# Study on Failure Mechanism of Mudstone Based on Digital Core and Digital Volume Correlation Method
## 4 Evolution Characteristics of Digital Core Fracture Model
### Spatial Distribution of Minerals in Rock Failure Process  
Quartz is one of the main minerals of mudstone, and the existence of this mineral has a significant influence on the mechanical properties of mudstone. \[D_{eq}=\sqrt[3]{\frac{6V_{3d}}{\pi}} \tag{1}\]  
The calibration analysis algorithm can be used to calculate the particle volume distribution parameters in the extracted mineral particle model, and then the equivalent diameter distribution can be calculated by using the equivalent diameter Formula (1), and the diameter of each particle can be counted to establish the particle equivalent diameter distribution histogram, as shown in Figure 9 and Table 3. According to the results of calculation and statistics, the diameter of quartz mineral particles in the mudstone sample was mainly distributed in the range of 25-100 pixels, and the scanning resolution was 15.4 \(\upmu\)m/pixel. According to the equivalent diameter formula, the diameter of quartz particles in mudstone samples was distributed between 0.38 and 1.54 mm, and the proportion of quartz particles with 0.38 mm diameter was the highest, accounting for 64.7% of all quartz particles. Figure 8: Change of pore coordination number during mudstone loading. Figure 9: Histogram of equivalent diameter distribution of quartz particles. The particles with different equivalent diameters were characterized in space, and the particles in different positions were statistically analyzed, with the influence of the distribution of quartz particles with different particle sizes on the damage and its change law analyzed in depth. Figures 10 and 11 show the spatial distribution of quartz particles in the initial unstressed state of mudstone specimens. A total of 19,962 quartz particles were collected by CT scanning. The equivalent diameter of mineral particles larger than 75 voxels was divided into large particles, and those with equivalent diameters less than 75 voxels were divided into small particles. Among them, there were 656 large particles, accounting for 3.28% of the total, and 19,302 small particles, accounting for 96.72% of the total. The aggregate quartz particles were 1487, accounting for 7.42% of the total. In order to show the spatial distribution of quartz mineral particles more simply and clearly with different particle sizes, as well as to further show the relationship between particles and fracture development, the display and observation were carried out from the perspective of 45\({}^{\circ}\) and overlooking, respectively. Each surface observed was consistent with the position of digital core modeling and CT scanning of mudstone sample, as shown in Figure 12.  
From the spatial distribution of small particles, the small quartz particles were basically uniformly distributed in the whole body of the mudstone sample; the number was relatively large; and the distribution was relatively concentrated in the XOY section, forming an accumulation zone that ran through the whole body of the sample, with the mineral zone on the other side being relatively scattered, and there being no obvious aggregation law. The occurrence relationship between them was essentially consistent with the macroscopic analysis of mineral composition, having a good corresponding relationship. By comparing the spatial distribution of quartz particles with different equivalent diameters, we found  
Figure 11: Spatial distribution of large-size mineral particles. Figure 10: Spatial distribution of small size mineral particles. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mean/Pixel** &
\begin{tabular}{c} **Standard** \\ **Deviation/Pixel** \\ \end{tabular} & **Max/Pixel** & **Min/Pixel** & **Quantity** \\ \hline
38.93 & 34.68 & 328.98 & 22.35 & 19,961 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Particle equivalent diameter distribution parameter table. that there was no special aggregation of quartz particles in mudstone samples, and the spatial distribution rules of quartz particles of the two sizes were very similar.