# Mechanical Analysis of DS in Horizontal Directional Drilling
## 4 Analysis and Application of Engineering Case
### The Construction Stage of the Pilot Hole  
The 12-1/4 in drill bit is used in the construction stage of the pilot hole. The construction method of drilling from both ends to the middle is adopted, and the DS dynamics model of 3200 m on the entrance side is established with the actual working condition parameters. The thrust force is 20T, 30T, and 40T, and the model is calculated respectively. The x and y directions are defined as shown in Figure 11. Finally, the spatial displacement distribution of DS is shown in Figure 12.  
When the thrust force is 20T, the spatial displacement distribution of the horizontal DS is shown in Figure 12a. The displacement of the DS from the end of the building up section to the drill bit fluctuated less in the y direction with a amplitude of 25 mm. Due to the influence of DS size, the displacement in the y direction changed markedly at the connection position of different types of DS, such as the position at 1200 m and the position at 2600 m. The x direction DS had obvious sinusoidal buckling fluctuation in many places, with a peak value of 105 mm. In summary, when the thrust force was 20T, sinusoidal buckling of the DS occurred and is located below the borehole. Figure 10: Three degrees of DS deformation (Unit: m). (**a**) The DS did not buckle. (**b**) The DS showed sinusoidal buckling. (**c**) The DS showed helical buckling. When the thrust force increases to 30T, helical buckling first appeared on the 6-5/8 in DS in the horizontal section, as shown in Figure 12b. The displacement of the DS in the direction-direction fluctuated significantly, and the DS adhered to the borehole wall at both ends of the 6-5/8 in DS, resulting in obvious helical buckling. The displacement amplitude of the DS on the entrance side was 50 mm in the direction-direction and 150 mm in the direction-direction. The displacement amplitude of the DS on the drill bit side is 40 mm in the direction-direction and 120 mm in the direction-direction. Helical buckling occurred in some DSs, resulting in a significant increase in the DS's drag and torque, which made axial force and torque not effectively transmitted to the drill bit. The bit's rock-breaking efficiency decreased. Drilling assembly needs to be optimized, such as adding stabilizers to the buckling position. When the thrust force is 40T, the buckling degree of DS continues to increase. At this time, the 7-5/8 in DS on the left side of the horizontal segment also presented significant helical buckling (Figure 12c). However, there is no helical buckling in the right 5-1/2 in DS. The reason is that the left DS had severe helical buckling, which led to the failure of drilling pressure to transfer effectively to the right DS so that the axial force of the right DS did not reach the critical value of helical buckling. The displacement of the DS in the borehole can be seen intuitively from Figure 12c. The inner-circle represented the helical buckling of the 7-5/8 in DS, the outer circle represented the helical buckling of the 6-5/8 in DS, and the lower arc represented the sinusoidal buckling of the 5-1/2 in DS. The distribution of DS contact force and DS torque is shown in Figure 13. As can be seen from the DS displacement distribution in Figure 12, when the thrust force is 20T, sinusoidal buckling deformation occurred to DS of various sizes. When the thrust is 30T or 40T, the obvious spiral buckling deformation is shown in DS. This will definitely affect the contact force between the DS and the borehole wall. When the thrust is 20T, the contact force between the DS and the borehole wall is not evenly distributed at the position where the sinusoidal buckling deformation occurred. At this point, the average contact force of each DS node is less than 2 kN, and the contact force at the part where no deformation occurs is only 0.65 kN. When the thrust is 30T, the contact force of each drill strip node reached up to 6 kN.