With the wide application of the artificial ground freezing method in municipal underground engineering, the annular layout of freezing pipes is often adopted to form a frozen soil cylinder. However, there is still no analytical solution that can calculate the temperature distribution of frozen soil formed in this case. In this paper, a mathematical model of a steady-state temperature field of single-circle freezing is established, in which the inside of the freeze ring is completely frozen; that is, the temperature of all excavation sections is below the freezing point. Then, the analytical solution of temperature distribution is deduced through the complex variable method and potential superposition method. Comparison results of the analytical solution with those of the numerical simulation show that the analytical solution is precise enough. The temperature distribution of the main section and the intersection is approximately the same on the inner side, but the freezing effect of the main section is relatively better near the freezing pipes and outside the freeze ring. Besides, according to the derived analytical solution and common freezing parameters, a simplified formula to calculate the temperature field with enough accuracy was proposed, and the error can be controlled below 1‰. Finally, based on the simplified formula, a calculation method for frozen soil thickness and the average temperature is also given in this paper.

In this paper, the effects of the cement content and excavation speed parameters on the improvement effect of the artificial freezing method and the characteristics of frozen walls are studied by means of a field test, numerical simulation and theoretical model. The optimization effect of the cement content in the artificial freezing method is studied. It is found that 10% is the best content, which can maximize the freezing wall thickness and grouting effect, and promote uniform distribution of the temperature field. At the same time, the influence of the excavation speed on the stress and settlement of the foundation soil is analyzed. It is pointed out that the increase of the excavation speed will aggravate the settlement and stress redistribution, which may threaten the building structure. The evaluation method proposed in this paper verifies that the construction deformation and settlement control are within the safety standards and provides theoretical support and construction guidance for tunnel engineering.

The freeze-sealing pipe roof (FSPR) method has been applied to the Gongbei tunnel of the Hongkong–Zhuhai–Macau Bridge, which is the first application of this method in the world. The purpose of the ground-freezing method is soil waterproofing. Temperature is an important indicator for measuring the freezing effect; however, the FSPR method involves unsteady-state conjugate heat transfer between frozen soil, steel pipes, concrete, air, and other media. This paper proposes an unsteady-state conjugate heat transfer model and establishes a global solution algorithm of a strong coupling governing equation based on the virtual density method. Then, a calculation based on COMSOL software is realized and validated. The sensitivity of different factors such as initial formation temperature, different soil layers, and brine temperature on the freezing effect was studied by simulating the FSPR model. It is concluded that the brine temperature had a greater impact on the freezing effect, followed by the soil layer, whereas the formation temperature had the least impact. For muddy silty clay, if the brine temperature is −20 °C, it takes 44 days to meet the design requirements of 2 m. If the brine temperature is −30 °C, 27 days is enough. When the formation temperature is 20 °C, it takes 20 days for medium gravel sand to reach the thickness of the freezing curtain, and 32 days for muddy silty clay. Compared to other soil layers, the freezing effect of the medium gravel sand is relatively better. This research has a certain impetus to similar multimedia freezing heat transfer issues.

In order to solve the problem of sealing water and bearing capacity of a connected aisle in an underwater shield tunnel, a double‐circle horizontal freezing method was adopted for ground reinforcement in the connected aisle of Maliuzhou Tunnel, which is China’s first shield tunnel with superlarge diameter built in a composite stratum. This paper proposed a new double‐row‐pipe freezing model for the calculation of frozen wall thickness based on analytical solution to steady‐state temperature field. Besides, field measurement and transient numerical studies of the active freezing period were also carried out to study the freeze‐sealing effect. The results show that frozen wall thickness obtained by analytical solutions agrees well with numerical simulation results, which verifies the applicability of the newly proposed calculation method. Field analysis indicates that soil temperature gradually approaches a stable value which is far below the freezing point, and a reliable water‐sealing curtain can be formed around the designed connected aisle. Maximum impact of soil excavation on the frozen wall is about 10°C, and reducing exposure time of excavation surface can effectively alleviate the weakening of frozen wall. To obtain comprehensive analysis for freezing wall thickness, a more reasonable arrangement of temperature‐measuring holes is expected in future freezing engineering.

The freezing construction of the end of the new shield tunnel has a mechanical impact on the surrounding structures. Few studies exist on the reasonable range of soil reinforcement near the shield tunnel and the influence of frost heave on the existing structure during the freezing process. To explore the influence of horizontal freezing of a proposed tunnel on existing underground structures, a three-dimensional numerical model of ‘thermal-mechanical’ coupling was established based on the horizontal freezing reinforcement project applied in a shield receiving end, and the temperature field distribution characteristics of different freezing stages were obtained. After confirming that the frozen wall had reached the design thickness based on the temperature field, the mechanical effects of frost heave on the existing structures were investigated, including the side tunnel, the upper subway tunnel, and the end diaphragm wall. The results showed that the frost heave pressure was mainly distributed in the structure near the freezing zone, while the structure far away from the freezing zone was relatively less affected by frost heave. By defining the strong and weak influence sections, we introduced the influence coefficient η to quantify the frost heave effect on the side tunnel. Under the condition that the thickness of the frozen wall was constant, the strong influence range of the side tunnel reached 1.4 times the freezing length of the proposed tunnel at a distance of 3.6 times the frozen wall thickness. The farther the clearance between the side tunnel and the proposed tunnel was, the smaller the influence coefficient η was, and the shorter the strong influence section was. The frost-heaving effect generated by freezing at the shield tunnel receiving end was more pronounced along the diameter of the freezing pipes, while axial release strength was comparatively weaker. This research can provide a reference for evaluating the influence of freezing construction on adjacent underground structures.