# How to use periodic boundaries for triaxial test simulation after erosion

Since the erosion problem is a boundary value problem, a non-periodic boundary is used to simulate erosion, and the confining pressure is applied through six walls. After erosion, perform a triaxial experiment. In order to reduce the volume of the representative unit and want to use periodic boundaries, how to realize the conversion from non-periodic boundary to the periodic boundary without disturbing the sample？

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 Revision history for this message Jan Stránský (honzik) said on 2021-11-04: #1

Hello,

in general, it is not straightforward to change non-periodicity => periodicity

> In order to reduce the volume of the representative unit and want to use periodic boundaries,

so you are going to simulate a (much) smaller periodic sample out of original non-periodic sample?

> how to realize the conversion from non-periodic boundary to the periodic boundary without disturbing the sample？

One option is to create a new periodic sample, preserving characteristics of the original sample.
Not straightforward either..

Cheers
Jan

 Revision history for this message Zhicheng Gao (zhichenggao) said on 2021-11-04: #2

Dear Jan,
Thank you for your response, this is my reply and new questions,

> In order to reduce the volume of the representative unit and want to use periodic boundaries

Yes, I first prepare the sample by isostatic compression in all directions and then apply a water pressure difference between the upper and lower interfaces in a certain direction, use PFV to solve it to simulate the erosion process, and then perform a triaxial test. In order to be able to perform quantitative analysis, it is necessary to use a representative unit, but the representative unit with a non-periodic boundary requires too many particles, so after the erosion, I want to use the periodic boundary to reduce the number of particles in the representative unit.

>One option is to create a new periodic sample, preserving characteristics of the original sample. Not straightforward either..
The specific process is to save the position and size information of the particles, then read the information of the particles, and generate these particles one by one? Is it possible to directly generate the periodic boundary and then delete the wall?

 Revision history for this message Zhicheng Gao (zhichenggao) said on 2021-11-04: #3

Dear Jan,

 Revision history for this message Jan Stránský (honzik) said on 2021-11-04: #4

> Is it possible to directly generate the periodic boundary and then delete the wall?

It is possible, but it would result in something different than you want.
You can delete walls, you can extract certain area, you can also set periodic boundary conditions, it is no problem.
The problem is that at the "faces" the particles would not match on opposite faces. It would behave like there would be a crack every cell distance.
(The periodicity would work ok, however)

> The specific process is to save the position and size information of the particles, then read the information of the particles, and generate these particles one by one?

This would be too easy :-D
I meant to create a new periodic packing from scratch. But instead of creating a random packing, you would need to impose the eroded characteristics.
The challenge is how to identify the "characteristics" and then how to impose them on the packing.

Cheers
Jan

 Revision history for this message Zhicheng Gao (zhichenggao) said on 2021-11-04: #5

>The problem is that at the "faces" the particles would not match on opposite faces. It would behave like there would be a crack every cell distance.
(The periodicity would work ok, however)

I know what you mean, that is, the particles up and down in the same direction will not be embedded in the grooves formed by the particles. I want to know if this will have a big impact on the results of the three-axis experiment? After the erosion, the particle distribution is not uniform and it is anisotropic. Can period boundary be used for the anisotropic sample?

>I meant to create a new periodic packing from scratch. But instead of creating a random packing, you would need to impose the eroded characteristics.
The challenge is how to identify the "characteristics" and then how to impose them on the packing.

This feature is also what I am researching. In other words, is it best to delete the wall directly and impose periodic boundary conditions?

 Revision history for this message Jan Stránský (honzik) said on 2021-11-04: #6

> I want to know if this will have a big impact on the results of the three-axis experiment?

For sure it will have some impact.
If "big impact", it depends on your definition of what "big" is.

> Can period boundary be used for the anisotropic sample?

yes, definitely.

> This feature is also what I am researching. In other words, is it best to delete the wall directly and impose periodic boundary conditions?

I am not sure what you mean here, please be more specific (e.g. "diretly" w.r.t. what?).

Cheers
Jan

 Revision history for this message Zhicheng Gao (zhichenggao) said on 2021-11-05: #7

> This feature is also what I am researching. In other words, is it best to delete the wall directly and impose periodic boundary conditions?
I am studying the effect of erosion on granular materials.