Material Modeling Support For PFC

The PFC model provides a synthetic material consisting of an assembly of rigid grains that interact at contacts. This synthetic material encompasses a vast microstructural space, and only a small portion of this space has been explored. For example, the bonded-particle modeling methodology provides a rich variety of microstructural models in the form of bonded materials ([Potyondy2015c]; [Potyondy2004c]) [1]. The PFC model includes both granular and bonded materials as well as an interface that can be inserted into the bonded materials. The material-modeling support that is provided for PFC is described in [Potyondy2017a]. The material-modeling support package consists of a consistent set of FISH functions, which we call the PFC FISHTank (or fistPkg). The PFC FISHTank provides a state of the art embodiment of four well-defined materials and a user-defined material to support: practical applications (via boundary-value models made from these materials), and scientific inquiry (via further exploration of the microstructural space described above) [2].

The following three particular instances of a bonded material are created and defined by the material-modeling support package. A contact-bonded material is a granular assembly in which the linear contact bond model exists at all grain-grain contacts at the end of the material-finalization phase [3]; new grain-grain contacts that may form during subsequent motion are assigned the linear model. A parallel-bonded material is a granular assembly in which the linear parallel bond model exists at all grain-grain contacts at the end of the material-finalization phase; new grain-grain contacts that may form during subsequent motion are assigned the linear model. A flat-jointed material is a granular assembly in which the flat-joint model exists at all grain-grain contacts with a gap less than or equal to the installation gap at the end of the material-finalization phase; all other grain-grain contacts as well as new grain-grain contacts that may form during subsequent motion are assigned the linear model. A smooth-jointed interface can be inserted into the bonded materials by identifying the contacts near the interface, and replacing their contact models with the smooth-joint model.

Bonded materials are analagous to intact rock, which can be viewed as an aggregate of crystals and amorphous particles joined by varying amounts of cementing materials. The bonded materials produced by the material-genesis procedure in the material-modeling support package approximate an intact compact rock with average homogeneous isotropic properties at a scale larger than the material granularity. The synthetic material is analogous to brittle cookie dough that has been solidified by baking and for which grain size corresponds with dough granularity. The granularity is quantified by means of its resolution (or number of grains across a relevant dimension).

A rich variety of microstructures can be produced by modifying the bonded material itself. Such microstructures are obtained either by modifying the properties of the grains and cement or by modifying the packing fabric. The grain properties are size and shape. The cement properties are deformability and strength as well as evolving damage. The cement properties are embodied in the contact model, but the macroscopic material behavior is also sensitive to the ways in which new contacts form and contacts deemed to be broken behave. The packing fabric is affected by the size distribution and shapes of the grains as well as the material pressure. Structural features at a scale larger than the material granularity can be overlaid on the base material. These features include voids, material regions and joints (see [Potyondy2015c]).

Damage in the bonded materials consists of bond-breakage events. In the contact- and parallel-bonded materials, the entire interface breaks, whereas in the flat-jointed material, the elements break. Each breakage event is denoted as a crack; thus, a fully broken interface in a 2D flat-joint contact with four elements contains four cracks. Cracks in the flat-jointed material are shown here.

The material-modeling support memorandum ([Potyondy2017a]) describes: the PFC model, the synthetic materials and interface, the material-genesis procedure that creates the material, and the testing procedures that perform standard rock-mechanics laboratory tests upon the material. The tests are used to measure mechanical properties and observe microstructural behavior. The properties and behaviors are typically compared with that of the physical material. The material-modeling support package includes examples of each synthetic material. A concise summary of the package capabilities follows.

Material genesis of linear, contact-bonded, parallel-bonded, flat-jointed and user-defined materials in polyaxial, cylindrical and spherical vessels. Material grains can be either balls or clumps. Material tests are compression (confined, unconfined and uniaxial strain), diametral-compression and direct-tension. Microstructural monitoring includes properties (such as grain-size distribution) with microstructural plot sets and crack monitoring for bonded materials.

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[Potyondy2015c](1, 2, 3) Potyondy, D.O. “The Bonded-Particle Model as a Tool for Rock Mechanics Research and Application: Current Trends and Future Directions,” Geosystem Engineering, 18(1), 1–28 (2015), DOI:10.1080/12269328.2014.998346.
[Potyondy2017a](1, 2, 3) Potyondy, D.O. “Material-Modeling Support in PFC [fistPkg25],” Itasca Consulting Group, Inc., Technical Memorandum ICG7766-L (March 16, 2017), Minneapolis, Minnesota.
[Potyondy2004c]Potyondy, D.O., and P.A. Cundall. “A Bonded-Particle Model for Rock,” Int. J. Rock Mech. & Min. Sci., 41(8), 1329–1364 (2004).


[1][Potyondy2015c] summarizes the development of the bonded-particle modeling methodology, generalizes our view of the BPM to consist of a base material (of rigid grains joined by deformable and breakable cement at grain-grain contacts) to which larger-scale joints can be added, describes and classifies the rich variety of microstructural models that can be produced, discusses current limitations and suggests avenues for further development.
[2]The PFC FISHTank has been developed and maintained by Itasca since PFC was first released in 1995. It has been used both internally on Itasca consulting projects, and has been provided to users as a service because most users do not have the time and/or expertise to construct such a set of functions themselves and are, instead, more interested in applying them to particular applications. The PFC FISHTank can serve as a starting point for such users. The algorithms contained within the PFC FISHTank are intended for use by those who are comfortable with computer programming and knowledgeable about the FISH scripting language. For such users, the algorithms can serve as a starting point for applying PFC to solids-based applications and/or for performing standard rock-mechanics tests upon bonded or granular particle assemblies. Time and resource constraints have precluded us from incorporating this functionality directly into the source code (and thereby making it a part of the basic command set). Further, the algorithms have not been tested with the same rigor as the basic command set. The PFC FISHTank has been applied primarily to modeling rock and unbonded granular materials. When applying the algorithms to systems with differing characteristics, it may be necessary to modify some of the control parameters. Also, many of the algorithms (such as those used to obtain a dense packing with low locked-in stresses) involve simulation of highly nonlinear processes, and thus cannot be guaranteed to behave stably for all cases of different input parameters. For these reasons, the concepts underlying the particular implementations of these algorithms are described in detail in [Potyondy2017a] to enable the user to extend or fine-tune specific algorithms for specialized applications.
[3]The bonded materials created by the material-modeling support package are produced within a material vessel to form a homogeneous, isotropic, and well-connected grain assembly with a specified non-zero material pressure. The material-genesis procedure consists of a packing phase followed by a finalization phase. Each material is defined by a set of material properties. These properties control the material-genesis procedure, install the desired contact model at selected contacts, and assign contact-model properties (which include properties for contacts that may form subsequent to material finalization).