Title Calculation Method of Artificial Ground Frozen Soil Frozen and Heave Caused by Layers and Structural Deformation

Objective The artificial ground freezing method is widely applied in the construction of tunnels through highly saturated soft soil layers. However, the phenomenon of frozen soil expansion can adversely effect the safety of overlying structures. As the number of projects involving this freezing method beneath such structures continues to increase, scholars are increasingly concerned about the deformation of these structures caused by frost heave. Despite this, the calculation methods and interaction laws governing the deformation of overlying structures during the freezing process remain unclear, highlighting the need to predict surface and structural deformations. This study aims to address the frost heave issue related to the macroscopic manifestation of water migration in frozen soil. Methods It derives formulas and parameter values by using Peck’s equation to calculate the deformation of overlying strata induced by frost heave. Consequently, it establishes an appropriate frost heave formula to compute the amount of frost heave generated during the freezing process. Based on construction experience, the study provides a range of reduction coefficients for frost heave in various cities. Through moisture migration experiments, the velocity of water migration during freezing is determined, and an empirical calculation method for the radius of the freezing front is derived. Additionally, a formula to calculate the increase in volume of frozen soil is developed. By comparing and analyzing the dimensions of frost heave mounds under different freezing wall diameters (3.0, 4.8, 5.2, and 6.0 m), it is discovered that the sizes of frost heave mounds produced by different diameters are nearly identical. Results and Discussions It is found that the burying depth of the freezing wall (z0) has a significantly greater impact on the shape of the frost heave mound curve than the diameter of the freezing wall. Thus, the burying depth of the freezing wall emerges as a crucial factor influencing the size of the frost heave mound in overlying strata. Drawing inspiration from Mair’s approach, a calculation formula suitable for computing the deformation of overlying strata at different depths induced by frost heave is formulated. This formula enables the calculation of the width of the frost heave mound based on the burying depth of the freezing wall (z0) and the depth of the structure’s base plate (z), and proposes empirical values for k1 and k2. Utilizing measured data from a freezing project in Zhengzhou, the volumetric increase rate of soil moisture during the freezing process is calculated, revealing that the increase in frozen soil volume caused by water migration is 42 times greater than the increase in situ moisture-frozen soil volume. The calculated values obtained using the frost heave formula closely approximate the measured values, satisfying the requirements for safety evaluation and analysis during the construction process. With the continuous expansion of urban subway tunnel construction in highly saturated soft soil layers, the number of projects involving the artificial ground freezing method beneath overlying structures is expected to increase annually. Conclusions The research findings provide calculation methods for estimating the deformation of overlying structures in freezing-undercrossing engineering projects, serving as effective references for freezing design and construction. By adopting targeted measures such as structural pre-reinforcement or frost heave control, significant risks, including damage to overlying structures during the freezing-under-crossing process, can be avoided. Furthermore, the research outcomes establish a theoretical foundation and calculation reference for the technical research and application of the artificial ground freezing method in high-risk underground engineering fields. © 2024 Sichuan University. All rights reserved.