New in 4.0

The new material-genesis procedure employs the following steps:

1. The material vessel is filled with a dense packing of frictionless particles at an initial particle size distribution throughout the material vessel.

2. The particle sizes can be refined in regions that are defined by named ranges. The refinement regions and levels (0 = no refinement) to produce a graded assembly with smaller particles inside the refinement regions are shown in the image below. Each particle in a refinement region is replaced by two smaller particles that have the same total volume as the original particle, and this replacement process is repeated for each particle until the specified refinement level is reached.

Left: the refinement regions and the level of refinement (l) applied to the particles. Middle: the particles in each refinement region that will be affected are shown. Right: The resulting particles after refinement has been completed.

3. If the initial grain shape is a clump, then each particle in the system described in steps 1 and 2 above is replaced by a clump with the same volume as that particle. The clump is easily defined using a clump template that specifies radius and position of any number of particles composing the clump. The procedure automatically calculates the volume of the clump, computes the scale factor and scales the clump, and randomly orients and positions the clump centroid at the centroid of the original particle.

4. A specified isotropic stress is obtained (Potyondy and Cundall, 2004). If the grain shape is circular or spherical, then floating particles (those with less than a user-specified number of contacts, usually set to three) are removed. The final specimen is produced by adding contact and/or parallel bonds (if desired).

Left: the particles after the clump-insertion procedure. Middle: the material after frictionless packing. Right: clumps and contact forces after isotropic stress installation (bonds will be added at all contacts with a non-zero force).

Together, particle-size refinement and clumping can have significant impact on specimen properties, including friction angle, coordination number, porosity, stiffness, etc.

The Effect of Clumps

Defining complex clump shapes can be done by simply defining the disk/sphere locations and radii of a unit clump. An initial disk/sphere packing (as described above) is then replaced by an equivalent volume unit clump with a random orientation.

Studies have shown that the use of multi-particle clumps increases the effective friction angle of the PFC specimen as compared to spherical particles.* This, in turn, can yield a more realistic representation of the macroscopic material behavior.

Results of simulated triaxial testing on spherical and clumped particles.

After the clump is defined, multiple material micro-properties and size refinement is accomplished automatically by defining the desired ranges for modification and degree of size refinement, as seen in the figure below.

Examples of two specimens generated using the clump base units shown in the figure above containing a core zone of different micro-properties and two levels of refinement to produce a graded material (finer towards the middle).

Slope Stability describes a project that makes complete use of the enhanced material genesis techniques available in PFC 4.0.

 

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*M.E. Pierce et al. "PFC3D modeling of caved rock under draw," in Numerical Modeling in Microemchanics via Particle Methods, Proceedings of the International PFC Symposium, Gelsenkirchen, Germany, 6-8 November 2002. Heinz Konietzky, Editor. Taylor & Francis, 2004.

The joint geometry of a single smooth-joint contact is defined by a plane that is comprised of two initially coincident planar surfaces. The two contacting particles are permanently associated with the two surfaces, one per side. The contact force-displacement law provides Coulomb sliding with dilation. During each time step, the relative displacement increment between the ball surfaces is decomposed into components normal and tangential to the joint surfaces. These components are multiplied by the shear and normal joint stiffnesses to produce increments of joint force.

standard contact model (relative normal and tangential displacements with respect to the contact orientation) smooth joint model (relative normal and tangential displacements with respect to the joint orientation)

The joint is described as "smooth" because particles that have been assigned a smooth-joint contact may overlap. This insures that the particles will "slide" as expected along the joint, rather than be forced to move around one another.

motion of upper particle with an ordinary contact when subjected to a lateral force motion of upper particle with a smooth-joint contact when subjected to a lateral force

Frictional joints may be modeled as collections of smooth-joint contacts.

The above image shows a PFC2D model with a single, through-going frictional joint. At left the specimens are shown with the initial definition of the joint in blue. The smooth-joint contacts are shown in red. The specimens are subjected to uniaxial compression as part of an unconfined-compression test. The velocity fields for both models, shown at right, indicate that the specimens fail by sliding along the joint.

Replay

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The above animation shows a PFC2D specimen that contains a through-going joint with friction coefficient of zero. The bottom layer of particles is fixed, a wall is placed at left to stop the motion of the upper block, and gravity acts downward. Note that as displacements occur new smooth-joint contacts are created between particles that have come into contact as a result of large shearing motion.

For a complete, detailed technical specification of the smooth-joint model, please see the document (from the manual) "Smooth-Joint Model" [428Kb].

LOP Slope shows a practical application that uses the smooth-joint contact model.