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Design of Combined footing vs. Single Footing(3)

I have got a general question about the design of a combined footing vs. a single footing. I have just finished a design of a single footing for a storage silo. It is founded on grade, with a soil bearing capacity of 3 ksf. My footing will be a 19 ft by 19 ft by 3 ft thick footing, reinforced top and bottom by #6 at 12" O.C. top & bottom each way. I analyzed for overturning moment, sliding for gravity loads, wind and seismic forces.
Now, I have to enlarge my footing to take into consideration the construction of a similar footing for similar loads just adjacent to my current footing.
I would not be constructing the whole combined footing all at once, because the while the first storage silo is for present use, the second one is for future. In effect, I would only be constructing, say 11/3, or even 11/4 of the combined footing for now.
Would designing a combined footing for two of these storage silo structures be the best way to do it? I would design a combined footing for both of the structures, but only construct, say 11/3 of the combined footing, leaving the rest to be constructed when it is required. Is this the best approach? Intuitively, I would think that my previous design would also work, but I just need to double the size of the footing. Would this be correct?
In fact, I would also intuitively think, without starting my design, that doubling my previous design would be conservative, and that my combined footing could actually be smaller in footprint and thickness? Would this also be accurate?
What would be the best way to approach the design of a combined footing?
What is the best way to allow for the construction of the rest of the footing? Mild steel dowels embedded in the first footing, and greased on the exposed end? Any other suggestions? Thanks. 

In my opinion, you would be better off to look at the two footings independantly and make sure the soil bearing capacity is not exceeded in the footing influence overlap area in the future when the two are finally constructed.
The loading on a combined footing will be totally different since you will have to consider the load case where one silo is full and the other empty; introducing bending moments in the combined footing that an individual footing wouldn't have. 

kslee1000 (Civil/Environmental) 
21 Apr 09 9:02 
I agree with jheidt2543. In you stability analysis, do not forget to add a case for influences from future construction. 

Thank you very much, jheidt2543 and kslee1000. I've got two questions, though.
One is, what is the best way to evaluate the footing overlap influence area? Would this be a factor if I design a combined footing, or would it only be a factor if I design two separate footings. Why would two separate footings be better than a single combined footing? Is it because they are built at different times?
Another question I've got is adding the case for influences from future construction. What are the major influences do I need to consider, and what is the best way to go about it? Thanks again. 

kslee1000 (Civil/Environmental) 
21 Apr 09 13:48 
For combined footing with columns to be placed in different stages, the controlling bearing pressure can be confusing, since for an unknown time period, the footing has only one column load, that is eccentric to the center of the footing, that are to be determined by two column loads. (Confused already? :)
If use indivisual footing, the overlap pressure cones will increase soil bearing pressure, thus settlement. If the two footings' bottom are to be at the same elevation, I don't see much problem with bearing, ask your geotech engr. on settlement. If the latter is higher than the former, then you have to check both. When using this scheme, at least one side of the footing will be exposed for the construction of the latter, does it has adversed effects on the footing (especially lateral stability, OT)? Do I have adequate space in between the footings without over crowed the space (shoring, form works). Just a few things to think about. 

(2) BigH (Geotechnical) 
21 Apr 09 22:08 

Take a look at the link BigH supplied. Figure 2 shows the overlap area I described (a picture is worth...).
Thanks BigH for a really spot on link!
That paper also shows the problem of uneven loading, which for a combined footing is magnified due to the filling and unloading of the adjacent silos, which causes big flucutations in bending moments. 

BigH (Geotechnical) 
22 Apr 09 7:27 
Bozozuk also has a paper in the Canadian Agriculture Engineering Journal 1973 or so. It downloaded but wouldn't print  go figure. I knew about the original paper (he also has a classic on ground movements due to trees)  but I googled "silo foundation failures Bozozuk" and got the hit to the paper I noted above. 

Having read all the contributions above, I submit that a single foundation is an economic option for the structures.
You have to check 3 conditions;
1. Condition of the two silos, filled to the brim. Check that there is adequate FoS against bearing failure and settlement within limit.
2. Using the dimensions of the foundation in condition 1, check for FoS against bearing failure for one fully filled tank without the other.
3. Same as above but with the tank on the other side fully filled without the first tank.
If the 3 conditions are ok, there should not be any problem. 

Delijosi:
I agree with the conditions you list that have to be satified (along with wind load), I think the point made was that a combined footing solution requires more engineering and more rebar in the construction because of the negative slab moments than two separate foundations. They both will work, it's just a matter of economics. 

You need to consider the settlements. If you build two silos close together on a common mat and load them simultanelously, they will tend to tilt towards each other. If you build one on the combined mat and load it before building the second, silo No. 1 will tilt away from silo No. 2; then when both are loaded, they will tilt towards each other. The relative movement at the tops will be greater in the second case, and that movement will affect anything that joins the two silos, such as conveyors and catwalks. Moment in the center of the mat will first be negative, then positive.
Unless the settlements are expected to be inconsequential, it would be best to support the silos on individual footings separated far enough apart to keep the tilting effect small. Your geotech can determine that minimum separation from settlement analyses.
Of course, if the soil is uniform, there is in theory an ideal separation between the two silos on a common foundation that will result in uniform settlement of both, but only if they are loaded simultaneously the first time they are filled. 

kslee1000 (Civil/Environmental) 
25 Apr 09 9:10 
Delijosi:
If you have deceided go with seperate footings on a staged construction, the investigation should look like:
1. Two silos with varies filling scheme and loading combinations to find max. stress anainst the allowable with a conservative FOS. Adjust footing sizes to achieve this. 2. Two silos fully loaded to find the overlap in stress bulbs, and estimate differential settlement. Adjust footing distance to eliminate, or minimize effect of overlapping.
It may require several iterations to reach a safe design. If either criterion (bearing, settlement) couldn't be satisfied, suggest to consider pile/pier foundations. 

aeoliantexan You said: Quote:You need to consider the settlements. If you build two silos close together on a common mat and load them simultanelously, they will tend to tilt towards each other.
I don't think that is correct. The two silos would be loading the combined footing uniformly, so they should have no tendency to tilt towards each other. If the owner wants the future silo to be close to the present silo, a combined footing is necessary in order to avoid overlapping of stress bulbs, hence tilting silos. My suggestion in that case, is to build only the footing required for the first silo but place additional reinforcement required for the future combined footing. This would stop at the common face with mechanical anchors provided at the bulkhead. That way, the first silo stresses the soil uniformly throughout its life. If and when the second silo is built, it would be best to pick a time when the first silo is as close to empty as possible. The reinforcement for the new silo would be fastened to the previously placed mechanical anchors and concrete would be cast against the face of the existing foundation. The surface would be intentionally roughened for bond. If, on the other hand, the owner does not require the two silos to be close together, the separate foundations are the simplest way to go. BA 

BAretired, Your are correct that two adjacent identical silos on separate foundations will tend to tilt towards each other due to the overlapping of the stresses, just as the paper in BigH's link depicts. Joining the two foundations doesn't eliminate the overlap, it introduces a moment at the connection that resists the tilting. Because of this moment, the developed bearing pressure is reduced near the connection and increased at the outside ends. The bearing pressure is not uniform; the settlement is (if the mat is sufficiently rigid and strong).
The distribution of bearing pressure across the combined mat is whatever is needed to make the mat settle uniformly. It will depend on the compressibility of the soil at various depths, so it is unique to the site. The moment at the center of the mat cannot be accurately predicted without considering the compressiblity of the soil. A model that represents the soil as a single layer of springs won't do the job; there are lots of layers.
I believe that this phenomenon is not well appreciated and falls into the crack between the geotechnical engineers and the structural engineers. We're both lucky that safety factors are included in the structural design and tend to cover our ignorance. Trouble comes when we get outside normal practices.
I believe that a proper FE model analysis can address this issue, but lack the skills to try. I'd be interested in hearing from someone who has tried. Perhaps we could start another thread.
By the way, I have seen a mat foundation supporting two silos that cracked in the middle and allowed the silos to tilt towards each other. 

aeoliantexan, I heartily agree that "We're both lucky that safety factors are included in the structural design and tend to cover our ignorance". If two silos are placed symmetrically on a 19' x 38' x3' deep rectangular pad such that the resultant load is directly over the center of footing, then the pressure under that footing would be uniform and there would be a single bulb of pressure forming in the soil below the footing. This assumes that the two silos are filled simultaneously with silage of the same density. If one silo is emptied and the other remains full, the resultant load shifts towards the full silo. When the eccentricity of total load becomes 38/6 = 6'4", the pressure varies from 2p to 0 where p is the average pressure. If the eccentricity exceeds 6'4", the effective area of footing is reduced but the pressure distribution remains triangular. During all of this, the bulb of pressure changes shape considerably. The variations in pressure will result in differential settlement. If the footing remains rigid, both silos will tilt toward the loaded side. For that reason, it is advantageous to maintain the same level of silage in the two silos. So far as settlements are concerned, I agree that it depends on the soil properties. Soil is not a perfectly elastic material. I don't think a finite element analysis would shed much light on the subject unless you can input a realistic array of soil properties throughout the volume of the bulb of pressure. BA 

kslee1000 (Civil/Environmental) 
29 Apr 09 10:46 
From my limited understanding on soil behaviors, I think there are two ways to yield resulting uniform settlement.
1. Flexible mat. The resulting soil pressure is close to uniform, thus the settlement. However, I don't think it would work for highlocalized concentrate load like the silos. 2. Rigid block. The settlement would be forced to be uniform, disregard of the soil pressure distributions, since the block can't deform (negligible, if any). However, tilting (uneven settlement) could be a problem.
Piles may be one way out, if both do not work? Please comment. 

kslee, We have not been told the size of the silos, but I am assuming they are about 18' in diameter. They could be flat bottomed or hopper bottomed. In the first case, the load is uniformly spread over the silo area. In the second case, it is likely carried by columns arranged in a circular ring. Either way, with a thickness of three feet, the footing must be considered rigid and the pressure uniform or in the case of different silage heights, uniformly varying. The pressure for any combination of loads can be reasonably well predicted if the footing is deemed to be a rigid body. Settlement, on the other hand is not so easily predicted, particularly if the properties of the soil are variable. pob11646 indicated that the soil had an allowable bearing pressure of 3 ksf. If this is adequate for the loaded silos, there is no need to consider piles. Piles could be an option but the type of pile and the allowable load would have to come from geotechnical recommendations. BA 

kslee1000 (Civil/Environmental) 
29 Apr 09 12:39 
BA:
Yes, we can agree on the settlement needs to be work out by our pals at geotect department :)
Please note my big "IF". Since I don't know how critical that would be  leteral movement when one full, one empty. Actually, I am quite interested in hearing more from our pals on this, also how rigid is rigid (relative to soil) in geotechnical views. 

kslee1000, I'm delighted that you joined the conversation. Uniform, trapezoidal and triangular contact stress distributions are convenient for designing footings that at least satisfy statics, but they are far from what actually happens beneath the foundation. Geotechs are pretty well agreed that uniform stresses do not produce uniform settlements, due to geometric stress distribution. The thin floor of a steel storage tank applies a pretty uniform stress. Elastic analysis indicates that the vertical stress at most any depth directly beneath the edge of the tank is just about onehalf the stress under the center. Numerous authors have reported that the settlement of a flat tank floor produces a bowlshaped floor, with the edge settlement usually less than half the center settlement. It is also well established by elastic analysis, but much less widely recognized by practitioners, that rigid foundations do not generate uniform vertical stresses in the soil. Elastic analysis indicates that the vertical stress under the center of a rigid circular load on an elastic half space is roughly onehalf the average stress, P/A. The stress at a radius of 95% of the footing radius is about 120% of the average, and the stress at the edge approaches, inconveniently, infinity. Obviously, the stress at the edge will be limited by the shear strength of the soil. If the footing is supporting a central column, the bending moment at the center must be considerably higher than the moment calculated using a uniform bearng pressure. It amazes me that the industry has not really addressed this issue, and I would like to hear others' insights on the subject. Numerous elastic equations and charts can be seen in "Elastic Solutions for Soil and Rock Mechanics" by Poulos and Davis, now available in pdf at http://www.ce.ncsu.edu/usucger/PandD/PandD.htmAs for the silos, if they are to go on a combined mat, I would recommend that it be reinforced conservatively. 

kslee1000 (Civil/Environmental) 
30 Apr 09 9:35 
ae:
Excellent explanation. It is always a pleasure to review some topics been put on shelf for a while, and refresh our mind. Thanks. 

ae, I have to admit, that comes as news to me. I always assumed that the pressure under a footing carrying a column load at its centroid was safely taken as uniform pressure. If anything, I thought, the pressure would be larger directly under the column, sort of a bell shaped curve with the maximum ordinate in the middle. In the case at hand, we have a circular silo supported on a square footing or two silos supported on a rectangular footing. The pressure on the floor of each silo might be uniform or the entire load might be carried by a circular ring of columns. We don't know. It would appear that some conservatism is warranted in the design of the reinforcement. BA 



