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# Rigidity of pile cap

## Rigidity of pile cap

(OP)
Dear altruists, to analyse the pile group (attached), should the pile cap be considered rigid or not? The shear span to depth ratio is more than 2 (2.6). However, it's very common to consider pile cap rigid, and I guess L-pile can not assign a flexible pile cap (I'm a structural designer). I'm trying to understand if the assumption of rigid pile cap is valid here or not? Does it only depend on the shear span to depth ratio or there are other methods of considering rigidity of pile cap? FYI, There is a 500 mm thick hollow column sitting on the pile cap and the cap is 2700 mm thick. There could be other arrangements of piles, but let's assume due to project constraints we can't change any of the dimensions in the cap and the pile locations. On a side note, would you design shear reinforcement in the cap under the hollow column portion when the column is subjected to significant lateral force that causes moment demand? Any suggestion would be highly appreciated. Thanks.

### RE: Rigidity of pile cap

Honestly, it probably doesn't make much difference as far as the force in the piles go. If this cap isn't 100% rigid, it's close.

Now, I think the rigid vs flexible question can make some difference in the shear and moment demand on the concrete cap. But, my guess, is it won't really affect the reinforcement chosen.

### RE: Rigidity of pile cap

(OP)
Thanks Josh. If we go with rigid cap, won't we be missing the demand on top of the pile due to rotation (if it was flexible)?

### RE: Rigidity of pile cap

How deep is your embedment into the cap? That will have a bigger impact on rotation than the cap itself.

If you're concerned about the flexibility of the cap, think of it this way: for rotation to develop in the cap at the pile to cap interface, what would have to happen to the surrounding concrete? In other words, is that kind of movement possible without cracking the concrete or yielding the reinforcing? My guess is no. You can also consider the relative stiffnesses of the connected elements. With a 1m pile connected to a 14m pile cap, which one will bend? (Hint: it isn't the pile cap).

### RE: Rigidity of pile cap

(OP)
Pham, thanks for your insight. I thought about it, if I take the stiffness ratio (EI/L rato for cap and pile: correct me if I'm wrong) of the cap to pile, it's around 18. It surely shows that the pile will crack and yield first. But what stiffness ratio is good enough to say the cap is good enough to consider rigid? Any reference on this? Are we compromising safety of the structure anyway here?

### RE: Rigidity of pile cap

How would you design the top reinforcing for that pile cap if you assume it to be rigid. 0.0018 * b*d? I think that's probably going to be enough whether it's analyzed as rigid or flexible.

### RE: Rigidity of pile cap

(OP)
You are right Josh. It's enough.

### RE: Rigidity of pile cap

In my opinion, a pile cap is flexible if beam behavior can occur between enclosed piles. When shear concern far outweigh flexural, the cap is rigid (similar to deep beam behavior).

### RE: Rigidity of pile cap

The rigidity of the cap is relative to the axial stiffness of the supports (the concrete piles). I've done an analysis of a bridge abutment on steel piles of similar proportions. I applied a point load at the location of one of the piles, with the pile removed, and checked the deflection of the cap. Then I applied the same load to the pile and calculated the axial deformation (it was driven to refusal, so I assumed the tip didn't move). I compared the vertical deflection of the cap to the vertical movement of the top of the pile under the same load. I determined that it was about 95% rigid. (The axial deformation of the pile was about 20 times the bending deflection of the cap under the same load) You might be able to try something similar for your pile cap. I would guess that unless your piles are founded solidly on shallow bedrock, your results would be similar to mine.

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

### RE: Rigidity of pile cap

If this was modeled in RisaFoundation, why do you have to assume it's rigid. Risa will even consider the soil stiffness even if it's on piles because some portion of the cap is still supported on soil.

I always thought..
You assume rigid if you do manual calculation. If you have FEA foundation software, let it compute the stiffness of the cap.

### RE: Rigidity of pile cap

I don't believe it is good practice to consider soil stiffness / soil bearing for a pile cap.
I would assume the piles carry all the load.

### RE: Rigidity of pile cap

I've always been told not to consider any soil stiffness if it's a pile supported foundation. Supposedly, the soil may pull away from the foundation eventually leaving little contact. Maybe due to frost / thaw cycles or such. Therefore, it's not considered a good idea to rely on soil resistance.

### RE: Rigidity of pile cap

Josh, I'm just saying RISA has that feature.

### RE: Rigidity of pile cap

(OP)
I'm not familiar with RISA (since I'm not dealing with the geotechnical part). As a structural designer, should I tell the geotechnical engineer to consider the cap as rigid or not? I agree with Josh on not relying on the soil under the cap.
What if we consider it rigid and there is some flexibility in the cap, are we compromising safety here?
What if the pile cracks or reaches the capacity on top?

### RE: Rigidity of pile cap

Why geotechnical require this information? Pile cap is designed after the structural guys get feed back on pile characteristics and behaviors (diameter, spacing, displacement/deflection, bending, axial force limit..etc). The structural usually required to provide the maximum loads to the geotechnical for pile analysis and design use only.

### RE: Rigidity of pile cap

(OP)
Geotechnical engineers run the pile group analysis and provide the demands on piles based on the maximum load given by structural engineers. But the rigidity of the cap will affect the analysis geotechnical engineers are doing (e.g. the moment demand on top of the pile).

### RE: Rigidity of pile cap

If you know pile axial capacity, and spacing requirement, then you can start design by using the structure reactions to determine number of piles required, and pile layout. Design of pile cap is identical to footing design, but the difference in support mediums - pile vs soil. Once you get cap dimension including depth determined, just provide that info to the geotechnical guys to determine whether it is rigid, or flexible.

### RE: Rigidity of pile cap

Sorry, I thought you were advocating that considering both piles and soils springs was the best way to do it. And, I wanted to push back on it.

Note: I was involved in one project (a nuclear job) where the facility did consider both soil resistance and piles. But, that was a peculiarity of that facility....

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