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.

The incorporation of steel fibers into the natural soil is generally considered to be a novel and effective way to reduce the amount of frost heave induced by an artificial freezing process in underground engineering. In order to analyze the frost heave behavior of the steel fiber improved soil, a one-dimensional frost heave test under the open recharge system was conducted in this paper, focusing on the influence of steel fiber content, size, and soil properties. The results show that small amounts of steel fibers in the soil will not significantly affect the freezing process and temperature distribution, while the water-conducting properties of the steel fibers and the effect of limiting the ice lens growth can reduce the frost heave rate of the samples incorporated with 0.5% steel fibers by 26.93%. At the same time, the reduction effect of the frost heave rate increases linearly with the increase of steel fiber content and length but weakens with the increase of steel fiber diameter. In terms of soil property influence, the frost heave rate of the clay samples was reduced by 14.31% compared to the silt samples, while the water migration was reduced by 11.99%. In addition, the cementation of the steel fibers with the soil will also inhibit the growth of the ice lens and reduce the external water migration, thus significantly lowering the frost heave rate. The results can provide a reference for the research of the frost deformation of similar modified soils.

In order to study the development law of the irregular hole freezing temperature field, combined with the shield solution project of the Nanjing Water Supply Corridor, the distribution characteristics and influencing factors of the irregular freezing temperature field of the river bottom shield machine are studied by numerical simulation. The following conclusions are obtained: (1) The extension length of the outer ring pipe is correlated approximately positively with the thickness and average temperature of the freezing wall at the bottom of the cup. The thickness increases by 0.25 m, and the average temperature decreases by 1.25 °C for every 1 m increase in the extension length. (2) The intersection time decreases logarithmically with the increase in the extension length of the outer ring tube. (3) As the ratio of the axial angle between the two adjacent tubes in the weak area of the outer ring tube becomes larger, the temperature of the weak point in the center of the two tubes increases approximately linearly. The midpoint temperature of the two tubes increases by 3.3 °C for every 1 increase in the angle coefficient. (4) With the increase in the opening angle of the inner ring hole, the thickness and average temperature change, respectively, at 150 d are not more than 0.15 m and 0.6 °C. The results show that under the irregular freezing form, the angle and length of the outer ring pipe have a great influence on the temperature field, and the angle of the inner ring pipe has little influence on the final distribution of the temperature field. The average temperature and the temperature distribution of the weak points show a trend of decreasing first and then increasing along the shield advancing direction, reaching a minimum near the cutterhead.