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Seismic loads on Retaining walls

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I am struggling with understanding the intent of references and codes for
seismic analysis of retaining walls. Several references suggest the Seed and
Whitman approach to determine additional lateral soil force due to
earthquake: 

P = (3/4*Kh)*1/2*Ws*H^2 = 3/8*Kh*Ws*H^2 

where: Kh = peak ground acceleration 
	 Ws = soil unit weight 
	 H  = soil height behind wall 
   and P  = additional lateral soil force due to earthquake applied at 0.6H
above the base 

Using IBC, the peak ground acceleration would be 0.40*Sds. 

But the references I have do not show examples of the application of this
lateral force in combination with other forces for evaluating sliding
stability or wall strength. For example, is the lateral inertia of the wall
mass calculated separately and included in the lateral force analysis? And
is the lateral inertia due to the weight of soil above the heel and toe also
added? 

The US Army Corps of Engineers manual EM 1110-2-2502 recommends the
Mononobe-Okabe method to determine the lateral force due to earthquake and
also states to add "the inertia force of the wall, including that portion of
the backfill above the heel or toe of the wall". The inertia is determined
by multiplying the mass directly by the peak ground acceleration. 

It makes sense to me to add the inertia due to the wall mass, but also
adding the inertia due to the soil weight above the heel and toe can add
considerable lateral force and seems overly conservative, since the soil is
not a rigid mass. Including these soil masses can significantly increase the
lateral seismic forces for design. So how do others handle the combination
of lateral forces? 

The code is also unclear about the application of the R-value for retaining
wall design. Table 1622.2.5(1) in the 2000 IBC does not explicitly refer to
retaining walls, although item 14 for "other distributed mass cantilever
structures" would appear to apply. But is the R-value applied for sliding
and overturning analyses as well as for concrete design? It makes sense to
me to apply R for concrete design to account for the ductility of the
material. But R should not affect the sliding and overturning, since
stability is directly impacted by the ground acceleration and since
inclusion of R would reduce the effective factor of safety.  

Furthermore, Section 1806.1 of the 2003 IBC states that "Retaining walls
shall be designed for a safety factor of 1.5 against lateral sliding and
overturning." It does not state whether this safety factor applies to
seismic loading conditions nor whether this applies using service loads or
factored loads. What is the intent of the code? I usually reduce the
required factor of safety to 1.1 for seismic conditions vs 1.5 for normal
loading conditions, based on EM 1110-2-2502, Table 4-1. 

In general, it is rather unclear as to what the intent is of the building
codes for such designs. I am interested in how other engineers have
interpreted the seismic provisions for retaining walls. 


William C. Sherman, PE 
(Bill Sherman) 
CDM, Denver, CO
Phone: 303-298-1311
Fax: 303-293-8236
email: shermanwc(--nospam--at)cdm.com

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