## 3 Analysis of the Individual Factors Affecting the Stability of the Skid-and-Mud-Return Line
### Effect Analysis of Drilling Ship Motion
The bending moment remains almost constant between about 2000 m and 500 m and shows a peak at 120 m when reaching the water surface, as shown in Figure 3d. Similarly, Figures 4-6 show the effects of different attack angles on the skid-and-mud-return line for the recurrence periods of 5, 10, and 25 years, respectively. In a 1-year recurrence period, the maximum equivalent stress at an attack angle of 90\({}^{\circ}\) is only 300 MPa, which is lower than the yield strength of V150 steel (1115 MPa). Therefore, the operation can be conducted within a 1-year recurrence period. In a 5-year recurrence period, at an attack angle of 0\({}^{\circ}\) and 180\({}^{\circ}\), the maximum equivalent stress ranges from 200 MPa to 300 MPa, guaranteeing normal operations. At an attack angle of 45\({}^{\circ}\) and 135\({}^{\circ}\), the maximum equivalent stress is about 850 MPa and 900 MPa, respectively. These are lower than the yield strength of V150 steel, guaranteeing the operation. However, at an  
Figure 6: Effects of drilling vessel motion on the stability of the skid-and-mud-return line with different attack angles in a 25-year recurrence period: (**a**) equivalent stress, (**b**) displacement, (**c**) rotation angle, and (**d**) bending moment. attack angle of 90\({}^{\circ}\), the maximum equivalent stress is about 1150 MPa. This exceeds the yield strength of V150 steel. In this case, the ship's orientation needs to be adjusted to change the attack angle for operation. In a 10-year recurrence period, at an attack angle of 0\({}^{\circ}\) and 180\({}^{\circ}\), the maximum equivalent stress is about 300 MPa, allowing for operations. At an attack angle of 135\({}^{\circ}\), the maximum equivalent stress is about 1000 MPa, guaranteeing the operation. However, at an attack angle of 45\({}^{\circ}\) and 90\({}^{\circ}\), the maximum equivalent stress exceeds the yield strength of V150 steel (1115 MPa), preventing the operation. In a 25-year recurrence period, at an attack angle of 0\({}^{\circ}\) and 180\({}^{\circ}\), the maximum equivalent stress is close to 400 MPa, allowing for operations. However, at attack angles of 45\({}^{\circ}\), 90\({}^{\circ}\), and 135\({}^{\circ}\), the maximum equivalent stress exceeds the yield strength of V150 steel, preventing the operation. To analyze the effects of the recurrence period on the stability of the skid-and-mud-return line, the effects of the recurrence period of 1 year, 5 years, 10 years, and 20 years on the stability of the skid-and-mud-return line are selected with an attack angle of 90\({}^{\circ}\). The analysis results are shown in Figure 7. They indicate that the equivalent stress, displacement, and rotation angle of the skid-and-mud-return line increases with an increase in the recurrence period. It is observed that the increase is the most significant from 1 year to 5 years. However, the maximum bending moment of the skid-and-mud-return line decreases with an increase in the recurrence period. The maximum equivalent stress is 300 MPa, 1100 MPa, 1300 MPa, and 1600 MPa, respectively, as shown in Figure 7a. The maximum displacement is 30 m, 80 m, 90 m, and 100 m, respectively, as shown in Figure 7b. The maximum rotation angle is 0.25 rad, 0.325 rad, 0.35 rad, and 0.375 rad, respectively, as shown in Figure 7c. The maximum bending moment is 3.1 kN\(\cdot\)m, 3.3 kN\(\cdot\)m, 3.5 kN\(\cdot\)m, and 3.8 kN\(\cdot\)m, respectively, as shown in Figure 7d. Figure 7: Effects of drilling ship motion on the stability of the skid-and-mud-return line with an attack angle of 90\({}^{\circ}\) in different recurrence periods: (**a**) equivalent stress, (**b**) displacement, (**c**) rotation angle, and (**d**) bending moment. As the water depth decreases for the skid-and-mud-return line, equivalent stress, displacement, and rotation angle all increase.