# Fine Characterization Method of Concrete Internal Cracks Based on Borehole Optical Imaging
## 3 Morphological Characteristics Analysis of Cracks
### Analysis of Crack Orientation  
The extension orientation of the crack is very important for describing the morphological characteristics. An accurate understanding of the crack orientation is very important for analyzing the cause of crack initiation and subsequent repair. When the crack intersects with the borehole, two cracks will appear on the expanded image of the borehole wall, as shown in Figure 8. The crack may intersect with the borehole at any angle, and when the crack does not pass through the borehole center, the orientation of the crack cannot be directly seen on the borehole wall image. Figure 8 shows the calculation principle of the crack orientation at any position on the borehole wall. Suppose that at a certain depth in the borehole wall image, the two points on the crack are \(A_{1}\) and \(A_{2}\), respectively, then the orientation of the crack at this depth can be expressed as Equation (1):  
\[\gamma=\frac{1}{2L}(x_{1}+x_{2})\times 360^{\lx@math@degree}\pm~{}90^{\lx@math@degree} \tag{1}\]  
where \(\gamma\) is the orientation of the crack. \(x_{1}\) and \(x_{2}\) are the distances from \(A_{1}\) and \(A_{2}\) to the leftmost side (\(0^{\circ}\)) of the borehole wall image, respectively. \(L\) is the perimeter of the borehole. In this paper, the crack orientation at different depths in nine boreholes was calculated, and the statistical results are shown in Figure 9. It should be pointed out that the orientation can be calculated only when two cracks appear in the borehole wall image. (1) In borehole zk15 + 025, although the upper and lower cracks were not continuous, the orientation of the two cracks was very close, both distributed in the range of [142\({}^{\circ}\),158\({}^{\circ}\)], and the crack orientation at the orifice was 151\({}^{\circ}\). (2) In borehole zk14 + 896, the change in crack orientation was relatively gentle, distributed in the range of [114\({}^{\circ}\),143\({}^{\circ}\)], and the fracture trend at the orifice was 143\({}^{\circ}\). (3) In borehole zk14 + 931, the crack orientation was distributed in the range of [133\({}^{\circ}\),144\({}^{\circ}\)]. (4) In borehole zk15 + 018, affected by the intersection of adjacent boreholes, only one crack appeared in the borehole wall image of the first 0.5 m, so the orientation of the crack cannot be calculated before 0.5 m. After 0.5 m, the crack orientation continued to change, gradually deflecting from the initial position of 145\({}^{\circ}\) to the due east direction until 80\({}^{\circ}\). (5) In borehole zk14 + 994, there was only one crack in the borehole wall image of 0.5-0.8 m due to the intersection of adjacent boreholes, so the crack orientation could not be calculated in this section. The crack orientation of this borehole was distributed in the range of [94\({}^{\circ}\),129\({}^{\circ}\)], and the crack orientation at the initial position was 112\({}^{\circ}\). Before 0.9 m, the change in crack orientation was very small, and the crack orientation suddenly changed significantly within the range of 0.9-1 m, increasing from 94\({}^{\circ}\) to 129\({}^{\circ}\). (6) In borehole zk14 + 819, the crack orientation continued to decrease from the initial position of 184\({}^{\circ}\) to 125\({}^{\circ}\). (7) In borehole zk14 + 858, the orientation of the crack changed little before 0.9 m, and the orientation of the crack at the orifice was 132\({}^{\circ}\). After passing through the concrete interface, the crack orientation changed significantly, continuously decreasing from 114\({}^{\circ}\) to 19\({}^{\circ}\). (8) In borehole zk14 + 870, the crack orientation changed little, distributed in the range of [103\({}^{\circ}\),132\({}^{\circ}\)], and the crack orientation at the orifice was 132\({}^{\circ}\). (9) In borehole zk14 + 903.5, the crack orientation was distributed within the range of [122\({}^{\circ}\),165\({}^{\circ}\)], and the crack orientation at the initial position was 165\({}^{\circ}\). Figure 8: Calculation principle of crack orientation in borehole wall image.