Soil stress beneath strip footings

[magudfe]

Hi,
I have the following problem designing the foundation of a structure composed by an heavy loaded part connected to a lighter part.
The heavy loaded part of the structure is based on a mat foundation. The other part is based on strip footings. The strip footings are connected to the mat foundation.

In the FEM model I insert the k value (subgrade modulus for the foundation), in order to model the behavior of the soil.
The k value depends on the width of the foundation, thus I insert different value for strip footings and for mat foundation (k value for strip footings in this case is around 5 times bigger than k value for mat foundation). The analysis shows big settlements under the mat foundation, and smaller settlements under the strip footings.
In corrispondance of the connection between strip footings and mat foundation, the settlements are similar, thus the soil stress beneath strip footings is much bigger than the soil stress beneath the mat foundation (this because I obtain the soil stress multiplying the settlements by the k value, that is different according to the width of the section).
This result seems not normal, leading to soil stress beneath the strip footings more than double those obtained with hand calculation.
Keep on going on this way, the only solution seems to define only one mat foundation for the whole structure.

What is you opinion/suggestion about this?

Thanks in advance.

 

[LCruiser]

What are the strata below? This required much more information.

 

[msucog]

without knowing nearly enough information to hazard a sufficient guess, i'm confident that you've got a rather complicated scenario. if you haven't do so already, enlist a good geotech. perform soil test borings, lab testing, settlement analysis, etc and work through this with the geotech.

 

[fattdad]

The subgrade modulus will not properly address the stresses in the soil strata with depth. You need a geotechnical soil profile (i.e., soil modulus or 1-d consolidaiton characterists and water table information) to evaluate the settlement response of the mat. Additionally, the stresses of the slab will affect the stresses beneath the strip footing and together, the strip footing will move depending on the mat stress and the wall loads.

Hope this helps.

f-d

¡papá gordo ain’t no madre flaca!

 

[magudfe]

Below the soil layers encountered:
-top sands (from 0 level to -2.5m)
-quaternary sands medium dense to dense with deformation modulus Es=70-90MPa (from -2.5m to -12m)
-clayey quaternary sands with deformation modulus Es=60-80MPa (from -12m to -14m)
-sandy loam (weak soil properties) with deformation modulus Es=15-30MPa (from -14m to -25m)
-footbase sands (dense sand) with deformation modulus of Es=80-100MPa (from -25m to -30m)

The level of underground water is -10m
The bottom level of foundation is -2.5m / -3.5m.
The mat foundation has a dimension of 14x35m2
The strip footings are 1.5m width and 16m long.
Mat foundation and strip footings tranfer an average stress on soil of 200KN/m2.

Regarding the sandy loam layer, draw down settlements due to the low Es-values of the encountered clays are considered, and the expected settlements in this scenario are around 3 to 6 cm. For this reason we are performing a plant initiation with constant and distributed life loading in order to reduce the settlements to 2 cm.

 

[kslee1000]

You would definitely require the help (to explore and interpret the under laying soil) from a geotechnical engineer. However, from structural analysis point of view, you should grid the mat (3D or 2D plate element), and segamentize the strip footing (2D beam element). Then obtain and apply the spring constant (k=E*A, area tributary to the common node) to the nodal points. You may vary E to reflect the type of soil ecountered in varies locations.

 

[magudfe]

Thanks, yes I am doing it, but the problem is that the subgrade modulus [force/lenght^3] depends not only on the soil layer below, but also on the width of the foundation. Bigger is the width, smaller is k value. This is why I find k values so different for strip and for mat.
Once defined k, I multiply it by the influence area in order to define the spring stiffness for the FEM model.

The mat foundation moves down and drags down the strip footings. Can this effect cause the failure of the soil beneath the strip footings but not beneath the slab, even if the 2 foundations are very near and connected?
Anyway, I will advise with the geothecnical engineer.

 

[kslee1000]

I think there is misconception on how to derive and apply the k (spring constant) values for footings large and small combined together (as in your case). You do need helps from the geotechnical engineer to evaluate the soil and advise. Here are questions from structural point of view, is there any restriction on differential settlement for these two parts? Can you seperate the two parts by expension joint rather than rigidly connecting the two? I, myself, need to dig into the text book to find out relationship between footing area and soil modulus.

 

[magudfe]

The differential settlement restriction are severe. Moreover the upper structure is rigid, therefore even if I separate the two foundation, the rigidity of the upper structure will let the strip footings follow the mat.
Regarding k I'm using the Vesic theory indicated in Bowles "Foundation analysis and design". It is indicated that k=Es/B/(1-m^2) where m is the Poisson's ratio, B the width of foundation and Es the deformation modulus.

 

[Mccoy]

"It is indicated that k=Es/B/(1-m^2) where m is the Poisson's ratio, B the width of foundation and Es the deformation modulus"

Which values did you figure out for Es and m?

Shallowest layer? Weighted mean of layers? Else?

Did you use m-values as suggested by Bowles'tables or some more specific indications (0.15 to 0.2 for sands, 0.5 for clayey soils below GW)?

Vesic's formula does not account for influence factors due to the geometry of the setup. When using subgrade modulus to assess overall serviceability and not structural serviceability of the foundation structure problems may arise especially in mat foundations on layered soils...

Anyway, your final result (mat yielding remarkably and dragging down strip foudnations) would also agree with the presence of the weaker layer within the mat's influence area)

 

[magudfe]

I used Es=58Mpa for the mat, Es=80 for strip; Poisson ratio m=0,3.
"Vesic's formula does not account for influence factors due to the geometry of the setup", do you mean that I should consider the Steinbrenner factor?