Three-dimensional Frost Heave Prediction Model Based On Stochastic Medium Theory In Tunnel Freezing Period

Artificial ground freezing method is a special type of stratum reinforcement technology,which has been widely used in the construction of subway tunnel engineering.In the construction of the subway tunnel freezing method,due to the unreasonable design or improper construction of the frozen tunnel,the formation will cause a large amount of frost heave deformation,which will lead to damage to the underground pipelines and the surface buildings,resulting in greater economic losses.Therefore,in the tunnel freezing period,a reasonable mathematical model should be adopted to predict the frost heave deformation caused by freezing.In this paper,theoretical analysis,case analysis and verification are used as methods to combine the existing frost heaving prediction model to study the three-dimensional frost heave prediction model of the tunnel during frozen periods,and to further analyze the three-dimensional frost heave deformation distribution law caused by frozen tunnel construction.The established three-dimensional prediction model was applied to the actual freezing method construction project.The main research contents and results are as follows:1)Based on the existing two-dimensional freezing-dilation time prediction model of the frozen period of the tunnel,taking into account the freezing temperature of the soil,and considering the wall temperature of the freezing tube as a constant,the single-tube freezing theory and the plate freezing theory are used to study the freezing.Analytical solutions of frozen fronts before and after the intersection of the wall,according to the frost heave rate formula of the frozen soil,using the random medium theory,taking into account the formation process of the frozen wall,an improved prediction model of the two-dimensional frost heave of the tunnel during freezing periods was established.2)Based on the improved two-dimensional frost heave diachronic prediction model for tunnel freezing period,taking into account the characteristics of the inclined radial distribution of the frozen pipe group in the actual construction of the tunnel,the temperature field in front of the frozen wall is calculated using the single-tube freezing theory,and frozen After the circle,the temperature field is calculated by theplate-freezing theory.According to the frost heave rate formula of the frozen soil,the time-dependent prediction model of the three-dimensional frost heaving deformation of the tunnel during freezing period is established by using the random medium theory and taking into account the formation process of the frozen wall.3)Taking the freezing construction of a certain subway tunnel in Beijing as a case,the proposed three-dimensional frost heave prediction model for tunnel freezing period was applied to the actual freezing project,and the calculation program of the prediction model was made using Maple mathematics software.The calculation and analysis were carried out and compared with the measured results of the frost heaving site to verify the applicability and reliability of the three-dimensional frost heave prediction model.Based on the improvement of the existing two-dimensional frost heave prediction model,this paper expands the frost heaving prediction model from two-dimensional to three-dimension,proposes the three-dimensional frost heave expansion prediction model for the frozen period of the tunnel,and the research results can be used to artificially freeze the subway tunnel.The design and construction of the law provides a theoretical basis and has important engineering practical value.