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The International Journal of GeomechanicsVolume 1, Number 4, 477–506 (2001)

Static Response of Reinforced SoilRetaining Walls with Nonuniform

ReinforcementK. Hatami, R.J. Bathurst, and P. Di Pietro

Received April 13, 2001

GeoEngineering Centre at Queen’s-RMC, Department of Civil Engineering,Royal Military College of Canada, Kingston, Ontario, Canada

GeoEngineering Centre at Queen’s-RMC, Department of Civil Engineering,Royal Military College of Canada, Kingston, Ontario, Canada

Maccaferri Gabions, Inc., Williamsport, Maryland, USA

ABSTRACT. The structural response of reinforced-soil wall systems with more than one reinforcement

type (nonuniform reinforcement) is investigated using a numerical approach. The selected reinforcement

types and mechanical properties represent actual polyester geogrid and woven wire mesh products. The

model walls are mainly of wrapped-face type and have different reinforcement lengths, arrangements, and

stiffness values. Additional wall models with tiered and vertical gabion facings are included for comparison

purposes. The numerical simulation of wall models has been carried out using a finite difference-based

program and includes sequential construction of the wall and placement of reinforcement at uniform

vertical spacing followed by a sloped surcharge. The wall lateral displacements and backcalculated

lateral earth pressure coefficient behind the facing in all nonuniform reinforcement wall models show a

clear dependence on relative stiffness values of reinforcement layers at different elevations. An equation is

proposed that can be used to predict the maximum reinforcement load in nonuniform reinforced wrapped-

face walls of given backfill types and reinforcement configurations similar to those investigated in this

study.

I. Introduction

Reinforced soil retaining walls offer economic advantages over conventional retaining wallsystems. The cost advantage of reinforced soil walls over conventional forms of retaining wall

Key Words and Phrases. Numerical modeling, retaining walls, reinforced soil, geosynthetics, nonuniform rein-forcement.Acknowledgements and Notes. The funding for this project was provided by research grants from the NaturalSciences and Engineering Research Council of Canada and Maccaferri Gabions, Inc.K. Hatami, corresponding author.

© 2003 ASCE DOI: 10.1061/(ASCE)1532-3641(2001)1:4(477)ISSN 1532-3641

478 K. Hatami, R.J. Bathurst, and P. Di Pietro

systems (e. g., gravity walls) increases with the height of the wall (Figure 1). The cost ofreinforcement constitutes an important part of the total cost of a reinforced soil retaining wall andcan be as great as about 25% of the cost of the wall, depending on the wall height, backfill type,and design loading conditions [2, 3]. This study addresses the possibility of further reducing thetotal cost of a reinforced soil wall by optimizing the use of more than one reinforcement type.

FIGURE 1 Cost of different retaining wall types as a function of height (after Koerner et al. [1]). Notes: (1) MSE =Mechanically Stabilized Earth Walls; (2) Crib/bin walls are gravity wall structures formed by a soil mass confined byinterlocking concrete, metal or timber elements.

The reinforcement load in reinforced soil walls is commonly calculated from classic activeearth pressure theory using the so-called contributory area approach [4, 5]. In this approach, thelateral earth pressure distribution from Rankine or Coulomb earth pressure theory is integratedover a distance equal to the spacing between reinforcement layers and the resultant load (demand)is assigned to the target reinforcement layer. In a tall retaining wall, the reinforcement load canvary with depth over a wide range of values. In such a case, more than one reinforcement type orspacing pattern along the wall height may be desirable. An example is a 12.6-m-high wrapped-face wall in Seattle, Washington [6, 7] (Rainier Avenue wall), where four different reinforcementtypes with different tensile strength values were used in order to keep reinforcement spacinguniform. The ultimate wide-width tensile strength values [8] for the reinforcement types in thewall ranged from 31 kN/m to 186 kN/m. In general, stronger reinforcement products are typicallystiffer materials. In the Rainier Avenue wall, the reinforcement secant modulus values at 5% strainfrom standard in-isolation laboratory index tensile tests ranged from 198 kN/m to 1068 kN/m.The ratio of minimum and maximum reinforcement index strength values was similar to thecorresponding ratio for the reinforcement stiffness. The placement of a stiffer reinforcementlayer will attract more load to the stiffer region of the reinforced zone. Therefore, the possibilityof exceeding the tensile strength of the stiffer reinforcement layer must be checked. However, the

Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 479

load increase of the type discussed here cannot be addressed rigorously using conventional limit-equilibrium analysis approaches in combination with the contributory area method. This may bea more important issue for geosynthetic reinforcement products compared to much stiffer metallicreinforcement materials where variations of reinforcement stiffness and maximum reinforcementload are not as significant [9].

The influence of a single reinforcement type with a given stiffness and length on wall responsehas been the subject of previous investigations [10]–[15].

Ho and Rowe [10] and Rowe and Ho [11, 12] found that the reinforcement stiffness, verticalspacing and length to wall height ratio, L/H , are important parameters that influence the wall dis-placement response. Ho and Rowe [10] found little variation in the magnitudes of reinforcementload and soil stress for L/H values larger than 0.7. It is worth noting that the ratio L/H = 0.7 isthe minimum reinforcement length ratio recommended by FHWA [4] and AASHTO [5] designguidelines for static stability of reinforced soil walls. A design chart to predict wall deforma-tions as a function of L/H and reinforcement type (i. e., extensible geosynthetic or inextensiblemetallic) appears in the current FHWA [4] and AASHTO [5] guidelines.

Ho and Rowe [10] concluded that placing equally spaced reinforcement layers with L/H =0.7 is an efficient reinforcement distribution and recommended over other distribution patternsof reinforcement in reinforced soil walls. Rowe and Ho [13] showed that the magnitude of walllateral displacement is influenced by the soil friction angle and a reinforcement stiffness factor,�, defined as� = J/(KaγHSv). Here, J is the reinforcement stiffness, Ka is the Rankine activeearth pressure coefficient, γ is the soil unit weight, H is wall height, and Sv is the vertical spacingbetween reinforcement layers.

Helwany et al. [14] used a calibrated finite element model to investigate the effects of wallheight, backfill type, and reinforcement stiffness on the response of reinforced soil walls witha hard facing. They found that the stiffness of geosynthetic reinforcement has an importantinfluence on wall displacement response when the backfill shear strength and stiffness values arelow.

Bathurst and Hatami [15] showed that for a typical 6-m-high propped-panel wall, therewas no significant difference in the distribution of maximum reinforcement load at the end ofconstruction for uniform reinforcement schemes with different stiffness values in the range oftypical geosynthetic materials. However, reinforcement layers with a stiffness value representativeof steel strip materials showed higher reinforcement loads.

All the above studies examined reinforced soil walls with one reinforcement type only. Thereare currently no guidelines that directly consider the influence of different stiffness reinforcementlayers on the distribution of tensile load in reinforced soil wall systems.

In this article, extended results of a numerical study [16] are reported where the potential forreducing the reinforcement cost by combining different reinforcement products is explored. Dif-ferent nonuniform reinforcement configurations were examined while ensuring that wall modelswere structurally stable and no reinforcement yielding or pull-out would occur. The assumptionof no slippage between the soil and reinforcement was adopted to simplify the numerical model-ing and to focus the study on the effect of reinforcement layers with different stiffness values onwall response. The term nonuniform reinforcement in this article is used generically to identifyreinforced soil walls in which two or more reinforcement types are used.

The wall models in the current study are largely of wrapped-face type with a battered facingand different reinforcement arrangements: single reinforcement type (uniform reinforcement);two reinforcement types placed separately in top and bottom sections of the wall (grouped rein-


forcement); two reinforcement types in alternating layers (alternating reinforcement); and config-urations with three reinforcement types (mixed reinforcement). In addition, a limited investigationof the influence of tiered and vertical gabion-faced wall construction on the wall structural per-formance was undertaken.

The numerical analyses were carried out using the program FLAC [17]. The structuralresponse of wall models at end of construction is presented in terms of facing lateral displacement,maximum reinforcement load, and equivalent lateral earth pressure coefficient,Kh, backcalculatedfrom the reinforcement load. The focus of the current study is on the influence of nonuniformreinforcement stiffness configurations on wall response. The reinforcement vertical spacing ineach model wall was kept constant. Therefore, the effect of variable reinforcement spacing on wallresponse is not addressed here. A number of other studies have been cited where the influencesof reinforcement geometrical arrangement and variable spacing are investigated [10, 13, 18]. Itis worth noting that the numerical study reported in this article is restricted to a limited rangeof material properties and geometry. In addition, the numerical models have not been calibratedagainst monitored wrapped face full-scale walls. However, instrumented walls of the type reportedhere are very rare and, the only case reported in the literature that the writers are aware of doesnot contain sufficiently high-quality data to render a calibration exercise warranted. Therefore,the results of the study may be best interpreted in terms of relative performance of the wallcase studies investigated. However, the numerical approach, soil, and reinforcement modelsused in this study have been successfully used to reproduce the measured response of a heavilyinstrumented, full-scale segmental retaining wall by the RMC Geotechnical Research Group [19].The predicted response of the wall from the numerical simulation showed a very good match withthe actual, measured results. In addition, the finite difference numerical model used in this studyhas been used to replicate the numerical results of a generic, reinforced soil propped-panel wallthat was simulated using the finite element method [15]. Despite slightly different assumptionsfrom what were made in the finite element simulation [20], the results compare satisfactorily.These comparison studies provide confidence about different detailing aspects of the numericalmodel (e. g., staged construction feature, interfaces, reinforcement/soil interaction properties,etc.) so that it can be used to investigate the influence of different parameters (e. g., reinforcementstiffness) on the wall response. In addition, the numerical modeling results do provide valuableinsight regarding the influence of reinforcement stiffness and arrangement on wall performanceunder idealized conditions.

II. Wall models

A. General description and geometry

A total of 21 numerical wall models are included in the parametric study. The geometry andreinforcement configuration of wall models are shown in Figure 2. The reinforcement stiffnessvalues are listed in Table 1. The numerical model set consists of nineteen 8-m-high wrapped-facemodel walls (Walls 1-12 and 15-21, Figure 2). The wall models are considered to representtypical heights for wrapped-face retaining walls based on a survey of reinforced soil retainingwalls constructed in the United States [21]. One model wall with a vertical gabion facing [Wall 13,Figure 2(d)] was investigated to examine the influence of facing type and batter on wall behavior.In addition, a model wall with a combined wrapped-face and gabion facing configuration [Wall14, Figure 2(e)] was included in the study to examine the influence of a tiered wall configurationon structure response.

Each of the wrapped-face model walls has an inclined facing with a batter angle β = 20◦from vertical. Each structure includes a broken-back slope (sloped surcharge) with an initial


FIGURE 2 Walls with uniform and nonuniform reinforcement configurations. Notes: see Table 1; all dimensions inmeters.


TABLE 1

Reinforcement Stiffness and Arrangement of Wall ModelsReinforcement Reinforcement Reinforcement

Wall stiffness stiffness at bottom, stiffness at top,No. Figure 2 configuration Jb (kN/m) Jt (kN/m) R0.7

1 a Grouped 5500 1000 32372 b Alternating 5500, 1000 5500, 1000 32373 a Grouped 1000 5500 32374 a Uniform 3250 3250 32375 a Grouped 8000 2000 49796 b Alternating 8000, 2000 8000, 2000 49797 a Grouped 2000 8000 49798 a Uniform 5000 5000 49799 a Grouped 5500 5000 522810 a Uniform 2000 2000 199211 a Uniform 8000 8000 796712 c Mixed 8000, 4000, 2000 348613 d Mixed 8000, 4000, 2000 348614(1) e Uniform 5500 169215 f Uniform 5500 with Sv = 1.0m 136916 f Uniform 8000 with Sv = 1.0m 199217 g | Uniform 2000 134918 g | Uniform 5000 337219 g 〉 (2) Uniform 8000 539420 g | Alternating 2000 (L = 4.0m), 8000 (L = 8.0m) 433621 g | Alternating 8000 (L = 4.0m), 2000 (L = 8.0m) 2407

Notes: (1) L = 3m, also includes longer, less stiff reinforcement layers [see Figure 2(e)]; (2) Alternating length schemes.

2H:1V slope.

A fixed boundary condition representing a rigid foundation is assumed at a depth of 0.5 mbelow the lowermost reinforcement layer in all wall models. In addition, the foundation soil zonein numerical models is extended to a distance of 2.25 m in front of the wall toe and to a height of1.25 m above the rigid foundation. The wall models have a total width of 25 m, in order to containany shear failure wedge that can develop in the retained backfill under the end-of-constructionloading condition.

B. Reinforcement stiffness and arrangement

The reference reinforcement length, L, in all wall models (except for Wall 14 and shorterreinforcement layers in Walls 17-21) is 8 m, which corresponds to a length-to-height ratioL/H =1 for the reinforced soil zone. This reinforcement length is larger than the minimum lengthratio L/H = 0.7 in accordance with FHWA [4] recommendations for static stability of wallswith sloping surcharge fills. In addition, L/H = 1 (compared with the minimum value of0.7) provides sufficient average reinforcement length (i. e., L/H = 0.75) in model walls 17-21with alternating half- and full-length reinforcement schemes [Figure 2(g)]. The vertical spacingbetween the reinforcement layers, Sv , is constant and equal to 0.5 m in all model configurationsexcept Walls 15 and 16.


The stiffness, J , of planar reinforcement materials (including geosynthetic products) isnormally expressed in terms of the tensile force per unit width of reinforcement, T , for unit strain(i. e., units of kN/m) as (Figure 3):

J = T

ε(1)

where ε is the tensile strain in the reinforcement. The reinforcement is modeled as plane-strain

FIGURE 3 Mechanical response parameter definition for reinforcement.

sheets with the same cross-sectional area, perimeter and stiffness values as those of an equivalentnumber of cable elements per unit length of the wall (i. e., perpendicular to the model wallplane). The reference reinforcement stiffness values are chosen from properties reported forwoven wire mesh and polyester geogrid reinforcement products [22]–[25]. However, additionalstiffness values are included in this investigation to extend the range of the parametric study andto capture a wider range of geosynthetic reinforcement products manufactured from high-densitypolyethylene (HDPE) and polypropylene (PP) polymers. In the following, the wall configurationsare described with reference to Figure 2 and Table 1.

1. Figure 2(a)

Walls 1, 3-5, and 7-11 include both uniform and nonuniform reinforcement layouts. Thenonuniform layouts in these walls are referred to as grouped reinforcement configurations thatinclude two different reinforcement types in the bottom and top halves of the reinforced soil zone.


Walls 4 and 8 contain uniform reinforcement with stiffness values equal to the average ofstiffness values in Walls 1-3 and 5-7, respectively.

Wall 9 is a variation of Wall 8 with two slightly different reinforcement stiffness values in agrouped reinforcement configuration.

Walls 10 and 11 are uniformly reinforced with each of the component reinforcement typesused in Walls 5-7.

2. Figure 2(b)

Walls 2 and 6 are constructed with alternating reinforcement arrangements composed ofreinforcement layers with significantly different stiffness values.

3. Figure 2(c)

Wall 12 is a wrapped-face wall constructed with a mixed reinforcement arrangement usingthree different stiffness values that decrease in magnitude toward the top of the wall.

4. Figure 2(d)

Wall 13 is identical to Wall 12 with respect to reinforcement configuration but with a verticalgabion facing.

5. Figure 2(e)

Wall 14 is a combined (tiered-wrapped face) cross section, which is included in this studyas an example tiered wall configuration. The wall consists of an inclined wrapped-face sectionseated on a vertical gabion facing system with a combination of short secondary reinforcementlengths (L = 3 m) and longer primary reinforcement layers placed at vertical spacings of 2 m.The shorter reinforcement layers (L = 3 m) in the gabion and wrapped-face sections of the wallare different products (i. e., woven wire mesh and polyester geogrid) but have the same stiffnessvalues (J = 5500 kN/m).

6. Figure 2(f)

Walls 15 and 16 are uniform reinforcement walls with a reinforcement spacing, Sv , twiceas large as the reference spacing used in the other model walls (i. e., Sv = 1 m). This value forreinforcement vertical spacing is within the typical range (i. e., 0.3 m < Sv < 1.5 m) used inreinforced soil wall structures [20]. However, reinforcement spacing values as low as 0.15 m andas large as 1.8 m have been reported in the literature for actual walls [21].

7. Figure 2(g)

Walls 17-21 include uniform and alternating reinforcement stiffness configurations withalternating reinforcement length over the height of the wall.

C. Reinforcement quantity

In this study, the amount of reinforcement in each model wall is quantified using the rein-forcement stiffness, length, and vertical spacing. The amount of reinforcement supply for a wall


of given height, H , is proportional to the ratio JL/Sv . The demand from lateral earth pressurebehind the wall is proportional to KahγH

2 where γ is the backfill unit weight and Kah is thehorizontal component, active Coulomb earth pressure coefficient given by:

Kah = Ka cos[δ +

(α − π

2

)](2)

where

Ka = sin2(α + ϕ)

sin2 α sin(α − δ)[1 +

√sin(ϕ+δ) sin(ϕ−θ)sin(α−δ) sin(α+θ)

]2. (3)

In equations (2) and (3), φ is the backfill soil friction angle, δ is the friction angle betweenthe backfill and a hard facing, α is the wall batter angle from horizontal (i. e., α = π/2 + β)and θ is the backfill surcharge slope. The active earth pressure coefficient is considered in thelateral earth pressure demand formulation because a plastic, active zone typically develops inreinforced zones with geosynthetic reinforcement materials due to their relatively low stiffnessvalues (i. e., compared with metallic reinforcement stiffness). The reinforcement ratio, Rλ, isintroduced here as a non-dimensionalized, single-valued parameter to quantify the reinforcementsupply-to-demand ratio for a wall model of given height and backfill material as:

Rλ =∑n

i=1Ji lf i (λ)Li

Svi

KahγH 2(4)

where Ji , Li , and Svi are the stiffness, length and vertical spacing (contributory height) of re-inforcement layer i, respectively, and, n denotes the total number of reinforcement layers. Thelength factor, lf i , of the reinforcement layer i is defined as:

lf i(λ) = 1 + Li/H − λ

Li/H + λ(5)

where λ is a reference reinforcement length-to-wall height ratio that corresponds to an optimumL/H ratio value for the stability of reinforced soil walls. The value for λ is taken as 0.7 inaccordance with the results of previous numerical and experimental studies reported in Section I.However, a lower value for λ (i. e., optimum L/H ratio for wall stability) may be considered forhigher backfill friction angles [26]. The mathematical expression of equation (5) represents thedirect influence of reinforcement length on wall stability for the range Li/H ≤ λ and its reducedeffect for Li/H > λ as was found in a number of earlier studies [10, 13, 15, 27]. The parameterRλ defined in equation (4) includes both reinforcement supply and backfill friction angle whichare the two most important parameters influencing the horizontal displacement of reinforced soilwalls [13]. Specifically, a higher magnitude for the parameter Rλ indicates a stronger backfilland/or greater reinforcement supply in the wall, both of which would result in lower wall lateraldisplacement.

Equation (4) can be understood to be an indicator of the reinforcement cost. The reinforce-ment ratio values for the wall models with λ = 0.7 (i. e., R0.7) are listed in Table 1.

D. Soil

The backfill soil and sloped surcharge are modeled as purely frictional, elastic-plastic materi-als with the Mohr–Coulomb failure criterion. The friction angle, dilation angle and unit weight ofbackfill (including the sloped surcharge) are assumed as φ = 32◦, ψ = 12◦, and γ = 18 kN/m3,


respectively. The bulk modulus and shear modulus values of the backfill material are assumed asK = 16 MPa and G = 9.6 MPa, respectively.

Greater strength and elastic property values were assigned to the foundation region in wallmodels with a gabion facing (Walls 13 and 14 in Figure 2) in order to provide sufficient foundationbearing resistance and stiffness directly below the facing (i. e., φ = 35◦, (cohesion) c = 5 kPa,ψ = 12◦, K = 800 MPa, and G = 480 MPa). These values were used to ensure stability andare believed to have had little influence on the toe lateral restraint of gabion facing wall modelscompared to the lateral restraint due to the embedded toe of wrapped-face models. This expecta-tion is confirmed by examining the calculated lateral displacement response of the correspondingmodel walls close to the foundation region [i. e., Walls 12 and 13 in Figure 4(c)].

The rockfill in the gabion baskets is modeled as a frictional material with a Mohr–Coulombfailure criterion similar to the backfill but, with a higher friction angle (i. e., φ = 40◦).

It is worth noting that a hyperbolic model [28] would better represent the state of soil stiffnessas a function of confining stress in the soil. However, using the more complicated hyperbolicmodel (i. e., compared with linear elastic model) requires consistently accurate values for thesoil stiffness parameters (e. g., km, ke,m, n,Rf in the hyperbolic model) from experimental datafor any meaningful gain over the use of the simpler constant stiffness model. To the best ofthe authors’ knowledge, such measured data for the backfill of actual wrapped-face walls arenot available. In addition, the introduction of these additional parameters in the model wouldnecessitate a significant set of parametric studies on the effect of hyperbolic parameters on theoverall wall response, which is avoided at this stage of study. The focus of the current study is theinfluence of reinforcement stiffness and configuration on model wall response for a given linearelastic soil model.

III. Numerical approach

The numerical simulations were carried out with the assumption of plane-strain conditions.The simulations modeled the sequential bottom-up construction of the wall facing, soil, reinforce-ment, and sloped surcharge. A fixed boundary condition in the horizontal direction was assumedat the numerical grid points at the backfill far-end boundary. The backfill and facing units (whereapplicable) of each wall model were elevated in lifts of 0.5 m, and the reinforcement layers wereplaced in the model as each reinforcement elevation was reached. The numerical results presentedhere correspond to the end of construction for each wall after the placement of the entire slopedsurcharge.

The numerical models at each stage were solved to equilibrium with a prescribed tolerancebefore placing the next lift of soil and reinforcement layer. The wrapped-face portion of eachreinforcement layer at the facing (i. e., between two subsequent reinforcement layers) was assignedthe same mechanical properties as those of the lower layer. The reinforcement layers, includingthe wrapped-face portions and gabion facing, were modeled using linear elastic, perfectly plasticcable elements with tensile yield strength, Ty and negligible compressive strength (Figure 3).The cable elements (reinforcement) interact with the backfill material through grout interfaces.The stiffness and strength of the grout interface—which was modeled as a spring-slider system—were set to kb = 100 MPa and sb = 1 MPa, respectively. Details of the soil-reinforcement groutinterface are reported by Itasca [17]. The maximum reinforcement load at the end of constructionin all model walls examined was less than the yield strength of reinforcement materials used ineach model.


IV. Results

A. Wall lateral displacements

1. Effect of reinforcement stiffness arrangement

Figure 4 shows the calculated lateral displacement, Xd , of walls at end of construction.Parameter h in the figure is elevation measured from the wall base (Figure 2). The data in Figure 4include the numerical results for most of the model walls to illustrate important differences inwall response. The displacement responses of Walls 1 and 3 are close to the responses of Walls 5and 7, respectively, and are not shown for clarity of the plots.

In Figure 4(a), Wall 11—with uniformly stiff reinforcement over the entire height—showsthe smallest amount of lateral displacement. Replacing half of the reinforcement layers witha less stiff reinforcement material (Walls 5–7 with identical R0.7 values in Table 1) increasesthe wall lateral displacement. However, the maximum displacement value and the displacementdistribution pattern depend on the reinforcement arrangement. Placing the less stiff reinforcementin the upper half of the wall (Wall 5) results in local bulging of the facing in the upper half of the wallheight. The wall lateral displacement within the lower half does not increase noticeably comparedto Wall 11. Placing the less stiff reinforcement in the lower half of the wall height (Wall 7) resultsin a considerable increase in wall lateral displacement in the lower half of the wall height (byabout 70% on average in comparison with Wall 11). Distributing the less stiff reinforcementmaterial evenly between stiff reinforcement layers (Wall 6) results in a wall displacement profilesimilar to the displacement response of uniformly reinforced Wall 11 but with larger lateraldisplacement magnitude at all reinforcement elevations. The amount of displacement increase inWall 6 compared to Wall 11 is uniform over the wall height and about half the maximum valueobserved in either of the grouped reinforcement arrangements (i. e., Walls 5 and 7). Therefore,an alternating reinforcement scheme appears to be a more effective reinforcement arrangementthan grouped schemes with the same reinforcement ratio value to limit wall lateral displacement.

A comparison of displacement results for Walls 2 and 4 as well as those of Walls 6 and8 in Figure 4(b) shows the influence of using an alternating reinforcement arrangement withthe same average reinforcement stiffness as an otherwise, identical configuration with uniformreinforcement. The alternating reinforcement configurations show only a slightly larger amountof deformation at end of construction compared with uniformly reinforced walls. Accordingly,the deformation response of walls with alternating reinforcement stiffness arrangement can beconsidered to be practically the same as (and therefore can be estimated from) the response ofuniformly reinforced walls with identical reinforcement ratio values.

The influence of mixed reinforcement arrangement on wall displacement for a wrapped-facewall is illustrated in Figure 4(c). The reinforcement ratio of mixed-reinforced Wall 12 (with agradually decreasing reinforcement stiffness toward the top) is 70% of the reinforcement ratioof Wall 6 (Table 1). However, displacement response of Wall 12 (maximum value 0.033 m)is only slightly greater than displacement response of Wall 6 (maximum value 0.028 m) thatcontains several layers of stiffer reinforcement. Therefore, the intuitive scheme of reducingreinforcement stiffness with height appears to be a cost-effective configuration that would notresult in a significantly larger wall displacement compared to the alternating scheme. However, thereduction of reinforcement stiffness with elevation using an alternating reinforcement arrangementis more desirable (i. e., compared with grouped schemes) to avoid local, excessive deformationof the facing along the wall height.


FIGURE 4 Lateral displacement profiles of reinforced model walls (numbers on plots refer to wall models in Table 1).


2. Gabion facing vs. battered wrapped-face wall

The effect of facing type and batter on wall displacement can be examined in Figure 4(c).Wall 12 with an inclined wrapped face at 20◦ to the vertical generated less lateral displacementat the end of construction than Wall 13 constructed with a vertical gabion facing. It may beconcluded that the effect of an inclined face may be more effective than a vertical wall constructedwith a relatively stiffer gabion column in reducing wall displacement. The displacement plots inFigure 4(c) also show that the pattern of displacement profiles between wrapped-face and gabionfacing walls is quite different. The maximum end-of-construction displacement occurs muchhigher up the face of the gabion wall (∼ 0.75H ) compared to the wrapped-face wall (∼ 0.35H ).The displacement of the wrapped-face wall is considered to be due to lateral spreading of thebackfill under soil self-weight, while the pattern of displacement for the vertical gabion wall isdue to rotation of the facing column about the toe.

3. Effect of reinforcement arrangement and vertical spacing

Figure 4(d) shows that the displacement response of a uniformly reinforced wall (Wall 8) ispractically indistinguishable from the response of a corresponding wall with grouped reinforce-ment configuration where the stiffness values of the two reinforcement groups are not substantiallydifferent (Wall 9 with variation of J within 10% and difference in R0.7 equal to 5% with respectto Wall 8). Comparison of the plots in the same figure shows that the combined influence ofreduced reinforcement length and tiered wall construction (Wall 14) results in greater facing dis-placements than Wall 9. However, comparison of displacements for Walls 14 (R0.7 = 1692) and15 (R0.7 = 1369) shows that the combined influence of tiered wall construction and reduced rein-forcement length is more effective in controlling wall deformation than a battered wrapped-facestructure constructed with a wider reinforcement spacing.

Figure 4(e) further illustrates the influence of reinforcement stiffness and spacing on walldeformation. Wall 11 (R0.7 = 7967) is uniformly reinforced with reinforcement stiffness J =8000 kN/m. Replacing the reinforcement with a considerably less stiff material (J = 2000 kN/m)increases average wall deformation by a factor of 2 (Wall 10, R0.7 = 1992). On the other hand,doubling the vertical spacing between the reinforcement layers (i. e., Sv = 1 m – Wall 16,R0.7 = 1992) while maintaining reinforcement stiffness of J = 8000 kN/m results in substantialincreases in wall lateral displacement (increase in maximum value by about a factor of 5) withsignificant local bulging between reinforcement layers. The displacement magnitude of Wall 16is excessive from a serviceability standpoint and may be considered to have failed. It can beconcluded that using a larger number of lower stiffness reinforcement layers at relatively lowerspacing is more effective to reduce wall deformations than stiffer reinforcement layers with awider spacing. This finding appears to be more important for wrapped-face walls compared toprevious results on propped-panel retaining wall systems [13]. It is worth noting that a smallerSv value does not necessarily result in a longer construction time. Experience with wrapped-facereinforced soil walls in the past has shown that a larger reinforcement spacing requires morecomplicated forming systems [21]. Accordingly, the time saved using less number of lifts istypically cancelled by the increased forming time.

The above results (including those discussed in Section 1) suggest that reducing reinforce-ment stiffness with height while maintaining constant vertical spacing is recommended overincreasing the spacing with height (as reported for a number of reinforced soil walls constructedin the past [3, 21], [29]–[33]) to limit the facing lateral displacement and ensure the stability ofthe structure.


4. Effect of reinforcement length

Figure 4(f) shows plots of wall displacement at end of construction for the uniform rein-forcement case with J = 8000 kN/m (Wall 11, R0.7 = 7967) and three alternating reinforcementschemes. In one scheme (Wall 19, R0.7 = 5394), the length of every other reinforcement layer(L = 4 m) is one half of the reinforcement length of the reference case, Wall 11. In anotherscheme (Wall 6, R0.7 = 4979), a less stiff reinforcement (J = 2000 kN/m) is placed in an alter-nating scheme with the reference reinforcement (i. e., J = 8000 kN/m). In the third alternatingscheme (Wall 20, R0.7 = 4336), the less stiff reinforcement is truncated to half length (L = 4 m)and is placed alternating with the full-length, stiff reinforcement. The uniform reinforcementcase of Wall 8 (R0.7 = 4979) with average reinforcement stiffness value comparable to the caseof Wall 6 is also shown for comparison.

Results of Figure 4(f) show that the magnitude and profile shape of lateral displacements ofwalls with the above reinforcement configurations are only marginally different. The displacementresponse of Wall 19 is slightly smaller than the response magnitude of Wall 6. The displacementresponse of Wall 20 is almost the same as the response of Wall 6. It can be concluded that reducingthe length of reinforcement for every other layer is a viable strategy to reduce the required amountof reinforcement with little impact on the displacement response of the wall.

The effect of alternating reinforcement length scheme on wall displacement response isfurther examined in Figure 4(g). In the figure, three pairs of displacement profile curves are shown.Each pair includes wall models with uniform and alternating reinforcement length schemes. Thereinforcement stiffness for each pair is uniform. The reinforcement stiffness values for the threepairs are 2000 kN/m (Walls 10 and 17), 5000 kN/m (Walls 8 and 18) and 8000 kN/m (Walls 11and 19). Figure 4(g) shows that the displacement response of uniformly reinforced retainingwalls increases only slightly by reducing the reinforcement length of every other layer by half.The amount of increase is less for stiffer reinforcements and is almost undetectable for the stiffreinforcement case of Walls 11 (R0.7 = 7967) and 19 (R0.7 = 5394).

Figure 4(h) shows plots of displacement response for Walls 10, 20, and 21. It can be seen thatreplacing every other reinforcement layer (of Wall 10 with J = 2000 kN/m) with a half-lengthlayer but with a considerably stiffer reinforcement (i. e., J = 8000 kN/m) can result in noticeablereduction of wall lateral displacement (cf. Walls 10, R0.7 = 1992 and 21, R0.7 = 2407). Thereduction in wall lateral displacement will be greater by adopting a long-stiff, short-secondaryreinforcement scheme (Wall 20, R0.7 = 4336) for the same total length of reinforcement material(i. e., compared to Wall 21).

5. Effect of reinforcement ratio on wall displacement

Figure 5 summarizes the variation of maximum wall lateral displacement with reinforcementratio, R0.7, for all wall models listed in Table 1. The wall lateral displacements are normalizedwith respect to reinforcement spacing, Sv . The following main observations can be made byinspecting Figure 5:

1. The wall lateral displacement, normalized to reinforcement vertical spacing, shows aconsistent trend of reduction in magnitude with reinforcement ratio value for all modelwalls examined. The presence ofSv in the normalized parameter (Xd)max/Sv emphasizesthe significance of reinforcement spacing in the magnitude of wall lateral displacementcompared with the influence of reinforcement length and stiffness. This is in contrastto displacement response of propped-panel walls where the influence of reinforcementvertical spacing on wall lateral displacement (normalized to wall height) due to soil


FIGURE 5 Variation of normalized wall lateral displacement with reinforcement ratio. Notes: (1) all simulation casesexcept for the solid circles (Sv = 1 m) correspond to reinforcement vertical spacing Sv = 0.5 m; (2) data groups denotedby numbered lines indicate similar configurations with different reinforcement ratio values (i. e., from one data group toanother).

self weight has been found to be negligible [13, 34] provided that the value of � (seeSection I) remains the same and no reinforcement slippage occurs.

2. The alternating reinforcement length schemes provide the lowest wall displacement re-sponse magnitude for a given reinforcement ratio value. The magnitude of wall lateraldisplacement for a given reinforcement ratio value increases with reinforcement config-uration in the following order (data points along each of the lines 1 and 2 in the figure):(1) uniform stiffness and alternating length; (2) uniform stiffness and length; (3) uni-form length and alternating stiffness; (4) grouped stiffness (uniform length) with stifferreinforcement at the bottom; and (5) grouped stiffness (uniform length) with less stiffreinforcement at the bottom. The magnitude of wall lateral displacement is less sensitiveto reinforcement configuration for greater reinforcement ratio values (cf. lines 1 and 2).

3. An estimate of the optimal reinforcement configuration that will minimize the reinforce-ment cost can be made from Figure 5.

B. Reinforcement loads

1. Load distribution with height

Figure 6 shows the distributions of maximum reinforcement load, Tmax, for the wrapped-facewalls at the end of construction. The plots in Figure 6(a) summarize the reinforcement loads forwalls with a single reinforcement type and two different reinforcement spacing values.


FIGURE 6 Distributions of maximum reinforcement load (wrapped-face walls only). (Cont.).


FIGURE 6 (Cont.). Distributions of maximum reinforcement load (wrapped-face walls only). (Cont.).


FIGURE 6 (Cont.). Distributions of maximum reinforcement load (wrapped-face walls only).


In general, reinforcement loads increase linearly with depth until the rigid frictional foundationboundary is approached. Earth pressure developed at the bottom of each wall is carried by themodel boundary and therefore the reinforcement load at the bottom of the wall is attenuated.At the end of construction, the magnitude and distribution of maximum reinforcement load inuniform reinforcement schemes are essentially independent of reinforcement stiffness for therange J = 1000 to 8000 kN/m examined in this study. This observation is consistent with theresults of previous numerical studies by the authors and others on propped-panel walls at end ofconstruction [11, 12, 15, 34, 35]. However, these earlier studies revealed that the distribution ofreinforcement loads with wall height was essentially uniform. Therefore, it can be concludedthat the type of facing (i. e., propped panel viz. flexible wrapped-face) has a large influence onboth the distribution and magnitude of reinforcement load. This conclusion is also consistentwith the results of full-scale experimental geosynthetic reinforced-soil wall tests reported byBathurst et al. [36] who examined the influence of hard-face and wrapped-face construction onthe development of reinforcement loads on a series of 3.6-m-high retaining wall structures.

The reinforcement load response in model walls with grouped or alternating reinforcementarrangements is different from load response of uniformly reinforced walls [Figure 6(b)]. Ingrouped reinforcement schemes with considerably different stiffness values in the top and bottomsections of the wall, the stiffer reinforcement attracts more load than the less stiff reinforcement.For example, in Walls 1, 3, 5, and 7 the variation of reinforcement load with depth is significantlyinfluenced by the grouped arrangement of reinforcement stiffness. In Walls 1 and 5, the maximumreinforcement load is greater and practically constant over the lower half of the wall height. Thereason is that these walls undergo relatively large displacement in the upper half due to the lessstiff reinforcement in that region [see Wall 5, Figure 2(a)]. This sheds additional load on the upperreinforcement layers in the lower half of the wall and changes the generally linear load variationwith depth to a more uniform distribution.

For walls with reinforcement spacing Sv = 0.5 m, the largest reinforcement load and thelargest local deviation from a smooth load distribution with elevation occurs in alternating re-inforcement schemes [Walls 2 and 6 in Figure 6(b)]. It appears that reinforcement layers withsignificantly different stiffness values in a wall with an alternating reinforcement scheme act asprimary and secondary reinforcement layers, respectively, with the stiffer reinforcement layersattracting larger lateral earth loads. It can be argued that the effective spacing, Sv , between pri-mary layers results in a stiff reinforcement load magnitude that is equivalent to the magnitudeexpected for a uniformly reinforced wall with 0.5 < Sv < 1 m [Figure 6(c)].

Figure 6(d) shows the plots of reinforcement load distribution for uniformly reinforced wallsand walls with constant reinforcement stiffness and alternating length scheme. It can be concludedthat with the exception of a slightly staggered pattern at the top, reducing the length of every otherreinforcement layer by one half has essentially no effect on maximum reinforcement load in thewall.

Figure 6(e) summarizes the comparison of reinforcement load distribution plots for modelwalls with uniform reinforcement stiffness J = 8000 kN/m (Wall 11) and selected other rein-forcement schemes that include reinforcement layers with J = 8000 kN/m. The results shown inFigure 6(e) indicate that reducing the length of every other reinforcement layer while maintain-ing the same reinforcement stiffness value (Wall 19) is the only cost-saving strategy among thealternatives examined that would not result in a significant increase in maximum reinforcementload with respect to uniform reinforcement schemes.

Figure 6(f) shows reinforcement load distributions corresponding to two contrasting rein-forcement configurations with different lengths and stiffness values (Walls 20 and 21 in Table 1).Plots of reinforcement load response for uniform stiffness cases of Walls 10 and 17 are also


shown in the figure. Comparison of load distribution plots for Walls 17, 20, and 21 with theplot for Wall 10 indicates that maximum loads in different reinforcement layers are essentiallyproportional to their relative stiffness values regardless of reinforcement length in alternatingreinforcement arrangements.

2. Effect of reinforcement ratio on reinforcement load

Figure 7 summarizes the magnitude of maximum reinforcement load in wall models listedin Table 1. An inspection of the figure shows that greater reinforcement load magnitudes developin walls with a vertical facing, large reinforcement spacing, or alternating scheme with significantstiffness differences between reinforcement types. The magnitude of maximum reinforcementload is otherwise almost the same for all other reinforcement configurations and does not showany dependence on the reinforcement ratio value. The reinforcement loads and backfill shearstrain at end of construction are shown in Figure 8, which further illustrate the above observationsfor wall models listed in Table 1. Plots of Figure 8 for Walls 15 and 16 indicate large soil strainand reinforcement load at the facing. Large soil strain and reinforcement load have been reportedas the possible reasons for the failure of an actual wrapped-face wall [21].

FIGURE 7 Variation of maximum reinforcement load in each wall with reinforcement ratio. Notes: (1) all simulationcases except for the solid circles (Sv = 1 m) correspond to reinforcement vertical spacing Sv = 0.5 m.

C. Lateral earth pressure coefficient

Figure 9 shows the distribution of normalized lateral earth pressure coefficient Kh/Kah

acting behind each wall (wrapped-face configurations only) where:


FIGURE 8 Shear strain in backfill and reinforcement load at end of construction. Notes: contour intervals = 0.2 %;Tmax in kN/m. (Cont.).


FIGURE 8 (Cont.). Shear strain in backfill and reinforcement load at end of construction. Notes: contour intervals= 0.2 %; Tmax in kN/m. (Cont.).


FIGURE 8 (Cont.). Shear strain in backfill and reinforcement load at end of construction. Notes: contour intervals= 0.2 %; Tmax in kN/m.


FIGURE 9 Normalized equivalent lateral earth pressure coefficient of wrapped-face walls. (Cont.).


FIGURE 9 (Cont.). Normalized equivalent lateral earth pressure coefficient of wrapped-face walls.

Khi = Tmaxi

γ (H − hi) Sv. (6)

In equation (6), Khi is the earth pressure coefficient corresponding to reinforcement layer i,Tmaxi is the maximum reinforcement load in layer i and hi is the elevation of reinforcementlayer i measured from the rigid foundation. It is worth noting that earth pressure coefficient,Khi , calculated from equation (6) is an equivalent design parameter which corresponds to themobilized load in reinforcement layers. The Khi values calculated from equation (6) for thebottom reinforcement layers do not represent the true value of the lateral earth pressure coefficientnear the toe which is close to the at rest value, Ko. Equation (6) overestimates the value ofKhi forthe top reinforcement layer due to its small depth in the backfill. Accordingly, the interpretationof the results for lateral earth pressure coefficient in the following sections is limited to the middlesection of the wall height where boundary effects are minimal.

For uniform reinforcement configurations with Sv = 0.5 m and for all reinforcement stiff-ness values examined [Figure 9(a)], the lateral earth pressure coefficient along the wall height(except for the regions near the top and bottom boundaries) was found to be constant and closeto the theoretical value, Kah. This observation can be expected from the data in Figure 6(a) andequation (6). According to equation (6), a linearly increasing reinforcement load with depth isequivalent to constant Kh values over the backfill depth. A similar conclusion can be reachedfor the cases with Sv = 1.0 m. However, the elevation range with constant Kh value in the lattercase is not as great as the range for Sv = 0.5 m case. This is because the greater reinforcementvertical spacing of Sv = 1.0 m results in a larger wall deformation and excessive load in the rein-forcement layers. Nonetheless, results of Figure 9(a) indicate that for the range of reinforcementstiffness values examined, a uniform reinforcement distribution in wrapped-face walls results inKh values over the middle portion of the wall height that are close to Kah and independent of


reinforcement stiffness. Reinforcement forces at the top of walls greater than values calculatedfrom earth pressure theories have been noted in earlier numerical simulation work [13, 15] andfull-scale experimental wall tests [36].

The variation of normalized lateral earth pressure coefficient with depth in Figure 9(b)shows a clear influence of relative reinforcement stiffness values in all reinforced wall modelswith nonuniform reinforcement configuration. In Walls 2 and 6 with alternating reinforcement,the value of Kh at elevation h depends on the stiffness of reinforcement layer at elevation h. Ingrouped reinforcement Walls 3 and 7,Kh has two distinct and practically constant values, whereasin Walls 1 and 5 with the less stiff reinforcement type grouped in the top section of the wall, Kh

decreases linearly with depth in the bottom half of the structure. This is due to constant maximumreinforcement load over the lower half of the wall height as explained in Section 1.

Plots of equivalent earth pressure coefficient for selected model walls with uniform rein-forcement stiffness are shown in Figure 9(c). The plots in the figure include pairs of wall caseswith uniform and alternating reinforcement length (Table 1). It can be seen that the distributionof equivalent earth pressure coefficient over a major portion of the wall height is not affected byadopting the alternating length scheme except for a few layers at the top where the magnitudeof Kh is influenced by short reinforcement length. The variation of Khi with the stiffness ofreinforcement layers for nonuniform reinforcement models can be formulated as:

Khi/Kavh = C (Ji/Jav)α (7)

where Kavh and Jav are average values of Khi and Ji over a selected middle height of the walls.The reinforcement load data within the first meter from the top and bottom of each wall modelwere disregarded in calculating the values of Kavh to exclude boundary effects. The valuesof C and α were obtained based on a regression analysis of model results and are presented inTable 2. Inspection of the values forC and α in the table indicates that the value of coefficientC isessentially constant and very close to 1 for all nonuniform reinforced wall configurations includedin the study. This confirms that the equivalent lateral earth pressure coefficient behind wrapped-face walls with nonuniform reinforcement scheme is largely dependent on J and practicallyindependent of depth. The value of exponent α depends on the reinforcement arrangement. Ina nearly uniform reinforcement design (Wall 9), the value of α is almost zero, which indicates auniform distribution of lateral earth pressure coefficient throughout the middle wall height that isindependent of reinforcement stiffness, J [see also Figure 9(a)]. When reinforcement is groupedinto two separate regions with significantly different stiffness values, the lateral earth pressurecoefficient, Kh, is stiffness dependent and is influenced by the reinforcement arrangement. Thisdependence is least when the stiff reinforcement is placed in the bottom half of the wall height(Walls 1 and 5 with α ∼ 1/8). The value of Kh is more strongly dependent on J in the caseof alternating reinforcement as compared to grouped reinforcement arrangements for the samereinforcement material types (Walls 2 and 6 with α ∼ 2/3). When the reinforcement layersare placed in a mixed configuration where stiffness gradually decreases with height (Wall 12)or where the stiffer reinforcement is collectively placed on the top of the softer reinforcement(Walls 3 and 7), Kh is moderately dependent on J (α ∼ 1/3 − 1/2).

In cases with alternating reinforcement length (i. e., Walls 20 and 21), the values of Cand α are comparable to those in with wall models with uniform reinforcement length. Theonly exception is the value of α in Wall 21 where the stiff reinforcement is placed in half length(L = 4.0 m) alternating with the full-length (L = 8.0 m), less stiff reinforcement. The contrastingscheme of Wall 20 appears to be a better design because it allows the stiff reinforcement withsufficient length to develop maximum load while ensuring adequate reinforcement length againstpullout.


TABLE 2

Wall Models Earth Pressure Parameters (Wrapped Face, Nonuniform ReinforcementStiffness)Wall Reinforcement stiffness Earth pressure parameters [Equations (7) and (8)]No. configuration C η = Kavh/Kah ηC α

1 grouped 1.03 1.06 1.09 0.132 alternating 1.06 1.07 1.13 0.673 grouped 1.07 1.06 1.14 0.445 grouped 1.02 1.03 1.04 0.126 alternating 1.04 1.05 1.09 0.647 grouped 1.04 0.99 1.03 0.339 grouped 1.00 0.97 0.97 -0.0312 mixed 1.03 1.02 1.06 0.4520 alternating | alternating 1.04 1.09 1.13 0.6721 alternating | length 1.03 1.15 1.19 0.41Average value: 1.03 1.03 1.07

V. Calculation of earth pressure coefficient for reinforcement design

Equation (7) suggests a preliminary design approach to determine the lateral earth pressurecoefficient in reinforced soil retaining wall systems with nonuniform reinforcement schemes. Theright-hand side of equation (7) is known once the reinforcement configuration is decided on. Onthe other hand, the value of Kavh can only be calculated after the Khi values for all reinforcementlayers are determined. Table 2 includes the ratio, η, between the calculated average earth pressurecoefficient (i. e., average value between reinforcement layers), Kavh, and Kah for wrapped-face,nonuniform reinforcement scheme models in Table 1. Equation (7) with the substitution ofη = Kavh/Kah can be rewritten in the form:

Khi = ηC

(Ji

Jav

)α

Kah . (8)

Inspection of Table 2 reveals that the value of ηC for the wrapped face model walls with nonuni-form reinforcement stiffness configurations is practically equal to 1.1. Accordingly, the expectedmaximum reinforcement load in the layer with stiffness Ji can be calculated using the contributoryarea approach [equation (6)] as:

Tmaxi = 1.1γKahSv (H − hi) (Ji/Jav)α (9)

where all the parameters are as defined previously and the values for α are given in Table 3 fordifferent reinforcement configurations of wrapped-faced walls investigated in this study.

VI. Conclusions

The possibility to economize on reinforcement supply in reinforced soil retaining wall sys-tems is investigated using a numerical simulation approach. A total of 21 wall models withdifferent reinforcement layouts and stiffness values are included in the study. The walls aremainly of wrapped-face type with the reference reinforcement length to wall height ratio equalto 1.

The response of retaining wall models are presented in terms of facing lateral displacementand distribution of maximum reinforcement load along the wall height. The equivalent horizontal


TABLE 3

Suggested Values for α in Equation (9) (Nonuniform Reinforcement)Reinforcement stiffness configuration α

| Uniform length 2/3Alternating | | Stiff reinforcement long (L = H ) 2/3

| Alternating length || | Stiff reinforcement short (L = H/2) 1/2

| Stiff reinforcement within the top half 1/3–1/2Grouped |

| Stiff reinforcement within the bottom half 1/8

Mixed (Gradual decrease of stiffness toward the top) 1/2Notes: Reinforcement stiffness range (J = 1000 − 8000 kN/m); Magnitude of stiffness difference between reinforcement groups: afactor of 2 or greater.

earth pressure coefficient corresponding to each reinforcement layer is calculated from the max-imum reinforcement load and is plotted against the height of wall models. A reinforcement ratioparameter is introduced to quantify the reinforcement supply for stability analysis of wrapped-face wall models. The cost of reinforcement can be expected to increase with reinforcement ratiovalue for each wall model.

The numerical results showed that the displacement profile of walls with alternating rein-forcement was more consistent in shape and magnitude to walls with equivalent (i. e., identicalreinforcement ratio value) uniform reinforcement than the displacement profile of walls withgrouped reinforcement schemes. The grouped category of walls typically showed larger dis-placements particularly in regions with less stiff reinforcement.

The mixed reinforcement configurations with reduced stiffness toward the wall top did notresult in significantly larger lateral wall displacements compared with walls with uniform re-inforcement using the stiffest reinforcement type. Results of the study showed that a batteredwrapped-face wall produces significantly smaller lateral displacements than a wall with identicalreinforcement configuration and a vertical gabion facing. Taken together, the results of the studysuggest that reducing the stiffness of reinforcement layers placed at small spacing is the preferredstrategy to minimize facing deformation rather than using stiffer reinforcement layers at a greaterspacing.

Another approach for economic reinforced soil wall design is to reduce the length of everyother reinforcement layer by 50% while maintaining the same stiffness value. This approach wasfound to be the best method to reduce the reinforcement supply requirement while maintainingwall serviceability and performance.

Designing the wall with a battered face, where possible, can further reduce the amount ofreinforcement required to maintain the wall lateral displacement within tolerable limits. Themaximum reinforcement load in each layer is shown to be dependent primarily on the relativestiffness of the reinforcement layer with respect to other layers regardless of the stiffness andlength arrangement. The variation of maximum reinforcement load with wall height in bothprimary and secondary layers in alternating schemes was similar to the distribution for uniformlyreinforced wall cases and increased linearly with depth. However, the magnitude of maximumreinforcement load was larger than the maximum load in uniform reinforcement schemes withthe same reinforcement spacing.


The equivalent lateral earth pressure coefficient was found to be constant in the middleportion of wrapped-face walls with uniform reinforcement stiffness. The magnitude of each earthpressure coefficient was comparable to the value predicted from Coulomb earth pressure theory(horizontal component) for the entire range of stiffness values examined. Empirical equationsare proposed that can be used to calculate the earth pressure coefficient distribution along thewall height and the maximum reinforcement load in each layer for a given wrapped-faced wallreinforcement layout and backfill properties. The topmost reinforcement layer may need to bedesigned for as great as three times the value from Coulomb earth pressure theory using thecontributory area method.

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