Numerical simulation method of thermal-mechanical coupling of frozen pipes in artificial ground freezing method

Abstract

The present invention relates to a numerical simulation method for thermomechanical coupling of frozen pipes during artificial ground freezing, comprising the following steps: establishing a geometric model for numerical simulation and performing meshing; conducting experiments to obtain curves of soil physical parameters changing with temperature during freezing and thawing after the soil is frozen; inputting all obtained curves into a freezing pipe temperature adjustment module and a soil parameter adjustment module obtained through secondary development; setting initial and boundary conditions; inputting the changes in volumetric strain caused by temperature field changes into a mechanical calculation module, and calculating the final soil volumetric strain changes and stress changes based on the geometric model of the soil. The present invention can achieve automatic adjustment of the freezing pipe temperature over time, can determine the soil state based on temperature, and adjust soil parameters, thereby achieving thermomechanical coupling calculations, thereby making the numerical simulation results more accurate and achieving more precise numerical simulations of frost heave and thaw settlement.

Description

Technical Field

[0001] The invention relates to the field of building construction, and in particular to a numerical simulation method for thermal-mechanical coupling of freezing pipes constructed using an artificial ground freezing method. Background Art

[0002] Artificial ground freezing involves driving freezing pipes into the target stratum. These pipes absorb heat from the surrounding soil, freezing it and forming a frozen wall curtain to achieve both water-stopping and reinforcement. Because it combines both reinforcement and water-stopping, it is applicable to complex geological conditions (such as groundwater-rich strata and weak strata), is unrestricted by support range and depth, and offers high reliability, a simple construction process, and generates no construction waste or pollutes the surrounding stratum or groundwater. This method is more in line with energy conservation, emission reduction, and green development initiatives. As a result, artificial ground freezing is gaining increasing popularity among engineers and has been widely used in urban subway construction in recent years.

[0003] Currently, due to the lack of comprehensive theoretical support, artificial ground freezing construction primarily relies on numerical simulation to aid design. This simulation focuses on simulating the temperature field of the frozen ground during freezing and the mechanical response of the surrounding frozen soil (frozen wall) during excavation after freezing. In current numerical simulations, these two modules are considered relatively independent and simulated separately. This approach does not significantly impact linear elastic materials, which can be analyzed independently. However, for nonlinear elastic materials, where the mechanical response of the soil is related to the accumulated strain, thermomechanical coupling must be considered. Furthermore, for general soils, their fundamental physical parameters are significantly affected by temperature after freezing, so thermomechanical coupling must be considered to accurately analyze the mechanical behavior during excavation. Furthermore, freezing construction often causes surface frost heave and thaw settlement, which can adversely affect existing buildings. Analysis and estimation of frost heave and thaw settlement caused by freezing require thermomechanical coupling calculations. However, due to the lack of thermomechanical coupling analysis, the analysis of frost heave and thaw settlement caused by artificial ground freezing construction is often incomplete or inaccurate. Summary of the Invention

[0004] In response to the above-mentioned shortcomings in the existing technology, the present invention provides a numerical simulation method for the thermal coupling of freezing pipes during the construction of artificial ground freezing method, which solves the technical problems in the existing technology that thermal coupling is not considered in the numerical simulation of the construction of artificial ground freezing method, and the analysis of frost heave and thaw settlement caused by the construction of artificial ground freezing method is missing or inaccurate.

[0005] The present invention discloses a numerical simulation method for thermal-mechanical coupling of freezing pipes constructed by artificial ground freezing method, comprising the following steps:

[0006] S1. Establish the geometric model for numerical simulation and perform mesh division;

[0007] S2. Conducting experiments to obtain the curves of soil physical parameters changing with temperature during the freezing and thawing process after the soil is frozen;

[0008] S3, inputting the curve obtained in S2 into the freezing pipe temperature adjustment module and soil parameter adjustment module obtained through secondary development;

[0009] S4. Input the freezing temperature, thermal expansion coefficient of unfrozen soil, and set the initial and boundary conditions of external stress, displacement and temperature;

[0010] S5. Determine the time step, and simultaneously, the freezing pipe temperature adjustment module obtained by secondary development adjusts the temperature boundary of the freezing pipe according to the time step and obtains the adjustment result;

[0011] S6. Calculate the instantaneous temperature distribution change according to the adjustment result of S5 and obtain the instantaneous temperature distribution;

[0012] S7, the soil state judgment module obtained by secondary development, judges the soil state according to the temperature distribution change and temperature distribution;

[0013] S8, adjusting soil parameters according to the instantaneous temperature distribution using a soil parameter adjustment module obtained through secondary development based on the soil state determined in S7;

[0014] S9, calculating the instantaneous change in soil volume strain caused by the temperature field change based on the result of adjusting the soil parameters in S8 and the instantaneous temperature distribution change;

[0015] S10. Input the volume strain change caused by the temperature field change into the mechanical calculation module to calculate the final soil volume strain change and stress change according to the geometric model of the soil.

[0016] The numerical simulation method for thermal-mechanical coupling of frozen pipes constructed by artificial ground freezing method of the present invention is further improved in that the calculations of S5-S10 are performed once in each time step.

[0017] The numerical simulation method of thermal coupling of freezing pipes constructed by the artificial ground freezing method of the present invention is further improved in that the physical parameters of the soil after the soil is frozen include the temperature change curve of the freezing pipe with time, the freezing temperature, the thermal expansion rate of the unfrozen soil, the elastic modulus of the soil after the soil is frozen with the temperature change curve, the Poisson's ratio with temperature change curve, the cohesion with temperature change curve, the friction angle with temperature change curve, the frost heave rate with temperature change curve, the thaw settlement rate with temperature change curve, the thermal conductivity coefficient with temperature change curve and the specific heat capacity with temperature change curve; in S3, all the curves obtained in S2 are respectively input into the freezing pipe temperature adjustment module and the soil parameter adjustment module obtained by secondary development.

[0018] The numerical simulation method for thermal coupling of freezing pipes constructed by the artificial ground freezing method of the present invention is further improved in that, in S2, the temperature change curve of the freezing pipe is measured with time according to the experiment; the freezing temperature of the soil is measured according to the freezing temperature test; the thermal expansion rate of the soil is measured according to the experiment; the elastic modulus and Poisson's ratio of the soil during freezing and thawing are measured with temperature according to the resonance column test; the cohesion and friction angle during freezing and thawing are measured with temperature according to the triaxial test; the frost heave rate and thaw settlement rate during freezing and thawing are measured with temperature using a frost heave and thaw settlement meter; the thermal conductivity during freezing and thawing is measured with temperature according to the frozen soil thermal conductivity test; and the specific heat capacity during freezing and thawing is measured with temperature using a specific heat capacity tester.

[0019] The numerical simulation method for the thermal coupling of the frozen pipe in the artificial ground freezing method of the present invention is further improved in that, when secondary development is performed in S3, the temperature change curve of the measured frozen pipe over time is obtained by curve fitting to obtain an analytical expression and is imported into the freezing pipe temperature adjustment module obtained by the secondary development; the curve of the soil elastic modulus, Poisson's ratio, cohesion, friction angle, thermal expansion coefficient, thermal conductivity and specific heat capacity changing with temperature during the freezing and melting process is also obtained by curve fitting to obtain an analytical expression and is imported into the soil parameter adjustment module obtained by the secondary development.

[0020] The numerical simulation method for the thermal coupling of the freezing pipe constructed by the artificial ground freezing method of the present invention is further improved in that the geometric model time is input into the freezing pipe temperature adjustment module, the analytical expression of the freezing pipe temperature change curve imported by the S3 method is output to correspond to the temperature of the freezing pipe surface, and this temperature is applied to the temperature boundary corresponding to the freezing pipe.

[0021] The numerical simulation method of thermal coupling of freezing pipes constructed by the artificial ground freezing method of the present invention is further improved in that, during secondary development in S7, a soil state judgment module is developed. The temperature change and temperature of a single volume unit can be obtained according to the temperature field change and the temperature field. The temperature change and temperature of this single volume unit are input into the soil state judgment module to judge the state of each volume unit. When the temperature is higher than the freezing temperature, it is an unfrozen state; when the temperature is lower than the freezing temperature and the temperature change is positive, it is a melting process state; when the temperature is lower than the freezing temperature and the temperature change is negative, it is a freezing process state.

[0022] The numerical simulation method for thermal-mechanical coupling of frozen pipes in artificial ground freezing construction according to the present invention is further improved in that, when performing S8, it is determined whether to input the geometric model temperature into the soil parameter adjustment module according to the judgment result of S7, and if the judgment result indicates that the soil is not frozen, this step is skipped;

[0023] If the result is that the freezing process state is frozen, the temperature of each volume unit is input into the soil parameter adjustment module, and the analytical expression of the soil elastic modulus, Poisson's ratio, cohesion, friction angle, frost heave rate, thermal conductivity, and specific heat capacity during the freezing process is output and assigned to each soil unit.

[0024] The judgment result is that the melting process state is frozen. Similarly, the temperature of each volume unit is input into the soil parameter adjustment module, and the analytical expression of the soil elastic modulus, Poisson's ratio, cohesion, friction angle, melting settlement rate, thermal conductivity and specific heat capacity imported by the S3 method during the melting process with the temperature change curve is output and the corresponding elastic modulus, Poisson's ratio, cohesion, friction angle, thermal conductivity, melting settlement rate and specific heat capacity are assigned to each soil unit.

[0025] Compared with existing technologies, the present invention has a positive and significant effect. It can automatically adjust the freezing pipe temperature over time, determine the soil state based on temperature, and adjust soil parameters, thereby achieving thermodynamic coupling calculations. This makes numerical simulation results more accurate, and enables more precise numerical simulation of frost heave and thaw settlement. This solves the technical problems of existing technologies that fail to consider thermodynamic coupling in numerical simulations of artificial ground freezing construction, as well as omissions or inaccuracies in the analysis of frost heave and thaw settlement caused by artificial ground freezing construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0027] Figure 1 The present invention provides a flow chart of a numerical simulation method for thermal-mechanical coupling of freezing pipes constructed using the artificial ground freezing method.

[0028] Figure 2 The figure is a schematic diagram of the soil geometry model for the numerical simulation method of thermal-mechanical coupling of the freezing pipes constructed by the artificial ground freezing method of the present invention.

[0029] Figure 3 This is a schematic diagram of the geometric model of the tunnel and the freezing pipe in the numerical simulation method of the thermal-mechanical coupling of the freezing pipe constructed by the artificial ground freezing method of the present invention.

[0030] Figure 4 The present invention provides experimental data on the change of freezing pipe surface temperature over time and a corresponding fitting curve diagram for the numerical simulation method of thermal coupling of freezing pipes constructed using the artificial ground freezing method.

[0031] Figure 5 The present invention provides test data and corresponding fitting curves showing the elastic modulus changing with temperature during the freezing and melting process of the numerical simulation method for thermal-mechanical coupling of the freezing pipe constructed by the artificial ground freezing method.

[0032] Figure 6 The present invention provides a graph showing experimental data of Poisson's ratio changing with temperature during freezing and melting, and a corresponding fitting curve for a numerical simulation method for thermal coupling of a freezing pipe constructed using the artificial ground freezing method.

[0033] Figure 7 The present invention provides a numerical simulation method for the thermal coupling of a freezing pipe constructed using the artificial ground freezing method, and provides test data and a corresponding fitting curve showing changes in cohesion with temperature during the freezing and melting process.

[0034] Figure 8 The present invention provides a numerical simulation method for the thermal coupling of a freezing pipe constructed using the artificial ground freezing method, and provides test data on the change of friction angle with temperature during freezing and melting, as well as a graph of the corresponding fitting curve.

[0035] Figure 9 The present invention provides a graph of test data and corresponding fitting curves showing changes in the frost heave coefficient and thaw settlement coefficient with temperature during the freezing and thawing process for a numerical simulation method for thermal coupling of a freezing pipe constructed using the artificial ground freezing method.

[0036] Figure 10The present invention provides a graph showing test data of thermal conductivity changing with temperature during freezing and melting processes and a corresponding fitting curve for a numerical simulation method for thermal coupling of a freezing pipe constructed using the artificial ground freezing method.

[0037] Figure 11 The present invention provides experimental data and a corresponding fitting curve graph showing the change of specific heat capacity with temperature during the freezing and melting process of the numerical simulation method for thermal coupling of the freezing pipe constructed by the artificial ground freezing method. DETAILED DESCRIPTION

[0038] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0039] Artificial Ground Freezing (AGF), also known as "freezing," utilizes artificial refrigeration (generally using ammonia-brine freezing pipes) to freeze groundwater, transforming natural rock and soil into frozen ground. This technique increases its strength and stability, isolates groundwater from underground projects, and allows for underground construction to proceed under the protection of a frozen wall. Essentially, it uses artificial refrigeration to temporarily alter the properties of rock and soil to strengthen the ground.

[0040] Thermomechanical coupling: In this invention, thermomechanical coupling has two meanings. One is that temperature changes cause temperature strain, which in turn affects stress; the other refers to the fact that after freezing, the mechanical parameters of the soil change with temperature, thus affecting the mechanical response of the soil. This invention primarily considers the impact of thermodynamic calculations on mechanical calculations, and does not consider the impact of mechanical calculations on thermodynamic calculations.

[0041] like Figure 1 As shown, the present invention provides a numerical simulation method for thermal-mechanical coupling of freezing pipes in artificial ground freezing method, comprising the following steps:

[0042] S1. Establish the geometric model of numerical simulation and perform mesh division. The geometric model of numerical simulation is established based on the three-dimensional explicit Lagrangian finite volume method software FLAC3D, such as Figure 2 As shown, the size of the geometric model is 80m×80m×40m (length×width×height), as shown in Figure 3As shown, the figure shows a tunnel 1, a freezing pipe 2, and a communication channel 3. The upper part of the yellow part is the communication channel 3, and the lower part of the yellow part is the pump room 4. The tunnel is located 20m underground and has a 0.3m thick shield segment lining. The left and right center lines of the tunnel are 14m apart. In this embodiment, the geometric model is meshed by the Rhino plug-in Griddle, where the minimum grid size is 0.15m and the maximum grid size is 8m. At the same time, the freezing pipe is partially encrypted to improve its accuracy.

[0043] S2. Conducting experiments to obtain the curves of soil physical parameters changing with temperature during the freezing and thawing process after the soil is frozen;

[0044] S3, inputting the curve obtained in S2 into the freezing pipe temperature adjustment module and soil parameter adjustment module obtained through secondary development;

[0045] S4. Input the freezing temperature, thermal expansion coefficient of unfrozen soil, and set the initial and boundary conditions of external stress, displacement and temperature;

[0046] S5. Determine the time step, and simultaneously, the freezing pipe temperature adjustment module obtained by secondary development adjusts the temperature boundary of the freezing pipe according to the time step and obtains the adjustment result;

[0047] S6. Calculate the instantaneous temperature distribution change according to the adjustment result of S5 and obtain the instantaneous temperature distribution;

[0048] S7, the soil state judgment module obtained by secondary development, judges the soil state according to the temperature distribution change and temperature distribution;

[0049] S8, adjusting soil parameters according to the instantaneous temperature distribution using a soil parameter adjustment module obtained through secondary development based on the soil state determined in S7;

[0050] S9, calculating the instantaneous change in soil volume strain caused by the temperature field change based on the result of adjusting the soil parameters in S8 and the instantaneous temperature distribution change;

[0051] S10. Input the volume strain change caused by the temperature field change into the mechanical calculation module to calculate the final soil volume strain change and stress change according to the geometric model of the soil.

[0052] Specifically, when the test operation is performed, the soil involved in the freezing method construction to be simulated is tested. In S4, inputting the freezing temperature is inputting the freezing temperature of the soil into the numerical simulation software.

[0053] Preferably, the operations S5-S10 are performed once in each time step to obtain the soil volume strain change and stress change in each step.

[0054] Preferably, the physical parameters of the soil after freezing include the temperature change curve of the freezing pipe with time, the freezing temperature, the thermal expansion rate of the unfrozen soil, the elastic modulus of the soil after freezing with temperature change curve, the Poisson's ratio change curve with temperature change curve, the cohesion change curve with temperature change curve, the friction angle change curve with temperature change curve, the frost heave rate change curve with temperature change curve, the thaw settlement rate change curve with temperature change curve, the thermal conductivity change curve with temperature change curve and the specific heat capacity change curve with temperature change curve; in S3, all the curves obtained in S2 are respectively input into the freezing pipe temperature adjustment module and the soil parameter adjustment module obtained by secondary development.

[0055] Preferably, in S2, the temperature variation curve of the freezing pipe is measured according to the experiment, such as Figure 4 As shown in the figure, the horizontal axis is time, the unit is day, the vertical axis is temperature, the unit is ℃, the dots are the test data of the freezing pipe surface temperature, and the curve is the temperature best fitting curve;

[0056] The freezing temperature of the soil is measured according to the freezing temperature test; the thermal expansion rate of the soil is measured according to the test;

[0057] According to the resonant column test, the soil elastic modulus changes with temperature during freezing and thawing were measured, as shown in Figure 2. Figure 5 As shown in the figure, the horizontal axis is temperature, the unit is ℃, the vertical axis is elastic modulus, the unit is MPa, the circles are the test data of the freezing process, the solid curve is the best fitting curve of the freezing process, the squares are the test data of the melting process, and the dotted curve is the best fitting curve of the melting process;

[0058] According to the resonant column test, the soil Poisson's ratio curves with temperature during freezing and thawing were measured, as shown in Figure 2. Figure 6 As shown in the figure, the horizontal axis is temperature, the unit is ℃, the vertical axis is Poisson's ratio, the circles are the experimental data of the freezing process, the solid curve is the best fitting curve of the freezing process, the squares are the experimental data of the melting process, and the dotted curve is the best fitting curve of the melting process;

[0059] According to the triaxial test, the cohesion curves with temperature during freezing and melting were measured, as shown in Figure 2. Figure 7 As shown in the figure, the horizontal axis is temperature, the unit is ℃, the vertical axis is cohesion, the unit is MPa, the circles are the test data of the freezing process, the solid curve is the best fitting curve of the freezing process, the squares are the test data of the melting process, and the dotted curve is the best fitting curve of the melting process;

[0060] According to the triaxial test, the friction angle variation curves during freezing and melting were measured respectively, such as Figure 8 As shown in the figure, the horizontal axis is temperature, the unit is ℃, the vertical axis is friction angle, the unit is degree, the circles are the test data of the freezing process, the solid curve is the best fitting curve of the freezing process, the squares are the test data of the melting process, and the dotted curve is the best fitting curve of the melting process;

[0061] The frost heave rate and thaw settlement rate were measured with the frost heave and thaw settlement instrument respectively during freezing and thawing. The frost heave rate was expressed by the frost heave coefficient, and the thaw settlement rate was expressed by the thaw settlement coefficient. Figure 9 As shown in the figure, the horizontal axis is temperature, the unit is ℃, the vertical axis is the frost heave coefficient and thaw settlement coefficient, the unit is ℃ -1 , the circles are the experimental data of frost heave coefficient, the solid curve is the best fitting curve of frost heave coefficient, the squares are the experimental data of thaw settlement coefficient, the dotted curve is the best fitting curve of thaw settlement coefficient;

[0062] According to the thermal conductivity test of frozen soil, the thermal conductivity curves of freezing and melting processes are respectively measured as follows: Figure 10 As shown in the figure, the horizontal axis is temperature, the unit is ℃, and the vertical axis is thermal conductivity, the unit is W·(m·K) -1 , the circles are the experimental data of the freezing process, the solid curve is the best fitting curve of the freezing process, the squares are the experimental data of the melting process, and the dotted curve is the best fitting curve of the melting process;

[0063] Use a specific heat capacity tester to measure the specific heat capacity versus temperature curve during freezing and melting, such as Figure 11 As shown in the figure, the horizontal axis is temperature, the unit is ℃, and the vertical axis is specific heat capacity, the unit is kJ·(kg·K) -1 The circles are the experimental data of the freezing process, the solid curve is the best fitting curve of the freezing process, the squares are the experimental data of the melting process, and the dotted curve is the best fitting curve of the melting process.

[0064] Preferably, when secondary development is performed in S3, the curve of the measured temperature change of the freezing pipe over time is obtained by curve fitting to obtain an analytical expression and is imported into the freezing pipe temperature control module obtained by secondary development; the curve of the soil elastic modulus, Poisson's ratio, cohesion, friction angle, thermal expansion coefficient, thermal conductivity and specific heat capacity changing with temperature during freezing and melting is also obtained by curve fitting to obtain an analytical expression and is imported into the soil parameter control module obtained by secondary development. Specifically, secondary development is performed based on the fish language of FLAC3D, and based on the measured test data of the freezing pipe surface temperature changing with time, the least squares method is used to fit the exponential form equation shown in formula (1) to obtain the analytical expression of the curve as shown in formula (1). Figure 3 The data are shown in Figure 1 and input into the freezing pipe temperature control module obtained through secondary development. Similarly, the same processing is performed on the test data of soil elastic modulus, Poisson's ratio, cohesion, friction angle, thermal expansion coefficient (freeze heave rate / thaw settlement rate), thermal conductivity, and specific heat capacity during freezing and thawing with temperature changes to obtain their analytical curves as shown in Figure 1. Figure 5 , Figure 6 , Figure 7 , Figure 8 , Figure 9 , Figure 10 ,and Figure 11 As shown in the figure, it is imported into the soil parameter adjustment module obtained through secondary development.

[0065]

[0066] Among them, y is the fitting dependent variable; x is the fitting independent variable; y0, A, and t are the fitting parameters.

[0067] Preferably, the geometric model time is input into the freezing pipe temperature adjustment module, and the analytical expression of the freezing pipe temperature change curve imported by the S3 method outputs the corresponding freezing pipe surface temperature, and this temperature is applied to the temperature boundary corresponding to the freezing pipe.

[0068] When performing S4, the freezing temperature is input according to the test data, which is -0.6°C in this embodiment and the thermal expansion coefficient of the unfrozen soil, which is 1×10 -5 ℃ -1 . Set the initial displacement. In this embodiment, the initial displacement is zero. Set the displacement boundary conditions. For the displacement boundary, the top boundary is the free displacement boundary, the lower boundary is the fixed boundary, and the normal displacement of the surrounding boundaries is the fixed boundary. Set the initial stress. In this embodiment, the initial stress is the initial ground stress. Set the stress boundary conditions. In this embodiment, no stress boundary conditions are set. Set the initial temperature. In this embodiment, the initial temperature of the soil is 20°C. Set the temperature boundary conditions. In this embodiment, the top is set to a constant temperature boundary with a temperature of 20°C. Other surfaces are defaulted to adiabatic boundaries. For the freezing pipe, the temperature boundary changes according to time.

[0069] When performing S5, the geometric model time is input into the freezing pipe temperature adjustment module, and the freezing pipe surface temperature change curve over time is imported into this module through the S3 method. The freezing pipe temperature adjustment module will output the corresponding freezing pipe surface temperature and apply this temperature to the corresponding temperature boundary of the S4 freezing pipe, thereby realizing real-time adjustment of the freezing pipe temperature.

[0070] In S6, the time step is determined. In the FLAC3D software, the time step is automatically determined by the program based on the model accuracy requirements and characteristic time. At the same time, based on the adjustment results of the temperature boundary of the freezing pipe in S5, the instantaneous temperature distribution change is calculated and the instantaneous temperature distribution is obtained. The specific calculation principle is as follows:

[0071] In FLAC3D, thermodynamic problems with given initial and boundary conditions are solved by combining the energy conservation equation and the heat conduction equation. First, several relevant variables are introduced:

[0072] Characteristic length L c :

[0073]

[0074] Among them, V s is the total volume; Q s Transfer heat to the boundary.

[0075] Thermal diffusivity κ:

[0076]

[0077] Where k is the thermal conductivity; ρ is the material density; C v is the specific heat capacity of the material.

[0078] Characteristic time t c :

[0079]

[0080] Where k is the thermal conductivity; L c is the characteristic length.

[0081] Energy conservation equation:

[0082] The temperature calculation process complies with the law of conservation of energy, and its differential form can be expressed as formula (5):

[0083]

[0084] Where: q i,i is the heat inflow vector, q v The amount of heat stored per unit volume.

[0085] Generally speaking, changes in energy and volumetric strain can cause changes in temperature. The relationship between them can be determined using formula (6):

[0086]

[0087] Among them, M th and β th is the material constant and T is the temperature.

[0088] In FALC3D, it is assumed that the change of strain will not affect the temperature (this assumption is reasonable for common liquids and solids). Under this assumption, Equation (6) can be simplified to Equation (7):

[0089]

[0090] Where ρ is the density of the material; C v is the specific heat of the material.

[0091] Combining equations (7) and (5) we can obtain the differential relationship between the inflow heat, the self-heat and the temperature, equation (8):

[0092]

[0093] Among them, q i,i is the heat inflow vector, q v is the heat stored per unit volume, ρ is the density of the material; C v is the specific heat of the material.

[0094] Law of heat conduction:

[0095] For a static, homogeneous, isotropic solid, the heat conduction law obeys Fourier's heat conduction law. This law states that the heat flow and the temperature gradient are linearly related. This relationship can be expressed by equation (9):

[0096]

[0097] Where q is the temperature and k is the thermal conductivity; is the temperature gradient.

[0098] Preferably, when secondary development is performed in S7, secondary development is performed based on the fish language of FLAC3D software to develop a soil state judgment module. The temperature change and temperature of a single volume unit can be obtained according to the temperature field change and the temperature field. The temperature change and temperature of this single volume unit are input into the soil state judgment module to judge the state of each volume unit. When the temperature is higher than the freezing temperature, it is an unfrozen state; when the temperature is lower than the freezing temperature and the temperature change is positive, it is a melting process state; when the temperature is lower than the freezing temperature and the temperature change is negative, it is a freezing process state.

[0099] Preferably, when performing S8, it is determined whether to input the geometric model temperature into the soil parameter adjustment module according to the judgment result of S7, and if the judgment result is that the temperature is not frozen, this step is skipped;

[0100] If the result is that the freezing process state is frozen, the temperature of each volume unit is input into the soil parameter adjustment module, and the analytical expression of the soil elastic modulus, Poisson's ratio, cohesion, friction angle, frost heave rate, thermal conductivity, and specific heat capacity during the freezing process is output and assigned to each soil unit.

[0101] The judgment result is that the melting process state is frozen. Similarly, the temperature of each volume unit is input into the soil parameter adjustment module, and the analytical expression of the soil elastic modulus, Poisson's ratio, cohesion, friction angle, melting settlement rate, thermal conductivity and specific heat capacity imported by the S3 method during the melting process with the temperature change curve is output and the corresponding elastic modulus, Poisson's ratio, cohesion, friction angle, thermal conductivity, melting settlement rate and specific heat capacity are assigned to each soil unit.

[0102] When performing S9, the instantaneous change in soil volume strain caused by the temperature field change is calculated based on the adjustment results of S8 and the instantaneous temperature distribution change. The calculation principle is as follows:

[0103] Because free thermal expansion does not cause any angle change, it will not affect the shear strain. Therefore, the strain increment under free thermal expansion conditions can be expressed as Equation (9):

[0104] Δε ij =α t ΔTδ ij (9)

[0105] Where: ε ij is the strain increment, α t is the linear expansion / contraction coefficient; δ ij is the symbol of Kronecker Delta (Kronecker function).

[0106] During step S10, the volumetric strain changes caused by the temperature field changes are input into the mechanical calculation module. The final volumetric strain changes and corresponding stress changes are calculated based on the structural geometry model of the soil. The calculations of steps S5-S10 are performed once in each time step.

[0107] The present invention can realize automatic adjustment of the freezing pipe temperature over time, can realize soil state judgment and soil parameter adjustment based on temperature, thereby realizing thermomechanical coupling calculation, thereby making the numerical simulation results more accurate, and realizing more precise numerical simulation of frost heave and thaw settlement, solving the technical problems in the prior art of not considering thermomechanical coupling when conducting numerical simulation of the construction of artificial ground freezing method, and the lack or inaccurate analysis of frost heave and thaw settlement caused by the construction of artificial ground freezing method.

[0108] The parts not mentioned in the present invention are the same as the existing technology or can be implemented by using the existing technology. The above description is only the preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as the preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modifications to the equivalent embodiments of equivalent changes by using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiment based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A numerical simulation method for thermal-mechanical coupling of frozen pipes in artificial ground freezing construction, characterized in that: The steps include: S1. Establish the geometric model for numerical simulation and perform mesh division; S2. Conducting experiments to obtain the curves of soil physical parameters changing with temperature during the freezing and thawing process after the soil is frozen; S3, inputting the curve obtained in S2 into the freezing pipe temperature adjustment module and soil parameter adjustment module obtained through secondary development; S4. Input the freezing temperature, thermal expansion coefficient of unfrozen soil, and set the initial and boundary conditions of external stress, displacement and temperature; S5. Determine the time step, and simultaneously, the freezing pipe temperature adjustment module obtained by secondary development adjusts the temperature boundary of the freezing pipe according to the time step and obtains the adjustment result; S6. Calculate the instantaneous temperature distribution change according to the adjustment result of S5 and obtain the instantaneous temperature distribution; S7, the soil state judgment module obtained by secondary development, judges the soil state according to the temperature distribution change and temperature distribution; S8, adjusting soil parameters according to the instantaneous temperature distribution using a soil parameter adjustment module obtained through secondary development based on the soil state determined in S7; S9, calculating the instantaneous change in soil volume strain caused by the temperature field change based on the result of adjusting the soil parameters in S8 and the instantaneous temperature distribution change; S10, inputting the volume strain change caused by the temperature field change into the mechanical calculation module to calculate the final soil volume strain change and stress change according to the geometric model of the soil; The physical parameters of the soil after freezing include the temperature variation curve of the freezing pipe with time, freezing temperature, thermal expansion rate of unfrozen soil, elastic modulus variation curve of the soil after freezing with temperature, Poisson's ratio variation curve, cohesion variation curve, friction angle variation curve, frost heave rate variation curve, thaw settlement rate variation curve, thermal conductivity variation curve and specific heat capacity variation curve; In S3, all the curves obtained in S2 are input into the freezing pipe temperature adjustment module and soil parameter adjustment module obtained through secondary development respectively; In S2, the temperature variation curve of the freezing pipe was measured with time according to the test; the freezing temperature of the soil was measured according to the freezing temperature test; the thermal expansion rate of the soil was measured according to the test; the elastic modulus and Poisson's ratio of the soil during freezing and thawing were measured with temperature according to the resonant column test; the cohesion and friction angle during freezing and thawing were measured with temperature according to the triaxial test; the freeze heave rate and thaw settlement rate during freezing and thawing were measured with temperature using a freeze heave and thaw settlement instrument; the thermal conductivity during freezing and thawing was measured with temperature according to the frozen soil thermal conductivity test; the specific heat capacity during freezing and thawing was measured with temperature using a specific heat capacity tester; During secondary development in S3, the measured temperature change curve of the freezing pipe over time is obtained through curve fitting to obtain an analytical expression and imported into the freezing pipe temperature adjustment module obtained through secondary development; the temperature change curves of the soil elastic modulus, Poisson's ratio, cohesion, friction angle, thermal expansion coefficient, thermal conductivity and specific heat capacity during the freezing and melting processes are also obtained through curve fitting to obtain analytical expressions and imported into the soil parameter adjustment module obtained through secondary development.

2. The numerical simulation method for thermal-mechanical coupling of frozen pipes in artificial ground freezing construction according to claim 1, characterized in that: The operations S5-S10 are performed once in each time step.

3. The numerical simulation method for thermal-mechanical coupling of frozen pipes in artificial ground freezing construction according to claim 1 is characterized in that: The geometric model time is input into the freezing pipe temperature adjustment module, and the analytical expression of the freezing pipe temperature change curve imported by the S3 method outputs the corresponding freezing pipe surface temperature, and this temperature is applied to the corresponding temperature boundary of the freezing pipe.

4. The numerical simulation method for thermal-mechanical coupling of frozen pipes in artificial ground freezing construction according to claim 1, characterized in that: During secondary development in S7, a soil state judgment module was developed. Based on the temperature field changes and temperature field, the temperature changes and temperatures of a single volume unit can be obtained. The temperature changes and temperatures of this single volume unit are input into the soil state judgment module to determine the state of each volume unit. When the temperature is higher than the freezing temperature, it is an unfrozen state; when the temperature is lower than the freezing temperature and the temperature change is positive, it is a melting process state; when the temperature is lower than the freezing temperature and the temperature change is negative, it is a freezing process state.

5. The numerical simulation method for thermal-mechanical coupling of frozen pipes in artificial ground freezing construction according to claim 4 is characterized in that: When performing S8, it is determined whether to input the geometric model temperature into the soil parameter adjustment module according to the judgment result of S7. If the judgment result is that the temperature is not frozen, this step is skipped; If the result is that the freezing process state is frozen, the temperature of each volume unit is input into the soil parameter adjustment module, and the analytical expression of the soil elastic modulus, Poisson's ratio, cohesion, friction angle, frost heave rate, thermal conductivity, and specific heat capacity during the freezing process is output and assigned to each soil unit. The judgment result is that the melting process state is frozen. Similarly, the temperature of each volume unit is input into the soil parameter adjustment module, and the analytical expression of the soil elastic modulus, Poisson's ratio, cohesion, friction angle, melting settlement rate, thermal conductivity and specific heat capacity imported by the S3 method during the melting process with the temperature change curve is output and the corresponding elastic modulus, Poisson's ratio, cohesion, friction angle, thermal conductivity, melting settlement rate and specific heat capacity are assigned to each soil unit.

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