Shield tail brush replacement freezing temperature field stochastic analysis and design method considering soil parameter spatial variability

Abstract

The invention belongs to the technical field of freezing temperature fields, and particularly discloses a shield tail brush replacement freezing temperature field stochastic analysis and design method considering soil parameter spatial variability, and the method comprises the following steps: obtaining engineering parameter and soil thermal parameter basic data; establishing a deterministic freezing temperature field model and performing benchmark analysis; constructing a soil thermal parameter 3D random field; performing 3D random freezing temperature field analysis based on Monte Carlo simulation; evaluating the thickness statistical characteristics and reliability of the frozen wall; determining a design expansion coefficient; the invention discloses freezing scheme optimization design considering random characteristics. According to the method, the three-dimensional random thermal value model fusing the random field theory and Monte Carlo simulation is established, the soil variability is systematically considered, the safety and economy of shield tunneling machine tail brush replacement operation are improved, and the limitation of traditional 2D cold region frozen soil stochastic analysis is broken through.

Description

Technical Field

[0001] This invention relates to the field of freezing temperature field technology, and more specifically to a stochastic analysis and design method for freezing temperature field during shield tail brush replacement that takes into account the spatial variability of soil parameters. Background Technology

[0002] When using the shield tunneling method for tunnel excavation, the shield tail brush, as a core component of the annular seal, inevitably experiences wear during long-term excavation due to factors such as shield posture adjustments, compression, and friction with the tunnel lining segments. Its sealing effect determines the safety and stability of the tunnel construction process. Repairing and replacing the worn tail brush requires ground reinforcement to create a safe working environment. Among various ground reinforcement technologies, artificial freezing is widely used in major tunnel engineering projects due to its high reliability, strong controllability, and excellent waterproof performance. When using artificial freezing for reinforcement, the low-temperature fluid circulating inside the freezing pipe causes a phase change in the surrounding soil, forming a continuous frozen wall. This frozen wall isolates groundwater, stabilizes the strata, and provides a safe working space for tail brush replacement. The safety of this process depends on the evolution of the freezing temperature field, and the spatial variability of soil thermal parameters is the core factor leading to the uncertainty of the freezing temperature field. Therefore, it is necessary to accurately quantify the impact of this uncertainty on the reliability of the freezing project.

[0003] Existing technologies employ deterministic finite element method (FEM) simulation, assuming uniform soil thermal parameters, to investigate the development characteristics of the freezing temperature field. However, existing methods still have the following problems or shortcomings: In practical engineering, deterministic analysis ignores the inherent spatial variability and autocorrelation of natural soil, failing to reflect fluctuations in actual engineering, affecting the reliability of freezing operations, and leading to overly conservative or overly aggressive freezing system designs. Furthermore, stochastic analysis pays less attention to artificial freezing in warmer regions, especially in scenarios like shield tunneling machine tail brush replacement, where the development of a three-dimensional frozen wall needs to be considered; relevant methods are even scarcer in these cases. Therefore, existing technologies cannot quantify the impact of soil thermal parameter variability on the freezing temperature field during shield tunneling tail brush replacement, lacking analytical methods and design tools that balance reliability and practicality. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a stochastic analysis and design method for the freezing temperature field of shield tail brush replacement that considers the spatial variability of soil parameters. This method overcomes the shortcomings of neglecting the spatial variability of soil parameters and the difficulty in accurately assessing the performance of the frozen wall and the safety of the operation in the current freezing temperature field. By establishing a three-dimensional stochastic thermal numerical model that integrates stochastic field theory and Monte Carlo simulation, the spatial variability of soil thermal parameters is captured. Furthermore, the influence of key stochastic parameters on the performance of the frozen wall is analyzed. At the same time, a reliability-based design tool is developed, thereby improving the safety and economy of shield machine tail brush replacement operations and solving the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for stochastic analysis and design of the freezing temperature field for shield tail brush replacement considering the spatial variability of soil parameters, comprising the following steps: S1. Obtain basic data on engineering parameters and soil thermal parameters; S2. Establishment of a deterministic freezing temperature field model and benchmark analysis; S3, Construction of 3D random field for soil thermal parameters; S4. Analysis of 3D random freezing temperature field based on Monte Carlo simulation; S5. Statistical characteristics and reliability assessment of frozen wall thickness; S6. Determine the design expansion factor; S7. Optimization design of freezing scheme considering random characteristics.

[0006] Preferably, the replacement of the shield tail brush includes the following steps: When replacing the tail shield brush during tunnel construction, specially made segment rings with pre-embedded frozen pipe sleeves are assembled in advance at the target location. After the specially designed segment ring is installed in place and detached from the tail of the tunnel boring machine, liquid nitrogen is introduced into the installed freezing pipe to start the freezing process, forming a closed freezing wall around the gap at the tail of the tunnel boring machine. Once the frozen wall reaches the design requirements, remove one segment from the temporary segment ring to expose the shield machine tail brush below, and replace the damaged tail brush segment in the exposed area. Repeat the above process to remove adjacent segments of the temporary segment ring one by one, and replace the corresponding tail brush section until all damaged tail brushes in the tunnel circumference direction are replaced.

[0007] Preferably, step S1 specifically includes the following steps: S11. Collect engineering parameters such as the dimensions of the tunnel boring machine, tunnel segments, and frozen pipes, as well as the geological formation and confined water level. S12. The thermal conductivity, heat capacity, and latent heat of each soil layer in frozen and unfrozen states were determined through indoor tests. S13. Calculate the mean value of thermal parameters using geostatistical methods. Coefficient of variation (COV) Δ (like, ), horizontal and vertical fluctuation range Vertical fluctuation range To clarify the spatial variability of soil thermal parameters.

[0008] Preferably, step S1 specifically includes: building a three-dimensional finite element model and setting boundaries and initial conditions, and outputting the evolution law of the freezing temperature field over time and the growth characteristics of the frozen wall.

[0009] Preferably, step S3 specifically includes the following steps: S31. Based on the statistical characteristics of thermal parameters, construct the thermal conductivity... λ Specific heat capacity c Phase transition latent heat L The 3D random field is discretized into finite element parameters; S32. The covariance function is used to characterize the structural correlation of parameters between different spatial points; S33. The continuous random field is discretized into random variables corresponding to the finite element grid using the local averaging method. That is, a representative random variable is assigned to each finite element, which is the spatial average value within the unit volume. A variance reduction function is introduced to quantize the relationship between the point scale and the spatial average scale parameter and to eliminate local fluctuation interference. Then, following the process of "determining statistical parameters → initializing uncorrelated Gaussian field → decomposing the correlation matrix by Choreski → constructing a correlated Gaussian random field → converting it to a correlated non-Gaussian random field", a thermal parameter random field corresponding to the finite element grid is generated.

[0010] Preferably, in step S4, the 3D random freezing temperature field analysis based on Monte Carlo simulation specifically includes: S41. Define random variables and deterministic variables; S42. Input the statistical characteristics of the random field; S43. Determine the number of Monte Carlo simulations, N; S44. Establish a three-dimensional finite element model, and perform mesh discretization and numbering; S45. Write a program to generate N sets of discretized random fields of three soil parameters corresponding to the finite element mesh; S46. For each random field implementation, call the deterministic finite element solver to calculate the transient temperature field; S47. After completing N simulations, calculate the mean, standard deviation, and failure probability of the output results to quantify the uncertainty range of the freezing temperature field.

[0011] Preferably, the statistical characteristics and reliability assessment of the frozen wall thickness specifically include: Extract frozen wall thickness data under different working conditions, and define the reliability of the freezing project as "actual frozen wall thickness". ≥ Design thickness The probability of reliability is calculated based on the thickness cumulative distribution function (CDF) curve, with different coefficients of variation.

[0012] Preferably, step S6 specifically includes: proposing a design expansion coefficient to ensure stable target reliability for critical operations at the tail of the tunnel boring machine. Based on the design expansion coefficients corresponding to the target reliability under different coefficients of variation, plot the design expansion coefficient curves and analyze them. The changing pattern; the expansion coefficient The formula is expressed as follows: ; In the formula: For the corresponding target reliability Minimum freezing thickness, For design thickness.

[0013] Preferably, step S7 specifically includes: S71. Determine the design thickness of the frozen wall. The target reliability is determined based on the engineering risk level. ; S72. Characterizing soil variability: Soil thermal parameters are measured through field sampling and laboratory tests, and its random field characteristics are calculated using geostatistical methods. COV Δ , , ; S73, Calculation Using the cumulative distribution function of frozen thickness corresponding to the measured coefficient of variation, the reliability of the target can be obtained through inversion. Corresponding minimum thickness ; S74. Determine the design expansion factor According to the measured coefficient of variation COV Δ and target reliability Choose an appropriate design expansion factor ; S75. Optimize design parameters: Calculate the adjusted design thickness. If freezing time is a key control parameter, the design expansion factor is converted into a freezing time expansion factor to determine the minimum freezing duration. S76. Verification and Iterative Optimization: Verify through numerical simulation whether the adjusted design meets the requirements under specific site variability conditions. If not, readjust the design expansion factor. And repeat the above steps; S77. Freezing Scheme Optimization: Deploy temperature sensors to monitor the development status of the frozen wall in real time, and update the design expansion coefficient based on the monitoring data. The freezing scheme is dynamically adjusted to ensure that reliability targets are met.

[0014] The beneficial effects of this invention are: 1) This invention provides a stochastic analysis and design method for the freezing temperature field of shield tail brush replacement considering the spatial variability of soil parameters. By establishing a three-dimensional stochastic thermal numerical model that integrates stochastic field theory and Monte Carlo simulation, the method systematically considers soil variability, improves the safety and economy of shield tail brush replacement operation, and breaks through the limitations of traditional 2D stochastic analysis of frozen soil in cold regions. 2) This invention analyzes the influence of key random parameters on the performance of the frozen wall, providing a theoretical basis for parameter sensitivity analysis of artificial freezing projects; this invention also develops a reliability-based design tool to optimize the freezing design parameters for the tail brush replacement of the tunnel boring machine by characterizing soil variability; this invention is simple, practical, and easy to promote. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the steps of the present invention regarding the stochastic analysis and design method for replacing the freezing temperature field of the shield tail brush, which takes into account the spatial variability of soil parameters. Figure 2 The following is a finite element mesh diagram after discretization of the 3D random field in the embodiment of the present invention: (a) shows the overall distribution and refinement of the finite element mesh in the deterministic analysis, and (b) shows the overall distribution and refinement of the finite element mesh in the random analysis. Figure 3a The Hangzhou case COV is an example of this invention. Δ =3. Mean (left) and variance (right) distribution of temperature under freezing time t=10d; Figure 3b The Hangzhou case COV in the embodiments of the present invention Δ =3. Distribution of mean (left) and variance (right) of temperature under freezing time t=20d; Figure 3c The Hangzhou case COV in the embodiments of the present invention Δ =3. Distribution of mean (left) and variance (right) of temperature under freezing time t=30d; Figure 4 This is a Monte Carlo simulation convergence curve diagram in an embodiment of the present invention; Figure 5 Designing expansion coefficients in embodiments of the present invention With target reliability, COV Δ Relationship diagram; Figure 6 This is a schematic diagram of the design expansion coefficients corresponding to the target reliability under different coefficients of variation in an embodiment of the present invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] Please see Figure 1 This invention provides a technical solution: a method for stochastic analysis and design of the freezing temperature field for shield tunnel tail brush replacement considering the spatial variability of soil parameters, comprising the following steps: S1. Obtain basic data on engineering parameters and soil thermal parameters; S2. Establishment of a deterministic freezing temperature field model and benchmark analysis; S3, Construction of 3D random field for soil thermal parameters; S4. Analysis of 3D random freezing temperature field based on Monte Carlo simulation; S5. Statistical characteristics and reliability assessment of frozen wall thickness; S6. Determine the design expansion factor; S7. Optimization design of freezing scheme considering random characteristics.

[0018] Furthermore, the shield tail brush replacement implementation steps include: This example uses a tunnel tail brush replacement project as the calculation background. The tail brush replacement operation is carried out in the following steps: 1) When it is necessary to replace the shield tail brush during tunnel construction, special segment rings with pre-embedded frozen pipe sleeves are assembled in advance at the target location; 2) After the specially designed segment rings are installed in place and detached from the tail of the tunnel boring machine, liquid nitrogen is introduced into the installed freezing pipes to start the freezing process. A closed freezing wall is formed around the gap at the tail of the tunnel boring machine, effectively sealing the annular space and preventing water and soil from entering; 3) Once the frozen wall reaches the design requirements (thickness 1m, average temperature -15℃), carefully remove one segment from the temporary segment ring to expose the shield machine tail brush below, and replace the damaged tail brush section in the exposed area. 4) Repeat the above process: remove adjacent segments of the temporary segment ring one by one, replace the corresponding tail brush section, until all damaged tail brushes in the tunnel circumference direction are replaced.

[0019] Furthermore, the acquisition of basic data on engineering parameters and soil thermal parameters includes: S11. Collect engineering parameters such as the dimensions of the tunnel boring machine, tunnel segments, and frozen pipes, as well as the geological formation and confined water level. S12. The thermal conductivity, heat capacity, and latent heat of each soil layer in frozen and unfrozen states were determined through indoor tests. S13. Calculate the mean value of thermal parameters using geostatistical methods. Coefficient of variation (COV) Δ (like, ), horizontal and vertical fluctuation range Vertical fluctuation range This study clarifies the spatial variability of soil thermal parameters, providing a basis for subsequent stochastic modeling.

[0020] Furthermore, the data collected in this embodiment includes: shield diameter 11.68 m; segment outer diameter 11.3 m, inner diameter 10.3 m, width 2.0 m; freezing pipe spacing 1 m, outer diameter 94 mm, wall thickness 5 mm; measured pressure water level -3.8 m to -4.0 m; the strata traversed by the tunnel axis are, in sequence: ②2 layer (silty clay with silt), ③2 layer (sandy silt), ③3 layer (silt with silt), ④ layer (silty clay), ⑤1 layer (sandy silt), ⑦2 layer (silt), and ⑧ layer (gravel layer). The material parameters and parameters of each soil layer determined by indoor tests are shown in Table 1; the coefficient of variation of the soil thermal parameters is initially set to 0.2, with a horizontal fluctuation range of... and vertical fluctuation range Take 20 m and 1.0 m respectively.

[0021] Table 1 Soil physical parameters ; Furthermore, the establishment and benchmark analysis of the deterministic freezing temperature field model include: building a three-dimensional finite element model and setting boundaries and initial conditions, and outputting the evolution law of the freezing temperature field over time and the growth characteristics of the frozen wall.

[0022] Firstly, a three-dimensional finite element model was established using Abaqus software. The dimensions of the three-dimensional finite element model were determined to be 15m (length, tunnel axis) × 42m (width, tunnel radial) × 42m (height, vertical) to avoid boundary effects. Each part of the model was discretized using 8-node linear heat transfer elements (DC3D8) suitable for transient heat conduction analysis (number of elements: 9734 for soil, 4600 for tunnel segments, and 800 for the shield machine shell). The mesh was refined in key areas of the model analysis, and a gradient mesh was used in the far-field region, as shown in Figure 2(a). A constant temperature boundary condition was used for the freezing pipe, with the temperature set at -110 ℃. A 0.4 W / m² boundary was applied to the bottom boundary of the model.2 The surface heat flux density; the top boundary adopts surface film conditions, the ambient temperature is 25℃, and the film coefficient is 19.12W / (m²). 2 •℃); the lateral boundary is an adiabatic boundary; the inner surface of the tunnel segment in contact with air is treated with a surface film, with an ambient temperature of 20℃ and a film coefficient of 4.11 W / (m). 2 •℃); the heat transfer coefficient at the interface between the pipe segment and the soil is 100,000 W / (m²). 2 •℃). Initial temperature field presets for model nodes: initial temperature of tunnel segments and shield machine shell is 20℃; initial temperature of soil is... T The temperature of 0 is distributed in a gradient along the vertical direction, and its value transitions from 25°C at the bottom to 25°C at the surface, according to the following expression:

[0023] In the formula, h This indicates the height of the node from the bottom of the model.

[0024] Secondly, ignoring the spatial variability of soil thermal parameters, the spatiotemporal distribution of soil temperature field was solved using Abaqus software. After post-processing the simulation results, the baseline pattern of the frozen wall was obtained: an initial closed low-temperature zone is formed after 4 days of freezing, a continuous frozen wall is formed after 18 days, and a complete water-proof curtain is developed after 30 days, providing a benchmark for the "uncertainty bias" of subsequent random analysis.

[0025] Furthermore, the construction of the 3D random field for soil thermal parameters includes: S31. Based on the statistical characteristics of thermal parameters, construct the thermal conductivity... λ Specific heat capacity c Phase transition latent heat L The 3D random field is discretized into finite element parameters; when Take respectively The decomposition of each parameter is shown in the following equation. Optionally, this invention considers this random field as a three-dimensional stationary random field, that is, the mean and variance of the soil parameters do not change with spatial coordinates.

[0026]

[0027] In the formula: Represents spatial coordinates in a rectangular coordinate system; The mean of the parameters; Standard deviation; It is a zero-mean random function.

[0028] S32. The covariance function is used to characterize the structural correlation of parameters between different spatial points, for a given location. Random field of soil parameters at the location If its one-dimensional probability density function is Then random field Mean function Sum of variance functions It can be defined as:

[0029]

[0030] Coefficient of variation (COV) Δ ,like, The coefficient of variation (COV) is a standardized statistic that measures the relative variability of soil parameters. It directly affects the magnitude of uncertainty in subsequent discretization and Monte Carlo analysis. Δ It can be represented as:

[0031] The variability of soil parameters is not a purely random distribution, but rather possesses inherent spatial structural characteristics—parameter attributes are more similar in nearby locations than in more distant locations. This spatial correlation can be precisely quantified using the covariance function, which can comprehensively describe spatial variability from a mathematical perspective. For any two points... and The covariance function is defined as:

[0032] To eliminate the influence of dimensions, the covariance function is standardized to obtain the correlation function. :

[0033] In practical applications, the correlation of soil parameters at any two points is widely represented using the exponential covariance model:

[0034] In the formula: Let be a separating vector, representing any two points and Distances along each coordinate axis; , These represent the horizontal and vertical fluctuation ranges, respectively.

[0035] S33. To realize finite element analysis, the continuous random field of soil thermal parameters is discretized. The local averaging method is used to discretize the continuous random field into random variables corresponding to the finite element grid. That is, each finite element is assigned a representative random variable, which is the spatial average value within the unit volume. The variance reduction function is introduced to quantify the relationship between the point scale and the spatial average scale parameter and to eliminate local fluctuation interference.

[0036] In the spatial domainH Above the random field of soil The average is defined as:

[0037] In the formula: x For spatial domain H Spatial coordinate vector within.

[0038] According to the above formula, The mean and variance can be expressed as:

[0039]

[0040] In the formula, As the variance reduction function, it can be derived as follows:

[0041] In the formula, The separation vector in the random field is h The correlation function between two points.

[0042] unit and The cross-covariance of the spatial correlation between the two can be expressed as:

[0043] Then, following the process of "determining statistical parameters → initializing uncorrelated Gaussian fields → decomposing the correlation matrix by Choreski → constructing correlated Gaussian random fields → converting to correlated non-Gaussian random fields", thermal parameters corresponding to the finite element mesh are generated. Three-dimensional random field. Firstly, determine the statistical parameters. Through indoor experiments and field surveys, determine the statistical parameters for each thermal parameter, including the mean. ,variance Coefficient of variation (COV) Δ and fluctuation range ( ).

[0044] Secondly, an uncorrelated Gaussian field is initialized. For each thermal parameter and each Monte Carlo sample, an uncorrelated standard Gaussian random matrix is ​​generated:

[0045] Thirdly, the Choreski decomposition of the correlation matrix. This involves constructing a spatial correlation matrix based on statistical parameters. , where the element is

[0046] In the formula, For unit j1 and j 2. The distance between the centroids.

[0047] For the correlation matrix Perform the Choleski decomposition:

[0048] In the formula, The lower triangular Choreski factor, for The transpose of .

[0049] Fourthly, a relevant Gaussian random field is constructed. A relevant standard Gaussian random field is generated through matrix multiplication:

[0050] The obtained matrix It contains standard Gaussian random fields with specified spatial correlations, where each row represents a sample of a spatially correlated parameter field. Representing the i In the nth sample j The standard Gaussian random field components corresponding to each unit; m The number of samples in the Monte Carlo simulation, i.e., the number of random field sample groups generated; n This represents the number of elements in the finite element model.

[0051] Fifthly, the process involves converting the random field to a correlated non-Gaussian random field. This transforms the correlated Gaussian random field into one that includes the mean (…). ),variance( ) and coefficient of variation (COV) Δ The physical parameter field, when Take respectively The formula is as follows:

[0052] In the formula, For the first i In the nth sample j Thermal conductivity of each unit; For the first i In the nth sample j Specific heat capacity of each unit; For the first i In the nth sample j The latent heat of phase transition of each unit; This is the average value of the thermal conductivity; This is the average specific heat capacity; This represents the average latent heat of phase transition. is the coefficient of variation of thermal conductivity; is the coefficient of variation of specific heat capacity; The coefficient of variation is the latent heat of phase change. , , The first digit represents the thermal conductivity, specific heat capacity, and latent heat of phase change, respectively. i In the nth sample j The standard Gaussian random field components corresponding to each unit.

[0053] In this embodiment, based on the statistical characteristics of soil thermal parameters obtained in step S1, the random field is considered as a three-dimensional stationary random field; the covariance function is used to characterize the structural correlation of parameters between different spatial points; and the local averaging method is used to discretize the continuous random field into random variables corresponding to a finite element mesh. The coefficient of variation of the soil thermal parameters is initially set to 0.2, with a horizontal fluctuation range of... and vertical fluctuation range The values ​​were 20m and 1.0m, respectively. To investigate the influence of different random field characteristics on the freezing temperature field, sensitivity analysis was conducted by changing parameters such as the coefficient of variation, vertical fluctuation range, horizontal fluctuation range, and freezing time. The working condition settings for the coefficient of variation, vertical fluctuation range, horizontal fluctuation range, and freezing time are shown in Table 2.

[0054] Table 2. Baseline and Sensitivity Analysis Parameters ; Furthermore, the aforementioned 3D random freezing temperature field analysis based on Monte Carlo simulation includes: Define random and deterministic variables; input the statistical characteristics of the random field; determine the number of Monte Carlo simulations N (N depends on the required precision of the output variable statistical indicators); establish a three-dimensional finite element model, and perform mesh discretization and numbering; based on the method described in S3, write a program to generate N sets of discretized random fields for the three soil parameters corresponding to the finite element mesh; for each random field implementation, call the deterministic finite element solver to calculate the transient temperature field; after completing N simulations, calculate the mean, standard deviation, and failure probability of the output results to quantify the uncertainty range of the freezing temperature field. The calculation formulas are as follows:

[0055] In the formula: N The number of samples; i Sample number ( ); The response variable of interest; For indicator functions, when The value is 1 if it is true, and 0 otherwise. Representation and response variable The relevant limit state function; This represents the mean of the response variable of interest; Standard deviation; and This represents the probability of failure.

[0056] In this embodiment, random variables are defined as thermal conductivity, heat capacity, and latent heat, while deterministic variables are engineering parameters, boundary condition parameters, and material fixed parameters. Based on the statistical characteristics of the random field input in step three: coefficient of variation, vertical fluctuation range, and horizontal fluctuation range, convergence analysis is performed according to Figure 4. When the sample size is ≥50, the mean (0.67m) and standard deviation (0.07m) of the frozen wall thickness tend to stabilize. The number of Monte Carlo simulations N is determined to be 200, and 200 Monte Carlo simulations are performed. The model construction is consistent with the deterministic model. After mesh discretization and numbering, it is shown in Figure 2(b). After completing 200 simulations, the mean and variance of the temperature at each spatial point are calculated. Figure 3 shows the coefficient of variation COV. Δ Under the condition of 0.3, the isopleths of the average temperature and temperature variance on the vertical mid-plane of the freezing pipe after 10, 20, and 30 days of freezing were analyzed. The quantification of temperature field uncertainty revealed that the mean temperature field trend is consistent with the deterministic results (radial expansion), reflecting the central trend of the freezing process; the variance peak of the variance temperature field appears at 0.8~1.2m on the outer wall of the tunnel, showing obvious uncertainty characteristics.

[0057] Furthermore, the statistical characteristics and reliability assessment of the frozen wall thickness include: Extract frozen wall thickness data under different operating conditions (coefficient of variation, fluctuation range, freezing time), and define the reliability of the freezing project as "actual frozen wall thickness". ≥ Design thickness The probability of [the probability] is calculated using the following formula:

[0058] In the formula: For the frozen thickness to be less than the design thickness The cumulative probability, R Indicates reliability. P It represents probability.

[0059] Based on the thickness cumulative distribution function (CDF) curve, the reliability under different coefficients of variation is calculated to quantify the risk of insufficient freezing caused by soil variability.

[0060] Based on the simulation results in step S4, the thickness data under different working conditions were extracted and the cumulative distribution function curves were plotted. Under different working conditions (as shown in Figure 5), the mean thickness of the frozen wall varies with the coefficient of variation (COV). Δ As COV increases, its standard deviation decreases, and its standard deviation decreases with increasing COV. Δ The reliability increases with increasing COV. Furthermore, calculations of reliability under different coefficients of variation revealed that the reliability of frozen thickness increases with increasing COV. ΔThe coefficient of variation (COV) decreases monotonically as it increases. Δ When the coefficient of variation (COV) is 0.1, the reliability reaches 0.88, indicating a high probability of meeting design requirements. However, when the COV increases to 0.3, the reliability drops sharply to 0.09, meaning that only 9% of cases achieve the design thickness. This indicates that the COV of the soil's thermal parameters is highly variable. Δ The coefficient of variation is a key factor affecting the thickness of the frozen wall, and the two are negatively correlated: the larger the coefficient of variation, the smaller the average frozen thickness and the higher the uncertainty; the high variability of the soil will bring serious risks of insufficient freezing, which may damage the impermeability of the frozen wall.

[0061] Furthermore, the determination of the design expansion coefficient includes: proposing a design expansion coefficient to ensure stable target reliability for critical operations at the tail of the tunnel boring machine. Based on the design expansion coefficients corresponding to the target reliability under different coefficients of variation, plot the design expansion coefficient curves and analyze them. The changing pattern; the expansion coefficient The formula is expressed as follows: ; In the formula: For the corresponding target reliability Minimum freezing thickness, For design thickness.

[0062] In this embodiment, and For example, calculate the required... and As shown in Table 3, and the design expansion coefficient curve is plotted as shown in Figure 6. Analysis reveals that for all coefficients of variation, the design expansion coefficient... All depend on the target reliability The monotonically increasing value reflects the need for a larger design expansion factor to offset uncertainties, given the higher reliability requirements.

[0063] Table 3 Design expansion factor with target reliability of 0.9 ; Furthermore, the optimization design process for the freezing scheme considering random characteristics includes: Based on the above reliability analysis and design expansion factors, a closed-loop design process of "parameter acquisition—simulation—evaluation—optimization—verification" is constructed. The design steps are as follows: (1) Clarify engineering requirements: Determine the design thickness of the frozen wall = 0.58 m, and the target reliability is determined based on the engineering risk level. = 0.9; (2) Characterizing soil variability: Soil thermal parameters were measured through field sampling and laboratory tests, and its random field characteristics were calculated using geostatistical methods: Unfrozen thermal conductivity =1.5175W / (m·℃), freezing thermal conductivity =2.0725W / (m·℃), unfrozen specific heat capacity =1659.5 J / (kg·℃), specific heat capacity upon freezing =991J / (kg·℃), latent heat = 20 m, coefficient of variation COV Δ = 0.2, Level = 20 m、 = 1 m; (3) Calculation Using the cumulative distribution function of frozen thickness corresponding to the measured coefficient of variation, the reliability of the target can be obtained through inversion. Corresponding minimum thickness =0.546 m; (4) Determine the design expansion factor According to the measured coefficient of variation COV Δ and target reliability Choose an appropriate design expansion factor =1.06; (5) Optimize design parameters: Calculate the adjusted design thickness =0.615 m. If freezing time is a critical control parameter, the design expansion factor can be converted into a freezing time expansion factor to determine the minimum freezing duration. (6) Verification and iterative optimization: Verify whether the adjusted design meets the requirements under specific site variability conditions through numerical simulation. If not, readjust the design expansion factor. And repeat steps (5)-(6); (7) On-site monitoring: Temperature sensors are deployed to monitor the development status of the frozen wall in real time, and the design expansion coefficient is updated based on the monitoring data. The freezing scheme is dynamically adjusted to ensure that reliability targets are met.

[0064] This invention establishes a three-dimensional stochastic thermal numerical model that integrates stochastic field theory and Monte Carlo simulation, systematically considering soil variability, thereby improving the safety and economy of shield machine tail brush replacement operations and breaking through the limitations of traditional 2D stochastic analysis of frozen soil in cold regions.

[0065] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0066] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” as used in the embodiments of this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0067] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0068] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0069] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A stochastic analysis and design method for the freezing temperature field during shield tail brush replacement considering the spatial variability of soil parameters, characterized in that... Includes the following steps: S1. Obtain basic data on engineering parameters and soil thermal parameters; S2. Establishment of a deterministic freezing temperature field model and benchmark analysis; S3, Construction of 3D random field for soil thermal parameters; S4. Analysis of 3D random freezing temperature field based on Monte Carlo simulation; S5. Statistical characteristics and reliability assessment of frozen wall thickness; S6. Determine the design expansion factor; S7. Optimization design of freezing scheme considering random characteristics.

2. The method for stochastic analysis and design of the freezing temperature field for shield tail brush replacement considering the spatial variability of soil parameters according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11. Collect engineering parameters such as the dimensions of the tunnel boring machine, tunnel segments, and frozen pipes, as well as the geological formation and confined water level. S12. The thermal conductivity, heat capacity, and latent heat of each soil layer in frozen and unfrozen states were determined through indoor tests. S13. Calculate the mean value of thermal parameters using geostatistical methods. μ Δ Coefficient of variation (COV) Δ Horizontal and vertical fluctuation range Vertical fluctuation range To clarify the spatial variability of soil thermal parameters.

3. The method for stochastic analysis and design of the freezing temperature field for shield tail brush replacement considering the spatial variability of soil parameters according to claim 1, characterized in that: Step S2 specifically includes the following: S21. Use Abaqus software to build a three-dimensional finite element model and preset the initial temperature field of the model nodes; S22. Ignoring the spatial variability of soil thermal parameters, the spatiotemporal distribution of soil temperature field is solved using Abaqus software. The baseline law of frozen wall is obtained after post-processing the simulation results.

4. The method for stochastic analysis and design of the freezing temperature field for shield tail brush replacement considering the spatial variability of soil parameters according to claim 1, characterized in that: Step S3 specifically includes the following steps: S31. Based on the statistical characteristics of thermal parameters, construct the thermal conductivity... λ Specific heat capacity c Phase transition latent heat L The 3D random field is discretized into finite element parameters; S32. The covariance function is used to characterize the structural correlation of parameters between different spatial points; S33. The continuous random field is discretized into random variables corresponding to the finite element grid using the local averaging method. That is, a representative random variable is assigned to each finite element, which is the spatial average value within the unit volume. A variance reduction function is introduced to quantize the relationship between the point scale and the spatial average scale parameter and to eliminate local fluctuation interference. Then, following the process of "determining statistical parameters → initializing uncorrelated Gaussian field → decomposing the correlation matrix by Choreski → constructing a correlated Gaussian random field → converting it to a correlated non-Gaussian random field", a thermal parameter random field corresponding to the finite element grid is generated.

5. The method for stochastic analysis and design of the freezing temperature field for shield tail brush replacement considering the spatial variability of soil parameters according to claim 4, characterized in that: The process of "determining statistical parameters → initializing uncorrelated Gaussian fields → decomposing the correlation matrix by Choreski → constructing correlated Gaussian random fields → converting to correlated non-Gaussian random fields" is as follows: Determine the statistical parameters: Determine the statistical parameters for each thermal parameter, including the mean. ,variance Coefficient of variation (COV) Δ and the range of horizontal and vertical fluctuations Vertical fluctuation range ; Initialize an uncorrelated Gaussian field: For each thermal parameter and each Monte Carlo sample, generate an uncorrelated standard Gaussian random matrix. A ; Choreski decomposition of correlation matrix: constructing spatial correlation matrix based on statistical parameters ; for spatial correlation matrix Perform the Choleski decomposition: ； In the formula, The lower triangular Choreski factor, for The transpose of the matrix; Constructing a correlated Gaussian random field: Generating a correlated standard Gaussian random field through matrix multiplication: ； The obtained matrix It contains a standard Gaussian random field with specified spatial correlation, where each row represents a sample of a spatially correlated parametric field; Representing the i In the nth sample j The standard Gaussian random field components corresponding to each unit; m The number of samples in the Monte Carlo simulation, i.e., the number of random field sample groups generated; n The number of elements in the finite element model; Convert to a correlated non-Gaussian random field: Convert a correlated Gaussian random field into one that includes the mean. ,variance and coefficient of variation COV Δ The physical parameter field, when Take respectively When, the formula is as follows: ； In the formula, For the first i In the nth sample j Thermal conductivity of each unit; For the first i In the nth sample j Specific heat capacity of each unit; For the first i In the nth sample j The latent heat of phase transition of each unit; This is the average value of the thermal conductivity; This is the average specific heat capacity; This represents the average latent heat of phase transition. is the coefficient of variation of thermal conductivity; is the coefficient of variation of specific heat capacity; The coefficient of variation is the latent heat of phase change. , , The first digit represents the thermal conductivity, specific heat capacity, and latent heat of phase change, respectively. i In the nth sample j The standard Gaussian random field components corresponding to each unit.

6. The method for stochastic analysis and design of the freezing temperature field for shield tail brush replacement considering the spatial variability of soil parameters according to claim 1, characterized in that: Step S4 specifically includes: S41. Define random variables and deterministic variables; S42. Input the statistical characteristics of the random field; S43. Determine the number of Monte Carlo simulations, N; S44. Establish a three-dimensional finite element model, and perform mesh discretization and numbering; S45. Write a program to generate N sets of discretized random fields of three soil parameters corresponding to the finite element mesh; S46. For each random field implementation, call the deterministic finite element solver to calculate the transient temperature field; S47. After completing N simulations, calculate the mean, standard deviation, and failure probability of the output results to quantify the uncertainty range of the freezing temperature field.

7. The method for stochastic analysis and design of the freezing temperature field for shield tail brush replacement considering the spatial variability of soil parameters according to claim 1, characterized in that: The aforementioned statistical characteristics and reliability assessment of the frozen wall thickness specifically include: Extract frozen wall thickness data under different working conditions, and define the reliability of the freezing project as "actual frozen wall thickness". ≥ Design thickness The probability of reliability is calculated based on the cumulative distribution function (CDF) curve of thickness, under different coefficients of variation.

8. The method for stochastic analysis and design of the freezing temperature field for shield tail brush replacement considering the spatial variability of soil parameters according to claim 1, characterized in that: Step S6 specifically includes: to ensure stable target reliability for critical operations at the tail of the tunnel boring machine, proposing a design expansion coefficient. Based on the design expansion coefficients corresponding to the target reliability under different coefficients of variation, plot the design expansion coefficient curves and analyze them. The changing pattern; the expansion coefficient The formula is expressed as follows: ； In the formula: For the corresponding target reliability Minimum freezing thickness, For design thickness.

9. The method for stochastic analysis and design of the freezing temperature field for shield tail brush replacement considering the spatial variability of soil parameters according to claim 1, characterized in that: Step S7 specifically includes: S71. Determine the design thickness of the frozen wall. The target reliability is determined based on the engineering risk level. ; S72. Characterizing soil variability: Soil thermal parameters are measured through field sampling and laboratory tests, and its random field characteristics are calculated using geostatistical methods. COV Δ , S v ; S73, Calculation Using the cumulative distribution function of frozen thickness corresponding to the measured coefficient of variation, the reliability of the target can be obtained through inversion. Corresponding minimum thickness ; S74. Determine the design expansion factor According to the measured coefficient of variation COV Δ and target reliability Choose an appropriate design expansion factor ; S75. Optimize design parameters: Calculate the adjusted design thickness. If freezing time is a key control parameter, the design expansion factor is converted into a freezing time expansion factor to determine the minimum freezing duration. S76. Verification and Iterative Optimization: Verify through numerical simulation whether the adjusted design meets the requirements under specific site variability conditions. If not, readjust the design expansion factor. And repeat the above steps; S77. Freezing Scheme Optimization: Deploy temperature sensors to monitor the development status of the frozen wall in real time, and update the design expansion coefficient based on the monitoring data. The freezing scheme is dynamically adjusted to ensure that reliability targets are met.

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