## 6 Conclusions  
This paper presented an analytical solution for predicting the ground deformation caused by jacking construction of parallel rectangular pipes. On the basis of [PERSON]'s solution and the Stochastic medium theory, the main factors causing ground deformation were considered, including soil loss, additional thrust, friction force, and grouting pressure. A three-dimensional numerical simulation and case study were carried out to verify the effectiveness of the analytical model. the ground deformation law and relevant parameters were discussed. The following conclusions can be drawn:  
1. A comparison of the numerical simulation and engineering case study showed that the proposed method can successfully predict ground surface settlement. In addition, this method can also take into account the asymmetry of the settlement curve caused by different construction sequences.
2. The influence range of the longitudinal settlement curve was about 8 m (four times the pipe jacking width). In the range of 5 m before and after excavation face, the settlement changed dramatically, while pipe jacking construction could cause great disturbance to the soil within this range. The maximum settlement value of the total transverse surface settlement curve tended to be located between previous constructed pipes. The influence range of the transverse surface settlement was about five times the pipe width.
3. Compared with the pre-construction pipe, the post-construction pipe of the parallel pipe jacking had a larger influence range in the transverse direction, and the surface settlement trough was wide and shallow. With the decrease in the stratum influence angle of the post-construction pipe jacking, the position of the maximum settlement value moved to the pre-construction pipe jacking area, and the settlement value decreased gradually.
4. The convergence value has a great influence on the surface settlement curve. By controlling the soil loss during construction, the surface settlement can be effectively controlled. Therefore, thixotropic fluids should be used to reduce the disturbance of the stratum. At the same time, compensation grouting should be used to reduce the soil loss.  
In order to simplify the calculation process, several assumptions were made in the model. For example, the rectification and tilt of the jacking machine were not considered. In the actual pipe jacking construction process, the various factors affecting stratum deformation are not independent, and there will be a dynamic coupling effect on the ground deformation. These problems need to be further studied.  
Conceptualization, Y.W., Q.F. and X.L.; methodology, Y.W.; software, Y.W.; validation, X.L., J.W. and Q.F.; formal analysis, Y.W. and X.L.; investigation, Y.W., J.W., X.L. and Q.F.; data curation, D.Z. and Q.F.; writing--original draft preparation, Y.W.; writing--review and editing, X.L., J.W. and Q.F.; visualization, Y.W.; supervision, D.Z.; project administration, D.Z.; funding acquisition, D.Z. and X.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant numbers 51738002 and 52108363.  
Not available.