# Numerical Analysis of Friction Reduction of Grouting in Long-Distance Pipe Jacking
## 1 Introduction  
The pipe jacking method is a trenchless underground pipeline installation technique, with advantages, such as a short construction period and minimal environmental impact, leading to significant economic benefits [1]. In recent years, with increasing engineering demands, pipe jacking construction has been evolving towards larger diameters and longer distances. In long-distance pipe jacking, the jacking force is one of the key parameters for the selection of pipe segments, the jacking machine, and the working shaft [2]. Typically, the jacking force comes from the front resistance and the frictional resistance. As the jacking distance increases, the frictional resistance around the pipe also increases, thus increasing the required jacking force [3], particularly in ultra-long-distance pipe jacking [4]. If a precise calculation of the jacking force can be achieved, it will significantly contribute to practical engineering applications. Currently, many scholars have conducted extensive research on grouting for friction reduction in pipe jacking. In terms of the slurry materials and interaction between slurry and soil, [PERSON] et al. [5] and [PERSON] and [PERSON] [6] analyzed the properties of a thixotropic slurry, the grouting mechanism, and the use of a bentonite slurry to reduce the jacking resistance. [PERSON] et al. [7] conducted experiments showing that the slurry can reduce the friction resistance in saturated sandy soil to 63.1%. [PERSON] et al. [8] analyzed the relationshipbetween the microscopic structure of slurry and friction resistance through laboratory tests, finding that friction resistance increases with time. The effectiveness of grouting lubrication in pipe jacking largely depends on the selected grouting material. Currently, commonly used grouting materials include a bentonite slurry, cement grout, polymers, and composite slurries. Bentonite slurry is composed of bentonite, CMC (carboxymethyl cellulose), soda ash, and water, characterized by its swelling and thixotropic properties. Bentonite primarily consists of potassium, calcium, and sodium, montmorillonite, with a typical concentration of approximately 5%. When mixed with water and stirred, bentonite forms a suspension. When static, the montmorillonite particles transition from a dispersed state to a gel structure. Upon agitation, the particle structure is disrupted and redistributes, forming a viscous and flowable colloidal liquid. Once the suspension is stationary again, the gel structure re-forms, a property known as thixotropy. Due to its low cost and excellent performance, the bentonite slurry is the preferred material for pipe jacking projects. Cement grout is one of the most basic and commonly used materials in pipe jacking grouting. It has good flowability and strength, enabling it to form a solid structure during the grouting process, effectively reinforcing the soil layer, and improving the bearing capacity and stability of the soil. Polymers primarily consist of materials, such as an epoxy resin slurry and polyurethane slurry and are highly suitable for engineering projects that require excellent reinforcement effects, impermeability, and high durability. The composite slurry mainly includes a cement-sodium silicate slurry and cement-sodium silicate-fly ash slurry. It has a short settling time and high early strength, along with strong fluidity at the beginning, making it suitable for soil layers that require rapid reinforcement and projects with high environmental protection requirements. In terms of the application of grout in friction reduction for pipe jacking, [PERSON] et al. [9] studied the variation pattern of the jacking force under grouting conditions in silty strata through model tests. The tests showed that the viscosity and condensation force of the slurry play a major role in reducing the friction resistance and surface settlement. As the slurry settles or consolidates, the liquid phase (usually water) starts to drain or evaporate, causing the solid particles to come closer together.