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Seismic Slope Stability

Surveys of earth dam performance during earthquakes suggest that embankments constructed of materials that are not vulnerable to severe strength loss as a result of earthquake shaking generally perform well during earthquakes [Seed et al., 1978]. The potentially catastrophic consequences of an earth embankment material that undergoes severe strength loss during earthquake shaking is demonstrated by the near failure of the Lower San Fernando dam as a result of the 1971 San Fernando earthquake [Seed et al., 1975]. The center and upstream sections of the dam slid into the reservoir because a large section within the dam liquefied. The slide movement left only 1.5 m of earth fill above the reservoir level. Fortunately, the reservoir level was 11 m below the original crest at the time of the earthquake. Still, because of the precarious condition of the dam after the main shock, 80,000 people living downstream of the dam were ordered to evacuate until the reservoir could be lowered to a safe elevation.
Therefore, Considerable attention has been focused over the last few decades on developing procedures to analyzethe seismic performance of earth embankments [e.g., Newmark, 1965; Seed, 1979; Marcuson et al., 1992]. The first issue that must be addressed is an evaluation of the potential of the materials comprising the earth structure to lose significant strength under cyclic earthquake loading. Saturated cohesionless materials (gravels, sands, and nonplastic silts) that are in a loose state are prime candidates for liquefaction and hence significant strength loss. Experience has shown that cohesionless materials placed by the hydraulic fill method are especially vulnerable to severe strength loss as a result of strong shaking. A modified version of the Seed and Idriss [1982] simplified method has been employed to evaluate the liquefaction potential of cohesionless soils in earth slopes and dams [see Seed and Harder, 1990]. Certain types of clayey materials have also been shown to lose significant strength as a result of cyclic loading. If clayey materials have a small percentage of clay-sized particles, low liquid limits, and high water contents, the material’s cyclic loading characteristics should be determined by cyclic laboratory testing [Seed and Idriss, 1982].
The embankment, however, may undergo some level of permanent deformation as a result of the earthquake shaking. With well-built earth embankments experiencing moderate earthquakes, the magnitude of permanent seismic deformations should be small, but marginally stable earth embankments experiencing major earthquakes may undergo large deformations that may jeopardize the structure’s integrity. Simplified procedures have been developed to evaluate the potential for seismic instability and seismically induced permanent deformations [e.g., Seed, 1979; Makdisi and Seed, 1978], and these procedures can be used to evaluate the seismic performance of earthen structures and natural slopes.
In pseudostatic slope stability analyses, a factor of safety against failure is computed using a static limit equilibrium stability procedure in which a pseudostatic, horizontal inertial force, which represents the destabilizing effects of the earthquake, is applied to the potential sliding mass. The horizontal inertial force is expressed as the product of a seismic coefficient, k, and the weight, W, of the potential sliding mass (Fig. 1) If the factor of safety approaches unity, the embankment is considered unsafe. Since the seismic coefficient designates the horizontal force to be used in the stability analysis, its selection is crucial. The selection of the seismic coefficient must be coordinated with the selection of the dynamic material strengths and minimum factor of safety, however, as these parameters work together to achieve a satisfactory design. For earth embankments, case histories are available which have guided the selection of these parameters. For example, Seed [1979] recommends using appropriate dynamic material strengths, a seismic coefficient of 0.15, and a minimum factor of safety of 1.15 to ensure that an embankment composed of materials that do not undergo severe strength loss performs satisfactorily during a major earthquake.
A significant limitation of the pseudostatic approach is that the horizontal force, representing the effects of an earthquake, is constant and acts in only one direction. With dynamically applied loads, the force may be applied for only a few tenths of a second before the direction of motion is reversed. The result of these transient forces will be a series of displacement pulses rather than complete failure of the slope. Normally, a certain amount of limiting displacement during an earthquake event is considered tolerable. Hence, if conservative strength properties are selected and the seismic coefficient represents the maximum disturbing force (i.e., maximum shear stress induced by the earthquake on the potential sliding surface; see Seed and Martin, 1966), a factor of safety of one is likely to ensure adequate seismic performance. Other conservative combinations of these parameters could be developed, but their use must be evaluated in the context that their use in analysis ensures a design that performs well during earthquakes (i.e., tolerable deformations).
Seismically induced permanent deformations are generally calculated using a Newmark-type procedure. The Newmark [1965] analysis assumes that relative slope movements would be initiated when the inertial force on a potential sliding mass was large enough to overcome the yield resistance along the slip surface, and these movements would stop when the inertial force decreased below the yield resistance and the velocities of the ground and sliding mass coincided. The yield acceleration is defined as the average acceleration producing a horizontal inertial force on a potential sliding mass which gives a factor of safety of one and can be calculated as the seismic coefficient in pseudostatic slope stability analyses that produces a safety factor of one. By integrating the equivalent average acceleration [see Bray et al., 1993] acting on the sliding surface in excess of this yield acceleration as a function of time, the displacement of the slide mass can be estimated. A commonly used procedure for calculating seismically induced permanent deformations has been developed by Franklin and Chang [1977] and computer programs are available [e.g., Pyke and Beikae, 1991]. Simplified chart solutions have been developed by Makdisi and Seed [1978] for earth embankments.
An emerging area of concern in many regions of the world is the seismic performance of waste fills. For example, recent U.S. federal regulations (40 CFR 258-USEPA 1991: Subtitle D) require that municipal solid waste landfills located in seismic impact zones be designed to resist earthquake hazards. Since these designated seismic impact zones encompass nearly half of the continental U.S., these regulations are having a pronounced impact on the design of new landfills and the lateral expansion of existing landfills. The results of a comprehensive study of the effects of the characteristics of the waste fill, subsurface soils, and earthquake ground motions are presented in Bray et al. [1993]. The investigators found that the seismic loading strongly depends on the dynamic properties and height of the waste fill. General design considerations regarding the seismic stability of solid waste landfills are discussed in Repetto et al. [1993].

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