Inversion method and system for hydrothermal coupling and freezing depth of heterogeneous slope in cold region

Abstract

The embodiment of the invention discloses a cold region heterogeneous slope hydrothermal coupling and freezing depth inversion method and system, and the method comprises the steps: obtaining air temperature day-by-day change data of a research region, and carrying out the fitting of the air temperature day-by-day change data, and obtaining an air temperature day-by-day change equation; basic physical parameters of a soil body are determined, and a soil body parameter random field is constructed; constructing a numerical simulation model according to site information of a research area, determining a calculation method of a temperature field and a moisture field, and applying corresponding hydrothermal boundary conditions on the basis of the numerical simulation model to obtain a hydrothermal coupling numerical model; importing a soil parameter random field into the hydrothermal coupling numerical model, and establishing a random hydrothermal coupling model considering the soil parameter heterogeneity; and performing analog calculation on the random hydrothermal coupling model, outputting temperature and moisture change characteristics of the model at different time and positions, determining the freezing depth according to the temperature and moisture change characteristics, and performing statistical analysis on a calculation result. According to the method, the non-uniformity of soil parameters is considered, and the accuracy of predicting the freezing depth is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of cold region engineering, and in particular relates to an inversion method and system for water-heat coupling and freezing depth of non-homogeneous slopes in cold regions. Background Art

[0002] In recent years, infrastructure construction in cold regions has flourished. The freeze-thaw damage of infrastructure in cold regions is mainly caused by water and heat transfer in the soil, which leads to frost heave, thaw settlement, cracking and deterioration of mechanical properties of the soil, thus seriously shortening the service life of the infrastructure and posing a serious threat to the construction and operation safety of cold region projects. Freezing depth is one of the most important parameters for cold region engineering design. Freezing depth is a unique climate indicator in seasonally frozen soil areas, which depends not only on changes in air temperature, but also on soil moisture content and underground heat transfer. Accurate prediction of soil temperature and moisture distribution in cold regions is an important basis for cold region engineering design, and can provide a scientific basis for the safety and long-term stability of the project.

[0003] There are three common methods for determining freezing depth: field observation, analytical method and numerical calculation. Field observation is a way to directly obtain freezing depth data by deploying temperature measuring points or frozen soil observation instruments for monitoring. However, the harsh environmental conditions in cold regions, the high maintenance costs of long-term monitoring equipment and data transmission limit the field observation of soil hydrothermal characteristics and freezing depth. Analytical methods (such as the Stefan formula) predict freezing depth through simple calculations based on empirical formulas and thermal equilibrium assumptions. This method requires idealized assumptions about terrain conditions, soil properties and climatic factors, ignores the complex dynamic characteristics of the freezing process, and is difficult to accurately reflect the changing laws of frozen soil hydrothermal interactions. Numerical calculation is considered to be one of the most effective methods for studying freezing depth and frozen soil hydrothermal coupling processes. Due to the significant heterogeneity and spatial variability of soil in frozen areas, the soil is composed of gravel, sand, silt, clay and a mixture of different minerals, and has undergone complex geological deposition and weathering, resulting in significant spatial differences in parameters such as thermal conductivity, specific heat capacity and permeability.

[0004] However, most current value models regard soil parameters as fixed values, ignoring the heterogeneity of soil parameters, resulting in deviations in the prediction of freezing depth, leading to local freezing damage to infrastructure in cold regions. Therefore, it is necessary to establish a seasonal frozen soil water-heat coupling model that takes into account the heterogeneity of soil parameters, invert the water-heat coupling characteristics and freezing depth of seasonal frozen soil, calculate the statistical characteristics of soil temperature, water content and freezing depth, and provide effective theoretical support and technical guidance for the design of infrastructure in cold regions and frost damage management. Summary of the invention

[0005] One purpose of the present invention is to address the deficiencies of the prior art and provide an inversion method for hydrothermal coupling and freezing depth of non-homogeneous slopes in cold regions. The method can make up for the defect that the traditional hydrothermal coupling model regards soil parameters as constants, analyze the statistical characteristics of temperature and water content of seasonal frozen soil at different times and locations, calculate the change of freezing depth, and provide a certain reference for engineering design and frost damage control in cold regions.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A method for inversion of water-heat coupling and freezing depth of non-homogeneous slopes in cold regions comprises the following steps:

[0008] Step 1: Obtain the daily temperature variation data of the study area and fit it to obtain the daily temperature variation equation;

[0009] Step 2: Determine the basic physical parameters of the soil, perform statistical analysis on the basic physical parameters, and construct a random field of soil parameters;

[0010] Step 3: construct a numerical simulation model based on the site information of the study area, determine the calculation method of the temperature field and the moisture field, and apply corresponding hydrothermal boundary conditions to the numerical simulation model based on this to obtain a hydrothermal coupling numerical model;

[0011] Step 4: Import the random field of soil parameters into the hydrothermal coupling numerical model to establish a random hydrothermal coupling model that takes into account the non-uniformity of soil parameters;

[0012] Step 5: simulate and calculate the random water-heat coupling model, output the temperature and moisture variation characteristics of the model at different times and locations, determine the freezing depth accordingly, and perform statistical analysis on the calculation results.

[0013] Furthermore, the basic physical parameters of the soil in step 2 include density, water content, thermal conductivity, specific heat capacity, and saturated permeability of the soil.

[0014] Furthermore, in step 2, random fields are constructed for the thermal conductivity and specific heat capacity of the soil.

[0015] Furthermore, in step 2, the value ranges of thermal conductivity, specific heat capacity and permeability coefficient of the soil are obtained, and their statistical characteristics including correlation length, mean and standard deviation are determined. Considering the non-negativity of soil parameters, the log-normal distribution is used to construct the random field of soil parameters.

[0016] Furthermore, the calculation method of the temperature field in step 3 is:

[0017]

[0018] In the formula, C is the specific heat capacity of the soil, T is the temperature, t is the time, and v is w is the seepage velocity of liquid water in the soil, ρ w and ρ i denote the density of water and ice respectively, λ is the thermal conductivity of soil, c w is the specific heat capacity of water, L is the latent heat of water-ice phase change, θ i is the volumetric ice content.

[0019] Furthermore, the calculation method of the moisture field in step 3 is:

[0020]

[0021] In the formula, θ u is the volumetric unfrozen water content, θ i is the volumetric ice content, ρ w and ρ i denote the density of water and ice respectively, D is the water diffusion coefficient of the soil, k is the permeability coefficient of the soil, y represents the ordinate of the node, and S is the groundwater recharge;

[0022] When the temperature is lower than the freezing temperature of the soil, the θ u It maintains a dynamic equilibrium relationship with negative temperature, and the calculation method is:

[0023]

[0024] Where a1 and b1 are empirical parameters related to soil type, T f is the freezing temperature of the soil.

[0025] Furthermore, in step 3, the given temperature boundary conditions are: the bottom boundary of the model is a constant temperature boundary and a heat flux boundary, the upper boundary adopts the fitted daily temperature variation equation, and the left and right boundaries are insulation boundaries;

[0026] Moisture boundary conditions: The moisture content of the soil below the groundwater level remains constant, rainfall and evaporation are not considered, and the remaining boundaries are impermeable boundaries.

[0027] Another object of the present invention is to provide a system for realizing the above-mentioned cold region heterogeneous slope water-heat coupling and freezing depth inversion method, comprising:

[0028] The temperature simulation module is used to obtain the daily temperature variation data of the study area and fit it to obtain the daily temperature variation equation with the best fitting degree;

[0029] The soil parameter random field construction module is used to determine the basic physical parameters of the soil, perform statistical analysis on the basic physical parameters, and construct the soil parameter random field;

[0030] A hydrothermal coupling numerical model building module is used to build a numerical simulation model based on the site information of the study area, determine the calculation method of the temperature field and the moisture field, and based on this, apply corresponding hydrothermal boundary conditions to the numerical simulation model to obtain a hydrothermal coupling numerical model;

[0031] The random hydrothermal coupling model building module is used to import the random field of soil parameters into the hydrothermal coupling numerical model and establish a random hydrothermal coupling model that takes into account the non-uniformity of soil parameters;

[0032] The freezing depth calculation statistics module is used to simulate and calculate the random water-heat coupling model, output the temperature and moisture change characteristics of the model at different times and locations, determine the freezing depth based on this, and perform statistical analysis on the calculation results.

[0033] An electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method when executing the computer program.

[0034] A computer-readable storage medium stores a computer program, which implements the steps of the method when executed by a processor.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention takes into account the non-uniformity of soil parameters, performs statistical analysis on the basic physical parameters of the soil to construct a random field of soil parameters, and imports the random field of soil parameters into a hydrothermal coupling numerical model, establishes a random hydrothermal coupling model that takes into account the non-uniformity of soil parameters, and simulates and calculates the temperature and moisture of the soil, thereby improving the accuracy of the prediction of the freezing depth, making up for the defect that the traditional hydrothermal coupling model regards the soil parameters as constants, and can more accurately analyze the statistical characteristics of the temperature and moisture content of seasonal frozen soil at different times and locations, and calculate the changes in the freezing depth, providing a certain reference for engineering design and frost damage control in cold regions. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a flow chart of the inversion method of water-heat coupling and freezing depth of non-homogeneous slopes in cold regions involved in an embodiment of the present invention;

[0037] Figure 2 It is a fitting diagram of the daily average temperature monitoring data of the research area in the example of the present invention;

[0038] Figure 3 A random field distribution diagram of thermal conductivity of soil generated in an example of the present invention;

[0039] Figure 4 A random field distribution diagram of soil volume heat capacity generated in an example of the present invention;

[0040] Figure 5A diagram of a random hydrothermal coupling numerical model constructed in an example of the present invention;

[0041] Figure 6 The slope temperature field distribution diagram provided by the example of the present invention, wherein (a) is the slope temperature average value distribution diagram of 172d, and (b) is the slope temperature standard deviation distribution diagram of 172d;

[0042] Figure 7 The unfrozen water content distribution diagram of the slope volume provided by the example of the present invention, wherein (a) is the average value distribution diagram of the unfrozen water content at 172 days, and (b) is the standard deviation distribution diagram of the unfrozen water content at 172 days;

[0043] Figure 8 Maximum freezing depth distribution diagram provided for examples of the present invention. DETAILED DESCRIPTION

[0044] The technical solutions in the embodiments of the present invention will be described clearly and completely below in combination with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0045] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0046] The present invention will be further described below in conjunction with specific embodiments, but the present invention is not limited thereto.

[0047] The embodiment of the present invention discloses a method for inversion of water-heat coupling and freezing depth of non-homogeneous slopes in cold regions, such as Figure 1 As shown, the following steps are included:

[0048] Step 1: Obtain the daily temperature variation data of the study area, and fit it to obtain the daily temperature variation equation with the best fitting degree;

[0049] This example uses a road cutting slope in Yanji City, Jilin Province as the research subject, which is located in the seasonal frozen soil area of ​​Northeast China. The daily temperature change data of Yanji City from 2016 to 2019, including the highest temperature, the lowest temperature and the average temperature, are obtained from the China Meteorological Data Network. The daily average temperature change data from 2016 to 2019 are fitted to obtain the temperature change equation with the best fitting degree; Figure 2 As shown, the annual variation equation of the daily average temperature is: Goodness of fit R 2 It is 0.90, and the starting time is November 1st.

[0050] Step 2: Determine the basic physical parameters of the soil, perform statistical analysis on the basic physical parameters, and construct a random field of soil parameters;

[0051] In this embodiment, on-site sampling is carried out according to the "Code for Design of Building Foundations" (GB5007-2011) to classify the soil in the study area. According to geological survey data, the slope soil type studied is silty clay, and the initial groundwater level is 10m below the foot of the slope. The basic physical parameters of the soil are determined through existing literature and indoor tests, including the density, moisture content, thermal conductivity, specific heat, saturated permeability, soil-water characteristic curve, etc. of the soil; among them, the indoor test is carried out according to the "Standard for Geotechnical Test Methods" (GB / T50123-2019). The dry density of the soil finally obtained in this embodiment is about 1.57g / cm 3 The volume moisture content of the soil is about 34%, the average thermal conductivity of the soil is 2.0W / (mK), and the average specific heat capacity is 2160kJ / (m 3 K), and the saturated permeability coefficient is 6.4×10 -8 m / s.

[0052] The thermal conductivity and volume heat capacity of the soil were statistically analyzed, and the correlation length in the horizontal direction was determined to be 10m, the correlation length in the vertical direction was 1m, and the coefficient of variation was 0.25. The random fields of the thermal conductivity and specific heat capacity of the soil were constructed using log-normal distribution, such as Figure 3 and 4 shown.

[0053] Step 3: construct a numerical simulation model based on the site information of the study area, determine the calculation method of the temperature field and the moisture field, and apply corresponding hydrothermal boundary conditions to the numerical simulation model based on this to obtain a hydrothermal coupling numerical model;

[0054] The height of the slope in this embodiment is 16m, the width is 30m, the distance from the foot of the slope to the bottom is 8m (considering the maximum depth of the annual change in formation temperature, the distance from the bottom of the model to the ground is not less than 8m), and the slope ratio of the slope is 1:1. A numerical simulation model is constructed based on the above slope site information, and the numerical simulation model is meshed. When meshing, it is necessary to reasonably adjust the shape and size of the unit grid according to the numerical calculation effect.

[0055] The temperature field is calculated based on Fourier's heat transfer law, and the moisture field is calculated based on Richard's equation. In this embodiment, the heat conduction equation considering the water-ice phase change and heat convection is:

[0056]

[0057] In the formula, C is the specific heat capacity of the soil, T is the temperature, t is the time, and v is wis the seepage velocity of liquid water in the soil, ρ w and ρ i denote the density of water and ice respectively, λ is the thermal conductivity of soil, c w is the specific heat of water, and L is the latent heat of water-ice phase change.

[0058] The generalized water migration equation during soil freezing and thawing can be expressed by the Richard equation:

[0059]

[0060] In the formula, θ u is the volumetric unfrozen water content, θ i is the volume ice content, D is the water diffusion coefficient of the soil, k is the permeability coefficient of the soil, y represents the ordinate of the node, and S is the groundwater recharge.

[0061] When the temperature is lower than the freezing temperature of the soil, the θ u It maintains a dynamic equilibrium relationship with negative temperature, and the calculation method is:

[0062]

[0063] In this embodiment, a1 and b1 are set to 0.34 and 0.47 respectively, T f It is -0.3℃.

[0064] In this embodiment, the corresponding hydrothermal boundary conditions applied to the numerical simulation model are:

[0065] Temperature boundary conditions: The bottom boundary of the model is a constant temperature boundary of 8°C and a heat flux boundary of 0.02W / m 2 , the upper boundary adopts the fitted daily temperature variation equation; the left and right boundaries are insulation boundaries;

[0066] Moisture boundary conditions: The moisture content of the soil below the groundwater level remains constant, the initial volume moisture content of the soil is 34%, rainfall and evaporation are not considered, and the remaining boundaries are impermeable boundaries.

[0067] Step 4: Import the soil parameter random field into the hydrothermal coupling numerical model. In this embodiment, the thermal conductivity and specific heat capacity of the soil are regarded as random fields, and a random hydrothermal coupling model considering the non-uniformity of soil parameters is established. The random hydrothermal coupling model is as follows: Figure 5 As shown;

[0068] Step 5, simulate and calculate the random water-heat coupling model, output the temperature and water variation characteristics of the model at different times and locations, determine the freezing depth accordingly, and perform statistical analysis on the calculation results;

[0069] In this embodiment, the number of Monte Carlo simulations is first determined to be 200, and then the random hydrothermal coupling model is batch simulated and calculated 200 times. After that, the temperature and moisture content information at different positions and times are output, and the changes in soil temperature and moisture content are studied based on the statistical analysis method. The distance from the freezing temperature isotherm of -0.3°C to the ground is defined as the freezing depth. Figure 6 (a) The average value and (b) standard deviation of soil temperature at 172 days. At this time, the freezing period ends, and there is still a frozen soil interlayer inside the slope. The maximum standard deviation of soil temperature can reach 0.43℃. Figure 7 (a) The mean value and (b) standard deviation of the volume unfrozen water content at 172 days. When the freezing period ends, the maximum standard deviation of the unfrozen water content in the soil can reach 5%, which shows that ignoring the heterogeneity of soil parameters may lead to inaccurate prediction of soil hydrothermal properties. Figure 8 The red dotted line represents the deterministic analysis value. The maximum freezing depth is 2.05m, the minimum is 1.51m, and the standard deviation is 0.10m. The deterministic analysis result obtained by treating soil parameters as constants based on the existing technology is 1.70m, which underestimates the maximum freezing depth. Therefore, the design based on this will lead to freeze-thaw damage in cold region projects.

[0070] The embodiment of the present invention further provides a system for implementing the above-mentioned cold region heterogeneous slope water-heat coupling and freezing depth inversion method, comprising:

[0071] The temperature simulation module is used to obtain the daily temperature variation data of the study area and fit it to obtain the daily temperature variation equation with the best fitting degree;

[0072] The soil parameter random field construction module is used to determine the basic physical parameters of the soil, perform statistical analysis on the basic physical parameters, and construct the soil parameter random field;

[0073] A hydrothermal coupling numerical model building module is used to build a numerical simulation model based on the site information of the study area, determine the calculation method of the temperature field and the moisture field, and based on this, apply corresponding hydrothermal boundary conditions to the numerical simulation model to obtain a hydrothermal coupling numerical model;

[0074] The random hydrothermal coupling model building module is used to import the random field of soil parameters into the hydrothermal coupling numerical model and establish a random hydrothermal coupling model that takes into account the non-uniformity of soil parameters;

[0075] The freezing depth calculation statistics module is used to simulate and calculate the random water-heat coupling model, output the temperature and moisture change characteristics of the model at different times and locations, determine the freezing depth based on this, and perform statistical analysis on the calculation results.

[0076] In another embodiment, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method when executing the computer program.

[0077] In another embodiment, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method are implemented.

[0078] The above are only preferred embodiments of the present invention, and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the contents of the specification of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for inversion of water-heat coupling and freezing depth of non-homogeneous slopes in cold regions, characterized in that: The following steps are involved: Step 1: Obtain the daily temperature variation data of the study area and fit it to obtain the daily temperature variation equation; Step 2: Determine the basic physical parameters of the soil, perform statistical analysis on the basic physical parameters, and construct a random field of soil parameters; Step 3: construct a numerical simulation model based on the site information of the study area, determine the calculation method of the temperature field and the moisture field, and apply corresponding hydrothermal boundary conditions to the numerical simulation model based on this to obtain a hydrothermal coupling numerical model; Step 4: Import the random field of soil parameters into the hydrothermal coupling numerical model to establish a random hydrothermal coupling model that takes into account the non-uniformity of soil parameters; Step 5: simulate and calculate the random water-heat coupling model, output the temperature and moisture variation characteristics of the model at different times and locations, determine the freezing depth accordingly, and perform statistical analysis on the calculation results.

2. The inversion method for hydrothermal coupling and freezing depth of non-homogeneous slopes in cold regions according to claim 1 is characterized in that: The basic physical parameters of the soil in step 2 include the density, water content, thermal conductivity, specific heat capacity, and saturated permeability of the soil.

3. The inversion method for hydrothermal coupling and freezing depth of non-homogeneous slopes in cold regions according to claim 2 is characterized in that: In step 2, random fields are constructed for the thermal conductivity and specific heat capacity of the soil.

4. The inversion method for hydrothermal coupling and freezing depth of non-homogeneous slopes in cold regions according to claim 2 is characterized in that: In step 2, the value ranges of thermal conductivity, specific heat capacity, and permeability of the soil are obtained, and their statistical characteristics including correlation length, mean, and standard deviation are determined. Considering the non-negativity of soil parameters, the log-normal distribution is used to construct the random field of soil parameters.

5. The inversion method for hydrothermal coupling and freezing depth of non-homogeneous slopes in cold regions according to claim 1 is characterized in that: The calculation method of the temperature field in step 3 is: In the formula, C is the specific heat capacity of the soil, T is the temperature, t is the time, and v is w is the seepage velocity of liquid water in the soil, ρ w and ρ i denote the density of water and ice respectively, λ is the thermal conductivity of soil, c w is the specific heat capacity of water, L is the latent heat of water-ice phase change, θ i is the volumetric ice content.

6. The inversion method for hydrothermal coupling and freezing depth of non-homogeneous slopes in cold regions according to claim 1 is characterized in that: The calculation method of the moisture field in step 3 is: In the formula, θ u is the volumetric unfrozen water content, θ i is the volumetric ice content, ρ w is the density of water, ρ i is the density of ice, D is the water diffusion coefficient of the soil, k is the permeability coefficient of the soil, y represents the ordinate of the node, and S is the groundwater recharge; When the temperature is lower than the freezing temperature of the soil, the θ u It maintains a dynamic equilibrium relationship with negative temperature, and the calculation method is: Where a1 and b1 are empirical parameters related to soil type, T f is the freezing temperature of the soil.

7. The inversion method for hydrothermal coupling and freezing depth of non-homogeneous slopes in cold regions according to claim 1 is characterized in that: In step 3, the given temperature boundary conditions are: the bottom boundary of the model is a constant temperature boundary and a heat flux boundary, the upper boundary adopts the fitted daily temperature variation equation, and the left and right boundaries are insulation boundaries; Moisture boundary conditions: The moisture content of the soil below the groundwater level remains constant, rainfall and evaporation are not considered, and the remaining boundaries are impermeable boundaries.

8. A system for implementing the method for inversion of hydrothermal coupling and freezing depth of non-homogeneous slopes in cold regions as described in any one of claims 1 to 7, characterized in that: include: The temperature simulation module is used to obtain the daily temperature variation data of the study area and fit it to obtain the daily temperature variation equation with the best fitting degree; The soil parameter random field construction module is used to determine the basic physical parameters of the soil, perform statistical analysis on the basic physical parameters, and construct the soil parameter random field; A hydrothermal coupling numerical model building module is used to build a numerical simulation model based on the site information of the study area, determine the calculation method of the temperature field and the moisture field, and based on this, apply corresponding hydrothermal boundary conditions to the numerical simulation model to obtain a hydrothermal coupling numerical model; The random hydrothermal coupling model building module is used to import the random field of soil parameters into the hydrothermal coupling numerical model and establish a random hydrothermal coupling model that takes into account the non-uniformity of soil parameters; The freezing depth calculation statistics module is used to simulate and calculate the random water-heat coupling model, output the temperature and moisture change characteristics of the model at different times and locations, determine the freezing depth based on this, and perform statistical analysis on the calculation results.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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