## 1 Introduction  
In underground municipal engineering, the pipe jacking method is widely used for underground utility corridors and small-diameter tunnels because of its advantages of high construction speed and low overall cost. However, the impact of construction on the surrounding strata remains a challenging issue that urgently needs to be addressed. To address the issue of stratum response caused by pipe jacking construction, multifaceted and multilevel research studies have been conducted. It has been reported that ground loss has the greatest impact on stratum deformation, followed by the side friction of the machine head and, finally, the grouting pressure [1, 2]. In addition, [PERSON] et al. [3] and [PERSON] et al. [4] considered the effects of additional thrust at the front, grouting pressure, and pipe-soil friction, and used the Mindlin displacement solution to develop a surface settlement prediction model based on the stochastic medium theory. [PERSON] et al. [5] proposed a parallel rectangular pipe jacking ground disturbance analysis model based on [PERSON]'s solution and stochastic medium theory. [PERSON] et al. [6], [PERSON] et al. [7], [PERSON] et al. [8], and [PERSON] et al. [9] considered the pipe-soil side friction coefficient and established numerical models based on the displacement control method to predict the jacking force. [PERSON] et al. [10] predicted the jacking force in frozen soil, compared a series of numerical simulations with theoretical values, and proposed a calculation model for jacking force in frozen soil. By introducing the effective friction coefficient, [PERSON] et al. [11] established a calculation method of jacking force that takes into account lubrication and pipe-soil-slurry interaction. The coefficient reflects the contact state of pipe-soil-slurry and the influence of slurry resistance on reducing friction resistance. Additionally, research has shown that friction is closely related to the jacking force. [PERSON] et al. [12] proposed a new rectangular pipe-soil contact model for friction prediction. Experiments performed by [PERSON] et al. [13] showed that continuous injection of bentonite can significantly reduce the friction coefficient, while intermittent injection can reduce it to half of the value without injection. [PERSON] et al. [14] conducted a three-dimensional model test on the grouting effect of the pipe jacking tunnel in the silty soil layer. It was found that the viscosity and cohesion of the mud had a significant effect on reducing the friction resistance and ground settlement. The construction needs to pay more attention to the mud parameters. [PERSON] et al. [15] discovered through field tests that the friction between the pipe segment and the surrounding rock was influenced by the filler and lubricating slurry and derived a formula for the calculation of jacking friction. A comparison with measured data verified the applicability of this formula for rock strata. [PERSON] et al. [16] proposed a new method for predicting slurry pipe jacking frictional resistance by fully considering the effects of lubrication, soil characteristics, and design parameters. In the study of deviations in jacking parameters, [PERSON] et al. [17] analysed the jacking parameters and found that the greater the jacking speed, the greater the surface settlement, and that the stability of the jacking force has a significant impact on surface settlement. [PERSON] et al. [18] analysed surface settlement during pipe jacking construction of a pipe curtain group and found that surface settlement is positively correlated with jacking speed. [PERSON] et al. [19] studied the relationship between jacking parameters and ground settlement based on numerical simulations and concluded that the greater the jacking force, the greater the ground uplift value in front. In summary, most of the current research on pipe jacking focuses on the patterns and causes of ground deformation, surface settlement prediction, jacking force prediction, and friction calculation.