## 4 Comparison and Analysis
### Comparison of an Actual Drill Path Design  
Another example containing mechanical design, the drill path of the Maxi-HDD Qin River crossing project in China [4], was tested to support this method of predesigning trajectory. The crossing project, including two parallel HDD crossing with 1016 mm diameter and 1750 m driven length, was located at an alluvial plain where the Yellow River and the Qin River intersect. Consisting of a 7\({}^{\circ}\) entry angle, 8\({}^{\circ}\) exit angle, 2290 m entry and exit radius of curved segments, 1015 m horizontal segment, 33.50 m maximum burial depth and 29.78 m minimum burial depth below the riverbed, the drill path was carefully designed manually for preventing blowout, as shown in Figure 22.  
According to the engineering data provided in the literature [4], the geometrical design parameters are limited in the ranges given in Table 7. The minimum bending radius limitation was given differently for two cases, 2000 m and 2300 m, to illustrate its effects on trajectory design.  
In terms of mechanical design, heavy loam is used to evaluate the maximum allowable mud pressure, including 1.57 g/cm\({}^{3}\) dry density, 20.0 kPa cohesion, 15.0\({}^{\circ}\) friction angle, and 0.74 coefficient of lateral earth pressure. The _MAP_ predicted at the location of minimum burial depth is 1.63 MPa, which is very close to the real pressure of about 1.7 MPa [4]. All segments of the trajectory were tested for the pressure predictions through the whole process of geometric design.  
Figure 21: The convergence progress of length of central straight segment: \(L_{3}\).  
As shown in Figure 23 and Table 8, although the fitting similarity is largely reduced from the last example (mostly due to the difference of parameters ranges), both cases of trajectory design by IRMO show a great similarity with the actual design. The parameter design results arrive at similar trends as the previous conclusions. With the different minimum bending radius, the entry straight segment (\(L_{1}\)) is designed with nearly 50 m difference while the other parameters are not much different in design. It proves that the fitting similarity has less influence on the design results than we thought. The design parameters could be designed suitably by fitting with the catenary trajectory. What is more, there is no need for extra length optimization due to the tiny differences in the total length of the designs caused by strict limitations, especially for the central segment length \(L_{3}\).  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameters of Catenary Trajectory** & **Parameters of Five-Segment Trajectory** \\ \hline Horizontal distance of exit and entry point: & Length of the entry straight segment, \(L_{1}\)\(\in\)[1, 100] m; \\ A = 1750 m & Length of the central segment, \(L_{3}\)\(\in\)[1000, 1500] m; \\ Vertical distance of exit and entry point: H = –1 m & Radius of curved segments, & _case_ 1: \(R_{2}\)\(\&\)\(R_{4}\)\(\in\)[2000, 3000] m; \\ Casing unit weight: \(q\) = 100 kg/m & & \\ Pullback force: \(Np\) = 1,000,000 kgf & Inclination angle of the entry straight segment, \(\theta_{2}\)\(\in\)[\(-\)18, 5] \({}^{\circ}\); \\  & Inclination angle of the exist straight segment, \(\theta_{4}\)\(\in\)[5, 18] \({}^{\circ}\); \\ \hline \end{tabular}
\end{table}
Table 7: Parameters and range setting.  
Figure 22: The drill path profile of Maxi-HDD Qin River crossing project [4].