Dear Satish,

the dilation angle of a soil is not constant with respect to the plastic deformation, from the physical point of view this is means that the dilation of the soil reduces as the soil deformation increases, you can notice that in the experimental results of a direct shear test. To be honest I can not know if your convergence problem is due to dilation angle but you can find below some information in order to take account the dilation angle in a more realistic way. Please keep in mind that the relationship between the dilation angle and the equivalent plastic strain is strongly depended on your soil and you need a direct shear test in order to calibrate it. You can find more information here Article Permanent earthquake‐induced actions in buried pipelines: Nu...

In Abaqus you can add a field parameter in your Mohr-Coulomb material and add more values of internal angle of friction and dilation angles with respect to this parameter, below you can find the corresponding lines of an input file. The values below are indicative, at "Mohr Coulomb,dependencies=1" the first value of each line is the internal angle of friction the second is the dilation angle and the third is the plastic equivalent strain (PEMAG, not PEEQ).

**

** MATERIALS

**

*Material, name=SAND

*Density

1.8,

*Depvar

1,

*Elastic

8000., 0.3

*user defined field

*Mohr Coulomb,dependencies=1

37.0, 0.1,0.0

45.0, 8.,0.016

37.0, 0.1,0.09

37.0, 0.1,10.

*Mohr Coulomb Hardening

2.,0.

**

Moreover please find below the corresponding subroutine:

subroutine usdfld(field,statev,pnewdt,direct,t,celent,time,

1 dtime,cmname,orname,nfield,nstatv,noel,npt,layer,kspt,kstep,kinc,

2 ndi,nshr,coord,jmac,jmtyp,matlayo,laccflg)

c

include 'aba_param.inc'

c

character*80 cmname,orname

character*3 flgray(15)

dimension field(nfield),statev(nstatv),direct(3,3),t(3,3),time(2),

* coord(*),jmac(*),jmtyp(*)

dimension array(15),jarray(15)

c

c Get PEmag from previous increment. Passed in as array(8)

call getvrm('PE',array,jarray,flgray,jrcd,

$ jmac, jmtyp, matlayo, laccflg)

field(1) = abs(array(4))

statev(1)=field(1)

c

return

end

I hope you will find this helpful, good luck with your research efforts.

Best Regards

gregory

My first thought is that you problem might be related to deformations rather than shear strength.

Dear Marcelo,

What exactly do you mean with deformations? Can you please make it a bit clear?

Negative eigenvalues are generally related to stability problems. I do not have this problem when i use clay model (c=50kPa). However, I have the problem when i use sand model ( even I am defining 5kPa cohesion ). In my opinion, there might be tension stresses developing in the sand and that causes stability problems. I tried to use some constraints to overcome this issue but until now I could not manage to do it. I really appreciate for any help.

Emre

Finally, I have solved the problem. As I expected, the problem is related to that instability occurs in sand model during the analysis. I changed the boundary conditions and my model worked properly without any "negative eigenvalues" errors.

Emre

Congratulations!

Very thank you for your advice, dear Xiaoben Liu.

Hello Emre

please could you try to explain in more details .

i have the same problem when i input the parameters of the sand.

friction angle 37

young's modulus 40 MPa

density 1530 kg/m^3 

when i am using Mohr coulomb is asking for the value of the cohesion which should be zero(0) for  the sand . anyway i have tried to input a small value like 1 KPa but it does not work. i have kept trying til 35 KPa and from this value was ok. but it is not realistic number.

could Emre help me of this problem?

or anyone have solve it befor/

many thanks

Dear Hasan,

Can I know more on how did you overcome the stability problem with modeling sand using the Mohr-Coloumb model. I am having similar difficulty with negative eigenvalues.

Thank you

Satish

Dear Satish,

Please check your boundary conditions. Because, improper BC's may be the reason of the instability in model. Due to this instability, you can have this issue related to negative eigenvalues.

I hope it helps.

Best regards

Emre

Dear All,

In general Mohr-Coulomb model is not converge easily especially in complex problems with sand. I have noticed that you can obtained the realistic transverse pipe-soil interaction simply by using a classical Mohr-Coulomb model with internal angle of friction equal to residual value and dilation angle equal to zero. Nevertheless, sometimes the dilation angle can help in converge. If you expected large deformation in your soil then the use of a constant value of dilation angle will lead to over estimation of the transverse pipe-soil interaction. An easy way to avoid this problem (if you are using ABAQUS)) is to define different set parameters for your soil which are function of plastic equivalent strain. You can update these parameters using a very simple subroutine named usdfld.

Best regards

gregory

Dear Gregory,

I have found that when I model clay with zero friction angle, the solution easily converges, but when I model sand with high friction angle values, then the convergence is slow and sometimes the solution does not converge at all. Is this because of dilation angle? I set the dilation angle to phi - 30. Also, how would you define different set of parameters based on plastic strain if you have limited data with work with? Is there any relationships, for example, relation between dilation angles and equivalent plastic strains?

Best regards,

Satish