When Φi is zero, it is not clear whether Φcs is zero or not.

When a test with frictionless particles such as glass particles is performed, it yields a non-zero Φcs value. 

Using DEM program, it is possible to set to Φi = 0. In this study, PFC3D (Particle Flow Code in 3 Dimensions) as a DEM program is used to simulate the triaxial test.

It is possible to derive the critical state friction angle from a triaxial test using the DEM (discrete element method) program by assuming the interparticle friction angle.

In this study, the relationship between interparticle friction angle and critical state friction angle is investigated by using the PFC3D program.