General Analytical Framework for Design of Flexible Reinforced Earth Structures

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General Analytical Framework for Design of FlexibleReinforced Earth Structures

Jie Han, P.E.1; and Dov Leshchinsky2

Abstract: Current design methods divide reinforced earth structures into walls and slopes by using an arbitrary face inclination of 70°as the boundary. The required maximum strength of reinforcement computed for reinforced walls are significantly higher than thatcomputed for reinforced slopes even if the inclination is practically the same. Presented is a general analytical framework for design offlexible reinforced earth structures regardless of the slope face inclination. In fact, the framework is consistent for any structural geometryand any applicable slope stability analysis although, for demonstration purposes, the simple Culmann formulation is utilized for simplegeometry with zero batter. Using an adequate slope stability formulation, the required tensile resistance of reinforcement for a given layoutis calculated so as to produce the same prescribed factor of safety anywhere within the reinforced zone. That is, using the design shearstrength of the soil, the required reinforcement resistance along each layer is computed to fully mobilize this shear strength for all possibleslip surfaces. That is, a baseline solution is produced for an ideal long-term strength of reinforcement at any location. Consequently, therequired strength of the connection between each reinforcement layer and the facing unit can also be determined. This connection strength,however, assumes small facing units with negligibly small shear and moment resistance. Parametric study is conducted to demonstrate thereasonableness of the presented framework. It is shown that the required tensile resistance and connection strength depend on factors suchas: reinforcement length; intermediate reinforcement; percent coverage; and quality of fill. When compared with the current AASHTOdesign for walls, the required maximum long-term strength of the reinforcement as well as the required connection strength in theproposed approach are substantially smaller.

DOI: 10.1061/�ASCE�1090-0241�2006�132:11�1427�

CE Database subject headings: Soil stabilization; Retaining walls; Tensile strength; Connections; Limit equilibrium; Geosynthetics;Slope stability; Safety factors; Soil structure.

Introduction

Current design methods �e.g., AASHTO 2002; BSI 1995� con-sider reinforced walls as structures with a batter less than 20°whereas reinforced slopes are inclined at an angle of 70° or less.Obviously, such distinction is arbitrary as there is nothing magicalwith the 70° boundary. Further, design of walls commonly utilizeslateral earth pressures whereas design of slopes uses limit equi-librium �slope stability� type of analysis. Consequently, there is anabrupt change in the required reinforcement strength and lengthwhen reaching the arbitrary boundary between so-called rein-forced walls and slopes. No rational explanation for this incom-patible behavior, basically designing the same structure, exists.

The term “reinforced earth structures” herein refers to bothreinforced walls and slopes. This paper’s title descriptor “flex-

1Associate Professor, Dept. of Civil, Environmental, and ArchitecturalEngineering, Univ. of Kansas, 2150 Learned Hall, 1530 W. 15th St.,Lawrence, KS 66045-7609 �corresponding author�. E-mail: [email protected]

2Professor, Dept. of Civil and Environmental Engineering, Univ. ofDelaware, Newark, DE 19716. E-mail: [email protected]

Note. Discussion open until April 1, 2007. Separate discussions mustbe submitted for individual papers. To extend the closing date by onemonth, a written request must be filed with the ASCE Managing Editor.The manuscript for this paper was submitted for review and possiblepublication on March 21, 2005; approved on May 22, 2006. This paper ispart of the Journal of Geotechnical and Geoenvironmental Engineer-ing, Vol. 132, No. 11, November 1, 2006. ©ASCE, ISSN 1090-0241/
2006/11-1427–1435/$25.00.
JOURNAL OF GEOTECHNICAL AND GEOE

J. Geotech. Geoenviron. Eng.

ible” implies that all system components �i.e., soil, reinforcement,facia� can move or deform sufficiently to allow for a limit equi-librium state to develop. Walls and slopes utilizing block or simi-lar small facing units, reinforced with geosynthetics and havingconnection to the facing that yields plastically �e.g., frictionalconnection�, are classified as flexible. Hence, this paper is appli-cable to a rapidly growing category of mechanically stabilizedearth structures which are both economically and aestheticallyattractive.

Generally, design of geosynthetic reinforced structures can bedone using the following methods: �1� Numerical �continuum-based� methods �e.g., Rowe and Ho 1992; Leshchinsky and Han2004�: This approach utilizes a numerical scheme generallyknown as finite element or finite difference method. It can accu-rately replicate soil-structure interaction, simulate construction,consider complex boundary conditions, and produce the displace-ment field. The main challenge is the availability of data suitablefor such refined analysis as well as the need for an experiencedanalyst to properly perform such an analysis. �2� Empirical ap-proach �e.g., Allen et al. 2003�: Based on field data for a varietyof geosynthetic reinforced walls, all having simple geometry, themaximum force in each layer was correlated with an estimatedvalue of the plane strain internal friction angle. Such an approachis useful for walls having similar geometries to those which wereused for curve fitting of the empirical model including simplelayout of reinforcement. Further, such an approach provides littleinformation about the optimal layout of the reinforcement. �3�Lateral earth pressure: The attractive feature of lateral earth pres-
sure theory �Rankine� is its simplicity. However, its application is
NVIRONMENTAL ENGINEERING © ASCE / NOVEMBER 2006 / 1427

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limited to walls. Moreover, even for simple geometry, reinforcedwalls grossly violate the conditions for which Rankine’s lateralearth pressure theory is valid �e.g., the presence of reinforcementlayers changes the principal stress orientation within the mass�.Careful attempts to measure it on the back of the facing blocks�Ling et al. 2005� demonstrate its elusive value. Clearly, the lat-eral earth pressure approach cannot be extrapolated to slopes andmultitiered walls. �4� Limit equilibrium: This analysis quantifiesthe margin of safety of the system against a state of imminentfailure. It has been used successfully for design of major geotech-nical structures for decades. One limitation of limit equilibrium inconjunction with reinforced soil applications is its inability topredict the force distribution along each layer. However, experi-ence with geosynthetic-reinforced earth structures shows that itsmaximum mobilized strength for all layers is approximately uni-form. Hence, the practice of geosynthetic-reinforced slope designallows the use of properly modified slope stability analysis toaccount for the reinforcement effects while assuming that eachreinforcement layer will contribute its long term strength �e.g.,Elias 2001�. In fact, comparison between the global stability pre-dicted by a common limit equilibrium analysis �Bishop method�and a continuum mechanics-based analysis which account forlocal conditions shows good agreement �Leshchinsky and Han2004�.

Leshchinsky and Perry �1987�, Leshchinsky �1992, 1999�, andLeshchinksky et al. �1995� used the log spiral failure mechanismto determine the required reinforcement long term strength. It wasassumed that the connection capacity is equal to the requiredreinforcement strength at each elevation. The length of the rein-forcement was calculated so as to ensure sufficient rear-end pull-out resistance as well as resist compound type of failure. That is,the required strength of the top layer was first calculated consid-ering a log spiral emerging within the contributory area of thatlayer. This was followed by calculating the strength needed for alayer below using the already calculated strength of the top layeras a known quantity. This process continued to the bottom layerthus defining the long term strength of all layers, the requiredreinforcement length, and, indirectly, an assumed and overly con-servative value of the required connection strength. Although thereinforcement strength was calculated to yield a prescribed factorof safety along the critical slip surface, the safety factor at otherlocations within the reinforced mass was larger.

Baker and Klein �2004a,b� modified the top-down approach byLeshchinsky �1992�. Their objective was to find the reinforcementforce needed for the same prescribed factor of safety everywherewithin the reinforced mass �i.e., following the notion of safetymaps presented by Baker and Leshchinsky 2001�. The requireddistribution of reinforcement tensile force was first determined forthe upper layer considering its contributory area. Unlike Lesh-chinsky �1992�, they computed the required resistance at eachpoint where the slip surface intersected the reinforcement layer.When calculating the required strength for the layer below, thetensile resistance distribution along the layer above was consid-ered as known, having the distribution calculated in the previousstep. This approach does not consider the contribution of rein-forcement layers as being equal, even if enabled by pullout resis-tance, when intersecting a potential slip surface but rather, thetop-down approach determines the capacity of each layer abovethe layer of interest regardless of the current analyzed slip sur-face. To conduct a parametric study, Baker and Klein �2004a,b�used a planar slip surface �Culmann 1866�. They showed that theline along which maximum reinforcement force develops is not
along a single slip surface and that it is close to the facing. Their
1428 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGIN


calculated maximum required tensile resistance is larger than thatproduced by Rankine’s lateral earth pressure. However, experi-mental data �e.g., Allen et al. 2003� shows that Rankine’s valuesare about twice as much as those in reality.

Many design charts for geosynthetic-reinforced slopes, basedon limit equilibrium analysis, are available �e.g., Leshchinsky andVolk 1985; Schmertmann et al. 1987; Leshchinsky and Boedeker1989; Jewell 1990�. Although instructive, these charts do not pro-vide a framework for design of geosynthetic-reinforced slopesand walls considering all aspects of stability especially facingconnection, different structural geometries, and boundary condi-tions. These charts do not provide the distribution of requiredtensile resistance along each reinforcement layer.

Objective

The objective of this work is to present a general unified frame-work for limit equilibrium analysis to facilitate the design of flex-ible reinforced earth slopes and walls. The framework yields arational methodology to find the distribution of required tensileresistance along each reinforcement layer for a given reinforcedslope/wall problem so that the factor of safety on the strength ofsoil is uniform everywhere within the reinforced soil zone. Suchan objective is different from the conventional approach wherethe long-term strength of the reinforcement is given �typicallyconstant along its length except for either end where pullout pre-vails� and many trail slip surfaces are tested seeking the criticalone. The safety factors at all other locations are larger than theminimum value implying the reinforcement is excessively strong,however, without quantification of what is “excessive” strength.The conventional approach is a minimization process in which therequired strength of the reinforcement producing a prescribed fac-tor of safety is sought and this strength is required only along thecritical surface. The presented framework is a maximization pro-cess in which the maximum required tensile resistance of thereinforcement everywhere is sought so as to obtain an optimalstructure in which the factor of safety is the same everywhere�i.e., each slip surface is equally critical�. This approach is funda-mental, producing the spatial solution for the required tensile re-sistance of the reinforcement along its length so as to yield aconstant factor of safety. Practically, it indicates the effectivenessof a final design showing zones within which there is no need forreinforcement based on a given layout while rendering the re-quired connection strength. The term “framework” is used to in-dicate that any slope stability analysis can be utilized provided itwas properly modified to accommodate reinforcement.

Unlike Baker and Klein �2004a,b�, the framework presentedhere ignores the moment/shear contribution by the facia. Moreimportantly, it assumes that all reinforcement layers contributeequally along each intersecting slip surface so as to produce astate of limit equilibrium. This contribution may be limited by theavailable pullout resistance at the rear or front of the reinforce-ment. The front pullout resistance depends on the connectioncapacity. If the pullout capacity at the rear of a layer is not suffi-cient, the strengths of other layers that are not controlled by pull-out need to be increased so as to render a desired factor of safety.Therefore, unlike Baker and Klein �2004a,b�, the line of maxi-mum tension passing through all layers is along a slip surface.This approach leads to required reinforcement strength that isabout half the value predicted by Rankine’s analysis. The pre-sented approach accounts for reinforcement length, spacing, inter-
action with confining soil, and structural geometry.
EERING © ASCE / NOVEMBER 2006

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Analytical Framework

For clarity, Culmann’s �1866� limit equilibrium analysis, modifiedto accommodate reinforcement, is used. However, this does notaffect the generality of the analytical framework. Note that Cul-mann assumes a single wedge planar slip surface and therefore,can be formulated without resorting to statical assumptions. Al-though such a failure mechanism is reasonable for near verticalslopes, it might not be conservative for flatter slopes as theircritical slip surface may not be planar �e.g., Han and Leshchinsky2004�. By solving the horizontal and vertical limit equilibriumequations for a vertical slope and granular soil, the total reinforce-ment force in the horizontal direction needed to produce a factorof safety of unity for an assumed Planar Surface I �Fig. 1�a��, TRI,e.g., is

TRI =�HI

2�sin �I − tan � cos �I�2Rctan �I�tan � sin �I + cos �I�

�1�

where ��unit weight of fill; ��friction angle of fill;�I=tan−1��HI−z1� /x1�, defined in Fig. 1 and Rc�coverage ratio ofreinforcement �varying between 1.0 for full coverage to 0 for noreinforcement�.

The distance to the Planar Surface I �Fig. 1�a��, measured fromthe wall’s face, along reinforcement layer i, can be calculated asfollows:

xIi = �HI − zi�tan �I �2�

Similarly, for slip surface J, the total reinforcement force can becalculated using Eqs. �1� and �2� by changing the notation indexfrom I to J.

The available pullout resistance measured from the front ofreinforcement layer i, where the soil within the sliding mass maymove outwards relative to the reinforcement but is restrained bythe facing unit thus resulting in connection load which, in turn,allows for tensile force development in the reinforcement, can becalculated as follows:

Tpo�F�i = Tci + 2xi�ziCiRc tan � �3�

where Tci�available connection strength between reinforcementlayer i and wall facing; xi�distance to a slip surface from the wallfacing along reinforcement layer i, e.g., for Slip Surface I,xi=xIi, as calculated in Eq. �2�; and Ci�interaction coefficientbetween reinforcement layer i and reinforced fill.

The available pullout resistance measured from the end of re-inforcement layer i can be calculated as follows:

Tpo�E�i = 2�L − xi��ziCiRc tan � �4�

Fig. 1. Definition and notation

where L�total length of the reinforcement layer i.



The procedure for determining the required tensile strengthdistribution along each reinforcement layer starts with the toplayer, Layer 1. Select a depth from the top of the wall towardLayer 2 as the current height of the wall section and examine slipplanes emanating from the toe of this “wall” section by changingthe x1 value in Fig. 2�a�. For each slip surface, the total reinforce-ment force can be calculated using Eq. �1�. For this case, the totalreinforcement force would be carried by Layer 1 as only onereinforcement layer exists in this wall section. By changing x1,the required tensile strength distribution along the reinforcementcan be obtained as shown in Fig. 2�a�.

When there are two reinforcement layers, the total reinforce-ment force for a specific slip surface �e.g., OC� should be dividedequally between these two reinforcement layers �i.e., Point C�andPoint I in Fig. 2�b��. Therefore, Curves A�B�C�DF� and GHIJKare calculated using Culmann’s equation. However, Layer 1 has arequired tension distribution as shown in Fig. 2�a� resulting froma slip surface emerging at point O �above Layer 2�. For compari-son, this distribution is also plotted in Fig. 2�b�. As the requiredtension from the previous analysis �ABCD� is higher than that forthe current need �A�B�C�D�, the required tension from the previ-ous analysis prevails. However, the required tension along DF� ishigher than that for DE. Hence, the required tension along DF�prevails. In summary, the required tension for Layer 1 is ABCDF��solid line� which represents a composite envelope generated byslip surfaces emerging at points O and O�. As Layer 1 carriesmore tension for the portion ABCD �thus producing a limit equi-librium state for surfaces emerging at O�, the remaining tensionfor Layer 2 should be reduced from GHIJ to G�H�I�J.

This distribution must be checked against the available pulloutresistance as computed from the front and end of each layer usingEqs. �3� and �4�; the required strength cannot exceed the availablepullout resistance. The minimum required connection strength in

Fig. 2. Distribution of required tension for limit equilibrium�note: � is uniformly mobilized�

Eq. �3� is determined in Fig. 3 by the required front-end pullout


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resistance line tangential to the curve of required tension �T� forlimit equilibrium at Point A to ensure the available pullout resis-tance generated by the front equal to or greater than the requiredtensile strength based on the total reinforcement force require-ment; i.e., Eq. �1�. From the connection to the point of tangency,there is excess pullout resistance except for Point A; i.e., theavailable strength between the front end and Point A is in excessof what is needed for limit equilibrium. This means that the re-quirement for a factor of safety of unity near the front end maynot be mathematically possible to satisfy as the pullout resistancemay impose somewhat larger value than needed in Eq. �1�; how-ever, this strength is typically only marginally excessive. Thisstatement is verified by the results presented later.

In Fig. 3, three different conditions are considered based onthe length of reinforcement: �1� excessive length; �2� ideal length;and �3� inadequate length. When the length of reinforcement isexcessive as shown in Fig. 3�a�, the available pullout resistancegenerated by the rear end is higher than the required reinforce-ment force; hence, pullout at the end cannot happen. Further, thereinforcement in the rear beyond the required T range is notneeded. When the length of the reinforcement is exactly asneeded �ideal design�, the available rear-end pullout resistanceline is tangential to the curve of the required tension for limitequilibrium at Point B as shown in Fig. 3�b�. However, when thelength of reinforcement is too short as shown in Fig. 3�c�, theavailable pullout resistance generated by the end is less than therequired reinforcement force �Eq. �1�� thus not enabling the resis-tance required by limit equilibrium. Lengthening the reinforce-ment or adding reinforcement layers is necessary in such a case.In essence, Figs. 3�a–c� indicate the design objective to obtain theideal length of the reinforcement considering its long-termstrength, pullout resistance, spacing, and strength of connection tothe facing.

Fig. 3. Distribution of required tension for limit equilibrium

If there are n reinforcement layers, the total reinforcement re-



sistance for each analyzed slip surface in Eq. �1� should be dis-tributed equally among all the reinforcement layers. However,upper layers with predetermined required resistance distributionscalculated for surfaces emerging at higher elevations should bechecked. If the predetermined required resistance at the same lo-cation is less than the current requirement, it should be updatedand the required resistance among layers should be readjustedaccordingly. Otherwise, the previous resistance is kept un-changed. If the slip surface is beyond the length of some rein-forcement layers, the total reinforcement resistance would bedistributed among the remaining reinforcement layers. This pro-cedure is clearly of a “bookkeeping” nature, therefore, it is ideallysuited as a computerized process. It should be noted that startingwith the top layer is computationally convenient and efficient;however, the search for the minimum strength producing a speci-fied factor of safety for all possible slip surfaces can be random.

This “numerical scan” of the reinforced and retained soil zoneproduces the required tensile resistance distribution along eachlayer so as to render a system in a limit equilibrium state for agiven design strength of the soil. The objective is to find therequired reinforcement resistance at any location so as to producethe same safety factor anywhere within the reinforced soil. Inactual design, however, one will use the minimal resistance as abaseline value that needs to be increased to account for durability,construction damage, and possible creep to select a reinforcementlayer with adequate ultimate tensile strength.

Parametric Study

To examine the analytical framework for design of flexible rein-forced earth structures as proposed in this paper, a parametricstudy was conducted selecting a baseline case to be comparedwith other cases where various parameters were changed. Theseparameters include reinforcement length, intermediate reinforce-ment layers, percent coverage, and fill quality.

Baseline Case

The dimensions and design parameters of the baseline case areshown in Fig. 4. An interaction coefficient of Ci=0.8 was used inthis analysis and the following parametric study. In practice,

Fig. 4. Dimensions and design parameters of the baseline case

higher values of interaction coefficient may be used for granular


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fills while lower values may be used for silty materials. As de-scribed earlier, the analysis procedures start with the top layer�i.e., Layer 1�.

The required tensile resistance distribution along Layer 1 forthe one layer case �H=1.2 m� is presented in Fig. 5�a�. This ten-sile resistance is only needed in the range from the wall facing toa distance of 1.1 m in order to maintain this wall section in a limitequilibrium state where any planar slip surface emanating fromthe “toe” mobilizes equally the design strength of the fill.Fig. 5�a� also includes the available pullout resistance as com-puted from the front and the rear end of the reinforcement. Thispullout resistance in the front is tangential to the required tensileresistance distribution curve, ensuring sufficient pullout resistanceto enable mobilization of the tensile resistance of the reinforce-ment. To render sufficient pullout resistance in the front for thiscase, the required connection strength is 2.0 kN/m. Note that thedifference in the required tensile resistance and the available pull-out capacity between the point of tangency and the face is smallthus demonstrating that in this segment the factor of safety ispractically the same as elsewhere. The available pullout resistanceat the end of the reinforcement is far more than the requiredtensile strength in this range thus making the selected length ex-cessively long.

When the wall height increases from 1.2 to 1.8 m, it contains

Fig. 5. Required tensile strength distributions for one to four layersof reinforcement �note: � is uniformly mobilized�

two reinforcement layers �Layers 1 and 2�. As shown in Fig. 5�b�,



the required tensile resistance along Layer 1 ranges from the wallface to a distance of 2.1 m, which is approximately double therange required for the wall height of 1.2 m �see Fig. 5�a��. Inaddition, the required maximum tensile resistance is increasedfrom 4.7 to 5.4 kN/m. The resistance distribution in the front forLayer 1 is dictated by the case with one reinforcement layer asshown in Fig. 5�a�. This demonstrates the iterative nature of thegeneralized procedure. It also shows the effects of layers interact-ing with each other using limit equilibrium analysis. The dashedline in Fig. 5�b� signifies the required tensile resistance if therequired front end pullout resistance and the subsequent connec-tion strength in the previous step of analysis �Fig. 5�a�� are ig-nored. Note that the required tensile resistance for Layer 1 is overa wider length than that for Layer 2 as shown in Fig. 5�b�. Themaximum required tensile resistance for Layer 1 is the same asthat for Layer 2 as they are equally capable of sharing the totalreinforcement force. In addition, the required connection strengthfor Layer 2 is less than that for Layer 1 as the layer above hasalready carried a higher load when shallower planar surfaces areconsidered.

The required tensile strength distributions of four reinforce-ment layers �H=3.0 m� are presented in Fig. 5�c�. Layers 1 and 2have the required tensile resistance distributed over the wholereinforcement length of 3.0 m whereas Layers 3 and 4 have lim-ited distributions. For all four reinforcement layers, the requiredmaximum tensile resistance is equal; i.e., pullout resistance wassufficient for maximum force in each layer to develop withouttruncation. However, the required connection strength for Layers3 and 4 is near zero. In other words, there is little need for theconnection strength of these two layers in terms of the stability ofthe wall. However, as the construction of the wall starts from thebottom up, there is a minimal requirement for the connectionstrength to enable the construction. In this case, the minimal re-quirement for the connection strength is 2.0 kN/m as demon-strated in Fig. 5�a� though it is not necessarily the required longterm strength. Fig. 6 shows a block wall system in which theblocks were removed �for demonstration purposes� and geotextileflaps at a lower elevation were cut away so that the exposedreinforced soil could be viewed. This temporary wall, constructed

Fig. 6. Geotextile reinforced wall with facing blocks at lowerelevations removed and geotextile flaps cut �courtesy: Bob Barrett,Yenter Companies, Colo., used with permission�

by Yenter Companies, Colorado, served as an access platform for


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a drill rig near a bridge abutment. The reinforcing woven geotex-tile was spaced 200 mm. Fig. 6 implies that for closely spacedlayers there is no reinforcement strength needed at the front end,at least in a short run. Although the backfill soil may have a traceof an apparent cohesion, this value alone cannot explain the ap-parent stability of a tall wall when the facing blocks are removed.It appears that the reinforcement layers provide this resistance andthe trace of cohesion prevents the outward “flow” of backfill con-fined between adjacent layers of reinforcement. The results implythat known field observations could be explained analytically.Conversely, current designs �AASHTO 2002; NCMA 1997� re-quire substantial connection strength for the situation shown inFig. 6.

Note in Fig. 5�c� the tensile resistance distribution along eachlayer is not necessarily smooth. This is a result of the fact that asdeeper planar surfaces are considered, top layers are entirelywithin the sliding mass and therefore, the load now has to becarried by smaller number of layers. In other words, higher tensileresistance may be required if fewer layers are intersected by theplanar surfaces. Consideration of curved slip surfaces may yieldmore critical results and thus smoother distribution. Also, the ef-fects of pullout resistance in the front and rear of each layer playa role in the required resistance of other layers.

It is interesting to examine how the required tensile resistancefor a specific reinforcement layer changes with an increase of thewall height. For example, select Layer 1 as shown in Fig. 7. Therequired tensile resistance distribution range and the maximumvalue increase with an increase of the wall height. The distribu-tions at the front and rear are limited by the available pulloutresistance of this layer. In this particular case, the connectionstrength for Layer 1 does not change with an increase of the wallheight. Simply, the upper 1.2 m of the wall, which is supported bythis layer at the connection, dictates the required connectionstrength regardless of bottom layers.

Effects on Tensile and Connection Strengths

Reinforcement LengthThe effects of two uniform reinforcement lengths, different fromthe baseline case, were investigated in this study: Short reinforce-ment �1.8 m� and long reinforcement �6.0 m�. The short rein-

Fig. 7. Variation of required tensile strength distribution for firstlayer with height of wall �note: � is uniformly mobilized�

forcement is equivalent to 60% the height of the wall whereas the



long reinforcement is equivalent to 200% the height of the wall.This L /H �L is the length of the reinforcement and H is the wallheight� range covers most of the MSE walls in practice. As shownin Fig. 8�a�, the short reinforcement limits the range of requiredtensile resistance distributions as compared with the baseline casein Fig. 5�c�. The maximum tensile resistance for Layers 1 and 2 islimited by their available pullout resistance. As a result, the maxi-mum required tensile resistance increases from 7.5 kN/m in thebaseline case to 12.1 kN/m so as to maintain the stability of thewall system. The second peak for Layer 4 �Fig. 8�a�� results fromplanar surfaces extending beyond the upper layers. Consequently,there are fewer layers to share the load with.

The required tensile resistance distributions for long reinforce-ments �L=6 m� are shown in Fig. 8�b�. The available pulloutresistance at the rear does not control the distribution for anyreinforcement layer since each layer is sufficiently embedded. Ascompared with the baseline case shown in Fig. 5�c�, Fig. 8�b�exhibits smooth continuity after the peak values because no criti-cal slip plane extends beyond any reinforcement length and alllayers are uniformly mobilized.

The effect of reinforcement length on the maximum requiredtensile resistance is also presented in Fig. 9. The short reinforce-ment requires higher tensile resistance. When the reinforcementlength is increased to a threshold value, however, further increaseof reinforcement length would not result in higher tensile resis-tance. For the baseline and long reinforcement cases, the requiredmaximum tensile resistance is constant at different depths. Thatis, the resistance of all layers is equally mobilized thus the resis-tance of reinforcement is used most efficiently; however, this is at

Fig. 8. Required tensile strength distributions with short or longreinforcement �note: � is uniformly mobilized�

the expense of longer reinforcement length. The uniform maxi-


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mum tensile resistance distribution for all layers was also ob-served in field and laboratory studies. For example, Fannin andHermann �1990� showed the results of field test for two steepslopes �2v :1h� reinforced with geogrids. The measured Tmax val-ues are approximately the same for all layers, especially whenuniform length of reinforcement is used. Based on centrifugaltests on geotextile reinforced steep slopes �2v :1h�, Zornberget al. �1998b� suggested that the proper distribution of Tmax withdepth, near failure, is almost uniform and not linear as implied byAASHTO. The companion paper �Zornberg et al. 1998a� sug-gested the use of limit equilibrium as a basis for design. Thereport by Allen and Bathurst �2001� represents data collectedfrom several instrumented full scale walls. Close examination ofthe presented data shows that Tmax is approximately the same forall layers. For the short reinforcement case, however, the maxi-mum required tensile resistance with depth is trapezoidal, whichis a common distribution shape of maximum tensile force mea-sured in the field. The total area �or length� of reinforcement ispart of the economic efficiency of the structure; i.e., use shorterbut stronger reinforcement to achieve the same stability as withlong but weaker reinforcement.

Fig. 9 also shows the maximum required tensile resistance ofthe reinforcement, Tmax, calculated following AASHTO usingRankine’s active lateral earth pressures. The distribution of Tmax

resulting from calculations following the AASHTO procedure isthe same for all three lengths of reinforcement. Note that thelength of 1.8 m means a ratio of L /H=0.60, a slightly shorterlength than the 0.70 required by AASHTO; however, the size ofthe active wedge allows to calculation of Tmax as presented. Asseen in Fig. 9, for the baseline case the maximum value of Tmax

from AASHTO, which is typically used to select the reinforce-ment, is about twice the value as calculated in the presentedframework even though the total required force is the same. Forshort reinforcement the two approaches yields closer value of themaximum Tmax. However, for all cases Tmax values near the crestfor the presented approach are higher than those predicted byAASHTO. As pullout resistive length for continuous geosyntheticreinforcement is relatively short, this length is practically easy tosatisfy.

The reinforcement length has an insignificant effect on theconnection strength since mainly shallower slip surfaces affect the

Fig. 9. Effect of reinforcement length on required maximum tensileresistance

connection load. In addition, the required connection strength de-



creases at lower elevations of reinforcement. Simply, the connec-tion strength required for upper layers combined with shallowplanar slip surfaces ensures sufficient stability. A figure demon-strating the statements in this paragraph was omitted due to pub-lication space limitation.

Intermediate ReinforcementThe inclusion of intermediate short layers makes the requiredtensile resistance distributions more complex as shown inFig. 10�a�. In this case, the lengths of primary and intermediatereinforcements are 3 and 1 m, respectively. There are severalpeak values along each primary layer of reinforcement as theshort intermediate layers does not contribute to the stability of thewall when the slip plane is beyond their ends. Also, the maximumtensile resistance for the top three intermediate reinforcement lay-ers is limited by their available pullout resistance in the rear.

Fig. 11 shows that the inclusion of intermediate reinforcementsreduces the maximum required tensile resistance for primary re-inforcement layers. The zigzag tensile resistance distributions areoften seen in field measurements of wrapped around MSE walls,which, by their nature, contain intermediate reinforcement layers.

The intermediate reinforcement layers play an important role

Fig. 10. Effect of intermediate reinforcement, percent coverage ofreinforcement, and fill quality on required tensile resistancedistributions

in reducing the required connection strengths as shown in Fig. 12.


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Percent CoverageThe influence of percent coverage �i.e., Rc=50% in this case� ofthe reinforcement on the required tensile resistance distribution ispresented in Fig. 10�b�. As compared with the baseline case, thereduction of percent coverage from 100 to 50% significantly in-creases the maximum required tensile and connection strengths.However, as shown in Fig. 10�b�, the required tensile resistanceof Layer 1 is controlled by the available pullout resistance in itsfront and rear ends as shown in dashed lines.

As expected, the reduction of percent coverage of reinforce-ment increases the required maximum tensile resistance in thereinforcement as shown in Fig. 11. The 50% reduction in percentcoverage results in more than 100% increase in the requiredmaximum tensile resistance. This is because Layer 1 is capable ofcarrying smaller load as its pullout resistance is decreased.

Fig. 12 shows that a low percent coverage �50%� of reinforce-ment requires much higher connection strength than a full cover-

Fig. 11. Effect of intermediate reinforcement, percent coverage, andfill quality on required maximum tensile resistance

Fig. 12. Effect of intermediate reinforcement, percent coverage, fillquality, and varying spacing on required connection strength



age �i.e., 100%� as the former provides less pullout resistance dueto the reduction of contact area between reinforcement and fill. Asshown in Fig. 12, the required connection strength for the 50%coverage case reaches 40–70% of the maximum tensile resistancewhile the baseline case �100% coverage� only requires less than30% of the maximum tensile resistance. Based on three instru-mented geosynthetic-reinforced retaining walls, the measuredload at the connection between the reinforcement and facingranged from 10 to 60% of the load using either NCMA orAASHTO as reported by Collin �1997�. Therefore, the generalrange of connection strength to maximum tensile resistance deter-mined from this proposed method is consistent with that mea-sured in the field.

Quality of FillThe required tensile resistance with low quality fill, having designshear strength value of �=20°, is presented in Fig. 10�c�. Ascompared with the baseline case �design value of �=30°�, therequired maximum tensile resistance and the connection strengthboth significantly increase. The rear portions of the tensile resis-tance distributions of Layers 1 and 2 are controlled by their avail-able pullout resistance in the rear.

As shown in Fig. 11, the low quality fill ��=20°� requireshigher maximum tensile resistance than the baseline case��=30°�. In addition, the distribution of the maximum tensileresistance with depth for the low quality fill is trapezoidal.

The effect of fill quality on the required connection strength ispresented in Fig. 12. As expected, the required connectionstrength, when a low quality fill is used, is much higher than thebaseline case as less pullout resistance is available for the rein-forcement in a low quality fill.

Conclusions and Design Implications

This study presents a general analytical framework for design offlexible reinforced earth structures, which allows for the use ofany adequate limit equilibrium analysis, without the arbitrarydistinction between reinforced slopes and walls. The parametricstudy shows that the proposed framework for analysis of flexiblereinforced earth structures can deal with all aspects of designrelated to stability. The following design implications can besummarized.1. For given reinforcement strength, there is a certain length of

reinforcement needed to maintain the stability of reinforcedearth structures. Shorter length requires higher tensile resis-tance of reinforcement. Conversely, overlength reinforce-ment results in dormant �not utilized� sections along its rearend.

2. For typical reinforced block walls with L /H=0.7, the re-quired maximum reinforcement resistance is about half thevalue rendered by AASHTO �2002�.

3. For typical reinforced block walls with 100% coverage, therequired connection strength is relatively low, less than about30% of Tmax. It should be pointed out that the required con-nection strength can significantly increase if low percent cov-erage and/or low quality fill and/or large spacing betweenreinforcement layers are adopted.

4. The use of intermediate reinforcement can reduce the re-quired connection strength and the maximum value of Tmax.

5. The strength of the soil used here is its design strength �i.e.,�=tan−1�tan��true� /FS� and hence, the required minimum
long term strength �resistance� of the reinforcement was

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computed at any location so as to fully mobilize the designvalue of both the reinforcement and �. The long term tensilestrength and connection strength of actual reinforcementshould be determined considering reduction factors of creep,installation damage, and durability, as commonly done indesign �e.g., AASHTO 2002�. These actual values should beequal or greater than the minimum required values obtainedfrom the analytical framework.

References

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General Analytical Framework for Design of Flexible Reinforced Earth Structures