Abstract A mathematical model describing the temperature field during tunnel construction with the method of horizontal freezing is presented considering various initial and boundary conditions such as ground temperature,surface convection and latent heat of phase change,etc. The heave rate of soil frosting was defined as the instantaneous volume strain and the deformation of frozen soil was considered orthotropic. The frost heave was assumed to occur mainly along the direction of heat flow(temperature gradient) and a coefficient to describe the deformation characteristic was introduced. The transient thermal strain components(frost heave strain components) were derived after the soil temperature reached the freezing temperature. A coupled thermal-stress elasto-plastic mathematical model for the frost heave of ground was presented. The model was implanted into the finite element software ABAQUS. A shallow subway tunnel of large section applying horizontal freezing was simulated numerically and the numerical results were compared with the field measured data,which verified the reliability of the numerical model and the necessity of considering the orthotropic frost heave deformation of frozen soil in the analysis of ground displacement.
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