Retaining wall displacement

[Okiryu]

Hi, does anybody have references on how to determine the amount of displacement of a retaining wall due to seismic forces? I am understand that there are FEM techniques but this is for a preliminary study so I am just looking for something that can be done manually. Thanks for your input.

 

[ATSE]

Not well defined.
See NCHRP Report 611 for a semi-readable explanantion. See Prof Bray (UCB) and Kramer (UW) for a slightly more high-powered approach.
For simplified analysis (done by almost everyone except PhDs), there is a tradeoff between the pseudo-acceleration used in the design lateral forces and the resulting permanent wall displacement (via Newmark charts / equations).
For design acceleration = 0.5A, where A is the peak ground acceleration (g), horiz wall displ = 10*A (inches). So for A = 0.5g, displ = 5". Seems a bit high to me, but that's what the smart guys say.
I think AASHTO commentary says expect 2" to 4" displ if using reduced (0.5A) accelerations. Seems like a good rule of thumb in the absence of other recommendations.
Even less well defined and understood is the permanent wall tilt.

 

[Okiryu]

ATSE, thanks for the references. I was able to download the NCHRP document. It is useful. I was also looking at Prof. Kramer's book (Geotechnical Earthquake Engineering) and found a simple method to calculate displacements. This method is the Whitman and Liao method. You may also find it useful for your practice.

Also, the code that I am using for my DoD project, indicates that the seismic coefficient should be Ss/2.5, which is actually my PGA. I found it high since as you mentioned most of the references suggest seismic coefficients less than the PGA.

Thanks again...

 

[Doctormo]

In my opinion, this is pretty much voodoo engineering when trying to predict retaining wall movement due to a seismic event. What are you going to do with this information that will most probably not be correct?

Richards & Elms has some good discussion on the concepts of the seismic event and structures. You would really have to know the seismic event profile to predict the movement thus one would have to acquire a lot of information to make an educated prediction then you would still probably not be correct, similar to settlement estimates that are routinely off by quite a bit.

You could design a wall for the full PGA and As and would probably still get seismic movement even though this would be considered the "no movement" situation. If the structure is extremely stiff to reduce movement, you would be designing for Ko vs. Ka conditions so this comes into play as well.

To me it is more of a minimal movement vs. significant movement situation where you can design for one or the other with the actual movement being somewhat indeterminate.

 

[Okiryu]

Doctormo, agree with you that this is a complex problem. But just wanted to check displacements for a preliminary evaluation of an existing wall. I do not have a FEM software available so I tried to do something practical based on an accepted method in geotechnical engineering practice.

 

[Doctormo]

If you can create an accurate static analysis model of the wall, you should be able to calculate the additional seismic force required to drop the sliding FS to 1.0. You could compare that to the expected pseudo-static force from the design PGA or As acceleration. If the structure can handle the maximum value, the movement would be small. If the seismic increase drops the FS <1.0 then some movement would be expected. You can look at the displacement formulas (Richards & Elms and other guides)and back-calculate what deformation would be required to reduce the Kh value to what the structure can tolerate before yielding.

This is pretty rough and would not tell you how much a wall might lean out or how much settlement or cracking you might get behind the wall after movement but it is better than nothing I suppose.

 

[Okiryu]

Doctormo, thanks for the advise. Our approach is similar to the one you described: we are trying to get the seismic force to get a FOS of 1, then calculate rough displacements using the Whitman and Liao method.