Frost heaven force

related with tunnel axial length and time

has three dimensional space-time characteristics in cold region tunnels. In order to establish a frost heave model for studying the change rule of frost heaven force

three dimensional temperature field model of cold region tunnels was firstly established based on the field test results

and the changing law of surrounding rock frozen depth was obtained by Stephen formula. On this basis

a new temperature-frost heave model was established in combination with freeze-thaw circle theory and weathering layer theory. The results show that the frozen depth of surrounding rock influenced by environment temperature has a trend of decrease with the increase of tunnel axial length and changes periodically with time. According to this new model

when the frozen depth is smaller than the weathering layer depth

the frost heaven force is only induced by the weathering layer; when the frozen depth is bigger than the weathering layer depth

the frost heaven force in induced by both the weathering layer and freeze-thaw circle. The change rule of frost heaven force is similar with the change rule of surrounding rock frozen depth.