Rigid pile cap design vs Pile cap as a continuous beam 1

[nrjdjjs]

Attached is a picture of a pile cap showing 3 columns (indicated by 3 square red boxes) supported by a pile cap resting on 16 piles (indicated by green circles). The pile cap is 1 meter thick. Based on the arrangement of piles and supports, what would be the best method to determine shears and moments in the pile cap?
If the pile cap is assumed rigid, using static equilibrium concepts and assuming the entire width of the mat, the pile moments in any direction may be determined by summing the moments from the pile reactions, the soil and footing weight and the moments due to column loads at any given location along the direction being considered.
If the pile cap is modeled as a continuous beam, most likely it would result in a very different set of moments as compared to the rigid analysis method described above.
My question is what is the best way to determine which method to use when designing the pile cap? Any insight would be sincerely appreciated. Any references in this regard would also be very valuable.
Thank you

 

[SlideRuleEra]

My question is what is the best way to determine which method to use when designing the pile cap?

I would start by comparing the ratio of maximum pile cap horizontal dimensions (10 meters) with pile cap thickness (1 meter), a ratio of 10:1. IMHO, this is borderline "thin" to consider the pile cap rigid. Assume a continuous beam for analysis.

In reality, if possible, I would make the cap 1.25 to 1.5 meters thick, assume the cap is rigid, and rest easy.

 

[nrjdjjs]

Thank you SlideRuleEra for your input.

Is there a good guideline or a reference that states when can a pile cap be considered rigid vs not?

Thank you

 

[OldDawgNewTricks]

Tomlinson suggests the dimensions shown in the figure below so that bending and shear forces are negligible. Strut-and-tie method used for design.

 

[BridgeSmith]

An approximate analysis I've used in the past is to remove a pile, apply a reference point load to the cap where the pile was removed, calculate the vertical deformation of the cap under that load. Compare that to the axial movement (due to settlement, deformation, etc.) under the same load. If the axial movement is, say, 10 times the deformation of the cap, the cap is about 90% of the way to being fully rigid, and you could probably model the cap as rigid, and get a fairly good approximation of the load distribution. If it's closer to equal movement/deformation, what I would do is analyze it both ways and take the worst case for each component from each case.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[nrjdjjs]

Hi BridgeSmith,

When you say axial movement, are you saying that the axial movement in the pile is compared to the vertical deformation of the pile cap or am I misunderstanding you?

Thank you

 

[OldDawgNewTricks]

The thickness that is required for a rigid assumption also depends on the pile layout. Bowles notes that for the simple four pile group shown in the figure above, the pile loads will be equal regardless of pile cap rigidity. But if you were to add a fifth pile directly under the column, then pile cap rigidity becomes significant. Bowles suggests that a rigid assumption is valid for a central load on a pile cap with thickness of 1.8 to 2 m and plan dimensions of 2 to 3 m, depending on pile spacing.

 

[BridgeSmith]

When you say axial movement, are you saying that the axial movement in the pile is compared to the vertical deformation of the pile cap or am I misunderstanding you?

Yes, that's what I meant. Sorry for the confusion.


Rod Smith, P.E., The artist formerly known as HotRod10

 

[SlideRuleEra]

nrjdjjs - Using various techniques, there have been many studies on how pile cap thickness affect its' rigidity. Conclusions often reveal that the same basic pile cap proportion (pile cap width to depth ratio of about 5:1 to 8:1) are needed for the cap to be considered rigid.

I attached a recent (2021) paper by investigators at Concordia University: "Role of Pile Cap Thickness in Pile-Cap Foundation". Here is an excerpt from that report. The comments made in blue on the graph are mine.

I learned the importance of this ratio decades ago (when calculations had to be simple, e.g with a slide rule) by experience. The ratio is not a real "answer", but a good "rule-of-thumb" to get an idea of what results of a proper analysis will show.

 

[nrjdjjs]

Hi SlideRuleEra - Thank you for the information.
Assuming that this study was done with a max horizontal dimension of 8 m, if let's say the length was 8 m, width was 3 m and the depth was 1 m, then does the Width:depth ratio refer to 3 or 8? In either case if the pile cap was 8X3X1, it seems the article says it could be considered a rigid pile cap based on the pile cap curvature. If my understanding is right, it seems that the design sketch that was included may behave like a rigid pile cap - borderline case with dimension of 10X3X1. Does the article talk about larger pile cap dimensions? I would appreciate if you would paste the article link.
Thank you

 

[SlideRuleEra]

nrjdjjs - For the ratio, use the maximum horizontal dimension... which is 8 m for the example in the paper paper and 10 m for your sketch.

For your other questions.. read the paper, which is attached to my post. But, if you want the link to the paper, here it is:

"Role of Cap Thickness in Pile Cap Foundation"

 

[nrjdjjs]

Thank you SlideRuleEra. Sorry I missed that you have included the pdf.