# Newmark's Method

**Topics:**Soil mechanics, Shear stress, Triaxial shear test

**Pages:**32 (6968 words)

**Published:**April 4, 2013

Seismic Slope Stability

Earthquakes expose slopes to dynamic loads that can reduce the soil shear strength and cause instability. During the past 30 years, signiﬁcant advances have been made in the understanding of earthquake ground motions, nonlinear stress–strain properties of soils, strength losses due to earthquake loading, and dynamic response analyses for earth slopes. This progress has resulted in development of sophisticated procedures for analyzing stability of slopes subjected to earthquakes. At the same time, advances have been made in the use of simpler procedures for screening analyses, to determine if more complex analyses are needed.

ANALYSIS PROCEDURES

Detailed, Comprehensive Analyses

Comprehensive analysis procedures are generally used for any large embankment or any slope or embankment where the consequences of failure are high or signiﬁcant soil strength losses occur. Although the speciﬁc details and steps of these procedures may vary, the general approach that is used is as follows (Seed, 1979; Marcuson et al., 1990):

1. Determine the cross section of the slope and underlying foundation that is to be analyzed. 2. Determine, with the aid of geologists and seismologists working as a team, the anticipated acceleration–time history for the ground beneath the dam. This should account for attenuation of motion away from the causative fault and ampliﬁcation of motion as waves propagate upward through foundation soils overlying the bedrock. 3. Determine the static and dynamic stress–strain properties of the natural soils and ﬁll materials within and beneath the slope.

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4. Estimate the initial static stresses in the slope or embankment prior to the earthquake. This may involve the use of static ﬁnite element analyses in which the sequence of construction is simulated, or simpler methods. 5. Perform a dynamic ﬁnite element analysis to compute the stresses and strains induced in the embankment by the earthquake acceleration– time history. 6. Estimate the reductions in shear strength and increases in pore water pressure that will result from the earthquake. The most sophisticated dynamic analyses may include computations of reductions in strength as an integral part of the dynamic analysis in step 5. 7. Compute the stability of the slope using conventional limit equilibrium procedures with the reduced shear strengths determined in step 6. This may require analyses using both undrained and drained shear strengths to determine which strengths are most critical. 8. If the analyses indicate that the slope will be stable after the earthquake, compute the permanent displacements. If strength losses due to cyclic loading are small, a Newmark-type sliding block analysis may be used for this purpose (Newmark, 1965). However, if strength losses are signiﬁcant, other methods should be used. For example, Seed (1979) showed that pseudostatic analysis procedures did not adequately reveal the problems with large displacement for the Upper Van Norman Dam, and he used the concept of a strain potential to evaluate the displacements. Conceptually, a complete nonlinear ﬁnite element analysis should be able to calculate any permanent displacements in a slope or dam; however, such analyses are very complex, involve considerable 161

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SEISMIC SLOPE STABILITY

uncertainties, and are seldom performed in practice. The details involved in evaluation of dynamic soil properties and performing the type of dynamic response analyses outlined above are beyond the scope of this book. However, simpler procedures, to determine if detailed analyses are needed, are described in the following sections.

One of the earliest procedures of analysis for seismic stability is the pseudostatic procedure, in which the earthquake loading is represented by a static force, equal to the soil weight multiplied by a seismic...

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