Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 382427, 12 pages

http://dx.doi.org/10.1155/2015/382427

## Correspondence Analysis of Soil around Micropile Composite Structures under Horizontal Load

^{1}Beijing Jiaotong University, No. 3, Shangyuancun, Haidian District, Beijing 100044, China^{2}Beijing Key Laboratory of Track Engineering, Beijing, China^{3}Beijing Engineering and Technology Research Center of Rail Transit Line Safety and Disaster Prevention, Beijing, China

Received 27 June 2015; Accepted 1 September 2015

Academic Editor: Fazal M. Mahomed

Copyright © 2015 Hai Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The current approach, which is based on conformal transformation, is to map micropile holes in comparison with unit circle domain. The stress field of soil around a pile plane, as well as the plane strain solution to displacement field distribution, can be obtained by adopting complex variable functions of elastic mechanics. This paper proposes an approach based on Winkler Foundation Beam Model, with the assumption that the soil around the micropiles stemmed from a series of independent springs. The rigidity coefficient of the springs is to be obtained from the planar solution. Based on the deflection curve differential equation of Euler-Bernoulli beams, one can derive the pile deformation and internal force calculation method of micropile composite structures under horizontal load. In the end, we propose reinforcing highway landslides with micropile composite structure and conducting on-site pile pushing tests. The obtained results from the experiment were then compared with the theoretical approach. It has been indicated through validation analysis that the results obtained from the established theoretical approach display a reasonable degree of accuracy and reliability.

#### 1. Introduction

Generally, the diameter of a micropile is about 70–300 mm in a small diameter filling pile [1]. The slenderness ratio is relatively big. Its preliminary application and exploitation were explored by Fondedile in Italy [2]. Micropile composite structures refer to antislide structures that are composed of several, miniature, and single piles with a cap lid at the pile tip, which jointly bears the horizontal load [3]. The structure adeptly adapts to shifting terrain during construction with small vibration and noise caused by the construction. It is characterized by a small pile diameter, rapid construction, and flexible piles. Thus, it has been widely used in building reinforcements, shake-proof, foundation underpinning, foundation excavation support, landslide control, and other types of engineering found in buildings [4–6].

Previous research on micropile structure mainly discussed ground stabilization, building and rectification, and so forth at vertical load bearing, which was specific to internal force deformation calculations, an analysis of micropiles, and the internal force calculation of a combination of micropile groups [7–9]. The initial research yielded some achievements. Cantoni et al. [10] proposed a design and calculation method based on reticular micropiles, working under the assumption that the retaining structure would need to be complex; when Macklin designed the anchorage retaining wall, he simplified it as gravity retaining walls in order to analyze the internal force of the micropile [11]; Feng et al. [12] proposed an interaction analysis model for the pile-rock soil and mass-piles found in flat micropile systems; they also established a mechanical model to calculate the internal force and deformation of a micropile system using a finite element method; Juran et al. [1] proposed a design approach using a mesh micropile reinforced slope, by assuming that the dense composite strengthening body formed by reticular micropiles, the internal soil mass, and the internal system were not subjected to tensile stress; furthermore, Brown and Shie [13] calculated a pile’s internal force by applying a nonlinear, elastic-plastic subgrade reaction method (called the curve method). However, there was less research on micropile structures under horizontal load. At present, most of the previously discussed engineering designs of micropiles adopt a calculation approach of specific to normal, antislide piles. However, the force model and design calculation theory of micropile composite structure have not been perfected yet. Establishing a calculation mode suitable for micropile composite structure and proposing a reasonable calculation method are urgently needed. Thus, this paper further explores research that capitalizes on this missed opportunity.

This paper discusses an analytical solution to stress and displacement distribution under horizontal load, based on the mechanics theory of two-dimensional elastic complex functions. Using the Winkler Foundation Beam Model, this paper assumes that the soil around a micropile stems from a series of independent springs. The rigidity coefficient of a spring can be obtained using the planar solution. After that, based on the deflection curve of the differential equation of an Euler-Bernoulli beam, the pile deformation and internal force calculation methods of a micropile composite structure under horizontal load can be derived using two modes, namely, by fixing one end, with the other end sliding, as well as fixing both ends. In the end, the paper suggests reinforcing highway landslides using micropile composite structures and conducting on-site pile pushing tests. The results obtained from the experiment have been compared to the theoretical approach to verify the accuracy and reliability of the theoretical approach.

#### 2. Establishment of the Plane Strain Solution Model of Micropiles

##### 2.1. Description of the Problem

Then, researching the effects of horizontal load on the micropiles, it is important to consider the internal force and deformation analysis of rigid disc hole structure around the semi-infinite space surface at the plane (rectangular coordinate system). As shown in Figure 1, the region is a region of semi-infinite space, except for the disc-structure, and is the distance between the soil around the pile and the center of the pile; is the radius of the disc-structure; and is the horizontal load applied in the center of the pile ( is component of direction; is component of direction). It is assumed that is the displacement under horizontal load applied in the center of the pile.