A method for predicting three-dimensional frost heaving deformation of stratum in subway tunnel freezing construction

Abstract

The application discloses a kind of stratum three-dimensional frost heaving deformation prediction methods of subway tunnel freezing method construction, first determine freezing construction position, obtain the soil layer parameter of undisturbed soil in freezing wall range, determine the thermal physical and mechanical parameters of soil body, the soil layer above freezing wall is layered according to its soil layer property and existing building (structure) And determine the layer where the frost heaving influence range is located;Subsequently, the unsteady temperature field of single freezing pipe and freezing front radius r (t) are calculated;According to the tunnel excavation type, the inner circle radius R1 (t) of freezing wall after freezing front is closed, outer circle radius R2 (t) is calculated, and the frost heaving area Δ (t) is calculated;Finally, the frost heaving displacement W i (t) is calculated.This prediction method comprehensively considers the thermal physical and mechanical properties of soil body, freezing time effect, soil layer freezing temperature and soil layer load factor, to determine the evolution law of freezing curtain and frost heaving deformation at different stages, improve the reliability and accuracy of stratum three-dimensional frost heaving prediction caused by freezing construction.

Description

Technical Field

[0001] This invention belongs to the field of subway tunnel construction technology, and in particular relates to a method for predicting three-dimensional frost heave deformation of strata during subway tunnel freezing construction. Background Technology

[0002] With rapid societal development, urban underground rail transit has also experienced rapid growth. Ground freezing, as a crucial method for soil reinforcement, is widely used in urban rail transit engineering, particularly in complex geological conditions such as water-rich, silty, and sandy strata, where its reinforcement effect is significant. However, artificial freezing causes a sharp drop in ground temperature, and the ground deformation induced by freezing construction in subway tunnels mainly manifests as adverse deformations of surrounding building foundations, tunnel linings, and station floors caused by frost heave. Therefore, accurately and reliably predicting the three-dimensional frost heave caused by freezing construction is crucial for the design of frozen walls and the protection of existing buildings. Several methods are generally used to study ground deformation: empirical methods, numerical simulation methods, and analytical methods, with analytical methods being the most commonly used. Analytical methods, based on rigorous mathematical derivation, can quantitatively consider the influence of geological parameters and freezing device parameters, making them a practical method for predicting ground deformation caused by tunnel freezing construction. However, current research on ground deformation caused by frost heave only yields the final ground heave value, without considering the time effect and actual conditions such as soil temperature, and therefore cannot accurately predict the freezing rate and frost heave displacement. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a method for predicting three-dimensional frost heave deformation of the ground during the freezing construction of subway tunnels. This method can effectively solve the problem of uneven frost heave caused by the freezing construction of subway tunnels, while avoiding adverse deformation to the foundations of surrounding existing buildings and tunnel linings.

[0004] Technical solution: The method for predicting three-dimensional frost heave deformation of ground strata during subway tunnel construction using the freezing method of the present invention includes the following steps:

[0005] (1) Determine the location of the freezing construction, obtain the soil layer parameters of the original soil within the freezing wall area, determine the thermophysical and mechanical parameters of the soil, divide the soil layer above the freezing wall into layers and determine the layer where the frost heave influence range is located.

[0006] (2) Calculate the unsteady temperature field and freezing front radius r(t) of a single freezing pipe;

[0007] (3) Based on the tunnel excavation type, calculate the inner radius R1(t) and outer radius R2(t) of the freezing front after the freezing wall intersects, and calculate the frost heave area Δ(t) using the following formulas (1) and (2):

[0008]

[0009]

[0010] In the formula: t is the freezing time; ε f ε is the soil frost heave rate under load; f0 ρ is the soil frost heave rate under no load; P is the load of the layer where the frost heave influence range is located, kPa; b is a constant 0.001; B is a coefficient; r is the freezing radius;

[0011] (4) Calculate the frost heave displacement W i (t).

[0012] Furthermore, in step (1) of the prediction method, the thermophysical and mechanical parameters of the soil are the soil density ρ, thermal diffusivity α, thermal conductivity k, specific heat c, latent heat of phase change L, and frost heave rate ε under no load. f0 ,in, .

[0013] Furthermore, in step (2) of the prediction method, the unsteady temperature field of the single freezing tube is obtained by the following equations (3) and (4):

[0014]

[0015]

[0016] In the formula: T f The differential equation for the temperature field in the frozen region; T u The differential equation for the temperature field in the unfrozen region; T c T represents the wall temperature of the freezing pipe. d E represents the freezing temperature of the soil mass. For homogeneous soil layers, it represents the freezing temperature of a single soil mass; for heterogeneous soil layers, it represents the freezing temperature of the soil mass within the radius of the freezing front. i Represents an exponential integral function; r0 is the diameter of the freezing pipe; α f α is the thermal diffusivity of the frozen area; T0 is the initial ambient temperature; α u is the thermal diffusivity of the unfrozen area.

[0017] Furthermore, in step (2), the radius r(t) of the frozen front is obtained by the following equations (5) and (6):

[0018]

[0019]

[0020] In the formula: k f k is the thermal conductivity of frozen soil. u is the thermal conductivity of unfrozen soil; A is a coefficient.

[0021] Furthermore, in step (3) of the prediction method, the inner radius R1(t) and outer radius R2(t) of the freezing front after the freezing wall overlaps are obtained by the following equations (7), (8), and (9):

[0022]

[0023]

[0024]

[0025] In the formula: R d T is the radius of the frozen pipe distribution. c ' represents the average temperature of the frozen tube wall after the loop is closed; η represents the longitudinal direction of the frozen tube in the cylindrical coordinate system.

[0026] Furthermore, in step (4) of this prediction method, the frost heave displacement W i (t) is obtained from the following equation (10):

[0027]

[0028] Where: h i β is the height of the layer where the frost heave influence range is located from the tunnel; β is the main influence angle of the overlying soil layer on the frozen wall; θ is the polar angle in the polar coordinate system; z is the z-direction coordinate in the spatial coordinate system; x is the x-direction coordinate in the spatial coordinate system; y is the y-direction coordinate in the spatial coordinate system; ζ is the length direction of the freezing pipe in the cylindrical coordinate system; φ is the circumferential angle in the cylindrical coordinate system.

[0029] Furthermore, this prediction method .

[0030] Furthermore, the latent heat of phase change L in this prediction method is obtained by the following equation (11):

[0031]

[0032] In the formula: L w The latent heat of water; ρ d w is the dry density of the soil; w0 is the moisture content; w u This represents the moisture content of the unfrozen soil.

[0033] Beneficial effects: Compared with the prior art, the significant advantages of this invention are: This prediction method integrates the thermophysical and mechanical properties of the soil, considers factors such as freezing time effect, soil freezing temperature and soil load, calculates the unsteady temperature field of a single freezing pipe and the freezing front r(t), and then calculates the inner radius R1(t), outer radius R2(t) and frost heave region Δ(t) of the freezing front after the freezing wall intersects, based on the shape of the frozen area, determines the frost heave influence range and calculates the frost heave displacement of the layer in which the frost heave influence range is located, so as to determine the evolution law of the freezing curtain and frost heave deformation at different stages, improve the reliability and accuracy of the prediction of three-dimensional frost heave of the strata caused by the freezing construction of subway tunnels, and ensure that the prediction results are more conducive to providing reliable data reference and theoretical basis for actual construction. Attached Figure Description

[0034] Figure 1 Schematic diagram of the frost heave layering of this invention;

[0035] Figure 2 This is a diagram illustrating the unsteady freezing front pattern of a single freezing tube according to the present invention.

[0036] Figure 3 This is a diagram illustrating the unsteady freezing front pattern after the frozen walls intersect, as described in this invention.

[0037] Figure 4 This is a schematic diagram of the formation uplift caused by frost heave in the unit of the present invention;

[0038] Figure 5 This is a schematic diagram of the frost heave of the ground at t=60 during the freezing construction of this invention;

[0039] Figure 6 This is a schematic diagram of the frost heave of the ground layer at t=90 during the freezing construction of this invention. Detailed Implementation

[0040] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0041] The schematic diagram of the frost heave layering of the present invention is as follows: Figure 1 As shown in the figure, the unsteady freezing front pattern of a single freezing tube is as follows: Figure 2 As shown in the diagram, the unsteady freezing front pattern after the freezing walls intersect is as follows: Figure 3 As shown in the diagram, the formation uplift caused by unit frost heave is as follows: Figure 4 As shown, the schematic diagram of frost heave between the ground and the stratum at t=60 during the freezing construction of Example 1 is as follows: Figure 5 As shown, the schematic diagram of frost heave between the ground and the stratum during the freezing construction at t=90 in Example 1 is as follows. Figure 6 As shown.

[0042] The present invention provides a method for predicting three-dimensional frost heave deformation of ground strata during subway tunnel construction using the freezing method, comprising the following steps:

[0043] (1) Determine the location of the freezing construction, obtain the soil layer parameters of the undisturbed soil within the freezing wall area, and determine the soil's thermophysical and mechanical parameters, including soil density ρ, thermal diffusivity α, thermal conductivity k, specific heat c, latent heat of phase change L, and frost heave rate ε under no load. f0 The soil layer above the frozen wall was divided into layers according to its soil properties and the location of the building, and the layer where the frost heave effect was located was determined.

[0044] in, .

[0045] (2) Calculate the unsteady temperature field and freezing front radius r(t) of a single freezing pipe using the following equations (3), (4), (12), (5), (6), and (11):

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] In the formula: T f The differential equation for the temperature field in the frozen region; T u The differential equation for the temperature field in the unfrozen region; T c T represents the wall temperature of the freezing pipe. d E represents the freezing temperature of the soil mass. For homogeneous soil layers, it represents the freezing temperature of a single soil mass; for heterogeneous soil layers, it represents the freezing temperature of the soil mass within the radius of the freezing front. i Represents an exponential integral function known in the art; r0 is the diameter of the freezing pipe; T0 is the initial ambient temperature; k f k is the thermal conductivity of frozen soil. u L is the thermal conductivity of unfrozen soil; A is the coefficient; L is the thermal conductivity of unfrozen soil. w The latent heat of water; ρ d w is the dry density of the soil; w0 is the moisture content; w u This represents the moisture content of the unfrozen soil.

[0053] α f Let α be the thermal diffusivity of the frozen region. u The thermal diffusivity of the unfrozen area is calculated using the following formula:

[0054]

[0055] (3) Based on the tunnel excavation type, calculate the inner radius R1(t) and outer radius R2(t) of the freezing front after the freezing wall intersects using the following formulas (7), (8), (9), (1), and (2), and calculate the frost heave area Δ(t) using the following formula:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] In the formula: t is the freezing time; ε f ε is the soil frost heave rate under load; f0 is the frost heave rate of the soil under no-load conditions; P is the load on this layer, kPa; b is a constant 0.001; B is a coefficient; r is the freezing radius; R d T is the radius of the frozen pipe distribution. c ' represents the average temperature of the frozen wall after the loop is closed; η represents the ordinate direction of the freezing tube in the cylindrical coordinate system.

[0062] (4) Calculate the frost heave displacement W of the layer where the frost heave influence range is located using the following formula (10). i (t):

[0063]

[0064] Where: h i β is the height of the layer where the frost heave influence range is located from the tunnel; β is the main influence angle of the overlying soil layer on the frozen wall; θ is the polar angle in the polar coordinate system; z is the z-direction coordinate in the spatial coordinate system; x is the x-direction coordinate in the spatial coordinate system; y is the y-direction coordinate in the spatial coordinate system; ζ is the length direction of the freezing pipe in the cylindrical coordinate system; φ is the circumferential angle in the cylindrical coordinate system.

[0065] Example 1

[0066] Example 1 of this embodiment selects the shallow buried large-section tunnel project on the south side of the section between Dabeiyao and the thermal power plant on the Fuxingmen-Bawangfen Line of Beijing Metro. This project is located directly below the Dayao Bridge to Guomao Bridge, where multiple crisscrossing underground pipelines are distributed in the stratum. Due to years of disrepair, seepage and other phenomena often occur. Therefore, the artificial freezing method is used for construction. In order to predict the three-dimensional frost heave deformation of the stratum in the frozen construction section, and considering the influence range of the freezing construction, the model size is selected as 40.0m long, 6.0m wide, and the tunnel burial depth is 10m. Soil parameters are obtained according to the actual working conditions, as shown in Table 1 below. The three-dimensional frost heave prediction method constructed by Equations (1) to (12) is used to simulate and obtain the frost heave cloud map of the stratum after 60 days and 90 days of frost heave, as shown in Table 1 below. Figure 5 and Figure 6 As shown in the example, the prediction method of the present invention can determine the range of frost heave influence and calculate the frost heave displacement of specific soil layers, so as to determine the evolution law of freezing curtain and frost heave deformation at different stages, improve the reliability and accuracy of the prediction of three-dimensional frost heave of strata caused by freezing construction of subway tunnels, and ensure that the prediction results are more conducive to providing reliable data reference and theoretical basis for actual construction.

[0067] Table 1 Soil and freezing pipe parameters

[0068]

Claims

1. A method for predicting three-dimensional frost heave deformation of strata during subway tunnel construction using the freezing method, characterized in that... Includes the following steps: (1) Determine the location of the freezing construction, obtain the soil layer parameters of the original soil within the freezing wall area, determine the thermophysical and mechanical parameters of the soil, divide the soil layer above the freezing wall into layers and determine the layer where the frost heave influence range is located. The thermophysical and mechanical parameters of the soil are: soil density ρ, thermal diffusivity α, thermal conductivity k, specific heat c, latent heat of phase change L, and frost heave coefficient ε under no-load conditions. f0 ,in, ; (2) Calculate the unsteady temperature field and freezing front radius r(t) of a single freezing pipe; (3) Based on the tunnel excavation type, calculate the inner radius R1(t) and outer radius R2(t) of the freezing front after the freezing wall intersects, and calculate the frost heave area ∆(t) using the following formulas (1) and (2): （1）； （2）； In the formula: t is the freezing time; ε f ε is the soil frost heave rate under load; f0 ρ is the soil frost heave rate under no load; P is the load of the layer where the frost heave influence range is located, kPa; b is a constant 0.001; B is a coefficient; r is the freezing radius; The inner radius R1(t) and outer radius R2(t) of the freezing front after the freezing wall layer intersects are calculated by the following formulas (7), (8) and (9): （7）； （8）； （9）； In the formula, R d T is the radius of the frozen pipe distribution. d This refers to the freezing temperature of the soil mass. For homogeneous soil layers, it represents the freezing temperature of a single soil mass; for heterogeneous soil layers, it represents the freezing temperature of the soil mass within the radius of the freezing front. T c ' represents the average temperature of the frozen pipe wall after the loop is closed, η is the ordinate direction of the frozen pipe in the cylindrical coordinate system; k f k is the thermal conductivity of frozen soil. u α is the thermal conductivity of unfrozen soil; f α is the thermal diffusivity of the frozen area; T0 is the initial ambient temperature; α u The thermal diffusivity of the unfrozen area; (4) Calculate the frost heave displacement W i (t): （10）； Where: h i β is the height of the layer where the frost heave influence range is located from the tunnel; β is the main influence angle of the overlying soil layer on the frozen wall; θ is the polar angle in the polar coordinate system; z is the z-direction coordinate in the spatial coordinate system; x is the x-direction coordinate in the spatial coordinate system; y is the y-direction coordinate in the spatial coordinate system; ζ is the length direction of the freezing pipe in the cylindrical coordinate system; φ is the circumferential angle in the cylindrical coordinate system.

2. The method for predicting three-dimensional frost heave deformation of strata during subway tunnel construction using the freezing method according to claim 1, characterized in that: In step (2), the unsteady temperature field of the single freezing tube is obtained by the following equations (3) and (4): ； ； In the formula: T f The differential equation for the temperature field in the frozen region; T u The differential equation for the temperature field in the unfrozen region; T c T represents the wall temperature of the freezing pipe. d E represents the freezing temperature of the soil mass. For homogeneous soil layers, it represents the freezing temperature of a single soil mass; for heterogeneous soil layers, it represents the freezing temperature of the soil mass within the radius of the freezing front. i Represents an exponential integral function; r0 is the diameter of the freezing pipe; α f The thermal diffusivity of the frozen area; T0 is the initial ambient temperature; α u is the thermal diffusivity of the unfrozen area.

3. The method for predicting three-dimensional frost heave deformation of strata during subway tunnel construction using the freezing method according to claim 1, characterized in that: In step (2), the radius r(t) of the frozen front is obtained by the following equations (5) and (6): ； ； In the formula: k f k is the thermal conductivity of frozen soil. u is the thermal conductivity of unfrozen soil; A is the coefficient.

4. The method for predicting three-dimensional frost heave deformation of strata during subway tunnel construction using the freezing method according to claim 1, characterized in that: The .

5. The method for predicting three-dimensional frost heave deformation of strata during subway tunnel construction using the freezing method according to claim 1, characterized in that: The latent heat of phase change L is obtained by the following equation (12): ； In this formula, L w For the latent heat of water, ρ d w is the dry density of the soil, w0 is the moisture content, and w u This represents the moisture content of the unfrozen soil.

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