###### Abstract  
Pipe jacking has been widely used in urban underground engineering construction in recent years. Prediction of ground deformation caused by pipe jacking is particularly important for the safety of construction. With regard to the densely arranged pipes used in the pipe roof structure method, an analytical model of stratum disturbance caused by jacking of parallel rectangular pipes is proposed on the basis of [PERSON]'s displacement solution and the stochastic medium theory. The influencing factors such as soil loss, additional thrust on the excavation face, friction between pipe jacking machine and soil, friction between subsequent pipes and soil, and the grouting pressure were comprehensively considered. Then, a 3D numerical simulation and a case study were conducted. The results showed consistent agreement with the analytical solution, and the proposed method can take into account the asymmetry of surface settlement curve induced by construction. A discussion of the ground deformation law shows that the proposed approach can reasonably predict the ground deformation and provide a reference for relevant pipe jacking construction. rectangular pipe jacking; analytical model; stratum settlement; stochastic medium theory; numerical simulation 2022123298. 2022123298.  
into established positions in the pipe roof working shaft. Then, the permanent reinforced concrete structure is formed in the pipes after the cutting of pipes and installation of steel bars. The pipe jacking process during pipe roof structure construction is a key construction step that needs to be investigated systematically. Scholars have carried out extensive research on the pipe roof structure method through in situ testing, laboratory testing, analytical calculation, and numerical simulation, and some inspiring results have been proposed. On the basis of the construction of Xinjizhi station project and the soil arch theory, [PERSON] et al. [14] deduced the relationship between the bearing constraint force of the arch axis and the geometric parameters of the model. Combined with the strength control condition of the vault and the arch footing, the equations for calculating pipe spacing could be obtained. At the same time, the whole construction process was monitored to ensure safety. It turned out that the maximum deformation occurred during the jacking of the layer 1-7 pipe, and the traditional Peck method was no longer applicable for this case. Hence, a modified Peck formula was proposed for the prediction of surface settlement during pipe jacking, and the results were in good agreement with the in situ monitoring data [10]. In order to study the mechanical response of tunnel lining and the ground surface subsidence during the excavation with the pipe roof structure method, [PERSON] et al. [15] conducted several field tests and numerical simulations for the relevant projects. The simulation results were consistent with the monitoring data, and the surface subsidence value was quite equal to the foundation. Compared with other construction methods, the pipe roof structure method can effectively reduce the ground surface subsidence, which is suitable for urban underground traffic construction  
Figure 1: Schematic of pipe roof structural method: (**a**) pipe jacking; (**b**) cutting and welding of pipes; (**c**) pouring of concrete; (**d**) large-scale excavation. projects. The tunnel crossing project of the Taiyuan Railway Station with the pipe roof structure method used 20 steel pipes, and the distance between these pipes was less than 165-265 mm. On the basis of this project, [PERSON] et al. [16] studied the jacking force of densely arranged pipes using a large-scale similar model test combined with engineering measured data. A pipe soil arching effect was formed during the construction of these pipes, thus causing a reduction in the jacking force. The modified formula could be used to predict the jacking force more accurately.