Capping beam support on piles

[hobo_ist]

Hi all,

First and foremost apologies for the length of this post. Please see the attached mark-ups to clarify what I'm going to try to explain. Not a geotech engineer so rusty in this department.

Clients contractor wants me to explore a way in which he can excavate (passive side) along 6 metres of a 30m length secant pile wall without using props. The excavation will be sloped at 45 degrees from top of capping beam to formation level (approx. 3mbgl). I won't bore you with the details of why it needs to be done this way.

A small section of the secant piles and capping beam will cantilever as a result (conservatively assumed as the full 6m length of excavation, even though the passive soil level varies due to the slope). The pile designer has confirmed the piles can cantilever to full excavation depth but deflections will exceed maximum allowable (obviously).

The pile designers calcs, done in WALLAP, do not account for the additional stiffness provided by the capping beam to tie together the piles, which should be beneficial for deflections. Consequently I'm having to assess if it's possible with a capping beam that's heavily reinforced so that it's stiff enough to rein in the deflections a little bit.

This is the approach I'm considering (see the mark-up drawing if clarification is needed). Please let me know if I'm way off the mark!

To model the 24m long section of "restrained" capping beam, I'm considering defining the support condition at each structural pile location as a spring with stiffness corresponding to the modulus of horizontal reaction of the passive soil.

Question:
What would be the best way to model the "cantilevering" section of the capping beam seeing as they're not failing while in cantilever(according to the pile designer) and providing some degree of restraint?


Thanks.

 

[SlideRuleEra]

For the assumptions made, I consider the capping beam to be 6 meter "cantilever with uniformly distributed load" over the length of the cantilever. That is l = 6m in this (drawn backwards from your sketch) diagram:

Since you are ignoring horizontal support from the sloped portion of soil, I would compensate by ignoring that the horizontal cantilever beam has some point of fixity that makes the true cantilever length > 6m.
To be more conservative, I just assume a horizontal point of fixity. Then the capping beam could have, say, 8m cantilever with the outer 6 meters uniformly loaded.

 

[hobo_ist]

Taking the assumption that the restrained side of the capping beam is fully fixed is what I want to try to avoid.

 

[SlideRuleEra]

Completely agree, and that is what I'm doing by assuming a "horizontal point of fixity". I just have to address problems like this the old-fashion way with simplifying assumptions that allow a reasonably accurate model (special fixed cantilever beam, in this case) that can be solved with only a calculator... or slide rule. If you are looking for advice on how to model in modern software, sorry can't help. I don't have (or know how to use) sophisticated engineering software... a consequence of being retired.

I do believe you are on exactly the right track to obtain a correct solution.

 

[PEinc]

I don't see how it can be assumed that the unexcavated piles (the first 24 meters from the left) support a uniform load. I would not use the above Figure 12 diagram. It seems to me that the unexcavated piles will support a decreasing amount of lateral load going from right to left. There is probably a decreasing triangular load or an exponentially decreasing load going from right to left along the 24 meters of wall, possible decreasing to no load at the far left end.

http://www.PeirceEngineering.com

 

[hobo_ist]

@PEinc

Indeed I don't think taking the unexcavated piles as a fully fixed support to a cantilevering beam is the approach I want to explore here (not wrong but overly conservative leading to more than necessary reinforcement).

As per my sketch (where I've incorrectly shown spring constant as E*d) I think considering each unexcavated structural pile as a spring is a bit more sensible as it allows the load to be distributed over a greater number of piles (right to left) than if one were to assume a fully fixed connection at the crest (or slightly more to the left as SRE is suggesting) of the batter.

If I were to assume this as a cantilever beam with spring supports as shown in the attachment in the OP then I would be ignoring the restraint provided to the "unsupported" 6m of capping beam by the cantilevering piles tied to it.

 

[hobo_ist]

I am leaning towards whether a sensible approach to model this would be to also apply springs to the cantilevering side.

The pile analysis (done in WALLAP) shows a deflection of 30mm in the cantilevering piles. To work out the spring constant for the cantilever piles, I'm thinking of applying a notional horizontal load at the pile head (say 5kN) and seeing what this does to the deflection. If deflections were to increase to, say 35mm, I would take the spring stiffness as 5/(35-30) = 1000kN/m. I'm unsure if this is the appropriate approach for this as I'm not a geotech engineer, so some input would be appreciated.

 

[hobo_ist]

Also worth a note.

The 33kN/m load shown in the OP is the "prop load" output from the WALLAP analysis if the piles were to be propped rather than cantilever.

 

[PEinc]

hobo_ist, you said, "...I would be ignoring the restraint provided to the "unsupported" 6m of capping beam by the cantilevering piles tied to it." I don't think the 6m of piles support the cantilevered beam. Rather, the cantilevered beam supports the 6m of piles.

http://www.PeirceEngineering.com