Footing on bedrock, rotational stiffness / degree of fixity

Question

Footing on bedrock, rotational stiffness / degree of fixity

isidor_ (Civil/Environmental)

(OP)

30 Aug 22 14:52

Hi,
I hope my first post ends up in the correct forum, I tried to search for relevant post to this subject.
(I am located in Europe so Eurocode applies for this)

I have been tasked with the design of the foundation for a structure. It will be braced against horizontal load by fixed concrete columns, alternative bracing methods are not possible.
The foundation will be cast footings on bedrock.
Almost everywhere there is sufficient deadload to stabilize against the overturning moment, and the base of the footings will be in compression (M/N<L/6 = eccentricity).
I got a question regarding the "Degree of fixity" from the engineer doing the precast superstructure, if they can assume fully fixed rigidity at the base of the columns in their FEM model, thus what spring stiffness they should set at the support.
I asked some colleagues about it but they have not computed it. (I know that fully fixed is a theoretical thing.)
If the whole of the footing base is in compression and the bedrock can take the compressive force then the movement should be minuscule is my assumption.
Any input into this would be greatly appreciated!
Thanks in advance,
Isidor_

EireChch (Geotechnical) · Answer 1 · 2022-09-02 12:49:28

The columns are fixed to a footing that is resting on rock. Horizontal translation (sliding) and overturning are possible modes of failure when considering horizontal loading.

You are only considering overturning, should you not also be considering the sliding potential?

What is resisting sliding? It is the base frictional force and any passive resistance from embedment. I do not believe that these would be hefty enough to provide zero movement so a fully fixed condition shouldn't be assumed.

le99 (Civil/Environmental) · Answer 2 · 2022-09-02 17:42:19

You should tell them the fixity used in sizing the footing. They shall apply the same fixity with compression-only spring in the vertical direction..

EireChch (Geotechnical) · Answer 3 · 2022-09-03 04:10:27

le99 - do you mean fixity used when sizing the foundation based on internal structural forces or sizing it based on bearing pressure required?

le99 (Civil/Environmental) · Answer 4 · 2022-09-03 19:22:29

Yes. The assumption on support fixity should be consistent throughout, the variable is the footing size.

mtu1972 (Structural) · Answer 5 · 2022-09-03 19:46:30

When I worked on Minnesota’s Iron Range our company had standard details that included “rock anchors”, to provide fixity for the foundations. They were rebar grouted into drilled holes in the rock and projected and bent into the footing. As this was ages ago I don’t have those details. My recollection is that we were using Working Stress loads and the embedded lengths in the rock were longer than the total development length in the footing.

gjc

Mccoy (Geotechnical) · Answer 6 · 2022-09-03 20:18:46

My attention was caught by the 'rotational stiffness' since it is rarely considered. The stiffness of bedrock (which bedrock?) is usually very large in translational stiffness, so much so that to all practical purposes we can assume a fixed constraint (especially if the bedrock exhibits few fractures and has a high compressive load). Translational stiffness is also dependent on embedment, if there is a good degree of coupling between foundation and soil/rock.

A few real-world values of the coefficient of subgrade reaction in a rock with 1000 m/s shear waves velocity (true bedrock according to EC-8 standards). Square footing 4*4 m^2 area, 1 m well-coupled embedment in rock. Static conditions values

vertical translation Winkler coefficient: 209 daNcm^-2
horizontal translation Winkler coefficient:: 206 daNcm^-2
Rotational rigidity around x or y axes: 9940190.5 daNcm^-1 rad^-1

By the way, spring stiffness is different from coefficient of subgrade reaction or winkler coefficient, different units as well. In the case of vertical translation, spring stiffness is 33477425 daN cm^-1, that is about 33.5 million kg on the foundation are needed to cause a settlement of one centimeter (33.5 thousand metric tons). Or a distributed load of 21 MPa. Practically, an almost infinite rigidity for not exceptional loads.

le99 (Civil/Environmental) · Answer 7 · 2022-09-03 21:47:31

Quote (Mccoy)
My attention was caught by the 'rotational stiffness' since it is rarely considered.

I agree. Because it always lies in between fixed and pinned conditions, and is very difficult to evaluate, if possible. So, mechanically "fix" the footing pad is a good idea.

isidor_ (Civil/Environmental) · Answer 8 · 2022-09-06 07:34:29

Stellar replies!
Didn't think I got any because the email notifications ended up in the junk mail folder -.-

EireChch
The horizontal force I have is about 50kN,whilst the (vertical) dead load is 5MN and the footings will be cast in holes in the rock so sliding should not be an issue according to my handler. The overturning moment is about 500kNm. (all loads above are for the load case with minimum V load and max horizontal)

le99
That's good input about only allowing compression in the foundation, they could lock the columns to the footings and set the footings support to only resist in compression aswell as with a plastic limit for the rock capacity if they want to go whole hearted for the fem design

mtu1972
Yes, that is an option we have and most likely will use where there is not enough vertical load balancing the overturning moment

Mccoy
The maximum stress in the bed rock atm is about 2,5MPa. We are waiting on the site testing on the rock after it has been leveled out by the "explosion" team (my English is failing me atm -.-)

le99
It will be fixed if it is needed, but it is a lot of columns and footings so I don't want to do it unless necessary

Hope i replied to all of you, I am out of office today so replying on my phone

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Footing on bedrock, rotational stiffness / degree of fixity