Analytical solution of soil deformation caused by vertical pipe jacking construction considering grouting pressure

As an emerging shaft construction technique, vertical pipe jacking significantly influences the surrounding soil deformation. Based on Mindlin's solution and the analogous stochastic medium theory method, this study integrates analytical solutions for soil deformation induced by multiple factors, including additional grouting pressure, the bulkhead additive thrust of the jacking machine, the frictional force between vertical pipe jacking machine and soil, the frictional force between follow-up pipes and soil, and ground loss. A comprehensive calculation formula for soil deformation under multi-factor conditions is derived, and the contribution of each influencing factor is analyzed. The results indicate that the overall trend of vertical displacement in soil is settlement, with the maximum settlement occurring at approximately 0.5 times the pipeline diameter from the pipe jacking centerline. Among the influencing factors, ground loss plays a dominant role in both vertical settlement and horizontal displacement, while other factors have relatively minor effects on soil deformation. Both the burial depth of the utility tunnel and the jacking distance influence soil deformation patterns.