A generalized theoretical numerical method for calculating the thermal conductivity of a heterogeneous random porous medium

Abstract

The application discloses a kind of generalized theory numerical calculation method of the thermal conductivity of multiphase random mixing porous medium, the method includes the following steps: step 1, obtain the porosity of soil sample;Step 2, obtain the thermal conductivity of soil particles;Step 3, obtain the effective thermal conductivity of soil sample and the full state thermal conductivity surface under the porosity of soil sample;Step 4, obtain the volumetric water content and ice content of soil sample.The application innovatively proposes the strategy of using extreme state to calculate the thermal conductivity of soil particles, realizes the double check of parameters, eliminates the calculation error caused by the difference of soil mineral composition, and can obtain the effective thermal conductivity of soil body by calculation using conventional soil parameters.Using the method of the application, the thermal conductivity of soil body can be predicted with high precision only by using easily obtained physical parameters, and online monitoring and inversion analysis can be carried out.This is especially suitable for large-scale engineering projects and soil thermal response prediction, which greatly saves time and economic cost.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering investigation and soil thermal property analysis technology, and relates to a method for calculating the thermal conductivity of soil, specifically a generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media. Background Technology

[0002] The thermal conductivity of soil is a key thermophysical property parameter in geotechnical engineering, characterizing the heat transfer capacity of soil. It directly determines the efficiency of heat transfer in the soil, thus affecting the stability and safety of engineering structures. Thermal conductivity directly impacts engineering calculations such as geothermal field analysis, frost heave and thaw settlement assessment of roadbeds and slopes in permafrost and seasonally frozen regions, service temperature field and thermal stress analysis of underground structures (tunnels, pipe galleries, pile foundations, etc.), and prediction of heat exchange efficiency of ground source heat pumps. Because natural soils generally exhibit multiphase coexistence and random distribution characteristics, and their phase composition changes significantly with variations in moisture content, pore gas, and freezing / thawing processes, exhibiting strong nonlinearity and complexity, thermal conductivity is not only a "material constant" but also a "state parameter" that varies with the soil's state. Therefore, it is urgently needed in engineering to reliably obtain thermal conductivity under different conditions for calculation and inversion.

[0003] Existing methods for obtaining the thermal conductivity of soil can be broadly categorized into three types: experimental measurement methods, empirical formula methods, and theoretical model prediction methods. However, existing technologies all have certain limitations in obtaining the thermal conductivity of soil.

[0004] Experimental determination of thermal conductivity is time-consuming, costly, and difficult to cover all conditions. While existing mainstream testing methods (such as the hot needle method and the protective hot plate method) can directly obtain the true value of thermal conductivity under specific conditions, obtaining the thermal property curves of a certain soil at different dry densities, different moisture contents, and throughout the entire freezing / thawing process requires the preparation of dozens or even hundreds of samples for time-consuming repeated tests. Experimental determination is a "post-hoc measurement," which cannot be predicted during the engineering design stage and is difficult to achieve rapid acquisition under large-scale, in-situ conditions.

[0005] Existing traditional empirical formulas lack physical mechanism support, and their fitting coefficients are heavily dependent on the soil type and regional data used when formulating the formula. Although empirical formulas can describe the laws under specific conditions to a certain extent, the lack of essential revelation of microstructure (such as the disturbance of heat flow by particles) leads to poor universality and a significant decrease in prediction accuracy when dealing with complex working conditions (such as ice-water phase change and different pore structures), and may even lead to orders of magnitude errors.

[0006] Existing thermal conductivity prediction models largely rely on statistical fitting of macroscopic experimental data. These models lack generality; relying solely on a limited number of discrete experimental points makes it difficult to encompass all possible combinations of operating conditions in nature. This hinders the construction of universal prediction models supported by robust physical mechanisms and prevents the accurate extrapolation of regional thermal property distributions using readily available conventional physical indicators (such as moisture content and porosity). For complex, non-homogeneous media like natural soils, which consist of three phases (solid, liquid, and gas) and even four phases (solid, liquid, gas, and ice) in frozen soil, existing theoretical models lack a unified, concise, and solvable closed-form analytical solution that can uniformly describe their thermal conductivity behavior.

[0007] Regardless of which method is used, only the effective thermal conductivity of the soil sample can be roughly estimated. Therefore, there is an urgent need for a calculation method based on rigorous physical mechanisms, rather than simple empirical fitting, that can uniformly describe the heat conduction law of soil in all states (including frozen state) and accurately obtain the thermal conductivity of soil samples. Summary of the Invention

[0008] To address the fundamental technical challenges in the long-standing research on soil thermal conductivity—namely, the lack of theoretical models, unclear physical mechanisms, and the inability of computational models to be universally applicable across phases—this invention provides a generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media. This method can accurately describe and predict the effective thermal conductivity of complex multiphase soils under all temperature and water-bearing conditions, and achieve a two-way quantitative correlation between thermal parameters and component parameters.

[0009] The objective of this invention is achieved through the following technical solution:

[0010] A generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media includes the following steps:

[0011] Step 1: Obtain the porosity of the soil sample :

[0012] The results were obtained indirectly through conventional geotechnical tests, and the specific steps are as follows:

[0013] Step 11: Obtain the specific gravity of soil particles Determining the specific gravity of soil particles using the specific gravity bottle method ;

[0014] Step 12: Obtain the dry density of the soil sample. Determining the dry density of soil samples using the ring cutter method or the wax sealing method. ;

[0015] Step 13: Calculate the porosity of the soil sample according to the formula. :

[0016]

[0017] Step 2: Obtain the thermal conductivity of soil particles :

[0018] The thermal conductivity of soil particles can be obtained through direct measurement or back-calculation verification. ,in:

[0019] The specific steps of the direct measurement method are as follows: Soil particles are prepared into a dense, non-porous solid sample, and their thermal conductivity is directly measured using a relevant thermal conductivity measuring instrument. ;

[0020] The specific steps of the reverse calculation verification method are as follows: First, the effective thermal conductivity of a pure dry or saturated soil sample is measured, and then the thermal conductivity of soil particles is calculated using a simplified soil-air or soil-water two-phase formula. ;

[0021] The soil-gas two-phase formula is as follows:

[0022]

[0023] The soil-water two-phase formula is as follows:

[0024]

[0025] In the formula, Let be the thermal conductivity of the soil particles. The thermal conductivity of air. The thermal conductivity of water, For effective thermal conductivity, This refers to the volumetric moisture content. This refers to the volumetric gas content;

[0026] Step 3: Obtain the effective thermal conductivity of the soil sample and the thermal conductivity surface of the soil sample under a certain porosity:

[0027] Step 31: Obtain the porosity of the soil sample in its unfrozen state. Thermal conductivity of soil particles Moisture content Volumetric moisture content and volumetric gas content ;

[0028] Step 32: Obtain the porosity of the soil sample under frozen conditions. Thermal conductivity of soil particles Moisture content Volumetric moisture content Ice content by volume and volumetric gas content ;

[0029] Step 33: Substitute the parameters obtained in Step 31 into the soil-water-gas three-phase formula, and the parameters obtained in Step 32 into the soil-water-gas-ice four-phase formula to calculate the effective thermal conductivity λ. Establish the effective saturation coefficient surface of the soil sample under this porosity, where:

[0030] The three-phase formula for soil-water-gas is:

[0031]

[0032]

[0033] The four-phase formula for soil-water-gas-ice is:

[0034]

[0035]

[0036] Step 4: Obtain the volumetric water content and ice content of the soil sample:

[0037] Step 41: Back-calculate the volumetric moisture content of the unfrozen soil sample. :

[0038] The effective thermal conductivity λ of the soil sample was obtained using a thermal conductivity testing device, and the porosity was obtained in step 1. The thermal conductivity of soil particles is obtained through step S2. , Substituting into the soil-water-gas three-phase formula, the soil moisture content can be calculated in reverse.

[0039] Step 42: Calculate the ice content of the soil sample volume under frozen conditions. :

[0040] The effective thermal conductivity λ of the soil sample is first obtained using a thermal conductivity testing device, and the porosity is then obtained in step 1. The thermal conductivity of soil particles is obtained through step S2. Volumetric water content was directly determined using nuclear magnetic resonance (NMR) technology. , Substituting the soil-water-air-ice four-phase formula, the volumetric ice content of the frozen soil sample is calculated.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] 1. Clear physical mechanism: This invention is based on the Laplace equation and effective medium theory (EMT) derivation, rather than simple empirical data fitting. It can truly reflect the microscopic heat conduction mechanism of solid soil particles, pores, water and ice inside the soil. It clearly describes the contribution of different phases to the thermal conductivity of the soil from a physical mechanism perspective. It breaks through the limitation that the classical theoretical model is only applicable to two-phase or simplified three-phase systems, and provides a unified and continuous theoretical description framework for the heat conduction behavior of complex multiphase soils.

[0043] 2. Wide Applicability: The theoretical model of this invention accurately describes the thermal conductivity characteristics of both unfrozen soil (three-phase) and frozen soil (four-phase), achieving normalization in the calculation of soil thermal properties. The calculation formula of this method can flexibly adapt to different state changes of soil, especially during freezing and thawing processes, accurately calculating the transformation of soil thermal conductivity between different phases (solid-water-air-ice). Furthermore, the model can adapt to different soil types and environmental conditions, thus enabling its wide application in soil thermal conductivity analysis under different regions and climatic conditions.

[0044] 3. High Precision, Reduced Reliance on Traditional Testing: This invention innovatively proposes a strategy for back-calculating the thermal conductivity of soil particles using extreme conditions (pure dry / saturated), achieving dual verification of parameters and eliminating calculation errors caused by differences in soil mineral composition. The method of this invention can calculate the effective thermal conductivity of soil using conventional geotechnical parameters (such as porosity and thermal conductivity of each phase), replacing traditional, expensive, and time-consuming experimental methods. The thermal conductivity of soil typically requires sample preparation and multiple experiments, which is not only costly but also complex. With the method of this invention, the thermal conductivity of soil can be predicted with high precision using readily available physical parameters, and online monitoring and inversion analysis are possible. This is particularly suitable for large-scale engineering projects and soil thermal response prediction, greatly saving time and economic costs. Attached Figure Description

[0045] Figure 1 This is a flowchart of a generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media.

[0046] Figure 2 This is a schematic diagram of the phase distribution of a typical unfrozen soil sample;

[0047] Figure 3 This is a schematic diagram of the phase distribution of a typical frozen soil sample;

[0048] Figure 4 It is the surface of the effective saturation coefficient of a soil sample under a certain porosity. Detailed Implementation

[0049] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0050] This invention provides a generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media. The method constructs an equation that correlates the effective thermal conductivity of soil (considered as a multiphase composite material composed of soil particles, water, air, and ice) with the content of each component and their respective thermophysical parameters, thereby accurately obtaining the effective thermal conductivity of the mixture. This solves the following technical problems:

[0051] 1. Core Problem Solved: This invention establishes a unified "Equation of State for Effective Thermal Conductivity of Multiphase Soils" in the field of soil heat conduction, overcoming the shortcomings of existing empirical formulas that lack physical mechanisms and cannot be universally applied across different states. Based on the Laplace equation and effective medium theory, this invention derives a set of analytical solution formulas with clear physical meaning, starting from the thermal perturbation of microscopic particles. For the first time, it unifies the thermal conductivity laws of soil under all states—dry, unsaturated, saturated, and frozen / thawed—within a mathematical framework, solving the fundamental problems of discontinuous calculation accuracy and poor applicability of existing models in different moisture content ranges and phase transition ranges (freeze / thaw).

[0052] 2. Addressing the critical issue of "difficulty in obtaining and verifying the thermal conductivity of solid phase (soil particles): Current methods for obtaining the thermal conductivity of soil particles rely on estimating from existing data or conducting complex experiments. This invention utilizes a proposed formula to construct a "dual verification inversion mechanism." Specifically, it uses two easily prepared and measured extreme states—"purely dry" and "fully saturated"—to inversely solve for the unique and true effective thermal conductivity of soil particles. This method does not rely on empirical estimation; it directly inversely calculates microscopic properties from macroscopic responses, solving the technical problem of inaccurate model input parameters leading to the complete failure of calculation results.

[0053] 3. This invention solves the problem of quantitatively calculating the multiphase components (especially ice content) within soil. In frozen soil engineering and cold region monitoring, directly obtaining the unfrozen water content and ice content within the soil usually requires destructive sampling or expensive nuclear magnetic resonance (NMR) equipment. The formula provided by this invention clearly defines the strict mathematical coupling relationship between thermal conductivity and the volume content of each phase (water, ice, and gas). Therefore, when the effective thermal conductivity of the soil sample is obtained in the field or through testing, the invisible ice or water content within the soil can be accurately calculated, solving the problem of the lack of low-cost, non-destructive component monitoring methods in engineering sites.

[0054] like Figure 1 As shown, the specific steps are as follows:

[0055] Step S101: Obtain the porosity of the soil sample :

[0056] Based on a comprehensive analysis of domestic and international models and formulas related to thermal conductivity, and using a multiphase random distribution model, perturbation theory, and effective medium theory, a new formula for calculating the thermal conductivity of multiphase soil samples is proposed, as follows:

[0057] Unfrozen state: Earth-water-air three-phase configuration:

[0058]

[0059]

[0060] Frozen state: Four-phase system of soil-water-air-ice:

[0061]

[0062]

[0063] In the formula, is the thermal conductivity of the soil particles; Let be the thermal conductivity of ice. W / (m·K); The thermal conductivity of air. W / (m·K); The thermal conductivity of water, W / (m·K); Effective thermal conductivity; The porosity of the soil sample; This refers to the volumetric water content. Ice content by volume; This represents the volumetric gas content.

[0064] Figure 2 , Figure 3 These are schematic diagrams of the phase distribution of a conventional unfrozen soil sample and a conventional frozen soil sample, respectively.

[0065] Porosity Porosity is defined as the ratio of pore volume to total soil volume. It can be indirectly calculated through conventional geotechnical tests. The specific method of obtaining it is as follows:

[0066] Obtain the specific gravity of soil particles The specific gravity of soil particles is determined using the hydrometer bottle method. This test should be performed in two parallel measurements, and the arithmetic mean of the results should be taken. The maximum permissible parallel difference should be ±0.02. , dimensionless.

[0067] Obtaining soil dry density Determining the dry density of soil samples using the ring cutter method or the wax sealing method. This test should be performed in two parallel measurements, with a maximum permissible parallel difference of ±0.03. Take their arithmetic mean, in units of 1000 ppm. .

[0068] The porosity of the soil sample was calculated using the formula. :

[0069]

[0070] Step S102: Obtain the thermal conductivity of soil particles. :

[0071] Thermal conductivity of soil particles The thermal conductivity of soil particles can be obtained either through direct measurement in relevant experiments, or by first determining the effective thermal conductivity of a pure dry or saturated soil sample and then using a simplified soil-air or soil-water two-phase formula to calculate the thermal conductivity of soil particles. (Pre-installation function).

[0072] Direct measurement method:

[0073] Soil particles were prepared into dense, non-porous solid samples, and their thermal conductivity was directly measured using relevant thermal conductivity measuring instruments. The unit is W / (m·K). This method is extremely difficult to use when preparing samples, and it is hard to ensure that the prepared soil sample is completely free of pores.

[0074] Inverse calculation verification method:

[0075] (1) Inverse calculation of pure dry state Prepare a dried soil sample (volume moisture content) =0, ice content per unit volume =0, at which point the volumetric gas content is 0. =n), measure its effective thermal conductivity in the dry state. The unit is W / (m·K). Substituting this into the simplified soil-air two-phase formula obtained in this invention:

[0076]

[0077] The thermal conductivity of the soil particles in the dry soil sample can be obtained through final calculation. .

[0078] (2) Saturation state back calculation Prepare a saturated soil sample (volume air content) =0, ice content per unit volume =0, at this point the volumetric water content is... =n), measure its saturated thermal conductivity. The unit is W / (m·K). Substituting this into the simplified soil-water two-phase formula obtained in this invention:

[0079]

[0080] The thermal conductivity of the soil particles in the dry soil sample can be obtained through final calculation. .

[0081] Thermal conductivity of soil particles You can choose to use the pure dry state back calculation method according to your own needs and the on-site experimental environment. Or saturation state back calculation .

[0082] Step S103: Obtain the effective thermal conductivity of the soil sample and the thermal conductivity surface of the soil sample under a certain porosity (main function):

[0083] When it is necessary to obtain the effective thermal conductivity of a target soil sample, it is necessary to first determine whether the soil sample is frozen, and then select the appropriate formula to solve it:

[0084] Unfrozen state: Earth-water-gas three-phase formula:

[0085]

[0086]

[0087] The above formula can be simplified into a cubic equation in one variable, such as... Using Cardan's quadratic formula:

[0088]

[0089] in:

[0090]

[0091]

[0092] After simplifying the three-phase formula for soil-water-gas, A, B, C, As shown below:

[0093]

[0094]

[0095]

[0096]

[0097] Then, the key parameters required for the calculation need to be obtained. This can be obtained through step S101. The moisture content of the soil sample can be obtained through step S102 by determining the mass moisture content using the drying method. The volumetric moisture content is obtained by converting dry density. :

[0098]

[0099] At this point, the volumetric gas content Substituting the above parameters into the soil-water-air three-phase formula, the effective thermal conductivity λ is obtained through calculation.

[0100] Frozen state: Four-phase formula of soil-water-air-ice:

[0101]

[0102]

[0103] Simplifying the four-phase formula into a quartic equation and then using the root-finding formula would be too complicated. Therefore, after obtaining the required key parameters, we can directly calculate the formula by substituting them into the equation.

[0104] Obtain the key parameters required for the calculation. This can be obtained through step S101. The moisture content of the soil sample can be obtained through step S102 by determining the mass moisture content using the drying method. The volumetric water content is obtained by combining the above with the dry density conversion. Volumetric water content of the soil sample (referring to unfrozen water content) and volumetric ice content These two parameters can be directly measured using nuclear magnetic resonance (NMR) technology, or estimated based on the temperature-freezing characteristic curve (SFCC) of the soil sample.

[0105] At this point, the volumetric gas content Substituting the above parameters into the four-phase formula of soil-water-air-ice, the effective thermal conductivity λ is obtained through calculation.

[0106] This formula can not only calculate the thermal conductivity of soil samples with different porosities under a specific state, but also establish a surface of the effective thermal conductivity of a soil sample with a certain porosity under different temperatures and moisture contents. When the temperature is above the freezing point, the soil sample has not frozen, and different effective thermal conductivityes can be obtained at different moisture contents. When the temperature is below the freezing point and continues to decrease, the effective thermal conductivity changes continuously with the volume changes of the water phase and ice phase within the soil sample pores.

[0107] The volumetric ice content at different temperatures can be obtained based on the freezing conditions of soil samples at different temperatures. Key parameters are then substituted into the soil-water-gas three-phase formula and the soil-water-gas-ice four-phase formula, combined with... Figure 4As shown, the effective saturation coefficient surface of the soil sample under this porosity can be finally established.

[0108] Step S104: Obtain the volumetric water content and ice content of the soil sample:

[0109] Auxiliary function 1: Back-calculate the volumetric moisture content of unfrozen soil samples :

[0110] If you want to obtain the volumetric moisture content of the soil sample The effective thermal conductivity λ and porosity of the soil sample can be obtained first using thermal conductivity testing equipment. The thermal conductivity of soil particles can be obtained through step S101. This can be obtained through step S102. Calculate the volumetric moisture content of the soil sample Substituting the soil-water-gas three-phase formula into the unfrozen state, the soil moisture content can be calculated in reverse.

[0111] Auxiliary function 2: Calculate the ice content of soil sample volume under frozen conditions. :

[0112] If you want to obtain the volumetric ice content of the soil sample The effective thermal conductivity λ and porosity of the soil sample can be obtained first using thermal conductivity testing equipment. The thermal conductivity of soil particles can be obtained through step S101. The volumetric water content can be obtained through step S102 by directly measuring it using nuclear magnetic resonance (NMR) technology. (Refers to the unfrozen water content), Substituting the values ​​into the four-phase formula for frozen soil (soil-water-gas-ice), we can obtain the volumetric ice content of the frozen soil sample.

[0113] Example:

[0114] Taking a certain underground silt in Heilongjiang Province as an example, according to Figure 2 , Figure 3 The phase distributions shown are illustrated with examples.

[0115] The specific gravity of soil particles was determined by the hydrostatic bottle method. The dry density of the soil sample was determined using the ring sampler method, which yielded a value of 2.656. It is 1.7 .

[0116]

[0117] Using the inverse calculation verification method:

[0118] Inverse calculation under pure dry conditions: After the prepared soil sample is dried, its effective thermal conductivity under dry conditions is obtained using a thermal conductivity measuring instrument. K. Substituting this into the simplified solid-gas two-phase form of the formula of this invention:

[0119]

[0120]

[0121]

[0122] Saturated state back calculation: The prepared soil sample is vacuum saturated, and its saturated thermal conductivity is obtained using a thermal conductivity measuring instrument. Substituting this into the simplified soil-water two-phase form of the formula of this invention:

[0123]

[0124]

[0125]

[0126] In summary, the thermal conductivity of soil particles in the soil sample... 2.2 is acceptable. .

[0127] The moisture content of soil samples was determined by the oven-drying method. =0.1235, combined with dry density conversion, the volumetric moisture content is obtained as follows:

[0128]

[0129] At this point, the volumetric gas content is:

[0130]

[0131] Substituting the above parameters into the soil-water-air three-phase formula, the effective thermal conductivity λ is calculated:

[0132]

[0133]

[0134]

[0135] The soil sample was frozen, and the volumetric water content of the soil sample was determined. (referring to unfrozen water content) and volumetric ice content These two parameters can be directly measured using nuclear magnetic resonance (NMR) technology. =0.05, =0.16.

[0136] At this point, the volumetric gas content is:

[0137]

[0138] Substituting the above parameters into the four-phase formula for soil-water-air-ice, the effective thermal conductivity λ is calculated as follows:

[0139]

[0140]

[0141]

[0142] A surface model of the effective thermal conductivity of underground silt at different temperatures and total moisture contents under various conditions can be constructed, such as... Figure 4 As shown.

[0143] If you want to obtain the volumetric moisture content of a soil sample, such as Figure 2 The effective thermal conductivity of the soil sample was first obtained using a thermal conductivity testing device, which yielded a value of λ = 1.13. The porosity was found to be n=0.36, and the thermal conductivity of the soil particles was... =2.2 .

[0144] Substituting the above parameters into the soil-water-air three-phase formula, the moisture content can be calculated in reverse:

[0145]

[0146]

[0147]

[0148] If you want to obtain the volumetric ice content of a frozen soil sample, such as Figure 3 The effective thermal conductivity of the soil sample was first obtained using a thermal conductivity testing device, which yielded a value of λ = 1.446. K was used to determine the porosity n = 0.36, and the thermal conductivity of the soil particles was... =2.2 Volumetric water content was directly determined using nuclear magnetic resonance (NMR) technology. =0.05.

[0149]

[0150] Substituting the above parameters into the four-phase formula for soil-water-gas-ice, its volumetric ice content can be calculated:

[0151]

[0152]

[0153]

Claims

1. A generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media, characterized in that... The method includes the following steps: Step 1: Obtain the porosity of the soil sample : The porosity of the soil sample was obtained indirectly through conventional geotechnical tests. ; Step 2: Obtain the thermal conductivity of soil particles : The thermal conductivity of soil particles can be obtained through direct measurement or back-calculation verification. ; Step 3: Obtain the effective thermal conductivity of the soil sample and the thermal conductivity surface of the soil sample under a certain porosity: Step 31: Obtain the porosity of the soil sample in its unfrozen state. Thermal conductivity of soil particles Moisture content Volumetric moisture content and volumetric gas content ; Step 32: Obtain the porosity of the soil sample under frozen conditions. Thermal conductivity of soil particles Moisture content Volumetric moisture content Ice content by volume and volumetric gas content ; Step 33: Substitute the parameters obtained in Step 31 into the soil-water-gas three-phase formula, and the parameters obtained in Step 32 into the soil-water-gas-ice four-phase formula to calculate the effective thermal conductivity λ, and establish the surface of the effective saturation coefficient of the soil sample under this porosity. Step 4: Obtain the volumetric water content and ice content of the soil sample: Step 41: Back-calculate the volumetric moisture content of the unfrozen soil sample. : The effective thermal conductivity λ of the soil sample was obtained using a thermal conductivity testing device, and the porosity was obtained in step 1. The thermal conductivity of soil particles is obtained through step S2. , Substituting into the soil-water-gas three-phase formula, the soil moisture content can be calculated in reverse. Step 42: Calculate the ice content of the soil sample volume under frozen conditions. : The effective thermal conductivity λ of the soil sample is first obtained using a thermal conductivity testing device, and the porosity is then obtained in step 1. The thermal conductivity of soil particles is obtained through step S2. Volumetric water content was directly determined using nuclear magnetic resonance (NMR) technology. , Substituting the soil-water-air-ice four-phase formula, the volumetric ice content of the frozen soil sample is calculated.

2. The generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media according to claim 1, characterized in that... The specific steps of step 1 are as follows: Step 11: Obtain the specific gravity of soil particles Determining the specific gravity of soil particles using the specific gravity bottle method ; Step 12: Obtain the dry density of the soil sample. Determining the dry density of soil samples using the ring cutter method or the wax sealing method. ; Step 13: Calculate the porosity of the soil sample according to the formula. :

3. The generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media according to claim 1, characterized in that... In step 2, the specific steps of the direct measurement method are as follows: the soil particles are prepared into a dense solid sample without pores, and its thermal conductivity is directly measured using a relevant thermal conductivity measuring instrument. .

4. The generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media according to claim 1, characterized in that... In step 2, the specific steps of the back-calculation verification method are as follows: First, the effective thermal conductivity of a pure dry or saturated soil sample is measured, and then the thermal conductivity of soil particles is back-calculated using a simplified soil-air or soil-water two-phase formula. .

5. The generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media according to claim 4, characterized in that... The soil-gas two-phase formula is as follows:

6. The generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media according to claim 4, characterized in that... The soil-water two-phase formula is as follows: In the formula, Let be the thermal conductivity of the soil particles. The thermal conductivity of air. The thermal conductivity of water, For effective thermal conductivity, This refers to the volumetric moisture content. This represents the volumetric gas content.

7. The generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media according to claim 1, characterized in that... The three-phase formula for soil-water-gas is as follows:

8. The generalized theoretical numerical calculation method for the thermal conductivity of multiphase random mixed porous media according to claim 1, characterized in that... The four-phase formula for soil-water-gas-ice is as follows:

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