CN116222493A - A Method of Measuring the Deformation of Subway Tunnel Using Inclination Sensor - Google Patents

Abstract

The invention relates to a method for measuring deformation of a subway tunnel by using an inclination sensor, which comprises the following steps: s1: selecting an existing subway tunnel, and installing inclination angle sensors, wherein all the inclination angle sensors are in signal connection with an external data collecting box; s2: calculating corresponding inclination angle change values to obtain deflection values of corresponding measurement areas; s3: calculating to obtain an actual value of each measuring area through a polynomial function, adding the deflection value of each measuring area to the deflection values of all measuring areas before the measuring area to obtain a calculated value, and comparing the calculated value with the actual value to obtain a relative error; s4: analyzing uncertainty of the inclination angle change value measured by the inclination angle sensor by adopting a Monte Carlo method; s5: and measuring the deformation test precision analysis of the existing subway tunnel by adopting a finite element simulation analysis method to the inclination sensor. The inclination angle sensor used by the method is convenient to install, can realize real-time monitoring, has high precision, and belongs to the technical field of subway tunnel deflection monitoring.

Description

A method for measuring subway tunnel deformation using inclination sensors

Technical Field

The invention relates to the technical field of subway tunnel deflection monitoring, and in particular to a method for measuring subway tunnel deformation by using a tilt sensor.

Background Art

During the construction of a certain subway project, the shield construction of the newly built tunnel will cause changes in the initial stress state of the surrounding soil, resulting in soil consolidation settlement, and then causing horizontal or vertical displacement of the surrounding soil. The internal structure of the subway and the interval equipment can only withstand limited deformation values. If it exceeds a certain limit, it may cause serious safety accidents. In this case, disturbance deformation monitoring is required.

With the continuous development of deflection deformation monitoring solutions, there are many deflection deformation monitoring solutions. Different deflection measurement solutions are selected by analyzing the operating environment, material structure and measurement location of the structure to be measured to cater to the characteristics of different structures. In the early days, there were total station method, dial indicator method, level method and theodolite method. The following introduces several deflection measurement methods.

(1) Electronic micrometer deflection measurement method

The electronic micrometer is a displacement measuring instrument with high accuracy that can automatically record digital data based on the mechanical micrometer. Since the electronic micrometer needs to be fixed under the structure to be measured, if the electronic micrometer is used on the bridge structure, it is only suitable for bridge deflection testing on dry rivers or shallow rivers.

(1) GPS deflection monitoring method

A GPS receiver is installed at each base point and the point to be measured. The two receivers are positioned using satellite navigation and positioning systems to determine the change in the position of the point to be measured relative to the base station, thereby obtaining the deflection value of the structure at the point to be measured. The advantages of this method are that the system has strong real-time performance and a wide measurement range, and is suitable for structures with poor geographical locations or large spans; the disadvantages are that the system is expensive and the vertical deflection measurement accuracy is only at the centimeter level.

(2) Connecting pipe liquid level deflection measurement method

The basic principle of measuring structural deflection by static leveling is to obtain the vertical deflection change of the measuring point by comparing the difference in the liquid depth of the level gauge at the measuring point and the reference point during the test. The change in the liquid level of the connected tube deflectometer directly reflects the deflection of a certain section of the structure, and does not require complex calculations. However, since the viscous damping coefficient of the liquid is very small, its own free oscillation takes a long time to decay. In the case of rapid load changes, the test results are greatly distorted. In addition, when measuring the structure, the lateral and vertical vibrations of the structure will also cause changes in the depth of the liquid in the tube, which in turn affects the test results. The advantage of this method is closed measurement, which is not affected by weather and other factors, and the reading is simple; the disadvantage is that the device is complicated to install and is only suitable for the measurement of drop bridges. The liquid viscous damping coefficient is small, and only static deflection and dynamic deflection with slow load changes can be measured.

(3) Optical deflection measurement method

Various optical-based deflection test methods can measure the dynamic and static deflections of structures and have been widely used in load tests. However, since a fixed point is needed to fix the equipment during the test, only a few spans of the bridge close to the abutments or dry bridges under the bridge deck can be measured. The advantages of this method are long-distance, non-contact measurement, high accuracy, and remote real-time detection. The disadvantages are that a measurement reference within a certain distance is required, the measurement range is limited, and it is easily affected by obstructions from objects and weather such as rain and snow, making it unsuitable for long-term monitoring of the deflection of large-span bridges.

(4) Deflection measurement method based on rotation angle

The principle of this method is to use an inclinometer to test the vertical rotation angle values of multiple control points on the vertical direction of the structural surface, and then calculate the deflection value from the inclinometer value based on a certain mathematical model. Compared with other test methods, this test method can simultaneously measure the deflection value at any position of the structure and the vertical rotation angle of the sensor arrangement point. The advantages of using an inclinometer to test structural deflection are: the rotation angle and deflection can be obtained at the same time; the deflection and rotation angle of the structure can be tested under dynamic and static loads; it is easy to install and does not require a static reference point; it is not affected by the weather and other environmental factors; it has high resolution and low cost. At the same time, the limitation of this method is that it has high requirements for the acquisition accuracy of the inclinometer and the real-time transmission of the acquired data.

Summary of the invention

In view of the technical problems existing in the prior art, the purpose of the present invention is to provide a method for measuring the deformation of a subway tunnel using a tilt sensor, which can realize real-time monitoring and high precision.

In order to achieve the above object, the present invention adopts the following technical solution:

A method for measuring the deformation of a subway tunnel using an inclination sensor, the method comprising the following steps: S1: selecting an existing subway tunnel, the existing subway tunnel being located below a subway tunnel to be constructed, dividing the existing subway tunnel into a plurality of measurement areas, installing an inclination sensor in each measurement area, all of the inclination sensors being connected to an external data collection box signal, and starting to collect inclination data; S2: using a Monte Carlo method to analyze the uncertainty of the inclination change value measured by the inclination sensor, the purpose of which is to improve the measurement accuracy of the measured inclination value; S3: using a finite element simulation analysis method to analyze the uncertainty of the inclination change value measured by the inclination sensor The purpose of the existing subway tunnel deformation test accuracy analysis is to calculate the theoretical value of the subway tunnel change through finite element simulation analysis; S4: The actual value of each inclination measurement area is obtained by polynomial function calculation, and the deflection value of each measurement area is added to the deflection value of all measurement areas before the measurement area to obtain the actual value. The S4 theoretical value and the actual value are compared to obtain the relative error, and its purpose is to calibrate the accuracy of the actual value of the inclination measurement; S5: Load the existing subway tunnel, and obtain the inclination change value of each measurement area before and after loading through the inclination sensor, and calculate the corresponding inclination change value to obtain the deflection value of the corresponding measurement area.

n为测量区的数量，倾角传感器安装在每个测量区长度方向的中点处。As a preferred embodiment, in step S1, the length of the existing subway tunnel is L, and the length of each measurement area is L ₁ , then

n is the number of measuring areas, and the inclination sensor is installed at the midpoint of the length direction of each measuring area.

As a preferred embodiment, the specific steps of using the Monte Carlo method to analyze the uncertainty of the tilt angle change value measured by the tilt sensor in step S2 are: the measured value θ (θ ₁ , θ ₂ . . . θ _n ) of each tilt sensor is the input value X, the deformation value y of the measuring area is the output value, and the connection formula between the input value and the output value is formula (7),

y _i =∑ ₁ L _i tanθ _i (7);

When n tilt sensors are arranged,

Y＝Δy ₁ +Δy ₂ +…+Δy _n ` (8);

Δy _i =L _i tanθ _mi ` (9);

θ _mi ~N(θ _i , δ ² )` (11);

Where: θ _i is the true value of the inclination at the i-th sensor, θ _mi is the measured value of the inclination at the i-th sensor, and δ is the standard deviation of the measured value of the inclination sensor.

As a preferred embodiment, in step S3, the specific steps of using the finite element simulation analysis method to analyze the accuracy of the tilt sensor measuring the deformation of the existing subway tunnel are as follows:

A: Use finite element software to build a subway tunnel model;

B: The deflection value of the measuring area is calculated using finite element software, and the deflection of the measuring area is fitted into the deflection curve of the subway tunnel.

As a preferred embodiment, in step S4, the specific steps of obtaining the actual value of each measuring area by polynomial function calculation are: taking the quintic function f(x)= ^x5 + ^x4 + ^x3 + ^x2 +x for precision analysis at x∈(0,8), dividing the quintic function curve into 8 equal measuring areas at x∈(0,8), and arranging an inclination sensor measuring point at the midpoint of each measuring area, taking the slope of the inclination sensor measuring point as the inclination value of the corresponding measuring area, multiplying the slope of each measuring area by the length of this measuring area as the deflection change of this measuring area, adding the deflection changes of all measuring areas before this measuring area to obtain the calculated value, substituting the x value into the function to obtain the deflection value called the actual value; and then comparing the calculated value with the actual value to obtain the relative error between the two.

As a preferred embodiment, in step S5, the step of calculating the corresponding inclination angle change value to obtain the deflection value of the corresponding measurement area is:

The deflection increment for each measuring area is:

Δω _i =L ₁ tanθ _i (4);

Then the deflection at the end of the i-th segment is the accumulation of the deflections of all the measurement areas in the previous i-1 segments, that is,

Wherein, _L1 is the length of the measuring area, _θi is the inclination change value at the midpoint of the i-th segment, i.e., the measurement value of the inclination sensor of the i-th segment, _Δωi is the deflection difference between the front and rear ends of the i-th segment, and _ωi is the deflection value at the end of the i-th segment.

As a preferred embodiment, in step B, the specific steps of fitting the deflection curve of the subway tunnel are: taking the distance between adjacent measurement areas as the x-coordinate and the deflection value as the y-coordinate, using Matlab to draw a deformation curve graph, and using CurveFitting to fit the deformation curve function; when fitting the deflection curve function, a Polynomial function is used for fitting;

The polynomial function at this time is:

f(x)=P1×x^7+P2×x^6+P3×x^5+P4×x^4+P5×x^3+P6×x^2+P7×x+P8;

P1 = 1.271e-10;

P2 = -2.357e-08;

P3 = 8.447e-07;

P4 = 7.683e-05;

P5 = -0.006277;

P6 = 0.139;

P7 = -0.8575;

P8 = -1.819;

Then its inclination function is:

f(x)=0.0000000008897×x^6-0.00000014142×x^5+0.0000042235×x^4+0.00030732×x^3-0.018831×x^2+0.278×x-0.8575;

The fitting deflection curve function is a 7th-order polynomial function, and the error is analyzed for the number of measurement areas n=7, 8, and 9 respectively.

Principle of the present invention:

1. The inclination sensor is an acceleration sensor that uses Newton's second law. It is a fixed inclination measuring instrument that uses a dual-axis inclination sensor developed and produced by micro-electromechanical systems as a sensitive element and is produced in combination with smart chip technology. It is used to observe the dual-axis inclination angle of structures such as bridges, buildings, and railways relative to the horizontal. It is suitable for the deformation of hidden parts that are difficult to observe by conventional geodetic methods, and can be used for long-term testing with an automated system.

2. Principle of deflection calculation. The solutions for converting deflection by inclination angle include using the least square method to obtain a set of optimal solutions and directly integrating the inclination function to obtain the deflection value. However, these methods all involve relatively complex mathematical calculations. Therefore, the simplest method of arranging measuring points and the deflection calculation method in the conversion process are selected for research: that is, n positions are selected on the structure to place inclination sensors, as shown in Figure 2, assuming that the structural deformation is within the linear range. By loading the structure, the inclination angle change value before and after loading is obtained, and the tangent value of the inclination angle is taken and multiplied by the distance of the measurement area to obtain the deflection value of the measurement area.

According to the knowledge of material mechanics, we know that the approximate differential equation of the deflection curve of the subway tunnel is:

If it is a straight subway tunnel with a constant cross section, its bending stiffness EI is a constant, and the above formula can be rewritten as:

EIω″＝-M(x) (2);

Integrating the above formula once can get the rotation angle equation of the subway tunnel, which is:

EIω′=-∫M(x)dx+C ₁ (3);

If equation (3) is integrated again, the deflection curve equation of the subway tunnel can be obtained.

In summary, the rotation angle of any cross section of the structure is equal to the rotation angle of the deflection curve at that point, that is, the angle between the tangent of the deflection curve at that point and the x-axis. The deflection of the subway tunnel and the rotation angle have a first integral relationship. Therefore, the deflection of the structure can be obtained by measuring the rotation angle of certain points when the structure is bent.

3. Principle of measurement area error analysis (relative error)

Calculating the deflection by the inclination measured by the inclination sensor is an indirect calculation method. First, the structure needs to be divided into measurement areas, and the deflection change of each measurement area is calculated by multiplying the measured inclination value by the length of the measurement area. The deflection change calculated by this method is an approximate value. The more measurement areas there are, the closer it is to the actual value.

There are many methods for calculating deflection based on the inclination sensor. The method used in this study is the measurement area superposition method. This method is simple to calculate, and its accuracy can meet the requirements, which can greatly reduce the time cost in the calculation process. However, the accuracy of the deflection calculation of this method is affected by the superposition of the measurement area, and only the deflection value at the end of each measurement area can be calculated. If the calculated deflection value is used to fit the deformation curve, there will be a certain error between the obtained deformation curve and the theoretical deformation curve.

Considering that the deformation curve of a subway tunnel is generally a continuous and smooth curve, and the deformation curve order of a subway tunnel under the action of load is generally not too high, a polynomial function can be used to fit the deformation curve of the subway tunnel. The polynomial function is a relatively simple function. Using the polynomial function to fit the deformation curve can easily calculate the inclination of the deflection deformation.

4. Analysis of uncertainty of inclination change value

Measurement is the process of using data to reflect observed phenomena and quantify non-quantifiable physical objects. Affected by factors such as measurement methods, measurement steps, operator familiarity, and environment, measurement results generally have uncertainty. Measurement uncertainty is a non-negative parameter that characterizes the dispersion of the measured value and is a quantitative representation of the quality of the measurement result.

Because the deflection value needs to be converted from the measured inclination value, the assessment of measurement uncertainty generally includes two stages: formulation and calculation, where calculation includes transfer and summary processes. The formulation stage generally includes defining the measured quantity (i.e. the quantity to be measured), identifying the measured input quantity (i.e. the quantity directly measured), generating a measurement model related to the measured quantity and the input quantity, and setting a probability distribution for the input quantity based on known information. The calculation stage includes transferring the probability distribution of the input quantity through a mathematical model to obtain the probability distribution of the output quantity. Using this probability distribution, we can derive the estimated value of the output quantity, the standard uncertainty, and the inclusion interval under the specified inclusion probability.

Since the possible values of the measured inclination angle and their corresponding probabilities cannot be listed one by one, the measured inclination angle value belongs to a continuous random variable. Therefore, its probability density function and distribution function can be calculated.

The first step in uncertainty assessment is to formulate the relationship between the input quantity and the measured value: first define a measured quantity Y, multiple input quantities X (X1, X2...Xn), and establish a mathematical model Y=f(X) that relates Y to X through the principle of measurement. Then, it is necessary to determine the probability density function of X based on the information obtained. The second step is to transfer the probability density function of X to Y through the model formula, thereby deriving the probability density function of Y. Finally, based on the probability density function of Y, we need to obtain: the expected value of Y, as the estimate of the quantity y; the standard deviation of Y, as the standard uncertainty of y u(y); and the confidence interval of Y with a specified inclusion probability.

When we know the probability density function of X, the most important step is to transfer the probability distribution. Monte Carlo method provides a general and effective method to numerically approximate the distribution function F(a) of the output quantity Y.

In formula (6), F(a) is the distribution function of the output quantity Y, and f(t) is the probability density function of Y, which is obtained by transferring the probability density function of the input quantity X through the Y=f(X) model. The Monte Carlo method is used to determine the approximate numerical representation F of the distribution function F(a) of Y. The core is to repeatedly sample the probability density function of the input quantity Xi and evaluate the model for each case. The distribution function contains all the known information about Y. F can be used to approximate any characteristics of Y, such as expectation, variance and inclusion interval, so as to obtain the estimated value, standard uncertainty and inclusion interval of the measured value Y. Increasing the number of sampling of the probability density function of the input quantity can improve the quality of the calculation results.

The probability transfer process using the Monte Carlo method is generally divided into the following steps. First, the number of Monte Carlo experiments M is selected, that is, the number of times the model is evaluated. Then the probability density function of the input quantity Xi is sampled to generate M quantities, and then the output quantity Y value corresponding to the model is calculated for each quantity to obtain the corresponding M model values. Finally, the estimated value y of Y and the uncertainty u(y) and other evaluation values are calculated based on the M model values. With this measurement uncertainty evaluation method, we can easily evaluate the uncertainty of the deformation measurement value measured by the inclination sensor.

In general, the present invention has the following advantages:

(1) The measurement method of the present invention has the advantages of high deflection data acquisition accuracy, stable data transmission, real-time and efficient data processing, and strong adaptability to engineering applications.

(2) The inclinometer is small and easy to carry. Its size is 120mm*150mm*40mm, and it can be carried in large quantities.

(3) The inclination sensor is easy to install, the measuring point is not easily damaged, the aluminum casing can ensure its long-term use, and it is not limited by measurement conditions and can be used in conditions without light.

(4) Compared with total stations, inclination sensors have low instrument costs and can be recycled.

(5) The inclination sensor has high test accuracy and can measure the inclination to 9 decimal places, while the deflection value measured by the total station can only be accurate to two decimal places.

(6) The inclination sensor can realize real-time monitoring in the office without supervision. By using the user platform and computer control, real-time monitoring can be realized, which greatly reduces the workload and the testing time on site. In addition, the data collection of the inclination sensor can be realized at a high frequency, that is, 20, 50, or 100 data can be collected in 1 second, which can truly achieve real-time monitoring.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a schematic diagram showing that an existing subway tunnel is divided into 13 measurement areas.

Figure 2 is a schematic diagram of the subway tunnel division used in the deflection calculation principle.

Figure 3 is a schematic diagram of the cross section of each monitoring point in the measurement area.

FIG4 is a graph showing the deflection curve measured by the inclination sensor.

FIG5 is a graph showing the variation of the deflection measured by the inclination sensor in the C1-C5 measurement area over time.

FIG6 is a graph showing the variation of the deflection measured by the inclination sensor in the C6-C9 measurement area over time.

FIG7 is a graph showing the variation of the deflection measured by the inclination sensor in the C10-C13 measurement area over time.

Figure 8 is a deformation curve diagram measured by the total station.

Figure 9 is a deformation curve diagram of the measuring points measured by the total station.

Figure 10 is a comparison of the deformation curves measured by the inclination sensor and the total station.

DETAILED DESCRIPTION

The present invention will be further described in detail below in conjunction with specific implementation methods.

This embodiment provides a method for measuring deformation of a subway tunnel using a tilt sensor, and the specific steps are as follows:

1. Select existing subway tunnels:

n为测量区的数量，在既有地铁受施工影响区域(13个测量区)布置13个倾角传感器，13个倾角传感器分别安装在13个测量区长度方向的中点处。Select an existing subway tunnel with a length of L. The existing subway tunnel is located below the subway tunnel to be built. According to the measurement accuracy analysis of the existing subway deflection deformation in this tunnel, it is divided into 13 measurement areas. The length of each measurement area is L _1. Then

n is the number of measurement areas. 13 inclination sensors are arranged in the existing subway construction-affected area (13 measurement areas). The 13 inclination sensors are installed at the midpoints of the length directions of the 13 measurement areas.

2. Install the sensor:

As shown in Figure 1 and Figure 3, 13 inclination sensors and 2 data collection boxes are deployed on site in the existing subway tunnel. The 13 measurement areas are C1-C13, of which C1-C5 measurement points are collected in data collection box No. 1 (400×300×150mm), and C6-C13 measurement points are collected in data collection box No. 2. The installation of the inclination sensor should be carried out according to the following steps.

(1) Preparation: Measure and determine the location of the tilt sensor monitoring point, and mark it on site, that is, the location of the monitoring point;

(2) The inclination sensor is fixed to the waist of the concrete segment in the subway tunnel with expansion screws, and the position is determined to ensure that the height does not affect the operation of the train;

(3) According to the distance of each monitoring point, cut the four-core wire and data wire to the appropriate length. Connect the data wire and four-core wire to the inclination sensor to the collection box. Use cross screws to fix the data wire and four-core wire of the inclination sensor to the receiver in the collection box;

(4) Check that the data line and the four-core wire of each inclination sensor are relatively independent in the collection box to ensure that each inclination sensor is in parallel;

(5) After installation, make a record of the inclination sensor installation.

(6) Perform a power supply test on the data acquisition box and collect the initial value of the inclination sensor.

As shown in Figure 1, 13 tilt sensors with an absolute accuracy of 20″ are actually deployed on site. The monitoring point range is shown in the following table.

Table 1 Monitoring point layout range

3. Tilt sensor data collection and analysis:

(1) Set the acquisition frequency and mode in the acquisition software.

(2) Click Start Measurement to send a collection command to the inclination sensor. The hardware can enable all inclination sensors to receive the command at the same time. After receiving the command, they will measure at the same time interval and store the measured data inside the inclination sensor.

(3) After sending the acquisition command, the sensor collects data at the same time interval. The collected data is first stored inside the sensor, and then the sensor returns the collected data to the terminal. After decoding the data, the sensor inclination value can be obtained.

Analysis of measured data of inclination sensor

During the construction of the subway tunnel, data from a week of passing through the existing tunnel section is analyzed. During the inclination sensor collection process, continuous data collection is achieved, and the user end can obtain an inclination collection value every minute. Therefore, the inclination sensor and its supporting system can be used to achieve real-time monitoring.

Table 2 Tilt angle values measured by the tilt sensor

Table 2 Tilt angle values measured by the tilt sensor (continued)

Table 2 Tilt angle values measured by the tilt sensor (continued)

Table 2 Tilt angle values measured by the tilt sensor (continued)

Table 2 Tilt angle values measured by the tilt sensor (continued)

Angle calculation inside the tilt sensor system

Temperature value: keep 1 decimal place, unit is ℃

t = temperature reading/32;

Temperature compensation coefficient:

s＝-0.0000005*t ³ -0.00005*t ² +0.0032*t-0.031;

Voltage conversion coefficient (before temperature compensation):

K ₁ = 16;

Angle value (before temperature compensation): retain 6 decimal places, unit is °

Voltage conversion coefficient (after temperature compensation): retain 6 decimal places

Angle value (after temperature compensation): retain 6 decimal places, unit is °

(4) The Monte Carlo method is used to analyze the uncertainty of the tilt angle change value measured by the tilt sensor; the measured value θ (θ ₁ ,θ ₂ ...θ _n ) of each tilt sensor is taken as the input value X, and the deformation value y of the measurement area is taken as the output value. The relationship between the input value and the output value is given by equation (7):

y _i =∑ ₁ L _i tanθ _i (7);

When n tilt sensors are arranged,

Y＝Δy ₁ +Δy ₂ +…+Δy _n ` (8);

Δy _i =L _i tanθ _mi ` (9);

θ _mi ~N(θ _i , δ ² )` (11);

Where: θ _i is the true value of the inclination at the i-th sensor, θ _mi is the measured value of the inclination at the i-th sensor, and δ is the standard deviation of the measured value of the inclination sensor.

(5) The finite element simulation analysis method is used to analyze the accuracy of the inclination sensor in measuring the deformation test of the existing subway tunnel. A: Use finite element software to construct a subway tunnel model; B: Use finite element software to calculate the deflection value of the measurement area, and fit the deflection of the measurement area to the deflection curve of the subway tunnel. In step B, the specific steps for fitting the deflection curve of the subway tunnel are: use the distance between adjacent measurement areas as the x-coordinate, the deflection value as the y-coordinate, use Matlab to draw the deformation curve graph, and use CurveFitting to fit the deformation curve function; when fitting the deflection curve function, a Polynomial function is used to fit; the polynomial function at this time is:

f(x)=P1×x^7+P2×x^6+P3×x^5+P4×x^4+P5×x^3+P6×x^2+P7×x+P8;

P1 = 1.271e-10;

P2 = -2.357e-08;

P3 = 8.447e-07;

P4 = 7.683e-05;

P5 = -0.006277;

P6 = 0.139;

P7 = -0.8575;

P8 = -1.819;

Then its inclination function is:

f(x)=0.0000000008897×x^6-0.00000014142×x^5+0.0000042235×x^4+0.00030732×x^3-0.018831×x^2+0.278×x-0.8575;

The fitting deflection curve function is a 7th-order polynomial function, and the error is analyzed for the number of measurement areas n=7, 8, and 9. The error between the calculated value and the theoretical value caused by the calculation of the segmentation is calculated. The error calculation is performed for the deflection of the existing subway tunnel.

Table 3 Segmentation error

Take the number of Monte Carlo experiments M = 1000 and perform 1000 simulation calculations on the calculated Y value.

Table 4 Deflection simulation calculation value y distribution mean (unit: mm)

Table 5 Standard deviation of y distribution of deflection simulation calculation value (unit: mm)

Table 6 95% confidence interval of single deflection simulation value (unit: mm)

Table 7 95% probability error interval of single deflection simulation calculation value

It can be seen from Tables 3 to 7 that when the absolute accuracy of the inclination sensor is different, the discreteness of the deflection calculation results is relatively small. When using inclination sensors with absolute accuracy of 0.01°, 0.005°, and 0.001°, the deflection errors are relatively small, and such an error range is acceptable in engineering applications. In the case of comprehensive consideration of measurement accuracy and economy, the solution of arranging 7 inclination sensors with an absolute accuracy of 0.01° in the affected area of the existing subway can meet the requirements.

4. Calculation of subway tunnel deflection:

The actual value of each tilt sensor is obtained by calculating the polynomial function, and the calculated value is obtained by adding the deflection value of each tilt sensor to the deflection values of all sensors before the sensor.

The steps to calculate the corresponding inclination change value to obtain the deflection value of the corresponding measurement area are:

The deflection increment for each measuring area is:

Δω _i =L ₁ tanθ _i (4);

Then the deflection at the end of the i-th segment is the accumulation of the deflections of all the measurement areas in the previous i-1 segments, that is,

Wherein, _L1 is the length of the measuring area, _θi is the inclination change value at the midpoint of the i-th segment, i.e., the measurement value of the inclination sensor of the i-th segment, _Δωi is the deflection difference between the front and rear ends of the i-th segment, and _ωi is the deflection value at the end of the i-th segment.

As shown in Figures 4 to 7, as time goes by, the deformation value of the existing tunnel continues to increase. The deflection values at the positions of the 6th, 7th, 8th, and 9th inclination sensors are larger than those at other positions. This is because these four inclination sensors are within the scope of the crossing stage (the intersection of the existing tunnel and the tunnel to be built), and the existing tunnel is most affected. The maximum deflection value of the existing tunnel is 1.86mm, which is less than the theoretical calculation value of 8.23mm by finite element simulation analysis, and meets the requirement that the warning value is less than 10mm.

5. Total Station Measurement Data

As shown in Figures 8 to 10, in order to verify the accuracy of this method of measuring tunnel deflection with the inclination sensor, 5 total station measuring points were set up at the same time during the measurement process, and the measuring points with the same cross-section layout of the inclination sensor were selected. The maximum value of the deflection value at the measuring point is 1.91mm, and the error with the inclination sensor measurement value is 2.6%. Therefore, the measurement results of the inclination sensor and the total station are consistent.

Comparison of the measured results between the total station and the inclination sensor (Conclusion)

Compare the deformation curves measured by the inclination sensor with those by the total station.

It can be seen that the maximum deflection error of the measured deformation curves of the inclination sensor and the total station is 0.7 mm, and the deformation curves are not much different. It is feasible to use the inclination sensor to measure tunnel deformation. The comparison of the maximum deflection measurement values of the inclination sensor and the total station is shown in Table 8.

Table 8 Comparison of the maximum measured deflections of the two

The maximum deflection measurement error between the inclination sensor and the total station is 2.6%, and both are smaller than the theoretical calculated value, meeting the requirement of being less than the warning value of 10 mm.

VI. Conclusion

(1) The measured deflection curve obtained by the inclination sensor using the segmented superposition method has the same shape as the theoretical deflection curve, which shows the feasibility of the inclination sensor in tunnel deformation measurement.

(2) The maximum deflection value measured by the inclination sensor is 1.86 mm, which is smaller than the theoretical calculated value of 8.23 mm and smaller than the warning value of 10 mm. The existing tunnels will be affected by tunnel excavation, but are generally safe.

(3) The measurement value of the inclination sensor can reflect the real-time changes of the structure, and the results are reliable.

The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims (7)

1. A method utilizing an inclination sensor to measure deformation of a subway tunnel, characterized in that the method may further comprise the steps: S1: Select the existing subway tunnel, the existing subway tunnel is located under the subway tunnel to be built, divide the existing subway tunnel into multiple measurement areas, install inclination sensors in each measurement area, and all inclination sensors are Connect with the signal of the external data collection box, and start to collect the inclination data; S2: Using the Monte Carlo method to analyze the uncertainty of the inclination change value measured by the inclination sensor; S3: Using the finite element simulation analysis method to analyze the accuracy of the inclination sensor to measure the deformation test of the existing subway tunnel; S4: The actual value of each measurement area is obtained by polynomial function calculation, the calculated value is obtained by adding the deflection value of each measurement area to the deflection values of all measurement areas before the measurement area, and the relative error is obtained by comparing the calculated value with the actual value; S5: Load the existing subway tunnel, obtain the inclination change value of each measurement area before and after loading through the inclination sensor, and calculate the corresponding inclination change value to obtain the deflection value of the corresponding measurement area. 2. according to a kind of method utilizing inclination sensor to measure subway tunnel deformation according to claim 1, it is characterized in that: in step S1, the length of existing subway tunnel is L, and the length L of each measuring area ₁ , then

n is the number of measurement areas, and the inclination sensor is installed at the midpoint in the length direction of each measurement area. 3. according to a kind of method that utilizes inclination sensor to measure subway tunnel deformation according to claim 1, it is characterized in that: adopt Monte Carlo method to analyze the uncertainty of the inclination change value that inclination sensor measures in the step S2 The specific steps are: the measured value θ(θ ₁ , θ ₂ ...θ _n ) of each inclination sensor is the input quantity X, the deformation value y of the measurement area is the output quantity, and the relationship between the input quantity and the output quantity The formula is formula (7), y _i =∑ ₁ L _i tanθ _i (7); When n inclination sensors are arranged, Y＝Δy ₁ +Δy ₂ +…+Δy <sub>n`</sub> (8); Δy <sub>i</sub> = L <sub>i</sub> tanθ <sub>mi</sub> ` (9);

θ _mi ～N(θ _i , δ ² )` (11); Among them: θ _i is the true value of the inclination angle at the i-th sensor, θ _mi is the measured value of the inclination angle at the i sensor, and δ is the standard deviation of the measured value of the inclination sensor. 4. according to a kind of method utilizing inclination sensor to measure subway tunnel deformation according to claim 1, it is characterized in that: in step S3, adopt the concrete step of finite element simulation analysis method to inclination sensor measure existing subway tunnel deformation test precision analysis for, A: Use finite element software to build a subway tunnel model; B: Use the finite element software to calculate the deflection value of the measurement area, and fit the deflection of the measurement area to the deflection curve of the subway tunnel. 5. according to a kind of method utilizing inclination sensor to measure subway tunnel deformation according to claim 1, it is characterized in that: in step S4, the concrete step that obtains the actual value of each measurement area by polynomial function calculation is: get quintic function f(x)＝x ⁵ +x ⁴ +x ³ +x ² +x Carry out precision analysis at x∈(0,8), divide the quintic function curve at x∈(0,8) into 8 measurement areas , and arrange an inclination sensor measuring point at the midpoint of each measuring area, take the slope of the inclination sensor measuring point as the inclination value of the corresponding measuring area, and multiply the slope of each measuring area by the length of this measuring area as this The deflection change of the measurement area, plus the deflection change of all measurement areas before this measurement area is calculated, and the deflection value obtained by substituting the x value into the function is called the actual value; then the calculated value is compared with the actual value to obtain The relative error of the two. 6. according to a kind of method that utilizes inclination sensor to measure subway tunnel deformation according to claim 1, it is characterized in that: in step S5, the step that calculates the deflection value that corresponding inclination angle change value obtains corresponding measurement area is: each measurement area The deflection increment of is: Δω _i = L ₁ tanθ _i (4); Then the deflection at the end of the i-th segment is the accumulation of the deflection of all the measurement areas of the previous i-1 segment, namely

Among them, L ₁ is the length of the measurement area, θ _i is the inclination change value at the midpoint of the i-th segment, that is, the measured value of the inclination sensor of the i-th segment, Δω _i is the deflection difference between the front and rear ends of the i-th segment, and ω _i is the i-th Segment end deflection value. 7. according to a kind of method that utilizes inclination sensor to measure subway tunnel deformation according to claim 4, it is characterized in that: in step B, the concrete step of fitting out the deflection curve of subway tunnel is: the distance of adjacent measuring area is taken as The x-coordinate and the deflection value are used as the y-coordinate, use Matlab to draw the deformation curve, and use Curve Fitting to fit the deformation curve function; when fitting the deflection curve function, the Polynomial polynomial function is used to fit; The polynomial function at this time is: f(x)=P1×x^7+P2×x^6+P3×x^5+P4×x^4+P5×x^3+P6×x^2+P7×x+P8; P1=1.271e-10; P2=-2.357e-08; P3=8.447e-07; P4=7.683e-05; P5 = -0.006277; P6=0.139; P7=-0.8575; P8=-1.819; Then its inclination function is: f(x)＝0.0000000008897×x^6-0.00000014142×x^5+0.0000042235×x^4+0.00030732×x^3-0.018831×x^2+0.278×x-0.8575; The fitting deflection curve function is a polynomial function of degree 7, and the errors are analyzed for the number of measurement areas n=7, 8, and 9, respectively.

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