Stability of Geosynthetic Reinforced Soil Structures

8/12/2019 Stability of Geosynthetic Reinforced Soil Structures

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Stability of geosynthetic reinforced soil structures

33 The HorseshoeCovered Bridge FarmsNewark, DE. 19711, USA

Copyright 2002, ADAMA Engineering, Inc.All Rights Reserved (www.GeoPrograms.com)

Written by Dov Leshchinsky, Ph.D.

1 INTRODUCTION

Soil is an abundant construction material that, simi-lar to concrete, has high compressive strength butvirtually no tensile strength. To overcome thisweakness, soils, like concrete, may be reinforced.The materials typically used to reinforce soil arerelatively light and flexible, and though extensible,

possess high tensile strength. Examples of such ma-terials include thin steel strips and polymeric materi-als commonly known as geosynthetics (i.e., geotex-tiles and geogrids). When soils and reinforcementare combined, a composite material, the so-called'reinforced soil', possessing high compressive andtensile strength (similar, in principle, to reinforcedconcrete) is produced.

The increase in strength of the reinforced earthstructure allows for the construction of steep slopes,embankment over soft foundation, or various typesof retaining walls. Compared with all other alterna-

tives, geosynthetic reinforced soil structures arecost-effective. As a result, earth structures reinforcedwith geosynthetics are being constructed worldwidewith increased frequency, even in permanent andcritical applications (e.g., Tatsuoka and Leshchin-sky, 1994).

This paper describes a design process for geosyn-thetic-reinforced slope. It includes details of stabilityanalyses used to determine the required layout andstrength of the reinforcing material. This processserves as the basis for the computer program ReSlope(Leshchinsky, 1997, 1999). Recognizing the limita-

tions of ReSlope (e.g., available strength of the rein-

forcement at its front-end can be less than the requiredstrength; analysis of complex geometries; stability ofembankment reinforced at its base), the rational for amore complete stability analysis is presented. Thishas resulted in program ReSSA (Leshchinsky, 2002).Finally, the design of walls, which customarily adoptlateral earth pressure approach, is briefly discussed.This approach is used by national design procedures

such as AASHTO or NCMA (Collin, 1997) methods,which serve as the basis for program MSEW (Lesh-chinsky, 1999, 2000). An appendix provides com-parative summary of programs ReSlope, MSEW andReSSA.

2 DESIGN-ORIENTED ANALYSIS

2.1 General

Limit equilibrium analysis has been used for dec-ades in the design of earth slopes and embankments.

Attractive features of this analysis include experi-ence of practitioners with its application, simple in-put data, useful (though limited) output design in-formation, and results that can be checked for'reasonableness' through a different limit equilibriumanalysis method, charts, or even hand calculations.Consequently, extension of this analysis to the de-sign of geosynthetics reinforced slopes, embank-ments and retaining walls, where the reinforcementis tangibly modeled, is desirable. The main draw-backs of limit equilibrium analysis are its inability todeal with displacements and its limited representa-

tion of the interaction between dissimilar or incom-

ABSTRACT: A framework for stability analysis of reinforced soil structures is presented. It produces eco-nomical design of stable reinforced walls, slopes and embankments. Elements such as local, compound,global and direct sliding stabilities are ensured. This framework was implemented in program ReSlope.More complex and versatile stability analysis methods can use the presented framework as a generic template(e.g., program ReSSA uses it in an analysis-oriented fashion). Following the conceptual analyses is aninstructive parametric study. General guidelines about the selection of long-term geosynthetic and soilstrengths and a comparison with a case history are discussed. The meaning of factor of safety in the contextof reinforced soil structures is investigated showing it to be different for MSE walls and slopes. Some of the

factors of safety used in programs ReSSA, ReSlope and MSEW are not defined in the same way thus theirnumerical value has to be examined independently; however, when the factor of safety is one, all definitionsare equivalent. An appendix provides comparative summary of programs ReSlope, MSEW and ReSSA.
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patible materials comprising the soil structure.Typically, adequate selection of materials propertiesand safety factors should ensure acceptable dis-placements, including safe level of reinforcementdeformation.

In principle, inclusion of geosyntheticreinforcement in limit equilibrium analysis is astraightforward process in which the tensile force inthe geosynthetic material is introduced directly in theequilibrium equations to assess its effects on stability.However, the inclination of this tensile force at theassumed slip surface must be assumed. Physically, itsangle may vary between the as-installed (typicallyhorizontal) and the tangent to the potential slipsurface. By using a log spiral mechanism,Leshchinsky and Boedeker (1989) have demonstratedthat for typical cohesionless backfill, this inclinationhas little effect on both the required strength andlayout of reinforcement. Conversely, Leshchinsky(1992) pointed out that for problems such asreinforced embankments over soft soil, the inclination

of the reinforcing geosynthetic, located at thefoundation and backfill interface, plays a significantrole. The long-termvalue of cohesion used in designof manmade reinforced steep slopes or walls isnegligibly small and hence, inclination has littleeffects. Therefore, the force in such structures may beassumed horizontal without being overly conservative.In case of basal reinforcement of embankment oversoft soil, the uncertainties associated with defining thefoundation properties make it prudent to beconservative and assume the reinforcement force ishorizontal. Consequently, based on a practical

argument, the force inclination is assumed horizontal.A potentially significant problem in limit

equilibrium analysis of reinforced soil is the need toknow the reactive force in each reinforcement layer atthe limit state. Physically, this force may varybetween zero and the ultimate strength when the slopeis at aglobalstate of limit equilibrium. Assuming theactual force is known in advance, as is commonlydone in analysis-oriented approach, implies thereinforcement force is actually active, regardless ofthe problem. The designer then assumes the availableactive force of each reinforcement layer to ensure

that overall satisfactory state of limit equilibrium isobtained. The end result of such assumption mayyield an actual slope in which some layers actuallyprovide more force than their long-term availablestrength while other layers are hardly stressed. Toovercome the potential problem of local instability(reinforcement overstressing), a rational methodologyto estimate the required (i.e., reactive) reinforcementtensile resistance of each layer is introduced via a'tieback analysis' or internal stability analysis.

Consequently, the designer can verify whether anindividual layer is overstressed or understressed,regardless of the overall stability of the slope. Oncethis problem of 'local stability' is resolved, overallstability of the slope is assessed through rotational andtranslational mechanisms. The rotational mechanism(termed 'compound stability' or pullout analysis)examines slip surfaces extending between the slopeface and the retained soil. The force in thegeosynthetic layers in this limit-state slope stabilityanalysis is taken directly as the maximum availablelong-term value for each layer. The translationalanalysis ('direct sliding') is based on the two-partwedge method in which the passive wedge is slidingeither over or below the bottom reinforcement layer,or along the interface with the foundation soil.

The common factor of safety in stability analysis ofreinforced soil is equally applied to all failure-resistingcomponents (i.e., soils and reinforcement). This im-plies that all resisting elements are equally mobilized.Practice proves that such an approach combined with

the ability of geosynthetic to greatly deform producestructures in which all reinforcement layers are typi-cally mobilized uniformly (i.e., efficient use of rein-forcement). This definition of safety factor is used inReSSA thus making it applicable to marginally stableslopes where the overall factor of safety needs to beincreased via reinforcement.

A modified concept included in this paper relates toa versatile definition of factor of safety suitable for in-herently unstable unreinforced structures. It suggestsa rational and physically meaningful alternative to theconventional factor of safety used in slope stability. In

fact, this factor of safety can be measured in an actualstructure. This factor of safety is used in ReSlope.

2.2 On the factor of safety in reinforced soilstructures

Limit equilibrium analysis deals with systems thatare on the verge of failure. However, existing slopesare stable. To analyze such slopes, the concept offactor of safety,Fs, has been introduced. In unrein-forced slopes, Fsis used to replace the existing soil

with an artificial one, in which the shear strength ism = tan

-1(tan/Fs) and cm= c/Fswhere mand cm

are the design shear strength parameters of the arti-ficial soil. Alternatively, these values represent theaverage mobilized shear strength of the actual soil.Employing the notion of Fsin limit equilibrium re-duces the statical indeterminacy of a stable slopeformulation via use of Mohr-Coulomb failure crite-rion. It also provides an object for minimization inwhich the lowest value of Fs, considering all poten-


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tial failure surfaces and mechanism, is sought. Thephysical significance of the conventional factor ofsafety can be accepted in an average sense only; i.e.,the average reduction of shear strength so that thesliding mass will globally be at the verge of failure.Extensive experience with limit equilibrium analysishas produced engineering database providing ac-ceptable values ofFs.

Leshchinsky and Reinschmidt (1985) applied Fsequally to all shear-resisting components; i.e., soilsor reinforcement. This renders a factor of safety thatis equivalent to the one used in unreinforced slopes(e.g., symbolizing the same average reduction ofstrength of dissimilar materials that are attaining alimit equilibrium state simultaneously). In fact, thisdefinition is used also in most slope stability analy-ses of reinforced slopes (e.g., program ReSSA).Such definition produces a single number that signi-fies the state of global stability of a reinforced sys-tem, similar to unreinforced slopes, homogeneous orstratified.

Another definition ofFsthat also globalizes thereinforced system is presented in the federal designguidelines in the US (Elias and Christopher, 1997):

whereFsuis the factor of safety for the unreinforcedslope; Mr and Md are the resisting moment due toreinforcement layers and the total driving moment,respectively. MrandMdare calculated for the sameslip surface as Fsu. It should be noted that the sur-face (typically circle) yielding the minimumFsu is

not necessarily the one yielding the minimum Fs;the critical surface in reinforced problems is deeperthan the unreinforced one. Such an approach yieldsan overall factor of safety whose physical meaningis only valid in a global sense. However, it treats thereinforcement as pure moment (i.e., only Mrresult-ing from reinforcement force is considered; actualforce is not included in the equilibrium equations).Programs ReSSA and MSEW can use this definitionofFsas an option.

Extension of limit equilibrium stability analysisto reinforced steep slopes provides an opportunity to

introduce a modified definition for Fs. Rather thanextending the conventional definition ofFs, one canuse the fact that unstable soil structures are suffi-ciently stable solely due to the reinforcement tensileresistance. Hence, Fs for the soil alone in this caseis unity everywhere along a slip surface (i.e., a plas-tic hinge develops mobilizing the full availablestrength of the soil). For this state, the required rein-forcement force needed to restore a state of limitequilibrium can be calculated. As an example, see

Figure 2 where a log spiral mechanism is used. Thestability of the slope now hinges on the reinforce-ment strength. Hence, the actual factor of safety canbe defines as:

Fs

)2(

trequired

tavailable=

where tavailableis the long-termavailable strength andtrequired

is the strength required for stability (i.e., for alimit equilibrium state of the composite reinforcedsystem). This definition signifies a factor of safetywith respect to the available strength of the rein-forcement. Such Fs can actually be measured.

This modified definition of Fs is based on thepremise that the soil will attain its full strength be-fore the reinforcement ruptures; i.e., the soil will at-tain an active state exactly as assumed in design ofretaining walls including those reinforced with geo-synthetics. Geosynthetic materials are ductile, typi-cally rupturing at strains greater than 10% thus may

allow sufficient deformations to develop within thesoil to reach active state. In reality, most of the de-formation for the active state will occur during con-struction as the geosynthetic mobilizes its strength.In fact, this definition is similar to the one used inMSE walls (e.g., Elias and Christopher, 1997;Collin, 1997); the design (available) shear strengthparameters of the soil are fully used and then a fac-tor of safety is applied on the long-term strengthofthe reinforcement only. Details of the consequencesof this definition are given elsewhere (Leshchinsky,2000). Programs ReSlope and MSEW allow the

user to use this definition of Fs while programReSSA can reproduce it upon some manipulation(i.e., analyze a reinforced system repetitively whilereducing the strength of the reinforcement until theresulted overallFsis 1.0; the soil now is in an activestate; increase the reinforcement strength to obtainsafe long-term value).

)1(/MdMrFsuFs +=

Figure 1. Notation and convention


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Figure 2. Log spiral slip surface and its statical

implications

2.3 Internal stability analysis

Internal stability analysis is used to determine therequired tensile resistance of the each layer neededto ensure that the reinforced mass is safe against in-ternal collapse due to its own weight and surchargeloading. In the context of retaining walls, thisanalysis identifies the tensile force needed to resistthe active lateral earth pressure at the face of a steepslope. That is, the tensile force needed to restrainthe unstable slope from sliding. The reinforcementtensile force capacity is made possible through suf-ficient anchorage of each layer into the stable soilzone located behind the active zone. It is assumedthat at the face of the slope, some type of facing re-stricts soil movement relative to the reinforcement;hence, the full long-term strength of the geosyntheticis available at the face of the slope. This assump-tion is utilized in ReSlope; however, the actual

strength available at the face (connection strength) isused in ReSSA or MSEW. While MSEW considersinternal stability explicitly (as does ReSlope),ReSSA looks for the most critical situation regard-less whether it is surficial, deep, compound or directsliding.

Figure 1 shows notation and convention. Rein-forcement is comprised of primary and secondarylayers. Only primary layers are considered inReSlope; in ReSSA or MSEW the effects of inter-

mediate reinforcement are considered. Furthermore,ReSSA is applicable also to base-reinforced em-bankments over soft soil. In practice, secondarylayers allow for better compaction near the face ofthe steep slope and thus reduce the potential forsloughing. In walls it may alleviate connectionloads (Leshchinsky, 2000). The secondary layers arenarrow (typically 1 m wide), installed only if theprimary layers are spaced far apart (e.g., more thanabout 0.6 m apart). At the slope face, the geosyn-thetic layers may be wrapped around the exposedportion of the soil mass or, if some cohesion exists,the layers may simply terminate at the face as shownin Figure 1.

In general, the following rational could be usedwith any type of stability analysis. It is most conven-ient to use it in conjunction with log spiral stabilityanalysis since the problem then is statically determi-nate. This analysis produces the location of the criti-cal slip surface and subsequently, the necessary reac-tive force in the reinforcement. While ReSlope

utilizes the log spiral, ReSSA is using for rotationalfailure circular arcs combined with Bishop stabilityanalysis. MSEW uses planar slip surfaces for internalstability following Rankin or Coulomb lateral earthpressure theories (MSEW is restricted to very steepslopes having an angle larger than 70, i.e., walls).

The log spiral mechanism makes the problem stati-cally determinate. For an assumed log spiral failuresurface, fully defined by the parameters xc, ycand A,the moment equilibrium equation about the pole canbe written explicitly without resorting to statical as-sumptions (Figure 2). Consequently, by comparing the

driving and resisting moments, one can check whetherthe mass defined by an assumed log spiral is stable forthe design values of the shear strength parameters: dand cd and the distribution of reinforcement force tj.This check is repeated for other potential slip surfacesuntil the least stable system is identified. That is, untilthe maximum required restoring reinforcement forceis found. The termsKhandKv(Figure 2) represent theseismic coefficients introducing pseudo-static forcecomponents. It is assumed to act at the center of grav-ity of the critical mass. To simplify the presentation,no surcharge is shown in Figure 2; however, including

it in the moment equation is straightforward.Figure 3 illustrates the computation scheme for es-

timating the tensile reaction in each reinforcementlayer. In STEP 1, the soil mass acting against Dn isconsidered. Note that layer n is wrapped around theslope face to form facingDn(Figure 3) thus makingit physically feasible for a mass of soil to be laterallysupported rendering local stability. That is, a 'facingunit'Dn(i.e., an imaginary facing element in the frontedge of the reinforced soil mass) prevents slide of un-


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stable soil above it. This facing is capable of provid-ing lateral support through the development of thenecessary tensile force in the geosynthetic (reaching,at most, its long-term strength). While this assump-tion exists in ReSlope, MSEW and ReSSA allow forreduced strength at the front-end signifying possiblelow-strength connection to a facing element (MSEW)or simply front-end pullout (ReSSA). Note that mas-sive stabilization of slope requires reinforcement awayfrom the face thus making the front-end strength lesssignificant unless surficial stability is of concern.

ReSlope uses the moment equilibrium equation tofind the critical log spiral producing max(tn), employ-ing the free-body diagram shown in Figure 3 whileexamining many potential surfaces. The resulted tncounterbalances the horizontal pressure againstDnandthus, signifies the reactive force in layer n. That is,the resulted tn represents the force needed to restoreequilibrium and hence stability. Note that Dn waschosen to extend down to layer n. This tributary areaimplies a 'toe' failure activating the largest possible re-

action force. In MSEW the reinforcement reaction iscalculated based on lateral earth pressure satisfyinghorizontal equilibrium at each elevation. In ReSSA,the user can verify that any given layer supplies suffi-cient force to render satisfactory Fs.

In STEP 2, the force against Dn-1 is calculated.Dn-1extends from layer n to layer (n-1). Using themoment equilibrium equation, max(tn-1), required toretain the force exerted by the unstable mass againstDn-1, is calculated. When calculating tn-1, the reac-tion tn, determined in STEP 1, is known in magni-tude and point of action. Hence, the reactive force

in layer (n-1)is the only unknown to be determinedfrom the moment equilibrium equation.

Figure 3 shows that by repeating this process inReSlope, the distribution of reactive forces for all re-inforcing layers, down to t1, are calculated whilesupplying the demand for a limit equilibrium state ateach reinforcement level. Application of appropri-ate factor of safety to the required reinforcementstrength should ensure selection of geosynthetic pos-sessing adequate long-term strength. In MSEW, thereaction is determined by using the lateral earthpressure and the tributary area of each layer. Con-

versely, in ReSSA, the available Fs at each elevationare checked while considering rotational and transla-tional failure and the existing long-term strength ofthe reinforcement. In ReSSA the approach is analy-sis-oriented (i.e., given the layout and strength of re-inforcement, find the minimum Fs for the structure)whereas in ReSlope it is design-oriented (i.e., giventhe desired Fs, find the layout and strength of rein-forcement).

Note that cohesive steep slopes are stable up to acertain height. Consequently, the scheme in Figure 3may produce zero reactive force in top layers.Though these layers may not be needed for local sta-bility, they may be needed to resist compound failureas discussed in the next section.

The outermost critical log spiral in ReSlope definesthe extreme surface as dictated by Layer 1. Inconventional internal stability analysis (e.g., MSEW)it signifies the extent of the 'active zone'; i.e., it is theboundary between the sliding soil mass and the stablesoil. Consequently, reinforcement layers are anchoredinto the stable soil to ensure their capacity to developthe calculated tensile reaction tj(Figure 4). The 'sta-ble'soil, however, may not be immediately adjacent tothis outermost log spiral and therefore, some layersshould be extended further to ensure satisfactory sta-bility (see next section).

Note in Figures 3 and 4 that the reinforcement lay-ers are wrapped around the overlying layer of soil toform the slope face. However, in slopes that are not

as steep (say, i


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Figure 3. Scheme for calculating tensile reaction inreinforcement layers

2.4 Compound and pullout stability analysisFor a given geometry, pore-water pressure distributionand (dand cd), the internal stability analysis providethe required tensile resistance at the level of each rein-forcement layer. It also yields the trace of the outer-most log spiral defining the 'active' soil zone, a notioncommonly used in conjunction with analysis of retain-ing walls. In reinforced soil structures, the capacity ofthe reinforcement to develop the required tensile resis-tance depends also on its pullout resistance; i.e., thelength anchored into the stable soil zone. If theboundary of this stable zone is indeed defined by the'active' one, then potential slip surfaces that extendinto the soil mass further than the outermost log spiralin Figure 4, outside or within the effective anchoragelength, will never be critical. However, such potentialsurfaces may render reduced pullout resistance sincethe effective anchorage length is shortened. That is,the reduced tensile resistance capacity along these sur-faces could potentially produce a globally unstablesystem. Consequently, a conventional slope stabilityapproach is used to determine the required reinforce-

ment length so that compound failures (i.e., surfacesextending into the unreinforced soil zone) will not belikely to occur. The term conventional refers to thenature of the analysis in which global stability issought (recall that internal stability looks at local sta-bility at the elevation of each reinforcing layer). Theobjective of the compound analysis is to find theminimum length of each reinforcement layer neededto ensure adequate stability against rotational failures.

Internal stability analysis yields the required rein-forcement strength at each level (in ReSlope andMSEW). In actual practice, however, specified rein-forcement layers will have allowable strengths in ex-cess of that required (i.e., tj t(allowable)j whereas tallowable tavailable and tavailable is the long-term strength). Theend result of specification of reinforcement strongerthan needed is that actually only mreinforcement lay-ers, extending outside the active zone and into thestable soil, are globally needed. That is, the mlayersare sufficient to maintain stability of the active mass.Internally, however, layers (m+1) through n are also

needed to ensure local stability as implied in thescheme presented in Figure 3. The minimum numberof layers, m, is calculated using the following equa-tion:

)3(

11)(

=

=

n

jtj

m

jt jallowable

Note that mis the number of layers, counting from thebottom, capable of developing a total tensile resistanceequal to (or slightly greater than) the net total rein-

forcement force obtained from the internal stabilityanalysis. When m = n, the compound stability degen-erates to that introduced by Leshchinsky (1992). Themlayers are assumed to contribute their full allowablestrength simultaneously to global stability when com-pound stability of the reinforced system is examined.The assumption of simultaneous availability of rein-forcement strength is commonly used in limit equilib-rium stability analysis of reinforced slopes and is sup-ported by (scattered) field data.

Embedding the layers immediately to the right ofthe outermost log spiral obtained in the internal sta-

bility analysis, so that tallowablefor layers 1through mand tj for layers (m+1) through n can developthrough pullout resistance, ensures that, in an aver-age sense, the mobilized friction angle, mob, alongthis log spiral is equal to, or slightly less than, d.The upper layers (m+1) through n (see points A, Band C in Figure 5) are not needed for the global sta-bility of the active mass and therefore, from a theo-retical view point could be ignored at points A, Band C. Note that the mobilized friction angle, mob,


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represents the required friction angle to produce alimit equilibrium state while using the allowable re-inforcement strength. Hence, when mob< d, a fic-titious situation is analyzed; i.e., the system is actu-ally stable since the available soil strength, asexpressed by d, is larger than needed, mob, for alimit equilibrium state. Only when mob= d limitequilibrium state achieved.

At this stage of ReSlopes analysis, which uses de-sign-oriented approach, layers 1through mare length-ened to a test body defined by an arbitrary log spiralextending between the toe and the crest, to the right ofthe outermost log spiral (Figure 5). Each layer be-yond the slip surface is embedded so that the calcu-lated t(allowable)jcan be developed; mobfor this surfacewill be smaller than d used in design (i.e., for thislayout, the internal stability outermost surface is mostcritical). The upper layer is truncated in a numericalsense (i.e., tm= 0), and the moment equilibrium equa-tion for the arbitrary log spiral is used to checkwhether mob= d. If mob= dthan layer mis suffi-

ciently long (see point D in Figure 5); otherwise,lengthen this layer and repeat calculations until satis-factory length is found. A satisfactory length impliesthat the critical log spiral passing through point Dyields a stable system for the design friction angle, d;all feasible log spirals between this one and the out-ermost log spiral from the internal stability have mob< dindicating they represent less critical mechanisms(note that the strength of layers 1through mis avail-able between these two log spirals).

The process is repeated to find the required lengthof layer (m-1)(Figure 5). Since layers above were al-

ready truncated, they no longer contribute tensile re-sistance to deeper slip surfaces. Once the process hasbeen repeated for all layers down to layer 1, the lengthof all layers (curve DEFGH in Figure 5), required toensure that mobdoes not exceed dfor all possible logspiral failure surfaces, has been determined. The proc-ess in ReSlope is slightly conservative since the fullanchorage lengths to resist pullout are specified be-yond points D, E, F and G. This simplification is con-servative since, contrary to the compound analysisprocedure, it ensures the following: t(allowable)mat pointD (not zero resistance at D); t(allowable)m-1at point E (not

zero resistance at E); and so on. However, since theanchorage length of planar geosynthetic sheet is typi-cally small relative to its total required length in prac-tical problems, this simplification is reasonably con-servative. Programs ReSSA and MSEW do not usethis simplification; the actual available strength of re-inforcement at its intersection with the slip surface iscalculated and used in the stability analysis.

Compound critical surfaces emerging above the toeare also possible and consequently, the procedure in

Figure 5 is repeated for slip surfaces emergingthrough the face of the slope. Subsequently, layerspreviously truncated are lengthened, if necessary, toensure that mobd. While other surfaces can passthrough the reinforcement and the foundation,ReSlope ignoresthose (it assumes competent founda-tion). However, ReSSA fully accounts for such sur-faces.

A layout similar to the envelope ABCDEFG willcontain, at least, mpotential slip surfaces, all havingthe same minimal safety factor against rotational fail-ure (Figure 5). However, because of practical consid-erations, a uniform or linearly varying length of layersis specified in practice. As a result, the number ofsuch equally critical slip surfaces is reduced in actualstructure since most layers are longer and typically,some are stronger than optimally needed. ReSlopeignored the extra stability attained by longer thanneeded reinforcement (recall that its objective is tofind the minimum length of reinforcement that pro-duces a target value of Fs against rotational failure).

ReSSA considers the actual layout by accounting forthe actual specified length and strength of reinforce-ment (its objective is to calculate Fs for a given layoutand strengths).

Finally, anchorage lengths are calculated to resistpullout forces that are equal to the required allowablestrength of each layer multiplied by a factor of safetyFs-po. In these calculations the overburden pressurealong the anchored length and the parameter definingthe shear strength of the interface between soil and re-inforcement are used. In ReSlope, this parameter, Ci,termed the interaction coefficient. It relates the inter-

face strength to the reinforced soil design strength pa-rameters:tan(d)and cd. In ReSSA and MSEW it re-lates to the full strength of the soil but a factor ofsafety ensures that the actual capacity would be atleast 1.5 times greater than that needed.

The interaction coefficient is typically determinedfrom a pullout test. The required anchorage length oflayer jmust equal tj / {jCi[tan(d)+cd]} where jsignifies the average overburden pressure above theanchored length. Adding the anchorage length to thelength needed to resist compound failure produces thetotal length required to resist internal and compound

failures.


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Figure 4. Tensile reaction transferred into soil next

to active zone

2.5 Direct sliding analysis

Specifying reinforcement layout that satisfies a pre-scribed dagainst rotational failure does not ensuresufficient resistance against direct sliding of the re-inforced mass along its interface with the foundationsoil, or along any reinforcement layer. The rein-forcement length required to ensure stability againstfailure due to direct sliding, Lds, can be determinedfrom a limit equilibrium analysis that satisfies forceequilibrium; i.e., the two-part wedge method. Sucha conventional approach is used in ReSlope andMSEW. However, ReSSA is consistent with LEanalysis and therefore, it uses Fs against direct slid-ing (Spencer method) that accounts for the strengthof the reinforcement should failure propagatethrough the geosynthetic layers.

Figure 6 shows the notation used in defining thegeometry and forces in the two-part wedge analysis.First, an initial value of Lds is assumed. Then, for anassumed interwedge force inclination, , the maxi-mum value of the interwedge force, Pmax, is found byvarying while solving the two force equilibrium

equations for the active Wedge A. This interwedgeforce signifies the resultant of the lateral earth pres-sure exerted by the backfill soil on the reinforced soil.Next, the vertical force equilibrium equation forWedge Bis solved considering the vertical componentof the lateral thrust of the active wedge (i.e.,Pmaxsin).The reactionNBis obtained and the base sliding resist-ing force of Wedge B, TB, is calculated. While thisprocedure is used in ReSlope and, with some limita-

tions in MSEW, in ReSSA the method used isSpencer and all equations of equilibrium are satisfied.

When calculating TB, the coefficient Cds is used(Cds = the interaction coefficient between the rein-forcement and the soil as determined from a directshear test). If the bottom layer is placed directly overthe foundation soil, two values of Cdsare needed: onefor the interface with the reinforced soil and the otherfor the interface with the foundation soil.

In ReSlope and MSEW, the actual factor ofsafety against direct sliding, Fs-ds, is calculated bycomparing the resisting force with the driving force:

)4(cos P

TBF dss =

This factor of safety corresponds to the assumedvalue ofLds. In case it is unsatisfactory, the value ofLdsis changed and the process is repeated for WedgeA and Wedge Buntil the computed factor of safetyagainst direct sliding equals to the prescribed value.

In ReSSA the definition of the factor of safetyagainst direct sliding is equally applied to the soilsshear strength and reinforcement layers intersectionthe slip surface. That is, in ReSSA the rotationaland translational Fs have the sane physical signifi-cance; in ReSlope the significance is different andthus comparing values rendered by these two pro-grams could be misleading.

The assumed value of may have significant in-fluence on the outcome of the analysis. Selecting>0 implies the retained soil will either settle rela-tive to the reinforced soil and/or the reinforced soil

will slide slightly as a monolithic block thus allow-ing interwedge friction to develop. Some rein-forcement layers will typically intersect the inter-wedge interface (especially if i < 70 ). However,unlike program ReSSA, ReSlope ignores the tensileresistance of these reinforcement layers. Conse-quently, selecting a value of in between (2/3)dand dcould be viewed as a conservative choice.

The technique for incorporating seismicity into theforce equilibrium analysis is shown in Figure 6. In apseudo-static approach, however, large seismic coeffi-cients may produce unrealistically large reinforced

soil block, Wedge B. In this case, a permanent dis-placement type of analysis is recommended (i.e.,Newmark's stick-slip model; e.g., Ling, Leshchinskyand Perry, 1997). Alternatively, one may eliminateinertia from Wedge B, analogous, in a sense, toMononobe-Okabe model used in analysis of gravitywalls. Only the 'dynamic' effects on Pare superim-posed then on the statical problem. ReSlope allowsfor the elimination of wedge B; ReSSA and MSEWdo not allow for such elimination.


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Figure 6. Two-part wedge mechanism used in directsliding analysis

Figure 5. Length required to resist compound and pullout failures

2.6 Commentary

1. The factor of safety used in program ReSlope iscompatible with that used in reinforced walls ininternal stability analysis (e.g., MSEW). Likewalls, unreinforced unstable slopes thus enablingthe soil to mobilize its full strength (i.e., attain anactive state).

2. The presented approach assumes the foundation tobe competent and therefore, deepseated failureswere not considered. This approach wasimplemented in ReSlope. However, thecomputational procedure can be modified for slipsurfaces that penetrate the foundation soil.Program ReSSA uses a generic approach thatallows for soft foundations, complex geometryincluding reinforced embankments.

3. The approach can be modified to include anytype of limit equilibrium analysis. In case ofgeneralized approach, separation into directsliding and compound stability is not needed(e.g., ReSSA). However, search routines ingeneralized methods must be capable ofcapturing critical surfaces of greatly differentgeometries (ReSSA allows for rotational failureusing Bishops and 2- and 3-part wedges usingSpencers).


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4. Possibility of surficial failure is ignored in thepresented procedure (i.e., ReSlope). It can bemodified to deal with this issue by assigning lowor zero reinforcement strength at the faceprovided the geosynthetic is not wrappedaround. However, for steep slopes, strict limitequilibrium analysis will indicate insufficientstability at the surface. The empirical concept ofsoil plug is assumed to be valid for closelyspaced reinforcement layers. Programs ReSSAand MSEW directly address the potential issue ofsurficial stability.

5. Program MSEW follows accepted practice for thedesign and analysis of MSE walls. Hence, itincludes checks for bearing capacity (consideringthe reinforced soil as a coherent mass) andeccentricity (or overturning). Both failure modesare adopted from conventional retaining walldesign and may not be applicable for flexibleMSE structures. Deepseated stability (used inReSSA and ReSlope) serves as a much more

rational approach than bearing capacity (usingMeyerhof approach for eccentric load).Overturning failure is unrealistic mode of failure.

In the strict context of analysis, log spiral slip surfaceis valid for homogenous soil only. However, in thecompound failure analyses (Figure 5), this surfacepasses through both reinforced and retained soil andpossibly, even through the foundation soil. As an ap-proximation, one can use an averaging technique,considering the compound failure surface lengths inthe reinforced soil and in the retained soil, to find

equivalent values for dand cdto be used in analysis.The value of the equivalent d is used to define thetrace of the log spiral passing through the reinforcedand retained soils. This approximation approach isused by ReSlope. Program ReSSA considers the ac-tual soil properties in each zone through which the slipsurface passes. The trade off is using a less rigorousstability analysis (from statical standpoint): Bishopand Spencer. In practice, however, both methodstypically yield quite accurate results.

3 DESIGN CONSIDERATIONS

3.1 General

The presented approach is based on the state of lim-iting equilibrium. Such a state deals, by definition,with a slope that is at the onset of failure. Applica-tion of adequate safety factors should ensure accept-able margins of safety against the various failure

mechanisms analyzed. It is implicitly assumed thatthe different materials involved (i.e., the geosyn-thetic materials and soils) will all contribute theirdesign strengths simultaneously to attain a state oflimit equilibrium. For materials reaching a constantplastic shear strength after some deformation (e.g.,soils), such an assumption is realistic. However, notall materials in the reinforced soil system possessthis idealized plasticity. Consequently, the follow-ing guidance is provided for selecting material prop-erties.

3.2 Progressive failure and soil shear strength

Slip surface development in soil is a progressivephenomenon, especially in reinforced soil where re-inforcement layers delay the formation of a surfacein their vicinity (e.g., Huang et al., 1994), or it maybe overstressed locally thus greatly deforming orcreeping locally. Leshchinsky et al. (1995) recom-mended that the design values of and c(i.e.,d, cd)

should not exceed the residual strength of the soil.This would ensure that at the state of a fully devel-oped slip surface, the shear strength used in the limitequilibrium analysis is indeed attainable all alongthe slip surface.

Use of residual strength has clear cost implica-tions in the design of reinforced slopes. The re-quired strength of the reinforcement increasessomewhat; however, the required length of rein-forcement increases significantly since deeper slipsurfaces are predicted. For compacted granular soil,an increase in length of 30 to 50% might typically be

required. This additional length makes constructionmore difficult, especially if space constraint exists(e.g., widening existing embankment), thus render-ing construction more expensive than just the cost ofextra reinforcing material. Hence, this combinedwith what currently appears as overly conservativedesigned reinforced slopes create a need to introducea less conservative design approach.

Based on some experimental evidence, Leshchin-sky (2001) suggested the following hybrid procedurefor design when granular compacted fill is used:a. Use peakand limit equilibrium analysisto locate

the critical slip surfaces. These surfaces will beutilized to determine the required layout of geo-synthetic layers (i.e., length and spacing).

b. Use residual along traces of the critical slip sur-faces determined in (a) to compute the requiredgeosynthetic strength. That is, in internal stabil-ity use peakto locate the slip surface and the useresidual in the limiting equilibrium equations todetermine the geosynthetic reactive force. Incompound analysis use residual in the limiting


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equilibrium equations to assess the required rein-forcement strength along slip surfaces deter-mined using peak.

It is entirely possible that the backfill in flexibly re-inforced slopes will deform (during or after con-struction) mobilizing the soil beyond its peakstrength. Therefore, the stability of such slopes mayhinge then upon the strength of the reinforcement.Consequently, the reinforcement strength becomescritical to stability in case residual strength develops.Note that the hybrid approach recognizes that slipsurfaces will form and have a trace based on the soilpeak strength. However, possible development ofprogressive failure is also recognized and at thisstate, the ductile and potentially creeping reinforce-ment should be sufficiently strong to keep the sys-tem stable. It should be noted that in a sense, Ta-tsuoka et al. (1998) proposed a similar hybridapproach, however, it was limited to seismic designof reinforced walls.

The proposed procedure may result in signifi-cantly shorter reinforcement as compared to usingresidual. However, the required reinforcementstrength will be somewhat larger than that computedwhen using peak. Leshchinsky (2001) proposed asimple procedure when using ReSlope. For ReSSAor MSEW the process is straightforward.

If cohesive fill is used, extreme care should be usedwhen specifying the cohesion value. Cohesion hassignificant effects on stability and thus the required re-inforcement strength. In fact, a trace of cohesion mayindicate that no reinforcement at all is needed at the

upper portion of the slope. However, over the longrun, cohesion of manmade embankments tends todrop and nearly diminish (normally consolidatedclay). Since long-termstability of reinforced slopes isof major concern, it is perhaps wise to ignore the co-hesion altogether. It is therefore recommended tolimit the design value of cohesion to a maximum ofabout 5 kPa. It should be pointed out, however, thatend-of-construction analysis must also be conducted ifa soft foundation is present. In this case stabilityagainst deepseated failure must be ensured.

3.3 Reduction factors related to geosynthetics

Limit equilibrium analysis assumes that the geosyn-thetic will not mobilize its full strength before thedesign strength of the soil is attained. Formally,there is no consideration of deformations. One canenvision a scenario in which very stiff reinforcementwill have its strength mobilized, potentially reachingits design value before the soil mobilizes itsstrength. This may lead to overstressing and subse-

quently, premature rupture of the reinforcement, vio-lating the analysis premise that its tensile resistancewill be available simultaneously with the soilstrength. The result might be local, or even global,collapse. However, since geosynthetics are ductile(typically, rupture strain greater than 10%), largestrains may develop locally in response to over-stressing thus allowing the soil to deform and mobi-lize its strength as assumed in the analysis and asneeded for stability. Over twenty years of experi-ence indicate that lack of stiffness compatibility isnot a problem when using limit equilibrium design.

To ensure that indeed some overstressing of the re-inforcement without breakage is possible, an overallfactor of safety is specified. This factor multiplies thecalculated minimal requiredreinforcement strength ateach level. Typical values for this factor range fromFs-u=1.3 to 1.5. The strength of the factored rein-forcement should be available throughout the designlife of the structure. To achieve this, reduction factorsfor installation damage (RFid), durability (RFd), and

creep (RFcr) should be applied so that geosyntheticspossessing adequate ultimate strength, tult, could be se-lected. That is, the specified geosynthetic should havethe following short-term ultimate strength:

t

)7()()()()( RFrRFdRFcrRFid

F ustrequiredult

)( =

Table 1 shows typical range of values used for vari-

ous polymeric materials. The values of RFid

andRFdare site specific. For typical reinforced soil con-

ditions (i.e., near neutral pH), degradation should

not be a problem when using typical reinforcingpolymeric materials. The creep reduction factor,

RFcr, depends, to large extent, on the polymer typeand the manufacturing process. The term ultimate

strength, tult, should correspond to the result obtained

from the short-term wide-width tensile test, following,

for example, ASTM D4595-86 procedure. Typically,the strength at 5% elongation strain in the wide-width

test is reported as well. Some designers concerned

with performance prefer to use this value as 'tult.' Itshould be noted that performance (i.e., deformations)

of slope and embankments is less critical than that of

walls and therefore, the 5% 'limit' is unnecessary andis overly conservative for most practical purposes. In

fact, it is conservative even for walls.

Finally, if seismicity is considered in the design, thereduction factor against creep can be set to one.Simply, since the duration of the superimposed


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increases the sloughing resistance and prevents surfi-cial failures. If wrap-around is specified (necessary inslopes steeper than about 50), secondary reinforce-ment can be used to wrap the slope face as well. Itshould be backfolded at least 1 mback into soil, sameas the wrapping primary layers. Secondary rein-forcement can also be used with wire cage facing,gabions, or even modular blocks in segmental retain-ing walls.

Figure 7. Practical layout of reinforcement

4 RESULTS AND CASE HISTORY

4.1 Typical results

Figure 8, reproduced from Leshchinsky and

Boedeker (1989), shows the required tensile forcecalculated using internal stability analysis versuspeak and slope inclination. It should be noted thatLeshchinsky and Boedeker (1989) used a variationalcalculus technique to facilitate the generation of re-sults, however, the results are identical to those pro-duced using the scheme presented in this paper.This figure is limited to cohesionless slopes. Theordinate K represents the non-dimensional value ofthe calculated tjand, in a sense, is equivalent to Kain lateral earth pressures (Ka is equivalent to Ran-kins if the reinforcement force is horizontal and toCoulombs if this force is inclined). Notice that forreasonable range of peak, the difference in requiredK as a function of assumed reinforcement force ori-entation at the slip surface is small. This differenceis the largest for vertical slopes. The value of each tjcan be calculated from this chart following the ra-tional presented in Figure 3. That is, start with j = 1and top layer to find tnfor which H equals Dn, thengo to j = 2 and layer n -1 to find tn-1where H equalsDn+Dn-1and tn is known, and so on. Alternatively,

one can use this chart as an approximation. That is,the overburden pressure at the middle of a tributaryarea of a reinforcing layer can be calculated and thenbe multiplied by the tributary area and by the coeffi-cient K obtained from the chart. Note that soil pos-sessing low such as 15or 20is not likely to ex-hibit peak shear characteristics; it is presented in thisand following figures for instructive purposes unlessone uses the chart for a case where design= residual=

peak.

The K value in Figure 8 is the same as Rankinsfor horizontal reinforcement force; for vertical wallsit would produce the same tensile force mobilized ineach reinforcement layer as in MSEW (thus makingReSlope useful in terms of accepted design for bothwalls and slopes). ReSSA and the compound stabil-ity module of ReSlope will require half the maxi-mum strength rendered from Figure 8 since it as-sumes uniform mobilization of the reinforcementforce at a LE state.

Figure 9 shows the outermost traces of critical log

spirals obtained from internal stability analysis. It isfor the horizontal inclination of geosynthetic force(for traces when reinforcement is tangential, seeLeshchinsky and Boedeker, 1989). Notice that forvertical slopes, the surfaces are practically planar in-clined at angle of (45+ peak/2). Also notice that aspeak decreases, the slip surfaces become signifi-cantly deeper thus implying longer required lengthof reinforcement.

No charts are shown for required length based oncompound stability analysis. The results in this casewill depend on the selected reinforcement strength.

The interested reader is referred to Leshchinsky etal. (1995) to view some typical surfaces. In general,compound failure will not control the length in nearvertical slopes provided the reinforcement is closelyspaced and uniform in strength. However, thiswould not necessarily be the case if geosyntheticlayers with variable length and/or strength is speci-fied. Program ReSlope and ReSSA are ideallysuited for this mode of failure.

Figure 10 shows the length of reinforcement re-quired to resist direct sliding. It is constructed forstrength related to peak shear strength, direct sliding

coefficient, Cds, equals one, and a factor of safety toresist direct sliding, Fs-ds, equals 1.5. Figure 10 (top)represents the case where full friction is developedalong the interface between the two wedges (i.e., =peak) while Figure 10 (bottom) shows the conserva-tive case where = 0. Generally, it can be seen that asthe slope flattens, the length of reinforcement in-creases. Also, the friction angle and the interwedgeangle have significant effects on length. Notice thatfor 45 slopes combined with = 45, no reinforce-


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ment is needed, however, if one uses design< peaktherequired length will increase. In this case, one coulduse lower Fs-dsin lieu of smaller . While these resultscorrespond to ReSlope and MSEW, ReSSA uses slopestability analysis for direct sliding and therefore layerslength may depends also on layers strength.

4.2 Case history

Fannin and Herman (1990) report the results of afield test of a well-instrumented full-scale slope.One tested slope in which no intermediate rein-forcement layers were used is adequate for compari-son with the discussed progressive failure approachand program ReSlope.

Figure 8. Calculated tensile reaction for cohesionlessslopes

Figure 10. Required length to resist direct sliding as

function of peak shear angle and slope inclination(assuming all soils possess same strength/density)

The slope height was 4.8 m and its inclinationwas 1H:2V (Figure 11). The backfill soil was a uni-formly graded medium to fine sand, compacted to aunit weight of 17 kN/m

3. The plane strain residual

internal angle of friction is reported to be 38. Un-fortunately, the peak angle is not reported. The lay-out of the uniformly spaced geogrids is shown inFigure 11. The force distribution in each geogrid

layer was measured using load cells. Only the fac-ing was constructed of a wire mesh, which is con-sidered equivalent to wrap-around face. Followingconstruction, the wall was surcharged with soilplaced to a depth of 3 m. Since no details are given,it is assumed that the slope of the this surcharge fillwas 2H:1V.


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The outermost internal failure surfaces using theapproach presented in this paper are containedwithin the reinforced zone (Figure 11) for residual=38. Since peakis unknown, the corresponding slipsurface is not plotted, however, because peak islarger than residual, the critical slip surfaces would beeven shallower (i.e., certainly contained within thereinforced zone). The long-term allowable geogridstrength is not reported, but it can be verified that itsvalue is much larger than the measured forces.

Figure 9. Outermost traces of internal slip surfaces

Hence, all compound slip surfaces are also con-tained within the reinforced soil. Assessment of di-rect sliding reveals that Fs-ds for the layout used isbetween 1.5 and 2.0.

The actual layout is not the same as required inFigure 5 (i.e., not minimum lengths but rather uni-form lengths) and therefore, back-analysis using thepresented design-oriented analysis (ReSlope) canonly suggest a probable range of feasible values.The probable range for each layer is between the re-


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quired forces needed for internal stability and forcompound failure. The approach (ReSlope) speci-fies the maximum value of this probable range indesign. Table 2 shows the comparison betweenmeasured values and those predicted using residual=38.

The agreement exhibited in Table 2 is consideredgood. Repeating calculations for the problem forpeak= 43, one gets tj= 11.1 kN/m; for peak= 41,one gets t

j = 13.3 kN/m. The measured (actual)

value of tjwas 15.3 kN/m. Fannin and Herman re-port only the total sum of forces for the surchargedcase. The measured value is 22.2 kN/m whereas thecalculated one (residual= 38) is 21.1 kN/m.

Strain measurements by Fannin and Herman indi-cates the location of maximum force is shallowerthan that implied by residual(i.e., implied by the traceof slip surface shown in Figure 11). Use of peakasproposed by Leshchinsky (2001) will also produceshallower surfaces.Looking at the measured tension values (Table 2),

one sees that the mobilized force in the reinforce-ment is approximately uniform among all layers.Such observation supports the approach used inReSSA and in ReSlope if one examines the com-pound failure mode.

Figure 11. Configuration of Norwegian Wall

5 CONCLUSION

A framework for assessing the stability of slopesand embankments reinforced with geosynthetics hasbeen presented. The analyses involved are based onlimit equilibrium. These analyses ensure that thereinforced mass is internally and externally stable. Aphysically meaningful definition of factor of safety,which is relevant to an unstable soil structure unlessreinforced, is introduced.

The presented stability analyses includerecommendations regarding the selection of soil shearstrength parameters and safety factors. Recognizingthe limitations of limit equilibrium analysis, especiallywhen applied to soil structures comprised of materialspossessing different properties (i.e., such as soil andpolymeric materials) and the potential for progressivefailure, a hybrid approach for selecting soil shearstrength is recommended. The peak shear strengthparameters of the soil should be used to determine thecritical slip surfaces (i.e., the reinforcement layout).Superimposing on these critical slip surfaces theresidual strength of the soil and solving the limitequilibrium equations provide an estimate of therequired reinforcement strength in case progressivefailure is likely to develop.

The presented design procedure has been imple-mented in ReSlope (Leshchinsky, 1997, 1999). Themechanism and analysis used can be replaced withother stability methods such as program ReSSA(Leshchinsky, 2002). The approach is comprehensive

and economical; experience proves it is safe. WhileReSSA is based on pure slope stability approach,ReSlope is based on a hybrid approach. That is, itsrigorous Internal Stability mode yield results conven-tionally used in the design of MSE walls reinforcedwith geosynthetics whereas its Compound Stabilitymode corresponds to reinforced slope stability analy-sis. Consequently, its results are compatible withthose of program MSEW (Leshchinsky, 1999, 2000);however, it does not deal with stability aspects thatcould be important for walls (e.g., connectionstrength). It provides a layout that automatically can

resist compound failure, an aspect that cannot be ad-dressed by lateral earth pressure methods used in de-sign of walls.

REFERENCES

Collin, J. (1997). Design Manual for SegmentalRetaining Walls. 2

nd Edition, National Concrete

Masonry Association (NCMA).Elias, V. and Christopher, B.R. 1997.Mechanically Stabilized Earth Walls and

Reinforced Steep Slopes, Design and ConstructionGuidelines. FHWA Demonstration Project 82.Report No. FHWA-SA-96-071.Fannin, J. and Herman, S. 1990. Performancedata for sloped reinforced soil wall. CanadianGeotechnical Journal, 27(5), 676-686.


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Huang, C.-C., Tatsuoka, F., and Sato, Y. 1994.Failure mechanisms of reinforced sand slopesloaded with a footing. Soils and Foundations,Journal of the Japanese Society of GeotechnicalEngineering, 34(2), 27-40.Leshchinsky, D. 1992. Keynote paper: Issues ingeosynthetic-reinforced soil. Proceedings of theInternational Symposium on Earth ReinforcementPractice, held in Nov. 1992 in Kyushu, Japan.Editors: Ochiai, Hayashi and Otani. Published byBalkema, 871-897.Leshchinsky, D. 1997. Software to FacilitateDesign of Geosynthetic-Reinforced Steep Slopes.Geotechnical Fabrics Report, Vol. 15, No. 1, 40-46.Leshchinsky, D. 1999. Putting Technology toWork: MSEW and ReSlope for Reinforced Soil-Structure Design. Geotechnical Fabrics Report,Vol. 17, No. 3, April, pp. 34-38.Leshchinsky, D. 2000. Alleviating Connection

Load. Geotechnical Fabrics Report,October/November, Vol. 18, Number 8, 34-39.Leshchinsky, D. 2000. On the Factor of Safety inReinforced Steep Slopes. ASCE, GeotechnicalSpecial Publication, Ed.: Zornberg andChristopher, No. 103, 2000, pp. 337-345.Leshchinsky, D. 2001. Design Dilemma: UsePeak or Residual Strength of Soil. Geotextilesand Geomembranes, Vol. 19, No. 2, pp. 111-125.Leshchinsky, D. 2002. Design Software forGeosynthetic-Reinforced Soil Structures.

Geotechnical Fabrics Report, Vol. 19,Marc/April, pp. 44-49.Leshchinsky, D. and Boedeker, R. H. 1989.Geosynthetic reinforced earth structures. Journalof Geotechnical Engineering, ASCE, 115(10),1459-1478.Leshchinsky, D., Ling, H. I., and Hanks, G. 1995.Unified Design Approach to Geosynthetic-Reinforced Slopes and Segmental Walls.Geosynthetics International, Vol. 2, No. 5, 845-881.Leshchinsky, D. and Reinschmidt, A.J. 1985.

Stability of membrane reinforced slopes.Journalof Geotechnical Engineering, ASCE 111(11),1285-1300.Ling, H.I., Leshchinsky, D. and Perry, E.B.Seismic Design and Performance of Geosynthetic-Reinforced Soil Structures. Geotechnique, Vol.47, No. 5, 1997, pp. 933-952.Tatsuoka, F. and Leshchinsky, D. 1994. Editors:Recent Case Histories of PermanentGeosynthetic-Reinforced Soil Retaining Walls,

Proceedings of SEIKEN Symposium, held inNovember, 1992 in Tokyo, Japan, published byBalkema, 349 pages.Tatsuoka,F., Koseki, J., Tateyama, M., Munaf, Y.and Hori, N. 1998. Seismic stability against highseismic loads of geosynthetic-reinforced soilretaining structures. Keynote lecture,Proceedings of the 6

th International Conference

on Geosynthetics, Atlanta, Georgia, Vol. 1, 103-142.Taylor, D.W. 1937. Stability of earth slopes.Journal of the Boston Society of CivilEngineering, 24(3), 197-246.Yoshida, T. and Tatsuoka, F. 1997. Deformationproperty of shear band in sand subjected to planestrain compression and its relation to particlecharacteristics. Proceedings of the 14

th

International Conference on Soil Mechanics andFoundation Engineering, Hamburg, September,237-240, Balkema.


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Table 2. Reinforcement forces under self-weight loading

Calculated MeasuredLayer No. j

/Elevation

[m]

InternalFailure, tj

[KN/m]

CompoundFailure, tj/n

[kN/m]

Probable Range[kN/m]

MaximumForce,[kN/m]

1 /0.0 4.1 2.13 2.1 4.1 1.062 / 0.6 3.5 2.13 2.1 3.5 2.253 / 1.2 2.9 2.13 2.1 2.9 2.014 / 1.8 2.4 2.13 2.1 2.4 2.34

5 / 2.4 1.8 2.13 1.8 2.1 2.006 / 3.0 1.3 2.13 1.3 2.1 1.467 / 3.6 0.8 2.13 0.8 2.1 1.928 / 4.2 0.2 2.13 0.2 2.1 2.26

tj 17.0 17.0 15.3


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Appendix

ReSSA, ReSlope, MSEW: Comparative SummaryFor complete details, see features of each program posted at www.GeoProgram.com

ProgramApplicable toMSEStructure:

SlopeAngle

Reinforce-ment

GeometryMaximum No.of Soils

Water

MSEW Walls1 70-90Geosynthetic or

Metallic

Simple,

two-tiered,

bridge abut-

ment, back to

back

Reinforced

soil, retained soil,

and 5 other soils

Phreatic

surface used

onlyin global

stability

ReSlopeSlopes &

Walls210-90 Geosynthetic Simple

Reinforced

soil, retained soil,

foundation soil

Phreatic

surface

ReSSASlopes, Walls

& Embankment310-90

Geosynthetic or

Metallic

Nearly anycomplex ge-

ometry

25 different

soils; reinforce-

ment can be em-

bedded in all soils

Phreatic

surface or pie-

zometric lines;

effective, total

or mixed stress

analysis

1MSEW is strictly for MSE walls (following AASHTO or NCMA). A slope stability module (Bishop) is

available to check global stability. Reinforcement must be embedded in a prismatic shape non-cohesivehomogeneous soil; the retained soil is non-cohesive. Additional 5 layers of soil can be specified for globalstability analysis. Water is invoked only in global stability.

2ReSlope is a design-orientedprogram that conducts local and global stability checks. The local stabil-

ity check is analogous with the one used in MSEW. It does notdeal with facia (it assumes 100% connec-tion strength). It also does not deal with eccentricity, overturning, and bearing capacity (though deepseatedfailure is assessed). It inherently assumes competent foundation.

3ReSSA uses a global slope stability framework (i.e., it assumes all reinforcement layers are equally

mobilized). This means that if used in walls, the reinforcement strength might be insufficient for local sta-bility (experience shows that this is not an issue with geosynthetics). It considers various failure mecha-nisms; however, no overturning and bearing capacity are explicitly checked.
http://www.geoprogram.com/http://www.geoprogram.com/


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ProgramStrength

of Connec-tion:

SurchargeUnreinforced

Slopes/Walls

Types ofStabilityAnalysis

2

Mechanisms

MSEW 0 - 100%

Uniform and

strip (live and

dead), horizon-

tal, point, and

isolated

No

Internal,

direct sliding,eccentricity

(overturning),

connection,

pullout, bear-

ing capacity,

and global

Planar, 2-part

wedge (simpli-

fied), Meyerhof,

Circular (Bishop)

ReSlope 100%1Uniform and

stripNo

Internal,

compound,

deepseated

Log spiral and

circular for deep-

seated (Bishop)

ReSSA 0 - 100%Uniform and

strip

Yes (can run asa generic slope sta-

bility program)

Rotationaland transla-

tional

Circular

(Bishop), 2- and 3-

part wedge(Spencer); effects

of reinforcement s

included if inter-

sects slip surface

1ReSlope ignores surficial failure assuming 100% connection strength

2 Factor of safety in ReSSA is consistent regardless whether rotational or translational analysis is

used; this factor applies equally to all elements resisting failure (i.e., shear strength parameters of soilsand reinforcement resistance, if available); the factor for pullout represents a ratio of resisting force andpullout force. In MSEW this factor is applied only on the reinforcement strength in Internal Stability; itrepresents ratio of resisting force and driving force in direct sliding and pullout; it represent ratio of mo-ments in overturning; it represents the ultimate foundation capacity over the actual load, considering ec-centric load and Meyerhof method. In ReSlope the user can specify different factor for the soil shearstrength and for the reinforcement strength when dealing with Internal Stability or Compound (thus mak-ing this approach adaptable to conventional approach to walls or to slopes); ratio of forces in pullout re-sistance and in direct sliding; reduction of soils shear strength when deepseated failure (Bishop) is used.

Stability of Geosynthetic Reinforced Soil Structures

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