Seismic Lateral Pressures on Retaining Walls 5

[DCBII]

What do I use for lateral pressures on a retaining wall? Is there something similar to the active earth pressure coefficient for seismic loads?

How about for a basement wall restrained by a floor diaphragm at the top?

I have seen people use inverted pressure triangles but I am unsure of where this procedure came from and if it is a commonly accepted method. I also don't know where they come up with their pressures. Is it something the geotechnical engineer usually provides?

Any help would be appreciated. I don't have a lot of experience in this area.

 

[FixedEarth]

This is a vast field. There is the geotechnical side of retaining structures and any Soil Mechanics book will have at least two chapters on it. For example "Soils and Foundations" by Lieu and Evett is very practical text.

For the structural portion of it, it is beautifully covered in "Basics of Retaining Wall Design" by Hugh Brooks. Both books are on Amazon This will build your library and will give you time to absorb the fundamentals.

 

[weab]

I believe that the inverted triangle was standard procedure as of about 10 years ago or so. I don't know if it is still standard since I haven't done much geotechnical for a while. I have seen this provided in soils reports from the geotech. Perhaps there are ways to determine this yourself, but I find much of this sort of stuff to be too "black box". I recommend a geotech report.

 

[muuddfun]

Look at the following reference, it will explain a lot about where the loads come from. It also shows that the inverted triangular distribution is incorrect.


PEER 2007/06 - Development of Improved Procedures for Seismic Design of Buried and Partially Buried Structures
Linda Al Atik, Nicholas Sitar

http://peer.berkeley.edu/publications/peer_reports/reports_2007/web_706_ATIK_Sitar.pdf

 

[dgillette]

I never really understood the inverted triangle, but Al Atik and Sitar (and others, I think) have flipped it back over to ~0 at the top and max at the bottom.

 

[irawanfirmansyah]

DCBII,
To calculate seismic earth pressure diagram, we can divide retaining walls into 2 groups:
- Yielding walls, such as cantilever walls
- Nonyielding walls, such as basement walls (braced by basement floors).

Triangular earth pressure diagram is applicable for the 1st group of walls, whereas "close to inverted triangular pressure diagram" is applicable to the 2nd group of walls.

You have to use numerical method to get the real shape of the "close to inverted triangular pressure diagram" (larger pressure close to the top)

You can use Mononobe Okabe method to calculate seismic pressure for yielding walls, and Seed & Whithman method or Wood method to get simplified Nonyielding walls pressure diagram.
Look at the book titled "Geotechnical Earthquake Engineering" by Steven L. Kramer

 

[vulcanhammer]

Probably the best reference I've got is this:

http://www.vulcanhammer.net/geotechnical/itl9211.pdf

I also have the Atik and Sitar paper as well.

Also:

http://www.vulcanhammer.net/geotechnical/retaining.php

http://www.vulcanhammer.net/geotechnical/soil-dynamics.php

http://www.pz27.net

 

[Geostructsparks]

The seismic active pressure is generally computed using some method (Mononobe-Okabe eqn for example) then divided back into static and seismic components. The static pressure is still applied as conventional (triangular for a non-braced wall, rectangular for braced wall). The additional earthquake pressure (deltaK = Ka - Kae) can be applied, depending on the author, at the mid-height of the wall (rectangular distribution) or 2/3 height (inverted triangle). At least one of the most recent papers I have read (2010, last month), however, indicates the active earthquake pressure still is at 1/3 of the wall height similar to the static active pressure.

Using the Mononobe-Okabe equation, most sources recommend using the horizontal seismic coefficient as half of the peak ground acceleration (PGA), and not considering any vertical seismic coefficient. Unless the PGA is above about 0.2g, seismic design with lower factor of safety generally does not exceed the static design with static FOS. If you have uphill slopes, the pressures may be considerably higher.

For braced walls, there are different ideas, none of which appear to be verified with theory or testing. One (AASHTO LRFD bridge design manual) is to use M-O to get the pressure, but any braced or restrained wall should use Kh=1.5*PGA. I think this is a bit severe, I don't recommend it unless designing per that code. Another idea would be to proportionally add the active earthquake component to Ko, the at-rest pressure (I have a paper by Hall, 1979). I suppose this depends on whether you are designing the wall for Ka or Ko initially.

Check with your geotech engineer to get recommendations for your project. We also have the M-O equation on our site.

 

[GPapazafeiropoulos]

Dear DCBII,

You can design a retaining wall either by considering
a) an upper limit for its distress or
b) an upper limit for its deformation.

In the first case the wall is designed against the dynamic earth pressures which it experiences due to the dynamic response of the retained soil, whereas in the second case the wall is designed with respect to the maximum deformation allowed in order for it to remain operational after the seismic event.

There are in general three types of retaining walls:
1-Walls which are assumed to displace laterally a sufficient
amount to produce a state of plastic equilibrium behind them.
2-Walls that are perfectly non-yielding, regardless of the dynamic response of the retained soil.
3-Walls that are able to deform is such an amount, which imposes to the retained soil to respond linearly elastically.

For each of these three categories of retaining walls, one of the two aforementioned methods of design can be selected.

So we have for the various methods used for seismic design:

a-1) Mononobe-Okabe (Mononobe & Matsuo 1929, Okabe 1926)
Seed-Whitman (Seed & Whitman 1970)
Steedman & Zeng 1990
Generalization of Steedman-Zeng (Choudhury & Nimbalkar 2006)
b-1) Richards & Elms 1979
Nadim & Whitman 1983
Whitman & Liao 1985
a-2) Matsuo & Ohara 1960
Wood 1973
Scott 1973
Veletsos & Younan 1994a
a-3 & b-3) Veletsos & Younan 1993, 1994b, 1997, 2000

Because during the dynamic loading there exists dynamic iteraction between the retaining wall and the retained soil, the issue of seismic design of walls is one of the most complicated problems of geotechnical earthquake engineering. Hence the numerous methods which I cited above. In general, the more constraints a retaining wall has along its height, the larger the magnitude of the dynamic earth pressures which it will sustain.

Engineering judgement plays an important role in the selection of the most suitable method for the design.

Best regards,

George Papazafeiropoulos
_______________________________________
Second Lieutenant, Hellenic Air Force
Civil Engineer (M.Sc.), Ph.D. Candidate

 

[tumbleleaves]

The bigger questions is: What is the justification for using these EQ pressures? I have no knowledge of failure of engineered conventional retaining walls, of any sort whether designed for EQ or not. Non-engineered walls yes, engineered walls no.

I am also hesitant about the MO equation. A very simplified equation similar to Rankine earth pressure theory. The theory requires a yielding wall and a sand, these conditions don't match most walls in building construction. Also, the force being contingent on the movement of the wall, the effective acceleration-force is a poor guess in 99% of the designs I've seen.

I've run into this recently: My understanding is that the new Building Code here in CA requires geotechs to include a seismic pressure in the report. This has resulted in very poor design work, because the geotech is just abiding, and so is the structural that designs to his report: None of them look at the wall as whole! Sometimes where displacements are fine the seismic pressures don't control, because the owner is acceptable to movement and it won't cause safety issues. But, instead you get an overly designed wall that is a tremendous waste, with a seismic design that will keep a wall from encroaching a few inches into an area outside the roadway shoulder in the middle of nowhere protecting nothing.

 

[JoshPlumSE]

I've been familiar with Mononabe - Okabe for years, but the other methods that GPapazafeiropoulos mentioned are new to me. So, thanks for educating me (I'll give you a star for that).

All that being said, I think we (structural engineers like me) could beneft from a better defined criteria for when seismic forces need to be considered in retaining wall design.

After all, tumbleleaves has a really good point.... The vast majority of existing retaining walls in California have NOT been designed considering seismic pressures. But, we haven't have many failures in past seismic events. At least not for the engineered walls. That might mean that we generally have enough sense to realize when wall failure (meaning significant deflection, not britte fracture) is truly a critical life-safety issue.... But, I also think that we're starting to get some very basic walls which are being totally overdesigned.

 

[dgillette]

Look in the October ASCE JGGE, "Seismic Earth Pressures on Cantilever Retaining Structures" by Linda Al Atik and Nick Sitar, p. 1324-1333. It's nice to see some centrifuge model tests to go with the theories and numerical models. Centrifuge models are the next best thing to a full scale experiment, and a whole lot cheaper.

Al Atik and Sitar put the triangle back the way Mononobe and Okabe had it originally, with the maximum at the bottom, not the top. They also suggest that it is unnecessarily conservative to use full M-O pressure.

 

[GPapazafeiropoulos]

Dear Joshplum,

Thank you for your comments and the star...

I think that the scarcity of the engineered retaining wall failures is due to the fact that they are usually overdesigned. The methods I mentioned in my previous post are intended to lower this conservatism, which, in cases of retaining walls of large length (e.g. in roads near unstable soil or rock slopes) can lead to huge economical losses.

Best Regards,

George Papazafeiropoulos

 

[InDepth]

I'm not sure about over design....but some geotechs like to think that retaining walls used in basement construction haven't failed because the soil arches between the building floor diaphragm (essentially releasing soil load seen by the wall). Furthermore, with buildings being built closer together with basement walls being built essentially up against each other, soil loads are essentially eliminated.

For cantilevered retaining walls it makes seense to be that the max is at the bottom...essentially slope stability with an added vectorial component. I guess that the magnitude of the force though is dependent on the eq frequencies as it corresponds to the natural frequency of the soil.

 

[ItsOnlyDirt]

I think InDepth has touch on the real issue, how much of the EQ do soils really see?.

I have been in large earthquakes (7.2) looking at major slopes that are failing in the static case, during the EQ they didnt fail, minor cracking yes, collapse no. It suggests to me that the EQ coefficients for structures are often way too high for soils providing some permanent deformantion can be tolerated.

The other thing to bear in mind is most soils behave in a near undrained manner during EQ loading.