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97 foundation material. Explorations often would be conducted potential for seismic instability becomes a key consideration to twice the slope height to define strength and compressibil- in some areas, particularly where critical lifeline transporta- ity properties of soil layers upon which the embankment will tion routes occur. be constructed. The geometry and properties of the fill will be determined on the basis of right-of-way widths and costs of 8.2 Current Practice importing fill material. From a seismic design perspective these types of slopes are Earthquake-induced ground accelerations can result in sig- routinely encountered as new roadways are constructed or nificant inertial forces in slopes or embankments, and these existing roadways are modified. Both the field investigation forces may lead to instability or permanent deformations. and the analysis of slope stability for these slopes are routinely Current practice for the analysis of the performance of slopes handled for gravity loading and, in more seismically active and embankments during earthquake loading is to use one of areas, for seismic loading. Performance of the constructed two related methods: slope during seismic loading generally has been very good, except where liquefaction of the foundation material occurs. 1. Limit equilibrium methods using a pseudo-static repre- In this case, the loss of foundation strength from liquefaction sentation of the seismic forces. In this approach, induced has led to embankment slope failures. seismic loads are used in a conventional limit equilibrium analysis to evaluate a factor of safety. The seismic loads are determined on the basis of the ground acceleration and 8.1.2 Natural Slopes the mass of soil being loaded. Natural slopes present more difficulties because of the wide 2. Displacement-based analyses using either the Newmark range of conditions that occur within these slopes. Relatively sliding block concept shown schematically in Figure 8-1 or uniform soil conditions can exist within the slope; however, more rigorous numerical modeling methods. In Figure 8-1, most often the slope involves layers of different geologic ma- when the acceleration exceeds the yield acceleration (that terials, and these materials often change from cohesionless to is C/D ratio = FS = 1.0), deformations accumulate leading cohesive in characteristic. Groundwater often is found within to permanent ground deformation. This procedure is sim- the slope, and sometimes the water is intermittently perched ilar to that adopted for retaining wall analysis as discussed on less permeable layers. in Chapter 7. Further complicating the evaluation of the natural slope is the geometry. In areas where soils have been overconsolidated Use of these methods for design has been widely adopted from glaciation, the slope angles can be steeper than 1H:1V, in the United States and in international design guidelines. even where the fines content is minimal. Likewise in moun- For example, methods are described in detail in the FHWA tainous areas the natural slopes can be marginally stable in the report titled Geotechnical Earthquake Engineering (FHWA, existing state. Other natural slopes that are relatively flat can 1998a) and a publication on Guidelines for Analyzing and have thin bedding planes characterized by very low friction Mitigating Landslide Hazards in California (SCEC, 2002). angles for long-term loading. Where located adversely to a planned slope cut, the removal of materials buttressing these 8.2.1 Limit Equilibrium Approach slopes can initiate large slides under gravity loading and re- activate slides during seismic events. The limit equilibrium approach involves introducing a Natural slopes are often the most difficult to characterize seismic coefficient to a conventional slope stability analysis in terms of layering and material characteristics. Access to and determining the resulting factor of safety. The seismic co- conduct site explorations can be difficult, particularly where efficient is typically assumed to be some percentage of the steep slopes exist. The variability of natural deposits forming site-adjusted PGA occurring at a site. The value can range the slope often makes it difficult to locate or adequately from less than 50 percent of the peak to the PGA, depending model soil layers critical to the evaluation of slope stability, on the designer's views or agency requirements. Typically, a either under gravity or seismic loading. slope is judged to be safe if the resulting factor of safety is From a seismic perspective, natural slopes are where most greater than 1.1 to 1.3. slope failures have been observed. Although there is no single As discussed in the FHWA publication, a wide variety of cause of past failures, many of these failures have occurred commercially available computer programs exist that can where slopes are oversteepened, that is, barely stable under perform both static and pseudo-static limit equilibrium gravity loading. The size of the failure can range from small analyses. Most of these programs provide general solutions to slides of a few yards of soil to movements involving thou- slope stability problems with provisions for using the simpli- sands of yards of soil. In highly seismic areas of the WUS, the fied Bishop, simplified Janbu, and Spencer's method of slices.
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98 Figure 8-1. Newmark sliding block concept for slopes. Potential sliding surfaces, both circular or polygonal, usually tions have a minor effect on the seismic stability evaluation can be prespecified or randomly generated. Commonly used for most cases. programs include PCSTABL (developed at Purdue Univer- A factor of safety is determined by applying the seismic co- sity), UTEXAS4 (developed at the University of Texas at efficient in the limit equilibrium stability program. An allow- Austin), SLOPE/W (distributed by Geo-Slope International), able factor of safety is selected such that behavior of the slope, and SLIDE (RocScience). in terms of permanent deformation, is within a range con- An important consideration in the limit equilibrium ap- sidered acceptable. A factor of safety (or C/D ratio) of more proach is that the rate of loading during the earthquake is rel- than 1.0 when using the peak seismic coefficient implies no atively fast. For this reason, in most cases undrained total slope movement, while a factor of safety less than 1.0 when stress strength parameters should be used in the stability using the peak seismic coefficient implies permanent move- model, rather than drained or effective stress parameters. The ment. Typically, the seismic coefficient is assumed to be 50 per- undrained total stress parameters are obtained from static cent of the peak, as noted above, reflecting the acceptance of strength tests conducted in the laboratory, from in situ 1 to 2 inches of permanent movement. In this case, as long as strength testing or from empirical relationships. the factor of safety is greater than 1.1 to 1.3, the deformations Although the rate effects associated with earthquake load- are assumed to be minimal. ing may result in a higher undrained strength during the first The drawback of the limit equilibrium approach lies in cycle of loading, various studies have shown that after 10 to the difficulty of relating the value of the seismic coefficient to 15 cycles of significant loading, as might occur during a seis- the characteristics of the design earthquake. Use of either the mic event, degradation of the undrained strength often oc- peak ground acceleration coefficient or the peak average hor- curs. In view of this potential for degradation, a conservative izontal acceleration over the failure mass, in conjunction with approach is to use the static undrained strength in the seismic a pseudo-static factor of safety of 1.0, usually gives excessively stability analysis. Where this simplification is questionable, conservative assessments of slope performance in earthquakes. cyclic loading tests can be conducted in the laboratory to ob- However, often little guidance on selection of the seismic tain a more precise definition of the strength parameters dur- coefficient as a fraction of the peak ground acceleration is ing cyclic loading. available to the designer. In the limit equilibrium approach, a seismic coefficient is Los Angeles County uses a nominal seismic coefficient of used to determine the inertial forces imposed by the earth- 0.15 and requires a factor of safety >1.1. The recently pub- quake upon the potential failure mass. The seismic coefficient lished guidelines by Southern California Earthquake Center used in the analysis is based on the site-adjusted PGA ad- (SCEC) (2002) for the State of California suggests reducing justed for wave scattering effects using the factor defined in peak ground acceleration map values in California by about Chapters 6 or 7. The vertical acceleration is normally set equal 0.3 to 0.6 (depending on earthquake magnitude and peak to zero based on studies that have shown vertical accelera- ground acceleration values) to ensure slope displacements are