Freezing method effect simulation system and evaluation method for emergency disposal of nuclear leakage

Abstract

This invention discloses a simulation system and evaluation method for the effectiveness of freezing in emergency response to nuclear leaks. The simulation system includes: a permeability barrier experimental system, a cryogenic cold bath system, and a frozen wall monitoring system. The frozen wall monitoring system includes: a radial-axial combined strain gauge, located near the freezing tube, comprising radial and axial strain gauges, used to monitor radial and axial frost heave strains generated during the formation of the frozen wall, respectively; an acoustic emission testing system, located near the freezing tube, for collecting acoustic emission signals, including a waveguide rod, an acoustic emission sensor attached to the surface of the waveguide rod, and a signal amplifier; and a CT scanning system, consisting of an X-ray source and a detector, used to monitor radionuclide permeation and porosity in the frozen wall region. The collected frost heave strain, acoustic emission signals, and porosity are sent to a data and image processing system for analysis. This invention can accurately monitor and evaluate the permeability barrier properties of the frozen wall and can be widely applied in the field of nuclear leak response.

Description

Technical Field

[0001] This invention relates to the field of nuclear leak treatment, and in particular to a system and evaluation method for simulating the effects of freezing in emergency nuclear leak response. Background Technology

[0002] If a disposal site for radioactive nuclear waste is damaged by natural disasters or human activities, large amounts of nuclear waste will breach the engineering and natural barriers of the storage facility and flow into the biosphere with groundwater, causing unpredictable losses. Due to the advantages of permafrost, such as low permeability, deformation resistance, and radiation resistance, the existing technology of artificial ground freezing for preventing nuclear wastewater leakage from nuclear power plants has good prospects for application and promotion. However, the current application effect of existing technologies lacks effective simulation systems and evaluation methods, resulting in a significant lag between theory and practice.

[0003] Currently, freezing methods are mostly used in subway construction and shaft and tunnel excavation projects. Research on freezing simulation devices and systems makes it difficult to achieve rapid and flexible adjustment of freezing pipe parameters. In addition, the key to freezing methods in emergency response to nuclear leaks lies in their rapid seepage prevention, which places higher demands on the accurate and rapid evaluation of the freezing wall's formation and stabilization process. However, existing technologies cannot meet the requirements for accurate monitoring of the freezing wall's seepage prevention properties, and the means of evaluating the effectiveness of freezing methods are relatively limited. Summary of the Invention

[0004] In view of this, the present invention provides a simulation system and evaluation method for the effect of freezing in emergency response to nuclear leaks, so as to accurately monitor and evaluate the impermeability of the frozen wall.

[0005] One aspect of the present invention provides a simulation system for the effect of freezing in emergency response to nuclear leaks, comprising: a seepage barrier experimental system, a cryogenic cold bath system, and a freezing wall monitoring system;

[0006] The seepage barrier experimental system includes a water supply tank, a peristaltic pump, a first filter screen, a second filter screen, a first water pipe, a second water pipe, a model box, multiple freezing pipes, and a waste liquid recovery tank. The water supply tank is connected to a first side of the model box via the first water pipe. The peristaltic pump is mounted on the first water pipe, which also has a water supply valve. The first filter screen is located inside the model box and forms an inlet chamber with the first side. The waste liquid recovery tank is connected to a second side of the model box via the second water pipe. The second filter screen is located inside the model box and forms an outlet chamber with the second side, which also has an outlet valve. The first and second sides are opposite faces, with the first filter screen parallel to the first side and the second filter screen parallel to the second side. The freezing pipes are located inside the model box and between the first and second filters. The diameter of the freezing pipes is adjustable, and their position is movable. All the freezing pipes are arranged side-by-side, and the plane formed by their side-by-side arrangement is parallel to the first and second filters.

[0007] The low-temperature cooling system is connected to the freezing pipe through an inlet pipe and an outlet pipe. The low-temperature cooling system exchanges antifreeze with the freezing pipe through a built-in circulation pump, and keeps the temperature of the antifreeze in the inlet pipe and the temperature of the antifreeze in the outlet pipe at a preset constant value.

[0008] The frozen wall monitoring system includes a radial-axial combined strain gauge, an acoustic emission testing system, a CT scanning system, and a data and image processing system. Both the radial-axial combined strain gauge and the acoustic emission testing system are positioned between the first filter and the second filter. The radial-axial combined strain gauge monitors the radial and axial frost heave strain generated during the formation of the frozen wall within the model box. The acoustic emission testing system collects acoustic signals generated during the formation of the frozen wall due to the volume expansion of the frozen soil caused by the water-ice phase change. A radionuclide solution containing KI is used as the CT contrast agent for the CT scanning system, which emits X-rays into the frozen wall region within the model box to obtain the seepage information and porosity of the radionuclide solution in the frozen wall region. The data and image processing system determines the impermeability of the frozen wall based on at least one of the frost heave strain, the characteristic parameters corresponding to the acoustic signals, and the porosity.

[0009] Optionally, each of the freezing tubes is provided with a pull ring, and pulling the pull ring is used to adjust the diameter of the freezing tube;

[0010] All the freezing tubes are mounted on a slide rail, and each freezing tube can move on the slide rail.

[0011] Optionally, the low-temperature cooling system is provided with a cooling bath tank inside, the cooling bath tank is used to hold antifreeze, and several rings of refrigeration pipes are arranged around the inner wall of the cooling bath tank, the refrigeration pipes are used to control the temperature of the antifreeze to the preset constant value.

[0012] Optionally, the combined radial-axial strain gauge includes a radial strain gauge and an axial strain gauge;

[0013] The radial strain gauge consists of a closed steel fiber coil and a first thin-film strain gauge bonded to the surface of the steel fiber coil; the surface of the steel fiber coil has a set roughness to fix the position of the radial-axial combined strain gauge.

[0014] The axial strain gauge consists of four steel fibers fixed radially within the steel fiber coil and a second thin-film strain gauge bonded to the contact position between each steel fiber and the steel fiber coil. Each steel fiber points towards the geometric center of the steel fiber coil.

[0015] The plane of the steel fiber coil is parallel to the first filter screen and the second filter screen.

[0016] Optionally, when the expansion of the frozen wall causes deformation of the steel fiber coil, resulting in a change in the resistance value of the sensitive grid inside the first thin-film strain gauge, the radial strain gauge acquires the first resistance value.

[0017] And / or,

[0018] When the expansion of the frozen wall causes deformation of the steel fiber, resulting in a change in the resistance value of the sensitive grid inside the second thin-film strain gauge, the axial strain gauge collects the second resistance value.

[0019] Wherein, the first resistance value and / or the second resistance value are used as the frost heave strain.

[0020] Optionally, the CT scanning system includes an X-ray source and a detector;

[0021] The X-ray source is used to generate X-rays and irradiate the area where the frozen wall is located inside the model box;

[0022] The detector is used to receive the X-ray signal generated by the X-ray penetrating the frozen wall inside the model box, convert the X-ray signal into a first digital signal, and send it to the data and image processing system.

[0023] The data and image processing system is used to perform three-dimensional reconstruction of the region where the frozen wall is located based on the first digital signal to obtain a reconstruction model; and to determine the seepage information of the nuclide solution penetrating the frozen wall and the porosity of the region where the frozen wall is located based on the reconstruction model.

[0024] Optionally, the acoustic emission testing system includes a waveguide rod, an acoustic emission sensor, and a signal amplifier;

[0025] The waveguide rod is used to propagate the acoustic signal;

[0026] The acoustic emission sensor is used to collect the acoustic signal;

[0027] The signal amplifier is used to filter and amplify the acoustic signal, convert the filtered and amplified acoustic signal into a second digital signal, and then send the second digital signal to the data and image processing system.

[0028] Optionally, the data and image processing system is used to extract the number of rings, the cumulative number of events, and the cumulative energy from the second digital signal as feature parameters corresponding to the sound signal;

[0029] Wherein, the ringing count is the number of times the amplitude of the acoustic signal exceeds a preset threshold voltage within a set time period; the cumulative event count is the number of acoustic emission events obtained by wave impact identification within the set time period, any signal in which the acoustic signal exceeds the signal threshold and causes any channel of the data and image processing system to acquire data is considered a wave impact, and a local material change that produces acoustic emission is considered an acoustic emission event; the cumulative energy is the area under the detector envelope of the acoustic emission event, used to reflect the relative energy and intensity of the acoustic emission event.

[0030] Optionally, the data and image processing system is used to determine the impermeability of the frozen wall based on at least one of the frost heave strain, the characteristic parameters corresponding to the acoustic signal, and the porosity, including:

[0031] The data and image processing system is used to determine a comprehensive evaluation expression based on the frost heave strain, the characteristic parameters corresponding to the acoustic signal, and the porosity, and to determine the impermeability of the frozen wall based on the comprehensive evaluation expression.

[0032] The comprehensive evaluation expression is as follows:

[0033] k i =αn e +β(aσ a +bσ r )+γ(cN r +dN s +eA e )

[0034] Where, k i As an evaluation index for barrier properties; n e The porosity is σ. a Let σ be the axial strain in the frost heave strain.r The radial strain is the strain in the frost heave strain; the characteristic parameters corresponding to the acoustic signal include the number of ringings, the cumulative number of events, and the cumulative energy, N. r N s A e The numbers represent the number of ringing events, the cumulative number of events, and the cumulative energy, respectively; α, β, and γ are the coefficients of the porosity, the frost heave strain, and the characteristic parameter, respectively; a is the weighting ratio of the axial strain, and b is the weighting ratio of the radial strain; c, d, and e are the weighting ratios of the number of ringing events, the cumulative number of events, and the cumulative energy, respectively.

[0035] Another aspect of the present invention provides a method for evaluating the effectiveness of freezing methods in emergency response to nuclear leaks, applied to the data and image processing system in the aforementioned simulation system for the effectiveness of freezing methods in emergency response to nuclear leaks. The evaluation method includes:

[0036] The radial and axial frost heave strains generated during the formation of the frozen wall inside the model box were obtained by measuring the radial-axial combined strain gauge.

[0037] Acquire acoustic signals generated by the volume expansion of frozen soil due to the phase change of water and ice during the formation of the frozen wall, collected by an acoustic emission testing system, and determine the characteristic parameters corresponding to the acoustic signals; the characteristic parameters include the number of ringings, the cumulative number of events, and the cumulative energy.

[0038] The permeation information and porosity of the radionuclide solution in the frozen wall area are obtained by emitting X-rays into the frozen wall area inside the model box by the CT scanning system; the radionuclide solution including KI is used as the CT contrast agent of the CT scanning system;

[0039] A comprehensive evaluation expression is determined based on the frost heave strain, the characteristic parameters corresponding to the acoustic signal, and the porosity, and the impermeability of the frozen wall is determined based on the comprehensive evaluation expression.

[0040] The comprehensive evaluation expression is as follows:

[0041] k i =αn e +β(aσ a +bσ r )+γ(cN r +dN s +eA e )

[0042] Where, k i As an evaluation index for barrier properties; n e The porosity is σ. a Let σ be the axial strain in the frost heave strain. r N represents the radial strain in the frost heave strain.r N s A e The numbers represent the number of ringing events, the cumulative number of events, and the cumulative energy, respectively; α, β, and γ are the coefficients of the porosity, the frost heave strain, and the characteristic parameter, respectively; a is the weighting ratio of the axial strain, and b is the weighting ratio of the radial strain; c, d, and e are the weighting ratios of the number of ringing events, the cumulative number of events, and the cumulative energy, respectively.

[0043] This invention measures the radial and axial frost heave strain generated during the formation of the frozen wall within the model box using a combined radial-axial strain gauge. It also acquires acoustic signals generated by the volume expansion of frozen soil due to the water-ice phase change during the formation of the frozen wall using an acoustic emission testing system. Furthermore, it emits X-rays into the frozen wall area within the model box using a CT scanning system to obtain the porosity of the frozen wall area. Finally, a data and image processing system can determine the impermeability of the frozen wall based on at least one of the characteristic parameters corresponding to the frost heave strain and acoustic signals, as well as the porosity. In other words, this invention can acquire the above three types of monitoring data and can evaluate the impermeability of the frozen wall based on at least one of the monitoring data, making the evaluation of the impermeability effect more accurate.

[0044] Moreover, by changing the radial size and position of the freezing tube, various experimental conditions can be obtained, thereby enabling the present invention to obtain more comprehensive monitoring data on the permeability of the frozen wall and to conduct a more comprehensive assessment of the permeability of the frozen wall. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 An optional example structural diagram of a system for simulating the effects of freezing methods in emergency response to nuclear leaks, provided by an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of a freezing tube provided in an embodiment of the present invention;

[0048] Figure 3 This is an example structural diagram of a radial-axial combined strain gauge provided in an embodiment of the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0050] It should be noted that although functional modules are divided in the device diagram, in some cases, the steps shown or described can be performed with a different module division than that in the device.

[0051] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0052] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used herein is for the purpose of describing embodiments of the invention only and is not intended to limit the invention.

[0053] Unlike existing freezing methods used in tunnels and shafts, the freezing method of this invention for nuclear leak emergency response should possess the characteristic of rapid seepage prevention. However, existing technologies cannot accurately monitor and assess the seepage prevention properties of the frozen wall. Furthermore, current freezing method simulation systems involve cumbersome adjustments to the freezing pipe parameters, leading to time-consuming and labor-intensive switching between different operating conditions. Therefore, a simulation system is urgently needed to explore the effectiveness of freezing methods in preventing nuclear leaks under different operating conditions.

[0054] Accordingly, this invention provides a simulation system and evaluation method for conveniently adjusting the parameters of the freezing tube and accurately identifying the impermeability of the frozen wall. This invention uses a pull ring to adjust the diameter of the freezing tube, which is fixed on a slide rail. The position of the freezing tube can be changed by moving it, ultimately achieving convenient control of the freezing tube parameters. This invention proposes three methods for monitoring the impermeability of the frozen wall and, based on the monitoring results of these three methods, provides a comprehensive evaluation expression for the impermeability effect of the freezing method. The first method utilizes the strong absorption of X-rays by iodine in KI. KI reagent is added to the seeping radionuclide solution, and CT is used to observe the penetration and seepage of the radionuclide solution in the frozen wall area. Simultaneously, CT scanning can also obtain information on the pore structure of the frozen wall area. The second method uses radial-axial combined strain gauges embedded in the frozen wall area to measure the magnitude of frost heave force, thus indirectly reflecting the impermeability effect of the frozen wall. The third method uses waveguide rods combined with acoustic emission technology to capture the acoustic emission signals generated by the water-ice phase transition during the formation of the frozen wall. The development status of the frozen wall is determined based on the number of rings, the cumulative number of events, and the cumulative energy.

[0055] The present invention will now be described in detail.

[0056] Reference Figure 1 This invention provides an optional example structural diagram of a freezing method effect simulation system for emergency response to nuclear leaks, including: a seepage barrier experimental system, a cryogenic cold bath system, and a freezing wall monitoring system.

[0057] First of all, Figure 1 The following is a description. Specifically, it includes a water supply tank 1, a peristaltic pump 2, a first filter screen 3, a second filter screen 4, a first water pipe 5, a second water pipe 6, a model box 7, a freezing pipe 8, a waste liquid recovery tank 9, a water inlet chamber 10, a water outlet chamber 11, a low-temperature cold bath system 12, a radial-axial combined strain gauge 13, a data and image processing system 14, an X-ray source 15, a detector 16, a waveguide rod 17, an acoustic emission sensor 18, a signal amplifier 19, a slide rail 20, a water supply valve 21, and a water outlet valve 22.

[0058] Next, the seepage barrier experimental system, the cryogenic cold bath system, and the frozen wall monitoring system in the emergency response nuclear leakage freezing method effect simulation system provided in the embodiments of the present invention will be described respectively.

[0059] The seepage barrier experimental system includes a water supply tank, a peristaltic pump, a first filter screen, a second filter screen, a first water pipe, a second water pipe, a model box, multiple freezing pipes, and a waste liquid recovery tank. The water supply tank is connected to a first side of the model box via the first water pipe. The peristaltic pump is mounted on the first water pipe, and a water supply valve is also installed on the first water pipe. The first filter screen is located inside the model box and forms an inlet chamber with the first side. The waste liquid recovery tank is connected to a second side of the model box via the second water pipe. The second filter screen is located inside the model box and forms an outlet chamber with the second side, and an outlet valve is also installed on the second water pipe. The first and second sides are opposite faces, with the first filter screen parallel to the first side and the second filter screen parallel to the second side. The freezing pipes are located inside the model box and between the first and second filters. The diameter of the freezing pipes is adjustable, and the position of the freezing pipes is movable. The freezing pipes are arranged side by side, and the plane formed by their side-by-side arrangement is parallel to the first and second filters.

[0060] Specifically, a peristaltic pump can introduce the radionuclide solution (KI can be added to the radionuclide solution as a CT contrast agent) from the water supply tank into the model box at different flow rates. After passing through the model box, the radionuclide solution flows into the waste liquid recovery tank through the outlet pipe. Filter screens are installed near the inlet and outlet of the model box to serve as inlet and outlet chambers, and are filled with coarse quartz sand to ensure that the radionuclide solution flowing into the soil laboratory is uniform and stable.

[0061] As a further optional implementation, each of the freezing tubes is provided with a pull ring, which is pulled to adjust the diameter of the freezing tube; all the freezing tubes are mounted on a slide rail, and each freezing tube can move on the slide rail. (Refer to...) Figure 2 This invention provides a schematic diagram of a freezing tube, including a freezing tube 801 and a pull ring 802.

[0062] Optionally, four freezing tubes with adjustable diameters via pull rings can be installed in the middle of the model box. The bottom of the freezing tubes is fixed to a movable slide rail, thus allowing for arbitrary adjustment of their horizontal position.

[0063] The low-temperature cooling system is connected to the freezing pipe through an inlet pipe and an outlet pipe. The low-temperature cooling system exchanges antifreeze with the freezing pipe through a built-in circulation pump, and keeps the temperature of the antifreeze in the inlet pipe and the temperature of the antifreeze in the outlet pipe at a preset constant value.

[0064] As a further optional implementation, the low-temperature cold bath system is provided with a cold bath tank inside, the cold bath tank is used to hold antifreeze, and several rings of refrigeration pipes are arranged around the inner wall of the cold bath tank, the refrigeration pipes are used to control the temperature of the antifreeze to the preset constant value.

[0065] Specifically, this constant value can be any temperature value below zero. When the low-temperature cooling bath system is started and this constant value is set, the circulation pump in the low-temperature cooling bath system pumps the antifreeze in the cooling bath tank into the freezing pipe. The antifreeze flowing back will be cooled down to the set temperature (i.e., this constant value) by the cooling pipes on the inner wall of the cooling bath tank. The antifreeze circulates in this way to achieve constant temperature control of the freezing pipe.

[0066] The frozen wall monitoring system includes a radial-axial combined strain gauge, an acoustic emission testing system, a CT scanning system, and a data and image processing system. Both the radial-axial combined strain gauge and the acoustic emission testing system are positioned between the first filter and the second filter. The radial-axial combined strain gauge monitors the radial and axial frost heave strain generated during the formation of the frozen wall within the model box. The acoustic emission testing system collects acoustic signals generated during the formation of the frozen wall due to the volume expansion of the frozen soil caused by the water-ice phase change. A radionuclide solution containing KI is used as the CT contrast agent for the CT scanning system, which emits X-rays into the frozen wall region within the model box to obtain the seepage information and porosity of the radionuclide solution in the frozen wall region. The data and image processing system determines the impermeability of the frozen wall based on at least one of the frost heave strain, the characteristic parameters corresponding to the acoustic signals, and the porosity.

[0067] Specifically, this embodiment of the invention provides a visualization method for evaluating the impermeability of a frozen wall: KI is added to the radionuclide solution as a CT contrast agent, and the process of the radionuclide solution penetrating the frozen wall can be observed using a CT scanning system. The impermeability of the frozen wall can be intuitively evaluated based on the seepage information of the radionuclide solution.

[0068] As a further optional implementation, the combined radial-axial strain gauge includes a radial strain gauge and an axial strain gauge, referring to... Figure 3 The present invention provides an example structural diagram of a radial-axial combined strain gauge, which includes a radial strain steel fiber coil 1301, a radial thin film strainer 1302, an axial strain steel fiber 1303, and an axial thin film strainer 1304.

[0069] The radial strain gauge consists of a closed steel fiber coil and a first thin-film strain gauge bonded to the surface of the steel fiber coil; the surface of the steel fiber coil has a set roughness to fix the position of the radial-axial combined strain gauge; the axial strain gauge consists of four steel fibers fixed in the radial direction of the steel fiber coil and a second thin-film strain gauge bonded to the contact position between each steel fiber and the steel fiber coil, each steel fiber pointing towards the geometric center of the steel fiber coil; wherein, the plane of the steel fiber coil is parallel to the first filter screen and the second filter screen.

[0070] When the expansion of the frozen wall causes deformation of the steel fiber coil, resulting in a change in the resistance value of the sensitive grid inside the first thin-film strain gauge, the radial strain gauge acquires a first resistance value; and / or, when the expansion of the frozen wall causes deformation of the steel fiber, resulting in a change in the resistance value of the sensitive grid inside the second thin-film strain gauge, the axial strain gauge acquires a second resistance value; wherein the first resistance value and / or the second resistance value are used as the frost heave strain.

[0071] Specifically, the radial strain gauge consists of a closed steel fiber coil and a thin-film strain gauge bonded to the surface of the steel fiber. The steel fiber surface has a certain roughness to prevent loosening under conditions of minimal friction with the soil. When the soil freezes and undergoes radial expansion deformation, the steel fiber coil embedded within it will deform accordingly, and the thin-film strain gauge bonded to its surface will also be compressed, causing a change in the resistance value of the sensitive grid inside the thin-film strain gauge. After the resistance value is transmitted to the data and image processing system, the strain value of the area covered by the strain gauge can be calculated. The axial strain gauge consists of four steel fibers fixed at the upper, lower, front, and rear extensions of the radial closed coil and thin-film strain gauges bonded at the contact points between the steel fibers of the two strain gauges. When the soil undergoes longitudinal frost heave deformation along the length of the model box, the strain gauge will tilt along with the axial steel fibers, resulting in a change in resistance value. This change is then converted into a strain reading by the data and image processing system. The measured strain value is proportional to the angle of tilt of the steel fiber. By combining the radial and axial strain test results of the frozen wall area, the strain distribution within the spatial area during the formation of the frozen wall can be accurately perceived.

[0072] As a further optional implementation, the CT scanning system includes an X-ray source and a detector;

[0073] The X-ray source is used to generate X-rays and irradiate the area where the frozen wall is located inside the model box;

[0074] The detector is used to receive the X-ray signal generated by the X-ray penetrating the frozen wall inside the model box, convert the X-ray signal into a first digital signal, and send it to the data and image processing system.

[0075] The data and image processing system is used to perform three-dimensional reconstruction of the region where the frozen wall is located based on the first digital signal to obtain a reconstruction model; and to determine the seepage information of the nuclide solution penetrating the frozen wall and the porosity of the region where the frozen wall is located based on the reconstruction model.

[0076] Specifically, X-rays are used as both the generating and receiving signals. By converting the invisible energy signal into a recordable electrical signal, a data and image processing system reconstructs the frozen wall using this electrical signal, thereby obtaining three-dimensional visualization information. The specific steps include: X-rays emitted from an X-ray source penetrate the frozen wall region of the model box and reach the detector. Due to the different absorption and attenuation effects produced by the interaction when X-rays penetrate different materials such as frozen soil, non-frozen soil, and porous media, the signals reaching the detector from different regions can be distinguished. The detector converts the captured X-ray signals into digital signals and transmits them to the data and image processing system. Optionally, the data and image processing system can use Avzio software to perform three-dimensional reconstruction of the frozen wall region based on the CT values ​​of each layer (obtained from the digital signals converted from the X-ray signals). Based on the reconstructed model, the seepage path of the KI-containing solution in the soil can be directly observed, and the porosity of the selected frozen wall region can also be directly quantified using Avzio software.

[0077] As a further optional implementation, the acoustic emission testing system includes a waveguide rod, an acoustic emission sensor, and a signal amplifier; the waveguide rod is used to propagate the acoustic signal; the acoustic emission sensor is used to acquire the acoustic signal; the signal amplifier is used to filter and amplify the acoustic signal, convert the filtered and amplified acoustic signal into a second digital signal, and then send the second digital signal to the data and image processing system.

[0078] Furthermore, the data and image processing system is used to extract the number of rings, the cumulative number of events, and the cumulative energy from the second digital signal as characteristic parameters corresponding to the sound signal.

[0079] Specifically, the acoustic signals generated by the water-ice phase change during the formation of the frozen wall are weak and difficult to capture directly using acoustic emission sensors. In this embodiment of the invention, a waveguide rod can be pre-embedded in the frozen wall region. During the formation of the frozen wall, the frozen soil expands due to the water-ice phase change. During this expansion, soil particles around the waveguide rod slide and collide with and rub against the waveguide rod. The acoustic signals generated by these processes are propagated by the waveguide rod and ultimately captured by the acoustic emission sensor. After passing through a 60dB signal amplifier to improve the signal-to-noise ratio and filter background noise, the electrical signal is converted into a digital signal, which is then processed and stored by a data and image processing system. The data and image processing system extracts feature parameters (ring count, cumulative event count, and cumulative energy) from the acquired acoustic signal (i.e., the digital signal converted from the electrical signal). These feature parameters represent the density of signals generated within a certain time period. The ringing count (unit: Times) is the number of times the signal amplitude exceeds a preset threshold voltage within a time period; the cumulative event count (unit: Times) represents the number of acoustic emission events identified from several wave impacts (any signal exceeding the signal threshold and enabling data acquisition by a channel is called a wave impact) within a time period, and a local material change that produces acoustic emission is called an acoustic emission event; the cumulative energy (unit: mV·ms) is the area under the detector envelope of the acoustic emission event, reflecting the relative energy and intensity of the acoustic emission event. All three characteristic parameters can reflect the volume expansion caused by the water-ice phase change during the formation of the frozen wall, and their magnitude increases with the freezing time of the frozen wall.

[0080] The data and image processing system of this invention is used to determine the impermeability of a frozen wall based on at least one of the frost heave strain, the characteristic parameters corresponding to the acoustic signal, and the porosity. That is, it provides three methods for determining the impermeability of a frozen wall. Optionally, this invention can comprehensively evaluate the impermeability of the frozen wall by combining the results measured by the three methods, as detailed below:

[0081] The data and image processing system is used to determine a comprehensive evaluation expression based on the frost heave strain, the characteristic parameters corresponding to the acoustic signal, and the porosity, and to determine the impermeability of the frozen wall based on the comprehensive evaluation expression.

[0082] The comprehensive evaluation expression is as follows:

[0083] k i =αn e +β(aσ a +bσ r )+γ(cN r +dN s +eA e )

[0084] Where, k i As an evaluation index for barrier properties; ne The porosity is σ. a Let σ be the axial strain in the frost heave strain. r The radial strain is the strain in the frost heave strain; the characteristic parameters corresponding to the acoustic signal include the number of ringings, the cumulative number of events, and the cumulative energy, N. r N s A e The numbers represent the number of ringing events, the cumulative number of events, and the cumulative energy, respectively; α, β, and γ are the coefficients of the porosity, the frost heave strain, and the characteristic parameter, respectively; a is the weighting ratio of the axial strain, and b is the weighting ratio of the radial strain; c, d, and e are the weighting ratios of the number of ringing events, the cumulative number of events, and the cumulative energy, respectively.

[0085] The frozen wall monitoring system of this invention may include a radial-axial combined strain gauge, an acoustic emission testing system, and a CT scanning system. The radial-axial combined strain gauge is deployed in the frozen wall region near the freezing pipe. It consists of two parts: a radial strain gauge encircling the soil sample cross-section and axial strain gauges extending in the upper, lower, front, and rear directions, respectively used to monitor the radial and axial frost heave strain generated during the formation of the frozen wall. The acoustic emission testing system includes a waveguide rod embedded near the freezing pipe, an acoustic emission sensor attached to its surface, and a signal amplifier. Furthermore, the CT scanning system, composed of an X-ray source and a detector, is used to monitor radionuclide seepage and porosity changes in the frozen wall region. Finally, the acquired frost heave strain, acoustic emission signals, and CT scan results are transmitted to a data image processing system for analysis.

[0086] This invention can solve the following problems existing in the prior art and has corresponding beneficial effects:

[0087] 1. Existing freezing method model systems do not consider convenient switching of freezing tube parameters. This invention proposes to change the diameter and position of the freezing tube using pull rings and slide rails, enabling rapid switching between different freezing tube conditions. By adjusting the freezing tube parameters, experiments under different conditions can be conducted on the same soil sample multiple times, greatly improving the efficiency of the model system and saving time and effort. It also allows for flexible and convenient adjustment of freezing parameters in existing freezing method model systems.

[0088] 2. This invention adds KI to the radionuclide solution as a CT contrast agent and observes the process of the radionuclide solution penetrating the frozen wall through CT scanning. This provides a visual way to evaluate the impermeability of the frozen wall, filling the current technical gap of lacking visualization methods for evaluating the impermeability of the frozen wall. It also provides an important way to determine whether the frozen wall is completely impermeable.

[0089] 3. Existing technologies for monitoring frost heave deformation in frozen soil generally employ displacement gauges and moisture meters. However, traditional thin-film strain gauges are ineffective for measuring the frost heave force generated during the formation of frozen walls. This invention proposes a method of measuring the frost heave strain generated during the formation of frozen walls by encircling a radial-axial combined strain gauge around the cross-section of the frozen wall area, providing a solution for frozen wall strain monitoring. By measuring the frozen wall formation process using a radial-axial combined strain gauge, this method fills the current technological gap in frozen wall strain monitoring. Furthermore, by combining the radial-axial strain results, the accuracy of strain testing within the three-dimensional space of the frozen wall can be greatly improved.

[0090] 4. Due to the weak signal generated by the water-ice phase transition in permafrost, existing technologies make it difficult to directly capture the ice formation signal using acoustic emission sensors. This invention proposes to use a metal waveguide rod to transmit the relatively obvious acoustic signal generated by the collision and friction between the waveguide rod and the frozen wall during the formation process to the acoustic emission sensor, thereby achieving accurate and comprehensive capture of the signal during the frozen wall formation process. This invention uses the waveguide rod to amplify the acoustic emission signal during the frozen wall formation process, effectively reducing the error caused by the difficulty of sensor recognition due to the weak acoustic signal of the water-ice phase transition, thus achieving accurate and comprehensive quantitative evaluation of the acoustic emission signal during the frozen wall formation process.

[0091] 5. Currently, there is a lack of accurate and comprehensive evaluation methods for the effectiveness of freezing methods. This invention proposes a comprehensive evaluation expression that integrates the porosity, frost heave strain, and acoustic emission signals measured by CT in the frozen wall area. It takes into account the changes in various physical parameters such as internal components, strain, and acoustic signals of the frozen wall. Compared with the errors that may be caused by measuring a single physical quantity in the existing technology, this invention can make the evaluation results more accurate and comprehensive.

[0092] This invention also provides a method for evaluating the effectiveness of freezing methods in emergency response to nuclear leaks, applied to the data and image processing system in the aforementioned simulation system for the effectiveness of freezing methods in emergency response to nuclear leaks. The evaluation method includes:

[0093] The radial and axial frost heave strains generated during the formation of the frozen wall inside the model box were obtained by measuring the radial-axial combined strain gauge.

[0094] Acquire acoustic signals generated by the volume expansion of frozen soil due to the phase change of water and ice during the formation of the frozen wall, collected by an acoustic emission testing system, and determine the characteristic parameters corresponding to the acoustic signals; the characteristic parameters include the number of ringings, the cumulative number of events, and the cumulative energy.

[0095] The permeation information and porosity of the radionuclide solution in the frozen wall area are obtained by emitting X-rays into the frozen wall area inside the model box by the CT scanning system; the radionuclide solution including KI is used as the CT contrast agent of the CT scanning system;

[0096] A comprehensive evaluation expression is determined based on the frost heave strain, the characteristic parameters corresponding to the acoustic signal, and the porosity, and the impermeability of the frozen wall is determined based on the comprehensive evaluation expression.

[0097] The comprehensive evaluation expression is as follows:

[0098] k i =αn e +β(aσ a +bσ r )+γ(cN r +dN s +eA e )

[0099] Where, k i As an evaluation index for barrier properties; n e The porosity is σ. a Let σ be the axial strain in the frost heave strain. r N represents the radial strain in the frost heave strain. r N s A e The numbers represent the number of ringing events, the cumulative number of events, and the cumulative energy, respectively; α, β, and γ are the coefficients of the porosity, the frost heave strain, and the characteristic parameter, respectively; a is the weighting ratio of the axial strain, and b is the weighting ratio of the radial strain; c, d, and e are the weighting ratios of the number of ringing events, the cumulative number of events, and the cumulative energy, respectively.

[0100] The application process of the present invention will be illustrated below with specific examples.

[0101] First, the seepage barrier test system was configured: the left inlet chamber of the model box was filled with coarse-grained quartz sand and then separated by a filter screen. The soil from the test stratum was dried, crushed, and sieved through a 2mm sieve, then divided into 5 equal portions and layered into the model box up to the outlet chamber position. After being separated by a filter screen, it was filled with coarse quartz sand. The water supply valve was opened and the outlet valve was closed, allowing the soil sample to soak in water for 24 hours, which was considered to be saturated. When filling to the corresponding positions, radial-axial combined strain gauges, the slide rails for the freezing tubes, and waveguide rods were embedded respectively. Four freezing tubes, made of seamless steel pipes, were installed at equal intervals on the slide rails and connected to a low-temperature cold bath filled with antifreeze. The temperature of the freezing tubes was maintained by circulating the antifreeze in the low-temperature cold bath.

[0102] Different concentrations (1g / L, 3g / L, 5g / L, 7g / L), types ( 137 Cs、 90 Sr、 129The radionuclide solution (I) was mixed with a 5 g / L KI solution and poured into the water supply tank. At the start of the experiment, the outlet valve was opened, and the mixture was pumped into the soil sample at a fixed flow rate using a peristaltic pump. Once the outflow rate stabilized, the low-temperature cooling system was activated. This system can be set to different freezing temperatures (-15℃, -25℃, -35℃, -45℃). The data and image processing system was then activated to begin signal acquisition. Radial-axial strain gauges were used to monitor the strain generated during the formation of the frozen wall. A CT scanning system was used to observe the penetration of the radionuclide solution into the frozen wall in real time, and three-dimensional images of the frozen wall formation process were captured. After importing these images into the data and image processing system, Avizo software was used for three-dimensional reconstruction to quantify the porosity. Waveguide rods and acoustic emission sensors were used to identify the acoustic signals generated during the freezing process.

[0103] When the phenomenon of nuclide penetration of the frozen wall observed by the CT scan system disappears, it can be considered that the frozen wall has achieved the ideal seepage prevention effect, and the experiment under this condition can be terminated. When conducting experiments under other freezing pipe parameters, it is not necessary to remove the soil. Simply loosen the soil in the frozen wall area and pull the freezing pipe pull ring and the freezing pipe on the moving slide rail to change the pipe diameter and position parameters. After changing the freezing pipe parameters, compact the loosened soil to start the experiment under another condition.

[0104] The permeability barrier effect of the frozen wall can be evaluated by combining the porosity, frost heave strain, and acoustic emission signals measured by CT scans of the frozen wall region at different times during the experiment: k i =αn e +β(aσ a +bσ r )+γ(cN r +dN s +eA e ).

[0105] Where k i n is the evaluation index for barrier properties. e To measure the porosity of the frozen wall region using CT, σ a σ is the axial strain measured by the combined strain gauge. r For the radial strain measured by the combined strain gauge, N r N s A e α, β, and γ represent the ringing number, cumulative event number, and energy in the acoustic emission results, respectively; α, β, and γ represent the influence coefficients of porosity, frost heave strain, and acoustic emission signal, respectively; a and b represent the influence weight ratios of each strain parameter; and c, d, and e represent the influence weight ratios of each acoustic emission parameter.

[0106] In some alternative embodiments, the disclosed methods are not limited to the operations and logic flow presented herein. Alternative embodiments are contemplated in which the order of various operations is altered and sub-operations described as part of a larger operation are executed independently.

[0107] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0108] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0109] The logic and / or steps described in this invention, for example, can be considered as a ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0110] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0111] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0112] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0113] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0114] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of the present invention.

Claims

1. A system for simulating the effects of freezing methods in emergency response to nuclear leaks, characterized in that, include: Infiltration barrier experimental system, low-temperature cold bath system, and frozen wall monitoring system; The seepage barrier experimental system includes a water supply tank, a peristaltic pump, a first filter screen, a second filter screen, a first water pipe, a second water pipe, a model box, multiple freezing pipes, and a waste liquid recovery tank. The water supply tank is connected to a first side of the model box via the first water pipe. The peristaltic pump is mounted on the first water pipe, which also has a water supply valve. The first filter screen is located inside the model box and forms an inlet chamber with the first side. The waste liquid recovery tank is connected to a second side of the model box via the second water pipe. The second filter screen is located inside the model box and forms an outlet chamber with the second side, which also has an outlet valve. The first and second sides are opposite faces, with the first filter screen parallel to the first side and the second filter screen parallel to the second side. The freezing pipes are located inside the model box and between the first and second filters. The diameter of the freezing pipes is adjustable, and their position is movable. All the freezing pipes are arranged side-by-side, and the plane formed by their side-by-side arrangement is parallel to the first and second filters. The low-temperature cooling system is connected to the freezing pipe through an inlet pipe and an outlet pipe. The low-temperature cooling system exchanges antifreeze with the freezing pipe through a built-in circulation pump, and keeps the temperature of the antifreeze in the inlet pipe and the temperature of the antifreeze in the outlet pipe at a preset constant value. The frozen wall monitoring system includes a radial-axial combined strain gauge, an acoustic emission testing system, a CT scanning system, and a data and image processing system. Both the radial-axial combined strain gauge and the acoustic emission testing system are positioned between the first filter and the second filter. The radial-axial combined strain gauge monitors the radial and axial frost heave strain generated during the formation of the frozen wall within the model box. The acoustic emission testing system collects acoustic signals generated by the volume expansion of frozen soil due to the water-ice phase change during the formation of the frozen wall. A radionuclide solution containing KI is used as the CT contrast agent for the CT scanning system, which emits X-rays into the frozen wall area within the model box to obtain the seepage information and porosity of the radionuclide solution in the frozen wall area. The data and image processing system determines the impermeability of the frozen wall based on at least one of the frost heave strain, the characteristic parameters corresponding to the acoustic signals, and the porosity. Each of the freezing tubes is equipped with a pull ring, and pulling the pull ring is used to adjust the diameter of the freezing tube; All the freezing tubes are mounted on a slide rail, and each freezing tube can move on the slide rail; The combined radial-axial strain gauge includes a radial strain gauge and an axial strain gauge; The radial strain gauge consists of a closed steel fiber coil and a first thin-film strain gauge bonded to the surface of the steel fiber coil; the surface of the steel fiber coil has a set roughness to fix the position of the radial-axial combined strain gauge. The axial strain gauge consists of four steel fibers fixed in the radial direction of the steel fiber coil extending in four directions (up, down, front, and back) and a second thin-film strain gauge bonded to the contact position between each steel fiber and the steel fiber coil. Each steel fiber points to the geometric center of the steel fiber coil. The plane of the steel fiber coil is parallel to the first filter screen and the second filter screen.

2. The system for simulating the effects of freezing in emergency response to nuclear leaks according to claim 1, characterized in that, The low-temperature cooling system is equipped with a cooling bath tank inside, which is used to hold antifreeze. Several rings of refrigeration pipes are arranged around the inner wall of the cooling bath tank, which are used to control the temperature of the antifreeze to a preset constant value.

3. The system for simulating the effects of freezing in emergency response to nuclear leaks according to claim 1, characterized in that, When the expansion of the frozen wall causes deformation of the steel fiber coil, resulting in a change in the resistance value of the sensitive grid inside the first thin-film strain gauge, the radial strain gauge collects the first resistance value. When the expansion of the frozen wall causes deformation of the steel fiber, resulting in a change in the resistance value of the sensitive grid inside the second thin-film strain gauge, the axial strain gauge collects the second resistance value. The first resistance value and the second resistance value are used as the frost heave strain.

4. The system for simulating the effects of freezing methods in emergency response to nuclear leaks according to claim 1, characterized in that, The CT scanning system includes an X-ray source and a detector; The X-ray source is used to generate X-rays and irradiate the area where the frozen wall is located inside the model box; The detector is used to receive the X-ray signal generated by the X-ray penetrating the frozen wall inside the model box, convert the X-ray signal into a first digital signal, and send it to the data and image processing system. The data and image processing system is used to perform three-dimensional reconstruction of the region where the frozen wall is located based on the first digital signal to obtain a reconstruction model; and to determine the seepage information of the nuclide solution penetrating the frozen wall and the porosity of the region where the frozen wall is located based on the reconstruction model.

5. The system for simulating the effects of freezing methods in emergency response to nuclear leaks according to claim 1, characterized in that, The acoustic emission testing system includes a waveguide rod, an acoustic emission sensor, and a signal amplifier; The waveguide rod is used to propagate the acoustic signal; The acoustic emission sensor is used to collect the acoustic signal; The signal amplifier is used to filter and amplify the acoustic signal, convert the filtered and amplified acoustic signal into a second digital signal, and then send the second digital signal to the data and image processing system.

6. The system for simulating the effects of freezing in emergency response to nuclear leaks according to claim 5, characterized in that, The data and image processing system is used to extract the ringing count, cumulative event count, and cumulative energy from the second digital signal as feature parameters corresponding to the sound signal; Wherein, the ringing count is the number of times the amplitude of the acoustic signal exceeds a preset threshold voltage within a set time period; the cumulative event count is the number of acoustic emission events obtained by wave impact identification within the set time period, any signal in which the acoustic signal exceeds the signal threshold and causes any channel of the data and image processing system to acquire data is considered a wave impact, and a local material change that produces acoustic emission is considered an acoustic emission event; the cumulative energy is the area under the detector envelope of the acoustic emission event, used to reflect the relative energy and intensity of the acoustic emission event.

7. The system for simulating the effects of freezing in emergency response to nuclear leaks according to claim 1, characterized in that, The data and image processing system is used to determine the impermeability of the frozen wall based on at least one of the frost heave strain, the characteristic parameters corresponding to the acoustic signal, and the porosity, including: The data and image processing system is used to determine a comprehensive evaluation expression based on the frost heave strain, the characteristic parameters corresponding to the acoustic signal, and the porosity, and to determine the impermeability of the frozen wall based on the comprehensive evaluation expression. The comprehensive evaluation expression is as follows: in, k i As an evaluation index for barrier properties; n e The porosity is mentioned above; σ a Let be the axial strain in the frost heave strain. σ r The radial strain is defined as the frost heave strain; the characteristic parameters corresponding to the acoustic signal include the number of ringing cycles, the cumulative number of events, and the cumulative energy. N r , N s , A e These are the number of rings, the cumulative number of events, and the cumulative energy, respectively. α , β , γ These are the coefficients for the porosity, the frost heave strain, and the characteristic parameter, respectively. a This is the weighting ratio of the axial strain. b The weighting ratio of the radial strain; c , d , e These are the weighting ratios of the ringing count, cumulative event count, and cumulative energy, respectively.

8. A method for evaluating the effectiveness of freezing methods in emergency response to nuclear leaks, characterized in that, The data and image processing system applied to the simulation system for the freezing effect of emergency response to nuclear leaks as described in any one of claims 1 to 7, wherein the evaluation method includes: The radial and axial frost heave strains generated during the formation of the frozen wall inside the model box were obtained by measuring the radial-axial combined strain gauge. Acquire acoustic signals generated by the volume expansion of frozen soil due to the phase change of water and ice during the formation of the frozen wall, collected by an acoustic emission testing system, and determine the characteristic parameters corresponding to the acoustic signals; the characteristic parameters include the number of ringings, the cumulative number of events, and the cumulative energy. The permeation information and porosity of the radionuclide solution in the frozen wall area are obtained by emitting X-rays into the frozen wall area inside the model box by the CT scanning system; the radionuclide solution including KI is used as the CT contrast agent of the CT scanning system; A comprehensive evaluation expression is determined based on the frost heave strain, the characteristic parameters corresponding to the acoustic signal, and the porosity, and the impermeability of the frozen wall is determined based on the comprehensive evaluation expression. The comprehensive evaluation expression is as follows: in, k i As an evaluation index for barrier properties; n e The porosity is mentioned above; σ a Let be the axial strain in the frost heave strain. σ r The radial strain is the strain in the frost heave strain. N r , N s , A e These are the number of rings, the cumulative number of events, and the cumulative energy, respectively. α , β , γ These are the coefficients for the porosity, the frost heave strain, and the characteristic parameter, respectively. a This is the weighting ratio of the axial strain. b The weighting ratio of the radial strain; c , d , e These are the weighting ratios of the ringing count, cumulative event count, and cumulative energy, respectively.

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