Some quick studies conducted by means of ADFNE series.

###### DFNE: Percolation Study

Used DFN model includes omnidirectional 3D fractures, randomly positioned in the space, and limited to Scale (Smax = [0.025…0.5]) and with Fracture Population (N = [25…500]). The following figures show an example and the obtained results from 100 realizations. From the figure (table) below it is clear that as the number increases the smaller sizes are percolating as well. Similarly for a fixed size, the larger the number of fracture, higher the percolation probability is. Indeed, the following study aimed to determine percolation threshold for a specified DFN model.

###### DFNE: Fracture Growth

In the following animation a simulation of fracture growth by means of tools in ADFNE 2.0 is shown. The constraints are touch-stop for every fracture during its growth. Every fracture could have different rates of growth, furthermore even directional growth could be different. Amazingly, insertion of the main structures such as tunnels and faults are incorporated with ease as shown. In the figure the fault has acted as isolating boundary between two its sides to mimic the real situations.

###### DFNE: Rock Blocks

ADFNE 2.0+ provides tools to generate rock blocks from any given DFN.

n this study, first the simulated fracture network has been subject of growth procedure by which a fully connected network is generated. The resulting is then fed to RockBlock function to generate legitimate polygons (rock blocks). The RockBlock function computes all important geometrical characteristics of the resulting rock blocks, as well. In terms of performance, for the following example all the above-mentioned stages together took only a few seconds.

The following demonstration is about the result of an efficient algorithm (developed at @) for generating rock blocks from any given 2D fracture network. In the figure, at the bottom the resulting rock blocks have gone some shrinkage to prove that the rock blocks are real polygons.

**Numerical Techniques For Block System Construction**

The following example relates to the topic of chapter 7 from Book: Fundamentals of Discrete Element Methods for Rock Engineering – Theory and Applications (Lanru Jing & Ove Stephensson). Indeed, the whole chapter is fully supported in ADFNE, where a single function call suffices to generate fully legitimate rock blocks from any given fracture network. In the figure, the numbers are areas for detected polygonal rock blocks. The color code (parula colormap) matches the size of computed areas.

###### DFNE: Rock Bridge Analysis

ADFNE 2.0+ includes numerous tools for geomechanical studies. The following figure shows the result of innovative method for detecting rock bridges in DFN models. Furthermore, the method classifies the bridges based on the potential breakage. In the figure the areas marked with yellowish color refers to rock bridges with highest potential for failure.

The developed algorithm can satisfactorily handle complicated scenarios, e.g., classification of rock bridges as well.

The optimum rock bridge path is automatically found and shown in the following example.

Any setup for study domain is implemented easily.

The developed algorithm works with any size of DFN and acts efficiently and fast. With the resulting path, the total length of rock bridges is also reported.

###### DFNE: Permeability

John P Harrison & John A Hudson in their book “Engineering rock mechanics: part 2 – Illustrative worked examples” in chapter 9 present some questions and answers. In the following demonstration questions 9.5 and 9.6 were answered by means of ADFNE 2.0+. I have also included the program code that produces the results. This is an effective demonstration of the usage of ADFNE as a reliable educational assistance tool.

The following short and simple program code (Matlab language) was used to conduct the above analysis. It does much more than the analyses introduced in the book. Furthermore, the results are in higher accuracy and reliability compared to the values provided in the book.