**4. Literature review**

Jewell et al. [8], Bonaparte et al. [9] and Verduin and Holtz [10] present design methods for earth slopes reinforced with geotextiles and/or geogrids using limit equilibrium method considering circular or/and bilinear wedges. Leshchinsky and Reinschmidt [11] and Leshchinsky and Boedeker [12] present an approach based on limit equilibrium and variational extremization of factor of safety of multilayer reinforced slope. Schneider and Holtz [13] present a design procedure for slopes reinforced with geotextiles and geogrids for a bilinear surface of sliding, considering porewater pressures and the initial stress conditions in the slope. Jewell [14] presented revised design charts for steep slopes valid for all reinforcement materials. Leshchinsky [15] and Leshchinsky et al. [16] used log-spiral failure mechanism to determine the required reinforcement long term strength. Zhao [17] and Michalowski [18] present kinematic limit analyses solutions for the stability of reinforced soil slopes. Shiwakoti et al. [19] conducted parametric studies to investigate the effect of geosynthetic strength, soil–geosynthetic interaction coefficients, vertical spacing of geosynthetics for soil slope/wall on competent foundation. Baker and Klein [20, 21] modified the top-down approach of Leshchinsky [15] to obtain the reinforcement force needed for a prescribed factor of safety everywhere within the reinforced mass. Han and Leshchinsky [22] present a general analytical framework for design of flexible reinforced earth structures, i.e., walls and slopes. Leshchinsky et al. [23] present a limit equilibrium methodology to determine the unfactored global geosynthetic strength required to ensure sufficient internal stability in reinforced earth structures. Leshchinsky et al. [24] introduced a limit state design framework for geosynthetic reinforced slopes and walls. Leshchinsky and Ambauen [25] present use of upper bound limit analysis (LA) in conjunction with discretization procedure known as discontinuity layout optimization (DLO). DLO-LA is an effective tool for establishing a critical failure mechanism and ensuing stability of the slope without the constraint or assumptions required in LE analysis. Shukla et al. [26] presented a review of design of reinforced slope and covers basic of methods in detail. Gao et al. [27] in their study considered three-dimensional effect on reinforced earth structure stability and to determine the required

strength and length of reinforcement using limit analysis. Song et al. [28] proposed new approach based on LE principle to evaluate stability of reinforced slope.

Free draining granular material is used conventionally for reinforced earth slope construction. However cohesive materials have also been used for construction of reinforced slopes in few cases. Very few design guidelines/methods are available for design of reinforced earth slope with marginal soil. Christopher et al. [29] provide design guidance (total stress analysis ignoring the drainage contribution of geocomposite for short term and effective stress analysis considering drainage in the long term) for reinforced soil structures using poorly draining backfills. Naughton et al. [30] improved the design method of Christopher et al. [29] and presented single stage effective stress analysis since excess pore pressure gets dissipated fully before construction of subsequent layers. Clancy and Naughton [31] used design approach of Naughton et al. [30] to design four steep slopes using fine-grained soils as backfill material and provided a method to determine the maximum height of each lift to allow dissipation of excess pore pressures in a 24-hour period for a 10 m high 70° slope. Giroud et al. [32] updated design method of Naughton et al. [30] for reinforced slopes and walls using draining geogrid, with focus on improved determination of the required transmissivity of the same. Naughton et al. [33] conducted a parametric study of design parameters of low permeability fill and concluded that for typical compressibility and consolidation parameters vertical spacing of the reinforcement of 0.5 m is adequate.

Abd and Utili [33] employed limit analysis approach and semi-analytical method for uniform slopes that provide the amount of reinforcement needed as a function of cohesion, c, and angle of shearing resistance, ϕ, of backfill, tensile strength of geosynthetic and of the slope inclination.

### **5. Design methods**

Geosynthetic reinforced slopes are designed to provide internal, external, global and surfacial stability. Surfacial stability determines the requirement of secondary reinforcement to ensure no shallow sloughing. The design process must address all possible failure modes that a reinforced (or unreinforced) slope would potentially experience. The design addresses internal stability (pull out and bond failures) for the condition where the failure surface intersects the reinforcement, external stability (sliding, overturning, bearing failures) for the condition where the failure surface is located outside and below the reinforced soil mass and compound stability for the condition where the failure plane passes behind and through the reinforced soil mass. In order to analyze a reinforced slope the requirements include the slope geometry, external and seismic loading, porewater pressure and/or seepage conditions, soil parameters and properties, the reinforcement parameters and properties, the interaction characteristics of the soil and the geosynthetic. The design of a reinforced soil slope determines the final geometry, the required number, spacing and lengths of reinforcement layers and measures to prevent sloughing or erosion of the slope face.

Methods originally developed for unreinforced slopes have been extended to reinforced slopes accounting for the presence of reinforcement. Methods available for analyzing geosynthetic reinforced soil slopes are (i) Limit equilibrium, (ii) Limit analysis, (iii) Slip line and (iv) Finite element methods.

#### **5.1 Limit equilibrium method**

Conventional geotechnical engineering approach to slope stability problems is to use limit equilibrium concepts on an assumed circular or non-circular failure

**19**

*Geoysynthetic Reinforced Embankment Slopes DOI: http://dx.doi.org/10.5772/intechopen.95106*

narrowed the gap between the two bounds.

using slip line method were given by Zhao [17].

studies [34–39].

**5.2 Limit analysis**

**5.3 Slip line method**

**5.4 Finite element method**

angle of dilation (

Technique' using FEM.

i.e., the wedge point.

**6.1 Jewell et al. design method**

deformation (E), Poisson's ratio (

ψ

surface and to arrive at a factor of safety. Factor of safety is estimated using moment and/or force equilibrium equations considering the reinforcing effect of geosynthetics. Several limit equilibrium methods have been used in various

Limit analysis is another method for solution of slope stability problems [17, 19, 25, 40–44]. It is based on plasticity theory and can be applied to slopes of arbitrary geometry and complex loading conditions. Using limit theorems, collapse load can be bracketed between lower and upper bounds even if it cannot be determined exactly. Recent approaches that combine finite elements and failure criterion have

Slip line method is based on stress characteristics and based on homogenization of the composite mass and suitable for continuous filament or fiber reinforced soil slopes. Failure criterion for geosynthetic reinforced soil composite was presented by Michalowski and Zhao [40]. Limit loads on geosynthetic reinforced soil slopes

Finite element method of analysis is generally based on quasi-elastic continuum

technique is used for design of slope considering the effect of reinforcement. In this approach no assumption needs to be made regarding nature of failure surface or its location as failure occurs "naturally" through the zones within the soil mass wherein the shear stresses attain values close to the strength of the soil. Details of this approach can be found in the works of Rowe and Soderman [45], Almeida et al. [46], Chalaturnyk et al. [47], Ali and Tee [48] and Griffith and Lane [49]. Software such as Plaxis, FLAC, etc., are available for the analysis by 'Soil Strength Reduction

), cohesion, c, angle of shearing resistance, ϕ,

) are required for design. Alternately, shear strength reduction

mechanics approach in which stresses and strains are estimated throughout the mass. In this method both deformation and strength parameters, viz., modulus of

υ

**6. Reinforced embankment slope design - Jewell method**

Jewell et al. [8] proposed a method of design based on Limit Equilibrium analysis and local check on individual reinforcement spacing for geogrid reinforced embankment slope for slope angles, β, ranging from 30° to 80°. Embankment soil is granular and the crest is horizontal. Length of reinforcement is based on (i) no overstressing of lower layers, (ii) no outward sliding along the interface between soil and reinforcement layer and (iii) no tension on the base. Two-part wedge analysis is used and critical wedge surface for failure is located by varying wedge angles θ1 and θ2 (**Figure 7**) and the location of intersection of the two wedge lines,

surface and to arrive at a factor of safety. Factor of safety is estimated using moment and/or force equilibrium equations considering the reinforcing effect of geosynthetics. Several limit equilibrium methods have been used in various studies [34–39].
