Lateral resistance in rock 2

[jdonville]

Two related questions as follows:

1) AASHTO HB-17 Figure 5.6.2A.b shows simplified earth pressures for cantilevered walls with discrete elements. The equation shown for resistance in rock is (as I read it):

Pp = (s*D)/{[1+tan(beta_prime)]*[D+2^0.5*b]}

Is this formula correct? It seems to me that this reading of the equation would tend to reduce the allowable Pp as the element width b increased. I suspect that the equation should read:

Pp = {(s*D)/[1+tan(beta_prime)]}*[D+2^0.5*b]

Confirmation of the second reading would be appreciated (provided that it is the correct answer!!!).

2) If this approach can be used for discrete vertical elements for cantilevered walls, can this approach be used to model the lateral resistance for drilled shaft rock sockets? I have looked around and can find no references for the stress distribution to use for lateral resistance of drilled shafts in this situation. References and/or links to same would be appreciated.

Many thanks (I will happily award purple stars for useful and/or enthusiastic responses),

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

 

[eric1037]

Jeff:

Try these:

Carter, J. P., and Kulhawy, F.H. (1992). "Analysis of laterally loaded shafts in rock." J. Geotech. Engrg., ASCE, 118(6)

Reese, L. C. (1997). "Analysis of laterally loaded piles in weak rock." J. Geotech. Geoenvir. Engrg., ASCE, 101(7)

Zhang, L., Ernst, H., and Einstein, H. H. (2000). "Nonlinear analysis of laterally loaded rock-socketed." J. Geotech. Geoenvir. Engrg., ASCE, 126(11)

 

[eric1037]

Jeff:

Here are a couple more references.

http://www.decf.berkeley.edu/~bearto/lateral.htm

http://www.modot.state.mo.us/business/manuals/documents/3.81_LRFDtitle.pdf

 

[jdonville]

eric,

The references are much appreciated.

All,

I still would like an answer to the first question, however, as I am sure that it will come up when I have no time to ask the group.

I will be posting question No 1 in the AASHTO forum, as well.

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

 

[Panars]

Jeff-

The equation in the 17th edition is incorrect. I have it penciled in correctly (as in your second equation) in my copy.

This was either discussed here awhile ago, or I discovered the error while reviewing earlier editions to find the correct figures for the footings near a slope.

I'll check to see if this was in a published errata when I'm in the office tomorrow.

I have used this equation for drilled shafts too, but I check to make sure the pile spacing isn't too close. The equation assumes that a wedge the same width as the shaft is pushed out of the ground. If the shafts are close, this may not be conservative. The equation gives results that are similar to Broms' equation for short laterally loaded piles.

 

[jdonville]

Peter (Panars),

Thanks for the sanity check. I did not find this correction in the E4 errata.

Would it be reasonable to take the shear strength term 's' as the rock mass UCS divided in half as follows:

Co = UCS of intact rock from lab testing
Cm = alphaE * Co, alphaE based on RQD
s = Cm/2

or is this unduly conservative?

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

 

[Panars]

It is not in the errata, but it is correct in the LRFD version of the AASHTO specs.

For alphaE, you are using the reduction factor for side resistance of drilled shafts in rock (4.6.5.3.1), correct?
That seems reasonable to me, but alphaE has a lower limit of 0.15. This means it doesn't get any lower for RQD<63. For very broken rock, you may have to treat is as a soil.

 

[cap4000]

Check out this thread 255-104024. Unreal Confusion. Good Luck.

 

[jdonville]

cap4000,

Thanks for refreshing my memory on that thread. I have found the Caltrans document you spoke of. Truly confusing.

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

 

[jdonville]

cap4000,

I think that the confusion may be abating

After looking at the Caltrans formula given on page 30 of this document:

http://www.dot.ca.gov/hq/esc/techpu...ridge-design-specifications/page/section5.pdf

Pp = [Sm*(Do+b*sqrt2)]/[1-tan(betaprime)]

the diagram shown indicates that this is the magnitude of the uniform pressure block assumed to act. 'betaprime' in the Caltrans example is measured as a negative angle, thus the unary minus in the demoninator term.

If we assume 'betaprime' to be measured as a positive angle when below the horizontal, and multiply by Do to obtain the equivalent force as shown in AASHTO HB-17, we get the second equation from my original post in this thread.

Not having HB-16 to compare against, I cannot say if this is consistent with the treatment by that version of the AASHTO specs.

I would very much like to have a citation of the paper showing the development of the formula. Would it be in Teng's Foundation Design, possibly? Anyone have a copy they can check and report back on?

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

 

[jdonville]

All,

After some digging through various materials, and looking for the wedge model that Panars mentioned, I think I have found a possible source - the cohesive soil wedge concept shown in FHWA SA-91-048 pp. 316-317 (the COM624P User Guide) attributed to Reese (1958) in Transactions of the ASCE vol. 123, p.1071.

Panars, is this the concept you referred to?

According to the COM624P publication,

Fp = s*b*D[tan(alpha)+{1+K}*cot(alpha)] ## shear along bottom of wedge and shear along face of pile ## + 1/2*gamma*b*D^2 ## normal force along bottom of wedge in horizontal direction ## + s*D^2*sec(alpha) ## shear force along sides of wedge ##

Playing with this equation for the ultimate resisting FORCE (NOT pressure!), assuming the angle alpha = 45 degrees, and neglecting the normal force on the bottom of the wedge, it seems to work out to approximately s*D*(D+b) with some simplification of the coefficients.

The upshot is that the AASHTO formula shown in the second equation from my original post in this thread seems valid and slightly conservative, assuming that the block/wedge failure mechanism is valid or is a conservative assumption.

cap4000, I think that we can lay this one to rest.

I hope that this has reduced the confusion, rather than increased it!

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

 

[jdonville]

Panars,

Based on some reflection, I think that the value of s (or sm, in Caltrans parlance) for applications involving drilled shafts should probably be taken as the value determined for qSR, for consistency.

Your thoughts?

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

 

[Panars]

The following is from the AASHTO LRFD commentary for Section 3.11.5.6:

"Where a vertical element is embedded in rock, i.e. Figure 2, the passive resistance of the rock is assumed to develop through the shear failure of a rock wedge equal in width to the vertical element, b, and defined by a plane extending upward from the base of the element at an angle of 45 degrees."

So the portion of the equation, sD(D+sqrt(2)b), is the shear strength of the rock mass times the area of the wedge subject to shearing (rectangular area along the wedge's hypotenuse at 45 degrees and two triangular areas on the side of the wedge). This is similar to Reese's soil wedge for cohesive soil.

I disagree about using qsr for the value of s or sm (it's sm in the LRFD specification too). The parameter qsr is the unit side resistance at the rock/concrete interface (i.e. a constructed joint). I think s could be taken as Cm/2, as you suggested earlier, or you can estimate it using the Hoek-Brown criteria.