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Behaviour of the Mohr-Coulomb criterion for JCFPMphys

Asked by Hélvio Peixoto

Hi,

once again I have a question about the JCFPM physics [1]. This time, it is about the Mohr-Coulomb criterion.

In the file [2], line 144, the maximum force allowed for the shear force is set as the sum of the maximum cohesive shear force (user defined via the particle material), and the friction force proportional to the normal force magnitude "Fn".

Knowing that Fn = kn * D [3], and that D may evaluate to negative values, Fn will eventually be negative. So, for the cases where Fn < 0:

1 - is it the expected behaviour that negative (tensile) normal forces decrease the shear resistance of the interaction?
2 - maxFs is compared against the norm of the tangential force. If |Fn*frictionAngle| > |phys->FsMax|, then maxFs < 0, and then the contact fails due to shear. Should this be allowed to occur, I mean, a negative maxFs?

Best regards,

Hélvio Peixoto

[1] - https://answers.launchpad.net/yade/+question/644244
[2] - https://github.com/yade/trunk/blob/master/pkg/dem/JointedCohesiveFrictionalPM.cpp#L144
[3] - https://github.com/yade/trunk/blob/master/pkg/dem/JointedCohesiveFrictionalPM.cpp#L118

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Robert Caulk
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Robert Caulk (rcaulk) said : 		#1

Hello Hélvio,

>In the file [2], line 144, the maximum force allowed for the shear force is set as the sum of the maximum cohesive shear force (user >defined via the particle material), and the friction force proportional to the normal force magnitude "Fn".

FsMax is not explicitly defined by the user. FsMax depends on the particle size and the user defined cohesion [1].

>1 - is it the expected behaviour that negative (tensile) normal forces decrease the shear resistance of the interaction?

Yes, a negative Fn should decrease the maximum allowable shear force if we believe Mohr-Coulomb criterion govern the interaction. See Figure 2 of [2].

>2 - maxFs is compared against the norm of the tangential force. If |Fn*frictionAngle| > |phys->FsMax|, then maxFs < 0, and then the >contact fails due to shear. Should this be allowed to occur, I mean, a negative maxFs?

Where are you seeing this? The scalarShearForce is compared to maxFs to determine if the interaction has failed in shear at line 147 [3].

Cheers,

Robert

[1] https://github.com/yade/trunk/blob/master/pkg/dem/JointedCohesiveFrictionalPM.cpp#L285
[2]Scholtès, L., & Donzé, F.-V. (2012). Modelling progressive failure in fractured rock masses using a 3D discrete element method. International Journal of Rock Mechanics and Mining Sciences, 52, 18–30. http://doi.org/10.1016/j.ijrmms.2012.02.009
[3]https://github.com/yade/trunk/blob/master/pkg/dem/JointedCohesiveFrictionalPM.cpp#L147

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Hélvio Peixoto (hfcpeixoto) said : 		#2

Robert,

thanks for clarifying that the reduction of the maximum allowable shear force is possible. I was aware of article [1], and was looking for confirmation.

As to my question 2-, maybe I wasn't clear enough. I will try to reformulate the question:

We already agreed that it is possible, and expected, that Fn assume negative values. Being that the case (Fn<0), then at line 144 [2] maxFs will be negative when |Fn*phys->tanFrictionAngle| > |phys->FsMax|. If maxFs is negative, then it will cause a shear failure, as in line 147[3] maxFs is compared against a vector norm (scalarShearForce), that is always positive. Should this be allowed to occur, I mean, a negative maxFs?

Cherrs,

Hélvio

[1]Scholtès, L., & Donzé, F.-V. (2012). Modelling progressive failure in fractured rock masses using a 3D discrete element method. International Journal of Rock Mechanics and Mining Sciences, 52, 18–30. http://doi.org/10.1016/j.ijrmms.2012.02.009
[2]https://github.com/yade/trunk/blob/master/pkg/dem/JointedCohesiveFrictionalPM.cpp#L144
[3]https://github.com/yade/trunk/blob/master/pkg/dem/JointedCohesiveFrictionalPM.cpp#L147

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Best Robert Caulk (rcaulk) said : 		#3

Hello Hélvio,

It depends on your assignment of microparameters: tensile strength, cohesion, and friction angle. Figure 2 [1] is going to help you understand the answer to this question visually. The assignment of Mohr-Coulomb criteria here is a fancy way to say that we are using the equation of a straight line to describe the frictional behavior between the particles. We truncate the line at FnMax.

Equation of the line:
Fs = FsMax + Fn*tan(phi)
you are worried about Fs <= 0 when Fn is negative:
FsMax + (-Fn)*tan(phi) <= 0
FsMax <= Fn*tan(phi)
this only holds as long as Fn < FnMax = tA (line truncation, see Figure 2 [1]) and we know FsMax = cA
So the only way for Fs <=0 is for:
cA <= tA*tan(phi)

So as long as c > t*tan(phi) (which are all microparameters set by user) then the model will never see a negative value for Fs. So taking Table 1[1] as an example: the tensile strength would need to be increased from 4.5 to 138 MPa for a negative Fs value to occur. I think most yade users are micromechanically savy enough to avoid this kind of blunder, but to answer your direct question "should this be allowed to occur?" Hmmm, maybe it is worth adding an error message to protect users from accidentally defining unphysical microparmeters.

[1]Scholtès, L., & Donzé, F.-V. (2012). Modelling progressive failure in fractured rock masses using a 3D discrete element method. International Journal of Rock Mechanics and Mining Sciences, 52, 18–30. http://doi.org/10.1016/j.ijrmms.2012.02.009

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Hélvio Peixoto (hfcpeixoto) said : 		#4

Robert,

thanks for the thorough explanation. This was exactly what I was trying to understand.

The idea of adding an error message sounds good enough.

Thanks again,

Hélvio

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Hélvio Peixoto (hfcpeixoto) said : 		#5

Thanks Robert Caulk, that solved my question.

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Bruno Chareyre (bruno-chareyre) said : 		#6

>maxFs will be negative when |Fn*phys->tanFrictionAngle| > |phys->FsMax|. If maxFs is negative, then it will cause a shear failure, as in line 147[3] maxFs is compared against a vector norm (scalarShearForce), that is always positive. Should this be allowed to occur, I mean, a negative maxFs?

If I understand correctly it needs a fix, and the fix is simply to take maxFs=max(0,maxFs).

>1 - is it the expected behaviour that negative (tensile) normal forces decrease the shear resistance of the interaction?

Expected by the author of these lines, yes, probably. As Robert suggests it is a conventional Mohr-Coulomb condition.
More generally, it is just a constitutive assumption, and as such it is not right nor wrong in a general sense.
In PFC the assumption is(*) more to take friction OR adhesion, without summing them at any point. Just another assumption.

Bruno

(*) or "was", at least, years ago.