## 3 Results and Discussion
### The Stratification Effects of Mode I Fracture Characteristics
#### 3.2.4 FPZ Length  
The FPZ, which characterizes the local deformation and fracture region surrounding the crack tip, is essential for a comprehensive understanding of material fracture mechanisms. The extent of the FPZ is closely associated with fracture toughness, as materials exhibiting higher fracture toughness generally possess a larger FPZ. This correlation indicates that such materials are capable of absorbing and dissipating greater amounts of energy prior to crack propagation. Consequently, following a detailed examination of fracture toughness, the subsequent focus will be on analyzing the FPZ length to achieve a more thorough understanding of the mechanical response and underlying micro-mechanisms of materials during crack propagationThe FPZ length is determined using the Digital Image Correlation (DIC) method, which digitizes deformation information on the specimen surface through advanced image processing techniques [42; 43]. To analyze the characteristics of the FPZ under varying stratification angles and numbers of stratification layers, the first image captured during the experiment is used as the reference for evaluating the FPZ length at the crack tip during the peak load stage. The procedure for calculating the FPZ length is illustrated in Figure 14a. Initially, a vertical sampling line, denoted as H1, is positioned from the initial crack tip. Subsequently, additional sampling lines, H2 and H3, are placed at intervals of 0.02 mm on either side of H1, and the corresponding horizontal displacement values for these lines are extracted from the subset of the image, as depicted in Figure 14b. Significant differences in horizontal displacement values are observed at the initial crack tip. However, as the sampling lines extend toward the upper boundary of the specimen, the disparity between the displacement values gradually diminishes, and they eventually converge. The range from the starting position of the sampling lines to this convergence point is defined as the FPZ length. To investigate the effect of stratification on the FPZ length in layered rocks, specimens with a stratification angle of \(\theta=0^{\circ}\) and varying numbers of stratification layers were selected. The FPZ lengths were measured under peak load conditions for specimens with 1 to 5 layers. The average FPZ lengths for these specimens were 8.1 mm, 7.47 mm,  
Figure 14: DIC determination method for FPZ dimensions: (**a**) DIC diagram and (**b**) the variations in FPZ length. Figure 13: The fracture toughness varies with different stratification numbers and stratification angles. 6.72 mm, 6.25 mm, and 5.97 mm, respectively, as shown in Figure 15. The data reveal a progressive decrease in FPZ length with an increasing number of stratification layers. This reduction can be attributed to the significantly lower strength of the stratification planes compared to the bedrock. As the number of stratification layers increases and the bedrock's thickness decreases, cracks more readily propagate through these weaker stratification planes, resulting in shorter FPZ lengths and reduced fracture toughness. The observed decrease in FPZ length follows an exponential decay trend, suggesting that while additional stratification layers lead to a reduction in FPZ length, this decrease asymptotically approaches a minimum value rather than continuing indefinitely. Figure 16 illustrates the effect of varying stratification angles on FPZ length, with the angle held constant and the FPZ length averaged across all specimens with different numbers of stratification layers. The data reveal a linear decrease in FPZ length as the stratification angle increases. This reduction can be attributed to the stratification planes facilitating crack propagation. Specifically, when the stratification planes are more aligned with the loading direction, cracks more readily slide and propagate along these weaker planes, resulting in shorter FPZ lengths.