Depth of influence for settlements

[Mccoy]

This is something which is really not too clear. The condition is the one where a rigid layer is not found near surface. In some textbooks, the depth of influence for calculating settlements Z_I is assumed to be the one where the load surcharge drops to 0.1 times the value of overburden. Somewhere else, they go up to Delta_Q= 0.3 or even 0.5 overburden.

Sometimes Z_I is assumed to be 2B, sometimes though especially in very wide foundations, ZI=B or event 0.5 B.

Bowles gives values of 5B, Burland & Burbidge give different values, Schmertmann says 1.5 B, chaos rules supreme. Apparently.

What do you guys use as a depth for the influence of loadings, either to calculate settlements or to figure out a weighted value of the modulus of subgrade reaction for foundations. Literature references are very much welcome.

 

[emmgjld]

"chaos rules supreme" -- You have nailed it, from my point of view.

As I do a large % of residential, My loads are small ... very small.
1-1/2 to 2 B is my default, based upon my local conditions (Western Colorado) when I am not considering the Expansive and/or Collapsible soils, mostly CL & ML-CL. Mostly in-house experience (40 years + my father's previous). For my experience, discussion of secondary consolidation is silly.

Due to competent strata at 15 to 90 feet, the local habit was to slap in steel pipe piling for heavier loads. Sorry I can be of no more help except to look up a lot of references.

 

[BigH]

I've always used 2B where B is the width of the footing unless it is a strip footing where I've used 4B. Usually settlement computations are only rough estimates only and to go, say, to 1.5 or 1.8 instead of 2 likely leads to the general fuzziness anyway. If I have a "harder" layer within this zone, etc. I have gone to Poulos and Davis' book on Elastic Methods to estimate the stress distributions and base, still on a rough 10% rule.

 

[oldestguy]

I just reviewed a discussion in an old 1959 ASCE Journal of Soil and Foundations Division by two California DOT bridge engineers. They were evaluating the proposed method for determining bearing capacity based on allowable settlements, by my former professor B.K. Hough, ASCE paper 2135 of that Division journal. Hough pushed his ideas with a limit of calculations at the 0.1 soil existing pressure. They compared 40 bridge sites where the Hough procedures were compared to actual settlements measured. There in 70% of the cases with low water table sand soil the method came within 10% of measured settlement. Maximum error was 40%. In 10 cases sand soil where water table was shallow, the method underestimated settlement by 30 to 40%. For clayey soils(15 cases) the computations ranged from exact to minus 50% error in predicting settlement.

I suspect a lot of the writers of texts just copied some other writer's advice, without doing those field measurements. Above the discussors used over 40 sites and the results seemed pretty good, so I have stayed with the 10% depth limit ever since. Never had any one complain that I missed it by any amount.

 

[BigHarvey]

I also use the 10% limit which was indicated to me by late prof Osterberg.

 

[BigH]

OldestGuy - any chance to get a copy of the paper/discussion? My journals only go back to 1975 (and they are in storage in Toronto). . . .

 

[oldestguy]

What's the best way? I can mail, copy on jpg file for two pages at a time 28 total pages. Discussion abut the same. See y0ur e mail.

 

[Ron]

2B

 

[oldestguy]

Guys:

If you run spread sheet settlement analysis summing results considering each foot a separate layer, you can judge what effect there is with depth and stop when your probable error percentage is reached, summing up the delta S amounts from there on down. I usually guess at a probable depth and let the spreadsheet do it's thing to a somewhat lower depth. Examining the results then is easy to see if I was OK. Never had to re-do the sheet.

 

[BigH]

@oldestguy- thanks; I will be home in August - perhaps you can send it there by snail mail along with spreadsheet? Again - love your take on things; FYI, I have original 1957 Krynine and Judd hardback book on Engr Geology and Tschebotarioff 1951 book as well . . .

 

[oldestguy]

OG here: some time on e mail give me the address. There should be two spreadsheets in your in box now. One was interesting: depth of comps was well beyond the 10% limit and the delta s numbers are all zero in the last several lines..

 

[Mccoy]

OG, by words alone I'm not able to understand exactly what you mean with your spreadsheet procedure. If you can, pls attach them to a post or send em to my mail address:
mccoy
2004
2004
at
Yahoo
dot
com

where it is a succession with no blanks nor spaces

 

[Mccoy]

Another aspect of the depth of influence is linked to the coefficient of subgrade reaction (winkler modulus) for foundations.

There are basically two simplified formulas for the CSR:

1) k = E/B mainly references by bowles, the poisson is omitted since in unsaturated media we can assume mu= 0.15
2) k= E/H mainly references by Horvath

Where B is the significant dimension of the foundation (usually its width) and H is the depth of the rigid layer, or the fictitious rigid layer: depth where settlements cease to be significant= our depth of influence for settlements.

Now, if H=B the two relations are identical. If depth of influence is >=2B, then equation #1 above may overestimate the CSR. The criterion where depth of influence is 0.1 overburden pressure would tend to make equation #1 usually pretty optimistic with respect to equation # 2

 

[BigH]

But then, Mccoy, isn't this all related to "elastic theory"; what about "particulate theory" (see Harr's book) . . .

One thing that seems to be clear, at least to me, is that no one really knows "precisely" where to stop . . . over the years the 10% rule seems to be reasonable. And in the end, if one computes a footing's settlement to even within 20%, they have had a pretty fine day.

 

[fattdad]

2B for square or rectangular footings. 4B for strip footings. To the depth where the delta sigma v is less than 10 percent different from the existing effective stress at depth.

Three good guidelines.

f-d

¡papá gordo ain’t no madre flaca!

 

[Mccoy]

Thanks guys for your useful inputs.

@ BigH: I fully agree on the significant degree of uncertainty related to settlements, what I'm out for though is some coherence into the conceptual framework which relates geotechnical settlements to the deflections used to calculate bending moments and shear in beams and mats structural analysis (using a Winkler soil model).
Going back to some old eng-tips threads, fattdad described the Winkler model as sensitive mostly to the more shallow layers, where the springs get in action. Another reading confirming that this seems to be the correct framework is Paul Mayne's "Unusual settlement..." article, which describes a case history of large setlements in a mat supporting a 13 floors building at Georgia tech.
So, the bottom line would be this pls correct me if something does not settle well with your reasonings and experience.
1) Mats (and other foundations types)must be analysed for structural integrity to bending moments and shear; a popular method to do this is by the coefficient of subgrade reaction. Such coefficient simplyfies the behaviour of soil at the soil-foundation interface. The moments and shear are governed by a depth of influence z_p which is smaller than the depth of influence governing geotechnical settlements
2) After the structural check has been carried out by the above Winkler method, a further check should be carreid out, which involves the layers located further below those which govern structural integrity. This is the realm of geotechnical settlements, which may cause excessive total and differental settlements, cause of loss of serviceability to the structure, even if the foundations remain sound. Here the depth of influence z_p is larger and approaches the values provided by you guys in the above threads, usually 2 to 4 B or a value determined by the 10% rule (Always in absence of a rigid shallow layer)
The above reasonings at least would put some order in the chaos which apparently rules the subject.
I've just been browsing the NIST publication 'Soil-Structure Interaction for Building Structures'.
The authors give a z_p= (BL)^0.5 where B=half width of foundation, L= half lenght of foudation.

So, depth of influence for a 10m*20m mat would be z_p = 7 m, less than B actually. When calculating the settlements we usually would use a Greater depth, depending also upon the value of loading.
With the above rule, a square foundation has a depth of influence equal to half the lenght of its side.

Bottom line: geotechnical settlements analysis and settlements derived from SSI analysis are two different realms, we shouldn't mix them as this would be equivalent to mix apple with oranges. Long-term consolidation settlements are a subset of geotechnical settlements and should not be a part of SSI analysis, unless maybe the structural is interested in designing its slab considering the deflections caused by consolidation many years after building, if this makes some sense.
The post came out a little longer than foreseen, but pls gimme your opinions if the above sounds reasonable and if there are some aspects which I didn't include in my ruminations.

 

[GeoPaveTraffic]

Maybe I'm missing something, been working too many hours lately.

But it seems that the NIST proceedure would only work for foundation soils that do not get softer with depth. As you have pointed out; we would typically look at consolidation effects to a much greater depth and it only makes sense that deeper soils would also effect a flexible or semi-flexible mat foundation.

Again, maybe I missed the point but 0.7B just doesn't sound right for anything but a uniform soil or a soil that is getting stiffer with depth.

Mike Lambert

 

[Mccoy]

GeoPave, I'm just wondering if consolidation settlements, a long-term phenomenon, should be considered in the structural analysis of foundations. Structurals tell me that reinforced concrete has viscous properties which tend to accommodate significant stresses without damage if such stresses are developed throughout a very long time. Of course long term settlements should be verified for structural serviceability but that would not imply structural rupture of foundations due to excessive bending moments and shear. I may be wrong of course, the above is just a line of reasoning.
I agree with your reasoning that if soil gets stiffer with increasing depth than the depth of influence is larger. However, in my tentative line of reasoning, bending moments and shears are mainly influenced by the shallower layers, those located within 0.7 B underneath the foundation, as suggested by NIST.
The structure should then be verified against excessive settlements, immediate and long term.
I also find there is a drawback in my reasoning, because differential settlements can cause bending moments and shear, although maybe again, most of moments and shear potentially dangerous to the foundation may take place due to displacement of the shallowest layers.

Some sources in the literature would support what I'm saying, for example the cited NIST report, Horvath, Mayne. Too often I see an unusually small depth of influence when speaking of modelling a foundation by the springs method, unusual by the standard of geotechnical analysis of settlements.
Is this another difference between geotechnical methods and structural procedures, which has no real technical reasons to exist? Or is there a scientific truth in such a difference? Not every author differentiates, some authors speak about constrained modulus to use for correlations in the determination of the coefficient of subgrade reaction for foundations, without going into the details of drained or undrained modulus.

 

[BigH]

There's two depths of influence - 1) depth of influence for shear stability (bearing capacity) - (typically, I have always thought, for most standard footings that is in the order of 0.7B) and 2) depth of influence for settlement (serviceability) based on the pressures being transmitted to depth. The actual bearing pressures to be used usually will be due to settlement of course.

 

[Mccoy]

BigH, thanks for pointing that out, actually yes, that 0.7B number is closer to the depth of influence for shear stability or callapse than the usual depth of influence for settlements or serviceability. Maybe bearing capacity and bending moments - shear on foundation members share a similar failure mechanism?

Although, when a large mat becomes convex downward because of excessive immediate settlements I imagine that too would be cause of anomalous bending moments and shear stresses in the mat structure.