Expansive soil slope hydrothermal coupling numerical simulation method and equipment and storage medium

Abstract

The invention discloses an expansive soil slope hydrothermal coupling numerical simulation method and device and a storage medium. The expansive soil slope hydrothermal coupling numerical simulation method comprises the steps of obtaining moisture flux and heat flux according to meteorological data and soil parameters of an area where a to-be-studied expansive soil slope is located, and substituting the moisture flux and the heat flux into a hydrothermal coupling model of the expansive soil slope as boundary conditions, solving to obtain the hydrothermal field distribution of the expansive soil slope; wherein the hydrothermal coupling model is constructed according to a water field control equation and a temperature field control equation. According to the expansive soil slope hydrothermal coupling numerical simulation method, the accuracy, practicability and timeliness of expansive soil slope simulation are improved, and the practice of expansive soil area slope engineering can be well guided.

Description

Technical Field

[0001] This invention relates to a numerical simulation method, equipment, and storage medium for hydrothermal coupling of expansive soil slopes. Background Technology

[0002] Expansive soil slopes are widely distributed. Because expansive soil is rich in hydrophilic clay minerals such as illite and montmorillonite, it exhibits significant expansion and contraction characteristics, making it highly susceptible to various engineering geological problems under climatic influences. Under climatic influences, the moisture and temperature fields within expansive soil slopes change rapidly, and these changes also alter the hydrothermal parameters of the slopes. Traditional in-situ monitoring techniques for expansive soil slopes are limited by cost and operational methods, making it difficult to obtain accurate hydrothermal field distributions across the entire space. Furthermore, traditional numerical simulation methods rarely consider the impact of climatic influences on numerical model parameters and boundary conditions.

[0003] For example, patent CN109736157A discloses a method for predicting the deformation of expansive soil subgrade based on humidity balance. It establishes a two-dimensional finite element numerical model of the expansive soil embankment based on humidity balance, obtains the spatiotemporal distribution law of humidity, and then uses the formula for wet expansion deformation to obtain the initial and final stress states of the subgrade. However, this method only obtains the humidity field and its stress-strain state in the subgrade, without considering the distribution of the hydrothermal field in expansive soil engineering.

[0004] Existing numerical simulation methods mostly assume the soil under ideal conditions, rarely considering the variability of real climate, resulting in insufficient accuracy compared to actual monitoring results of expansive soil slope engineering. Furthermore, existing slope hydrothermal coupling numerical models are mostly only accurate enough to obtain daily average temperature and moisture fields, unable to capture real-time changes in slope hydrothermal fields at short timescales (e.g., every half hour or ten minutes); and their simulation time ranges are relatively short, mostly unable to provide numerical simulations of slope hydrothermal fields over continuous months or even a year. Therefore, there is a need to develop a numerical simulation method that considers the effects of climate to achieve real-time distribution of expansive soil slope hydrothermal fields.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method, equipment, and storage medium for hydrothermal coupling numerical simulation of expansive soil slopes, which improves the accuracy, practicality, and timeliness of expansive soil slope simulation and provides better guidance for slope engineering practices in expansive soil areas.

[0007] The first aspect of the present invention provides a numerical simulation method for hydrothermal coupling of expansive soil slopes, comprising: obtaining water flux and heat flux based on meteorological data and soil parameters of the area where the expansive soil slope to be studied is located; substituting the water flux and heat flux as boundary conditions into the hydrothermal coupling model of the expansive soil slope; and solving for the hydrothermal field distribution of the expansive soil slope; wherein the hydrothermal coupling model is constructed based on the water field control equation and the temperature field control equation.

[0008] In some preferred embodiments, the moisture field control equation is as follows:

[0009] in, For finite element space, The boundary of the finite element space. and Let these represent the integrals over the finite element space and over the boundary of the finite element space, respectively. N r For shape function, C φ and C φT These are the isothermal volumetric capacity and volumetric heat capacity of water, respectively. k φ and k φT This represents isothermal moisture diffusivity and thermal moisture diffusivity. and These represent the matrix suction head during the simulation and in the initial state, respectively. T and T 0 These represent the temperatures during the simulation and in the initial state, respectively. For the density of the liquid, k Let be the permeability coefficient of liquid water. and These represent the flow rates of liquid water and vapor through the atmosphere-soil interaction interface, respectively. In some preferred embodiments, the temperature field governing equation is as follows:

[0010] in, For finite element space, The boundary of the finite element space. and Let these represent the integrals over the finite element space and over the boundary of the finite element space, respectively. N s For shape functions, C T and C TφThese are the volumetric heat capacity and the isothermal volumetric capacity of water, respectively. k T and k Tφ These represent the thermal conductivity of the soil structure and the rate of water diffusion within the soil structure, respectively. and These represent the matrix suction head during the simulation and in the initial state, respectively. T and T 0 These represent the temperatures during the simulation and in the initial state, respectively. This represents the heat flux through the atmosphere-soil interaction interface. In some preferred embodiments, meteorological data for the area where the expansive soil slope under study is located includes rainfall, air temperature, wind speed, solar radiation, and relative humidity.

[0011] In some preferred embodiments, the soil parameters of the area where the expansive soil slope to be studied is located include the expansive soil water characteristic curve, permeability coefficient, and thermal conductivity coefficient.

[0012] In some preferred embodiments, the hydrothermal coupling model follows an energy balance at the atmosphere-soil interaction interface of the atmosphere and expansive soil slope, as shown in equation (1): (1) The hydrothermal coupling model follows mass conservation at the atmosphere-soil interaction interface of the atmosphere and expansive soil slope, as shown in equation (2): (2) in, R n Net radiative flux, G For soil heat flux, L E For latent heat flux, H For sensible heat flux; P For rainfall, I nf For infiltration flux, R off Soil surface runoff rate, E a This represents the actual water flux generated by evaporation. I nt For plant water interception flux; Will G and I nt As input boundary conditions for the hydrothermal coupling model.

[0013] In some more preferred embodiments, in equation (1) above,

[0014]

[0015]

[0016]

[0017] ,

[0018]

[0019]

[0020] The calculation is obtained by integrating the above formulas. G ,in, R si The solar radiation value was obtained through monitoring. R so Solar radiation on a sunny day. T a Let σ be the average temperature monitored every ten minutes, and let σ be the Stefan-Boltzmann constant. a c and b c These are empirical parameters related to the cloud. a 1 and b 1 It is an empirical parameter related to emissivity, where α is the soil surface reflectivity and the daily average saturated vapor pressure is... e d From daily average dew point temperature T d calculate; EL msl The elevation of the site above average sea level. R sa It is solar radiation from outside the Earth; and These are the solar time angles at the beginning and end of the considered period, respectively; L v The heat of vaporization of water, The thermal conductivity of air, This represents the air temperature gradient at the atmosphere-soil interaction interface.

[0021] In some more preferred embodiments, in equation (2) above, P , I nt and R off Actual water evaporation was obtained through in-situ monitoring. E a The calculation is as follows:

[0022]

[0023]

[0024]

[0025] in, E a and E p These represent actual evaporation and potential evaporation, respectively. u For wind speed, h a Relative humidity, a and b These are empirical parameters; e 0 represents the vapor pressure at the soil surface. e s This is the saturated vapor pressure at the soil surface. e a It is the vapor pressure of air; T s and T a These are the soil surface temperature and the air temperature, respectively. For substrate suction head, W w It is the relative molecular mass of water. R It is the ideal gas constant.

[0026] In some preferred embodiments, the hydrothermal coupling model uses FreeFem++ to create a finite element mesh and set initial conditions.

[0027] In some preferred embodiments, the hydrothermal field distribution includes simulation results of soil temperature at different depths and simulation results of soil volumetric water content at different depths.

[0028] A second aspect of the present invention provides a hydrothermal coupling numerical simulation device for expansive soil slopes, comprising a processor and a memory, wherein the memory is used to store instructions, and the processor is used to execute the hydrothermal coupling numerical simulation method for expansive soil slopes according to the instructions.

[0029] A third aspect of the present invention provides a computationally readable storage medium comprising a computer program that, when executed by a processing terminal, causes the processing terminal to perform the described numerical simulation method for hydrothermal coupling of expansive soil slopes.

[0030] The beneficial effects of this invention are as follows: The hydrothermal coupling numerical simulation method for expansive soil slopes of the present invention systematically considers the impact of climate on expansive soil slopes, and is more accurate and scientific. It can reflect the changes in short-term hydrothermal field distribution over long-term time scales, and can better monitor and prevent geological disasters and engineering geological problems of expansive soil slopes. Attached Figure Description

[0031] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a flowchart of a numerical simulation method for hydrothermal coupling of expansive soil slopes according to an embodiment of the present invention.

[0033] Figure 2 This is a finite element model mesh for an expansive soil slope according to an embodiment of the present invention.

[0034] Figure 3 This refers to the initial temperature conditions for an expansive soil slope model according to an embodiment of the present invention.

[0035] Figure 4 This is the initial condition for the volumetric water content of an expansive soil slope model according to an embodiment of the present invention.

[0036] Figure 5 This is the initial condition of matrix suction for an expansive soil slope model according to an embodiment of the present invention.

[0037] Figure 6 This is a comparison chart of the simulated temperature and the in-situ monitored temperature at a location 5cm above the ground surface in the middle of the slope, according to an embodiment of the present invention.

[0038] Figure 7 This is a comparison chart of the simulated volumetric water content and the in-situ monitored volumetric water content at a location 5cm above the ground surface in the middle of the slope, according to an embodiment of the present invention. Detailed Implementation

[0039] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, so that the advantages and features of the present invention can be more readily understood by those skilled in the art. It should be noted that the description of these embodiments is for the purpose of aiding understanding the present invention, but does not constitute a limitation thereof.

[0040] The embodiment provides a numerical simulation method and equipment for hydrothermal coupling of expansive soil slopes that comprehensively considers the effects of climatic factors such as rainfall and evaporation, and takes into account both long-term and short-term real-time responses, so as to achieve accurate, stable, real-time, and long-term simulation of the changes in the hydrothermal field of expansive soil slopes.

[0041] Figure 1 A flowchart illustrating an embodiment of a numerical simulation method for hydrothermal coupling of expansive soil slopes is shown. (Refer to...) Figure 1 As shown, the numerical simulation method for hydrothermal coupling of expansive soil slopes includes: obtaining water flux and heat flux based on meteorological data and soil parameters of the area where the expansive soil slope under study is located; substituting the water flux and heat flux as boundary conditions into the hydrothermal coupling model of the expansive soil slope; and solving for the hydrothermal field distribution of the expansive soil slope. The hydrothermal coupling model is constructed based on the water field control equation and the temperature field control equation.

[0042] In this specific embodiment, a small meteorological observation station is first deployed within the area of ​​an expansive soil slope to acquire meteorological data and soil hydrothermal field parameters in real time. The meteorological data from the observation station is used to calculate the surface heat flux and water flux of the soil, serving as the input boundary conditions for the model. On-site information such as vegetation conditions, initial conditions, and soil layer information is used as input to the model. The FreeFem++ open-source software is used to construct and solve a hydrothermal coupling model of the expansive soil slope within a finite element framework, outputting the simulated soil moisture field and temperature field. By comparing and analyzing the simulation results of the hydrothermal field with the in-situ observation data, the effectiveness of the model can be demonstrated, and the spatiotemporal evolution of the hydrothermal field of the expansive soil slope under climate influence can be explored from multiple perspectives.

[0043] In this embodiment, the hydrothermal coupling model uses FreeFem++ to establish a finite element mesh and set initial conditions. The FreeFem++ software solves partial differential equations using the finite element method, employs the C++ programming language, and integrates a network generator, a linear equation solver, posterior network adaptation, and result visualization. Figure 2 The finite element mesh of the expansive soil slope established in the embodiment is shown. Figures 3 to 5 The initial conditions for the model regarding temperature, volumetric water content, and matrix suction are shown. In other embodiments, the MPM method can also be used for numerical simulation, but the continuity is not as good as in this embodiment.

[0044] 1. Construction of numerical models The governing equations of the numerical model are divided into the moisture field governing equation and the temperature field governing equation. They are rewritten into their corresponding if forms so that the FreeFem++ software can solve them based on the finite element framework.

[0045] The governing equations for the moisture field are as follows:

[0046]

[0047]

[0048]

[0049] The weak form of the water field governing equation is:

[0050] in, and These represent the flow rates of liquid water and vapor through the atmosphere-soil interaction interface, respectively.

[0051] The governing equation for the temperature field is:

[0052]

[0053]

[0054]

[0055] The weak form of the temperature field governing equation is:

[0056] In the formula, This represents the heat flux through the atmosphere-soil interaction interface.

[0057] The weak forms of the two equations above are the core governing equations of the fully coupled hydrothermal theoretical model of unsaturated soil.

[0058] 2. Calculation of boundary conditions for the numerical model The boundary conditions of the numerical model are calculated from meteorological data and soil parameters obtained from the local area. The meteorological data includes rainfall, air temperature, wind speed, solar radiation, and relative humidity. The soil parameters include the soil-water characteristic curve of expansive soil, permeability coefficient, and thermal conductivity.

[0059] In this embodiment, the values ​​and descriptions of the above parameters and other constant parameters are shown in Table 1.

[0060] Table 1

[0061] Atmosphere-soil interaction occurs at the soil surface. For exposed soil, during rainfall, rainwater is lost primarily through infiltration and surface runoff. Simultaneously, due to heat transfer and vapor pressure gradients at the soil surface, water evaporation also occurs. Solar radiation is the only source of energy for the soil surface, but only solar radiation acting on the surface contributes to water evaporation, i.e., net solar radiation. The numerical model follows energy balance and mass conservation at the atmosphere-soil interaction interface of the atmosphere and expansive soil slopes, and their expressions are as follows:

[0062] In the formula, R n (W / m2) represents the net radiative flux. G (W / m2) represents the soil heat flux. L E (W / m2) represents latent heat flux. H (W / m2) represents the sensible heat flux; P (m / s) represents rainfall. I nf (m / s) represents the infiltration flux. R off (m / s) represents the soil surface runoff rate. E a (m / s) represents the actual water flux during evaporation. I nt (m / s) represents the water interception flux of the plant.

[0063] The net radiative flux is calculated as follows:

[0064] In the formula, solar radiation R si (W / m2) is obtained from monitoring results. T a (°C) represents the average temperature monitored every ten minutes, and σ is the Stefan-Boltzmann constant, which has a value of 5.67108 W / (m2K4). a c and b c These are empirical parameters related to the cloud. a 1 and b 1 It is an empirical parameter related to emissivity. a c and b c The values ​​are 1.35 and 0.35 respectively; a 1 and b1 The values ​​are taken as 0.35 and 0.14 respectively; α is the soil surface reflectivity, with a value of 0.23; daily average saturated vapor pressure e d From daily average dew point temperature T d calculate:

[0065] Sunny solar radiation R so (W / m2) is expressed as:

[0066] In the formula, EL msl (m) represents the elevation of the site above the mean sea level; R sa (W / m2) represents solar radiation from outside the Earth. R sa The calculation method is as follows:

[0067] and These are the solar time angles (in radians) at the beginning and end of the considered period, respectively. The calculation methods for both are as follows:

[0068] In the formula, It is the solar time angle at the center of the cycle; (h) is the length of the period under consideration.

[0069] Latent heat flux can be determined by actual evaporation, while sensible heat flux is calculated as follows:

[0070] In the formula, L E (W / m) 2 Latent heat flux represents the amount of water evaporation and the heat of vaporization. L v The product of (J / kg); H (W / m) 2 ( ) represents the sensible heat flux. The thermal conductivity of air is 0.025 W / mK. This represents the air temperature gradient at the atmosphere-soil interaction interface.

[0071] In the mass balance equation P ,I nt and R off Actual water evaporation can be obtained through in-situ monitoring. E a The calculation model is as follows:

[0072] In the formula, E a (m / s) and E p (m / s) represent actual evaporation and potential evaporation, respectively; u (m / s) represents wind speed; h a Relative humidity (%) a and b These are empirical parameters, obtained through environmental chamber testing. a = 0.022, b = 0.031. According to the Kelvin equation, the relative humidity of the soil surface is calculated as follows:

[0073] Soil surface vapor pressure e 0. Saturated vapor pressure at soil surface e s air vapor pressure e a The calculation method is as follows:

[0074]

[0075]

[0076] In the formula, T s (°C) and T a (°C) represents the soil surface temperature and air temperature, respectively; (m) represents the substrate suction head; W w This is the relative molecular mass of water, with a value of 18.016 × 10⁻⁶. -3 kg / mol; R It is the ideal gas constant, with a value of 8.31 J / mol·K.

[0077] The calculation is obtained by integrating the above formulas. G and I nt , which serves as the input boundary condition for the numerical model.

[0078] 3. Numerical model simulation results Based on the governing equations of the numerical model, a two-dimensional finite element numerical model of the expansive soil slope is constructed. The calculated boundary conditions of the numerical model are then substituted into the model to obtain the hydrothermal field distribution of the expansive soil slope every ten minutes under climatic influence. For example, the model is solved using FreeFem++ software.

[0079] From the obtained two-dimensional cloud map, the hydrothermal field distribution data at any point can be exported. In this embodiment, the simulation results at a location 5cm from the ground surface in the middle of the slope are selected, and the results obtained through in-situ monitoring can be used to verify and evaluate the accuracy of the numerical simulation results, such as... Figure 6 and Figure 7 As shown. Figure 6 and Figure 7 In the diagram, the black curve represents the result of numerical simulation performed according to the method described in the embodiment, while the red curve represents the result obtained by the original detection using a temperature and moisture content testing device.

[0080] This embodiment also provides a numerical simulation device for hydrothermal coupling of expansive soil slopes, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-described numerical simulation method for hydrothermal coupling of expansive soil slopes.

[0081] This embodiment also provides a computer-readable storage medium. The computer-readable storage medium stores a computer program that, when executed by a processor, implements the aforementioned numerical simulation method for hydrothermal coupling of expansive soil slopes. The computer-readable storage medium includes, but is not limited to, FLASH memory, read-only memory, magnetic disk, or optical disk.

[0082] The implementation plan systematically considers the impact of climate on expansive soil slopes, offering higher accuracy and a more scientific approach. It can reflect short-term changes in hydrothermal field distribution over long timescales, enabling better monitoring and prevention of geological hazards and engineering geological problems on expansive soil slopes. Its more systematic approach combines on-site monitoring with numerical simulation, achieving a closed-loop process from data collection to assessment. The implementation plan focuses on the study of expansive soil slopes, considering the impact of climate on the hydrothermal field of expansive soil slopes. Its simulation method is more accurate, has a longer timescale, and can simulate real-time hydrothermal field distribution every ten minutes.

[0083] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains; the term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0084] As indicated in this specification and claims, the terms "comprising" and "including" only indicate the inclusion of expressly identified steps and elements, and these steps and elements do not constitute an exclusive list; the method or apparatus may also include other steps or elements. The term "and / or" as used herein includes any combination of one or more of the associated listed items.

[0085] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains; the term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0086] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. Those skilled in the art will understand that all or part of the steps carried out by the methods of the above embodiments can be implemented by a program instructing related hardware, the program being stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiments.

[0087] In this embodiment, the functional units can be integrated into one processing module, or each unit can exist physically separately, or two or more units can be integrated into one module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0088] The storage media mentioned above can be read-only memory, disk, or optical disk, etc.

[0089] Any step described in any method or process claim may be performed in any order, and is not limited to the order presented in the claims. The limitation of method + function or step + function is used only if all of the following conditions are met in a particular claim: a) it expressly states "method for..." or "step for..."; b) it expressly states the corresponding function. Structures, materials, or actions supporting the method + function are expressly described in the description herein. Therefore, the scope of the invention should be determined solely by the appended claims and their legal equivalents, and not by the description and examples given herein.

[0090] The above embodiments are merely illustrative of the technical concept and features of the present invention, and are preferred embodiments. Their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly, and they should not be construed as limiting the scope of protection of the present invention. All equivalent transformations or modifications made according to the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A numerical simulation method for hydrothermal coupling of expansive soil slopes, characterized in that, include: Based on meteorological data and soil parameters of the area where the expansive soil slope to be studied is located, the water flux and heat flux are obtained. The water flux and heat flux are then substituted as boundary conditions into the hydrothermal coupling model of the expansive soil slope to solve for the hydrothermal field distribution of the expansive soil slope. The hydrothermal coupling model is constructed based on the water field control equation and the temperature field control equation.

2. The numerical simulation method for hydrothermal coupling of expansive soil slopes according to claim 1, characterized in that, The governing equation for the moisture field is as follows: ； in, For finite element space, The boundary of the finite element space, and Let these represent the integrals over the finite element space and over the boundary of the finite element space, respectively. N r For shape functions, C φ and C φT These are the isothermal volumetric capacity and volumetric heat capacity of water, respectively. k φ and k φT This represents isothermal moisture diffusivity and thermal moisture diffusivity. and These represent the matrix suction head during the simulation and in the initial state, respectively. T and T 0 These represent the temperatures during the simulation and in the initial state, respectively. For the density of the liquid, k Let be the permeability coefficient of liquid water. and These represent the flow rates of liquid water and vapor through the atmosphere-soil interaction interface, respectively.

3. The numerical simulation method for hydrothermal coupling of expansive soil slopes according to claim 1, characterized in that, The temperature field control equation is as follows: ； in, For finite element space, The boundary of the finite element space, and Let these represent the integrals over the finite element space and over the boundary of the finite element space, respectively. N s For shape functions, C T and C Tφ These are the volumetric heat capacity and the isothermal volumetric capacity of water, respectively. k T and k Tφ These represent the thermal conductivity of the soil structure and the rate of water diffusion within the soil structure, respectively. and These represent the matrix suction head during the simulation and in the initial state, respectively. T and T 0 These represent the temperatures during the simulation and in the initial state, respectively. This represents the heat flux through the atmosphere-soil interaction interface.

4. The numerical simulation method for hydrothermal coupling of expansive soil slopes according to claim 1, characterized in that, Meteorological data for the area where the expansive soil slope to be studied is located includes rainfall, air temperature, wind speed, solar radiation, and relative humidity.

5. The numerical simulation method for hydrothermal coupling of expansive soil slopes according to claim 1, characterized in that, The soil parameters of the area where the expansive soil slope to be studied are the soil-water characteristic curve, permeability coefficient, and thermal conductivity.

6. The numerical simulation method for hydrothermal coupling of expansive soil slopes according to claim 1, 4, or 5, characterized in that, The hydrothermal coupling model follows an energy balance at the atmosphere-soil interaction interface of the atmosphere and expansive soil slope, as shown in equation (1): （1） The hydrothermal coupling model follows mass conservation at the atmosphere-soil interaction interface of the atmosphere and expansive soil slope, as shown in equation (2): （2） in, R n Net radiative flux, G For soil heat flux, L E For latent heat flux, H For sensible heat flux; P For rainfall, I nf For infiltration flux, R off Soil surface runoff rate, E a This represents the actual water flux generated by evaporation. I nt For plant water interception flux; Will G and I nt As input boundary conditions for the hydrothermal coupling model.

7. The numerical simulation method for hydrothermal coupling of expansive soil slopes according to claim 6, characterized in that... In the above formula (1), ； ； ； ； ， ； ； ； The calculation is obtained by integrating the above formulas. G ,in, R si The solar radiation value was obtained through monitoring. R so Solar radiation on a sunny day. T a Let σ be the average temperature monitored every ten minutes, and let σ be the Stefan-Boltzmann constant. a c and b c These are empirical parameters related to the cloud. a 1 and b 1 It is an empirical parameter related to emissivity, where α is the soil surface reflectivity and the daily average saturated vapor pressure is... e d From daily average dew point temperature T d calculate; EL msl The elevation of the site above average sea level. R sa It is solar radiation from outside the Earth; and These are the solar time angles at the beginning and end of the considered period, respectively; L v The heat of vaporization of water, The thermal conductivity of air, The air temperature gradient at the atmosphere-soil interaction interface; In the above formula (2), P , I nt and R off Actual water evaporation was obtained through in-situ monitoring. E a The calculation is as follows: ； ； ； ； in, E a and E p These represent actual evaporation and potential evaporation, respectively. u For wind speed, h a Relative humidity, a and b These are empirical parameters; e 0 represents the vapor pressure at the soil surface. e s This is the saturated vapor pressure at the soil surface. e a It is the vapor pressure of air; T s and T a These are the soil surface temperature and the air temperature, respectively. For substrate suction head, W w It is the relative molecular mass of water. R It is the ideal gas constant.

8. The numerical simulation method for hydrothermal coupling of expansive soil slopes according to claim 1, characterized in that, The hydrothermal coupling model is established using FreeFem++ to create a finite element mesh and set initial conditions; the hydrothermal field distribution includes simulation results of soil temperature at different depths and simulation results of soil volumetric water content at different depths.

9. A numerical simulation device for hydrothermal coupling of expansive soil slopes, comprising a processor and a memory, characterized in that, The memory is used to store instructions, and the processor is used to execute the numerical simulation method for hydrothermal coupling of expansive soil slopes according to any one of claims 1 to 8.

10. A computationally readable storage medium comprising a computer program, characterized in that, When the computer program is executed by the processing terminal, the processing terminal performs the numerical simulation method for hydrothermal coupling of expansive soil slopes as described in any one of claims 1 to 8.

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