Drilled shaft with rock anchorage

[leo5cn]

I have a 6' dia. RC drilled shaft sitting on bed rock 20' below grade.
Above the bed rock are compact to loose granular soils.
Top of the shaft is loaded by compression, uplift and shear.
The weight of the shaft and skin friction together do not offer enough uplift resistant capacity.
I am thinking about using rebars anchored to rock.
When I check the deflection at the ground level, the shaft is assumed free to rotate since the shaft is modeled as rigid and all soil layers are linear springs, therefore the bottom of the shaft's shear and moment are zero.
If I use rebars to anchor into rock, the bottom of shaft would be fixed and the shear and associated moment would pass down to the surface of the bedrock.
My question is if I don't consider the lateral resistance of soil above bed rock, I would get the full shear and moment, but that would be too conservative. Can anyone offer me more logical design approach?

 

[hokie66]

How much additional uplift capacity do you need? I would think the best way is to build your pile, then drill it centrally to install a rock anchor of the capacity required. You don't get "full shear and moment" at the bottom of a pile just because it is anchored to the rock.

 

[leo5cn]

Thanks. I could get away with the uplift if I auger 8' dia. footing. The question is construction has already ordered 6' rebar cage and I don't know if the bed rock is solid or fractured.
Without considering the bottom anchorage, the pier would be analyzed as linear deflection, the rotation point is somewhere along the pier, and the bottom is turned and laterally moved, so there's zero moment and shear.
Now we are fixing the bottom with rebar rings grouted to rock. If I don't take the soil springs into account, which means no lateral resistance along the pier. I would get a 20' long 6' dia. contilever column, therefore the "full moment and shear". I would check tension and shear of the rebar, also the development length within the rock. Again, that would an overkill, because the lateral resistance is there.
How do I mathematically model the pier with the bottom fixed, meanwhile, a number of linear springs with horizontal subgrade modulus offer lateral support. So that I could get a reasonable moment and shear.
The classic Brom's method and linear deflection method for short (in my case, L/D <4) rigid drilled shaft all assume the bottom is free to move.
Are there softwares that I could input the top (free head) and bottom (fixed) conditions, and spring constants for each layer of soil (say 1' per layer), then I get the shear and moment diagram?
I hope I explained the situation well.

 

[aeoliantexan]

LPILE plus by Ensoft will allow you to input a shear-resistance curve at the pile tip. Or you could model the pile with a one-or two-foot penetration into the bedrock. Run the model and see what you get for shear at the top of the bedrock. The moment will still go to zero at the tip.

 

[leo5cn]

Thanks, I know LPILE is popular for augered footing.

"The moment will still go to zero at the tip." ?? I am perplexed, if I fix the tip (either with rebars anchored to rock or drilled the entire shaft to rock), how could the moment be zero? We just assume the tip is pinned to the rock and the moment equilibrium is all by the lateral soil springs above bed rock??? That would be good for moment resistant rebar cage within the concrete pier, but how do I determine the tension for the rebars anchored to rock? only tension from uplift, no bending at all?

 

[hokie66]

It is not practical just to continue a rebar cage into rock. Who is going to get down in that hole and do the drilling? You don't even know if the rock is "solid or fractured". Either socket the whole pile into the rock or use rock anchors to provide the uplift capacity you need, as I suggested above. You are overthinking, and dwelling too much on modelling rather than practicality.

 

[leo5cn]

I agree with you, Hokie. In fact, I am requesting the rock shear value and going to use 2 rock anchors to resist the uplift only.

What if I use 4 rock anchors, or more than that? Would the spacing between rock anchors be considered bending arm?

Anchoring rebar cage is out of question. But using a number of rock anchors would give a strong moment. So using 1 or 2 rock anchors gives an uplift resistant connection only, but using more would make it a fixed connection.

The thing is when I intentionally make it a fixed tip, how do I proportionate the moment taken by soil with given properties, thus the rest of the moment by the rock anchors?

 

[hokie66]

Nothing is ever either completely fixed or pinned. Almost every connection I can think of is somewhere in between, and I fail to see that a few rock anchors in a 6' diameter pier would result in much bending resistance at the rock surface. Even if it did, it would be conservative for lateral loading to consider the base connection as pinned.

 

[FixedEarth]

The induced shear and moment in the shaft are only zero at the tip if your pier is long enough AND your pier diameter & F'c are adequate for the applied shear and moment loads. Shear and moment are not automatically zero just because you used beam on elastic springs. Try Lateral Foundation software to model it. It will give you shear, moment and deflection with pier depth. You can then see how much your pier moves. I like 0.01 inch or 0.25 mm or less movement at the pier tip. This is not a function of L/D but is related to soils, pier geomter, top of pier connection and applied loadings.

The other point is extending a smaller pier into Bedrock, will not necessarily fix the tip. You will get a higher lateral subgrade moduls and consequently less deflection but not necessarily "fixed" tip. How weathered is your Bedrock?

Consider checking with the geotechnical engineer to run uplift capacity analysis with constant diameter & with belled bottom at least to verify your uplift capacity values. Post a skecth showing the loadings, geometery and soils information so that we can give you more input.

Once you get your induced maximum moment, simply factor it to get your Mu and then design your reinforcement.

 

[leo5cn]

To "Hokie66":

Yes, it's conservative for lateral loading when the base is pinned, vice versa, it's conservative for rock anchors (say, #18 deformed rebars) when the based is fixed. It all depends on how you model and it's always murky. You can model pinned when you design the rebar cage, meanwhile, model it fixed when you design the rock anchors. Again, going back to square one, can we get a fraction of the moment and shear instead of zero or full?

To "FixedEarth":

Thanks for your input. But I double you will ever achieve 0.01" deflection unless your lateral force is extremely small. When your shaft is long, yes, moment and shear will go zero. But that's a different animal, it's slender, the design limit state would be flexure of the shaft rather than failure of soil, which is for short rigid shaft. The elastic spring method's limit state is servicibility, you never get 0.01" deflection unless the shaft diameter is extremly big, and we assume if the big transient horizontal force (wind) goes away, the elastic deformation of soil will bounce back.

I am new to geotechnical design but find it very interesting, it's almost like art.