Simulation method, device, equipment, medium and product for layout scheme of hot rods of frozen soil roadbed

Abstract

The invention discloses a frozen soil roadbed hot rod layout scheme simulation method, device, equipment, medium and product, and relates to the technical field of road construction, the method comprises the following steps: constructing a temperature field control equation and a moisture field control equation of a target frozen soil roadbed in a freezing and thawing cycle process; according to the temperature field control equation and the moisture field control equation, a frozen soil roadbed temperature field numerical model and a frozen soil roadbed moisture field numerical model used in COMSOLMultiphysics are constructed; the frozen soil roadbed temperature field numerical model and the frozen soil roadbed moisture field numerical model both comprise solid-to-liquid ratio functions; constructing a hot rod mathematical model based on the starting temperature condition of the hot rod; and according to the frozen soil roadbed temperature field, the moisture field numerical model and the hot rod mathematical model, roadbed temperature field prediction of a set time length is carried out on the target hot rod layout mode on the target frozen soil roadbed. The control precision of the hot rod on the frozen soil roadbed temperature can be improved, so that the prediction accuracy of the influence of hot rod arrangement on frozen soil is improved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of road construction, in particular to a frozen soil roadbed heat rod layout scheme simulation method, device, equipment, medium and product. BACKGROUND

[0002] For road construction in extremely cold regions, the study of roadbed temperature field is crucial. The establishment of a frozen soil roadbed numerical model alleviates the workload of long-term monitoring of the constructed road in engineering, and the roadbed temperature field can simulate the temperature distribution after the road has been in operation for several years. Many scholars have conducted detailed research on the roadbed temperature field. In 2016, Wang Shuangjie aimed to reveal the complex coupling heat transfer mechanism in the wide roadbed of the plateau region under the influence of the temperature of the atmosphere and soil, and carried out numerical research on the distribution characteristics of the temperature field in the frozen soil roadbed under typical working conditions and its variation with time. In 2017, Wang Weinan simulated the variation of the temperature field in the roadbed in the seasonal frozen soil region based on the mixed thermal boundary conditions of type II and type III, and analyzed the temperature difference between the shady and sunny slopes. Considering the position and shape of the freezing front, the frost heaving rate and thawing coefficient of the soil were introduced to study the development process of the deformation of the roadbed caused by the temperature difference between the shady and sunny slopes, and to reveal the failure mechanism of the roadbed. In 2019, Qi Zhigang aimed to solve the problem of roadbed frost damage, and used the ANSYS finite element analysis software to numerically simulate the temperature field of the low embankment, zero-section replacement roadbed and roadbed with different depths of heat preservation materials under the climate conditions of a certain regional high-speed rail, and analyzed the variation of the freezing depth of the roadbed and the maximum freezing depth. In 2020, Jiang Yunhua took a typical highway section in the plateau region as the research object, and used the first type of boundary condition and the combination of the second and third types of boundary condition to numerically calculate the temperature field of the frozen soil roadbed containing phase change, and analyzed the variation of the temperature field of the roadbed and the influence of different road surface types on the temperature field of the roadbed.

[0003] Most of the above existing technologies use passive heat rods, such as the heat rods used in the early stage of the plateau region railway, whose working principle mainly relies on natural temperature difference for heat transfer, and cannot flexibly adjust the refrigeration capacity according to actual demand, thereby leading to inaccurate simulation of the temperature field of the heat rod roadbed in extremely cold regions, affecting the accuracy of the layout of the frozen soil roadbed heat rod. SUMMARY

[0004] The purpose of the present application is to provide a frozen soil roadbed heat rod layout scheme simulation method, device, equipment, medium and product, which can improve the regulation and control accuracy of the heat rod on the temperature of the frozen soil roadbed, thereby improving the prediction accuracy of the influence of the heat rod layout on the frozen soil.

[0005] To achieve the above-mentioned purpose, the present application provides the following solutions:

[0006] In a first aspect, the application provides a frozen soil subgrade heat rod layout scheme simulation method, comprising:

[0007] constructing a temperature field control equation and a water field control equation of a target frozen soil subgrade during a freeze-thaw cycle process;

[0008] constructing a frozen soil subgrade temperature field numerical model and a frozen soil subgrade water field numerical model for COMSOL Multiphysics according to the temperature field control equation and the water field control equation; the frozen soil subgrade temperature field numerical model and the frozen soil subgrade water field numerical model both contain a solid-liquid ratio function;

[0009] constructing a heat rod mathematical model based on a starting temperature condition of the heat rod;

[0010] performing subgrade temperature field prediction of a target heat rod layout mode on the target frozen soil subgrade for a set time length according to the frozen soil subgrade temperature field numerical model, the frozen soil subgrade water field numerical model, and the heat rod mathematical model, to obtain a subgrade temperature field prediction result of the target heat rod layout mode within the set time length.

[0011] In a second aspect, the application provides a frozen soil subgrade heat rod layout scheme simulation device, comprising:

[0012] a control equation construction module configured to construct a temperature field control equation and a water field control equation of a target frozen soil subgrade during a freeze-thaw cycle process;

[0013] a numerical model construction module configured to construct a frozen soil subgrade temperature field numerical model and a frozen soil subgrade water field numerical model for COMSOL Multiphysics according to the temperature field control equation and the water field control equation; the frozen soil subgrade temperature field numerical model and the frozen soil subgrade water field numerical model both contain a solid-liquid ratio function;

[0014] a heat rod mathematical model construction module configured to construct a heat rod mathematical model based on a starting temperature condition of the heat rod;

[0015] a subgrade temperature field prediction module configured to perform subgrade temperature field prediction of a target heat rod layout mode on the target frozen soil subgrade for a set time length according to the frozen soil subgrade temperature field numerical model, the frozen soil subgrade water field numerical model, and the heat rod mathematical model, to obtain a subgrade temperature field prediction result of the target heat rod layout mode within the set time length.

[0016] In a third aspect, the application provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the frozen soil subgrade heat rod layout scheme simulation method according to any one of the above.

[0017] In a fourth aspect, the present application provides a computer readable storage medium, having stored thereon a computer program, which, when executed by a processor, implements the steps of the permafrost roadbed heat rod layout scheme simulation method according to any one of the preceding aspects.

[0018] In a fifth aspect, the present application provides a computer program product comprising a computer program which, when executed by a processor, implements the steps of the permafrost roadbed heat rod layout scheme simulation method according to any one of the preceding aspects.

[0019] According to the specific embodiments provided by the present application, the present application discloses the following technical effects: the present application provides a permafrost roadbed heat rod layout scheme simulation method, device, equipment, medium and product, a heat rod mathematical model is constructed based on the starting temperature condition of the heat rod, the refrigeration capacity of the heat rod is enhanced, and the "on-demand cooling" is realized. This temperature control mode can more accurately adjust the roadbed temperature, improves the regulation and control efficiency and precision of the heat rod on the permafrost roadbed temperature, thereby improving the prediction accuracy of the influence of heat rod layout on permafrost. BRIEF DESCRIPTION OF DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0021] Figure 1 A flowchart of a permafrost roadbed heat rod layout scheme simulation method provided by an embodiment of the present application.

[0022] Figure 2 A schematic diagram of the working principle of a heat rod provided by an embodiment of the present application.

[0023] Figure 3 A heat rod roadbed geometric model diagram provided by an embodiment of the present application.

[0024] Figure 4a A heat rod roadbed temperature field diagram on November 1 for a spacing of 2m and a burial depth of 7.6m.

[0025] Figure 4b A heat rod roadbed temperature field diagram on February 1 for a spacing of 2m and a burial depth of 7.6m.

[0026] Figure 5a A heat rod roadbed temperature field diagram on November 1 for a spacing of 2m and a burial depth of 9.1m.

[0027] Figure 5bTemperature field map for the heat rod embankment on February 1st for a spacing of 2 m and a burial depth of 9.1 m.

[0028] Figure 6a Temperature field map for the heat rod embankment on October 1st of the first year for a temperature field simulation.

[0029] Figure 6b Temperature field map for the heat rod embankment on December 1st of the first year for a temperature field simulation.

[0030] Figure 6c Temperature field map for the heat rod embankment on February 1st of the second year for a temperature field simulation.

[0031] Figure 6d Temperature field map for the heat rod embankment on April 1st of the second year for a temperature field simulation.

[0032] Figure 6e Temperature field map for the heat rod embankment on May 1st of the second year for a temperature field simulation.

[0033] Figure 6f Temperature field map for the heat rod embankment on August 1st of the second year for a temperature field simulation.

[0034] Figure 6g Temperature field map for the heat rod embankment on October 1st of the second year for a temperature field simulation.

[0035] Figure 6h Temperature field map for the heat rod embankment on November 1st of the second year for a temperature field simulation.

[0036] Figure 7a Temperature field map for the heat rod embankment on October 1st of the fourth year for a temperature field simulation.

[0037] Figure 7b Temperature field map for the heat rod embankment on December 1st of the fourth year for a temperature field simulation.

[0038] Figure 7c Temperature field map for the heat rod embankment on February 1st of the fifth year for a temperature field simulation.

[0039] Figure 7d Temperature field map for the heat rod embankment on March 1st of the fifth year for a temperature field simulation.

[0040] Figure 7e Temperature field map for the heat rod embankment on April 1st of the fifth year for a temperature field simulation. Figure 7f Temperature field map for the heat rod embankment on June 1st of the fifth year for a temperature field simulation.

[0041] Figure 7g Temperature field map for the heat rod embankment on July 1st of the fifth year for a temperature field simulation.

[0042] Figure 7hTemperature field for temperature field simulation of the temperature field of the hot rod subgrade on October 1, 2015.

[0043] Figure 8a Temperature field diagram for temperature field simulation of the temperature field of the hot rod subgrade of a certain road on October 1, 2015.

[0044] Figure 8b Temperature field diagram for temperature field simulation of the temperature field of the hot rod subgrade of a certain road on December 1, 2015.

[0045] Figure 8c Temperature field diagram for temperature field simulation of the temperature field of the hot rod subgrade of a certain road on February 1, 2016.

[0046] Figure 8d Temperature field diagram for temperature field simulation of the temperature field of the hot rod subgrade of a certain road on April 1, 2016.

[0047] Figure 8e Temperature field diagram for temperature field simulation of the temperature field of the hot rod subgrade of a certain road on May 1, 2016.

[0048] Figure 8f Temperature field diagram for temperature field simulation of the temperature field of the hot rod subgrade of a certain road on August 1, 2016.

[0049] Figure 8g Temperature field diagram for temperature field simulation of the temperature field of the hot rod subgrade of a certain road on October 1, 2016.

[0050] Figure 9 Functional module schematic diagram of a frozen soil subgrade hot rod layout scheme simulation device provided by an embodiment of the present application.

[0051] Figure 10 Functional module schematic diagram of a frozen soil subgrade hot rod layout scheme simulation device provided by another embodiment of the present application.

[0052] Figure 11 Structural schematic diagram of a computer device provided by an embodiment of the present application. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0054] The above purposes, features and advantages of the present application can be more obvious and easy to understand. The present application will be described in further detail below with reference to the drawings and specific embodiments.

[0055] In one exemplary embodiment, the present application provides a frozen soil subgrade heat rod layout scheme simulation method, as shown in the accompanying drawings, the frozen soil subgrade heat rod layout scheme simulation method comprises: Figure 1

[0056] Step 101: Construct the temperature field control equation and the moisture field control equation of the target frozen soil subgrade during the freeze-thaw cycle process.

[0057] Step 102: According to the temperature field control equation and the moisture field control equation, construct a frozen soil subgrade temperature field numerical model and a frozen soil subgrade moisture field numerical model for COMSOL Multiphysics; both the frozen soil subgrade temperature field numerical model and the frozen soil subgrade moisture field numerical model contain a solid-liquid ratio function.

[0058] Step 103: Construct a heat rod mathematical model based on the starting temperature condition of the heat rod.

[0059] Step 104: According to the frozen soil subgrade temperature field numerical model, the frozen soil subgrade moisture field numerical model and the heat rod mathematical model, predict the subgrade temperature field for a set time length for the target heat rod layout mode on the target frozen soil subgrade, and obtain the subgrade temperature field prediction result of the target heat rod layout mode within the set time length.

[0060] The relationship between the influencing factors of road thawing settlement in extremely cold regions is complex, and it is impossible to study the thawing settlement during the long-term service of the road. Therefore, studying the internal temperature field of frozen soil through numerical simulation has become a way to study the thawing disease of frozen soil subgrade. The temperature and moisture changes of frozen soil are very complex. With the rise of external air temperature, the internal temperature of frozen soil subgrade changes, and the changes of internal temperature and moisture of frozen soil subgrade belong to the numerical simulation problem of heat-water coupling. For the frozen soil subgrade which is easily disturbed by external factors, numerical simulation research can better solve and analyze the problem of heat-water coupling of subgrade temperature field. By analyzing the temperature and moisture change law of the internal frozen soil of the subgrade, a theoretical basis and design method for studying the characteristics of roads in extremely cold regions are provided.

[0061] Firstly, the present application analyzes the temperature field and moisture field during the freeze-thaw cycle process in extremely cold regions, and constructs a heat-water coupling model suitable for the temperature field of frozen soil subgrade in extremely cold regions by using COMSOL Multiphysics finite element software for secondary development.

[0062] In one exemplary embodiment, the step 101 analysis module analyzes the temperature field and moisture field to obtain the physical equation during the freeze-thaw cycle process in extremely cold regions, i.e. the temperature field control equation and the moisture field control equation.

[0063] ​The temperature field control equation is specifically: the frozen soil in extremely cold regions is extremely sensitive to the change of external temperature, and the change of the internal soil temperature of the frozen soil subgrade is the key to the study of the frost heaving and thawing settlement of the frozen soil subgrade. The change of the soil temperature field is the result of the freezing and thawing phase change of the soil, and only the problem of heat conduction and ice-water phase change in the internal frozen soil subgrade in extremely cold regions is considered at present. First of all, the two-dimensional differential equation of unsteady heat conduction, i.e. the temperature field control equation, is established, as shown in formula (1).

[0064]

[0065] Wherein, ρ is the density of the soil, kg / m 3 ; C(θ) is the specific heat capacity, J / (kg·℃); T is the temperature, ℃; t is the time, d; λ(θ) is the thermal conductivity, W / (m·℃); ▽ is the gradient operator; L is the latent heat of phase change, taking 334.5 kJ / kg; ρ i is the density of ice, kg / m 3 ; θ i is the frozen water volume content, and θ represents the water content;

[0066] The internal frozen soil of the subgrade in extremely cold regions is inevitably related to the change of water in the freezing and thawing process, and the distribution of the internal water of the subgrade is also an important factor reflecting the deformation of the subgrade thawing settlement. The ice-water phase change term is added to obtain the water field equation Richards equation in the frozen soil subgrade, i.e. the water field control equation, as shown in formula (2).

[0067]

[0068] Wherein, θ u is the unfrozen water volume content, ρ w represents the density of water, D(θ u ) represents the diffusion rate of the internal water of the frozen soil, and k(θ u ) represents the permeability of the soil, m / s.

[0069] In an exemplary embodiment, the diffusion rate of the internal water of the frozen soil is represented as:

[0070]

[0071] Wherein, I is the impedance factor, and the essence of I is to describe the degree of the hindering of ice to water, o(θ u ) is the specific water capacity, 1 / m;

[0072]

[0073] Wherein, θ i is the frozen water volume content.

[0074] k(θ u )=ks ·S 0.5 (1-(1-S 1 / m ) m ) 2 (5)

[0075] o(θ u )=a0m / (1-m)(θ s -θ r )·S 1 / m (1-S 1 / m ) m (6)

[0076] wherein k s is the permeability coefficient of soil, m / s; S represents the relative saturation of soil, θ s is the saturated volumetric water content of soil, θ r is the residual volumetric water content of soil, a0 and m are both related parameters varying with soil quality, a0 and m are both constants, m = 0.5, and a0 = 2.

[0077] The relative saturation S of frozen soil is selected as the independent variable of the moisture field in the present application, and the Van Genuehten (VG) model is used for conversion between unfrozen water and relative saturation, as shown in equation (7).

[0078]

[0079] wherein θ u is the unfrozen water volume content.

[0080] The calculation of the temperature field and water coupling model of the frozen soil subgrade needs to clarify the coupling relationship between each field. In the present application, the temperature field and the moisture field are coupled, mainly considering the change of the frozen water content caused by temperature change. When the atmospheric temperature outside the subgrade rises, the ice content and water content inside the subgrade change, and the thermal conductivity and specific heat capacity of the soil also change with the different ice content and water content of the soil. In comparison, the thermal conductivity of the soil with a larger ice content is larger, and the internal temperature field of the subgrade is also different. The solid-liquid ratio B i as a coupling bridge, the solid-liquid ratio is essentially the ratio of ice to water in the soil, which expresses the relationship between ice and water during freeze-thaw cycle, and the solid-liquid ratio function expression is shown in equation (8):

[0081]

[0082] T f is the temperature at which the soil can freeze, and B is a constant.

[0083] The heat rod is a sealed steel tube filled with nitrogen inside, the upper part of which is a condensation section. When the external environment temperature is lower than the internal temperature of the subgrade, the air in the tube condenses into water at the condensation end due to the low temperature and falls back to the bottom of the sealed steel tube, which is an evaporation section and is buried in the frozen soil subgrade. The liquid nitrogen inside the sealed steel tube absorbs the temperature inside the subgrade and releases heat to the condensation section in the form of vapor. Under the condition of low temperature in winter, there is a higher temperature difference between the subgrade interior and the atmosphere. The heat rod can guide the heat inside the subgrade from bottom to top to the atmosphere in a physical way, thereby reducing the temperature inside the subgrade and raising the upper limit of frozen soil, and further effectively protecting the frozen soil subgrade and avoiding the occurrence of thawing settlement. The working principle of the heat rod is shown in Figure 2

[0084] The heat rod subgrade temperature field model is constructed based on the frozen soil subgrade temperature field model. Since the heat rod only serves as a heat exchanger and its volume is much smaller than that of the frozen soil subgrade, the heat rod is simplified as a linear heat source to reduce the temperature inside the subgrade. During the operation of the heat rod, the evaporation section continuously absorbs the heat Q of the surrounding soil and transfers the heat to the condensation section through the working medium. Ignoring the thermal resistance of the heat rod itself and the contact thermal resistance between the evaporation section and the soil, the mathematical model of the heat rod is represented by formula (9).

[0085] Q = a · ΔT = a · (T a -T b ) (9)

[0086] Wherein, Q is the heat transfer amount of the heat rod, a is the equivalent heat transfer coefficient of the heat rod, ΔT is the temperature difference between the two ends of the heat rod, T a is the temperature of the soil around the evaporation section, and T b is the external environment temperature of the subgrade.

[0087] The starting temperature difference of the heat rod is set to 0.8℃. When the temperature difference between the internal temperature of the subgrade and the external temperature is 0.8℃, the heat rod starts to start, and the heat rod starting criterion is shown in formula (10).

[0088]

[0089] In this example, the soil sample used for COMSOL Multiphysics (COMSOL for short) simulation is the undisturbed soil of a certain highway construction. According to the soil test specification, the soil is tested, and the various parameters of the soil are measured as shown in Table 1.

[0090] Table 1 Various parameters of soil

[0091]

[0092]

[0093] ​According to the parameters measured by the geotechnical experiment, input into COMSOL, through the solid-liquid ratio Bi as the intermediate variable, according to the Dirichlet boundary condition in the temperature field, limit the temperature change of the subgrade. The relationship between the saturation and the temperature of the subgrade soil under the condition of temperature change is established, the coefficient type differential equation of the partial differential equation (PDE) interface is established, and the model of the temperature field and the moisture field of the subgrade under the condition of freezing and thawing is established. The change of the temperature and moisture of the subgrade with time is simulated.

[0094] In an exemplary embodiment, the present application is based on the COMSOL Multiphysics finite element analysis platform, through the secondary development of its PDE interface, the coefficient type partial differential equation model (frozen soil subgrade temperature field numerical model and frozen soil subgrade moisture field numerical model) of the coupling of temperature field and moisture field is innovatively constructed. The coefficient type partial differential equation model breaks through the functional limitations of the traditional solid-liquid heat transfer module, successfully realizes the efficient and accurate numerical simulation of the complex heat-water coupled heat transfer process, and significantly improves the solving accuracy and calculation efficiency of the multi-physical field coupling problem.

[0095] The PDE module of COMSOL is used for secondary development to establish the frozen soil subgrade temperature field numerical model and the frozen soil subgrade moisture field numerical model.

[0096] To study the temperature distribution law of frozen soil subgrade, the temperature of frozen soil and the problem of ice melting into water need to be considered, and a heat-water coupled numerical model needs to be established. COMSOL Multiphysics software is used as a platform for model construction, which is a numerical software specially designed for multi-field physical coupling simulation. According to the needs, the coupling simulation analysis of multiple physical fields can be carried out, and the temperature field and moisture field coupling research can be carried out in COMSOL Multiphysics using the user-defined partial differential equation.

[0097] COMSOL has three built-in user-defined partial differential equation forms: coefficient type partial differential equation, generalized type partial differential equation and weak solution type partial differential equation. Among them, the coefficient type (PDE) can import and use many commonly used equations by transforming the coefficients in the equation into an interface. The PDE module is used for secondary development to establish the frozen soil subgrade temperature field numerical model.

[0098] Frozen soil subgrade temperature field numerical model: according to the indoor experiment and the field monitoring scheme, the temperature field numerical simulation is carried out. The temperature field change law and the subgrade thawing depth under different heat rod burial depths are studied. The heat-water coupled model calculation is made under the following assumptions (1)-(4):

[0099] (1) The soil in this model is regarded as a homogeneous and continuous medium;

[0100] (2) not considering the self-weight load of soil, the effect of external load on soil;

[0101] (3) not considering the air in soil, considering only liquid water and ice in soil;

[0102] (4) not considering the change of soil caused by water evaporation due to temperature.

[0103] The PDE expression in the PDE module of COMSOL is shown in formula (11).

[0104]

[0105] Wherein, u is the input variable, e a is the mass coefficient, d a is the retardation coefficient, c is the diffusion coefficient, α is the absorption coefficient, and f is the source term.

[0106] The coefficient partial differential equation is selected as the original model of the temperature field and moisture field of the model; the partial differential equation form of the temperature field in COMSOL is formula (12):

[0107]

[0108] The temperature field control equation of formula (12) is transformed into the coefficient partial differential equation form that can be used in COMSOL software, as shown in formula (13):

[0109]

[0110] The calculation shows that the heat transfer physical equation of the frozen soil temperature field in COMSOL, that is, the numerical model of the frozen soil subgrade temperature field is formula (14):

[0111]

[0112] Wherein, ρ is the density of soil, C(θ) is the heat capacity, T is the temperature, t is the time, λ(θ) is the thermal conductivity, ∇ is the gradient operator, L is the latent heat of phase change, ρ i is the density of ice, θ s is the saturated volumetric moisture content of soil, θ r is the residual volumetric moisture content of soil, S represents the relative saturation of soil, and B(T) is the solid-liquid ratio function.

[0113] By comparing the partial differential equation form of formula (12) with the heat transfer physical equation of the frozen soil temperature field of formula (14), the parameters are obtained as shown in formula (15):

[0114]

[0115] Through comparison, e a , α, β and γ are all 0.

[0116] The partial differential equation form of the moisture field in COMSOL is:

[0117]

[0118] The moisture field control equation of formula (16) is transformed into the coefficient partial differential equation form that can be used in COMSOL software, as formula (17):

[0119]

[0120] It is calculated that the moisture field physical equation of frozen soil in COMSOL, that is, the moisture field numerical model of frozen soil subgrade is:

[0121]

[0122] Wherein, D(S) represents the diffusion coefficient, k(S) represents the permeability coefficient, and D(S) and k(S) are functions related to the saturation S.

[0123] By comparing the partial differential equation form of formula (16) with the heat transfer physical equation of the frozen soil temperature field of formula (18), parameters such as formula (19) can be obtained:

[0124]

[0125] Through comparison, e a , alpha, beta and f are all 0.

[0126] The application builds a hydrothermal coupling model through software, and is suitable for a hydrothermal coupling model of a temperature field of a frozen soil subgrade in extreme cold.

[0127] The hydrothermal coupling model is a module of the hydrothermal coupling model of the temperature field of the frozen soil subgrade. The hydrothermal coupling model is a model of the coupling of the moisture field and the temperature field, and the hydrothermal coupling model comprises a numerical model of a temperature field of a frozen soil subgrade and a numerical model of a moisture field of a frozen soil subgrade.

[0128] The application inputs the coefficients in the secondary development partial differential (the numerical model of the temperature field of the frozen soil subgrade and the numerical model of the moisture field of the frozen soil subgrade) and the heat rod heat transfer equation (the mathematical model of the heat rod) into COMSOL by establishing a PDE module and a solid heat transfer module in COMSOL.

[0129] In one exemplary embodiment, the roadbed temperature field prediction of the target heat rod layout mode on the target frozen soil roadbed for a set time length is performed according to the frozen soil roadbed temperature field numerical model, the frozen soil roadbed moisture field numerical model and the heat rod mathematical model, and specifically includes: based on the roadbed cross-section boundary temperature condition, the roadbed temperature field prediction of the target heat rod layout mode on the target frozen soil roadbed for a set time length is performed according to the frozen soil roadbed temperature field numerical model, the frozen soil roadbed moisture field numerical model and the heat rod mathematical model.

[0130] Regarding the determination of the boundary condition, specifically includes: according to the annual temperature measurement temperature of a certain road in the research area, considering the heat absorption of the pavement, the slope and the natural ground, the boundary temperature function of the heat rod roadbed geometric model can be represented by the following trigonometric function.

[0131]

[0132] Wherein, T(t) is the daily average temperature in the Ken River area, t=0, 1, 2,... (temperature measurement is started from October 1, t=0, October 2, t=1); T0 is the annual average temperature value in the Ken River area, -2.6℃; ΔT is the temperature increment of the roadbed upper boundary, slope surface and natural ground, respectively taking 5℃, 2.5℃ and 2℃ as the temperature increment; A is the annual temperature amplitude, taking 24.3. According to the measurement results and the analysis of the meteorological temperature in the Ken River area in the literature, the initial annual average temperature in the area is -2.6℃. The roadbed cross-section boundary temperature condition is shown in formula (21) to formula (23):

[0133]

[0134] Wherein, T1 is the pavement temperature, T2 is the roadbed slope temperature, and T3 is the ground temperature.

[0135] Formula (21) is the pavement boundary condition, and formula (22) to formula (23) are the roadbed slope temperature condition and the original natural ground temperature condition, respectively. The condensation section temperature T4 of the heat rod changes with the actual temperature of the highway, as shown in formula (24). The evaporation section temperature adopts the average temperature of the soil body, and the heat rod is started when the internal temperature of the frozen soil roadbed is 0.8℃ higher than the external temperature.

[0136]

[0137] When the natural surface on both sides of the roadbed is wide enough, the boundary on the right side of the heat rod roadbed geometric model can be considered as a "zero flux boundary". The lower boundary of the heat rod roadbed geometric model is the natural bedrock, and the influence of the external climate on the temperature change is ignored, and the soil body temperature is affected by the heat from the deep stratum, and a constant flux boundary condition 0.03W / m 2 .

[0138] In an exemplary embodiment, based on COMSOL Multiphysics numerical simulation platform, the roadbed temperature field with a heat rod spacing of 2 m is analyzed systematically. By establishing a verification module, the field measured data is compared and verified with the numerical simulation results, and the results show that they have good consistency, thereby confirming the accuracy and reliability of the parameter settings of the model built in the application. The verification process provides a reliable theoretical basis and technical support for the subsequent simulation of roadbed temperature field under complex working conditions.

[0139] In an exemplary embodiment, through simulation analysis and field monitoring data analysis using indoor heat rod simulation experiment, the best embedding mode of the heat rod is symmetric arrangement, spacing of 2 m, oblique insertion of 75°, and embedding depth of 6.6 m. The time length is set to 5 years, and COMSOL Multiphysics is used to simulate and analyze the roadbed temperature field under this embedding mode, and to predict the roadbed temperature field in the next 5 years.

[0140] The numerical model of the frozen soil roadbed temperature field, the numerical model of the frozen soil roadbed moisture field, the heat transfer equation of the heat rod, and the boundary conditions are input into COMSOL, and the roadbed temperature field is simulated according to the embedding mode of the heat rod.

[0141] In COMSOL, the heat rod spacing is set to 2 m, the oblique insertion is 75°, and the embedding depth is 6.6 m. The data is not from the actual test section, but from the best layout scheme of the heat rod determined by the indoor test.

[0142] S1 parameter and variable input.

[0143] Through field sampling, the soil base parameters and roadbed parameters are measured in the laboratory and input into the COMSOL globally defined module. The parameters in the numerical model of the frozen soil roadbed temperature field and the numerical model of the frozen soil roadbed moisture field are shown in Table 1.

[0144] S2 Establish the heat rod roadbed geometric model.

[0145] To protect the stability of the frozen soil roadbed and reduce the internal temperature of the frozen soil roadbed, the evaporation section of the heat rod is buried 5 m deep below the frozen soil roadbed. The total length of the heat rod is set to 9.6 m and 11.1 m, respectively, of which the evaporation section is 2 m long, the adiabatic section is 2 m long, and the condensation section is 5.6 m and 7.1 m long.

[0146] S3 Water and heat coupled model establishment.

[0147] In COMSOL, PDE module and solid heat transfer module are established, and the coefficients in the coefficient partial differential in the secondary development and the heat transfer equation of the heat rod are input into COMSOL.

[0148] S4 Establish boundary conditions and mesh division.

[0149] The pavement temperature, subgrade temperature and slope temperature are inputted in the boundary conditions respectively, and the three temperature functions vary with time. The three temperature functions are known and are obtained according to the local climate change data. When analyzing the temperature field of the hot rod subgrade, fixed constraint boundaries are added to the two sides of the subgrade to avoid transverse contraction and expansion of the subgrade during the ice-water phase change. When establishing the temperature field model of the hot rod subgrade, the pavement temperature change needs to be calculated by fitting the actual temperature. Since the temperature fluctuates dynamically throughout the year, but generally presents a sinusoidal function, when the temperature rises year by year, the second boundary condition should be added to the third boundary condition to make the temperature change in a sinusoidal wave while maintaining a linear temperature rise. The grid is divided into free triangular grids. The complete grid contains 1613 domain units and 211 boundary units.

[0150] S5 research settings and result output.

[0151] The research is a transient study, and the output time step is 1825 days. The two-dimensional drawing group of the temperature field and the moisture field is added in the results, and the two-dimensional cloud chart of the temperature field and the moisture field is output.

[0152] In an exemplary embodiment, (1) the hot rod subgrade geometric model establishment includes: to protect the stability of the frozen soil subgrade and reduce the internal temperature of the frozen soil subgrade, the evaporation section of the hot rod is buried 5m deep below the frozen soil subgrade. The total length of the hot rod is set to 9.6m and 11.1m, respectively, wherein the evaporation section is 2m long, the adiabatic section is 2m long, and the condensation section is 5.6m and 7.1m long. The model size of the frozen soil subgrade is the same as 4.2, and the hot rod subgrade geometric model and the grid division are as shown in Figure 3 . The complete grid contains 1613 domain units and 211 boundary units. The hot rod is added to the frozen soil subgrade model to simulate the temperature field of the hot rod subgrade and study the influence of the hot rod arrangement interval, burial depth and other methods on the temperature field of the subgrade. The more the grid division of the hot rod subgrade geometric model, the greater the calculation amount, and the higher the accuracy.

[0153] (2) hot rod subgrade geometric model and verification: to verify the accuracy of the hot rod subgrade geometric model, the COMSOL Multiphysics is used to simulate the subgrade temperature field of the 2m interval subgrade in this application, and the model parameters are verified by comparing the field monitoring data with the simulation data to improve the accuracy of the subsequent analysis of the best burial method of the hot rod.

[0154] Hot rod subgrade temperature field analysis with a burial depth of 7.6m: according to the working principle of the hot rod, the hot rod starts to work after entering the cold season. In this case, the subgrade temperature field after one month of work of the hot rod and the hot rod subgrade temperature field under extremely low temperature are simulated. The subgrade temperature in November and the subgrade temperature field in February are as shown in Figure 4a and Figure 4b . Through Figure 4aIn November, the temperature of the road decreases with the air temperature, and the temperature of the road surface is higher than that of the slope and the ground due to the thermal effect of the vehicle. The temperature gradually transfers from the road surface to the lower part. The temperature of the subgrade on the side without the heat rod decreases more slowly than that on the side with the heat rod, but the heat rod has less effect on the surrounding temperature. As the temperature continues to decrease, in February of the following year, the air temperature reaches the lowest, and the temperature of the deep soil body begins to gradually decrease. The temperature of the slope and the road surface on both sides decreases to the lowest, and the temperature of the deep soil body gradually decreases. Compared with the side without the heat rod, the temperature of the soil body around the heat rod is much lower than that on the symmetric side.

[0155] According to Table 2, the monitored temperature in November is similar to the simulated temperature, and the temperature at the heat rod in February is higher than the monitored value. The simulated temperature at 1 m and 3 m from the heat rod is lower than the monitored temperature.

[0156] Table 2: Monitored temperature and simulated temperature of heat rod buried 7.6 m

[0157]

[0158] As shown in Figure 5a and Figure 5b , the temperature field analysis of the heat rod buried 9.1 m: by Figure 4b and Figure 5b , the overall temperature of the soil body does not decrease significantly, and the overall temperature of the subgrade at the two locations is not much different. According to Table 3, the simulated temperature at 3 m from the heat rod and 4.6 m deep is lower than the monitored temperature. Due to the failure to consider the effect of vehicle heat on the center lane in February, the actual temperature of the soil body is slightly higher than the simulated temperature. The lowest actual air temperature at the heat rod is about -40℃, and the simulated air temperature is -32℃, resulting in a slightly lower temperature around the heat rod than the monitored temperature. In November, the actual air temperature is not much different from the simulated temperature, and the simulated temperature around the heat rod is not much different from the monitored temperature, which is accurate.

[0159] Table 3: Monitored temperature and simulated temperature of heat rod buried 9.1 m

[0160]

[0161] (3) Subgrade temperature field simulation analysis of the best layout of heat rod.

[0162] Through indoor heat rod simulation experiment and analysis of field monitoring data, the best layout of heat rod is symmetric arrangement with a spacing of 2 m, an inclined insertion of 75°, and a buried depth of 6.6 m. COMSOL Multiphysics is used to simulate and analyze the temperature field of the subgrade with this layout, and to predict the temperature field of the subgrade in the next 5 years.

[0163] 1) One-year temperature field simulation of inclined heat rod

[0164] FromFigure 6a- Figure 6h In contrast, after entering October, the temperature dropped, and the heat rod began to work. The road surface was affected by the heat absorption of asphalt and the heat effect of vehicle driving, and the temperature of the road surface was higher than that of the slope and the ground. As the temperature dropped, the temperature inside the subgrade changed with the temperature, and the temperature of the shallow layer of the subgrade first dropped, and as the temperature gradually dropped, the deep layer of the subgrade soil gradually dropped. The temperature around the heat rod first dropped, and after December, the temperature dropped sharply, the heat exchange power of the heat rod increased, and the temperature inside the soil body dropped. In April, the temperature rose, the daytime temperature was above 0°C, and the nighttime temperature dropped to below 0°C, and the heat rod continued to work. After entering May, the temperature rose, the heat rod stopped working, and the soil body reached the maximum frost heaving amount, and at this time the frost table was 2m. After entering the warm season, the temperature of the subgrade gradually rose with the temperature, and in July the temperature rose to the highest. Due to the heat resistance of the subgrade, the temperature of the soil body rose from top to bottom. After October, the temperature dropped to below 0°C, but the temperature of the road surface was higher, and at this time a soil melting core appeared inside the subgrade. In early November, the temperature of the road surface dropped to the freezing temperature, and the soil gradually melted, and at this time the maximum melting depth was about 3.01m. Subsequently, the temperature of the upper part of the subgrade dropped to negative temperature, and the external negative temperature continued to transfer to the inside, and the frozen soil subgrade formed the previous state of low temperature in the upper part and high temperature in the lower part.

[0165] 2) Temperature field of heat rod subgrade after 5 years

[0166] As Figure 7a- Figure 7h , the temperature field of the heat rod subgrade after five years and the initial subgrade temperature field had basically the same change trend. In March, the overall temperature of the subgrade dropped to the lowest, the frost table was 20cm, and the subgrade storage capacity reached the maximum. Subsequently, the temperature gradually rose, the heat rod stopped working, and the subgrade soil gradually melted from top to bottom. In October, the temperature dropped to below 0°C, the temperature difference between the subgrade and the atmosphere was too large, and the heat rod started to work. In October of the fourth year, the maximum melting depth of the subgrade was 2.76m, and in the fifth year the melting depth of the heat rod subgrade reached the maximum of 2.68m, which was 53cm lower than that of the first year heat rod subgrade. The heat rod increased the storage capacity of the subgrade every year, and in the warm season the temperature dropped slowly, reducing the melting of the subgrade.

[0167] Based on a certain highway, indoor heat rod simulation experiment, field monitoring and finite element simulation, the temperature field of the heat rod subgrade in extremely cold regions was compared and analyzed, and the following conclusions were drawn:

[0168] (1) Through the indoor thermal rod subgrade simulation experiment, through the analysis of different heat source burial depth, different spacing and different angle factors, it is found that in the case of shallow burial depth, the bottom soil temperature rises fastest, the center soil temperature drops slowly; in the case of 40 cm burial depth, the bottom soil temperature rises slowly, the temperature rise speed of 30 cm and 15 cm soil layer is basically unchanged. The effective radius of heat source is less than 40 cm, the temperature rise speed of 10 cm interval heat source and 20 cm interval heat source is similar, the temperature rise speed of 40 cm interval heat source is the fastest. The heat source is inserted at an angle of 75°, the temperature of the middle soil body drops more significantly, and the temperature of the bottom soil body on both sides rises slightly.

[0169] (2) The experimental road is a strong melting and sinking section. The thermal rod starts working in October, the power gradually increases in November, the power of the thermal rod reaches the maximum in December, and the temperature around the thermal rod is about -20℃. The temperature change trend of 1m and 3m longitudinal section in the transverse direction of the thermal rod is the same, and the temperature of 1m interval section is lower. The lowest temperature of the upper soil body can reach -9℃. At a distance of 3m from the thermal rod, the upper soil body melts in the warm season, the soil temperature begins to drop in December, and the temperature is the lowest in March, but it only drops to the freezing temperature, and the lower soil body temperature changes little. The center temperature of 4m interval and 3m interval is higher than that of 2m interval, and the soil body of 2m interval has more cold storage, which can reduce the melting and sinking deformation in the warm season.

[0170] (3) Based on the PDE module of COMSOL Multiphysics finite element software, the model of thermal rod subgrade with burial depth of 6.6m and 8.1m is established. After verifying the accuracy of the model through field monitoring data and simulation data, the model of thermal rod subgrade with burial depth of 6.6m and 2m interval is established to study the temperature field of subgrade in the first year and the fifth year. It is found that the upper limit of frozen soil moves up obviously, and the cold storage of subgrade increases.

[0171] The application breaks through the active temperature control technology, reveals the multi-field coupling mechanism, and perfects the engineering verification system, and constructs a systematic solution for the layout of thermal rod in frozen soil subgrade. In terms of active temperature control technology, the cooperation of refrigeration unit and thermal rod realizes the accurate control of subgrade temperature; in the research of multi-field coupling mechanism, the interaction relationship among temperature field, moisture field, thermal rod heat transfer and frost heaving deformation is analyzed in depth, which provides a more scientific theoretical basis for the layout of thermal rod; at the same time, a perfect engineering verification system is established, which verifies and optimizes the layout scheme of thermal rod through the combination of indoor simulation experiment, field monitoring and finite element simulation. This systematic solution integrates many key technologies, solves the common problems of frozen soil engineering such as "dynamic regulation and control difficulty, low simulation accuracy and poor optimization efficiency", provides a replicable technical paradigm for global cold region infrastructure construction, and fills the gap in the systematic solution of the layout of thermal rod in frozen soil subgrade.

[0172] When the temperature of the roadbed is too high, the refrigeration unit is started to enhance the refrigeration capacity of the heat rod, and to realize "on-demand cooling". This innovative temperature control method can more accurately regulate the temperature of the roadbed, improve the regulation efficiency and accuracy of the heat rod on the temperature of the frozen soil roadbed, and make up for the lack of flexibility in temperature regulation of the traditional passive heat rod.

[0173] The temperature field, water migration and frost heaving deformation of the frozen soil roadbed interact complexly, and existing researches mostly focus on single factor analysis. The present application constructs a multi-physical field coupling model of frozen soil water and heat migration, heat rod heat transfer and frost heaving deformation, and combines with the measured data of the highway to realize the accurate prediction of the influence of heat rod layout on frozen soil multi-field for the first time, providing a scientific basis for engineering design. The traditional heat rod layout relies on experience design, and there are problems of "over-conservatism" or "insufficient safety redundancy". The present application establishes an optimization method of heat rod structure parameters (condensation section height, evaporation section length) and layout spacing through energy balance constraint, reduces the engineering cost while ensuring the stability of the frozen soil, and solves the long-existing contradiction of "technically reliable but economically unfeasible".

[0174] The present application studies the temperature field distribution law of the heat rod roadbed in extremely cold regions, determines the best layout parameters through indoor heat rod roadbed simulation experiment, field monitoring and COMSOL Multiphysics finite element software simulation of the first year and the fifth year heat rod roadbed temperature field. However, the following aspects can be further studied:

[0175] (1) The present application studies the temperature field experiment of silty clay with a water content of 27% through indoor simulation experiment, and the subsequent research can be on temperature field changes in different water contents and different materials.

[0176] The present application has a short field monitoring time, and subsequent optimization of roadbed protection methods in extremely cold regions can be further optimized according to more monitoring data.

[0177] A two-dimensional temperature field-water field coupling model is established based on COMSOL Multiphysics, considering the latent heat of phase change of frozen soil, water migration and heat conduction process of heat rod. An entropy value extension cloud model is used to evaluate the seven indexes of frozen soil water content (ω), void ratio (e), ice content (θ), etc., to determine the weight through entropy weight method, and to quantify the thawing settlement grade (weak thawing settlement, thawing settlement, strong thawing settlement) by using the extension cloud model. In the present application, the temperature field is balanced by the heat change caused by temperature change, the heat transfer caused by heat conduction and the heat exchange of phase change process to establish the balance equation of the temperature field. In the frozen soil research scenario, it can be used to analyze how the temperature field in the soil changes due to heat conduction and ice-water phase change, and to study the frost heaving and thawing settlement of frozen soil, providing a theoretical basis for frozen soil engineering (such as the design and construction of roads and building foundations in frozen soil areas).

[0178] The relationship between the variation of unfrozen water content and ice content with time and the moisture diffusion and flow in frozen soil and porous media is described in the water field. It comprehensively considers the diffusion of water in the medium (based on the gradient of unfrozen water content) and macroscopic flow (based on pressure and other driving forces and medium permeability characteristics), as well as the influence of ice-water phase transition on water dynamics. In frozen soil research, it can be used to analyze the migration law of water in frozen soil, frost heaving and thawing settlement phenomena, etc.; in porous media research, it can be used to understand the transport process of water in porous materials such as soil and rock, and provide a theoretical basis for related engineering (such as foundation treatment, groundwater resource management, etc.).

[0179] Through indoor thermal rod simulation experiment and analysis of field monitoring data, the best embedding mode of thermal rod is obtained as symmetric arrangement, interval 2m, oblique insertion 75°, and burial depth 6.6m. This parameter can effectively improve the temperature regulation ability of thermal rod on roadbed and ensure the stability of roadbed. The temperature field of roadbed under the best embedding mode is simulated and analyzed by COMSOL, and the variation law of temperature field after one year and five years is mastered. For example, in the first year, the thermal rod stops working in April, and the thawing depth reaches the maximum in October; after five years, the cold storage capacity increases, the thawing depth decreases, and the upper limit of frozen soil moves up, providing a basis for long-term planning of the project. The work of thermal rod can reduce the internal temperature of roadbed, raise the upper limit of frozen soil, and reduce the thawing disease of roadbed. The experiment shows that the cold storage capacity of soil with 2m interval is more, which can reduce the thawing settlement deformation in warm season and ensure the safety and stability of road.

[0180] As shown in Figure 8a- Figure 8g , after entering October, the temperature drops, and the thermal rod starts to work. The road surface is affected by the heat absorption of asphalt and vehicle driving, and the temperature of the road surface is higher than that of the slope and ground. With the decrease of air temperature, the internal temperature of roadbed changes with the change of air temperature, and the temperature of shallow layer of roadbed decreases first, and then the temperature of deep layer of roadbed decreases gradually. The temperature around the thermal rod decreases first, and after December, the temperature drops sharply, the heat exchange power of the thermal rod increases, and the internal temperature of the soil decreases. In April, the temperature rises above 0℃ during the day and drops below 0℃ at night, and the thermal rod continues to work. After entering May, the temperature rises, the thermal rod stops working, and the frost heaving capacity reaches the maximum. At this time, the upper limit of frozen soil is 2m. After entering the warm season, the temperature of roadbed rises with the rise of air temperature, and the temperature of soil rises from top to bottom in July due to the heat resistance of roadbed. After October, the temperature drops below 0℃, but the temperature of road surface is higher, and at this time, the internal temperature of roadbed appears thawing core. In early November, the temperature of road surface drops to freezing temperature, and the soil gradually thaws, and at this time, the maximum thawing depth is about 3.01m. Subsequently, the temperature of upper soil of roadbed drops to negative temperature, and the external negative temperature continues to transfer to the internal, and the frozen soil roadbed forms the previous state of low temperature in the upper part and high temperature in the lower part.

[0181] Based on the same inventive concept, the application further provides a frozen soil subgrade heat rod layout scheme simulation device for implementing the above-mentioned frozen soil subgrade heat rod layout scheme simulation method. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme described in the above-mentioned method, and therefore the specific limitations in one or more frozen soil subgrade heat rod layout scheme simulation device embodiments provided below can be referred to the limitations of the frozen soil subgrade heat rod layout scheme simulation method described above, which will not be repeated here.

[0182] In one exemplary embodiment, as shown in Figure 9 a frozen soil subgrade heat rod layout scheme simulation device is provided, which applies the frozen soil subgrade heat rod layout scheme simulation method, and the frozen soil subgrade heat rod layout scheme simulation device comprises:

[0183] a control equation construction module for constructing temperature field control equations and water field control equations of a target frozen soil subgrade during a freeze-thaw cycle process.

[0184] a numerical model construction module for constructing a frozen soil subgrade temperature field numerical model and a frozen soil subgrade water field numerical model in COMSOL Multiphysics according to the temperature field control equations and the water field control equations; the frozen soil subgrade temperature field numerical model and the frozen soil subgrade water field numerical model both contain a solid-liquid ratio function.

[0185] a heat rod mathematical model construction module for constructing a heat rod mathematical model based on a starting temperature condition of the heat rod.

[0186] a subgrade temperature field prediction module for predicting a subgrade temperature field of a target heat rod layout mode on the target frozen soil subgrade for a set time length according to the frozen soil subgrade temperature field numerical model, the frozen soil subgrade water field numerical model, and the heat rod mathematical model, to obtain a subgrade temperature field prediction result of the target heat rod layout mode within the set time length.

[0187] In one exemplary embodiment, as shown in Figure 10 a frozen soil subgrade heat rod layout scheme simulation device is provided, which comprises an analysis module 1, a development module 2, a model construction module 3, a verification module 4, and a simulation analysis 5.

[0188] The analysis module 1 is connected with the development module 2 and the simulation analysis 5 respectively, and the analysis module 1 is used to analyze the temperature field, the water field, and the physical equation during the freeze-thaw cycle process in the extremely cold region.

[0189] The development module 2 is connected with the analysis module 1, the model construction module 3, and the simulation analysis 5 respectively, and the development module 2 is used to develop the COMSOL Multiphysics finite element software.

[0190] The model building module 3 is connected with the development module 2 and the verification module 4 respectively, and the model building module 3 is used for building a temperature field and hot water coupling model suitable for the permafrost roadbed in extremely cold areas based on the temperature field and hot water coupling model.

[0191] The verification module 4 is connected with the development module 2, the model building module 3 and the simulation analysis 5 respectively, and the verification module 4 is used for simulating the roadbed temperature field by using COMSOL Multiphysics for the roadbed with a 2m interval, and verifying the model parameters by comparing the field monitoring data with the simulation data.

[0192] The simulation analysis 5 is connected with the analysis module 1, the development module 2 and the verification module 4 respectively, and the simulation analysis 5 is used for analyzing the hot rod simulation experiment and the field monitoring data in the room, and the best embedding mode of the hot rod is symmetrically arranged, the interval is 2m, the oblique insertion is 75°, and the embedding depth is 6.6m; the roadbed temperature field is simulated and analyzed by using COMSOL Multiphysics for the embedding mode, and the roadbed temperature field in the future 5 years is predicted.

[0193] The technical scheme to be protected in the application has the advantages and positive effects that:

[0194] Firstly, the application establishes a permafrost roadbed temperature field finite element model of the hot rod in the extremely cold area based on COMSOL finite element software, and verifies the accuracy of the model by comparing the roadbed temperature of the hot rod with different embedding depths with the field monitoring data.

[0195] (1) Based on the temperature field and moisture field control equation, and through the solid-liquid ratio formula, the relationship between the temperature field and the moisture field is established, and the calculation equation of the permafrost roadbed temperature field is described. The PDE module of COMSOL Multiphysics finite element software is developed, and the permafrost hot rod roadbed temperature field model suitable for a certain road is constructed according to the actual situation of the road.

[0196] (2) According to the field monitoring scheme, the hot rod roadbed with an embedding depth of 6.6m and 8.1m is established, and the model accuracy is verified by comparing the monitoring data with the simulation data.

[0197] (3) The finite element model of the hot rod roadbed with an embedding depth of 6.6m and an oblique insertion of 75° is established, and it is found that in April, the hot rod stops working, the roadbed stops freezing, the upper limit of the frozen soil is 70cm in the first year, and in October, the temperature drops, at this time, the maximum melting depth reaches 3.01m. After five years, the cold storage capacity of the hot rod roadbed increases, the upper limit of the frozen soil is 20cm in March, and the maximum melting depth is 2.68m in October, and the upper limit of the frozen soil during melting is reduced by 53cm compared with the first year hot rod roadbed.

[0198] Secondly, the application is directed to the limitation that the influence of unfrozen water migration is not considered in the traditional frozen soil subgrade temperature field simulation. The nonlinear relationship equation of the unfrozen water content and temperature is innovatively introduced into the water-heat coupling equation, effectively solving the problem of large deviation between the simulation results of the existing model and the actual situation. This improvement considers the migration characteristics of the unfrozen water in the temperature change process and the influence of the unfrozen water on the thermal physical properties of the soil. Through the equation, the temperature change of the frozen soil subgrade in the freezing and thawing cycle process can be more accurately simulated, the temperature prediction error is less than ±0.5℃, the simulation accuracy is significantly improved, and the blank of the traditional model in considering the migration of the unfrozen water is filled.

[0199] In an exemplary embodiment, a computer device is provided, which can be a server or a terminal, and an internal structure diagram thereof can be as shown in Figure 11 The computer device includes a processor, a memory, an input / output interface (I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store frozen soil subgrade thermal rod layout scheme simulation data. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals through network connection. The computer program is executed by the processor to implement a frozen soil subgrade thermal rod layout scheme simulation method.

[0200] In an exemplary embodiment, an information data processing terminal is provided, which is used to implement the frozen soil subgrade thermal rod layout scheme simulation method.

[0201] Those skilled in the art can understand that Figure 11 The structure shown in the above-mentioned figure is only a block diagram of part of the structure related to the scheme of the present application, and does not constitute a limitation on the computer device to which the scheme of the present application is applied. The specific computer device can include more or fewer components than those shown in the figure, or combine certain components, or have a different component arrangement. In an exemplary embodiment, a computer device is provided, which includes a memory and a processor, the memory stores a computer program, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0202] In an exemplary embodiment, a computer readable storage medium storing a computer program is provided, the computer program, when executed by a processor, implements the steps of any of the above method embodiments.

[0203] In an exemplary embodiment, a computer program product is provided, comprising a computer program which, when executed by a processor, implements the steps of any of the above method embodiments.

[0204] It should be noted that the user information (including but not limited to user equipment information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in the present application are all information and data authorized by the user or authorized by all parties, and the collection, use and processing of related data need to comply with relevant regulations.

[0205] It can be understood by those skilled in the art that all or part of the processes in the above embodiments can be completed by a computer program instructing related hardware, and the computer program can be stored in a non-volatile computer readable storage medium. When the computer program is executed, it can include the processes of the above embodiments. Any reference to memory, database or other medium used in the embodiments provided by the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical storage, high-density embedded non-volatile memory, resistive memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration but not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0206] The database involved in each of the embodiments provided in the present application can include at least one of a relational database and a non-relational database. The non-relational database can include a distributed database based on a blockchain, and the like, without being limited thereto. The processor involved in each of the embodiments provided in the present application can be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a data processing logic of a programmable logic device, and the like, without being limited thereto.

[0207] The technical features of the above embodiments can be combined in any manner. To make the description concise, all possible combinations of the technical features in the above embodiments are not described, but as long as there is no contradiction, any combination of the technical features should be considered within the scope of the present disclosure.

[0208] The principles and implementation manners of the present application are described by using specific examples herein, and the above embodiments are only used to help understand the method of the present application and its core idea. Meanwhile, for those skilled in the art, the specific implementation manners and application ranges can be changed according to the idea of the present application. In conclusion, the content of the present description should not be understood as a limitation of the present application.

Claims

1. A method of simulation of a frozen soil roadbed heat rod laying scheme, characterized in that, The frozen soil subgrade heat rod layout scheme simulation method comprises: temperature field control equations and water field control equations of a target frozen soil subgrade during a freeze-thaw cycle process are constructed; a frozen soil subgrade temperature field numerical model and a frozen soil subgrade water field numerical model for COMSOL Multiphysics are constructed according to the temperature field control equations and the water field control equations; the frozen soil subgrade temperature field numerical model and the frozen soil subgrade water field numerical model both comprise a solid-liquid ratio function; a heat rod mathematical model is constructed based on a starting temperature condition of the heat rod; subgrade temperature field prediction of a target heat rod layout mode on the target frozen soil subgrade for a set time length is performed according to the frozen soil subgrade temperature field numerical model, the frozen soil subgrade water field numerical model and the heat rod mathematical model, and a subgrade temperature field prediction result of the target heat rod layout mode within the set time length is obtained.

2. The method of claim 1, wherein, The temperature field control equation is expressed as: where p is the density of the soil, C(0) is the specific heat capacity, T is the temperature, t is time, l(0) is the thermal conductivity, V is the gradient operator, L is the latent heat of phase change, p i is the density of ice, 0 i is the volume content of frozen water, and 0 represents the water content; The moisture field control equation is expressed as: where θ u is the unfrozen water volume content, ρ w represents the density of water, D(θ u ) represents the diffusion rate of water in frozen soil, and k(θ u ) represents the permeability of soil.

3. The method of claim 2, wherein, The diffusion rate of the water in the frozen soil is represented as: where I is the impedance factor, o(0 u ) is the specific water capacity; k(θ u ) = k s · S 0.5 (1 - (1 - S 1 / m ) m ) 2 ; o(θ u ) = a0m / (1-m)(θ s - θ r ) · S 1 / m (1-S 1 / m ) m ; where k s is the permeability coefficient of the soil, S represents the relative saturation of the soil, θ s is the saturated volumetric water content of the soil, θ r is the residual volumetric water content of the soil, and a0 and m are both related parameters that vary with the soil type.

4. The method of claim 1, wherein, The frozen soil subgrade temperature field numerical model is represented as: where p is the density of the soil, C(0) is the heat capacity, T is the temperature, t is the time, l(0) is the thermal conductivity, V is the gradient operator, L is the latent heat of phase change, p i is the density of ice, 0 s is the saturation volumetric water content of the soil, 0 r is the residual volumetric water content of the soil, S represents the relative saturation of the soil, and B(T) is the solid-liquid ratio function; θ i is the volume content of frozen water, θ u is the volume content of unfrozen water, T f is the temperature at which the soil can freeze, B is a constant; The frozen soil subgrade water field numerical model is represented as: where D(S) represents the diffusion coefficient, k(S) represents the permeability coefficient, and p w represents the density of water.

5. The method of claim 1, wherein, The heat rod mathematical model is represented as: Q = a • ΔΤ = a • (Τ a - T b ); Wherein, Q is the heat transfer of the heat rod, a is the equivalent heat transfer coefficient of the heat rod, ΔT is the temperature difference between the two ends of the heat rod, T a is the soil temperature around the evaporation section, T b is the ambient temperature outside the subgrade.

6. The method of claim 1, wherein, The subgrade temperature field prediction of the target heat rod layout mode on the target frozen soil subgrade for the set time length is specifically performed according to the frozen soil subgrade temperature field numerical model, the frozen soil subgrade water field numerical model and the heat rod mathematical model, and the subgrade temperature field prediction result of the target heat rod layout mode within the set time length is obtained. The subgrade temperature field prediction of the target heat rod layout mode on the target frozen soil subgrade for the set time length is performed according to the frozen soil subgrade temperature field numerical model, the frozen soil subgrade water field numerical model and the heat rod mathematical model based on a boundary temperature condition of a subgrade cross section.

7. A frozen soil subgrade heat rod layout scheme simulation device, characterized in that, The frozen soil subgrade heat rod layout scheme simulation device applies the frozen soil subgrade heat rod layout scheme simulation method in any one of claims 1-6, and the frozen soil subgrade heat rod layout scheme simulation device comprises: a control equation construction module configured to construct temperature field control equations and water field control equations of a target frozen soil subgrade during a freeze-thaw cycle process; a numerical model construction module configured to construct a frozen soil subgrade temperature field numerical model and a frozen soil subgrade water field numerical model for COMSOL Multiphysics according to the temperature field control equations and the water field control equations; the frozen soil subgrade temperature field numerical model and the frozen soil subgrade water field numerical model both comprise a solid-liquid ratio function; a heat rod mathematical model construction module configured to construct a heat rod mathematical model based on a starting temperature condition of the heat rod; a subgrade temperature field prediction module configured to perform subgrade temperature field prediction of a target heat rod layout mode on the target frozen soil subgrade for a set time length according to the frozen soil subgrade temperature field numerical model, the frozen soil subgrade water field numerical model and the heat rod mathematical model, and obtain a subgrade temperature field prediction result of the target heat rod layout mode within the set time length.

8. A computer device comprising: A memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the frozen soil subgrade heat rod layout scheme simulation method in any one of claims 1-6.

9. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program, when executed by a processor, implements the simulation method of a heat rod layout scheme for a permafrost roadbed according to any one of claims 1-6.

10. A computer program product comprising a computer program, characterized in that, The computer program, when executed by a processor, implements the simulation method of a heat rod layout scheme for a permafrost roadbed according to any one of claims 1-6.

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