Siesmic Bearing Capacity with Liquefied Ground

[muuddfun]

What do you consider to be the bearing capacity of ground that has liquefied?

I am checking a design for a large amusement park ride that was submitted to a city I review for.

The ride is 300 feet tall.
The ride was designed with a spread footing that is a hexagon that is 60 foot wide, with 24'-10" sides.

The wind load gives about 23,000 Kip*Ft overturning at maximum.
The seismic gives about 11,000 Kip*ft overturning.

The footing is 6 foot thick with the bottom set at 8 feet below the ground surface.

The groundwater is about 17 to 18 feet below grade.
The pga is about .6g
The top of the first liquefied layer is from 18 feet down to about 27.5 feet.

The soil profile is a silty sand down to about 15 feet, say phi of 30 deg.
From 15 to 18 feet is a silt.
Then from 18 to 27.5 is sand, and silty sand that is liquefiable.
From 27.5 to about 32 feet is silty sand that does not liquefy.
From 32 to 38 feet is another liquefiable layer.

From 38' down are several clay layers with thin sand layers in between that are liquefiable at 42.5 to 44 feet, and from 46.5 to 51 feet.
Below 51 feet is bedrock.

The residual shear strength of the liquefiable soil was given as a phi of 7 degrees in the geotech report.

Volumetric settlement was given as about 5 inches with differential settlement of 2.5 to 3 inches in 30 feet.

How would you calculate the gross bearing under liquefied conditions?
How would you calculate excess deformation under partial bearing loss due to soil strength loss under punching and partial shearing?

How do we determine if the ride structure will have less drift due to tilting of the foundation, than the code will allow?

There is an interesting article in the January 2010 issue of the JGGE on page 151 by Dasti et al, that explores some issues with mat foundation structures tested in the cetrifuge for liquefied ground.

I am wondering how certain we can be that a structure on a mat foundation will not have excessive tilt when the soil below liquefies?

Thanks

 

[InDepth]

For your size footing I doubt liquefaction will drop the whole footing. Differential settlment may be the issue like you indicated. There may also be a heaving case as the soil boils. Settlement rather than bearing is the issue, so work on avoiding settlement. Piles and micropiles are a quick solution to get past the liquefiable layer (but then you have to deal with downdrag due to liquefaction. For the cost of the footing you could invest a little more and jet grout the liquefiable layer beneath the footing and a specified distance out.

 

[FixedEarth]

If you were to do a static allowable net bearing capacity, due to the large mat footing area, you will get well over 6 ksf. Assuming GWT rises to the bottom of the mat, we get 50% reduction, so we are at 3 ksf (Terzaghi & Peck). Remembering that in short term seismic event, allowable B.C. can be increased by 1/3rd, reduction of shear strength is offset by increased allowable bearing pressure.

As mentioned, differential total settlement (static+seismic) is the value to watch. I doubt, diff. sett. associated with the second SAND layer would manifest itself to the ground surface. So take the total diff. sett. value of the SAND between 18 and 28 feet and look at the stiffness of the soil immediately below the mat footing. If your blow counts, say from 4 to 18 ft is at least twice that of strata from 18 to 28 ft, or the overconsolidated ration is above 2.0, then we can assume you have a layered soil system. This would markably increase the allowable B.C. and the total differential settlement actual after a seismic event would be less than calculated in the report.

In the end, you have 14 ft of non liquefiable layer over 10 ft of liquefiable (assuming bottom of mat is at 4 ft). With the constant vibrations, I would throw in 3 geogrid layers in the 6 ft below the mat. This would require excavation and maybe some shoring but it is either that or pile or ground treatment in the upper 28 feet.

I would not be concerned with tilt if the mat thickness gives a semi rigid stiffness.

 

[muuddfun]

In Depth: I suspect that bearing failure may be the dominant failure mechanism. I do not believe that the general bearing capacity equation from Terzagi is valid for this case however. As i understand it, that is only valid for the general shear case. I suspect that the footing will fail in some form of punching or localized shear combination. I do not think that volumetric settlement of the free field soil will control. I suspect that deformation from shearing will end up controlling.
I suspect your are correct about some soil heaving. How would you determine the amount of heaving that could occur during the liquefaction?

FixedEarth: The bottom of the mat is set at about 8 feet below grade. How does an increase in bearing capacity work for the short term with such a large loss of shear strength (on the order of 95 percent loss in the liquefied layer)? I usually use the 1/3 increase for siesmic events when I have normal ground. I decrease the bearing capacity when I am over liquefied soil.
The crust layer between the footing and the top of the liquefied zone is about 10 feet thick, the footing is 60 foot wide, so I would think that the footing would want to punch throught the crust layer into the soft layer below? How thick of a good layer of soil do you need in relation to the footing width to make a big difference in a multi layered system?

The total settlement of 5 inches was the siesmic settlement of the free field. The report calculates about 3/4 inch settlement under static conditions.

My primary concern with the design is life safety from excessive tilt of the base causing more than the 2 percent drift of the tower structure that is allowed by code. I would guess that the tilt would be caused by some small fraction of the wind load occuring during an earthquake and causing one side to dominate in the direction of excess pressure from the rocking of the structure from the earthquake. 2 percent of the tower height is 6 feet at the top, but the bending of the steel structure under siesmic will take up about 30 inches of the 72 inches according to the structural engineer. That leaves an allowable tilt of the base causing an additional 42 inches drift at the top. For a base of 60 feet wide out of a 300 feet tall tower this gives about 8 inches total differential movement from one end to the other, or 4 inches in 30 feet from center to edge. The report estimated 2.5 to 3 inches differential in 30 feet so that leaves me with 1 inch to spare from differential movement beyond the free field? Does this sound reasonable to you guys?

Also, I am reviewing the design documents for the City, so I can not make specific recommendations for design, just approve or reject the work submitted.

 

[FixedEarth]

A lot depends on the site PGA and the liquefaction procedure. What is the site PGA? Was the 2008 Idriss+Boulanger monograph used? PGA less than 0.4 g should not be a concern and insist on latest Idriss/Boulanger method.

I look for ratio of non-liquefiable thickness/liquefiable thickness, instead of footing width/liquefiable thickness. In you case, we have a plain strain problem and would not be concerned with localized shear failure.

The tilt-before the superstructure can tilt, there must be overturning accompanied by uplift of the mat. If the F.S. against mat uplift is say 2.0 when the % of footing in contact with the soil is 100%, then this would have sufficient safety built in. Check with the structural reviewer.

Also are the sediments older Alluvium? Ask the engineering geologist about his thoughts. Is the design fault considered active fault?

I Hope others can contribute to this involved project.

 

[muuddfun]

FixedEarth

The pga is about 0.6.
The liquefaction analysis was done following professor Seeds 2003 procedures. It checks fairly well also following Idriss and Boulanger, in spite of Professor Seed ripping Idriss and Boulanger to shreds (but that's a whole other story).

I am not sure I agree that the footing size is irrelevant.
The crust thickness to liquefied layer thickness is to determine surface manifestation? So why wouldn't the opposite be true for the pressure of something above to break through the crustal layer it would be related to the footing size by a large footing applying the load below it very deeply, as compared to a small footing?

For the 60 foot footing at the top of the liquefied layer we are only about 1/6 of B below. I would think for most small spread footings where I am either 1 or 2B or more below the footing at the top of my liquefied layer, then sure settlement takes over as the controlling factor. But at what point between those two different scenarios does bearing take over from settlement as the controlling factor. And if it does not when then does shearing under bearing load ever control a design?

Thanks for your thoughts FixedEarth, this problem is so tricky it has been driving me nuts, and it is good to hear someone else's input.

 

[Mccoy]

muudfun,my comments are qualitative.

With such a tricky projects, with the added uncertainties given by effects of moment and shear, why not to adopt a piled raft foundation? higher costs (in what proportion I do not know) would be compensated by guaranteed safety, even though the presence of liquefible layers would add to the cost of the deep foundation.

I mean, as an outside observer I see so many problems interacting together that I would be scared shootless to be stuck on that structure in the aftermath of an earthquake knowing it has no pilings below the foundation hexagon.
This if I survived the earthquake during the ride. But maybe it would all add to the overall excitement.

 

[BigH]

McCoy beat me to it. For all the hassles, it might just be better to pile the foundation. You might be able to use timber piles (if you live in an area that is conducive to timber). Piled raft is okay - but might require too thick of a raft - whereby individual footings under the structural columns might be better.

Recently (in the last three or so years if my gray cells are working),several investigators in the ASCE Geotechnical Journal (sorry I don't use the new "official" name and actually liked SMFE better) have produced seismic bearing capacity factors. You might want to check these out. I would look for any follow up discussions, though.

 

[BigInch]

Would stone columns be useful in this situation?

Let your acquaintances be many, but your advisors one in a thousand’ ... Book of Ecclesiasticus