Calculating the values of rock springs in Finite Element Software 3

[Just Some Nerd]

Hi all, needing a bit of guidance on this one as I can't seem to find good answers for the scenario I've got in my workplace. Thanks in advance for any help.

In my workplace here in Sydney, the overwhelming majority of our projects will be pad/strip/core footings embedded into rock. For the purposes of modelling structure behavior in finite element software (primarily ETABS, but others also) we need to model our larger footings with soil area springs for more correct behaviour of our structure.

The question I'd like to ask is what is the most appropriate method for calculating a footing spring when it comes to dense rock? Currently my workplace makes use of a calc sheet created for purpose at some point in the past by a 3rd party geotechnical engineer. The sheet was based upon some of Gazetas' equations for static stiffness (See tables 15.1, 15.2, etc. of the Foundation Engineering Handbook 1991 - Chapter 15). For our purposes these equations are very convenient as they only rely on knowing the Elastic Modulus & Poisson's ratio of the rock layer, and the dimensions of the footings we determine ourselves. While I don't have particular reason to doubt the engineer who provided this, neither I nor my company (we only deal with structure, not geotechnical matters) can be sure of the appropriateness of these equations with regards to a foundation embedded in rock, and much of the discussion in the chapter revolves around the dynamic behaviour of soils. Given our footings are almost always founded on stiff rock layers, are the static stiffness equations appropriate for use in our models? I am unconvinced concrete is going to be behaving like a suitably rigid foundation when sitting on rock with an elastic modulus in the 100s of MPa

A very basic rule of thumb alternative to our approach would be taking the allowable (service) bearing capacities for a rock layer + corresponding settlement provided by geotechnical reports and calculating an equivalent spring. Would this be more appropriate? Less accurate? Equally bad?

Would also welcome being pointed in the direction of alternative methods suited to foundations embedded in rock that are simple for us to calculate, given we never have much information beyond Elastic modulus, Poisson's ratio and allowable bearing capacity + the footing dimensions we determine ourselves

 

[MotorCity]

Seems to me that if you bear on rock, it is infinitely stiff (i.e. not a spring). A spring mechanism implies that there is a stiffness such that when a load is applied, a deflection results. I can't see how you would get that with rock. A load can be imposed on rock and increased until the rock fractures. There would not be any appreciable rebound or elasticity to rock.

 

[geotechguy1]

Of course there is a deflection when a load is applied, that's where the force to resist the load comes from. Otherwise we would all fall through the floor.

>The question I'd like to ask is what is the most appropriate method for calculating a footing spring

I thought for a bit about giving you some form of answer but, I think that the answer is actually that you need to contact a geotechnical engineer and get the stiffness parameters from them.

 

[Just Some Nerd]

Seems to me that if you bear on rock, it is infinitely stiff (i.e. not a spring). A spring mechanism implies that there is a stiffness such that when a load is applied, a deflection results. I can't see how you would get that with rock. A load can be imposed on rock and increased until the rock fractures. There would not be any appreciable rebound or elasticity to rock.

Rock is definitely very stiff - hence my line about being unconvinced that the spreadsheet given to us was appropriate for rock - but I don't believe it stiff enough to simply ignore imo. Geotechnical engineers tend to specify in their reports an allowable bearing capacity based on a settlement criterion, which implies some sort of pressure vs deflection relationship. In the case of footings under columns, we do in essence assume infinite stiffness as we won't model in a spring stiffness and instead will restrain the column base in translation with very little difference to results. In the case of larger footings under lift cores and the like however, the distribution of forces into the footing tends to be affected more substantially in a spring vs restraint comparison. It's also needed to model in an area spring to verify within the software that bearing capacities aren't being exceeded, as taking a vertical load and distributing it evenly doesn't work so well for a lift core footing as it might for a column footing.

I thought for a bit about giving you some form of answer but, I think that the answer is actually that you need to contact a geotechnical engineer and get the stiffness parameters from them.

I suspected about as much. I think I'll try push for my company to get another geotechnical engineer to provide us with an alternative process if possible - it would become quite a nuisance if we have to get a unique answer for each job rather than a verified method we can use to calculate for ourselves as often it's not so easy to get specific parameters out of geotechical engineers (at least in my part of the industry.

 

[1503-44]

Lay two flat plates together (no glue). One flexible, the other very rigid. Consider the bottom plate simply supported at all edges. Now put a load at the center of the flexible plate. Deflection of the flexible plate cannot be more than the deflection of the more rigid plate. The rock modulus controls the deflection of the footing.
Work the problem backwards from the rigid plate (the rock layer) deflection.
Using the deflection of the rock layer, calculate the stress in the concrete footing.
A simple beam on an elastic foundation analysis in Excel can tell you that when the springs have an equivalent modulus value N (10? I think) times the footing, or the footing's thickness approaches 25% of its span, the footing is, for all practical purposes, rigid.

The rock modulus can be estimated from typical values of rock type, or directly determined from shear wave tests.

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[Mccoy]

Given our footings are almost always founded on stiff rock layers, are the static stiffness equations appropriate for use in our models? I am unconvinced concrete is going to be behaving like a suitably rigid foundation when sitting on a rock with an elastic modulus in the 100s of MPa

I've been using the approximate solutions from Gazetas you cite and the rigorous solutions from Pais & Kausel. The hypothesis is that the foundation is rigid but it is shown that a nonrigid foundation is an acceptable approximation.

What happens in the presence of a rock mass which is not extremely fractured is that the spring stiffness turns out to be very high, relative to the foundation geometry.

I just tried the Pais & Kausel method, with a competent rock mass with a Vs= 1000 m/s .

A mat 10 by 12 meters[sup]2[/sup] , 0.5 m thick will have a static vertical modulus of soil reaction equal to 64 kg cm-3
On the same rock, a 3 by 3 meters[sup]2[/sup] footing will have a static vertical modulus of soil reaction equal to 262 kg cm-3

The numbers bespeak of a hugely stiff spring. Of course, even a uber stiff spring will settle with a comparatively huge load. In our case, the spring would settle one centimeter with a load of 64 kg cm-2 on the mat and 262 cm-2 on the footing. Those are values typical of pretty heavy structures.

 

[Settingsun]

Being in Sydney, you may be well aware of Pells, but here's a link in case you aren't. Better safe than sorry.

https://pellsconsulting.com.au/foundations-on-rock/