## 1 Introduction  
With the acceleration of urbanization, there is more and more urgency to develop underground resources to expand the space for human activity [1; 2]. Nevertheless, various complex geological conditions, such as water-rich sand, loose gravelly soil and silty clay with frozen-thawed sensitive characteristics, are encountered in underground engineering, and traditional geotechnical engineering methods face difficulties in solving such problems. Artificial ground freezing (AGF) is a method of artificial cooling that absorbs heat from the soil around the underground space to be excavated, gradually turning the natural soil into frozen soil and thus forming a dense frozen soil body. So, with its unique waterproof effect, adaptability to any complex geological conditions, flexible use and other characteristics, the geotechnical engineering community have paid more and more attention to AGF, which is now widely used in complex geotechnical engineering construction [3; 4; 5]. During the tunnel freezing period, ice intrusions such as ice crystals and interlayers formed in stratum frozen area will increase the volume of soil which is the frost heaving phenomenon of stratum. This phenomenon will be amplified when the stratum exits groundwater seepage, which brings difficulty to tunnel construction and damages the environment [6; 7; 8]. In view of this, domestic and foreign scholars have carried out much research by means of numerical simulation, model tests and field measurement. [PERSON] [9] represented the freezing characteristic function by combining the Young-Laplace law with the van Genuchten model. Then, a thermal-mechanical model of saturated media considering dynamic water-ice phase equilibrium was established and validated thorough model tests under various seepage velocities. [PERSON] [10] studied the development law of frozen wall in the process of artificial ground freezing under the construction of combined formation seepage by model test. [PERSON] [11] studied the evolution process of frost heaving force under thermo-mechanical coupling through a series of freezing tests under different constraint stiffness and temperature gradient, and proposed a method to measure formation frost heaving force under constraint conditions. [PERSON] et al. [12] proposed a prediction method with porosity as a variable using the finite difference method, and analyzed the physical changes of silty soil during freezing. [PERSON] [13] established an optimized prediction method for ground surface frost heaving during the freezing construction of a subway tunnel using AGF based on stochastic medium theory. [PERSON] et al. [14; 15] proposed a hydro-thermal coupling model considering ice-water phase change based on heat transfer theory and seepage theory. [PERSON] et al. [16] studied the evolution law of artificial frozen wall under seepage conditions in saturated gravel formations. [PERSON] [17] studied the diachronic evolution law of temperature field using COMSOL finite element software considering different seepage velocities (0.5, 1.0, 1.5 m/d). [PERSON] et al. [18] proposed a moisture-heat coupling model considering ice-water phase transition to quantify the temperature distribution in soil during the freezing process. [PERSON] et al. [19] adopted the same model to optimize the positions of freezing pipes around circular tunnel in seepage stratum with the velocity of 2.0 m/d. [PERSON] et al. [20] further revealed the development law of the frozen wall upstream, and downstream of the tunnel under seepage conditions, using a large-scale model test. The above researchers have made great contributions to the distribution laws of artificial freezing temperature and displacement fields; however, the research on the frost heaving laws of seepage strata during the freezing construction period is still insufficient. Therefore, in this paper, the finite element software COMSOL is selected to realize the hydro-thermal coupling in frozen stratum under seepage conditions.