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# Modelling soil stiffness as Spring Support

## Modelling soil stiffness as Spring Support

(OP)
Hi Guys

I am designing a reinforced strip footing, basically a groundbeam, with column loads of various magnitudes and at irregular intervals sitting on the beam. The beam will bear on clay. To design the beam rebar, I need to find the worst or biggest bending moments. The way I am thinking of doing this is to create a continuous beam with my structural software, with spring supports at say 500mm centres, and then place all the point loads on the beam. This will give me a bending moment diagram for the beam which I can use to calculate the reinforcement needed. What I need to know is what to use as spring stiffness when modelling the ground as spring supports. Spring stiffness is the load in kN needed for a certain deflection in metres. At least that is how it is input to my analysis program.

The safe ground bearing capacity of the ground supporting my beam is 150kN/m2, which should limit deflection to 10mm.
Does this mean that I can use my stiffness as 150/0.01 = 15000? I have tried this and it does seem to give realistic answers. Was just wondering if any of you have done similar calcs for raft foundations and beams.

Thanks

### RE: Modelling soil stiffness as Spring Support

I don't design foundations but the number you calculate has units of kN/m^3.  I think you need to multiply by the tributary area for the spring (unless it happens to be 1 m^2).

### RE: Modelling soil stiffness as Spring Support

This is essentially a Winkler idealized foundation and as such you should have your geotech provide a subgrade modulus to determine your springs.

Regards,
Qshake

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### RE: Modelling soil stiffness as Spring Support

sybie99

I basically do what you have done and then check sensitivity using say half and double the initial spring stiffness, it often doesn't make a lot of difference.

As I see it, you can calculate the subgrade modulus if your geotech has supplied expected settlement for a recommended bearing stress.

### RE: Modelling soil stiffness as Spring Support

How did you determine that an allowable bearing pressure will limit the settlement to 10mm?

My spacegass user manual which references the bowels textbook states that clayed soils with an ultimate bearing capacity between 200 and 400kPa (which would roughly equate to what you have) a typical modulus of subgrade reaction would be between 24,000 and 48,000kN/m^3. If your ground beam is say 600mm wide (2' wide) and you have modeled a spring every 300mm, than a soil spring constant of 4,320kN/m to 8,640kN/m might be a good estimate.

With these spring stiffnesses modeled, if you find that your soil is typically experiencing a bearing reaction of 150kPa/22psi, (27kN/6.1kips) than you would have allowed a settlement of 3.1 to 6.2mm (1.5 to 2.5").

The variation of bearing pressure will also be dependent on the stiffness of your ground beam. Typically for something like this, I would assumed that the ground beam is rigid and triangular bearing pressure distribution results to balance any eccentricities.

Like yourself, I am also looking for some good reference material on computer modelling of soil-structure interaction.

### RE: Modelling soil stiffness as Spring Support

asixth,
No comment about your approach, other than that your conversion mm to inches is off by a factor of 10.

### RE: Modelling soil stiffness as Spring Support

(OP)
Asixth

Thanks for the reply. The 150kPa and 10mm settlement is just a typical figure just used to illustrate the situation.

One thing, are you sure the spring stiffness should change or be affected by the width of your beam? I would think that soil stiffness remains constant no matter what your beam width? If I place a support every meter for 150kPa ground capacity allowing 10mm deflection, my stiffness would be 15000, if I place a support every 500mm, I would make the stiffness 7500. This gives similar results. I would then check that my support reactions do not exceed the allowable pressure, which for 150kPa SGBP and a 500mm wide beam with supports 1meter spacings would be 75kN

### RE: Modelling soil stiffness as Spring Support

some programs determione the spring stiffness for you after you input the soil modulus. Don't get confused as to what the program is asking for.

### RE: Modelling soil stiffness as Spring Support

sybie99

I definitely think that the spring stiffness modeled would be affected by the width of the beam if you are trying to establish a bearing pressure acting on your ground beam.

Modelling a spring stiffness as a support will only yield a reaction (force) and settlement (distance). To convert your reaction to a pressure you will need to consider the width of the beam.

Remembering most importantly that the analysis is a mathematical representation of a structure. Materials are not elastic. You will still need engineering judgment to establish whether your results are reasonable.

hokie

my conversions are horrible, I think this has been the second you have picked me up on my conversions between millimeters and inches. Just to clarify 25.4mm=1", so 3.1mm to 6.2mm would be more like 1/8" to 1/4".

### RE: Modelling soil stiffness as Spring Support

hmmm i think there is more to that than just dividing by deflection.. i think you need to run the program and check the deflection if it is over certain value that's where you decide if your assumed subgrade modulus is acceptable or you need to change it..

### RE: Modelling soil stiffness as Spring Support

If a bearing pressure of 150 kPa results in a deflection of 10 mm, then the spring constant for the soil is 15,000 kN/m3.  So where is the problem?

BA

### RE: Modelling soil stiffness as Spring Support

remember the bearing pressure normally has a safety factor thus the method is conservative, if all deflections are less than 10mm.

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that they like it

### RE: Modelling soil stiffness as Spring Support

Here is how I estimate subgrade modulus, if not provided by a geotechnical engineer:

The allowable bearing pressure for a given soil is really not a strength limit, but a settlement limit.  It is the value that will limit settlement to a given value (usually 1/2" in English units).  Therefore, I double this value to calculate the spring constant, which is the bearing pressure which will cause the soil to compress 1" (again, I am working in English units).

DaveAtkins

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