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# Horizontal seismic coefficient reduction

## Horizontal seismic coefficient reduction

(OP)
It is my understanding that "full" values of the horizontal seismic coefficient (Kh) are rarely applied in practice when using any pseudostatic approach available (Mononobe/Okabe, Seed/Whitman, etc). A geotech professor told me there are journals that justify the reduction of Kh for design purposes by means of claiming mass energy distribution effects (by Makdisi I believe) and some other phenomena. Does anybody knows of additional journal/reference/book that define/allow other reduction effects on Kh? The reason behind this is because having a range of 0.3 to 0.7 for Kh seems completely ridiculous, even taking into account California's high seismic activity. Thanks in advance.

### RE: Horizontal seismic coefficient reduction

Well it's very difficult to ignore the force effects, becasue they are very real.  However, if structures are allowed to undergo some "permanent deflection" a portion of those force effects are accomodated by a non-destructive change in position of the structure. One formula often used is:

Kh = 1.66 (Am) (Am/d)^0.24
Am = (1.45 - A)(A)

where d is allowable permanent deformation in millimeters.

### RE: Horizontal seismic coefficient reduction

MSEman - Do you have a reference for that eqn.?  It might be of value to me also, but I'd need the reference as backup.

Thanks,
DRG

### RE: Horizontal seismic coefficient reduction

Based on the FHWA Pub. GEC No. 3, Vol. 1, it is allowed to reduce the pseudostatic coeficient (kh) to half its value, since it is recognized that the method itself is highly conservative.

But in general, if you have a safety factor of about 1.15, your slope deformations should be less than a foot.

### RE: Horizontal seismic coefficient reduction

As geohec has stated, using half of (Kh) is very common.  However, this is not universally accepted.  If you search the literature you will find recommendations from 25% of Kh to 100% Kh.  Although I believe using the full Kh is VERY conservative, I have yet found a good argument for reducing it......other than just acknowledging that using the full Kh is conservative.

I think this is a case where Code requirements and Reality don't mesh well.  We are forced to use Kh in our analysis, but by using it it make all our models fail.  Therefore, we come up with "conventions" to convince ourselves that only using a fraction of the Kh is acceptable.  While at the end, we are only designing to mitigate for a smaller earthquake.

### RE: Horizontal seismic coefficient reduction

There's a table in Duncan and Wright's book on shear strength and slope stability that lays out all of the pseudostatic coefficients and their justifications (many of the methods also include reduced shear strengths). Pseudostatic analysis is more of an index test than anything else - the PGA is on the slope for a millisecond, so why should it govern anything, really?

### RE: Horizontal seismic coefficient reduction

there is a thread that previously discussed this but it appears to be missing...maybe it's still there but i couldn't find it in my responses for whatever reason. don't just blindly apply reductions without at least having some understanding of the implications. application of reductions should be done only when you recognize the increased deformation/movement that is anticipated to occur by using the reduction.

it's sort of like many soils--the strength testing suggest the use of say 8 ksf bearing pressure however when you run a settlement analysis, it indicates that 3 inches of settlement may occur. but then at 3ksf, you're down to 1/2 inch. if the structure can handle 3 inches of settlement, then go for it...if it cannot, then use the more appropriate lower value. here's some good links to nchrp 611 which is the most recent publication i've seen (the documentation in the links below is in line with the asce7 proposed revisions that i have seen):

http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_611.pdf
http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_611v2.pdf
http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_611appendix.pdf

### RE: Horizontal seismic coefficient reduction

Agree with howardoark, some people focus on PGA when it really does not govern since it occurs over a millisecond, and the slope is not a rigid body.  Design methods by Bray et al. (1998 and 2007) from UC Berkeley let you evaluate Kh value to use with corresponding estimated slope deformation.  He also discusses acceptable ranges of deformation.  The methods take into account the site seismicity, yield acceleration, and response of the slope.  This method is generally standard of practise in California (for simplified methods).

A new study coming out from Sitar at UC Berkeley shows how seismic earth pressures are significantly lower than those predicted by Mononobe-Okabe.

### RE: Horizontal seismic coefficient reduction

Hi moe333.  Know where I can get ahold of Sitar's report?  Retaining wall loads are QUITE important to us on several projects right now (and to the taxpayers and water users that would have to pick up the cost of modifying the walls if they don't measure up).  I had heard from one of his colleagues at Berkeley that it was coming, but didn't know if it's available to the public yet, how high his PHAs were, how study was done, etc.

Thanks,
DRG

### RE: Horizontal seismic coefficient reduction

Hi dgillette, I'm going to a dinner talk this week that Sitar is giving on the topic.  Will let you know Thursday when and where the paper will be available.

The summary I read said the measured load distribution was triangular, not inverted triangular.

### RE: Horizontal seismic coefficient reduction

Sorry I'm joining the discussion a little late.

The 'right' value of Kh has been quite of an issue recently in Italy due to the new seismic laws issued.

If Base  shear= kh*weight force of structure, It has been observed that kh is never equal to Ag/g, i.e: PGA, rather a part of it.

probably the Japanese came out with a first approximation by Noda's relationship (1976)

Later, kh in slopes has been most frequently related  to 0.5, and in Duncan & Wright's book, as howardoark says, a table of values ranging from 0.17 to 0.75 (or so) are reported.

It is true that pseudostatic analyses are only raw approximations, it is also true though that dynamic analyses are more complex, require a design seismic signal, yield as an output a displacement which is often awkward to handle (compared to a traditional factor of safety).

Recent research in the Italian territory has shown that the 'real' kh ranges from 0.18 to 0.28 in function of PGA, and soil type.

Analyses have been based on a comparison of newmark-type analyses and pseudostatic analyses, on slopes and on retaining walls.

It has always been evident that pseudostatic analyses of slopes and walls yielded overconservative results.

Especially walls turned out to be un-designable by the standard, traditional budgets allowed...

### RE: Horizontal seismic coefficient reduction

I'm not sure there is a "right" Kh value.  It is specific to the system you are trying to protect, the tolerable deformations, and the level of risk your project can accept ie; do you design for a 500 year return period, or 2,500 years?

### RE: Horizontal seismic coefficient reduction

You're right, the real value of the kh would be the quota of the weight force which makes up the shear force in relation to a given earthquake signal (horizontal component).

As you say, it's a function of many things among which structure ductility in buildings and soil ductility in slopes and walls.

The 'right' value I was referring to was a 'reference' value stemming from dynamic analyses

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