In the process of tunnelling with horizontal freezing method

soil volume expansion caused by freezing can produce the phenomenon of surface frost heave. Multiple frozen pipes are usually used to form frozen wall in the actual engineering. Before the circle-crossing period of frozen wall

surface frost heave is induced by superimposed expansion deformation of multiple frozen columns. After the circle-crossing period of frozen wall

surface frost heave is induced by expansion deformation of the whole frozen wall. In view of this

considering the formation process of frozen wall and based on stochastic medium theory

a duration prediction model of surface frost heave induced by tunnelling with horizontal freezing method is presented. Two value methods of freezing outer front radius and frost heave region outer radius are discussed at the same time. Finally

aiming at two engineering cases

surface frost heave displacements are analyzed by calculation model. Variations of surface frost heave displacements with time are obtained

which are compared with field measured results to verify reliability of the model. The model is applied to surface frost heave displacements prediction at any time of freezing period before tunnelling with horizontal freezing method

and can provide effective reference for reasonable determining freezing implementation scheme.