Use of Mononobe-Okabe equations in seismic design of retaining walls in shallow soils

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Published 16 November 2013
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Use of Mononobe-Okabe equations in seismic design of retaining walls in shallow soils

In pseudo-static analysis, the Mononobe-Okabe (M-O) solution is typically applied to determine
seismic earth pressures acting on retaining walls where resulting displacements are relatively
large. These equations require the input of a horizontal seismic coefficient which is frequently
chosen to be equivalent to the free-field Peak Ground Acceleration (PGA). Recent work by
Anderson et al. (2008) and Al Atik & Sitar (2008, 2010) have highlighted the conservatism of
derived earth pressures when applying PGA to the M-O method.

Based on dynamic numerical analysis using US-centric time histories, Anderson et al. (2008)
described the effects of wave-scattering and propose height-dependent scaling factors to reduce
PGA to derive earth pressures. Al Atik & Sitar (2010) studied earth pressure responses on
cantilever walls using centrifuge model testing and numerical analysis based on a number of
different acceleration time histories. They propose amongst other recommendations that for
both stiff and flexible walls, using 65% of the PGA with the M-O method provide a good
agreement with measured and calculated pressures.

This paper describes the analysis of cantilever retaining walls using deconvoluted acceleration
traces of 7 acceleration time histories appropriate for the shallow soils (Class C, NZS
1170.5:2004) of parts of the North Island (North A, Oyarzo-Vera et al., 2012) of New Zealand.
Results of numerical analyses for cantilever walls using Quake/W & Sigma/W 2012, based on
these deconvoluted traces, are presented. The calculated seismic earth pressures are compared
to the M-O method. It is shown that where maximum outward wall displacements at the top of
the wall fall between ~0.7% – 5% of the exposed wall height, calculated maximum dynamic
active forces (PAE) had a reasonable match against M-O derived forces based on a seismic
coefficient equal to 65% of the free-field PGA up to 0.3g. When free-field PGA exceeds 0.3g,
the analyses suggest that M-O derived forces based on 65% of free-field PGA over-predict
PAE. It is noted that these are geographic- and soil-specific recommendations, based on a
modelled wall height of 3m.

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Issue 1
Volume 38
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ISSN 0111-9532