Advances in Civil Engineering

Volume 2017 (2017), Article ID 9897658, 9 pages

https://doi.org/10.1155/2017/9897658

## Design Diagrams for the Analysis of Active Pressure on Retaining Walls with the Effect of Line Surcharge

Shiraz Art Institute of Higher Education, Shiraz, Iran

Correspondence should be addressed to Mohammad Karim Faghirizadeh; moc.liamg@hedazirihgaf

Received 2 November 2016; Revised 15 February 2017; Accepted 5 March 2017; Published 2 May 2017

Academic Editor: Pier Paolo Rossi

Copyright © 2017 Mojtaba Ahmadabadi and Mohammad Karim Faghirizadeh. 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

In this study, a formulation has been proposed to calculate the pressure on wall and determine the angle of failure wedge based on limit equilibrium method. The mentioned formulation is capable of calculating active pressure coefficient, culmination of forces in failure surface, and pressure distribution on wall with the effect of line surcharge. In addition, based on the proposed method, a simple formula has been proposed to calculate the angle of failure wedge by the effect of surcharge. Moreover, the proposed approach has the advantage of taking into account the effect of surcharge on elastoplastic environment by considering the parameters of soil and determining the extent to which the surcharge is effective in pressure distribution on the wall. However, in most previous methods and specifications, resultant lateral pressure from surcharge in elastic environment had been considered. Finally, based on the obtained results, the design diagrams for different soils and different surcharges have been proposed. According to these diagrams, pressure on wall, pressure distribution on wall, and angle of failure wedge will easily be achieved. Also, a computer program has been written in MATLAB software environment. Using the results of these codes, the pressure on wall with the effect of surcharge, the angle of failure wedge, and pressure distribution on wall will be determined.

#### 1. Introduction

The calculation of active soil pressure on retaining walls is of fundamental issues in foundation engineering. It is typically examined using the theory proposed by Coulomb [1] or Rankine theory [2]. On the other hand, active pressure is influenced by external loads affecting the soil behind the wall. In order to calculate the resultant lateral pressure on retaining walls caused by surcharge, Boussinesq method [3] is usually used that assumes a homogeneous and elastic behavior for soil. On the other hand, referring to the difference between the results of elastic methods by Boussinesq [3], Das [4] proposed equations with the assumption of elastic behavior to calculate the surcharge with actual values.

Gerber [5] and Spangler [6] examined the effect of surcharge on lateral pressure on retaining wall caused by a concentrated load using large-scale tests. The principles of the theory of elasticity to study the effects of line surcharge were initially used by Misra [7] and for strip surcharge by Jarquio [8]. In addition, Motta [9] offered a method for extensive uniform surcharges using developed Coulomb formulation and calculated active pressure on wall with the effect of surcharge according to the angle of failure wedge.

Seismic stability of retaining walls due to the effect of surcharge was studied by Caltabino et al. [10]. The researchers considered the effect of earthquake as quasi-static based on the method presented by Okabe [11] and Mononobe and Matsuo [12].

Using experimental results, Georgiadis and Anagnostopoulos [13] compared the result of pressure on shields under surcharge with those of different methods, including elastic stress distribution, and approximation of 45-degree slope, as well as the results of Coulomb method. As a result, elastic approach has a significant difference with real values. Kim and Barker [14] studied the impact of live surcharge caused by traffic load on retaining walls. The researchers proposed an analytical approach to calculate horizontal active pressure on retaining wall using equivalent bending moment method.

Using the theory of Coulomb, Greco [15–18] investigated the effect of strip surcharge on active pressure on nonreinforced retaining walls and presented an analytical method for the calculation of pressure and the resultant effect point. AASHTO [19] and US Army Crops [20] specifications proposed an analytical method for calculating resultant lateral earth pressure caused by surcharge according to the type of surcharge incurred on the wall. Cheng [21] presented lateral pressure coefficient in seismic state for cohesive-friction soils and surcharges.

Basha and Basudhar [22] examined the stability of reinforced soil structures under seismic conditions using limit equilibrium method and assuming logarithmic spiral wedge failure. The researchers imposed seismic acceleration on reinforced soil structures using quasi-static method.

Ghanbari and Taheri [23] calculated the pressure on wall and reinforced force with the effect of surcharge on reinforced soil walls, under the assumption of Ahmadabadi and Ghanbari [24]. The results for changes in the angle of failure wedge with the size of the surcharge suggest that increasing the amount of surcharge will result in an increase in the angle of failure wedge; however, by changing the distance of the surcharge from the wall, the angle of failure wedge does not change any more. The results of their research indicate that with increasing the distance of surcharge from the wall, the lateral pressure of soil will be reduced and when it is out of the angle of failure wedge, it has no effect on active earth pressure.

In this paper, a simple solution has been presented to calculate active pressure on wall with effect of line surcharge using limit equilibrium method. In the previously proposed methods, either the effect of friction angle between soil and wall was neglected or complex and lengthy solutions were required. The primary objective of the research was to develop a simple method based on limit equilibrium that can calculate the angle of failure wedge and force distribution on wall with the effect of surcharge. Then the effect of angle of internal friction angle, the amount of line surcharge, the distance of line surcharge from the wall, and the angle of internal friction of soil will be discussed.

#### 2. Formulation for the Calculation of Pressure on Retaining Walls with the Effect of Line Surcharge

According to Figure 1, a retaining wall where is the angle of internal friction between soil and wall will be considered. If the hypothetical angle of failure wedge forms the angle with the horizon, according to Figure 2, the angle which calculates the greatest amount of pressure on the wall with the line surcharge can be shown with and without the surcharge, it can be shown with . To achieve the desired formulation, the following assumptions can be considered:(1)The failure surface is considered as a page.(2)The analysis is based on the limit equilibrium method.(3)The failure surface passes from the wall.(4)The soil mass is considered homogeneous.(5)The behavioral model intended for cohesive soil is elastoplastic model of Coulomb.According to Figure 1, with the line surcharge, equilibrium equations for a hypothetical failure wedge can be written as follows:By solving the three equations for each experimental wedge, , , and for the th failure wedge () are obtained. Now, in the proposed formulation in order to determine the angle of failure wedge, the amount of active pressure on wall is calculated for different angles of failure wedge; then the angle that gives maximum active pressure is recorded as the angle of failure wedge, where is the active soil pressure without surcharge with , is the active soil pressure with the effect of line surcharge with , and is the added pressure on wall under line surcharge.Given the distance of surcharge from the wall, in order to calculate the pressure on wall (), three modes are considered.