**5.2 Limit analysis**

*Slope Engineering*

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.

strength of geosynthetic and of the slope inclination.

**5. Design methods**

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

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)

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

Limit analysis, (iii) Slip line and (iv) Finite element methods.

**5.1 Limit equilibrium method**

**18**

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 narrowed the gap between the two bounds.
