# Impact of Arch Dam Cracking on Monitoring Data
## 4 Discussion  
An analysis was conducted to evaluate the effects of doubling the crack length on changes in recordings (Figure 9). Displacement increments below 0.01 mm were excluded to prevent distortion from relative comparisons of small values. After removing outliers, the average multiplication factor for doubling crack length was 2.34. A trend shift was observed as displacement transitioned from upstream to downstream, at values of 65 m (crack 1), \(-\)65 m (crack 2), and \(-\)75 m (crack 3). Figures 10 and 11 examine the effect of doubling crack depth on changes in recorded displacements. Displacement increments below 0.01 mm were excluded. Excluding outliers, the average multiplication factor for doubling crack depth was 2.6. Figure 12 analyzes the displacement increments of upstream crack 1 under varying simulation parameters. It uses the configuration causing the largest displacements (crack  
Figure 11: Effect of doubling the depth on the displacements (length of two cantilevers) in crack 1 (**left**), crack 2 (**center**), and crack 3 (**right**). Orange square: coronation. Blue circle: medium height. Gray triangle: lower height. Vertical gray line: monitoring point. Figure 9: Effect of doubling the length on displacements in crack 1 (**left**), crack 2 (**center**), and crack 3 (**right**). Orange square: coronation. Blue circle: medium height. Gray triangle: lower height. Vertical gray line: monitoring point. 1.2U*) as a reference. Displacement increments for halving crack depth, halving crack length, and reducing the reservoir level by 20 m are compared across monitoring devices. It is determined that reducing the reservoir level by 20 m yields similar results to the reduction in crack depth or length. While reductions in crack depth and reservoir level produce comparable displacements and crack openings, halving crack length results in a similar average displacement reduction but with a distinct distribution and significantly different crack openings. Figure 13 compares the impact of reservoir level reduction on displacements recorded by monitoring devices for case 1.2U* (see Table A9 in the Appendix A). The average multiplication factors are 1.61 (12 m), 2.06 (16 m), 2.74 (20 m), and 3.26 (22 m). The results indicate a relationship ranging from 6.8 to 7.8 between reservoir level variation and the increment multiplication factor variation. A comparison is made between cracks with similar maximum openings (within a 4% tolerance), selected from each position (excluding position 4, where cracks do not open), and differing parameters. Numerical results are provided in Table A10 (Appendix A). Figures 14-16 present displacement data recorded by monitoring devices as a function of horizontal distance from the crack center, excluding crest records due to significant vertical  
Figure 12: Increases in radial displacements (and mean values) due to different configurations of crack 1. Figure 13: Effect of increasing the reservoir level on displacements (and mean values). distance variations. Cracks with similar openings exhibit comparable effects on monitoring device recordings. These figures demonstrate that the horizontal distance between the crack and the measurement point significantly affects crack detection. The difference between whether  
Figure 16: Comparison of different cracks causing 0.88 mm opening. Horizontal distance is rounded to 5 m intervals. Reservoir level for 1.1U*(b) is 625 m above sea level and for 1.2U*(c) is 623 m above sea level. Figure 14: Comparison of different cracks causing 1.25 mm opening. Horizontal distance is rounded to 5 m intervals. The reservoir level for 1.1U*(d) is 629.2 m above sea level. Figure 15: Comparison of different cracks causing 0.73 mm opening. Horizontal distance is rounded to 5 m intervals. Reservoir level for 1.1U*(c) is 623 m above sea level. the measuring point is 20 m or 40 m horizontally away may determine detection capability.