# Review on the Influence of Complex Stratum on the Drilling Trajectory of the Drilling Robot
## 3 Impact of Typical Complex Coal Seams on the Deviation of Drilling Tool Track
### Reasons for Hole Bending
\[\text{N}=\text{Pcos}\theta \tag{3}\]  
The drill tool will slide along the rock layer when the sliding force is greater than the friction resistance between the drill bit and the rock layer, and the drill hole will bend along the direction of the rock layer (shown in Figure 14c). The smaller the stratum angle \(\delta\), the bigger the sliding force. Figure 14a shows the drill bit entering a hard rock stratum from a soft rock stratum when the stratum angle is greater than the critical value. When the bit enters the layer, the force on the lip is unbalanced, and the combined force of the hole bottom reaction at the hard rock end on the layer is greater than the hole bottom reaction at the soft rock end. Not only does the drill bit have uneven breakage with asymmetric penetration rate and hole bottom at both ends, but also it will produce a tilting moment M, which will twist the drill bit and make it bend along the upward inclination direction of the ground--that is, perpendicular to the plane direction. The calculation of M is:  
\[\text{M}=\frac{2}{3}(\sigma_{\text{n}}-\sigma_{\text{m}})\Big{(}\text{R}^{2}- \chi^{2}\Big{)}^{\frac{3}{2}} \tag{4}\]  
where, \(\sigma_{\text{n}}\) is the indentation hardness of hard rock; \(\sigma_{\text{m}}\) is the indentation hardness of soft rock; R is the drill radius; X is the distance from the drill axis to the contact surface of soft and hard layers. Figure 14b shows the drill bit entering from hard rock stratum to soft rock stratum when the stratum angle is greater than the critical value. According to the unbalanced stress on the drill bit at the bottom of the hole, the drilling speed on the soft rock side of the drill bit on the layer is fast, while the drilling speed on the hard rock side is slow, and the resulting tilting torque makes the drill hole tend to bend downward toward the formation. To sum up, the bending direction of the borehole from hard rock strata to soft rock strata is exactly opposite to that from soft rock strata to hard rock strata when drilling in alternate soft and hard rock strata. (4) Influence of inclined broken-layered rock  
When the bit is drilling in the inclined broken-layered rock, the bit tooth is easy to break the rock in the up-dipping direction of the formation to form more rock cuttings. Due to the imbalance of rock breaking on both sides of the inclined broken formation, an additional oblique force is generated to force the bit to constantly change the drilling direction. Consequently, the well deviation occurs. To sum up, the regularity of borehole bending under the influence of geological factors is summarized as follows:  
(1) The bending strength of the borehole is smaller than that in heterogeneous rock when drilling in homogeneous rock. The higher the degree of anisotropy of the rock, the greater the bending strength of the borehole [75; 76; 77]. (2) The borehole bends in the direction perpendicular to the bedding plane when drilling in the rock with developed bedding and schistosity. The stratum angle of the borehole is greater than the critical value, the borehole direction is perpendicular to the strike of the stratum, the top angle drifts upward and the azimuth angle is stable. The borehole azimuth is oblique to the strike of the bedding plane, with both the top angle drifting upward and the azimuth angle bending, and the azimuth change tends to be perpendicular to the strike of the bedding plane. If the stratum angle of the borehole is less than the critical value, the borehole will slide along the stratum and the azimuth angle will vary. The bending strength of the borehole is related to the size of the stratum angle. The bending strength of the borehole is the largest when the layer angle is about 45\({}^{\circ}\)[75; 78; 79].