Numerical simulation method and device for water-heat coupling of freezing construction of structure in stratum

Abstract

This application proposes a hydrothermal coupling numerical simulation method and apparatus for freezing construction of structures in strata, comprising: establishing a temperature field control equation for simulating the hydrothermal coupling process; based on the established temperature field control equation, setting numerical simulation boundary conditions and initial conditions, and establishing a hydrothermal coupling finite element numerical model; obtaining the values ​​of at least some calculation parameters in the temperature field control equation from geological survey data, and obtaining an expression for the freezing characteristic curve based on strata soil sample tests; calculating the soil temperature T using the finite element numerical model according to the values ​​or expressions of the calculation parameters to determine the temperature field distribution, and calculating the unfrozen water content θ of the soil using the finite element numerical model according to the temperature T. u and soil ice content θ i To determine the distribution of the moisture field.

Description

Technical Field

[0001] This application relates to numerical simulation of construction processes, and more specifically, to a hydrothermal coupling numerical simulation method and apparatus for ground freezing construction. Background Technology

[0002] In modern society, constructing structures within underground strata is commonplace. Examples include subways, underground transportation pipelines, underground cables and fiber optic cables, and buildings within strata. Constructing structures within strata requires sufficiently stable soil, and engineers employ various methods to reinforce the soil before construction begins. Ground freezing is a widely used method for reinforcing soil strata, particularly suitable for water-rich strata. Ground freezing uses artificial refrigeration to freeze the water-bearing strata surrounding the structure to be constructed, forming a frozen wall that provides temporary support and waterproofing while meeting construction safety requirements. The excavation and construction of the structure then proceeds with the support and protection of this frozen wall.

[0003] During freezing construction, the temperature and moisture fields of the soil strata change in real time, a phase transition occurs between ice and water, and there is a coupling effect between the temperature and moisture fields of the soil. By conducting hydrothermal coupling numerical simulation of the strata before construction, workers can select appropriate operating parameters and corresponding construction methods to achieve optimized operational results.

[0004] However, the accuracy and universality of existing hydrothermal coupling numerical simulation methods urgently need to be improved. Summary of the Invention

[0005] The purpose of this application is to provide a hydrothermal coupling numerical simulation method and corresponding device for ground freezing construction, which has better simulation accuracy and universality than existing simulation methods and devices.

[0006] To achieve the above objectives, the first aspect of this application proposes a hydrothermal coupling numerical simulation method for freezing construction of structures in strata, which includes the following steps:

[0007] Establish the temperature field governing equations for simulating the hydrothermal coupling process:

[0008]

[0009] Where T is temperature, c m For the equivalent heat capacity of the soil, c w For the heat capacity of water, λ m ρ is the thermal conductivity of the soil. w L is the density of water. iw For the latent heat of the ice-water phase transition, u w Let c(T) be the formation water velocity, and θ be the characteristic curve of soil freezing. u The derivative of (T), i.e. And c m c w , λ m ρ w L iw u w c(T) are the calculation parameters of the temperature field control equation, and the temperature T is the variable to be calculated;

[0010] Based on the established temperature field control equations, numerical simulation boundary conditions and initial conditions are set to establish a hydrothermal coupled finite element numerical model.

[0011] The values ​​of at least some of the calculation parameters in the temperature field control equation are obtained from geological exploration data, and the expression of the freezing characteristic curve is obtained based on the soil sample experiment.

[0012] Based on the obtained calculation parameter values ​​or expressions, the soil temperature T is calculated using a finite element numerical model to determine the temperature field distribution of the hydrothermal coupling process. Furthermore, based on the calculated temperature T, the unfrozen water content θ of the soil is calculated using the finite element numerical model. u and soil ice content θ i To determine the moisture field distribution in the hydrothermal coupling process.

[0013] Alternatively, the original hydrothermal coupling governing equations can be used:

[0014]

[0015] Based on this, equation transformation conditions are set, and temperature field control equations are established according to these conditions.

[0016] Optionally, the conditions for equation transformation include:

[0017] First transformation condition: Soil water content θ of the stratum w Saturation, therefore, gives the first transformation equation:

[0018] ρ w θ w =ρ i θ i +ρ w θ u ;

[0019] Second transformation condition: Soil water content θ under saturation. w Constant, and therefore based on the first transformation equation, the second transformation equation is:

[0020]

[0021] The third transformation equation is obtained by performing a partial differential transformation on the second transformation equation:

[0022]

[0023] The original hydrothermal coupling control equation is transformed into a temperature field control equation based on the third transformation equation.

[0024] Optionally, the numerical simulation boundary conditions include: preset freezing pipe temperature and groundwater flow rate, and the numerical simulation initial conditions include preset formation initial temperature.

[0025] Optionally, the calculated parameter c in the temperature field control equation m c w , λ m ρ w L iw and u w The parameter θ was obtained from geological survey data and calculated through stratigraphic soil sample experiments. u The expression for (T) is obtained by calculating its derivative c(T).

[0026] Optionally, it is used to obtain the frozen characteristic curve θ u The soil sample experiments for (T) include: taking soil samples from the frozen wall region of the strata for indoor nuclear magnetic resonance (NMR) testing to obtain the freezing characteristic curve θ. u (T).

[0027] Optionally, establishing a hydrothermal coupled finite element numerical model includes: inputting the established temperature field control equations into the modeling module of the finite element numerical simulation device, and setting the numerical simulation boundary conditions and initial conditions to establish a hydrothermal coupled finite element numerical model.

[0028] Optionally, the hydrothermal coupled finite element numerical model uses the area where the freezing pipes in the stratum are located as the modeling starting point, establishes finite element meshes in the horizontal direction parallel to the surface and the vertical direction perpendicular to the surface, and uses the direction perpendicular to the surface and inward as the seepage direction.

[0029] Optionally, the hydrothermal coupling numerical simulation method is applicable to the simulation of hydrothermal coupling processes under seepage conditions and no seepage conditions.

[0030] According to a second aspect of this application, a hydrothermal coupling numerical simulation device for freezing construction of structures in strata is provided, comprising:

[0031] The first module is used to establish the temperature field control equations for simulating the hydrothermal coupling process.

[0032]

[0033] Where T is temperature, c m For the equivalent heat capacity of the soil, c w For the heat capacity of water, λ m ρ is the thermal conductivity of the soil.w L is the density of water. iw For the latent heat of the ice-water phase transition, u w Let c(T) be the formation water velocity, and θ be the characteristic curve of soil freezing. u The derivative of (T), i.e. And c m c w , λ m ρ w L iw u w c(T) are the calculation parameters of the temperature field control equation, and the temperature T is the variable to be calculated;

[0034] The second module is used to establish a hydrothermal coupled finite element numerical model based on the established temperature field control equations, setting numerical simulation boundary conditions and initial conditions.

[0035] The acquisition module is used to obtain the values ​​of at least some of the calculation parameters in the temperature field control equation from geological exploration data, and to obtain the expression of the freezing characteristic curve based on the stratigraphic soil sample experiment.

[0036] The calculation module is used to calculate the soil temperature T of the stratum using a finite element numerical model based on the obtained calculation parameter values ​​or expressions, in order to determine the temperature field distribution of the hydrothermal coupling process. Based on the calculated temperature T, it also calculates the unfrozen water content θ of the soil in the stratum using the finite element numerical model. u and ice content θ i To determine the moisture field distribution in the hydrothermal coupling process.

[0037] The technical solutions provided by the embodiments of this application may include the following beneficial effects: the temperature field control equation is established based on the experimentally measured freezing characteristic curve according to the numerical simulation method of this application, without the need to add empirical connection conditions, thus having a complete theoretical basis and improving the calculation accuracy; the temperature field control equation directly calculates the temperature field, and the water-thermal coupling numerical model established based on this can solve the water field in a simple way, simplifying the numerical simulation calculation of the water-thermal coupling process; the established water-thermal coupling numerical model is applicable to both seepage and non-seepage situations, has good universality, and allows for standardized procedural operations. Attached Figure Description

[0038] The accompanying drawings, which form part of this application, are used to provide a further understanding of the application and to make other features, objects, and advantages of the application more apparent. The illustrative embodiments and descriptions of this application are used to explain the application and do not constitute an undue limitation of the application. In the drawings:

[0039] Figure 1 This is an example flowchart of a hydrothermal coupling numerical simulation method for freezing construction of structures in strata according to an embodiment of this application;

[0040] Figure 2 This is an example of a hydrothermal coupled finite element numerical model according to an embodiment of this application;

[0041] Figure 3a and Figure 3b These are graphs of the frozen characteristic curve and its derivative used in the numerical simulation method according to the embodiments of this application;

[0042] Figure 4 For use Figure 2 Temperature field distribution diagram of the hydrothermal coupling process obtained by finite element numerical model calculation;

[0043] Figure 5a and Figure 5b For use Figure 2 The moisture field distribution map of the hydrothermal coupling process obtained by the finite element numerical model calculation, in which... Figure 5a This is a partial distribution map of unfrozen water fields. Figure 5b A partial distribution map of porous ice fields; and

[0044] Figure 6 This is a typical example of a soil freezing characteristic curve used in existing freezing construction methods. Detailed Implementation

[0045] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of protection of the present application.

[0046] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this application described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0047] In this application, the terms "upper," "lower," "left," "right," "front," "rear," "top," "bottom," "inner," "outer," "middle," "vertical," "horizontal," "lateral," and "longitudinal" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are primarily for the purpose of better describing this application and its embodiments, and are not intended to limit the indicated device, element, or component to having a specific orientation, or to be constructed and operated in a specific orientation.

[0048] Furthermore, in addition to indicating location or positional relationship, some of the aforementioned terms may also have other meanings. For example, the term "above" may also be used in some cases to indicate a certain dependency or connection relationship. Those skilled in the art can understand the specific meaning of these terms in this application based on the specific circumstances.

[0049] Furthermore, the terms "installation," "setup," "equipped with," "connection," "linked," and "socketing" should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral structure; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, or an internal connection between two devices, components, or parts. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0050] Below, for reference Figures 1 to 6 This application describes a hydrothermal coupling numerical simulation method for the freezing construction of structures in strata.

[0051] Before describing the implementation methods of this application, the terms related to the freezing construction method and numerical simulation that will be involved in this application will be explained.

[0052] Freezing construction method: Before constructing an underground structure, the water-bearing strata around the structure are frozen by artificial cooling to form a frozen wall that provides temporary load-bearing and water-proofing functions and meets the safety requirements of construction. The structure is then excavated and built under the protection of the frozen wall. It has the advantages of high reinforcement strength, good water-proofing, strong adaptability, and no pollution.

[0053] Hydrothermal coupling: a process or system in which temperature and moisture fields interact, with the moisture field comprising two phases: unfrozen water and ice. The governing equations for hydrothermal coupling are partial differential equations containing different field variables. In this application, the moisture and temperature fields in the freezing method construction process interact and influence the freezing effect.

[0054] Numerical simulation: This involves using computers to find approximate solutions to mathematical problems and displaying them graphically to study engineering and physical problems. In this application, numerical methods are used to solve the mathematical equations describing the artificial freezing problem and output the calculation results.

[0055] Freezing characteristic curve (unfrozen water content curve): Unfrozen water content θ in frozen soil u The curve showing the change with temperature T indicates a fixed relationship for a specific soil type, which can be determined through soil sample testing. Figure 6 As shown.

[0056] Empirical correlation equations: In numerical simulations, empirical equations are introduced in addition to theoretical equations during the establishment of mathematical governing equations. Their purpose is to ensure that the number of governing equations equals the number of unknowns, thereby guaranteeing that the equations are closed and solvable. Empirical correlation equations can describe objective laws, but they do not conform to strict theoretical laws; therefore, their accuracy and universality are limited.

[0057] The numerical simulation method for freezing construction of structures in strata, according to this application, will be described below. This numerical simulation method includes the following aspects.

[0058] First, the temperature field control equations for soil temperature during the hydrothermal coupling process in the freezing method are established for numerical simulation calculations. Numerical simulation calculations are essentially solving mathematical equations describing the target physical process; therefore, the derivation and selection of the control equations are the core of the simulation technology. The temperature field control equations established in this application are the relationship between the freezing characteristic curve and the formation water flow velocity and temperature. The calculation variable in the equations is temperature T; it is not necessary to calculate water field-related variables. The specific temperature field control equations are as follows:

[0059]

[0060] Where T is temperature, c m c is the specific heat capacity of the soil. w λ is the specific heat capacity of water. m ρ is the thermal conductivity of the soil. w L is the density of water. iw For the latent heat of the ice-water phase transition, u w Let c(T) be the formation water velocity, and θ be the characteristic curve of soil freezing. u The derivative of (T).

[0061] The temperature field governing equations established in this application have a sound theoretical basis and can improve calculation accuracy. Specifically, it is known in the art that groundwater seepage has a significant impact on the development of the temperature field during freezing construction, exacerbating the complexity of the freezing process. The temperature field governing equations according to this application include a seepage term u. wIt is applicable to hydrothermal coupling processes under both seepage and non-seepage conditions, and in particular, it can improve the accuracy and universality of numerical simulation methods for hydrothermal coupling under seepage conditions, which helps to optimize the freezing construction process.

[0062] This advantage can be seen, for example, by comparing it with the mathematical equations of the traditional sensible heat capacity method used for temperature field simulation calculations.

[0063] During freezing construction, the latent heat of the ice-water phase transition affects the development of the soil's temperature field. The total heat released by the ice-water phase transition depends on the total amount of water involved in the phase transition. Therefore, calculating the soil's temperature field requires calculating the amount of ice formation or reduction. This transforms the original heat transfer calculation into a hydrothermal coupling calculation, because the variables to be solved include not only temperature T but also ice content θ. i This increases the computational difficulty, especially for cases where the primary focus is on the temperature field.

[0064] The sensible heat capacity method is a traditional calculation method used for the hydrothermal coupling process in freezing construction methods. This method assumes that the phase change process occurs only within a specific temperature range near the phase change point and introduces an equivalent specific heat capacity c. eff This method approximates the latent heat of phase change and then calculates the soil temperature to determine the temperature field. A significant advantage of this method is that it eliminates the need to calculate variables related to the moisture field. By introducing equivalent specific heat capacity, the hydrothermal coupling control equations are simplified into temperature field control equations. Currently, it is widely used in temperature field calculations for frozen construction.

[0065] Although the sensible heat capacity method simplifies the calculation of hydrothermal coupling processes, its assumptions regarding the temperature range of latent heat of phase change lack sufficient theoretical basis. The latent heat of phase change only occurs within a specific temperature range, and the selection of this temperature range is merely an empirical assumption. In contrast, the improved temperature field governing equation proposed in this application correlates temperature T with the experimentally measurable freezing characteristic curve θ. u (T) and formation water velocity u w The correlation does not require assumed or defined ice-water phase transition ranges, thus avoiding issues of insufficient theoretical foundation and improving computational accuracy and reliability. Furthermore, based on the temperature field governing equations of this application, the freezing characteristic curve θ is used... u The differential term c(T) is used to calculate the temperature field, and its nonlinearity is reduced compared to the sensible heat capacity method.

[0066] In addition to the traditional sensible heat capacity method, the inventors of this application also provide several prior art references on the calculation of hydrothermal coupling processes to further demonstrate the advantages of the temperature field governing equations for hydrothermal coupling processes provided in this application. Specifically, these include:

[0067] [1] Li Zhiming. Study on multi-field coupling of frozen soil based on composite mixture theory [D]. Harbin Institute of Technology, 2021.

[0068] [2] Bai Qingbo, Li Xu, Tian Yahu, Fang Jianhong. Study on hydrothermal coupling equation and numerical simulation of frozen soil [J]. Chinese Journal of Geotechnical Engineering, 2015, 37(S2):131-136.

[0069] [3] Zhang Jinxun, Qi Yi, Yang Hao, Zhang Lei. Study on the formation law of horizontal plate with local freezing of multi-row pipe under seepage conditions in Beijing sand and gravel strata [J]. Chinese Journal of Rock Mechanics and Engineering, 2020, 39(S1):3188-3196.

[0070] [4] Cai Na, Ren Xukai, Chen Yang, Lan Xue, Liu Wan, Fu Qingwang, Feng Jiaowei, Fan Lei. Design method of artificial frozen soil curtain for unsteady temperature field [P]. Henan Province: CN103669376B, 2015-07-08.

[0071] [5] Yang Gengshe, Liang Bo, Li Gang, Wei Yao, Liu Fanglu, Pan Zhenxing. A simulation calculation method for the freezing and sinking process of coal mine vertical shafts [P]. Shaanxi Province: CN111460703A, 2020-07-28.

[0072] References 1 through 4 all involve research on the hydrothermal coupling process during the freezing construction of structures in strata, and propose corresponding hydrothermal coupling control equations. In Reference 1, the calculation variables for the equation are soil temperature T and formation water velocity u. w Ice content θ in the soil of the strata u In Reference 2, the calculation variables for the equation are soil temperature T and unfrozen water content θ. i Ice content θ i To solve for the ice content θ i References 1 and 2 both introduce empirical equations relating ice content to temperature, rather than the theoretical derivation and formation soil sample tests used in this invention. Therefore, the theoretical basis of the aforementioned hydrothermal coupling control equations is insufficient, resulting in low computational accuracy and limited universality. References 3 and 4 both belong to the traditional sensible heat capacity method, and their established equations both introduce the equivalent specific heat capacity c, representing the latent heat effect of phase change. eff Without calculating the ice content θ i In the case of c eff The phase transition is used to calculate temperature T. Furthermore, unlike this application, references 2 to 4 do not incorporate formation water velocity u. w The effect on the temperature field is not applicable to formations with seepage conditions. Reference 5 involves the simulation of the vertical shaft freezing drilling process, but does not include numerical simulation calculations of the hydrothermal coupling process.

[0073] The above comparison demonstrates that the temperature field governing equations for the hydrothermal coupling process presented in this application are significantly superior to existing technologies in terms of the theoretical foundation for establishing the equations. This provides an optimized mathematical basis for subsequently establishing an accurate and universal finite element numerical model and accurately determining the soil temperature and moisture fields.

[0074] According to this application, after establishing the improved temperature field governing equations for hydrothermal coupling numerical simulation, a finite element numerical model will be established based on these temperature governing equations. This finite element numerical model can be obtained through secondary program development using dedicated finite element software. During the establishment of the numerical model, computational boundary conditions and initial conditions for numerical simulation calculations must be set. The established hydrothermal coupling finite element numerical model is then used to calculate the temperature and moisture fields during the freezing construction process. Specific modeling and calculation methods are described below.

[0075] Based on the principles of this application, the values ​​or expressions of the parameters (i.e., the calculation parameters in the aforementioned temperature field control equations) used in the numerical model calculations can be obtained through geological survey data and field tests. These parameters include: the equivalent heat capacity of the soil, c. m The heat capacity of water, c w Soil thermal conductivity λ m The density of water ρ w The latent heat of phase transition of ice and water (L) iw Formation water velocity u w and the frozen characteristic curve θ u The derivative of (T) is c(T). According to one embodiment of this application, the calculation parameter c can be obtained from geological data. m c w , λ m ρ w L iw and u w Furthermore, the freezing characteristic curve θ can be obtained through on-site freezing experiments using soil samples from the strata. u The expression for (T) is obtained, and its derivative c(T) is calculated. In other embodiments, if more accurate simulation results are required, the above-mentioned calculation parameter c can be obtained through field soil sample experiments based on the actual situation of the strata. m c w , λ m ρ w L iw and u w One or more of the parameters. According to this application, the method for obtaining the calculation parameters in the temperature field governing equation is more accurate and reliable. On the one hand, the values ​​of the calculation parameters recorded in the geological survey data have been verified; on the other hand, the method used to obtain the freezing characteristic curve θ... u The measurement method for (T) is fast and convenient, and can accurately obtain the freezing characteristic curve θ. u(T). Currently, the commonly used method for measuring unfrozen water in formations to obtain the freezing characteristic curve θ is... u The methods (T) include: dilatometer method, isothermal calorimetry, time-domain reflectometry method, and nuclear magnetic resonance method. Accurate and reliable calculation parameters can further optimize the accuracy and reliability of numerical simulation results, and convenient acquisition methods also help save computational costs.

[0076] After establishing the hydrothermal coupling finite element numerical model and obtaining the relevant calculation parameters, the temperature field distribution and moisture field distribution of the hydrothermal coupling process will be determined accordingly. Specifically, based on the obtained calculation parameters c... m c w , λ m ρ w L iw , and u w The value of the temperature T during the hydrothermal coupling process is calculated using a finite element numerical model, along with the expression for the derivative c(T) of the freezing characteristic curve. This allows for the determination of the temperature field distribution during the hydrothermal coupling process. Furthermore, based on the calculated temperature T, the unfrozen water content θ of the soil is calculated using the finite element numerical model. u and soil ice content θ i Based on this, the moisture field distribution of the hydrothermal coupling process is determined. The moisture field distribution includes the distribution of unfrozen water content and ice content.

[0077] The foregoing describes the basic principles of the numerical simulation method for the hydrothermal coupling process during freezing construction according to this application. Compared with existing numerical simulation methods, the numerical simulation method according to this application has a complete theoretical foundation, reliable calculation accuracy, and standardized operation procedures, and is especially suitable for simulating the hydrothermal coupling process during freezing construction in water-rich strata with high flow velocities.

[0078] Based on the above concepts, Figure 1 A sample flowchart of the hydrothermal coupling numerical simulation method according to this application is specifically shown. Figure 1 As shown, this example numerical simulation method includes the following steps:

[0079] Step 1: Establish the temperature field governing equations. The equations are established through theoretical and formal transformations of the hydrothermal coupling governing equations. Specifically, the original hydrothermal coupling governing equations are provided:

[0080]

[0081] The equation is transformed based on this equation. This equation is the hydrothermal coupling control equation considering the influence of seepage, and is applicable to hydrothermal coupling simulations of ordinary formations without seepage and water-rich formations with seepage. The variables to be calculated include the temperature field variable T and the moisture field variable θ. iBased on the original equations, appropriate equation transformation conditions are set, and the temperature field control equations according to this application are obtained through mathematical transformation according to the set equation transformation conditions. The mathematical transformation process includes the transformation of the theoretical basis of the equations. The specific transformation method of the original control equations is as follows.

[0082] Typically, freezing construction is often carried out in water-rich strata (water-rich strata usually refer to strata with high soil moisture content, where the soil is considered to be in a water-saturated state, and may or may not have seepage depending on the actual geological conditions). Based on this, this application defines the soil as water-rich strata, thus possessing the first transformation condition: the soil's water content θ. w If saturation is achieved, then the following first transformation equation applies:

[0083] ρ w θ w =ρ i θ i +ρ w θ u .

[0084] Furthermore, without considering the volume change of soil in water-rich strata, the second transformation condition applies: the saturated water content θ of the soil. w If it remains constant, then based on the first transformation equation, we have the following second transformation equation:

[0085]

[0086] Performing a partial differential transformation on the second transformation equation yields the following third transformation equation:

[0087]

[0088] Where, θ u (T) is the freezing characteristic curve, and c(T) is the freezing characteristic curve θ. u The derivative of (T), i.e.: By setting transformation conditions for the equations, a frozen characteristic curve θ is introduced into the provided transformation equations. u (T) is used as a calculation parameter to establish the soil pore ice content θ. i The equation relating (moisture field variable) and temperature T (temperature field variable) (intermediate equation) has a clear physical meaning and a direct method for determining parameters. The accuracy of the temperature field control equation established based on this equation can also be improved.

[0089] Furthermore, using the third transformation equation mentioned above, the derivative c(T) of the freezing characteristic curve is used to remove the variable θ, which is related to the moisture field (specifically, the ice content of the soil), from the original hydrothermal coupling control equation. iOnly variables related to the temperature field are retained. Based on the third transformation equation, the original hydrothermal coupling control equation is transformed into the following temperature field control equation:

[0090]

[0091] This refers to the numerical simulation equations used to simulate the hydrothermal coupling process described above. In this improved temperature field governing equation, the variable to be calculated is temperature T, i.e., the field variable related to the temperature field of the hydrothermal coupling process. Based on the calculated value of temperature T, the unfrozen water content θ of the formation can be calculated. u and soil pore ice content θ i That is, the field variables related to the moisture field in the hydrothermal coupling process. As mentioned above, the other variables in this temperature field governing equation, used as calculation parameters for numerical simulation, can be obtained through geological data and field experiments. Therefore, this temperature field governing equation can calculate three hydrothermal coupling field variables using a single governing equation: temperature T, unfrozen water content θ, etc. u Ice content θ i The equations are simplified and the calculation process is straightforward. Furthermore, the transformation conditions for the temperature field control equations in this application are reasonably set, supported by clear theory, and have a solid theoretical foundation, eliminating the need to introduce empirical equations, thus improving the accuracy of numerical simulation calculations.

[0092] Step 2: Finite Element Numerical Model Development. The improved temperature field control equations described above serve as the basis for establishing a hydrothermal coupling numerical model, which is then built using the finite element method (FEM). For numerical simulations of freezing construction of structures in strata, the finite difference method (FDM) is currently the most widely used simulation method, while the FEM is less frequently used. The FEM is essentially a numerical solution of differential equations, while the FDM transforms differential equations into algebraic equations for numerical solution. According to the temperature field control equations of this application, the derivative of the freezing characteristic curve is used as a calculation parameter; therefore, the FEM is more suitable in terms of computational principles and the modeling process is more direct. The aforementioned finite element numerical simulation device can be commercial finite element software, such as COMSOL Multiphysics, where the modeling module is a built-in secondary development module. The improved temperature field control equations are input into the modeling module of the finite element numerical simulation device, boundary conditions and initial conditions for finite element numerical simulation are set, and a numerical model capable of simulating the hydrothermal coupling process of ice-water phase change and outputting the simulation results of the temperature and moisture fields is established. The boundary and initial conditions used in finite element numerical simulations will be illustrated with specific examples of hydrothermal coupling numerical simulations provided below.

[0093] Figure 2 An example of a finite element mesh for a hydrothermal coupled finite element numerical model according to an embodiment of this application is shown. Figure 2 As shown, this hydrothermal coupled finite element numerical model uses freezing pipes in the formation ( Figure 2 The area containing the white circular region is the starting point for modeling. Finite element meshes are established in the horizontal direction parallel to the ground surface and the vertical direction perpendicular to the ground surface. Figure 2 The finite element mesh shown is 1000mm × 1200mm, with the freezing pipe centered in the transverse direction. Furthermore, as mentioned above, seepage is considered in the numerical model of this application; therefore, the seepage direction is included in the finite element mesh, using a direction perpendicular to the ground surface and pointing inwards as the seepage direction, with a set flow velocity of 1.5m / d. Figure 2 As indicated by the middle arrow. Figure 2 The finite element mesh can be generated using typical free methods, mapping methods, or grid methods. The entire rectangular mesh region is composed of triangular meshes, and the triangular meshes in the diagonal region of the rectangle and the region near the freezing tube are joined together by rotation. The example output results of the temperature and moisture fields described later are obtained based on this finite element numerical model.

[0094] Step 3: On-site freezing characteristic curve test of soil samples. As mentioned above, the calculation parameters of the temperature field control equation of this application can be obtained from geological survey data or on-site experiments. The equivalent heat capacity of the soil, c... m The heat capacity of water, c w Soil thermal conductivity λ m The density of water ρ w The latent heat coefficient of ice-water phase transition L iw and formation water velocity u w These values ​​can be obtained from geological survey data. Table 1 shows example values ​​for the above calculation parameters.

[0095] Table 1 Examples of Calculation Parameter Values

[0096]

[0097] According to the embodiments of this application, undisturbed soil samples within the frozen wall region of the strata are subjected to indoor nuclear magnetic resonance tests to obtain the freezing characteristic curve θ of the soil. u The expression for (T) is given, and its derivative c(T) is calculated. Table 2 shows the relationship between soil temperature T and unfrozen water content θ according to the embodiments of this application. u The test results.

[0098] Table 2 Soil Freezing Characteristic Curve θ u (T) Test Results

[0099]

[0100]

[0101] The freezing characteristic curve θ can be obtained by fitting the above measurement results. u A graph of (T) and its derivative c(T). Figure 3a and Figure 3b The data are shown below, based on Table 2, regarding soil temperature T and unfrozen water content θ. u The frozen characteristic curve θ obtained from the test results u (T) and the calculated derivative of the freezing characteristic curve c(T). Based on the experimental measurement results in Table 2, the fitted soil freezing characteristic curve θ u (T) = 18.837(-T) -0.527 The derivative c(T) is calculated as: c(T) = -9.93(-T) -1.527 .

[0102] Based on the temperature field control equations and calculation parameters described above, the temperature T at each node of the soil during the hydrothermal coupling process can be calculated using the finite element numerical model of this application, thus determining the temperature field of the soil, as described below.

[0103] Step 4: Numerical simulation calculation of the hydrothermal coupling process of ice-water phase change during freezing method construction. After establishing the temperature field control equations, the finite element numerical model, and obtaining the calculation parameters required for the calculation, numerical simulation calculation is performed using the finite element numerical model according to this application to determine the temperature field and moisture field of the hydrothermal coupling process. The specific calculation process is as follows.

[0104] The obtained formation water flow velocity u w and the frozen characteristic curve θ u The formula for calculating the derivative c(T) is input into the finite element numerical model, based on the obtained calculation parameters c. m c w , λ m ρ w L iw and u w The value of determines the specific values ​​of the boundary conditions and initial conditions for the numerical simulation. These boundary conditions include the freezing characteristic curve θ for a specific geological region. u (T) and total soil porosity remain unchanged. The initial conditions for numerical simulation include the initial formation temperature, which can be set to 15℃ for example.

[0105] Subsequently, the soil temperature T was calculated using a finite element numerical model to determine the soil temperature field distribution in the frozen soil layer. Figure 4 For use Figure 2 The temperature field distribution diagram of the hydrothermal coupling process obtained from the finite element numerical model calculation. (See diagram below.) Figure 4 As shown, within the entire finite element mesh region, the temperature field relative to the freezing pipe ( Figure 4The white circular area in the center is symmetrical from left to right (horizontally). The temperature increases from the freezing pipe outwards to both sides. In the horizontal direction, temperatures below 5°C are limited to the area around the freezing pipe. In the vertical direction, the temperature field is asymmetrical relative to the freezing pipe. At the same location on both sides of the freezing pipe in the vertical direction, the soil temperature above the freezing pipe is higher than the soil temperature below it. Below the freezing pipe, temperatures below 5°C are also limited to the area around the freezing pipe, but the range of temperatures below 5°C increases significantly.

[0106] Furthermore, based on the freezing characteristic curve and the condition that the total porosity of the soil remains unchanged, the numerical model of this application will automatically output the unfrozen water content θ according to the obtained temperature field distribution. u and ice content θ i The distribution of water field was analyzed to obtain the coupled calculation results. Figure 5a and Figure 5b For use Figure 2 The moisture field distribution map of the hydrothermal coupling process obtained by the finite element numerical model calculation, in which... Figure 5a This is a partial distribution map of unfrozen water fields. Figure 5b This is a local distribution map of porous ice fields. (For example...) Figure 5a As shown, each of the three freezing tubes has its own unfrozen water area around it. Outside each unfrozen water area of ​​the freezing tubes, there is a common unfrozen water area. Furthermore, the unfrozen water content increases from the freezing tube outwards, and the distribution pattern of the unfrozen water content is similar to the distribution pattern of the temperature field below 5°C. Figure 5b As shown, there is only a common ice-containing area around the three freezing tubes. At the same time, the ice content is similar to that of unfrozen water. The ice content increases from the freezing tubes to the surrounding area, and the distribution pattern is similar to that of the temperature field below 5℃.

[0107] By comparing the numerically simulated temperature and moisture fields with experimental measurements, it can be seen that the finite element numerical simulation method of this application can effectively simulate the temperature and moisture fields of frozen soil under seepage and non-seepage conditions.

[0108] As can be seen from the above description and figures, the hydrothermal coupling numerical simulation method for the freezing process according to this application has the following advantages:

[0109] The temperature field governing equations do not incorporate empirical correlation equations, have a sound theoretical foundation, and avoid computational errors caused by the arbitrary selection of empirical parameters. Considering seepage in the formation, the distributions of temperature and moisture fields in both seepage-free and seepage-free conditions can be calculated, increasing universality. The temperature field calculation reduces the partial differential equations to one, while simultaneously considering the unfrozen water content θ. u and ice content θ iThe calculation does not require solving partial differential equations, simplifying the calculation process and improving computational efficiency. In addition, a dedicated numerical model was developed based on the improved control equations, and a standardized operating procedure integrating indoor testing, field investigation, and numerical calculation was provided, which is applicable to calculations under different working conditions and improves universality.

[0110] Furthermore, based on the principles of this application, a hydrothermal coupling numerical simulation device for freezing construction of structures in strata is also provided, used to implement the aforementioned hydrothermal coupling numerical simulation method, including:

[0111] The first module (equation construction module) is used to establish the temperature field control equations for simulating the hydrothermal coupling process:

[0112]

[0113] Where T is temperature, c m For the equivalent heat capacity of the soil, c w For the heat capacity of water, λ m ρ is the thermal conductivity of the soil. w L is the density of water. iw For the latent heat of the ice-water phase transition, u w Let c(T) be the formation water velocity, and θ be the characteristic curve of soil freezing. u The derivative of (T), i.e. And c m c w , λ m ρ w L iw u w c(T) are the calculation parameters of the temperature field control equation, and the temperature T is the variable to be calculated;

[0114] The second module is used to establish a hydrothermal coupled finite element numerical model based on the established temperature field control equations, setting numerical simulation boundary conditions and initial conditions.

[0115] The acquisition module is used to obtain the values ​​of at least some of the calculation parameters in the temperature field control equation from geological exploration data, and to obtain the expression of the freezing characteristic curve based on the stratigraphic soil sample experiment.

[0116] The calculation module is used to calculate the soil temperature T of the stratum using a finite element numerical model based on the obtained calculation parameter values ​​or expressions, in order to determine the temperature field distribution of the hydrothermal coupling process. Based on the calculated temperature T, it also calculates the unfrozen water content θ of the soil in the stratum using the finite element numerical model. u and ice content θ i To determine the moisture field distribution in the hydrothermal coupling process.

[0117] Specifically, the first module is used to establish the original hydrothermal coupling control equations:

[0118]

[0119] Based on this, equation transformation conditions are set, and temperature field control equations are established according to these conditions.

[0120] The second module (modeling module) is used to establish a finite element numerical model based on the temperature field control equations of the input numerical simulation device, set the numerical simulation boundary conditions and initial conditions.

[0121] The specific methods of execution of each unit in the above embodiments have been described in detail in the embodiments of the method, and will not be elaborated here.

[0122] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0123] Obviously, those skilled in the art should understand that the various units or steps of this application described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device, or fabricating them separately as individual integrated circuit modules, or fabricating multiple modules or steps into a single integrated circuit module. Thus, this application is not limited to any particular combination of hardware and software.

[0124] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A hydrothermal coupling numerical simulation method for freezing construction of structures in strata, characterized in that, Includes the following steps: Establish the temperature field governing equations for simulating the hydrothermal coupling process: ， in, T For temperature, The equivalent heat capacity of the soil. For the heat capacity of water, The thermal conductivity of the soil. The density of water, The latent heat of the ice-water phase transition. The velocity of the formation water. Soil freezing characteristic curve The derivative, i.e. ,and , , , , , The temperature field governing equations are the calculation parameters, and the temperature... T The variable to be calculated; Based on the established temperature field control equations, numerical simulation boundary conditions and initial conditions are set to establish a hydrothermal coupled finite element numerical model. The values ​​of at least some of the calculation parameters in the temperature field control equation are obtained from geological exploration data, and the expression of the freezing characteristic curve is obtained based on the stratigraphic soil sample experiment. The temperature of the soil in the stratum is calculated using the finite element numerical model based on the obtained calculation parameter values. To determine the temperature field distribution of the hydrothermal coupling process, based on the calculated temperature The unfrozen water content of the soil in the stratum was calculated using the finite element numerical model. θ u and ice content θ i In order to determine the moisture field distribution of the hydrothermal coupling process; Among them, the original hydrothermal coupling control equation is: Based on this, equation transformation conditions are set, and the temperature field control equation is established according to the equation transformation conditions. The equation transformation conditions include: First transformation condition: Soil moisture content of the stratum Saturation, therefore, gives the first transformation equation: ； Second transformation condition: the soil moisture content under saturation. Constant, and therefore based on the first transformation equation, a second transformation equation is derived: ； The third transformation equation is obtained by performing a partial differential transformation on the second transformation equation: ， According to the third transformation equation, the original hydrothermal coupling control equation is transformed into the temperature field control equation.

2. The hydrothermal coupling numerical simulation method according to claim 1, characterized in that, The numerical simulation boundary conditions include preset freezing pipe temperature and groundwater flow velocity, and the numerical simulation initial conditions include preset initial formation temperature.

3. The hydrothermal coupling numerical simulation method according to claim 1, characterized in that, The calculation parameters in the temperature field control equation , , , , and The data was obtained from the geological survey data and from the stratigraphic soil sample experiments. The expression is obtained by calculating its derivative. .

4. The hydrothermal coupling numerical simulation method according to claim 3, characterized in that, Used to obtain the freezing characteristic curve The aforementioned soil sample experiment includes: taking soil samples from the frozen wall region of the strata and conducting indoor nuclear magnetic resonance experiments to obtain the freezing characteristic curve. θ u (T ).

5. The hydrothermal coupling numerical simulation method according to any one of claims 1 to 4, characterized in that, The process of establishing the hydrothermal coupled finite element numerical model includes: inputting the established temperature field control equation into the modeling module of the finite element numerical simulation device, and simultaneously setting the numerical simulation boundary conditions and initial conditions to establish the hydrothermal coupled finite element numerical model.

6. The hydrothermal coupling numerical simulation method according to any one of claims 1 to 4, characterized in that, The hydrothermal coupled finite element numerical model uses the area where the freezing pipes in the stratum are located as the modeling starting point, establishes finite element meshes in the horizontal direction parallel to the surface and the vertical direction perpendicular to the surface, and uses the direction perpendicular to the surface and inward as the seepage direction.

7. The hydrothermal coupling numerical simulation method according to any one of claims 1 to 4, characterized in that, The described hydrothermal coupling numerical simulation method is applicable to the simulation of hydrothermal coupling processes under seepage conditions and no seepage conditions.

8. A hydrothermal coupling numerical simulation device for freezing construction of structures in strata, characterized in that, include: The first module is used to establish the temperature field control equations for simulating the hydrothermal coupling process. ， in, T For temperature, The equivalent heat capacity of the soil. For the heat capacity of water, The thermal conductivity of the soil. The density of water, The latent heat of the ice-water phase transition. The velocity of the formation water. Soil freezing characteristic curve The derivative, i.e. ,and , , , , , The temperature field governing equations are the calculation parameters, and the temperature... T The variable to be calculated; The second module is used to establish a hydrothermal coupled finite element numerical model based on the established temperature field control equations, setting numerical simulation boundary conditions and initial conditions. The acquisition module is used to obtain the values ​​of at least a portion of the calculation parameters in the temperature field control equation from geological exploration data, and to obtain the expression of the freezing characteristic curve based on the stratigraphic soil sample experiment; The calculation module is used to calculate the temperature of the soil in the stratum based on the obtained calculation parameters using the finite element numerical model. To determine the temperature field distribution of the hydrothermal coupling process, based on the calculated temperature The unfrozen water content of the soil in the stratum was calculated using the finite element numerical model. θ u and ice content θ i In order to determine the moisture field distribution of the hydrothermal coupling process; Among them, the original hydrothermal coupling control equation is: Based on this, equation transformation conditions are set, and the temperature field control equation is established according to the equation transformation conditions. The equation transformation conditions include: First transformation condition: Soil moisture content of the stratum Saturation, therefore, gives the first transformation equation: ； Second transformation condition: the soil moisture content under saturation. Constant, and therefore based on the first transformation equation, a second transformation equation is derived: ； The third transformation equation is obtained by performing a partial differential transformation on the second transformation equation: ， According to the third transformation equation, the original hydrothermal coupling control equation is transformed into the temperature field control equation.

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