required rock socket embedment for caissons 9to develop fixi

huangyhg

required rock socket embedment for caissons (to develop fixi
it seems like everyone uses 1 diameter of embedment to achieve this (i.e. fixity of the caisson to the rock). but i could have sworn i read (somewhere) that research has indicated that anywhere from 1 to 3 diameters may be required. can anyone recommend a (reliable) reference? thanks in advance!
1 diameter seems small to me.
i would suggest posting this on the foundation engineering forum to get some advice from the geotechs.
to better know forces and deflections, you need to model this with fea with soil springs and rock springs, based on lateral modulus. the caisson embedment should be at least the minimum bedrock penetration prescribed be the soils report.  
the soil/rock lateral stiffness is materially non-linear (p-y curve) but for the small caisson head deflection most se's are going to tolerate, a linearly elastic soil/rock spring is ok in my opinion.  doing material non-linear fea based on a geotechnical parameters known to one or two significant figures is "putting lipstick on a pig".
consider whether the top of your caisson is "fixed head" or "free head" and i usually model the caisson as having a cracked cross section (ieff = 0.5 igross) as a simplification.
the soil stiffness immediately at the top of the pier, the depth of overburden and the pier head bc's affect forces and deflections for laterally loaded piers much more so than the bedrock penetration is my experience.

from structural point view, you will need more than 1 dia to achieve full fixity, but 1 dia would be ok for a shear sucket/key, depending on the property of the rock.
  
rock mechanics is actually very different to soil mechanics. in rocks, the critical factor is usually not the strength of the rock, but the size and orientation of the existing failure planes(cracks).
for the bridges with drilled shafts i've designed, i've always used l-pile (p-y curves) to locate fixity.  i've found that unless the unsupported length of the shaft is very long, that it just doesn't take much embedment to achieve fixity.  i seem to recall the 1d rule of thumb, too, but i think aashto lfd recommends 3d minimum depending on orientation of bedding layers.
also nearly every geotech report i've seen says to ignore the top 5' or so of rock due to it either being weathered or to account for spoilage due to drilling.
i've also analyzed several signs on drilled shaft foundation and found similar results.