Discrete Dynamics in Nature and Society

Volume 2018, Article ID 6946492, 9 pages

https://doi.org/10.1155/2018/6946492

## Deformation Analysis of Reinforced Retaining Wall Using Separate Finite Element

^{1}School of Highway, Chang’an University, Xi’an 710064, China^{2}Shandong Provincial Communications Planning and Design Institute, Jinan 250031, China

Correspondence should be addressed to Xingli Jia; moc.anis@6210lxj

Received 18 December 2017; Accepted 5 July 2018; Published 5 September 2018

Academic Editor: Alicia Cordero

Copyright © 2018 Xingli Jia 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

In order to reveal the main factors affecting the deformation of reinforced soil retaining wall and the influence of various factors on the deformation, the constitutive relation is discretized into four aspects of soil, geogrid, wall panel, and contact surface, and discrete element matrices are, respectively, constructed, with the method of separate finite element. Based on the finite element geotechnical analysis technology platform, the deformation analysis model of reinforced soil retaining wall is established. Taking the modulus of foundation soil as the influencing factor of the foundation soil, taking the geogrid stiffness, length, and spacing as the influencing factors of geogrids, and taking the filling type of limestone, fly ash, and silty clay as the influencing factors of backfill in the wall, the horizontal and vertical deformations of reinforced retaining wall under different factors using the methods of controlling a single variable analysis are calculated. The results show that the increase of elastic modulus of foundation soil will reduce the vertical deformation of the wall but increase the horizontal deformation. The silty clay is not suitable as filler, and lime soil is slightly better than fly ash. The spacing between geogrids is 20 cm ~ 60 cm, which has less effect on wall deformation, but the horizontal deformation rapidly increases after the spacing increases to 80 cm, and other grid performance influencing factors also have the characteristic, where there exists a threshold. The wall will have a greater deformation when the threshold is not reached; a higher indicator of the grid to reduce the deformation of the retaining wall is not obvious after reaching the threshold.

#### 1. Introduction

As a typical flexible retaining structure, reinforced soil retaining wall has the characteristics of beautiful appearance, less occupation, good coordination, convenient construction, and strong adaptability [1, 2] and can improve the strength and stability of roadbed, is widely used in highway infrastructure construction, and has become an important part of highway infrastructure construction. However, due to the complicated engineering characteristics of the reinforced soil retaining wall itself, the nonlinear changes of various factors in different conditions, and the interaction between various factors, the deformation characteristics of the reinforced retaining wall are relatively complex.

The deformation of the reinforced retaining wall is affected by many factors, not only its wall structure and filling material, but also the properties of the reinforced material [3]. The deformation data of reinforced soil retaining wall can be observed by field observation, which is true and accurate [4], while lacking general applicability because of the variety of environment, construction technology, and operating status with strong individual differences.

Large-scale finite element simulation technology is introduced into the deformation analysis of reinforced earth retaining wall to reduce the analysis error caused by individual heterogeneity. The stress-strain characteristics and the interaction between soil effects [5, 6] of the material can be considered with the using of finite element method, to accurately simulate deformation trend of the wall. Clough [7] reviewed and derived the finite element incremental formulations for nonlinear static and dynamic analysis, including large displacements, large strains, and material nonlinearities, and the solution of static and dynamic problems involving large displacements and large strains are presented. Zhang [8] analyzed geogrid deformation, wall bottom pressure, and fracture plane of the retaining wall according to the field test on three different geogrid reinforced earth high retaining walls. The results show that there is a single peak in the pressure distribution at the bottom of the wall. Chen [9] gave out finite element modeling, which were performed on RSW with various fillings and foundations. The results indicate that a statistical function relationship exhibits between the maximum settlement and the facing slope at the bottom of RSW. Anastasopoulos [10] studied the seismic performance of a typical bar-mat retaining wall theoretically and experimentally, a series of reduced-scale shaking table tests are carried out with various kinds of earthquake excitation (real records and artificial multicycle motions), and the problem is carried out by finite element method. Mowafy [11] states that deformation caused by wall movement is an important indicator of reinforced earth retaining wall; the influence of reinforcement global stiffness, the height of the wall, the friction angle of the soil on the earth pressure coefficient, and the maximum wall displacement are important with the using of the finite element program, ANSYS. Yang [12] built finite element models that are used to simulate the behavior of large-scale geosynthetic reinforced soil retaining walls, showing that the constitutive models and finite element model can predict the important features of wall performance accurately. Ye [13] conducted a finite element analysis to simulate a reinforced earth retaining wall for embankment by using the finite element software Plaxis; the calculated results of reinforced earth retaining wall with three facing types are analyzed, including the lateral earth pressure and the vertical earth pressure, to investigate the influence of different facing types on the mechanical properties of the reinforced earth retaining wall for embankment. Bui [14] simulated postfailure behavior and large deformations of soils and retaining wall blocks in SRW systems, using a new computational framework based on smooth particle hydrodynamics (SPH) method, within which a new contact model is proposed to simulate the interaction between the soil and the blocks and between the blocks. Ouria [15] established the finite element model which is used to study the behavior of a CFRP reinforced wall based on the laboratory results for backfill soil and interface data. Ou [16] analyzed the retaining wall vertical deformation impact parameters such as reinforced spacing, foundation stiffness, and lateral deformation by using the nonlinear analysis software ADINA. The results indicate that rational design of grid, panel, foundation, cushion modulus, and thickness can effectively lessen the vertical deformation and uneven settlement of the retaining wall. Wu [17] used the analysis focused on the dynamic response characteristics of the wall under the influence of different reinforcement to study the dynamic properties of reinforced earth retaining walls under seismic load which were analyzed by using Plaxis.

The typical filling type, reinforced material, and wall structure are selected, and the constitutive relation and element matrix are constructed by using the separated finite element method, to find out the general rule of the deformation of reinforced soil retaining wall. The influence mode and degree of various factors on the deformation of reinforced earth retaining wall are analyzed, and the technical reference for improving the stability of the wall is finally provided.

#### 2. Theory and Method

##### 2.1. Constitutive Relation Model

The deformation of soil is determined by soil plasticity, and the basis of determining whether the soil makes plastic deformation is the yield function, reflecting the relationship between stress and strain of soil; soil constitutive relationship is the stress-strain relationship; the Molar Coulomb elastoplastic model (Mohr-Coulomb) is used in this study [18, 19]. The study of reinforcement materials is geogrid, which is a material of higher strength and modulus, buried and pulled in the filler layer by layer, the geogrid is identified as a one-dimensional linear rod unit that is subjected only to tension without stress and capable of axial strain only. Wall panels are made of concrete blocks, wall panels can be simplified as a plate model, and the linear elastic constitutive relations are used in geogrid and wall panels. Discrete analysis is used to separate the reinforced material from the soil, and there is a relative displacement between the two. The contact surface unit is set up between the two. The frictional resistance is generated during the relative movement of the reinforced material and the soil.

##### 2.2. Finite Element Matrix

The study is to solve the problem of plane strain, using the displacement method. The element matrix of each element of soil, geogrid, wall panel, and contact surface should be deduced, respectively, and the stress, strain, and displacement should be solved according to the corresponding matrix [20].

###### 2.2.1. Soil Element Matrix

The soil unit selects the triangular element body, and the displacement at the node is expressed as

The displacement at any place in the unit is expressed as

The displacement at the node is expressed as

Let

It can be obtained that

The shape function selected is expressed as

The element stiffness matrix is expressed as

According to the principle of virtual work

is solved:

where is the displacement at the node, is the displacement at any place in the unit, is the stress at any place in the unit, is the strain at any place in the unit, is the stiffness matrix of the unit, is the strain matrix of the unit, is the elastic matrix of the unit, and is the stress matrix of the unit, t is the thickness of the unit, the general value is 1.

###### 2.2.2. Geogrid Element Matrix

The constitutive relation of the geogrid element is linear elastic [21], and its stiffness matrix is defined as

is the elastic modulus of geogrid (KN/m^{2}); is the equivalent section area (m^{2}); is the length of the geogrid (m).

is the angle between the geogrid unit and the axis of the coordinate system.

The calculation methods of node force, node displacement, stress, strain, and deformation are the same.

###### 2.2.3. Wall Panel Element Matrix

The constitutive relation of the wall panel element is linear elastic, and its stiffness matrix is defined as

is the elastic modulus of the beam element of the wall panel; is the inertia moment of a section on a unit length; is unit length.

The element stiffness matrix above is established in natural coordinates, while the natural coordinates are not consistent with the overall coordinates in some cases that the conversion between the two coordinate systems needs to be performed, which is not described in detail herein.

The calculation methods of node force, node displacement, stress, strain, and deformation are the same.

###### 2.2.4. Contact Surface Element Matrix

The contact surface model is made up of four-node element matrix without thickness, which is composed of two contact surfaces 12 and 34 with a length of L, assuming that there are numerous microsprings between the two interfaces to connect. The 12 and 34 contact surfaces are connected in one block and can be regarded as a one-dimensional unit, before subjected to force [22]. The relationship between the soil element and the contact surface unit and the geogrid unit will be related to the relevant forces only at the junction. Assuming that the displacement mode is linear, the displacement of the node can be expressed as the displacement of each point in the direction of the contact surface along the length direction. The displacement in the direction of X coordinates is expressed by , and the displacement in the direction of the Y coordinates is expressed by .

The displacement of the top surface is as follows:

The displacement of the bottom is as follows:

The displacement of any point on the unit body of the contact surface can be interpolated by the node displacement, as follows:

where

Let

Get

According to the principle of virtual displacement, it can be obtained:The node displacement will be obtained by superimposing the stiffness matrix of each contact element on the global stiffness matrix; through the general balance condition of nodes, the stress and deformation are then obtained according to , .

##### 2.3. Deformation Analysis Model Based on the Separated Finite Element

The Plaxis is used to establish the finite element stability analysis model of the reinforced soil retaining wall. The interface unit is introduced in the modeling, which mainly includes the horizontal interface between the reinforced material and the filler, and the vertical interface between the wall panel and the filler. The triangular element of fifteen nodes is used in the division of the finite element meshes; the standard fixed boundary is selected. The materials used, such as geogrids, packing, foundation soil, and graded gravel, were taken from the site of the DeShang Expressway. The properties of the geogrid are shown in Table 1.