Mathematical model of temperature field and its analytical solution for Freeze-Sealing Pipe-Roof method induced by radial offset of adjacent jacking pipes

Abstract

In order to achieve the purpose of sealing water between adjacent jacked pipes in construction of long-distance and large-section tunnel, an innovative method called Freeze-Sealing Pipe Roof (FSPR) was applied to the Gongbei tunnel, which is a key part of Hong Kong-Zhuhai-Macau Bridge in China. Since the pre-constructed jacking pipes provides great convenience for flexible placement of freezing tubes inside, it is crucial to study the temperature field of different freezing states. This paper first established a new mathematical model considering radial offset of jacking pipe according to the practical engineering, and then the analytical solution to steady-state temperature field was also derived. Moreover, temperature distribution of four typical cross-sections were analyzed to evaluate the freezing effect on different paths. Results show that the analytical results are in good agreement with the numerical results, and the quasi-double-circle freezing model can be well applied to the practical problem of radial offset. Soil between steel pipes will be lowered to a sufficiently low temperature and form a fairly reliable water-sealing curtain. By designing the radial offset between freezing tubes in solid and hollow pipes, the freezing effect can be better ensured. The conclusions have important guiding significance for design and construction of FSPR method in future projects.