Method for testing stress tensor of solid medium

Abstract

The invention provides a device and a method for testing stress tensor of a solid medium. The device comprises a stress tensor measuring ball and a data acquisition instrument, the stress tensor measuring ball is embedded in a specified position in the solid medium; the data acquisition instrument is arranged outside the solid medium in a matched mode, one end of the data acquisition instrument is connected with the stress tensor measuring ball through a data line, and the data acquisition instrument is used for acquiring quasi-static and dynamic strain data of the stress tensor measuring ball. According to the invention, a plurality of independent stress components of the stress tensor can be calculated through axial strain measurement in multiple directions, and the problem that a traditional stress measurement method can only measure axial stress components or is low in shear stress measurement precision is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of solid stress measurement, and in particular to a method for testing the stress tensor of a solid medium. Background Art

[0002] Current stress measurement technologies primarily focus on unidirectional normal stress measurement. Their core principle is to indirectly infer normal stress values ​​by detecting local normal strain or pressure changes. While widely used in industry, these sensing technologies can only measure stress components in a single direction and cannot directly obtain complete information about the three-dimensional stress tensor. Furthermore, measurement accuracy decreases significantly when the stress direction deviates from the sensor's preset orientation.

[0003] Current three-dimensional stress measurement techniques primarily measure normal stress in three orthogonal directions. These techniques often rely on complex structures (such as multi-axis force sensors), resulting in large size, high cost, and significant interface interference. Furthermore, these methods can only measure normal stress in three directions, failing to measure shear stress or the stress tensor of the medium.

[0004] Hollow-enclosed strain gauges are a measurement tool widely used in geotechnical engineering and geomechanics. Their core function is to invert three-dimensional geostress from strain responses. A standard hollow-enclosed strain gauge is configured with 12 strain gauges evenly distributed along the inner wall of a hollow epoxy resin tube. By combining strain gauges in different orientations, they can cover six independent components of the three-dimensional stress tensor. After the strain gauge is inserted into the borehole, the core is decoupled from the original rock through a core casing. The strain recovery data from the core during the decoupling process are measured, and the initial stress field is calculated using elastic mechanics models. While hollow-enclosed strain gauges can interpret stress tensors, their ability to interpret shear stress is limited, and the sensor packaging process is complex.

[0005] The present invention proposes a method for calculating three-dimensional stress tensors by measuring normal stress in multiple directions, which can solve the problems of low calculation accuracy and complex sensor packaging in traditional methods. Summary of the Invention

[0006] In response to the technical problems existing in the above-mentioned background technology, the present invention proposes a device and method for testing the stress tensor of solid media. The device and method calculate multiple independent stress components of the stress tensor by measuring axial strain in multiple directions, which solves the problem that traditional stress measurement methods can only measure axial stress components or have low shear stress measurement accuracy. The device is suitable for accurate measurement of the stress tensor of solid media in fields such as geotechnical engineering testing, material mechanics testing, and engineering structure health monitoring.

[0007] In order to solve the above technical problems, the present invention provides a device for testing the stress tensor of a solid medium, which comprises a stress tensor measuring ball (1) and a data acquisition instrument (2);

[0008] The stress tensor measuring ball (1) is buried at a designated position inside the solid medium (4);

[0009] The data acquisition instrument (2) is matched and arranged outside the solid medium (4), and one end of the data acquisition instrument is connected to the stress tensor measurement ball (1) via a data line (3) for collecting quasi-static and dynamic strain data of the stress tensor measurement ball (1).

[0010] The device for testing the stress tensor of a solid medium, wherein: the stress tensor measuring ball (1) comprises a ball shell (11), a ball center fixing device (12) and an axial strain sensor (13) located inside the ball shell (11);

[0011] The spherical shell (11) is also matched with a circular hole (14) serving as a strain sensing area, and an analog-to-digital conversion chip is also provided inside; the analog-to-digital conversion chip has the functions of converting analog signals into digital signals and reading data of axial sensors with different ID numbers, and has a data input and output interface; the data input and output interface is fixed on the spherical shell (11);

[0012] The spherical center fixing device (12) is located inside the spherical shell (11), and is connected to the shell by means of ≥3 metal rods evenly distributed in space, and is made of the same material as the spherical shell (11);

[0013] The axial strain sensors (13) are evenly mounted on the outer circumference of the spherical center fixing device (12), and are connected to the analog-to-digital conversion chip inside the spherical shell (11) via a signal line; one end of each axial strain sensor (11) is fixed to the spherical center fixing device (12), and the other end is fixed to the circular hole (14), and the end portion is aligned with the outer circumference of the circular hole (14).

[0014] The device for testing the stress tensor of a solid medium, wherein: the data acquisition instrument (2) is connected to the data input and output interface of the analog-to-digital conversion chip via a data line (3).

[0015] The device for testing the stress tensor of a solid medium, wherein: the spherical shell (11) is a soft elastic sphere, and its elastic modulus is lower than that of the fixed medium (4).

[0016] The device for testing the stress tensor of a solid medium, wherein: the number of the axial strain sensors (13) is ≥6; the axial strain sensors (13) are strain gauges, fiber grating sensors or springs.

[0017] A method for testing the stress tensor of a solid medium, based on the above-mentioned device for testing the stress tensor of a solid medium, specifically comprises the following steps:

[0018] Step 1: Select a soft elastic sphere and evenly arrange a plurality of axial strain sensors (13) in the elastic sphere to construct a stress tensor measurement sphere (1);

[0019] Step 2: embed the constructed stress tensor measurement sphere (1) into the fixed medium (4) to be measured according to the set direction, and mark the local coordinate system;

[0020] Step 3: axial strain ε measured by the i-th axial strain sensor (13) i and the elastic modulus E of the surrounding solid medium (4), through the formula F i =Eε i , calculate the normal stress component F measured by the i-th axial strain sensor (13) i ;

[0021] Step 4: Construct the axial stress measurement vector F of the axial strain sensor (13):

[0022] F=[F1,F2,…,F N ] T ,N≥6;

[0023] In the above formula, F1, F2 and F N represent the normal stress components measured by the first, second and Nth axial strain sensors (13), respectively, T represents the transpose of the vector, and N is the number of axial strain sensors (13);

[0024] Step 5: Calculate the normal stress component F measured by the i-th axial strain sensor (13) according to the Cauchy stress theorem. i , construct the coefficient matrix A:

[0025]

[0026] In the above formula, a i 、b i 、c i is the direction vector component of the axial strain sensor (13) in the i-th direction; σ xx , σ yy , σ zz , σ xy , σ xz , σ yz is the stress tensor component; for the directions of N axial strain sensors (13), the dimension of the coefficient matrix A is N×6, and each row corresponds to the coefficient vector of one direction

[0027] Step 6: Calculate the stress tensor of the solid medium (4)

[0028] When N=6, directly solve the linear equation system σ=A -1F; when N>6, the regularized least squares method is used to calculate the stress tensor:

[0029] σ=(A T A+λI) -1 A T F;

[0030] Where λ is the Tikhonov regularization parameter;

[0031] Step 7: Compensate for the error caused by the temperature change factor and output the measurement result.

[0032] The method for testing the stress tensor of a solid medium, wherein: the error compensation in step 7 includes dynamically correcting the thermal drift error based on a pre-calibrated temperature-sensitivity relationship matrix; and optimizing the residual weight through the Huber loss function to suppress the influence of outlier measurements on the solution results.

[0033] The method for testing the stress tensor of a solid medium, wherein the thermal drift error is dynamically corrected based on a pre-calibrated temperature-sensitivity relationship matrix, specifically comprises the following steps:

[0034] Step 711: Conduct a temperature sensitivity calibration experiment for each axial strain sensor (13), specifically placing the axial strain sensor (13) in a constant temperature box and performing a temperature calibration experiment in the temperature range T∈[T min ,T max ] and perform stepwise temperature increase or decrease with a step length ΔT, and record the zero point output F of the axial strain sensor (13) at each temperature point. 0,i (T) and full-scale output F FS,i (T), where i represents the i-th axial strain sensor (13);

[0035] Step 712: Establish a polynomial model, that is, the temperature-sensitivity relationship of each axial strain sensor (13) channel can be modeled as:

[0036]

[0037] In the above formula, F nom is the rated full-scale output calibrated at room temperature, k 0,i 、k 1,i 、k 2,i are all polynomial coefficients;

[0038] Step 713: Construct a temperature-sensitivity relationship matrix based on the measurement results of each axial strain sensor (13):

[0039]

[0040] Step 714: According to the current temperature T cur, obtain F by linear interpolation from the temperature-sensitivity relationship matrix offset,i (T cur ) and S i (T cur ), assuming that the original axial stress measurement is F raw,i , calculate the stress value F after temperature compensation comp,i , the specific calculation formula is:

[0041]

[0042] The method for testing the stress tensor of a solid medium, wherein the Huber loss function is used to optimize the residual weight to suppress the influence of outlier measurements on the solution results, is specifically performed as follows:

[0043] Step 721: Use the Huber loss function to optimize the residual weight. The calculation formula is:

[0044]

[0045] Among them, r i is the residual of the i-th axial strain sensor (13), δ is the threshold;

[0046] Step 722: Set the objective function of the least squares algorithm to The weight w i Determined by the derivative of the Huber function;

[0047] Step 723: Perform iterative solution to obtain the corrected stress tensor. The specific solution process is as follows:

[0048] Set the initial solution: Calculate the initial stress tensor by the least squares method:

[0049] σ (0) =(A T A) -1 A T F comp ;

[0050] Calculate the residual: convert the stress calculated in the kth round into the axial stress in the direction of the i-th axial strain sensor (13), and calculate the difference with the measured value:

[0051] r i (k) =F comp,i -A i σ (k) ;

[0052] Update weights: Calculate the weight coefficient of the i-th axial strain sensor (13) in the k-th iteration by the difference between the measured value and the inverted value:

[0053]

[0054] Weighted solution: Calculate the stress of the k+1th iteration by introducing the weight coefficient matrix:

[0055] σ (k+1) =(A T W (k) A) -1 A T W (k) F comp ,in

[0056] Convergence judgment: When ||σ (k+1) -σ (k) When ||<ζ, the iteration is stopped and the calculation converges; wherein ζ is the iteration error. The method for testing the stress tensor of a solid medium, wherein: the coupling between the strain tensor measuring ball (1) and the solid medium (4) adopts cement mortar coupling, graded sand coupling or rapid gel coupling.

[0057] By adopting the above technical solution, the present invention has the following beneficial effects:

[0058] The present invention solves the problems of missing unidirectional lateral stress components and inaccurate three-dimensional shear stress measurements in traditional technologies by solving the three-dimensional stress tensor method through multi-directional normal stress measurements. It is suitable for geotechnical engineering testing, material mechanics testing, engineering structure health monitoring and other fields.

[0059] The present invention calculates multiple independent stress components of the stress tensor by measuring axial strain in multiple directions, solving the problem that traditional stress measurement methods can only measure axial stress components or have low shear stress measurement accuracy. It is suitable for accurate measurement of stress tensors of solid media in fields such as geotechnical engineering testing, material mechanics testing, and engineering structure health monitoring.

[0060] The present invention uses a soft ball as a force transmission carrier, effectively reducing interface stress disturbance and improving the test accuracy of the stress tensor.

[0061] The stress tensor measuring ball of the present invention can be connected in series using a data line, so that the stress tensor measurement of multiple points can be completed using one data line.

[0062] The present invention can improve the measurement accuracy of the stress tensor by increasing the number of axial strain sensors in the measuring sphere.

[0063] In the present invention, when the number N of axial strain sensors in the measuring sphere is greater than 6, the sensors are redundant. Therefore, when less than or equal to N-6 sensors fail unexpectedly, it will not affect the measurement and solution of the stress tensor. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0065] Figure 1 This is a schematic structural diagram of a device for testing the stress tensor of a solid medium according to the present invention;

[0066] Figure 2 A schematic structural diagram of a stress tensor measuring ball of a device for testing the stress tensor of a solid medium according to the present invention;

[0067] Figure 3 A flow chart of a method for testing the stress tensor of a solid medium according to the present invention;

[0068] Figure 4 This is a schematic diagram of measuring the disturbed stress tensor of the soil around the tunnel excavation according to Example 1 of the present invention;

[0069] Figure 5 This is a schematic diagram of measuring the disturbance stress tensor of the rock mass around the open-pit mine slope blasting according to Example 2 of the present invention. DETAILED DESCRIPTION

[0070] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0071] The present invention will be further explained below with reference to specific embodiments.

[0072] like Figure 1-2 As shown, this embodiment provides a device for testing the stress tensor of a solid medium, including a stress tensor measuring ball 1 , a data acquisition instrument 2 and a data line 3 .

[0073] The stress tensor measuring ball 1 is buried in a designated position inside the solid medium 4, and the coupling between the strain tensor measuring ball 1 and the solid medium 4 can be achieved by cement mortar coupling, graded sand coupling, rapid gel coupling, and other methods.

[0074] The stress tensor measurement sphere 1 comprises a spherical shell 11, a sphere center fixture 12, and an axial strain sensor 13 located within the spherical shell 11. The spherical shell 11 is provided with a circular hole 14 as a strain sensing area. An analog-to-digital conversion chip is also housed within the spherical shell 11. This chip converts analog signals into digital signals and reads data from axial sensors with different ID numbers. The chip has a data input / output interface fixed to the spherical shell 11. The spherical center fixing device 12 is located inside the spherical shell 11 and is connected to the spherical shell 11 by means of ≥3 metal rods evenly distributed in space, and the material is the same as that of the spherical shell 11; the axial strain sensor 13 serves as a measuring sensing element and is evenly installed on the outer circumference of the spherical center fixing device 12, and is connected to the analog-to-digital conversion chip inside the spherical shell 11 through a signal line; one end of each axial strain sensor 13 is fixed to the spherical center fixing device 12, and the other end is fixed to the circular hole 14 of the spherical shell 11 and the end is aligned with the outer circumference of the circular hole 14; at this time, when external force acts on the other end of the axial strain sensor 13 through the circular hole 14, the axial strain sensor 13 will deform, thereby realizing the measurement of axial strain.

[0075] The number of the axial strain sensors 13 should be ≥6, and each axial strain sensor 13 adopts various types such as strain gauges, fiber grating sensors, springs, etc.

[0076] The data acquisition instrument 2 is matched and arranged on the outside of the solid medium 4, and one end of the data acquisition instrument 2 is connected to the data input and output interface of the analog-to-digital conversion chip inside the ball shell 11 of the stress tensor measurement ball 1 through a data line 3; wherein, the data acquisition instrument 2 can collect quasi-static and dynamic strain data of the stress tensor measurement ball 1.

[0077] The elastic modulus of the ball shell 11 should be lower than that of the solid medium 4, and its material can be silicone, polyurethane elastomer, etc.

[0078] like Figure 3 As shown, the method for testing the stress tensor of a solid medium of the present invention specifically comprises the following steps:

[0079] S100 , selecting a soft elastic sphere and evenly arranging a plurality of axial strain sensors 13 in the elastic sphere to construct a stress tensor measurement sphere 2 .

[0080] S200 , embed the stress tensor measuring ball 2 into the fixed medium 4 to be measured according to a set direction, and mark the local coordinate system.

[0081] S300, according to the axial strain ε measured by the i-th axial strain sensor 13 i And the elastic modulus E of the surrounding solid medium 4, through the formula F i =Eε i, calculate the normal stress component F measured by the i-th axial strain sensor 13 i .

[0082] S400, constructing the axial stress measurement vector F of the axial strain sensor 13:

[0083] F=[F1,F2,…,F N ] T ,N≥6;

[0084] In the above formula, F1, F2 and F N They represent the normal stress components measured by the 1st, 2nd and Nth axial sensors respectively. In the above table, T represents the transpose of the vector, and N is the number of sensors.

[0085] S500, calculate the normal stress component F measured by the i-th axial strain sensor 13 according to the Cauchy stress theorem i , Construct the coefficient matrix A; where a i 、b i 、c i is the direction vector component of the axial strain sensor 13 in the i-th direction; σ xx , σ yy , σ zz , σ xy , σ xz , σ yz is the stress tensor component; for the directions of the N axial strain sensors 13, the dimension of the coefficient matrix A is N×6, and each row corresponds to the coefficient vector of one direction

[0086] S600, solve stress tensor

[0087] When N=6, directly solve the linear equation system σ=A -1 F; when N>6, the regularized least squares method is used to calculate the stress tensor:

[0088] σ=(A T A+λI) -1 A T F;

[0089] Where λ is the Tikhonov regularization parameter.

[0090] S700: Compensate for errors caused by factors such as temperature changes and output the measurement results. The error compensation in step S700 includes dynamically correcting thermal drift errors based on a pre-calibrated temperature-sensitivity relationship matrix, and optimizing residual weights using the Huber loss function to suppress the impact of outlier measurements on the solution results.

[0091] The above-mentioned dynamic correction of thermal drift error based on the pre-calibrated temperature-sensitivity relationship matrix is ​​as follows:

[0092] S711, carry out the temperature sensitivity calibration experiment of each axial strain sensor 13; specifically, place the axial strain sensor 13 in a constant temperature box, and min ,T max ] and perform stepwise temperature increase or decrease with a step length ΔT (e.g., 5°C) within a certain temperature range, and record the zero point output F of the axial strain sensor 13 at each temperature point. 0,i (T) and full-scale output F FS,i (T), where i represents the i-th axial strain sensor 13.

[0093] S712: Establish a polynomial model, that is, the temperature-sensitivity relationship of each axial strain sensor 13 channels can be modeled as: Among them F nom k is the rated full-scale output calibrated at room temperature (such as 25°C), 0,i 、k 1,i 、k 2,i are the polynomial coefficients.

[0094] S713. Based on the measurement results of each axial strain sensor 13, a temperature-sensitivity relationship matrix is ​​constructed, which is:

[0095] S714, according to the current temperature T cur , linearly interpolate from the coefficient matrix to obtain F offset,i (T cur ) and S i (T cur ), assuming that the original axial stress measurement is F raw,i , calculate the stress value F after temperature compensation comp,i The specific calculation formula is

[0096] The above-mentioned Huber loss function is used to optimize the residual weight to suppress the influence of outlier measurements on the solution results. The specific implementation steps are as follows:

[0097] S721. Use Huber loss function to optimize residual weight. The calculation formula is:

[0098]

[0099] Among them, r i is the residual of the i-th axial strain sensor 13 (the axial stress obtained by projecting the solved stress tensor onto the axial strain sensor 13 minus the measured value of the axial strain sensor 13), and δ is the threshold.

[0100] S722. Set the objective function of the least squares algorithm to The weight w i Determined by the derivative of the Huber function.

[0101] S723. Perform iterative solution to obtain the corrected stress tensor. The specific solution steps are as follows:

[0102] Set the initial solution: Calculate the initial stress tensor by the least squares method:

[0103] σ (0) =(A T A) -1 A T F comp ;

[0104] Calculate the residual: Convert the stress calculated in the kth round into the axial stress in the direction of the i-th sensor, and calculate the difference between the calculated and measured values:

[0105] r i (k) =F comp,i -A i σ (k) ;

[0106] Update weights: Calculate the weight coefficient of the i-th sensor in the k-th iteration by the difference between the measured value and the inverted value:

[0107]

[0108] Weighted solution: Calculate the stress of the k+1th iteration by introducing the weight coefficient matrix:

[0109] σ (k+1) =(A T W (k) A) -1 A T W (k) F comp ,in

[0110] Convergence judgment: When ||σ (k+1) -σ (k) When ||<ζ, the iteration stops and the calculation converges; where ζ is the iteration error.

[0111] Example 1:

[0112] Example 1 of the present invention is to measure the stress changes of the surrounding strata caused by tunnel excavation, such as Figure 4 ; A 10cm silicone sphere is selected as the stress tensor measurement sphere 1, and 6 spring sensors are installed on the sphere. The direction vectors of the 6 spring sensors are (1,0,0), (0,1,0), (0,0,1), A hole was drilled in the silty clay layer 15m to the left of the tunnel. The hole depth was 20m and the hole diameter was 15cm. A measuring ball was placed at the bottom of the hole and loose sand was used as the coupling material. A static data acquisition instrument 2 was used for data acquisition with an interval of 1 minute. After the tunnel was excavated, the surrounding rock stress field caused by the excavation disturbance was solved and the disturbance stress tensor was obtained as follows:

[0113] This embodiment 1 is a static measurement, measuring the change in stratum stress caused by excavation. The total measurement time is measured in days, so the sampling rate requirement is relatively low (one sample per minute), but the long-term stability requirement of the axial strain sensor 13 is high, so loose sand is used as a coupling agent (this type of coupling agent has a strong long-term coupling ability).

[0114] Example 2:

[0115] Example 2 of the present invention is the measurement of the dynamic stress effect of open pit mine step slope blasting on the surrounding strata. Figure 5 A 10cm polyurethane elastic ball was selected as the stress tensor measurement ball 1. Twelve axial strain sensors 13 (fiber grating sensors with a wavelength resolution of 1pm) were installed on the stress tensor measurement ball 1, and the 12 axial strain sensors 13 were evenly distributed on the hemispherical surface of the stress tensor measurement ball 1. Three boreholes were drilled at distances of 50m, 80m, and 110m from the mining face, each with a depth of 10m and an aperture of 15cm. The strain tensor measurement ball 1 was placed at the bottom of the hole, and cement mortar was used as a coupling agent to couple the strain tensor measurement ball 1 to the borehole. A dynamic data acquisition instrument 2 was used for data acquisition, with a sampling rate of 1000HZ. After a certain blasting mining, the dynamic stress amplitudes measured along the blast wave propagation direction were 50.3kPa, 45.1kPa, and 41.9kPa, respectively.

[0116] This embodiment 2 is a dynamic measurement, and the total measurement time is generally on the order of seconds. It is used to measure the dynamic stress changes caused by the blast, so the sampling rate is high. The sampling rate in this case is 1000HZ (one sample every 1 millisecond). Since the amplitude of the explosion stress is sometimes relatively large, it is easy to cause the measurement range of the axial strain sensor 13 to exceed the limit or the axial strain sensor 13 to be damaged by vibration. Therefore, during dynamic measurement, it is generally necessary to set up redundant axial strain sensors 13. Therefore, 12 axial strain sensors 13 are set up in this case.

[0117] The present invention calculates multiple independent stress components of the stress tensor by measuring axial strain in multiple directions, solving the problem that traditional stress measurement methods can only measure axial stress components or have low shear stress measurement accuracy. It is suitable for accurate measurement of stress tensors of solid media in fields such as geotechnical engineering testing, material mechanics testing, and engineering structure health monitoring.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A device for testing the stress tensor of a solid medium, characterized by: The device comprises a stress tensor measuring ball (1) and a data acquisition instrument (2); The stress tensor measuring ball (1) is buried at a designated position inside the solid medium (4); The data acquisition instrument (2) is matched and arranged outside the solid medium (4), and one end of the data acquisition instrument is connected to the stress tensor measurement ball (1) via a data line (3) for collecting quasi-static and dynamic strain data of the stress tensor measurement ball (1).

2. The device for testing the stress tensor of a solid medium according to claim 1, wherein: The stress tensor measuring ball (1) comprises a ball shell (11), a ball center fixing device (12) and an axial strain sensor (13) located inside the ball shell (11); The spherical shell (11) is also matched with a circular hole (14) serving as a strain sensing area, and an analog-to-digital conversion chip is also provided inside; the analog-to-digital conversion chip has the functions of converting analog signals into digital signals and reading data of axial sensors with different ID numbers, and has a data input and output interface; the data input and output interface is fixed on the spherical shell (11); The spherical center fixing device (12) is located inside the spherical shell (11), and is connected to the shell by means of ≥3 metal rods evenly distributed in space, and is made of the same material as the spherical shell (11); The axial strain sensors (13) are evenly mounted on the outer circumference of the spherical center fixing device (12), and are connected to the analog-to-digital conversion chip inside the spherical shell (11) via a signal line; one end of each axial strain sensor (11) is fixed to the spherical center fixing device (12), and the other end is fixed to the circular hole (14), and the end portion is aligned with the outer circumference of the circular hole (14).

3. The device for testing the stress tensor of a solid medium according to claim 2, wherein: The data acquisition instrument (2) is connected to the data input and output interface of the analog-to-digital conversion chip via a data line (3).

4. The device for testing the stress tensor of a solid medium according to claim 2, wherein: The ball shell (11) is a soft elastic sphere, and its elastic modulus is lower than that of the fixing medium (4).

5. The device for testing the stress tensor of a solid medium according to claim 1, wherein: The number of the axial strain sensors (13) is ≥6; the axial strain sensors (13) adopt strain gauges, fiber grating sensors or springs.

6. A method for testing the stress tensor of a solid medium, based on the device for testing the stress tensor of a solid medium according to any one of claims 1 to 5, characterized in that: The specific steps include: Step 1: Select a soft elastic sphere and evenly arrange a plurality of axial strain sensors (13) in the elastic sphere to construct a stress tensor measurement sphere (1); Step 2: embed the constructed stress tensor measurement sphere (1) into the fixed medium (4) to be measured according to the set direction, and mark the local coordinate system; Step 3: axial strain ε measured by the i-th axial strain sensor (13) i and the elastic modulus E of the surrounding solid medium (4), through the formula F i =Eε i , calculate the normal stress component F measured by the i-th axial strain sensor (13) i ; Step 4: Construct the axial stress measurement vector F of the axial strain sensor (13): F=[F1,F2,…,F N ] T ,N≥6; In the above formula, F1, F2 and F N represent the normal stress components measured by the first, second and Nth axial strain sensors (13), respectively, T represents the transpose of the vector, and N is the number of axial strain sensors (13); Step 5: Calculate the normal stress component F measured by the i-th axial strain sensor (13) according to the Cauchy stress theorem. i , construct the coefficient matrix A: In the above formula, a i 、b i 、c i is the direction vector component of the axial strain sensor (13) in the i-th direction; σ xx , σ yy , σ zz , σ xy , σ xz , σ yz is the stress tensor component; for the directions of N axial strain sensors (13), the dimension of the coefficient matrix A is N×6, and each row corresponds to the coefficient vector of one direction Step 6: Calculate the stress tensor of the solid medium (4) When N=6, directly solve the linear equation system σ=A -1 F; when N>6, the regularized least squares method is used to calculate the stress tensor: σ=(A T A+λI) -1 A T F; Where λ is the Tikhonov regularization parameter; Step 7: Compensate for the error caused by the temperature change factor and output the measurement result.

7. The method for testing the stress tensor of a solid medium according to claim 6, wherein: The error compensation in step 7 includes dynamically correcting the thermal drift error based on a pre-calibrated temperature-sensitivity relationship matrix; and optimizing the residual weight through the Huber loss function to suppress the influence of outlier measurements on the solution results.

8. The method for testing the stress tensor of a solid medium according to claim 7, wherein: The thermal drift error is dynamically corrected based on the pre-calibrated temperature-sensitivity relationship matrix. The specific steps are as follows: Step 711: Conduct a temperature sensitivity calibration experiment for each axial strain sensor (13), specifically placing the axial strain sensor (13) in a constant temperature box and performing a temperature calibration experiment in the temperature range T∈[T min ,T max ] and perform stepwise temperature increase or decrease with a step length ΔT, and record the zero point output F of the axial strain sensor (13) at each temperature point. 0,i (T) and full-scale output F FS,i (T), where i represents the i-th axial strain sensor (13); Step 712: Establish a polynomial model, that is, the temperature-sensitivity relationship of each axial strain sensor (13) channel can be modeled as: In the above formula, F nom is the rated full-scale output calibrated at room temperature, k 0,i 、k 1,i 、k 2,i are all polynomial coefficients; Step 713: Construct a temperature-sensitivity relationship matrix based on the measurement results of each axial strain sensor (13): Step 714: According to the current temperature T cur , obtain F by linear interpolation from the temperature-sensitivity relationship matrix offset,i (T cur ) and S i (T cur ), assuming that the original axial stress measurement is F raw,i , calculate the stress value F after temperature compensation comp,i , the specific calculation formula is:

9. The method for testing the stress tensor of a solid medium according to claim 7, wherein: The Huber loss function is used to optimize the residual weight to suppress the influence of outlier measurements on the solution results. The specific steps are as follows: Step 721: Use the Huber loss function to optimize the residual weight. The calculation formula is: Among them, r i is the residual of the i-th axial strain sensor (13), δ is the threshold; Step 722: Set the objective function of the least squares algorithm to The weight w i Determined by the derivative of the Huber function; Step 723: Perform iterative solution to obtain the corrected stress tensor. The specific solution process is as follows: Set the initial solution: Calculate the initial stress tensor by the least squares method: s (0) =(A T A) -1 A T F comp ; Calculate the residual: Convert the stress calculated in the kth round into the axial stress in the direction of the i-th sensor, and calculate the difference between the calculated and measured values: r i (k) =F comp,i -A i s (k) ; Update weights: Calculate the weight coefficient of the i-th sensor in the k-th iteration by the difference between the measured value and the inverted value: Weighted solution: Calculate the stress of the k+1th iteration by introducing the weight coefficient matrix: s (k+1) =(A T W (k) A) -1 A T W (k) F comp , among them Convergence judgment: When ||σ (k+1) -σ (k) When ||<ζ, the iteration stops and the calculation converges; where ζ is the iteration error.

10. The method for testing the stress tensor of a solid medium according to claim 7, wherein: The coupling between the strain tensor measuring ball (1) and the solid medium (4) adopts cement mortar coupling, graded sand coupling or rapid gel coupling.

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