here is an explanation.

Thank you. But I still don't understand how the horizontal stresses (sigma xx in Plaxis 2D) are influenced by Poisson's coefficient. The vertical and tangential stresses are not affected by it and all stresses are independent of Young's modulus. 

Actually I do not understand that the analytical equations are independent of material parameters, this means the results are identical whatever material is used?

During numerical calculation, the variation of assumed strain causes the variation of stress, and the relation is governed by constitutive law. In MC model, the bulk modulus is Poisson ratio dependent, then the resulting stress is Poisson ratio dependent as well.

here are the equations used to determine the stress state. as can be seen they are only dependent on the position of the point in the soil mass and on the applied load. they do not account for soil parameters. when i model the same problem in Plaxis, the obtained results are very similar with the ones obtained with these equations, except for the horizontal stress which seems to be dependent on Poisson's coefficient. The horizontal stress however comes close to the value obtained with the analytical equation when Poisson's coefficient is close to 0.5. 

Therefore, the strains are calculeted from stresses based on the constitutive law, and not the other way arround. In this case how are the stresses obtained? 

I assume that you have an assumption that soil is imcompressible in your analytical solution, this coincides with that Poisson ratio equals 0.5 in the elastic material.

Physically, stress causes strain. But in finite element solution, stress is calculated based on the assumed strain in each iteration, not the other way around.

Thank you for your answer. What I didn't understand was why stresses are independent of Young's modulus since they are obtained from the constitutive equation which involves both Young's modulus and Poisson's ratio. However, I neglected the fact that the constitutive matrix is also involved in the stiffness matrix which is used to determine the displacements. Hence, when stresses are obtained from the constitutive equation, Young's modulus is reduced.

What is the size of your Plaxis FE model? Did you check the ratio b/(width of the model) to be sufficiently small (e.g. 1/25 for q=1MPa)? Stresses are obtained to satisfy the equilibrium (or to minimize the work according to the precision criteria).

What about your initial stresses ... Do you solve the problem using weightless material or you you have some initial stresses ... Usually in elastic material the horizontal initial stresses are calculated using Ko which is Poisson's ratio dependent. 

Ayman Abed, the initial stresses are calculated with K0 but why do you say that K0 is Poisson's ratio dependent? K0 is calculated in Plaxis based on Jaky's formula :1-sin phi. 

Initial stresses and the boundary condition are the reason for the deviation you found between the analytical solution and the numerical solution by FE model in Plaxis. If you want to compare a FE solution and an analytical solution you have to first be sure you are solving the same problem.

For linear elastic material Ko = v/(1-v) where v is Poisson's ratio. I believe that your analytical solution is valid for linear elasticity ... so it would.be better for you to use linear elastic material model in your Plaxis calculations and then do the comparison.

Thank you Maria Datcheva and Ayman Abed for your answers and interest regarding this subject and my apologies for this late answer. The boundaries for the model are sufficiently large as not to affect the results and I do not believe the problem to be related to the initial stresses because I can easily determine them using Jaky’s equation. I believe that the problem is related to the way that the stresses are distributed in the soil mass strictly from the external load. I have found an answer to this problem in the following article: “Effect of variable linear elastic parameters on finite element prediction of soil compaction” by Raper R.L. and Erbach D.C. The article can easily be found on the internet and it states the following: ”…Young’s modulus does not affect the stress levels. It only has the effect of decreasing deformations and strains. Unfortunately, it is not as easy to determine the effects of modifying Poisson’s ratio. Because of the manner that Poisson’s ratio is incorporated into the stress-strain relationship, it is not intuitively obvious how its adjustment will affect the element stresses and strains.”. A more detailed explanation is given in the article.

Also, Ayman Abed, regarding your statement as to using linear elasticity: although I modeled the soil with Mohr-Coulomb, the applied load is sufficiently small as not to generate plastic points in the soil mass..so the soil behaves in a linear-elastic manner.

when the analysis is done by the Axisymmetry model, the out put of force vs displacement is obtained by the kN/rad. simply we multiply 2pi and get force in kN. in this case square footing (150x150mm) is half.

but when the same analysis is done the Plain stain model, the output is obtained kN/m. so which dimension is multiply to get force or how to calculate bearing capacity from this. use square footing 150x150

Note: in these two analysis condition is same but the result (output foce) is different

pictures are attached. please explain