Thedesign of reinforcement for safe,steep slopes requires a rigorous analysis.Thedesign ofreinforcementforthisapplicationiscritical,asfailureofthereinforcementwouldresultinfailure of the slope.The overall design requirements for reinforced slopes are similar to those for unreinforcedslopes: A limit equilibrium, allowable stress approach is used and the factor of safety mustbe adequate for both the short-term and long-term conditions and for all possible modes offailure.LRFD methodshavenotbeenfullydeveloped for eitherunreinforced or reinforcedslopes and are thus not included in this manual.As illustrated in Figure 8-1, there are three failure modes for reinforced slopesInternal, where the failure plane passes through the reinforcing elements..External, where thefailure surface passes behind and underneath the reinforced zone.Compound, where thefailure surface passes behind and through the reinforced soilzone.In some cases, the calculated stability safety factor can be approximately equal in two or allthree modes, if the reinforcement strengths, lengths and vertical spacings are optimized (Berget al.,1989).@InternalKCompound??ExternalFigure 8-1.Failure modes for reinforced soil slopes including internal failure within thereinforced soil zone,external failure entirely outside the reinforced soil zone, andcompound failure starting behind and passing through the reinforced soil zoneFHWA NHI-10-0258-Reinforced Soil Slopes8-3MSEWallsandRSS-VolIINovember2009
The design of reinforcement for safe, steep slopes requires a rigorous analysis. The design of reinforcement for this application is critical, as failure of the reinforcement would result in failure of the slope. The overall design requirements for reinforced slopes are similar to those for unreinforced slopes: A limit equilibrium, allowable stress approach is used and the factor of safety must be adequate for both the short-term and long-term conditions and for all possible modes of failure. LRFD methods have not been fully developed for either unreinforced or reinforced slopes and are thus not included in this manual. As illustrated in Figure 8-1, there are three failure modes for reinforced slopes: Internal, where the failure plane passes through the reinforcing elements. External, where the failure surface passes behind and underneath the reinforced zone. Compound, where the failure surface passes behind and through the reinforced soil zone. In some cases, the calculated stability safety factor can be approximately equal in two or all three modes, if the reinforcement strengths, lengths and vertical spacings are optimized (Berg et al., 1989). FHWA NHI-10-025 8 – Reinforced Soil Slopes MSE Walls and RSS – Vol II 8 – 3 November 2009 Figure 8-1. Failure modes for reinforced soil slopes including internal failure within the reinforced soil zone, external failure entirely outside the reinforced soil zone, and compound failure starting behind and passing through the reinforced soil zone
8.3.2Design of Reinforcement for Compaction AidFor the use of geosynthetics as compaction aids, the design is relatively simple.Assumingthe slope is safe without reinforcement, no reinforcement design is required.Place anygeotextile or geogrid that will survive construction at every lift or every other lift ofcompacted soil in a continuous plane along the edge of the slope.Only narrow strips, about4 to 6 ft (1.2 to 1.8 m) in width, at 8 to 18 in. (200 to 500 mm) vertical spacing are required.Where the slope angle approaches the angle of repose of the soil, it is recommended that aface stability analysis be performed using the method presented in the reinforcement designsection of Chapter 9.Where reinforcement is required by analysis, the narrow stripreinforcement maybe considered as secondary reinforcement used to improve compactionand stabilize the slope face between primary reinforcing layers.8.3.3Design of ReinforcementforSteepening Slopesand SlopeRepairFor steepened reinforced slopes (face inclination up to 70 degrees)and slope repair, design isbased on modified versions of the classical limit equilibrium slope stability methods asshown in Figure 8-2:Circular or wedge-type potential failure surface is assumed.The relationship between driving and resisting forces or moments determines the slopefactorofsafetyReinforcement layers intersecting the potential failure surface are assumed to increasethe resisting force or moment based on their tensile capacity and orientation. (Usually,the shear and bending strengths of stiff reinforcements are not taken into account.)Thetensile capacity of a reinforcement layer is taken as theminimum of its allowablepullout resistance behind (or in front of) the potential failure surface and its long-termallowabledesign strength, Tal.As shown in Figure 8-1, a wide variety of potential failure surfaces must be considered,including deep-seated surfaces through or behind the reinforced zone.For the internalanalysis, the critical slope stability factor of safety is taken from the internal unreinforcedfailure surface requiring the maximum reinforcement.This is the failure surface with thelargest unbalanced driving moment to resisting moment and not the surface with theminimum calculated unreinforced factor of safety. This failure surface is equivalent to thecritical reinforced failure surface with the lowest factor of safety.Detailed design ofreinforced zone is performed by determining the factor of safety with successively modifiedreinforcement layouts until the target factor of safety is achieved. External and compoundstability of the reinforced zone are then evaluated.FHWA NHI-10-0258-Reinforced Soil Slopes8-4MSEWalls andRSS-Vol IINovember2009
8.3.2 Design of Reinforcement for Compaction Aid For the use of geosynthetics as compaction aids, the design is relatively simple. Assuming the slope is safe without reinforcement, no reinforcement design is required. Place any geotextile or geogrid that will survive construction at every lift or every other lift of compacted soil in a continuous plane along the edge of the slope. Only narrow strips, about 4 to 6 ft (1.2 to 1.8 m) in width, at 8 to 18 in. (200 to 500 mm) vertical spacing are required. Where the slope angle approaches the angle of repose of the soil, it is recommended that a face stability analysis be performed using the method presented in the reinforcement design section of Chapter 9. Where reinforcement is required by analysis, the narrow strip reinforcement may be considered as secondary reinforcement used to improve compaction and stabilize the slope face between primary reinforcing layers. 8.3.3 Design of Reinforcement for Steepening Slopes and Slope Repair For steepened reinforced slopes (face inclination up to 70 degrees) and slope repair, design is based on modified versions of the classical limit equilibrium slope stability methods as shown in Figure 8-2: Circular or wedge-type potential failure surface is assumed. The relationship between driving and resisting forces or moments determines the slope factor of safety. Reinforcement layers intersecting the potential failure surface are assumed to increase the resisting force or moment based on their tensile capacity and orientation. (Usually, the shear and bending strengths of stiff reinforcements are not taken into account.) The tensile capacity of a reinforcement layer is taken as the minimum of its allowable pullout resistance behind (or in front of) the potential failure surface and its long-term allowable design strength, Tal. As shown in Figure 8-1, a wide variety of potential failure surfaces must be considered, including deep-seated surfaces through or behind the reinforced zone. For the internal analysis, the critical slope stability factor of safety is taken from the internal unreinforced failure surface requiring the maximum reinforcement. This is the failure surface with the largest unbalanced driving moment to resisting moment and not the surface with the minimum calculated unreinforced factor of safety. This failure surface is equivalent to the critical reinforced failure surface with the lowest factor of safety. Detailed design of reinforced zone is performed by determining the factor of safety with successively modified reinforcement layouts until the target factor of safety is achieved. External and compound stability of the reinforced zone are then evaluated. FHWA NHI-10-025 8 – Reinforced Soil Slopes MSE Walls and RSS – Vol II 8 – 4 November 2009
CENTER OF ROTATIONRSURCHARGEdDqAISxT(Continuous)HTs (Strip)1/3HTEVELe EMBEOMENT LENGTHFigure 8-2.Modified limit equilibrium analysis for reinforced slope design.For slope repair applications, it is also very important to identify the cause of the originalfailure to make sure that the new reinforced soil slope will not have the same problems. If awater table or erratic water flows exist, particular attention has to be paid to drainage. Innatural soils, it is also necessary to identify any weak seams that might affect stability.Themethod presented in this manual uses any conventional slope stability computer programand the steps necessary to manually calculate the reinforcement requirements for almost anycondition.Figure 8-2 shows the conventional rotational slip surface method used in theanalysis.Fairly complex conditions can be accommodated depending on the analyticalmethod used (e.g.,Modified Bishop, Spencer).The computer programResSA(ADAMA,2001)was developed by the FHWA to specifically perform this analysis.The rotational slip surface approach is used for slopes up to 70 degrees, although technicallyit is a valid method for evaluating even steeper slopes.Slopes steeper than 70 degrees aredefined as walls and lateral earthpressureprocedures in Chapter4applyFHWA NHI-10-0258 -Reinforced Soil Slopes8-5MSEWallsandRSS-VolIlNovember2009
Figure 8-2. Modified limit equilibrium analysis for reinforced slope design. For slope repair applications, it is also very important to identify the cause of the original failure to make sure that the new reinforced soil slope will not have the same problems. If a water table or erratic water flows exist, particular attention has to be paid to drainage. In natural soils, it is also necessary to identify any weak seams that might affect stability. The method presented in this manual uses any conventional slope stability computer program and the steps necessary to manually calculate the reinforcement requirements for almost any condition. Figure 8-2 shows the conventional rotational slip surface method used in the analysis. Fairly complex conditions can be accommodated depending on the analytical method used (e.g., Modified Bishop, Spencer). The computer program ReSSA (ADAMA, 2001) was developed by the FHWA to specifically perform this analysis. The rotational slip surface approach is used for slopes up to 70 degrees, although technically it is a valid method for evaluating even steeper slopes. Slopes steeper than 70 degrees are defined as walls and lateral earth pressure procedures in Chapter 4 apply. FHWA NHI-10-025 8 – Reinforced Soil Slopes MSE Walls and RSS – Vol II 8 – 5 November 2009
The assumed orientation of the reinforcement tensile force influences the calculated slopesafety factor.In a conservative approach, the deformability of the reinforcements is nottaken into account, and thus, the tensileforcesper unit width of reinforcement Tare assumedto always be in the horizontal direction of the reinforcements.When close to failure,however, the reinforcements may elongate along the failure surface, and an inclination fromthe horizontal can be considered.The above reinforcement orientations represent a simplifying assumption considering thereinforcement is not incorporated directly into the analysis of the slope.If a more rigorousevaluation isperformed inwhichthevertical andhorizontal componentsof thetensionforcesareincluded inthe equations of equilibrium,thenitcanbe shownthat anincreaseinnormalstress will occur for reinforcements with an orientation other than tangential to the failuresurface (Wright and Duncan, 1990). In effect, this increase in normal stress will result inpracticallythe same reinforcement influence on the safetyfactor whether it is assumed to acttangentially or horizontally. Although these equilibrium considerations may indicate that thehorizontal assumption is conservativefor discontinuous strip reinforcements,it should berecognized that the stress distribution near the point of intersection of the reinforcement andthe failure surface is complicated. The conclusion concerning an increase in normal stressshould only be considered for continuous and closely spaced reinforcements:it isquestionableand should notbe applied to reinforced slopes with widely spaced and/ordiscrete, striptype reinforcements.Tensile force direction is, therefore, dependent on the extensibility and continuity of thereinforcements used,and thefollowing inclination is suggested:Discrete,stripreinforcements:Tparallel to the reinforcements.?Continuous, sheetreinforcements:T tangent to the sliding surface.8.3.4Computer-Assisted DesignThe ideal method for reinforced slope design is to use a conventional slope stability computerprogram that has been modified to account for the stabilizing effect ofreinforcement.Suchprograms should account for reinforcement strength and pullout capacity,computereinforcedand unreinforced safety factors automatically,and have some searching routine to help locatecritical surfaces.The method may also include the confinement effects of the reinforcementon the shear strengthofthe soil in thevicinity ofthe reinforcement.FHWA NHI-10-0258-Reinforced Soil Slopes8-6MSE Walls and RSS - Vol IINovember2009
The assumed orientation of the reinforcement tensile force influences the calculated slope safety factor. In a conservative approach, the deformability of the reinforcements is not taken into account, and thus, the tensile forces per unit width of reinforcement Tr are assumed to always be in the horizontal direction of the reinforcements. When close to failure, however, the reinforcements may elongate along the failure surface, and an inclination from the horizontal can be considered. The above reinforcement orientations represent a simplifying assumption considering the reinforcement is not incorporated directly into the analysis of the slope. If a more rigorous evaluation is performed in which the vertical and horizontal components of the tension forces are included in the equations of equilibrium, then it can be shown that an increase in normal stress will occur for reinforcements with an orientation other than tangential to the failure surface (Wright and Duncan, 1990). In effect, this increase in normal stress will result in practically the same reinforcement influence on the safety factor whether it is assumed to act tangentially or horizontally. Although these equilibrium considerations may indicate that the horizontal assumption is conservative for discontinuous strip reinforcements, it should be recognized that the stress distribution near the point of intersection of the reinforcement and the failure surface is complicated. The conclusion concerning an increase in normal stress should only be considered for continuous and closely spaced reinforcements: it is questionable and should not be applied to reinforced slopes with widely spaced and/or discrete, strip type reinforcements. Tensile force direction is, therefore, dependent on the extensibility and continuity of the reinforcements used, and the following inclination is suggested: Discrete, strip reinforcements: T parallel to the reinforcements. Continuous, sheet reinforcements: T tangent to the sliding surface. 8.3.4 Computer-Assisted Design The ideal method for reinforced slope design is to use a conventional slope stability computer program that has been modified to account for the stabilizing effect of reinforcement. Such programs should account for reinforcement strength and pullout capacity, compute reinforced and unreinforced safety factors automatically, and have some searching routine to help locate critical surfaces. The method may also include the confinement effects of the reinforcement on the shear strength of the soil in the vicinity of the reinforcement. FHWA NHI-10-025 8 – Reinforced Soil Slopes MSE Walls and RSS – Vol II 8 – 6 November 2009
A number of reinforced slope programs are commercially available, several of which followthe design approach detailed in Chapter 9 of this manual.As previously indicated thedevelopment of program ReSSA was initially sponsored by theFHWA.ReSSA implicitlycontains the design approach in this manual, noted as the FHWA BishopMethod in theprogram's rotational stability analysis section, and contains the previous version of thismanual in the help screens.ResSA also provides alternate methods of analysis and the helpscreens describe those methods in detail including a theoretical discussion of the approachesFHWA does not exclude the use of other methods of analysis, especially those which aremorecomprehensive.However,theusermusthaveafundamentalunderstandingofwhichdesignmethod(s)arebeingused andhowthealgorithmsincorporatethereinforcementintothe stability analysis, with some programs using simplifying assumptions, while others applycomprehensiveformulation and correspondingly complicated computations.Appropriatefactors of safety must then be applied to account for uncertainties of the analytical methodand thegeotechnical and reinforcementmaterials.Some of theless sophisticatedprograms do not design the reinforcement but allowfor anevaluation of a given reinforcement layout.An iterative approach then follows to optimizeeither the reinforcement strength or layout.Many of these programs are limited to simplesoil profiles and, in some cases,simple reinforcement layouts.Also, external stabilityevaluation may be limited to specific soil and reinforcement conditions and a single mode offailure. In some cases, these programs are reinforcement-specific.With computerized analyses, the actual factor of safety value (FS) is dependent upon how thespecific program accounts for the reinforcement tension in the moment equilibrium equation.Themethod of analysis in Chapter 9 and in FHWABishop method in ReSSa, as well asmany others, assume the reinforcement force as contributing to the resisting moment, i.e.:Mr+T,RFSR(8-1)Mpwhere, FSRtherequired stabilityfactorofsafety-MRresisting moment provided by the strength of the soilMDdriving moment about the center ofthe failure circleTssum of tensile force per unit width of reinforcement (consideringrupture and pullout) in all reinforcement layers intersecting thefailuresurfaceRthe moment arm of Ts about the center of failure circle as shownin Figure8-2FHWA NHI-10-0258 - Reinforced Soil Slopes8-7MSE Walls and RSS -Vol IINovember2009
A number of reinforced slope programs are commercially available, several of which follow the design approach detailed in Chapter 9 of this manual. As previously indicated the development of program ReSSA was initially sponsored by the FHWA. ReSSA implicitly contains the design approach in this manual, noted as the FHWA Bishop Method in the program’s rotational stability analysis section, and contains the previous version of this manual in the help screens. ReSSA also provides alternate methods of analysis and the help screens describe those methods in detail including a theoretical discussion of the approaches. FHWA does not exclude the use of other methods of analysis, especially those which are more comprehensive. However, the user must have a fundamental understanding of which design method(s) are being used and how the algorithms incorporate the reinforcement into the stability analysis, with some programs using simplifying assumptions, while others apply comprehensive formulation and correspondingly complicated computations. Appropriate factors of safety must then be applied to account for uncertainties of the analytical method and the geotechnical and reinforcement materials. Some of the less sophisticated programs do not design the reinforcement but allow for an evaluation of a given reinforcement layout. An iterative approach then follows to optimize either the reinforcement strength or layout. Many of these programs are limited to simple soil profiles and, in some cases, simple reinforcement layouts. Also, external stability evaluation may be limited to specific soil and reinforcement conditions and a single mode of failure. In some cases, these programs are reinforcement-specific. With computerized analyses, the actual factor of safety value (FS) is dependent upon how the specific program accounts for the reinforcement tension in the moment equilibrium equation. The method of analysis in Chapter 9 and in FHWA Bishop method in ReSSa, as well as many others, assume the reinforcement force as contributing to the resisting moment, i.e.: FS R D SR M T RM (8-1) where, FSR = the required stability factor of safety MR = resisting moment provided by the strength of the soil MD = driving moment about the center of the failure circle TS = sum of tensile force per unit width of reinforcement (considering rupture and pullout) in all reinforcement layers intersecting the failure surface R = the moment arm of TS about the center of failure circle as shown in Figure 8-2 FHWA NHI-10-025 8 – Reinforced Soil Slopes MSE Walls and RSS – Vol II 8 – 7 November 2009