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SUMMARYA 3-D mathematical approach to slope stability, which is based on limiting equilibrium and variational analysis, is presented. In the initial formulation there are three unknown functions: the slip surface, the normal stress and the shear stress direction over this surface. The minimum factor of safety is sought through variational extremization. The analysis indicates that the factor of safety is independent of the normal stress distribution over the critical slip surface. It also indicates that the direction of the elementary shear force over the slip surface depends on the slip surface function, but not on the normal stress function. The analysis yields a non-linear first order partial differential equation, relating the slip surface and its first partial derivatives. By limiting the analysis to symmetrical problems an ordinary differential equation, governing the slip surface path on the plane of symmetry, is derived. This equation enables the development of a numerical procedure to determine the minimal factor of safety of symmetrical 3-D slopes. Two possible failure modes are determined for homogeneous slopes. One mode consists of finite 3-D sliding body and the second represents cylindrical failure. Numerical analyses for some simple cases of homogeneous slopes are presented. INTRODUCTlONA 2-D idealization of a slope subjected to 3-D conditions yields, in most practical cases, conservative results.with respect to stability. This, combined with the complexity of 3-D analysis, the difficulty of performing a 3-D experimental model test and the objective limitations of a 3-D post-failure investigation of a given prototype, apparently has not generated much research effort for 3-D conditions. Commonly observed failures indicate, however, that it has finite dimensions. Therefore, the application of 2-D stability is not always justified.Currently there are a few available 3-D stability methods which are based on the limiting equilibrium approach. Most of these methods, however, are not rigorous. The majority of the 3-D analysis methods developed treat the stability of rock However, the basic assumptions in rock stability analysis are often not applicable when applied to soil slopes.The simplest approach to 3-D slope stability is to compute the 2-D safety factor of several

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Seismic design procedures are proposed for geosynthetic-reinforced soil structures. The procedures are based on a pseudo-static limit equilibrium analysis, which considers horizontal acceleration and incorporates a permanent displacement limit. Internal and external stability analyses are conducted to determine the required strength and length of geosynthetic, considering different modes of failure. Parametric studies illustrate the effects of seismic acceleration on the design of reinforced soil structures having different slope angles and soil properties. For vertical slopes at small seismic acceleration, tieback/compound failure dictates the required geosynthetic length. The length required to resist direct sliding increases rapidly as the seismic acceleration increases. This length may become impractical at moderate design accelerations. For such cases, an alternative approach based on a tolerable displacement against direct sliding is proposed for design. The proposed procedures are compared with the performance of several geosynthetic-reinforced soil structures during recent major earthquakes. A detailed design example is included to illustrate usage of proposed procedures.