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Int. J. Struct. & Civil Engg. Res. 2015 Siddharth Mehta and Siddharth Shah, 2015

SEISMIC ANALYSIS OF REINFORCEDEARTH WALL: A REVIEW

Siddharth Mehta1* and Siddharth Shah2

1 PG Student, Marwadi Education Group of Institutions, Gauridad, Rajkot, Gujarat 360003.2 Head & Associate Professor, Marwadi Education Group of Institutions, Gauridad, Rajkot, Gujarat 360003.

*Corresponding author:Siddharth Mehta [email protected]

ISSN 2319 – 6009 www.ijscer.comVol. 4, No. 1, February 2015

© 2015 IJSCER. All Rights Reserved

Int. J. Struct. & Civil Engg. Res. 2015

Review Article

INTRODUCTIONReinforced soil retaining walls or reinforcedearth walls (commonly grouped asMechanically Stabilized Embankments –MSE) which are advantageous over traditionalretaining walls due to its long height.Reinforced earth wall was developed in 1970’sin USA. Reinforced earth is a compositematerial constructed with artificial reinforcingformed by interaction between frictional soiland reinforcing strips. MSE walls are typicallyconstructed using four structural components:(1) geogrid reinforcement; (2) wall facing; (3)retained backfill; and (4) reinforced backfill soil(Kishan, 2010).

The concept of seismic analysis of reinforced earth wall along with soil structure interaction isreviewed and discussed. A systematic summary of history and status of seismic analysis ofreinforced earth wall and soil structure interaction is proposed in these paper. Various methodsfor analysis considering different seismic parameters different soil conditions are discussedalong with work in numerical modelling. Parametric studies illustrate the effects of seismicacceleration on the design of reinforced retaining wall and also the forces in the reinforcements.

Keywords: Finite Element Modelling, Seismic Analysis, Soil Structure Interaction, ReinforcedEarth Wall

The facing also plays an important role inthe stability of the wall, which includes precastconcrete panels, dry cast modular blocks,metal sheet and plates, gabions, welded wiremesh, shotcrete, wood lagging and panels,and wrapped sheet of geosynthetics. One ofthe most important characteristics of RE is itsflexibility. For this reason it is ideal forstructures such as retaining walls on softfoundations.

The reinforcement improves the earth byincreasing the bearing capacity of the soil andreduces the settlement. It also reduce theliquefaction behavior of the soil. (Governmentof India, 2005). Reinforcement of soil, is

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practiced to improve the mechanicalproperties of the soil being reinforced by theinclusion of structural element such as granularpiles, lime/cement mixed soil, metallic bars orstrips, synthetic sheet, grids, cells, etc.

This mobilization of tensile strength isobtained by surface interaction between thesoil and the reinforcement through friction andadhesion. The reinforced soil is obtained byplacing extensible or inextensible materialssuch as metallic strips or polymericreinforcement within the soil to obtain therequisite properties.

Two methods found in current engineeringpractice for the dynamic response analysis ofreinforced-soil retaining-wall structures are:The first method is an iterative equivalent linearclassic approach, and the second is anincremental elastic approach (MuthucumarasamyYogendrakumar, 1992).

The problem of determining pseudodynamic pressure and its associated forceson a rigid vertical retaining wall is solvedanalytically using the horizontal slices methodfor both reinforced and unreinforced walls. Theuse of this method in conjunction with thesuggested equations and unknowns offers apseudo-dynamic method that is thencompared with the results of an availablesoftware. In the proposed method, differentseismic accelerations have been modelled atdifferent soil structure heights (Ghanbari,2008).

Seismic designs of geotechnical earthstructures, such as slopes, retaining walls,embankments and dams, are conductedroutinely using a pseudo-static approach. TheMononobe (1924) and Okabe (1924)approach for retaining wall design, is the mostwellknown pseudo-static procedures (Nouri,2008).

The internal stability of MSE walls relies onprotection against two Ultimate Limit States(ULSs): pull out and structural failure ofreinforcements. This study proposesequations for the resistances and loads thatreflect the physical processes involved in thepull out and structural failure ULSs and quantifythe uncertainties (Dongwook Kim and RodrigoSalgado, 2012).

It is considered an earth pressure approach

Figure 1: Cross Sectionof Reinforced Earth Wall

DESIGN AND ANALYSIS OFREINFORCED EARTH WALLThere are various methods used for the designof the reinforced earth wall. From the traditionaltill date all the methods are listed here. Mainlythere are two approaches for the design of thereinforced earth wall they are pseudo staticapproach and pseudo dynamic approach forthe design.

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where the solution is obtained by extendingCoulomb’s analysis. Pseudo-static stabilityanalysis that uses a mechanism at a prescribedfailure plane has been addressed by severalinvestigators (Seed and Goodman, 1964;Sarma, 1975; and Ling and Cheng, 1997).

These studies all assume the inertia forcedue to an earthquake horizontal accelerationfor a failure soil mass along a prescribed plane.The first seismic design procedure for metalstrip reinforced soil structures was proposedby (Richardson, 1975). It was based on theMononobe–Okabe analysis (1924) (Mononobe,1924; Okabe, 1924). A planar failure surfacewas assumed and a dynamic earth pressurecomponent was added to the static componentin determining the required reinforcementforce. Bonaparte et al. (1986) proposed apseudo-static limit equilibrium approach fordesigning reinforced slopes. The geosyntheticslength and strength required to resist thesefailure modes were presented in severaldesign chart. This approach does not considerpermanent displacement. Ling et al. (1997)conducted a seismic design for designinggeosynthetics-reinforced slopes base on apseudo-static limit equilibrium analysis, whichconsiders horizontal acceleration and

incorporates a permanent displacement limit.Internal and external stability analysisconducted to determine the required strengthand length of geosynthetics, consideringdifferent modes of failure. Different forcesacting on the wall are shown in Figure 2.

Design of Reinforced earth wall is to bechecked for botha) External Stabilityb) Internal Stability

External stability is often examined basedon the (Mononobe, 1929) a pseudo static limitequilibrium method that is a direct extensionof the static Coulomb theory for gravity walls(Mononobe and Matsuo, 1929). Internalstability is checked by dividing the reinforcedzone into an active and a resistive zone, basedon the premise that the horizontal inertial forcescaused by the seismic acceleration on themass of the active zone must be resisted bythe geosynthetic reinforcement, which must besufficiently anchored within the resistive zone(Rebecca M Walthall and Judith Wang, 2013).

Figure 2: Geometry and Acting Forces

Table 1: Seismic Stability usedin Pseudo Static Method

Failure Mode Factor of Factor of SafetySafety in in Limit

PWRI Equilibrium

Circular Sliding FS = 1.0 FS = 1.0

Sliding FS = 1.2 FS = 1.0

Overturning e L/3 e L/2

The sliding displacement behavior of theoverall system between the wall and theunderlying soil is typically examined using theNewmark sliding block method in conjunctionwith the M-O method. Design of MSE walls

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with inextensible reinforcements was, and stillis, performed by assuming the MSE structurebehaves as a rigid body, sizing it to resistexternal loads applied by the retained soil andby any surcharge, then verifying internalstability by checking reinforcement pullout andtensile rupture. This design method, derivedfrom basic soil mechanics, is known as theCoherent Gravity Method (Peter L Anderson,2013). Some standard factor of safety in PWRIand equilibrium are shown in Table 1.

The Tieback Wedge Method wasdeveloped by Bell (1975) as an extension ofthe trial wedge method from traditional soilmechanics (Huntington, 1957), and has alwaysbeen the appropriate design method forgeosynthetic-reinforced MSE walls. In an MSEwall with geosynthetic reinforcements, thefailure plane is assumed to develop along theRankine rupture surface defined by a straightline oriented at an angle of 45+/2 from thehorizontal and passing through the toe of thewall. This contrasts sharply with the CoherentGravity Method, where the shape of the bilinearboundary between the active and resistivezones is based on the location of maximumreinforcement tension, the failure plane doesnot actually develop, the active wedge doesnot displace, and the inextensibility of the steelreinforcements prevents structure deformation.

SEISMIC ANALYSIS ANDMODELLINGBathrust and Hatami studied in their researchwork the analysis of reinforced soil retainingwall.

The numerical models were excited at thefoundation elevation by a variable-amplitudeharmonic motion with a frequency close to the

fundamental frequency of the referencestructure.

The two-dimensional, explicit dynamic finitedifference program Fast Lagrangian Analysisof Continua (FLAC) was used to carry out thenumerical experiments. The response of thesame wall excited by a scaled earthquakerecord was demonstrated to preservequalitative features of wall displacement andreinforcement load distribution as thatgenerated using the reference harmonicground motion applied at 3 Hz.

The reference continuous panel wall is 6.0m high with six uniformly spaced reinforcementlayers (Figure). The wall facing was modelledas a continuous concrete panel with a thicknessof 0.14 m. The bulk and shear modulus valuesof the wall were Kw = 11,430 MPa and Gw =10,430 MPa, respectively. Poisson’s ratio forthe panel material was taken as Vw = 0.15. Thepanel was hinged at its base, as illustrated inFigure 1. The soil was modelled as a purelyfrictional, elastic-plastic material with a Mohr-Coulomb failure criterion and non-associatedflow rule. The friction angle of the soil was =35, dilatancy angle = 6, and unit weight =20 kN/m3.

Figure 3: Numerical Gridfor Reference Static Load Case

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The results of the FEM simulation ofreinforced continuous panel walls which isnumerically modelled in Figure 3 have beendemonstrated to be sensitive to meshconstruction details and material properties atthe reinforcement-wall connections (Rowe andHo, 1997; Andrawes and Yogarajah, 1994). Inthe current study, a simple connection modelwas adopted that involved attaching the endof the cable elements (reinforcement) to asingle grid point at the back surface of thecontinuous panel region.

successfully implemented in finite elementmodelling of the composite structure.

To illustrate the behavior of reinforcedretaining wall under seismic inertia force, acomputer program has been developed, whichcan be used to attain the critical inclination ofthe failure plan angle and required totalgeosynthetic force. The Geometric of soil-wallsystem (H, B1 and B2 in Figure) utilized in theparametric analysis is that considered byNadimand and Whitman (1983) (Whitman,1983). A series of parametric study have beencarried out in two cases (1) without presenceof the wall; and (2) with presence of the wallusing the geotechnical, geometrical anddesign parameters detailed in Table 2. Theobtained results of system, with presence ofwall are compared to those obtained for thecase of system without presence of wall.

Figure 4: Result Elevation> Displacement

The wall-soil interface was modelled usinga thin soil column, 0.05 m thick, directly behindthe facing panel. A no-slip boundary was usedbetween the thin soil column and the facingpanel. The soil-wall interface column materialwas assigned a friction angle i =20 and adilatancy angle i = 0. A similar thin soil layerwas introduced at the base of the soil regionbut was assigned the same properties as thereinforced and retained soil materials.Comparison of elevation v/s displacementgraph is shown in Figure 4. Rajagopa andBathrust (1995) evaluated that the strength andstiffness properties of component materialscan be determined from the results ofindependent routine laboratory tests and then

Figure 5 shows the critical inclination of thefailure plan angle; for different internal angleof soil friction () under static and seismicloadings (kh=0.0, 0.1, 0.15, 0.2, 0.25, and 0.3).The results show that for the certain value ofkh, the value of increases with increasingthe internal angle of soil friction (). It meansthat when internal angle of soil friction ()increases, the volume of the critical sliding

Table 2: ParametersDescription Value

Height of the wall 8

B1 0.8

B2 5

Unit weight of soil 18 kN/m3

Unit weight of wall 24 kN/m3

Internal angle of soil friction 10, 15, 20, 25, 30, 35, 40, 45

Soil Cohesion (C) 0

Coefficient of Seismic 0, 0.1, 0.15, 0.2, 0.25 0.3acceleration (Kh)

Coefficient of Seismicacceleration (Kv) 0

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mass reduces. Also, for the certain value of ,the critical inclination of the failure plan angle() decreases with increasing the value of kh.It means that when h k increases, the weightof the soil failure wedge; Ws (the volume ofthe critical sliding mass) increases.

in the form of load v/s displacement graph inFigure 7.

There are various finite element programssuch as Pl axis, FLAC, ANSYS, ABAQUS,MSC.MARC, etc., in which analysis can beperformed and different seismic parameterscan be evaluated.

COMPARING DESIGNMETHODSVarious methods were discussed above forthe design of Reinforced earth wall, at presentstage many traditional methods are outlined.From the above discussion it can be concludedthat extension of M-O equation, i.e., Pseudo

Figure 5: Failure Angle

The wall facing was comprised of five halfand ten full precast concrete panels, eachpanel measuring 1.5 m _ 1.5 m. Each structurewas overlaid by an untreated gravel sub layer,a ballast layer and one sleeper. The sleeperswere 2.4 m long, 0.3 m wide and 0.27 m high,perpendicular to the facing and in the centreof the interval between the concrete wallsshown in Figure 6.

Bourgeois (2011) evaluated that numericalmodels makes it possible to reproduce thetensile-force increments in the strips and thedisplacements induced by loads varying overa wide interval of values ranging from 90 to850 KN, this latter value being much larger thanthe standard axle loads. These models canalso be useful to discuss the influence ofgeometric parameters or mechanicalparameters on the global response of areinforced earth structure. Results are shown

Figure 6: Model Reinforced Earth Wall

Figure 7: Load v/s Displacement

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static approach is efficient method for thedesigning of Reinforced Earth Wall.

SOIL STRUCTUREINTERACTIONSoil structure interaction phenomena concernthe wave propagation in a coupled system:buildings erected on the soil surface (AK,1974). One of the important reasons for thisdifference is that part of the vibrational energyof the flexibly mounted structure is dissipatedby radiation of stress waves in the supportingmedium and by hysteretic action in the mediumitself. Analytical methods to calculate thedynamic soil structure interaction effects arewell established (Wolf, 1985).

Structure Soil Structure Interaction (SSSI),put forward in recent decades, means thedynamic interaction problem among the multi-structure system through soil-ground. To thewriter’s knowledge, it is (JE, 1973) in 1973 tocome up first with the SSSI designation for thisarea of study. Its additional name is DynamicCross Interaction (DCI).

Finite Element Method (FEM), an efficientcommon computing method widely used in civilengineering, discretizes a continuum into aseries of elements with limited sizes tocompute for the mechanics of the continuum.FEM can simulate the mechanics of soil andstructures better than other methods, deal withcomplicated geometry and applied loaded,and determine non-linear phenomena. SSIeffects turn out to be significant, and oneimmediate consequence is that erecting ordismantling a building or a group of buildingscould change the seismic hazard for theneighborhood. This leads to significantconceptual changes, especially concerning

seismic micro zonation studies, land-useplanning, and insurance policies. The basicconcept of SSI is visualized in Figure 8.

The most common soil-structure interactionSSI approach, used for three dimensional soil-structure systems, is based on the “addedmotion” formulation (Clough, 1993). Thisformulation is mathematically simple,theoretically correct, and is easy to automateand use within a general linear structuralanalysis program. In addition, the formulationis valid for free-field motions caused byearthquake waves generated from all sources.The method requires that the free-field motionsat the base of the structure be calculated priorto the soil structure interactive analysis.

CONCLUSIONIt can be evaluated from the above review thatvarious factors such as height of wall, internalfriction, and type of soil were considered inthe design of reinforced earth wall yet it hasshown considerable amount of damage inearthquake so it becomes important to studythe effect of soil structure interaction in theanalysis of reinforced earth wall to resist

Figure 8: SSI Model

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against the earthquake load. Thus soil structureinteraction becomes vulnerable in the analysisof reinforced earth wall.

Various seismic parameters along with soilstructure interaction has to be consider in thedesign of reinforced earth wall. Changing thedifferent parameters of reinforced earth wallcan lead to the efficient design but the effectof soil structure interaction can’t be neglected.

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