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# Gravity wall seismic design - inertial force?2

## Gravity wall seismic design - inertial force?

(OP)
Hello!
When designing a concrete gravity wall against sliding, overturning and bearing capacity in a seismic design situation by using a pseudo-static analysis, do you take into account the inertial force of the wall, expressed as Fi=W*k (where Fi - inertial force, W - wall self weight, k - horizontal coefficient of seismic acceleration)?
In every book I look, they explain the pressure the earth exerts on the wall, but they don't talk about the design of the wall after we defined the soil forces on the wall. For example, by using the Mononobe-Okabe method we take into account the inertial forces of the backfill, and that is all contained into the PAE force, but do we need to take the inertial force of the wall for the stability check?
Also, my question refers to making the design on the basis of stresses. In the other design method, where the design is based on allowable deformations, the inertial force of the wall is taken into account because it's needed to define the allowable ground acceleration.
As far as I remember, during classes in my faculty we never took the inertial force of the wall, but I found sources which take it.
What are your experiences regarding the subject?

### RE: Gravity wall seismic design - inertial force?

The inertial force of the wall and of the soil resting on it should be included, but not all of it concurrent with the seismic earth pressures. From AASHTO LRFD 2012 11.6.5.1:

"To investigate the wall stability considering the
combined effect of PAE and PIR and considering them not
to be concurrent, the following two cases should be
investigated:
• Combine 100 percent of the seismic earth pressure
PAE with 50 percent of the wall inertial force PIR and
• Combine 50 percent of PAE but no less than the
static active earth pressure force (i.e., F1 in
Figure 11.10.5.2-1), with 100 percent of the wall
inertial force PIR."

### RE: Gravity wall seismic design - inertial force?

(OP)
@avscorreia

Thank you, this is great information!
I wonder though, and I'd like to know, what recommendations do the other standards give and what procedures do engineers from other parts of the world use (I'm from Europe).
Eurocode 1998-5 only mentions that those inertial forces should be used, but doesn't specify how:
7.3.2.2. (1)P For the purpose of the pseudo-static analysis, the seismic action shall be
represented by a set of horizontal and vertical static forces equal to the product of the
gravity forces and a seismic coefficient.

### RE: Gravity wall seismic design - inertial force?

I'm from Europe as well and I used this AASHTO recommendation for the design of a semi-tunnel next to a slope in a high seismic area.

The reviewer didn't like our option and complained that we sould have used a consistent set of standards and concurrent inertial forces. We replied that the AASHTO recommendation was based on extensive studies by Al Atik and Sitar (2012), as is mentioned in the commentary to 11.6.5.1, and that EN1998-5, in point 7.3.1(1)P refers that "Any established method based on the procedures of structural and soil dynamics, and supported by experience and observations, is in principle acceptable for assessing the safety of an earth-retaining structure.". Our design was accepted at the time.

Hope it helps.

### RE: Gravity wall seismic design - inertial force?

By the way, the report that AASHTO refers to is available at the following location:

### RE: Gravity wall seismic design - inertial force?

Just having an analogy with piles seismic design...for seismic loading, there are two type of loadings that affects the structure: inertial and kinematic loadings. My understanding is that inertial loadings are inherent to the response of the structure. Kinematic loading is based on free field deformations (soil deformation due to the earthquake loading which can be considered as the earth lateral pressures in the case of retaining walls).

For pile seismic design in Japan, the inertial and kinematic loading are treated separately since they do not occur at the same time. Japanese approach for inertial and kinematic loading may be in agreement with avscorreia's input about the AASHTO guidelines - both inertial and kinematic loadings do not act 100% at the same time...

See page 25 the PDF of this document from Boulanger et al.:

https://faculty.engineering.ucdavis.edu/boulanger/...

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