifiers and Pagination:

Year: 2018
Volume: 12
First Page: 316
Last Page: 339
Publisher Id: TOCIEJ-12-316
DOI: 10.2174/1874149501812010316

#### Article History:

Acceptance Date: 7/9/2018
Electronic publication date: 25/10/2018
Collection year: 2018

#### Article Metrics:

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open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: (https://creativecommons.org/licenses/by/4.0/legalcode). This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Civil Engineering, Jiangsu University, Zhenjiang, Jiangsu, 212013, P.R. China, Tel: (0086)15951284152; E-mail: ljfdoctor@yahoo.com

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