# Mechanical Analysis of DS in Horizontal Directional Drilling
## 1 Introduction  
With the rapid development of the world economy, people's consciousness of environmental protection is getting stronger, and their pursuit of life quality is constantly improving. The green development mode integrating urban construction and environmental protection has gradually become mainstream nowadays. In the construction of the city, due to the needs of the underground infrastructure, many pipelines need to be laid, replaced, and repaired. The traditional excavation not only causes environmental and traffic damage but also wastes time and labor force. Therefore, HDD, which has many advantages such as small environmental damage, short construction period, and high comprehensive efficiency, has been widely applied as the mainstream technology in trenchless construction and has limitless application prospects. With the continuous increase of directional crossing distance, the construction conditions are harsher, and the long and thin DS shows more and more flexibility in the long and narrow holes. The serious buckling of DS and the huge drag and torque make the drill bit unable to drilling effectively are the important reasons for limiting the breakthrough of directional drilling distance. In severe cases, DS failure may even occur (Figure 1). Therefore, it is of great significance to study the relationship between DS buckling and drag and torque of DS and its influence on WOB transfer for directional crossing development [1; 2; 3; 4; 5; 6; 7; 8]. There are two methods to study the buckling problem of DS: Differential equations and energy methods. [PERSON] et al. [PERSON] et al. (2009) studied the relationship between thread pitch and axial force in helical buckling of tubing using the energy method. [PERSON] et al. [PERSON] et al. (2010) obtained the critical load of sinusoidal buckling of pipe column in the inclined borehole by energy method. [PERSON] and [PERSON] [PERSON] and [PERSON] (2011) used the energy method to obtain the critical load of helical buckling of pipe columns in a horizontal well. [PERSON] (1965); [PERSON] et al. (2010); [PERSON] et al. (2010); [PERSON] et al. (2010) has been doing a lot of research on the buckling problem through the differential equation. [PERSON] and [PERSON] (2011) and [PERSON] et al. (2011) studied the buckling and post-buckling behavior of pipe columns in detail through energy method and differential equation. On the problem of drag and torque of DS, the calculation and analysis model of drag and torque is developed on the basis of the \"Soft-String Model\" proposed by [PERSON] (1983) [PERSON] (1983). On the basis of large deformation theory, the effect of stiffness of drill column is considered and an improved Tension-Torque model is proposed by [PERSON] (1983). [PERSON] and [PERSON] and [PERSON] (2011) established the Steady-State Tension-Torque model on the basis of [PERSON]'s model, taking into account the motion of DS and the influence of drilling fluid. [PERSON] et al. [PERSON] et al. (2012); [PERSON] et al. (2012) have proposed a beam-column theory to solve the two-dimensional force and three-dimensional force of the drill column. [PERSON] et al. [PERSON] et al. (2012); [PERSON] et al. (2012) established the longitudinal vibration model and the torsional vibration model of DS and solved them by the difference method in the numerical method. [PERSON] et al. [PERSON] et al. (2012) proposed a new calculation model of drag and torque. [PERSON] (2013) treated the DS system as an S-M-C (spring-mass-damping) system using the finite element method. On the basis of [PERSON]'s principle, [PERSON] et al. [PERSON] et al. (2013) established the dynamic model of a three-dimension DS system with finite element method. With the development of HDD engineering to the direction of large pipe diameter and long span, the drag torque and buckling deformation of DS is becoming more and more serious.