Rock-Socketed Wall Elements

[WBell]

I am trying to calculate the required depth of embedment, D for a rock-socketed HP pile for a non-gravity cantilevered wall according to 2010 AASHTO LRFD Bridge Design Specifications. Specifically, I am using timber lagging spanning 6-8 feet between HP piles set in concrete filled 2'-6" diameter drilled holes. Figure 3.11.5.6-2, Subsection 3.11.5.6 shows a free body diagram of the wall and the forces applied to the vertical element (i.e., HP pile).
I have set up a MathCAD sheet which solves the model for the unknown variable, D. What I am not clear on is how to represent the force, F applied at a distance D from the depth of excavation. Considering equilibrium of forces in the lateral direction, I should be able to solve for D and F simultaneously, as there are two equations (summation of forces and moments) and two unknowns. What I am not sure of is how the force acting at the tip, F is calculated.

I will share the MathCAD sheet if that will be helpful for the discussion. Currently, the solution is indicating a socket depth of only 0.54 feet, for a retained soil height of 20' (phi = 30 degrees, unit weight = 120 pcf, surcharge load of 107 psf) and the shear strength of the rock is 1400 ksf. The shear strength is being taken from a sample set of rock core data from the North Carolina DOT.

If there are any design guidelines similar to those for drilled shafts, please advise. For example, when designing drilled shafts, the length of shaft used to develop friction forces is reduced at the top and bottom of the shaft to account for the disturbed soil.

 

[WARose]

As a minimum (for full fixity) I specify about 2-3D embedment into rock. In the past, I figured the side wall pressures using something like a post-in-ground method (ala Czerniak's paper, or a variety of other methods).

I have had a geotech do it for me via L-Pile. But usually that creates a shear "spike" you have to deal with it.

The allowable side wall pressures on the socket are typically about half of the allowable end bearing values. That part is hard to get out of geotechs because research is rare. I go more into that in this thread:

https://www.eng-tips.com/viewthread.cfm?qid=447822

 

[STrctPono]

What are the active and passive pressures that you are coming up with based on the in-situ soil/rock properties that you are using?

 

[bridgebuster]

The attached calculations may be of some help. They're for a seawall, which uses H piles socketed into rock. A concrete wall encases the piles. The wall was designed using the Standard Specifications. There's also a reference to a NYSDOT manual that I'll post next.

 

[WBell]

Thank you for the responses. I have attached Figure 3.11.5.6-2 which shows the forces acting on the vertical element embedded in rock, which in this case is an HP pile supporting timber lagging. The force acting on the rock socket is directly related to the shear strength of the rock, Sm in the figure. If I use an average value of shear strength taken from the unconfined compressive strength in the NCDOT rock database (Su = Qu/2 = 1400 ksf) the required depth, D is less than one foot, which may satisfy equilibrium conditions, but is not practical or safe from a construction standpoint.

If I reduce the shear strength to 4000 psf, which corresponds to Terzaghi's value for the unconfined strength of clay at a penetration resistance of N = 30, where Qu = 4 Tons / sq. ft., then the value of D = 4 feet, which seems reasonable. However, the socked diameter I am considering is 2.5 feet and if I ignore the first 2 feet of embedment, this would result in a socket 6 foot deep. As a minimum, I would like to embed the HP pile at least 3 x diameter = 7.5, say 8 feet.

 

[bridgebuster]

This is the NYSDOT manual I mentioned.

 

[r13]

bridgebuster,

The NYSDOT link is empty. Maybe it is locked?

 

[bridgebuster]

Attached is a section and elevation of the wall. I recall there's a sketch of the soil layers used in the calculations but I don't have it at home; the attached section could provide some clarity for the calculations.

 

[bridgebuster]

retired13, I don't know why the file didn't upload; below is a link to the manual; scroll down the page to GDP-11.

Link

Wayne, I did a down and dirty (non-LRFD) analysis assuming Sm = 4ksf, piles are 8'apart, & b=1' and came up with D=8'6"

 

[r13]

bridgebuster,

Thanks.

 

[bridgebuster]

happy reading retired13

 

[jdonville]

@bridgebuster, without a diagram indicating how the various forces/pressures are acting and what portions of the pile they are acting on, it is difficult to verify your calculation by scanning through it briefly.

@Wayne_Bell, the large concentrated force at the tip is that from passive resistance acting in the same direction of the active pressure above the cut line. This is due to the rotation of the pile about the point of fixity in the embedded length and is a resultant of the triangular pressure distribution acting at the pile tip. Several textbooks explain the development and calculation of this force. If you can find a copy of Braja Das' Principles of Foundation Engineering, the general form of the development is in Chapter 5 (Sheet Pile Walls). Naturally, whether one has cohesive or cohesionless soils will influence the shape of the soil pressure envelopes.

Note that in my most handy (2014) edition of LRFD, that the term in the denominator of the passive pressure for Fig 3.11.5.6-2 assumes that the angle beta' is NEGATIVE when the embedded side ground surface slopes downward away from the piles (as shown on the figure) so that the denominator term gets LARGER and the available passive resistance gets SMALLER with a cut-side ground surface sloping down and away.

 

[bridgebuster]

@jdonville - as I indicated on Saturday, I didn't have sketch at home. Unfortunately, I can't find it on the office server; the guys who did the wall are long gone. Perhaps that will be one of my retirement projects: recreate the loading diagram. I found a copy of what's called the final calculations; I was able to follow along without a sketch.