A soil displacement-temperature integrated measuring device and method based on fiber bragg grating

CN122689042APending Publication Date: 2026-09-04HEILONGJIANG PROVINCIAL INSTITUTE OF WATER CONSERVANCY (HEILONGJIANG PROVINCIAL SOIL & WATER CONSERVATION MONITORING STATION)
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Patent Information

Application Number
CN202611027446.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-07-10
Publication Date
2026-09-04

AI Technical Summary

Technical Problem

[0003]光纤布拉格光栅存在应变和温度的交叉敏感问题,即中心波长的变化同时受到应变和温度的影响

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Abstract

The application discloses a soil displacement-temperature integrated measuring device based on a fiber Bragg grating, which comprises an implantation beam for implanting into a soil body to be measured and bending along with deformation of the soil body, at least one pair of fiber Bragg grating sensors symmetrically arranged and fixed on two side surfaces of the implantation beam along the bending direction, and a fiber demodulation device connected with the fiber Bragg grating sensors and used for acquiring central wavelength data of each sensor. The application utilizes a symmetric packaging structure and a differential measurement principle, can synchronously acquire displacement and temperature information without an additional temperature compensation fiber, and is simple in structure, low in cost and suitable for long-term and reliable integrated monitoring of deep displacement and ground temperature of the soil body.
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Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering monitoring and fiber optic sensing technology, specifically to an integrated soil displacement-temperature measurement device and method based on fiber Bragg gratings. Background Technology

[0002] In fields such as slope stability, foundation pit engineering, and geological disaster monitoring, synchronous monitoring of soil deformation and temperature is of great significance. Fiber Bragg grating sensors, due to their advantages such as small size, resistance to electromagnetic interference, corrosion resistance, and ease of networking, have become a research hotspot in the field of soil monitoring.

[0003] Fiber Bragg gratings suffer from cross-sensitivity to strain and temperature, meaning that changes in the center wavelength are affected by both strain and temperature. Current solutions include: first, mathematical decoupling, which uses complex mathematical models and algorithms to separate the effects of strain and temperature; however, this method is computationally complex and relies on precise physical parameters. Second, strain-free fiber compensation, which uses a dedicated, unstressed fiber in the monitoring device to measure temperature and compensate for temperature drift in strained fibers; however, maintaining a completely strain-free fiber in engineering practice is challenging. Furthermore, while some existing studies have achieved simultaneous strain-temperature monitoring, their sensor structures are complex, difficult to manufacture, and expensive, making them unsuitable for large-scale field deployments and long-term monitoring.

[0004] Therefore, developing a simple, well-defined decoupling method, low-cost, and reliable integrated soil displacement-temperature measurement technology is an urgent technical problem to be solved in this field. Summary of the Invention

[0005] The purpose of this invention is to provide an integrated soil displacement-temperature measurement device and method based on fiber Bragg gratings to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A soil displacement-temperature integrated measurement device based on fiber Bragg grating, comprising:

[0008] An implanted beam is used to be inserted into the soil to be tested and bends as the soil deforms.

[0009] At least one pair of fiber Bragg grating sensors are symmetrically arranged and fixed on both sides of the implanted beam along the bending direction;

[0010] An optical fiber demodulation device is connected to the optical fiber Bragg grating sensor to acquire the center wavelength data of each sensor.

[0011] As a further aspect of the present invention: the implanted beam comprises:

[0012] The matrix layer is made of a material that matches the physical and mechanical properties of the soil being tested.

[0013] The encapsulation layer, located on both sides of the matrix layer, is used to adhere and fix the fiber Bragg grating sensor to the surface of the matrix layer;

[0014] A protective layer is applied to the outer side of the encapsulation layer and the fiber Bragg grating sensor for protection.

[0015] As a further aspect of the present invention: the matrix layer is made of random copolymer polypropylene, and its surface is roughened; the encapsulation layer is made of epoxy resin structural adhesive; and the protective layer is made of silicone.

[0016] As a further aspect of the present invention: the bottom end of the implanted beam is fixed on the base, and the base is used to constrain the bottom end of the implanted beam as a fixed point during installation.

[0017] A method for integrated soil displacement-temperature measurement based on fiber Bragg gratings includes the following steps:

[0018] Step 1: Insert the implant beam into the borehole of the soil to be tested, and ensure that the implant beam is in close contact with the surrounding soil;

[0019] Step 2: Obtain the center wavelength data of the fiber Bragg gratings at symmetrical positions on both sides of the implanted beam using fiber demodulation equipment, and calculate the change in center wavelength.

[0020] Step 3: Subtract the changes in the center wavelengths of the symmetrical gratings on both sides of the same position to eliminate the influence of temperature effect, and solve for the axial strain at the measuring point. Add the changes in the center wavelengths of the symmetrical gratings on both sides of the same position to eliminate the influence of strain effect, and solve for the temperature change at the measuring point.

[0021] Step 4: Based on the solved distribution of axial strain along the depth of the implanted beam, calculate the deflection at each point of the implanted beam using an integral method, and use the deflection as the lateral displacement of the soil at the corresponding depth.

[0022] As a further aspect of the present invention: the decoupling of strain and temperature in step three is based on the following relationship:

[0023]

[0024]

[0025] In the formula, and These represent the changes in the center wavelength of the symmetrical gratings on both sides. The center wavelength, The strain sensitivity coefficient, This is the temperature sensitivity coefficient. and These represent the axial strain of the two gratings, respectively. The change in temperature is given by the strain on both sides of the implanted beam when it bends, which satisfies... The axial strain can be obtained by subtracting the two equations. Add the two equations together to obtain the temperature change. .

[0026] As a further aspect of the present invention: the formula for calculating the deflection using the integral method in step four is:

[0027]

[0028] In the formula, To calculate the deflection of the beam implanted within the unit, This represents the distribution of axial strain along the depth direction after decoupling. For effective half beam height, and The integral constant is determined based on the boundary conditions, which include zero displacement and zero rotation at the bottom of the implanted beam, as well as the continuity of displacement and rotation at the connection point of adjacent computational units.

[0029] As a further aspect of the present invention, it also includes a method for determining the effective half-beam height. The calibration steps include: fixing one end of the implanted beam, applying a known displacement to the other end, acquiring the center wavelength change of each sensor and calculating the strain through an optical fiber demodulation device, acquiring the actual displacement values ​​of multiple comparison points on the implanted beam through an external displacement measurement device, and adjusting the effective half-beam height. The value of this value minimizes the error between the displacement calculated from the strain integral and the actual measured displacement; therefore, this value is chosen. The value is used as the calibration value.

[0030] As a further aspect of the present invention, it also includes a method for determining the temperature sensitivity coefficient. The temperature calibration procedure includes: after burying the device at the monitoring site, using the initial measurement data as a benchmark, simultaneously acquiring the ground temperature changes measured by the automatic temperature acquisition system at the same depth and at different times, as well as the temperature changes obtained by the device through decoupling calculations. The least squares method is then used to perform linear fitting on the two sets of temperature change data, and the slope obtained from the fitting is used as the temperature sensitivity coefficient. .

[0031] Compared with the prior art, the beneficial effects of the present invention are:

[0032] This invention utilizes the differential-mode and common-mode signals of a symmetrical fiber optic grating to achieve in-situ decoupling of strain and temperature, eliminating the need for additional temperature-compensating optical fibers and enabling simultaneous acquisition of displacement and temperature information at the measurement point. The device employs a slender beam with a composite structure as the sensing carrier, resulting in a simple and low-cost manufacturing process, facilitating mass production and on-site installation. The decoupling algorithm based on the differential principle has clear physical meaning and a simple calculation process. The fiber optic grating is encapsulated and protected by multiple layers of materials, enabling it to adapt to complex underground physicochemical environments and ensuring the stability and reliability of long-term monitoring. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the encapsulation structure of the implanted beam of the present invention.

[0034] Figure 2 This is a schematic diagram of the calculation method for converting strain into displacement in this invention.

[0035] Figure 3 This is a comparison chart of the results of the displacement calibration experiment of the present invention.

[0036] Figure 4 This is a comparison chart of temperature calibration results at three different depth points according to the present invention.

[0037] Figure 5 This is a comparison diagram of soil displacement data measured by the fiber optic grating monitoring tube and the sliding inclinometer of the present invention, where a is the monitoring result of the fiber optic grating and b is the monitoring result of the sliding inclinometer.

[0038] Figure 6 This is a graph showing the change of soil temperature at different depths over time, measured by the fiber optic grating monitoring tube of this invention.

[0039] Figure 7 This is a graph showing the change of soil temperature at different depths over time, measured by the Pt100 temperature sensor of this invention.

[0040] In the diagram: a - matrix layer, b - encapsulation layer, c - protective layer. Detailed Implementation

[0041] Various exemplary embodiments, features, and aspects of this application will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0042] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments.

[0043] Furthermore, to better illustrate this application, numerous specific details are provided in the following detailed embodiments. Those skilled in the art should understand that this application can be implemented even without certain specific details. In some instances, methods, means, and elements well-known to those skilled in the art have not been described in detail in order to highlight the main points of this application.

[0044] Example 1 Figure 3

[0045] like Figure 1 As shown, a soil displacement-temperature integrated measurement device based on a fiber Bragg grating includes:

[0046] An implanted beam is used to be inserted into the soil to be tested and bends as the soil deforms.

[0047] At least one pair of fiber Bragg grating sensors are symmetrically arranged and fixed on both sides of the implanted beam along the bending direction;

[0048] An optical fiber demodulation device is connected to the optical fiber Bragg grating sensor to acquire the center wavelength data of each sensor.

[0049] Preferably, the implanted beam comprises:

[0050] The matrix layer a is made of a material that matches the physical and mechanical properties of the soil to be tested;

[0051] Encapsulation layer b, located on both sides of matrix layer a, is used to adhere and fix the fiber Bragg grating sensor to the surface of matrix layer a;

[0052] Protective layer c is coated on the outer side of the encapsulation layer b and the fiber Bragg grating sensor for protection.

[0053] Preferably, the matrix layer a is made of random copolymer polypropylene, and its surface is roughened. Its elastic modulus is close to that of ordinary soil, allowing it to deform well with the soil. The surface of the pipe is roughened to enhance its adhesion to the subsequent encapsulation layer. The encapsulation layer b is an epoxy resin structural adhesive, and the protective layer c is silicone.

[0054] Preferably, the bottom end of the implanted beam is fixed to the base, and the base is used to constrain the bottom end of the implanted beam as a fixed point during installation.

[0055] Specifically, a series of fiber Bragg grating sensors, each with a different center wavelength, are symmetrically positioned on both sides of matrix layer a. The center wavelengths of the gratings are arranged sequentially from 1560nm to 1530nm from bottom to top to avoid signal crosstalk. Epoxy resin structural adhesive is used as the encapsulation layer b to adhere and fix the fiber gratings to the surface of the matrix layer, ensuring that the fiber and the beam deform in tandem. A layer of silicone is uniformly coated on the outermost layer of the beam to form a protective layer c, effectively preventing soil particle abrasion and groundwater erosion, and extending the lifespan of the components. The fiber grating is fixed to a nylon base at the bottom of the beam, with an outer diameter matching the inner diameter of the inclinometer tube, to form the fixed point boundary conditions required for displacement calculation. FC / APC fiber optic connectors are pre-installed at the upper ends of the fibers for connecting to a fiber optic demodulator.

[0056] A method for integrated soil displacement-temperature measurement based on fiber Bragg gratings includes the following steps:

[0057] Step 1: Insert the implant beam into the borehole of the soil to be tested, and ensure that the implant beam is in close contact with the surrounding soil;

[0058] Step 2: Obtain the center wavelength data of the fiber Bragg gratings at symmetrical positions on both sides of the implanted beam using fiber demodulation equipment, and calculate the change in center wavelength.

[0059] Step 3: Subtract the changes in the center wavelengths of the symmetrical gratings on both sides of the same position to eliminate the influence of temperature effect, and solve for the axial strain at the measuring point. Add the changes in the center wavelengths of the symmetrical gratings on both sides of the same position to eliminate the influence of strain effect, and solve for the temperature change at the measuring point.

[0060] Step 4: Based on the solved distribution of axial strain along the depth of the implanted beam, calculate the deflection at each point of the implanted beam using an integral method, and use the deflection as the lateral displacement of the soil at the corresponding depth.

[0061] Preferably, the decoupling of strain and temperature in step three is based on the following relationship:

[0062]

[0063]

[0064] In the formula, and These represent the changes in the center wavelength of the symmetrical gratings on both sides. The center wavelength, The strain sensitivity coefficient, This is the temperature sensitivity coefficient. and These represent the axial strain of the two gratings, respectively. The change in temperature is given by the strain on both sides of the implanted beam when it bends, which satisfies... The axial strain can be obtained by subtracting the two equations. Add the two equations together to obtain the temperature change. .

[0065] Preferably, the formula for calculating deflection using the integral method in step four is:

[0066]

[0067] In the formula, To calculate the deflection of the beam implanted within the unit, This represents the distribution of axial strain along the depth direction after decoupling. For effective half beam height, and The integral constant is determined based on the boundary conditions, which include zero displacement and zero rotation at the bottom of the implanted beam, as well as the continuity of displacement and rotation at the connection point of adjacent computational units.

[0068] Preferably, it also includes a method for determining the effective half-beam height. The calibration steps include: fixing one end of the implanted beam, applying a known displacement to the other end, acquiring the center wavelength change of each sensor and calculating the strain through an optical fiber demodulation device, acquiring the actual displacement values ​​of multiple comparison points on the implanted beam through an external displacement measurement device, and adjusting the effective half-beam height. The value of this value minimizes the error between the displacement calculated from the strain integral and the actual measured displacement; therefore, this value is chosen. The value is used as the calibration value.

[0069] Preferably, it also includes a method for determining the temperature sensitivity coefficient. The temperature calibration procedure includes: after burying the device at the monitoring site, using the initial measurement data as a benchmark, simultaneously acquiring the ground temperature changes measured by the automatic temperature acquisition system at the same depth and at different times, as well as the temperature changes obtained by the device through decoupling calculations. The least squares method is then used to perform linear fitting on the two sets of temperature change data, and the slope obtained from the fitting is used as the temperature sensitivity coefficient. Furthermore, temperature calibration can also be performed in the laboratory under different temperature conditions.

[0070] It should be noted that, in order to ensure measurement accuracy, two key parameters need to be calibrated.

[0071] Effective half beam height Displacement calibration: One end of the implanted beam is fixed to a plane to simulate the bottom constraint during installation, and known displacements are applied to the other end. A fiber optic demodulator is activated to record the center wavelength changes of the grating strings on both sides of the implanted beam, and the strain distribution at each measuring point is calculated using a decoupling algorithm. Simultaneously, multiple comparison points are set on the beam, and laser displacement gauges are used to accurately measure its actual displacement. The algorithm program is then called to adjust the effective half-beam height. The value is chosen to minimize the error between the calculated displacement value and the measured value of the laser displacement gauge. The calibration results are as follows: Figure 3 As shown.

[0072] Temperature sensitivity coefficient Temperature calibration: A long-term field comparison method was adopted. After the device was buried at the monitoring site, the initial measurement data was used as a benchmark. A high-precision automatic temperature acquisition system was deployed near the same monitoring hole as a reference standard for temperature measurement. Multiple points at different depths were selected to synchronously record the temperature change calculated by the fiber Bragg grating device and the actual temperature change measured by the high-precision system over a long period. The least squares method was used to perform linear fitting on the two sets of data, and the slope obtained from the fitting was the temperature sensitivity coefficient. The calibration results are as follows: Figure 4 As shown.

[0073] It should be noted that, according to Bragg's law, wavelengths satisfying the Bragg condition will be reflected, while other wavelengths will continue to propagate through the fiber optic grating, with the center wavelength... Satisfying Relationships ,in The effective refractive index of the fiber core. The period of the fiber Bragg grating. When the temperature and strain of the external environment change, the center wavelength of the fiber Bragg grating will shift, and the relative change in center wavelength is related to the strain. and temperature change The relationship is linear. Once the strain and temperature are decoupled, the strain and temperature can be calculated separately based on the change in the center wavelength.

[0074] When the implanted beam bends, one side is under tension and the other under compression, and the strain satisfies... Therefore, by subtracting the changes in the center wavelengths of the symmetrical gratings on both sides at the same location, the influence of temperature effect can be eliminated, and the axial strain at the measuring point can be calculated; by adding the changes in the center wavelengths on both sides, the influence of strain effect can be eliminated, and the temperature change at the measuring point can be calculated. This method achieves in-situ, self-compensating decoupling of temperature effect.

[0075] Treating the implanted beam as a slender beam, based on the beam bending theory, by decoupling the axial strain obtained from each measuring point along the beam and integrating it twice along the depth direction, and using boundary conditions such as zero displacement at the bottom of the beam and zero rotation angle, the deflection at any point on the beam can be calculated. This deflection represents the lateral displacement of the soil at that depth.

[0076] To verify the monitoring performance of this invention in a real geological environment, an in-situ test was conducted at a scientific observation site for erosion gullies in Harbin, China. The site reproduced a gully model with a maximum length of 25 meters, a maximum width of 4.5 meters, a maximum depth of 2.75 meters, and a catchment area of ​​1,000 square meters for a single gully.

[0077] The on-site deployment process is as follows: At the selected location, boreholes with a diameter of 120 mm and a depth ranging from 2 to 6 meters were drilled vertically. A conventional inclinometer tube with an outer diameter of 70 mm was embedded inside the borehole, and the gap between the tube wall and the borehole wall was filled with fine sand to ensure the inclinometer tube's adaptability to soil deformation. The calibrated device of this invention was placed inside the inclinometer tube, with the nylon base at the bottom in close contact with the bottom of the inclinometer tube to ensure the bottom is a stationary point. The gaps around the tube were filled with fine sand. After stabilization for 48 hours, the fiber optic demodulator was connected to start the measurement. Monitoring data was collected starting March 17, 2023, and this initial data was used as a reference for subsequent monitoring data.

[0078] Monitoring results show that the soil underwent varying degrees of displacement at different times. During the spring thaw, the soil shifted towards the free surface, with the maximum displacement of the surface soil gradually increasing. The monitoring also identified soil slippage at specific depths, meaning that the displacement directions of the upper and lower soil layers were opposite in adjacent data points. Compared with data from a traditional sliding inclinometer during the same period, the directions and locations of soil displacement revealed by both methods were essentially consistent. Figure 5 As shown, the accuracy of displacement measurement in this invention is verified. Because the fiber optic grating measurement points are continuous, the displacement profile obtained is more precise compared to that obtained by a sliding inclinometer.

[0079] Temperature monitoring results show that, Figure 6 As shown, the device of this invention accurately captures the seasonal variation patterns of soil temperature at different depths, including drastic fluctuations in surface temperature, maximum freezing depth, and the hysteresis effect of deep ground temperature. Compared with high-precision thermometers at the same depth, such as... Figure 7 The comparison of the measurement data shows that the temperature change trends and depths of the two are highly consistent, proving the long-term stability and reliability of the temperature measurement of this invention.

[0080] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

[0081] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A soil displacement-temperature integrated measurement device based on fiber Bragg gratings, characterized in that, include: An implanted beam is used to be inserted into the soil to be tested and bends as the soil deforms. At least one pair of fiber Bragg grating sensors are symmetrically arranged and fixed on both sides of the implanted beam along the bending direction; An optical fiber demodulation device is connected to the optical fiber Bragg grating sensor to acquire the center wavelength data of each sensor.

2. The integrated soil displacement-temperature measurement device based on fiber Bragg grating according to claim 1, characterized in that, The implanted beam includes: The matrix layer (a) is made of a material that matches the physical and mechanical properties of the soil to be tested; The encapsulation layer (b), located on both sides of the matrix layer, is used to attach and fix the fiber Bragg grating sensor to the surface of the matrix layer (a); A protective layer (c) is coated on the outer side of the encapsulation layer (b) and the fiber Bragg grating sensor for protection.

3. The integrated soil displacement-temperature measurement device based on fiber Bragg grating according to claim 2, characterized in that, The matrix layer (a) is made of random copolymer polypropylene and its surface is roughened; the encapsulation layer (b) is epoxy resin structural adhesive; and the protective layer (c) is silicone.

4. The integrated soil displacement-temperature measurement device based on fiber Bragg grating according to claim 1, characterized in that, The bottom end of the implanted beam is fixed to the base, which is used to constrain the bottom end of the implanted beam as a fixed point during installation.

5. A method for integrated soil displacement-temperature measurement based on fiber Bragg gratings as described in any one of claims 1-4, characterized in that, Includes the following steps: Step 1: Insert the implant beam into the borehole of the soil to be tested, and ensure that the implant beam is in close contact with the surrounding soil; Step 2: Obtain the center wavelength data of the fiber Bragg gratings at symmetrical positions on both sides of the implanted beam using fiber demodulation equipment, and calculate the change in center wavelength. Step 3: Subtract the changes in the center wavelengths of the symmetrical gratings on both sides of the same position to eliminate the influence of temperature effect, and solve for the axial strain at the measuring point. Add the changes in the center wavelengths of the symmetrical gratings on both sides of the same position to eliminate the influence of strain effect, and solve for the temperature change at the measuring point. Step 4: Based on the solved distribution of axial strain along the depth of the implanted beam, calculate the deflection at each point of the implanted beam using an integral method, and use the deflection as the lateral displacement of the soil at the corresponding depth.

6. The method for integrated soil displacement-temperature measurement based on fiber Bragg grating according to claim 5, characterized in that, The decoupling of strain and temperature in step three is based on the following relationship: In the formula, and These represent the changes in the center wavelength of the symmetrical gratings on both sides. The center wavelength, The strain sensitivity coefficient, This is the temperature sensitivity coefficient. and These represent the axial strain of the two gratings, respectively. The change in temperature is given by the strain on both sides of the implanted beam when it bends, which satisfies... The axial strain can be obtained by subtracting the two equations. Add the two equations together to obtain the temperature change. .

7. The method for integrated soil displacement-temperature measurement based on fiber Bragg grating according to claim 5, characterized in that, In the formula, To calculate the deflection of the beam implanted within the unit, This represents the distribution of axial strain along the depth direction after decoupling. For effective half beam height, and The integral constant is determined based on the boundary conditions, which include zero displacement and zero rotation at the bottom of the implanted beam, as well as the continuity of displacement and rotation at the connection point of adjacent computational units.

8. The method for integrated soil displacement-temperature measurement based on fiber Bragg grating according to claim 7, characterized in that, It also includes a method for determining the effective half-beam height. The calibration steps include: fixing one end of the implanted beam, applying a known displacement to the other end, acquiring the center wavelength change of each sensor and calculating the strain through an optical fiber demodulation device, acquiring the actual displacement values ​​of multiple comparison points on the implanted beam through an external displacement measurement device, and adjusting the effective half-beam height. The value of this value minimizes the error between the displacement calculated from the strain integral and the actual measured displacement; therefore, this value is chosen. The value is used as the calibration value.

9. The method for integrated soil displacement-temperature measurement based on fiber Bragg grating according to claim 6, characterized in that, It also includes a coefficient for determining temperature sensitivity. The temperature calibration procedure includes: after burying the device at the monitoring site, using the initial measurement data as a benchmark, simultaneously acquiring the ground temperature changes measured by the automatic temperature acquisition system at the same depth and at different times, as well as the temperature changes obtained by the device through decoupling calculations. The least squares method is then used to perform linear fitting on the two sets of temperature change data, and the slope obtained from the fitting is used as the temperature sensitivity coefficient. .