Device and method for measuring thermal characteristics of frozen soil based on thermal pulse method

Abstract

The present invention discloses a device and method for measuring the thermal properties of frozen soil based on the heat pulse method. The method comprises: heating a cylindrical heating probe with a heater at a constant power; a first temperature probe detecting the temperature of the cylindrical heating probe and uploading it to a cloud server via a transmission unit; and a data logger displaying the temperature data of the second temperature probe and the first temperature probe in real time; maintaining the temperature of the cylindrical heating probe constant; and obtaining a temperature penetration curve of the frozen soil sample under the heating of the cylindrical heating probe, and then obtaining the volume diffusivity and volume thermal conductivity of the frozen soil sample. The present invention can effectively maintain the maximum spatial temperature below freezing, thereby estimating the overall thermal properties of quartz sand and ice content, and improving the accuracy of estimating the overall thermal properties of frozen soil samples in cold regions.

Description

Technical Field

[0001] The present invention belongs to the technical field of frozen soil freeze-thaw, and relates to a device and method for measuring thermal characteristics of frozen soil based on a heat pulse method. Background Art

[0002] Freeze-thaw processes are important for quantifying the soil surface energy balance and its interaction with hydrological processes. Significant progress has been made over the past few decades in developing methods to measure soil ice content and improving the accuracy of these measurements. Thermal resistance temperature probes, differential scanning calorimetry, TDR, heat pulse methods, and nuclear magnetic resonance have enabled more accurate measurements of soil ice content in frozen soils. However, these methods still present some challenges, such as the fact that melting and refreezing of ice transfer a significant portion of its energy to phase change rather than heat conduction. Adjustments have been introduced to address these issues, such as assuming minimal ice melting, integrating latent heat flux into calculations, or using numerical models. However, these adjustments can lead to biased or inaccurate estimates of thermal properties, particularly in partially frozen soils.

[0003] Characterizing soil freezing and thawing processes remains hampered by the lack of methods to measure soil thermal properties during freezing or thawing conditions. When using existing heat pulse-based methods, heat is released over a relatively short period of time or / and with high heat fluxes to ensure accurate detection signals. This temperature rise at the probe surface can exceed freezing temperatures, leading to thawing of frozen soil and inaccurate soil thermal properties in the temperature range of -5°C to 0°C. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem in the prior art that the temperature rise of the probe surface of the heat pulse method may exceed the freezing point, thereby causing the frozen soil to melt, and the inability to accurately obtain the thermal properties of the soil within the temperature range of -5 degrees Celsius and 0 degrees Celsius, and to provide a frozen soil thermal characteristics measurement device and method based on the heat pulse method.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A device for measuring thermal characteristics of frozen soil based on a heat pulse method, comprising: a test assembly, a variable voltage control device, and a data processing device;

[0007] The test assembly includes a cylindrical heating probe, a first temperature probe and a second temperature probe; the cylindrical heating probe, the first temperature probe and the second temperature probe are all arranged in the frozen soil sample to be measured; the variable voltage control device is connected to the cylindrical heating probe and the first temperature probe to provide energy for the cylindrical heating probe, and the first temperature probe records the surface temperature of the heating probe; the data processing device is connected to the second temperature probe; the second temperature probe measures the temperature change of the frozen soil.

[0008] A further improvement of the present invention is:

[0009] Furthermore, the first temperature probe, the second temperature probe and the cylindrical heating probe are placed in parallel; the first temperature probe, the second temperature probe and the cylindrical heating probe are arranged horizontally or vertically in the frozen soil sample to be measured.

[0010] Furthermore, the data processing device includes a data recorder, a processing unit, a transmission unit and a cloud; the processing unit is connected to the cloud; the cloud is connected to the transmission unit, and the data recorder and the transmission unit are electrically connected to the first temperature probe and the second temperature probe; the transmission unit sends the collected data of the first temperature probe and the second temperature probe to the cloud for storage; the processing unit calls the stored data for analysis, and then stores the processed data again in the cloud; the data recorder displays the temperature data of the first temperature probe and the second temperature probe in real time.

[0011] Furthermore, the variable voltage control device includes a heater and a temperature controller; the heater is connected to the cylindrical heating probe via the temperature controller.

[0012] A method for measuring thermal characteristics of frozen soil based on a heat pulse method, using a device for measuring thermal characteristics of frozen soil based on a heat pulse method, the method comprising:

[0013] The cylindrical heating probe is heated at a constant temperature by a heater, the first temperature probe detects the temperature of the cylindrical heating probe, and the second temperature probe detects the temperature of the frozen soil, and the data is uploaded to the cloud through a transmission unit. At the same time, a data logger displays the temperature data of the cylindrical heating probe and the frozen soil in real time;

[0014] When the cylindrical heating probe reaches the target temperature, the temperature of the cylindrical heating probe is kept constant through the temperature controller;

[0015] When the frozen soil sample is heated by a cylindrical heating probe, the temperature penetration curve of the frozen soil sample and the energy received by the frozen soil sample are obtained, and then the thermal diffusion coefficient of the frozen soil sample is obtained;

[0016] Based on the heating time of the cylindrical heating probe and the heat output during the heating time, a total heat output of the cylindrical heating probe is obtained;

[0017] Obtain the volumetric heat capacity based on the energy received by the frozen soil sample, the total delivered energy of the cylindrical heating probe, and the volumetric diffusivity of the frozen soil sample;

[0018] Obtain the thermal conductivity based on the thermal diffusivity and the volumetric heat capacity.

[0019] Furthermore, when the cylindrical heating probe controls the energy output power of the heater through a temperature controller to keep the temperature of the cylindrical heating probe constant, specifically: when the temperature reading of the cylindrical heating probe drops to the preset lower temperature limit, turn on the heater power supply and heat with short pulses of low energy output power. After the heating period ends, turn off the heater power supply to keep the temperature of the cylindrical heating probe between the preset upper and lower temperature limits; continuously repeat this step until the measurement of the frozen soil sample ends.

[0020] Furthermore, obtain the temperature penetration curve of the frozen soil sample, specifically:

[0021] The one-dimensional transient heat conduction process in the cylindrical coordinate system is:

[0022]

[0023] where T is the temperature measured in the soil of the second temperature probe; r is the radial distance of the second temperature probe from the cylindrical heating probe; t is the time for measuring the temperature penetration curve of the frozen soil; the effective radius r e is the radial distance between the second temperature probe and the first temperature probe; r e The minimum value of is equal to the sum of the radii of the first temperature probe and the second temperature probe; D is the volumetric thermal diffusivity;

[0024] When heating the frozen soil with a constant temperature heat source, the target temperature T1 of the frozen soil is higher than the initial temperature T0 but lower than the freezing point;

[0025] At the same time, satisfying the initial condition (T(r, 0) = T0 (T0 < 0)) and the boundary condition (T(r e , t) = T1 (T0 < T1 < 0)), the solution in the Laplace space is as follows:

[0026]

[0027] where K0 represents the modified Bessel function of the second kind of order zero,

[0028]

[0029] where s is the representation of time t in the Laplace space after T(r, t) undergoes the Laplace transform;

[0030] Through the inverse Laplace numerical transform, obtain the spatial distribution T(r, t) of the temperature in the frozen soil at any time;

[0031] The root mean square error (RMSE) is used to evaluate the temperature penetration curve fitting, specifically:

[0032]

[0033] Where, the subscript i is the number of measured temperature responses; N is the total number of measured temperatures; T and represent the measured temperature and the predicted temperature, respectively.

[0034] Furthermore, the energy received by the frozen soil sample is:

[0035]

[0036] Wherein, the subscript i represents the i-th discrete spatial interval after the measurement space is radially discretized into M spatial intervals, and the spatial range is from r = r e The radial distance to T = T0;

[0037] Based on the heating time of the cylindrical heating probe and the heat output during the heating time, the total heat output of the cylindrical heating probe is calculated as follows:

[0038] The total output energy Q2(t) of the cylindrical heating probe is measured by the temperature controller; the heating cycle is with a given power P j and heating cycle tp j The total delivered energy is the sum of the delivered energy in each cycle, as shown below:

[0039]

[0040] Where L is the length of the cylindrical heating probe.

[0041] Furthermore, the energy received by the frozen soil sample, the total energy delivered by the cylindrical heating probe, and the volume diffusivity of the frozen soil sample are used to obtain the volume heat capacity, specifically:

[0042] By volume heat capacity C b =ρ b c b Available,

[0043]

[0044] Among them, ρ b is the density of the medium; c b is the specific heat capacity of the medium;

[0045] Based on the thermal diffusivity and volumetric heat capacity, the thermal conductivity is obtained as follows:

[0046] The bulk thermal conductivity of soil is:

[0047] λ b =DC b .

[0048] Furthermore, when the frozen soil is mixed with other substances, the total heat capacity of the quartz sand sample is

[0049] C=n i c i +n g c g +n s c s

[0050] Where n represents the volume fraction of frozen soil components, c i represents the specific heat capacity of ice; c g represents the specific heat capacity of air; c s represents the specific heat capacity of the solid;

[0051] In saturated frozen soil, the gaseous term is omitted, and the volume fractions of each are obtained based on the total heat capacity C and the specific heat capacities of solids and ice.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] The present invention uses a heater to heat a cylindrical heating probe at a constant power. A first temperature probe detects the temperature of the cylindrical heating probe and uploads it to the cloud via a transmission unit. Simultaneously, a data logger displays the temperature data of the second and first temperature probes in real time. The cylindrical heating probe temperature is maintained constant. As the frozen soil sample is heated by the cylindrical heating probe, a temperature penetration curve is obtained, followed by the volume diffusivity and volume thermal conductivity of the frozen soil sample. This invention effectively maintains the maximum spatial temperature below freezing, thereby estimating the overall thermal properties of quartz sand and ice content, improving the accuracy of estimating the overall thermal properties of frozen soil samples in cold regions. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0055] Figure 1 Schematic diagram of the topological structure of the device for measuring thermal characteristics of frozen soil based on the heat pulse method of the present invention;

[0056] Figure 2 Schematic diagram of the process of measuring thermal characteristics of frozen soil based on the heat pulse method of the present invention;

[0057] Figure 3 Schematic diagram of the constant temperature control process using a multi-pulse heating strategy;

[0058] Figure 4 Example plots of the spatial temperature distribution along the radial direction at different times t1, t2, and t3 estimated by the ILS model. DETAILED DESCRIPTION

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0060] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0061] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0062] In the description of the embodiments of the present invention, it should be noted that if the terms "upper," "lower," "horizontal," "inner," etc. appear, the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the inventive product is typically placed when in use. These terms are merely for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first," "second," etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0063] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0064] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0065] The present invention is described in further detail below with reference to the accompanying drawings:

[0066] See also Figure 1 , the present invention discloses a device for measuring thermal characteristics of frozen soil based on a heat pulse method, comprising: a test component, a variable voltage control device and a data processing device;

[0067] The test assembly includes a cylindrical heating probe, a first temperature probe and a second temperature probe; the cylindrical heating probe, the first temperature probe and the second temperature probe are all arranged in the frozen soil sample to be measured; the variable voltage control device is connected to the cylindrical heating probe and the first temperature probe to provide energy for the cylindrical heating probe, and the first temperature probe records the surface temperature of the heating probe; the data processing device is connected to the second temperature probe; the second temperature probe measures the temperature change of the frozen soil.

[0068] The first temperature probe, the second temperature probe and the cylindrical heating probe are placed in parallel; the first temperature probe, the second temperature probe and the cylindrical heating probe are arranged horizontally or vertically in the frozen soil sample to be measured.

[0069] The data processing device includes a data recorder, a processing unit, a transmission unit and a cloud; the processing unit is connected to the cloud; the cloud is connected to the transmission unit, and the data recorder and the transmission unit are both electrically connected to a first temperature probe and a second temperature probe; the transmission unit sends the collected data of the first temperature probe and the second temperature probe to the cloud for storage; the processing unit calls the stored data for analysis, and then stores the processed data again in the cloud; the data recorder displays the temperature data of the first temperature probe and the second temperature probe in real time.

[0070] The variable voltage control device comprises a heater and a temperature controller; the heater is connected to the cylindrical heating probe through the temperature controller.

[0071] See also Figure 2 The present invention discloses a method for measuring thermal characteristics of frozen soil based on a thermal pulse method, comprising:

[0072] S101. Based on the heater, the cylindrical heating probe is heated at a constant temperature. The first temperature probe detects the temperature of the cylindrical heating probe, and the second temperature probe detects the temperature of the frozen soil, and uploads it to the cloud through the transmission unit. At the same time, the data recorder displays the temperature data of the cylindrical heating probe and the frozen soil in real time;

[0073] S102. When the cylindrical heating probe reaches the target temperature, the temperature controller is used to keep the temperature of the cylindrical heating probe constant;

[0074] When the temperature reading of the cylindrical heating probe drops to the preset lower temperature limit, turn on the heater power supply and use a short pulse with a low energy output power for heating. After the heating period ends, turn off the heater power supply to keep the temperature of the cylindrical heating probe between the preset upper and lower temperature limits; continuously repeat this step until the measurement of the frozen soil sample ends.

[0075] S103. Under the heating of the cylindrical heating probe for the frozen soil sample, obtain the temperature penetration curve of the frozen soil sample and the energy received by the frozen soil sample, and then obtain the thermal diffusivity of the frozen soil sample;

[0076] Obtain the temperature penetration curve of the frozen soil sample, specifically:

[0077] The one-dimensional transient heat conduction process in the cylindrical coordinate system is:

[0078]

[0079] Among them, T is the temperature measured in the soil by the second temperature probe; r is the radial distance of the second temperature probe from the cylindrical heating probe; t is the time for measuring the temperature penetration curve of the frozen soil; the effective radius r e is the radial distance between the second temperature probe and the first temperature probe; r e The minimum value of is equal to the sum of the radii of the first temperature probe and the second temperature probe; D is the volumetric thermal diffusivity;

[0080] When heating the frozen soil with a constant temperature heat source, the target temperature T1 of the frozen soil is higher than the initial temperature T0 but lower than the freezing point;

[0081] At the same time, satisfying the initial condition (T(r, 0) = T0 (T0 < 0)) and the boundary condition (T(r e , t) = T1 (T0 < T1 < 0)), the solution in the Laplace space is as follows:

[0082]

[0083] Among them, K0 represents the second kind of zero-order modified Bessel function,

[0084]

[0085] Where s is the representation of time t in Laplace space after T(r,t) undergoes Laplace transform;

[0086] The spatial distribution of temperature at any time in frozen soil, T(r,t), is obtained through the Laplace numerical inverse transformation;

[0087] The root mean square error (RMSE) is used to evaluate the temperature penetration curve fitting, specifically:

[0088]

[0089] Where, the subscript i is the number of measured temperature responses; N is the total number of measured temperatures; T and represent the measured temperature and the predicted temperature, respectively.

[0090] The energy received by the frozen soil sample is:

[0091]

[0092] Wherein, the subscript i represents the i-th discrete spatial interval after the measurement space is radially discretized into M spatial intervals, and the spatial range is from r = r e The radial distance to T = T0;

[0093] S104, obtaining a total heat output of the cylindrical heating probe based on the heating time of the cylindrical heating probe and the heat output during the heating time;

[0094] The total output energy Q2(t) of the cylindrical heating probe is measured by the temperature controller; the heating cycle is with a given power P j and heating cycle tp j The total delivered energy is the sum of the delivered energy in each cycle, as shown below:

[0095]

[0096] Where L is the length of the cylindrical heating probe.

[0097] S105, obtaining a volume heat capacity based on the energy received by the frozen soil sample, the total energy delivered by the cylindrical heating probe, and the volume diffusivity of the frozen soil sample;

[0098] By volume heat capacity C b =ρ b c b Available,

[0099]

[0100] Among them, ρ b is the density of the medium; c bis the specific heat capacity of the medium;

[0101] S106 , obtaining a thermal conductivity coefficient based on the thermal diffusivity and the volumetric heat capacity.

[0102] The bulk thermal conductivity of soil is:

[0103] λ b =DC b .

[0104] When frozen soil is mixed with other substances, such as quartz sand sample, the total heat capacity of the quartz sand sample is

[0105] C=n i c i +n g c g +n s c s

[0106] ρ=n i ρ i +n g ρ g +n s ρ s

[0107] Where n represents the volume fraction of frozen soil components, c i represents the specific heat capacity of ice; c g represents the specific heat capacity of air; c s represents the specific heat capacity of the solid; ρ i represents the bulk density of ice; ρ g represents the volume density of air; ρ s It represents the bulk density of a solid;

[0108] In saturated frozen soil, the gaseous term is omitted, and the volume fractions of each are obtained based on the total heat capacity C and the specific heat capacities of solids and ice.

[0109] λ g The thermal conductivity of dry quartz sand is shown below:

[0110] λ b1 =7.5 1-Φ 0.51 Φ [(1-λ g )Sr+λ g ] 0.78Φ

[0111] Where Φ is the porosity, Sr is the residual water saturation, 7.5 is the thermal conductivity of quartz particles, and 0.51 is the thermal conductivity of water; λ g is the volume thermal conductivity of air;

[0112] When the pore space of quartz sand is filled with additional components, its content is estimated by the following formula:

[0113]

[0114] Among them, n qtz +nx=1;λ qtz , n x and n qtz ,λ x represent the thermal conductivity and volume fraction of quartz sand and additional components, respectively.

[0115] Example:

[0116] The present invention uses ice, quartz sand and a mixture as frozen soil samples; the quartz sand used has a particle size of 50 mesh, is composed of more than 99.8% SiO2, and has a porosity of Φ of 0.37. The experiments were conducted using a consistent setup: (1) a cylindrical sample with a diameter of 21 cm and a height of 14 cm was prepared and stored in a refrigerator throughout the experiment to maintain stable surface and ambient temperatures; (2) a cylindrical heating probe and a first temperature probe and a second temperature probe were installed in the sample before the freezing process to avoid air entrapment at the probe-sample interface during the drilling process; (3) a heating probe with a diameter of 6 mm, a length of 10 cm and an output power of 150 W was used; (4) the temperature of the heating source was manually adjusted by a voltage regulator, such as Figure 1 (5) Unless otherwise stated, the study assumes that the physical properties of the sample components remain unchanged regardless of temperature. All samples were pre-treated (frozen / thawed) for more than 24 hours before measurement.

[0117] The cylindrical heating probe and sample temperatures were continuously tracked using a first and second temperature probe. The tip of the first temperature probe was positioned vertically near the geometric center of the cylindrical heating probe. Temperature measurements from the first and second temperature probes were recorded and stored using a data logger. Temperature readings were taken at 1-second intervals and used to control energy delivery to the heater. The temperature time series data collected by the temperature probes were analyzed to estimate soil thermal properties, assuming a constant surface temperature at the heat source. Both the first and second temperature probes were calibrated using ice and boiling water.

[0118] A voltage regulator is used to adjust the energy delivery intensity to facilitate heat source temperature control. Specifically, the constant temperature of the heat source is achieved through the following steps:

[0119] Based on the heater heating the cylindrical heating probe at a constant power, the first temperature probe detects the temperature of the cylindrical heating probe, and the second temperature probe detects the temperature of the frozen soil, and uploads the data to the cloud through the transmission unit. At the same time, the data logger displays the temperature data of the cylindrical heating probe and the frozen soil in real time;

[0120] When the cylindrical heating probe reaches the target temperature, the power supply of the heater is turned off, and the energy delivery rate of the heater is reduced through the voltage regulator to keep the temperature of the cylindrical heating probe constant;

[0121] When the temperature reading of the cylindrical heating probe drops to a pre-defined lower temperature limit, the heater power is turned on and heating is performed using short pulses with a low energy transfer rate. After the heating period, the heater power is turned off to maintain the surface temperature of the cylindrical heating probe between the preset upper and lower temperature limits. This step is repeated until the frozen soil sample is completely thawed.

[0122] When the frozen soil sample is heated by a cylindrical heating probe, the temperature penetration curve of the frozen soil sample and the energy received by the frozen soil sample are obtained, and then the thermal diffusion coefficient of the frozen soil sample is obtained;

[0123] Based on the constant temperature time and the power consumed during the heating time of the cylindrical heating probe, the total delivered energy of the cylindrical heating probe is obtained;

[0124] The volume heat capacity is obtained based on the energy received by the frozen soil sample, the total transmitted energy of the cylindrical heating probe and the volume diffusivity of the frozen soil sample; the thermal conductivity coefficient is obtained based on the thermal diffusivity and the volume heat capacity.

[0125] In this paper, estimating the thermal properties of frozen soil depends on describing the heat transfer processes, which are mainly controlled by heat conduction in a static mixture of solid, aqueous, and gas phases. The model used to describe conductive heat transfer assumes that: (1) heat conduction is the only mechanism driving heat transfer in frozen soil; and (2) the physical properties of frozen soil are isotropic and homogeneous, that is, there is no spatial and temporal property variation. Therefore, when the thermal properties of soil change significantly during freezing and thawing, the model cannot estimate transient temperature changes.

[0126] The one-dimensional transient heat conduction process in the cylindrical coordinate system is:

[0127]

[0128] Where T is the temperature measured in the soil by the second temperature probe; r is the radial distance between the second temperature probe and the cylindrical heating probe; t is the time to measure the frozen soil temperature penetration curve; the effective radius r e is the radial distance between the second temperature probe and the first temperature probe; r e The minimum value of is equal to the sum of the radii of the first temperature probe and the second temperature probe; D is the volume thermal diffusivity;

[0129] When thawing frozen soil by a constant heat source, the target temperature T1 of the frozen soil is higher than the initial temperature T0 but lower than the freezing point;

[0130] Simultaneously satisfying the initial condition (T(r, 0) = T0 (T0 < 0)) and the boundary condition (T(r e , t) = T1 (T0 < T1 < 0)), the solution in the Laplace space is as follows:

[0131]

[0132] where K0 represents the modified Bessel function of the second kind of order zero,

[0133]

[0134] where s is the representation of time t in the Laplace space after the Laplace transform of T(r, t);

[0135] The root mean square error RMSE is used to evaluate the fitting of the temperature penetration curve, specifically:

[0136]

[0137] [[ID=2,3]]where the subscript i is the sequence of measured temperature responses; N is the total number of measured temperatures; T and represent the measured temperature and the predicted temperature, respectively.

[0138] Given specific r, r e and t, fitting the temperature penetration curve to the field or experimental temperature to obtain the volume diffusivity The spatial temperature range can be easily plotted as a function of the radial distance.

[0139] The energy received by the frozen soil sample is specifically:

[0140]

[0141] where the subscript i represents the i-th discrete spatial interval after discretizing the measurement space into M spatial intervals in the radial direction, and the spatial range is from r = r e to the radial distance at T = T0;

[0142] Based on the power consumed during the constant temperature time and the heating time of the cylindrical heating probe, the total delivered energy of the cylindrical heating probe is obtained, specifically:

[0143] See Figure 3 and Figure 4 ; The heating cycle consists of multiple pulsed heating intervals with a given power P j and a heating period tp <000007: Therefore, the total delivered energy is the sum of the energy delivered in each cycle, as follows:

[0144] <e000436>

[0145] ]>Where L is the length of the cylindrical heating probe.

[0146] The energy received by the frozen soil sample, the total energy delivered by the cylindrical heating probe, and the volume diffusivity of the frozen soil sample are used to obtain the volume heat capacity, which is specifically:

[0147] By volume heat capacity C b =ρ b c b Available,

[0148]

[0149] Among them, ρ b is the density of the medium; c b is the specific heat capacity of the medium;

[0150] The bulk thermal conductivity of soil is:

[0151] λ b =DC b (8)

[0152] When frozen soil is mixed with other substances, and quartz sand samples are mixed with it, the thermal properties of the quartz sand samples are

[0153] ρ=n i ρ i +n g ρ g +n s ρ s (9)

[0154] C=n i c i +n g c g +n s c s (10)

[0155] Where n represents the volume fraction of frozen soil components, ρ i represents the bulk density of ice; ρ g represents the volume density of air; ρ s represents the volume density of the solid; c i represents the specific heat capacity of ice; c g represents the specific heat capacity of air; c s represents the specific heat capacity of the solid;

[0156] The thermal conductivity of dry quartz sand is shown below:

[0157] λ b1 =7.5 1-Φ 0.51 Φ [(1-λ g )Sr+λ g ]0.78Φ (11)

[0158] Where Φ is the porosity, Sr is the residual water saturation, 7.5 is the thermal conductivity of quartz particles, and 0.51 is the thermal conductivity of water; λ g is the volume thermal conductivity of air;

[0159] When the pore space of quartz sand is filled with additional components, its content is estimated by the following formula:

[0160]

[0161] Among them, n qtz +nx=1;λ qtz , n x and n qtz ,λ x represent the thermal conductivity and volume fraction of quartz sand and additional components, respectively.

[0162] By maintaining the maximum temperature (i.e., the temperature of the cylindrical heating probe) below freezing, the proposed model effectively minimizes melting near freezing (-5 to 0°C). In colder permafrost (less than -5°C), melting can be avoided by setting the maximum temperature well below freezing. Therefore, the sensitivity of the input variables in the proposed model was analyzed using baseline case parameters, as shown in Table 1.

[0163] Table 1 Base case parameters for sensitivity analysis

[0164]

[0165] The above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be included in the scope of protection of the claims of the present invention.

Claims

1. A method for measuring thermal properties of frozen soil based on the heat pulse method, characterized in that: The measuring method comprises: The heater heats the cylindrical heating probe at a constant temperature. The first temperature probe detects the temperature of the cylindrical heating probe, and the second temperature probe detects the temperature of the frozen soil. The data is uploaded to the cloud through a transmission unit. At the same time, the data logger displays the temperature data of the cylindrical heating probe and the frozen soil in real time. When the cylindrical heating probe reaches the target temperature, the temperature of the cylindrical heating probe is kept constant through the temperature controller; When the frozen soil sample is heated by a cylindrical heating probe, the temperature penetration curve of the frozen soil sample and the energy received by the frozen soil sample are obtained, and then the thermal diffusivity of the frozen soil sample is obtained; Based on the heating time of the cylindrical heating probe and the heat output during the heating time, the total output energy of the cylindrical heating probe is obtained; The volumetric heat capacity is obtained based on the energy received by the frozen soil sample, the total output energy of the cylindrical heating probe, and the thermal diffusivity of the frozen soil sample. Based on thermal diffusivity and volumetric heat capacity, volumetric thermal conductivity is obtained; When the cylindrical heating probe controls the energy output power of the heater through the temperature controller, the temperature of the cylindrical heating probe is kept constant. Specifically, when the temperature reading of the cylindrical heating probe drops to a preset lower temperature limit, the heater power is turned on and short pulses of low energy output power are used for heating. After the heating period, the heater power is turned off to maintain the temperature of the cylindrical heating probe between the preset upper and lower temperature limits. This step is repeated until the frozen soil sample measurement is completed. The temperature penetration curve of the frozen soil sample is obtained as follows: The one-dimensional transient heat conduction process in the cylindrical coordinate system is: Where T is the temperature measured in the soil by the second temperature probe; r is the radial distance between the second temperature probe and the cylindrical heating probe; t is the time to measure the frozen soil temperature penetration curve; the effective radius r e is the radial distance between the cylindrical heating probe and the first temperature probe; r e The minimum value of is equal to the sum of the radius of the cylindrical heating probe and the first temperature probe; D is the thermal diffusivity; When the frozen soil is heated by a constant temperature heat source, the target temperature T1 of the frozen soil is higher than the initial temperature T0 but lower than the freezing point; Simultaneously satisfying the initial condition \(T(r,0)=T_0\), \(T_0 < 0\) and the boundary condition \(T(r e ,t)=T_1\), \(T_0 < T_1 < 0\), the solution in the Laplace space is as follows: Where K0 represents the second-kind zero-order modified Bessel function, Where s is the representation of time t in Laplace space after T(r,t) undergoes Laplace transform; The spatial distribution of temperature at any time in frozen soil, T(r,t), is obtained through the Laplace numerical inverse transformation; The root mean square error (RMSE) is used to evaluate the temperature penetration curve fitting, specifically: Wherein, subscript m is the series of measured temperature responses; N is the total number of measured temperatures; T m and represent the temperature measured and predicted in the soil by the second temperature probe, respectively; given a specific r, r e and t, fitting the temperature penetration curve to the field or experimental temperature to obtain the thermal diffusivity D; The energy received by the frozen soil sample is specifically: Wherein, the subscript i represents the i-th discrete spatial interval after the measurement space is radially discretized into M spatial intervals, and the spatial range is from r = r e The radial distance to T = T0; Based on the heating time and heat output of the cylindrical heating probe, the total output energy of the cylindrical heating probe is calculated as follows: The total output energy Q2(t) of the cylindrical heating probe is measured by the temperature controller; the heating cycle is with a given power P j and heating cycle tp j The total output energy is the sum of the energy delivered in each cycle, as shown below: Where L is the length of the cylindrical heating probe; The energy received by the frozen soil sample, the total output energy of the cylindrical heating probe, and the thermal diffusivity of the frozen soil sample are calculated to obtain the volume heat capacity, which is specifically: By volume heat capacity C b =ρ b c b Available, Among them, ρ b is the density of the medium; c b is the specific heat capacity of the medium; Based on the thermal diffusivity and volumetric heat capacity, the volumetric thermal conductivity is obtained as follows: The bulk thermal conductivity of soil is: λ b =DC b 。 2. The method for measuring thermal characteristics of frozen soil based on the heat pulse method according to claim 1, characterized in that: When frozen soil is mixed with other substances, such as quartz sand sample, the total heat capacity of the quartz sand sample is C=n i c i +n g c g +n s c s Among them, n i represents the volume fraction of ice in frozen soil, n g represents the volume fraction of air in frozen soil, n s represents the volume fraction of solid components in frozen soil, c i represents the specific heat capacity of ice; c g represents the specific heat capacity of air; c s represents the specific heat capacity of the solid; In saturated frozen soil, the gaseous term is omitted, and the volume fractions of each are obtained based on the total heat capacity C and the specific heat capacities of solids and ice.

3. The method for measuring thermal characteristics of frozen soil based on the heat pulse method according to claim 1, characterized in that: The measuring device adopted by the method includes: a test component, a variable voltage control device and a data processing device; The test assembly includes a cylindrical heating probe, a first temperature probe and a second temperature probe; the cylindrical heating probe, the first temperature probe and the second temperature probe are all arranged in the frozen soil sample to be measured; the variable voltage control device is connected to the cylindrical heating probe and the first temperature probe to provide energy for the cylindrical heating probe, and the first temperature probe records the surface temperature of the heating probe; the data processing device is connected to the second temperature probe; the second temperature probe measures the temperature change of the frozen soil.

4. The method for measuring thermal characteristics of frozen soil based on the heat pulse method according to claim 3, characterized in that: The first temperature probe, the second temperature probe and the cylindrical heating probe are placed in parallel; the first temperature probe, the second temperature probe and the cylindrical heating probe are arranged horizontally or vertically in the frozen soil sample to be measured.

5. The method for measuring thermal characteristics of frozen soil based on the heat pulse method according to claim 3, characterized in that: The data processing device includes a data recorder, a processing unit, a transmission unit and a cloud; the processing unit is connected to the cloud; the cloud is connected to the transmission unit, and the data recorder and the transmission unit are both electrically connected to a first temperature probe and a second temperature probe; the transmission unit sends the collected data of the first temperature probe and the second temperature probe to the cloud for storage; the processing unit calls the stored data for analysis, and then stores the processed data again in the cloud; the data recorder displays the temperature data of the first temperature probe and the second temperature probe in real time.

6. The method for measuring thermal characteristics of frozen soil based on the heat pulse method according to claim 5, characterized in that: The variable voltage control device includes a heater and a temperature controller; the heater is connected to a cylindrical heating probe via the temperature controller.

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