For some conditions, in particular for relatively flat slopes ~inclined
at less than about 10°!, permanent displacements are not
strongly influenced by the use of a single-component input motion
or by the orientation of that motion. For steeper slopes in
frictional materials, however, the single-component approach appears
to systematically underpredict slope displacement by an
amount that increases with increasing slope inclination. For
steeper slopes in cohesive soils, the application of a horizontal
recorded motion parallel to the slope tends to systematically overpredict
displacement, also by an amount that increases with increasing
slope angle. The lateral component ~parallel to the strike
of the slope! has no effect on cohesive slopes or on symmetric
failure surfaces in frictional slopes, but its consideration can result
in somewhat lower computed displacements for asymmetric
failure surfaces in frictional slopes.
The true two-dimensional and three-dimensional analyses are
more capable of predicting the permanent displacement of sliding
blocks subjected to actual three-dimensional earthquake motions
than the pseudotangential and true tangential approximations
commonly used in practice. Their response, however, depends on
the details ~amplitudes, frequency contents, durations, and phasing!
of all three components of the input motion. Given the approximate
nature of the sliding block concept, it might appear that
such details are not significant. However the value of the index of
permanent displacement produced by a sliding block analysis will
increase with increasing degree of accuracy with which the
block’s response to actual earthquake motions is modeled. For
most slope stability evaluations, a suite of motions with specified
amplitude, frequency content, and durations is identified and used
as input to seismic stability analyses.