Block gravel foundation heat conduction calculation method considering thermal radiation effect

Abstract

The invention belongs to the technical field of foundation protection, and particularly relates to a block gravel foundation heat conduction calculation method considering a thermal radiation effect, which comprises the following steps: collecting air, ground temperature and wind speed data of an area where a project is located, determining physical parameters of foundation soil and filling soil, and measuring foundation section parameters and block gravel physical parameters; calculating block gravel layer structure parameters and heat conduction and heat conduction coefficients; calculating a block gravel layer thermal radiation heat conductivity coefficient and a block gravel layer effective heat conductivity coefficient; and establishing a block gravel layer model, calculating the influence of the block gravel layer considering the thermal radiation effect on the permafrost of the foundation, and monitoring related calculation results. A theoretical basis is provided for design and calculation of the block gravel foundation, the problem that the heat radiation heat transfer influence is not considered in the heat transfer process of the block gravel layer is solved, the influence of the cooling characteristic of the block gravel layer on the heat state of permafrost of the foundation can be analyzed more accurately, and theoretical support and scientific basis are provided for engineering construction in cold regions.

Description

Technical Field

[0001] The invention relates to the technical field of foundation protection, and in particular to a heat conduction calculation method for a block gravel foundation taking into account the effect of heat radiation. Background Art

[0002] Permafrost refers to a special geological body at a certain depth below the surface, where the temperature remains below 0°C and remains frozen for two years or more. With climate warming and intensified human activities, the accelerated degradation of permafrost poses a great threat to the integrity of infrastructure and causes complex and diverse engineering diseases. According to forecasts, by 2050, about 30-50% of existing projects in permafrost areas in the Northern Hemisphere will be located in permafrost areas with high degradation risks, and nearly 70% of existing infrastructure in the area will be affected by permafrost degradation. In order to cope with the impact of climate change and human engineering structures on permafrost foundations, a series of active cooling methods have been proposed, such as block crushed stone layers, ventilation pipes, heat pipes and their composite structures. Block crushed stone layers have become one of the most widely used active cooling methods due to their excellent cooling effect and convenient construction, accounting for about 60% of cooling methods in permafrost areas.

[0003] The block gravel layer with significant cooling effect has been widely used to protect the permafrost melting under the engineering foundation in cold regions. As a highly permeable porous medium with a certain thickness, the pore air in the block gravel layer forms an unstable gradient due to temperature changes, which leads to the process of convective heat transfer and heat release inside the block gravel layer. At present, the research on the cooling mechanism of the block gravel layer mainly considers the heat conduction and convection heat transfer processes. However, it is found that thermal radiation can occur in gravel or rougher materials under field conditions, and in the determination of the effective thermal conductivity of the crushed stone samples (a combination of thermal conduction and thermal radiation), it is found that the effective thermal conductivity at ambient temperature is 97%-209% higher than that of pure thermal conduction. However, the influence of the cooling characteristics of the block gravel layer considering the thermal radiation effect on the permafrost of the foundation is insufficient. Therefore, there is an urgent need for a thermal conductivity calculation method for the block gravel foundation considering the thermal radiation effect, which can accurately analyze the influence of the block gravel layer on the permafrost of the foundation after considering the thermal radiation effect. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, it is necessary to add the thermal radiation effect that has not been considered in the heat transfer process of the crushed stone layer. The present invention provides a method for calculating the thermal conductivity of a crushed stone foundation taking the thermal radiation effect into consideration. The calculation method comprises the following steps: Step S1, collecting air, ground temperature, and wind speed data in the project area, determining the physical parameters of the foundation soil and fill, and measuring the foundation section parameters and the physical parameters of the block gravel; S101, collect air, temperature and wind speed data in the project area through the meteorological station, and fit the collected temperature and wind speed parameters into a periodic boundary condition formula; S102, determining the physical parameters of the foundation soil and fill soil according to the engineering design documents, and calculating and determining the thermal conductivity, volume heat capacity and phase change latent heat of the foundation soil and fill soil in frozen and unfrozen states; S103, considering that the soil layer is infinite in the longitudinal direction, ignoring the non-uniform effect in the length direction, simplifying it to a two-dimensional isotropic problem in the cross-sectional direction, measuring the dimensions of the foundation section, including width, height, and slope ratio; S104, determining the physical parameters of the block crushed stone material according to the engineering design documents, including density, thermal conductivity, specific heat capacity, equivalent particle size, permeability, and inertial resistance coefficient.

[0005] Step S2, calculating the empirical coefficient of the block gravel layer structure and the thermal conductivity coefficient of heat conduction; S201, the structural parameter is a function of the ratio of the thermal conductivity of air to that of the crushed stone layer. Based on the empirical coefficient of particle shape and cementation, the structural parameter of the crushed stone layer is calculated as: ; In the formula, is the structural parameter; is the thermal conductivity of the solid phase; is the thermal conductivity of the liquid phase; is the empirical coefficient of the structural parameter, when , the empirical coefficient of the crushed stone particle structure parameter is 0.54. hour .

[0006] S202, the thermal conductivity of the crushed stone layer is calculated as: ; In the formula, is the thermal conductivity of the crushed stone layer; n is the porosity.

[0007] Step S3, calculating the thermal radiation thermal conductivity of the crushed stone layer and the effective thermal conductivity of the crushed stone layer; S301, thermal radiation in the gravel layer only occurs in the gaps of the porous medium and strongly absorbs radiation during the transmission process. The radiation energy conservation equation of the spatial microelement can be obtained by integrating each term in the thermal radiation transfer equation over the entire space by 4π. The radiation energy equation vector of the full wavelength of the gravel layer is calculated as: ; Where: is the spectral radiation heat flux density vector exist x , y , z Components on the coordinates.

[0008] S302, the heat radiation propagation in the gravel layer is simplified as a gray fluid is confined between two infinite isothermal parallel plates of opaque material with gray diffusion surfaces, and the radiation heat flux is obtained by analogy with the heat exchange between the diffusion gray bodies: ; In the formula, ε 1 , ε 2 is the emissivity of different surfaces; T 1 , T 2 are the temperatures of different surfaces, σ is the Stefan-Boltzmann constant, which is 5.67×10 -8 W·m -2 ·K -4 .

[0009] S303, for surfaces with similar emissivity, the equation for radiative heat flux simplifies to: ; In the formula, ε is the emissivity of the surface of the gravel layer; d is the effective particle size; is the average temperature.

[0010] S304, in the heat transfer process of the crushed stone layer, the flow direction of the heat transfer by thermal radiation is the same as that of the heat conduction. The problem of heat transfer by thermal radiation is simplified to the problem of heat conduction whose thermal conductivity depends on the temperature change. The thermal conductivity of the crushed stone layer by thermal radiation is calculated as follows: ; In the formula, is the thermal radiation thermal conductivity.

[0011] S305, the energy equation for the block gravel layer is: ; In the formula, is the specific heat capacity; , is the effective volume heat capacity and effective thermal conductivity of the gravel layer.

[0012] S306, the radiation intensity of the local area of ​​the gravel layer can only be affected by the thermal radiation of the surface at the adjacent position, and the radiation energy can only propagate a short distance before being absorbed. The radiation heat transfer in the gravel layer becomes a diffusion process. The direction of thermal radiation transfer is the same as that of heat conduction. Therefore, it can be expressed in the same form as Fourier's law through diffusion approximation. The effective thermal conductivity of the gravel layer considering the thermal radiation effect is: ; In the formula, is the effective thermal conductivity of the crushed stone layer.

[0013] S307, the energy equation for the block gravel layer considering thermal radiation is: .

[0014] Step S4, establishing a block gravel layer model, calculating the impact of the block gravel layer on the permafrost of the foundation taking into account the effect of thermal radiation, and monitoring the relevant calculation results.

[0015] S401, after simulating and calculating the initial temperature field with the block gravel layer model, the influence of the cooling characteristics of the block gravel layer on the thermal state of the foundation permafrost is calculated based on the boundary temperature conditions and boundary wind speed conditions under the climate warming conditions; S402, verifying the model by comparing the measured monitoring point temperature with the simulated calculated monitoring point temperature; S403, evaluate the cooling effect of the rubble layer on the permafrost of the foundation under the action of thermal radiation by the heat flux change between the rubble layer and the soil layer monitoring surface and the ground temperature distribution map after 50 years of rubble layer action.

[0016] The beneficial effect of the present invention is that the present invention proposes a method for calculating the thermal conductivity of a crushed stone foundation taking into account the effect of thermal radiation, starting from the combined effect of the three heat transfer modes of the crushed stone layer. By taking into account the effect of thermal radiation in the crushed stone layer, the thermal radiation heat transfer treatment of the crushed stone layer is expressed as the effective thermal conductivity of the homogeneous material (taking into account the effect of thermal radiation) and the homogenization method that does not rely on the radiation transfer equation, and the influence of the crushed stone layer on the thermal state of the permafrost of the foundation taking into account the effect of thermal radiation is calculated, providing theoretical support and scientific basis for engineering construction in cold regions, and having great engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Figure 1 This is a flow chart of the heat conduction calculation method of the block gravel foundation considering the effect of heat radiation of the present invention; Figure 2 It is a schematic diagram of the air temperature fitting curve of the present invention; Figure 3 It is a schematic diagram of the calculation model of the block gravel layer of the present invention; Figure 4 The thermal radiation thermal conductivity of the present invention varies with temperature; Figure 5 It is a comparison diagram of the actually measured monitoring point temperature and the simulated calculated monitoring point temperature of the present invention; Figure 6 This is a diagram showing the change of bottom heat flux when the block gravel layer of the present invention is in the tenth year; Figure 7 This is the geothermal distribution diagram after the block gravel layer of the present invention has been in action for 50 years. DETAILED DESCRIPTION

[0019] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0020] The present invention provides a method for calculating heat conduction of a block and gravel foundation taking into account the effect of heat radiation, the method comprising the following steps: S1, collect the air, ground temperature and wind speed data in the project area, determine the physical parameters of the foundation soil and fill, and measure the foundation section parameters and the physical parameters of the block gravel; S2, calculate the structural parameters of the block gravel layer and the thermal conductivity coefficient of heat conduction; S3, calculating the thermal radiation conductivity of the block gravel layer and the effective thermal conductivity of the block gravel layer; S4, establish a rubble layer model, calculate the impact of the cooling characteristics of the rubble layer on the foundation permafrost considering the effect of thermal radiation, and monitor the relevant calculation results.

[0021] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments: like Figure 1 As shown, step S1, collect the air, ground temperature, and wind speed data of the project area, determine the physical parameters of the foundation soil and fill, and measure the foundation section parameters and the physical parameters of the block gravel: S101, collect air, temperature and wind speed data in the project area through the meteorological station, and fit the collected temperature and wind speed parameters into a periodic boundary condition formula.

[0022] Considering the boundary temperature conditions under the climate warming conditions: ; In the formula, T To calculate the temperature; T 0 is the annual mean temperature; A is the temperature amplitude; t h is time, unit is h; α0 is the initial phase.

[0023] Based on the collected local meteorological data, the boundary conditions required in the calculation process can be determined. The temperature function will be used as the temperature condition input, and the fitted air temperature curve is as follows: Figure 2 The boundary temperature conditions are shown below.

[0024] Air temperature: ; Natural surface temperature: ; Slope temperature: ; Top temperature: ; Air can pass through the block gravel structure under the forced action of wind. The wind speed boundary is applied to the PJ edge. The standard wind speed at a height of 10 m above the ground surface is determined based on monitoring data. v 10 The expression is as follows: ; The wind speed at other heights can be approximated by the following relationship: ; The boundaries on both sides of the model are adiabatic boundaries, and the bottom has a constant heat flux. .

[0025] S102, determine the physical parameters of the foundation soil and fill according to the engineering design documents, calculate and determine the thermal conductivity, volume heat capacity and phase change latent heat of the foundation soil and fill in the frozen and unfrozen states, and determine the specific physical parameters of the foundation soil and fill as shown in Table 1.

[0026] Table 1 Physical parameters of foundation soil and fill The apparent heat capacity method is used to deal with the latent heat of phase change in the water-containing medium in the calculation, assuming that the phase change of the water-containing medium in the model occurs in the temperature range When establishing the equivalent volumetric heat capacity, the temperature interval should be considered The influence of volume heat capacity of the medium when it is frozen and unfrozen is assumed and and thermal conductivity and The thermal conductivity and volume heat capacity of the foundation soil and the fill soil in the frozen and unfrozen states are determined independently of the temperature, so the simplified construction is and The expression is as follows: ; ; In the formula, , is the equivalent volume heat capacity and equivalent thermal conductivity of the medium, and is the volume heat capacity when frozen and unfrozen; and is the thermal conductivity when frozen and unfrozen; is the phase transition temperature of the aqueous medium; T is the phase change temperature interval of the aqueous medium; L is the latent heat of phase change per unit volume of aqueous medium.

[0027] S103, considering that the soil layer is infinite in the longitudinal direction, ignoring the uneven effect in the length direction, simplifying it to a two-dimensional isotropic problem in the cross-sectional direction, measuring the cross-sectional dimensions, including width, height, and slope ratio. The cross-sectional dimensions obtained through on-site measurement are: width 10.4m, slope ratio 1:1.5, fill height 3.6m, ballast fill height 0.6m, block gravel slope protection fill thickness 1.5m, and the specific block gravel layer calculation model is as follows: Figure 3 shown.

[0028] S104, determine the physical parameters of the block crushed stone material according to the engineering design documents, including equivalent particle size, permeability, and inertial resistance coefficient. The equivalent particle size of the block crushed stone is about 10 cm, so the permeability of the porous medium is k and the inertial drag coefficient B Take separately and The equivalent particle size of ballast stone is 5 cm permeability k and the inertial drag coefficient B Take separately and , the surface emissivity of the gravel is taken as 0.9.

[0029] like Figure 1 As shown, step S2, calculates the empirical coefficient of the block gravel layer structure and the thermal conductivity coefficient of heat conduction: S201, the structural parameter is a function of the ratio of the thermal conductivity of air to that of the crushed stone layer. Based on the empirical coefficient of particle shape and cementation, the structural parameter of the crushed stone layer is calculated as: ; In the formula, is the structural parameter; is the thermal conductivity of the solid phase; is the thermal conductivity of the liquid phase; is the empirical coefficient of the structural parameter, when , the empirical coefficient of the crushed stone particle structure parameter is 0.54. hour .

[0030] S202, the thermal conductivity of the crushed stone layer is calculated as: ; In the formula, is the thermal conductivity of the crushed stone layer; n is the porosity.

[0031] The measurement site is located in the Kaixinling Mountain area of ​​the Qinghai-Tibet Plateau, which is a continuous permafrost area with an altitude of about 4,600 m. The constant pressure specific heat and thermal conductivity of the air were determined to be 1.004 kJ·m -3 °C -1 and 0.02W·m -1 °C -1 , the density is ρ =0.641kg·m -3 , the dynamic viscosity is μ =1.75×10 5 kg·m -1 ·s -1 , the physical parameters of the crushed stone materials are shown in Table 2.

[0032] Table 2 Physical parameters of crushed stone materials like Figure 1 As shown, step S3, calculate the thermal radiation thermal conductivity of the crushed stone layer and the effective thermal conductivity of the crushed stone layer: S301, thermal radiation in the gravel layer only occurs in the gaps of the porous medium and strongly absorbs radiation during the transmission process. The radiation energy conservation equation of the spatial microelement can be obtained by integrating each term in the thermal radiation transfer equation over the entire space by 4π. The radiation energy equation vector of the full wavelength of the gravel layer is calculated as: ; Where: is the spectral radiation heat flux vector exist x , y , z Components on the coordinates.

[0033] S302, the heat radiation propagation in the gravel layer is simplified as a gray fluid is confined between two infinite isothermal parallel plates of opaque material with gray diffusion surfaces, and the radiation heat flux is obtained by analogy with the heat exchange between the diffusion gray bodies: ; In the formula, ε 1 , ε2 is the emissivity of different surfaces; T 1 , T 2 are the temperatures of different surfaces, σ is the Stefan-Boltzmann constant, which is 5.67×10 -8 W·m -2 ·K -4 .

[0034] S303, for surfaces with similar emissivity, the equation for radiative heat flux simplifies to: ; In the formula, ε is the emissivity of the surface of the gravel layer; d is the effective particle size; is the average temperature.

[0035] S304, in the heat transfer process of the crushed stone layer, the flow direction of the heat transfer by thermal radiation is the same as that of the heat conduction. The problem of heat transfer by thermal radiation is simplified to the problem of heat conduction whose thermal conductivity depends on the temperature change. The thermal conductivity of the crushed stone layer by thermal radiation is calculated as follows: ; In the formula, is the thermal radiation thermal conductivity; The thermal conductivity of the crushed stone layer varies with temperature. Figure 4 shown.

[0036] S305, the energy equation for the block gravel layer is: ; In the formula, is the specific heat capacity; , is the effective volume heat capacity and effective thermal conductivity of the gravel layer.

[0037] S306, the radiation intensity of the local area of ​​the gravel layer can only be affected by the thermal radiation of the surface at the adjacent position, and the radiation energy can only propagate a short distance before being absorbed. The radiation heat transfer in the gravel layer becomes a diffusion process. The direction of thermal radiation transfer is the same as that of heat conduction. Therefore, it can be expressed in the same form as Fourier's law through diffusion approximation. The effective thermal conductivity of the gravel layer considering the thermal radiation effect is: ; In the formula, is the effective thermal conductivity of the crushed stone layer.

[0038] S307, the energy equation for the block gravel layer considering thermal radiation is: .

[0039] like Figure 1 As shown, step S4 is to establish a block gravel layer model, calculate the influence of the cooling characteristics of the block gravel layer considering the effect of thermal radiation on the permafrost of the foundation and monitor the relevant calculation results: S401, after simulating and calculating the initial temperature field using the rubble layer model, the influence of the cooling characteristics of the rubble layer on the thermal state of the foundation permafrost is calculated based on the boundary temperature conditions and boundary wind speed conditions under the climate warming conditions.

[0040] S402, the model is tested by comparing the measured monitoring point temperature with the simulated calculated monitoring point temperature, and the monitoring temperature of the fill area 1.5m below the left shoulder is selected for comparison with the simulated temperature, such as Figure 5 shown.

[0041] S403, evaluate the cooling effect of the gravel layer under the action of thermal radiation by evaluating the heat flux change of the monitoring surface of the gravel layer and the soil layer, and select the instantaneous heat flux change diagram of the bottom of the gravel layer in the tenth year, such as Figure 6 As shown, positive values ​​indicate heat absorption, negative values ​​indicate heat release, and the negative sign represents heat release only.

[0042] S404, the geothermal distribution map after 50 years of the action of the rubble layer is used to evaluate the cooling effect of the rubble layer under the action of thermal radiation. Usually, the maximum seasonal melting depth in permafrost areas occurs in October. The geothermal distribution map on October 15 of the 50th year is selected, such as Figure 7 shown.

[0043] The present invention is a method for calculating the thermal conductivity of a crushed stone foundation considering the effect of thermal radiation. It proposes a method for expressing the thermal radiation heat transfer treatment of the crushed stone layer as the effective thermal conductivity of a homogeneous material (considering the effect of thermal radiation), and calculates the influence of the crushed stone layer on the thermal state of the permafrost in the underlying foundation under the effect of thermal radiation. The thermal radiation effect in the heat transfer process inside the crushed stone layer increases significantly with the increase of temperature, and causes the crushed stone layer to absorb additional heat in summer and transfer it to the permafrost in the foundation. Therefore, in the design of the crushed stone layer structure in permafrost area projects, the heat transfer process analysis should include the effect of thermal radiation to consider the additional heat absorption in summer.

[0044] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in this application can be executed in parallel, sequentially or in different orders, as long as the expected results of the technical solution disclosed in this application can be achieved, and this document is not limited here.

[0045] The above specific implementations do not constitute a limitation on the protection scope of this application. The above specific implementations by those skilled in the art do not constitute a limitation on the protection scope of this application. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principles of this application should be included in the protection scope of this application.

Claims

1. A method for calculating the thermal conductivity of a block gravel foundation taking into account the effect of thermal radiation, characterized in that: The following steps are involved: S1, collect air, ground temperature and wind speed data in the project area, determine the physical parameters of foundation soil and fill, measure foundation section parameters and physical parameters of block gravel; S2, calculate the structural parameters of the block gravel layer and the thermal conductivity coefficient of heat conduction; S3, calculating the thermal radiation conductivity of the block gravel layer and the effective thermal conductivity of the block gravel layer; S4, establish a rubble layer model, calculate the impact of the rubble layer on the permafrost of the foundation considering the effect of thermal radiation and monitor the relevant calculation results.

2. The method for calculating heat conduction of a crushed stone foundation taking into account the effect of heat radiation according to claim 1 is characterized in that: The energy equation of the block gravel layer region is: ； In the formula, is the specific heat capacity; , is the effective volume heat capacity and effective thermal conductivity of the gravel layer.

3. The method for calculating heat conduction of a crushed stone foundation taking into account the effect of heat radiation according to claim 1, characterized in that: The effective thermal conductivity of the crushed stone layer after considering the effect of thermal radiation is: ； In the formula, is the thermal conductivity of the crushed stone layer, is the thermal radiation conductivity.

4. The method for calculating heat conduction of a block gravel foundation taking into account the effect of heat radiation according to claim 3 is characterized in that: The thermal conductivity of the crushed stone layer is calculated as: ； In the formula, is the thermal conductivity of the solid phase; is the thermal conductivity of the liquid phase; n is the porosity.

5. The method for calculating heat conduction of a block gravel foundation taking into account the effect of heat radiation according to claim 4, characterized in that: The calculated block gravel layer structural parameters: ； In the formula, is the structural parameter; is the empirical coefficient of the structural parameter, when , the empirical coefficient of the crushed stone particle structure parameter is 0.

54. hour .

6. The method for calculating heat conduction of a block gravel foundation taking into account the effect of heat radiation according to claim 2, characterized in that: The full wavelength radiation energy equation vector of the gravel layer is calculated as: ； Where: is the spectral radiation heat flux density vector exist x , y , z Components on the coordinates.

7. A method for calculating heat conduction of a block gravel foundation taking into account the effect of heat radiation according to claim 6, characterized in that: The radiation heat flux is obtained by analogy with the heat exchange between diffuse gray bodies: ； In the formula, ε 1, ε 2 is the emissivity of different surfaces; T 1, T 2 is the temperature of different surfaces, σ is the Stefan-Boltzmann constant, which is 5.67×10 -8 W·m -2 ·K -4 .

8. The method for calculating heat conduction of a block-rubble foundation taking into account the effect of heat radiation according to claim 7, characterized in that: The equation for the radiative heat flux simplifies to: ； In the formula, ε is the emissivity of the surface of the gravel layer; d is the effective particle size; is the average temperature.

9. The method for calculating heat conduction of a block gravel foundation taking into account the effect of heat radiation according to claim 8, characterized in that: The thermal conductivity of the crushed stone layer is calculated as follows: ； In the formula, T For temperature.

10. A method for calculating heat conduction of a crushed stone foundation taking into account the effect of heat radiation according to claims 2 to 9, characterized in that: The energy equation considering thermal radiation in the gravel layer is: 。

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