Vibration-considered fine simulation method for excavation of cantilever heading machine

Abstract

The invention discloses a cantilever heading machine excavation refined simulation method considering vibration. The method comprises the steps that design data and geological condition data of a tunnel are obtained; according to the design data and the geological condition data of the tunnel, a refined numerical model of tunnel excavation is established; vibration displacements of the cantilever heading machine in the X (drilling direction) direction, the Y (horizontal direction) direction and the Z (vertical direction) direction during construction under various different working conditions are obtained; noise reduction is carried out by using wavelet transform, a vibration trend term is extracted, and rigid body displacement and vibration waves are decomposed; and the construction working condition is obtained, the excavation process of the numerical model is adjusted according to the milling and excavation path of the construction working condition, the vibration waves are loaded, and the deformation result of tunnel excavation is obtained. According to the method, the influence of the vibration on the excavation process is also considered besides the influence of the construction process of block excavation of the cantilever tunneling machine, and the vibration is subjected to noise reduction by utilizing wavelet transform, so that the precision of cantilever tunneling excavation simulation is improved, and a basis is provided for design and construction of related tunnels.

Description

Technical Field

[0001] The present invention relates to the technical field of cantilever tunneling, and in particular to a vibration-considered cantilever tunnel boring machine excavation refinement simulation method. Background Art

[0002] Against the backdrop of high noise and vibration in traditional drilling and blasting construction, and high construction costs and poor adaptability to adverse geological conditions in shield tunneling, cantilever tunnel boring machines (TBMs) integrate cutting, loading, transportation, and dust removal technologies, and offer better disturbance control, and have been widely used in urban underground space construction projects.

[0003] However, for simulating the excavation process, common existing stress release methods are applicable to all construction methods but are difficult to apply to large-scale models. The softening modulus method is often used in shield tunneling, and the gradient load release method can simulate the block excavation process more accurately, similar to the actual cantilever excavation process, but it does not adequately consider the impact of vibration loads. Furthermore, the vibration during cantilever excavation is relatively complex. Existing studies have considered cantilever excavation vibration as a triangular pulse pressure time-history function, but this duration is short and cannot reflect the longer duration of cantilever excavation. Furthermore, long-term cantilever excavation data often has complex vibration signals, requiring denoising. Summary of the Invention

[0004] In response to the above-mentioned deficiencies in the prior art, the present invention provides a refined simulation method for cantilever tunnel boring machine excavation taking vibration into consideration. In addition to considering the impact of the cantilever tunnel boring machine's block excavation construction process, the impact of vibration on the excavation process is also considered, and the vibration is reduced in noise using wavelet transform, thereby improving the accuracy of cantilever tunnel boring machine excavation simulation and providing a basis for the design and construction of related tunnels.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: a vibration-considered cantilever roadheader excavation refinement simulation method, comprising the following steps:

[0006] S1. Obtain tunnel design data and geological condition data;

[0007] S2. Establishing a refined numerical model of tunnel excavation based on the tunnel design data and geological condition data of step S1;

[0008] S3. Obtain the vibration displacement of the boom tunnel boring machine in the three directions of X (drilling direction), Y (horizontal direction), and Z (vertical direction) during construction under different working conditions;

[0009] S4, using wavelet transform to reduce noise and extract vibration trend terms, decomposing rigid body displacement and vibration waves;

[0010] S5. Obtain the construction conditions, and adjust the excavation process of the numerical model in step S2 according to the milling path of the construction conditions, and load the vibration wave in step S4 to obtain the deformation result of the tunnel excavation.

[0011] Furthermore, the tunnel design data and geological condition data include excavation section size, tunnel length, stratum distribution, surrounding rock mechanical parameters, excavation method, support parameters, etc.

[0012] Furthermore, in step S2, a refined numerical model of tunnel excavation is established, including the following sub-steps:

[0013] S21, establishing a geometric model based on the tunnel design data and geological condition data in S1;

[0014] S22. Determine the refined block excavation area of ​​the model within the analysis step according to the actual excavation method and divide the grid;

[0015] S23, assign material parameters and define boundary conditions;

[0016] S24. Apply gravity to perform initial ground stress balance.

[0017] Furthermore, the different working conditions in step S3 can be simplified into a combination of three reference working conditions, including: (1) drilling perpendicular to the tunnel face; (2) horizontal milling; and (3) vertical downward milling.

[0018] Furthermore, in step S3, the vibration displacement of the cantilever tunnel boring machine in different working conditions is obtained, and a vibration sensor needs to be installed on the cantilever tunnel boring machine to collect data.

[0019] Furthermore, the wavelet transform in step S4 provides a "time-frequency" window that changes with frequency. Through the scaling and translation operations of the wavelet basis, the signal is gradually subjected to multi-scale refinement analysis to complete the decomposition of high- and low-frequency signals. By utilizing the characteristic that the scale factor increases or decreases with frequency, by increasing or decreasing the window, adaptive analysis of high-frequency signals with high resolution and low-frequency signals with low resolution is achieved. In the wavelet decomposition process, the decomposition result of each layer is to decompose the low-frequency signal obtained by the decomposition of the previous layer into two parts: low-frequency and high-frequency. The signal x(t) is decomposed into:

[0020]

[0021] The function cluster composed of orthogonal wavelet basis is used to approximate the target time signal sequence, where the function cluster ψ a,τ The expression of (t) and wavelet basis ψ(t):

[0022]

[0023] Right now:

[0024]

[0025] Where: τ is the time factor and a is the scale factor.

[0026] Performing integral transformation on the function cluster, we can obtain the wavelet transform approximation expression of the original signal:

[0027]

[0028] Where: WT x (a,τ) is the wavelet transform approximation expression.

[0029] Adaptive soft threshold function is used to process high frequency coefficients:

[0030]

[0031] Where: cD1 is the detail coefficient of the first layer decomposition, N is the data length, and j is the decomposition level.

[0032] During wavelet transform, the effects of different wavelet bases vary greatly. Therefore, the most commonly used Daubechies wavelets DB1 to DB10 are used to perform a three-layer wavelet transform, and the wavelet base is optimized for each set of data. The denoising effect of the wavelet transform depends on the selection of the wavelet base and the setting of the denoising threshold. Since the noise component of the denoised sequence cannot be identified, in order to avoid distortion, it is generally believed that under the same threshold conditions, the closer the selected wavelet base is to the original sequence (that is, the smaller the root mean square error and the smaller the degree of distortion), the better. The root mean square error calculation formula is as follows:

[0033]

[0034] Where, is the wavelet transform value, y i is the true value, and n is the number of samples.

[0035] Furthermore, step S4 uses wavelet transform to reduce noise and extract vibration trend terms, decomposing rigid body displacement and vibration waves, including the following sub-steps:

[0036] S41, calculating the wavelet basis function ψ(t), translating to achieve full signal coverage, and scaling the scale factor a of the wavelet basis function;

[0037] Step S41 includes the following sub-steps:

[0038] S411, sequentially selecting wavelet basis functions ψ(t) from DB1 to DB10, and aligning the starting point of ψ(t) with the measured signal x(t);

[0039] S412, calculating the inner product of the wavelet basis function ψ(t) and x(t) to obtain the wavelet transform coefficient;

[0040] S413. Shift ψ(t) rightward by τ to obtain ψ(t-τ), and repeat steps S411 and S412 to achieve full signal coverage.

[0041] S414, scaling the scale factor a of the wavelet basis function, and repeating steps S411 to S413;

[0042] S42, calculating the RMSE value, and selecting a wavelet basis function according to the RMSE value, outputting the optimal wavelet basis, and completing the wavelet transform;

[0043] S43. Decompose rigid body displacement and vibration waves.

[0044] The rigid body displacement in step S43 is calculated by using the amplitude mean of the amplitude load curve, and the vibration wave is calculated by subtracting the rigid body displacement from the amplitude load curve.

[0045] Furthermore, step S5 includes the following sub-steps:

[0046] S51, applying the vibration wave obtained in step S4 in the form of displacement by inputting boundary conditions, specifically: applying vibration displacement in the corresponding axis direction to the surface of each excavation block with the X, Y, and Z axes as normal directions, and performing dynamic calculations through an implicit dynamic analysis step;

[0047] S52, use the static general analysis step to "kill" the corresponding blocks and complete the excavation;

[0048] S53, repeat S51 and S52 until all excavation blocks are excavated;

[0049] S54. Export the displacement of pre-buried measuring points (such as vault settlement, surface settlement, etc.).

[0050] The present invention has the following beneficial effects:

[0051] (1) The present invention considers the influence of vibration load on the cantilever excavation process and summarizes the continuous excavation vibration characteristics of the cantilever excavation method, which has clear engineering significance and improves the accuracy of cantilever excavation simulation;

[0052] (2) The present invention adopts a wavelet transform noise reduction method, combined with an adaptive soft threshold function, through three-layer wavelet transform and calculates the root mean square error to determine the optimal wavelet basis, thereby improving the noise reduction effect of the vibration signal while avoiding signal distortion. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This paper presents a refined simulation method for boom roadheader excavation considering vibration.

[0054] Figure 2 Schematic diagram of the numerical model for cantilever tunneling excavation construction.

[0055] Figure 3 Schematic diagram of the construction steps of cantilever tunneling excavation construction.

[0056] Figure 4 Schematic diagram of the cantilever tunneling benchmark excavation working condition.

[0057] Figure 5 Schematic diagram of vibration monitoring during cantilever tunneling construction.

[0058] Figure 6 Schematic diagram of the wavelet denoising results during the cantilever tunneling drilling process.

[0059] Figure 7 Schematic diagram of vibration load boundary conditions.

[0060] Figure 8 Schematic diagram of the comparison results between the vibration load gradient load release method and other simulation methods. DETAILED DESCRIPTION

[0061] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0062] like Figure 1 As shown, a vibration-considered cantilever roadheader excavation refinement simulation method includes the following steps:

[0063] S1. Obtain tunnel design data and geological condition data.

[0064] In an optional embodiment of the present invention, the present invention obtains design data and geological condition data of the tunnel.

[0065] The design data of the tunnel include: excavation section size, tunnel length, tunnel burial depth, excavation method, support parameters, and concrete elastic modulus.

[0066] Geological condition data include: stratum distribution, surrounding rock mechanical parameters, etc.

[0067] S2. Establish a refined numerical model of tunnel excavation based on the tunnel design data and geological condition data of step S1.

[0068] In an optional embodiment of the present invention, the present invention establishes a refined numerical model of tunnel excavation based on tunnel design data and geological condition data.

[0069] like Figure 2 As shown in FIG, the present invention provides a numerical model schematic diagram of cantilever excavation construction. Figure 3 As shown, the present invention provides a schematic diagram of the construction steps of cantilever excavation construction.

[0070] Step S2 includes the following sub-steps:

[0071] S21, establishing a geometric model based on the tunnel design data and geological condition data in S1;

[0072] S22. Determine the refined block excavation area of ​​the model within the analysis step according to the actual excavation method and divide the grid;

[0073] S23, assign material parameters and define boundary conditions;

[0074] S24. Apply gravity to perform initial ground stress balance.

[0075] S3. Obtain the vibration displacement of the boom tunnel boring machine in the three directions of X (drilling direction), Y (horizontal direction), and Z (vertical direction) during construction under different working conditions;

[0076] like Figure 4 As shown, the present invention provides a schematic diagram of a cantilever excavation benchmark excavation working condition.

[0077] In an optional embodiment of the present invention, the different working conditions in step S3 can be simplified to a combination of three reference working conditions, including: (1) drilling perpendicular to the tunnel face; (2) horizontal milling; and (3) vertical downward milling.

[0078] like Figure 5 As shown, the present invention provides a schematic diagram of vibration monitoring during cantilever tunneling construction.

[0079] In an optional embodiment of the present invention, in step S3, the vibration displacement of the cantilever tunnel boring machine during construction under different working conditions is obtained, and two vibration sensors are symmetrically placed on the boom suspension points of the cantilever tunnel boring machine to collect data.

[0080] S4, using wavelet transform to reduce noise and extract vibration trend terms, decomposing rigid body displacement and vibration waves;

[0081] like Figure 6 As shown, the present invention provides a schematic diagram of wavelet noise reduction processing results in a cantilever excavation drilling process.

[0082] In an optional embodiment of the present invention, the wavelet transform in step S4 provides a "time-frequency" window that changes with frequency. The signal is gradually subjected to multi-scale refinement analysis through the expansion and contraction operation of the wavelet basis to complete the decomposition of high-frequency and low-frequency signals. By utilizing the characteristic that the scale factor increases or decreases with frequency, the window is enlarged or reduced to achieve adaptive analysis of high-frequency signals with high resolution and low-frequency signals with low resolution. In the wavelet decomposition process, the decomposition result of each layer is to decompose the low-frequency signal obtained by the decomposition of the previous layer into two parts: low frequency and high frequency. The signal x(t) is decomposed into:

[0083]

[0084] The function cluster composed of orthogonal wavelet basis is used to approximate the target time signal sequence, where the function cluster ψ a,τ The expression of (t) and wavelet basis ψ(t):

[0085]

[0086] Right now:

[0087]

[0088] Where: τ is the time factor and a is the scale factor.

[0089] Performing integral transformation on the function cluster, we can obtain the wavelet transform approximation expression of the original signal:

[0090]

[0091] Where: WT x (a,τ) is the wavelet transform approximation expression.

[0092] Adaptive soft threshold function is used to process high frequency coefficients:

[0093]

[0094] Where: cD1 is the detail coefficient of the first layer decomposition, N is the data length, and j is the decomposition level.

[0095] During wavelet transform, the effects of different wavelet bases vary greatly. Therefore, the most commonly used Daubechies wavelets DB1 to DB10 are used to perform a three-layer wavelet transform, and the wavelet base is optimized for each set of data. The denoising effect of the wavelet transform depends on the selection of the wavelet base and the setting of the denoising threshold. Since the noise component of the denoised sequence cannot be identified, in order to avoid distortion, it is generally believed that under the same threshold conditions, the closer the selected wavelet base is to the original sequence (that is, the smaller the root mean square error and the smaller the degree of distortion), the better. The root mean square error calculation formula is as follows:

[0096]

[0097] Where, is the wavelet transform value, y i is the true value, and n is the number of samples.

[0098] In an optional embodiment of the present invention, the step S4 of using wavelet transform to reduce noise and extract vibration trend items, and decompose rigid body displacement and vibration waves, includes the following sub-steps:

[0099] S41, calculating the wavelet basis function ψ(t), translating to achieve full signal coverage, and scaling the scale factor a of the wavelet basis function;

[0100] Step S41 includes the following sub-steps:

[0101] S411, sequentially selecting wavelet basis functions ψ(t) from DB1 to DB10, and aligning the starting point of ψ(t) with the measured signal x(t);

[0102] S412, calculating the inner product of the wavelet basis function ψ(t) and x(t) to obtain the wavelet transform coefficient;

[0103] S413. Shift ψ(t) rightward by τ to obtain ψ(t-τ), and repeat steps S411 and S412 to achieve full signal coverage.

[0104] S414, scaling the scale factor a of the wavelet basis function, and repeating steps S411 to S413;

[0105] S42, calculating the RMSE value, and selecting a wavelet basis function according to the RMSE value, outputting the optimal wavelet basis, and completing the wavelet transform;

[0106] Specifically, in an optional embodiment of the present invention, since two symmetrical measuring points are arranged, the trend values ​​of the vibration curves in each direction of the two measuring points after wavelet transformation are respectively performed are averaged to obtain the trend value in each direction.

[0107] S43. Decompose rigid body displacement and vibration waves.

[0108] The rigid body displacement in step S43 is the amplitude mean of the amplitude load curve, and the vibration wave is the amplitude load curve minus the rigid body displacement.

[0109] S5. Obtain the construction conditions, and adjust the excavation process of the numerical model in step S2 according to the milling path of the construction conditions, and load the vibration wave in step S4 to obtain the deformation result of the tunnel excavation.

[0110] like Figure 7 As shown in FIG, the present invention provides a schematic diagram of vibration load boundary conditions. Figure 8As shown, the present invention provides a schematic diagram of the comparison results between the vibration load gradient load release method and other simulation methods.

[0111] In an optional embodiment of the present invention, step S5 includes the following sub-steps:

[0112] S51, applying the vibration wave obtained in step S4 in the form of displacement by inputting boundary conditions, specifically: applying vibration displacement in the corresponding axis direction to the surface of each excavation block with the X, Y, and Z axes as normal directions, and performing dynamic calculations through an implicit dynamic analysis step;

[0113] S52, use the static general analysis step to "kill" the corresponding blocks and complete the excavation;

[0114] S53, repeat S51 and S52 until all excavation blocks are excavated;

[0115] S54. Export the displacement of pre-buried measuring points (such as vault settlement, surface settlement, etc.).

[0116] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0117] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0118] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0119] Specific embodiments are used in the present invention to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

[0120] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A vibration-based cantilever roadheader excavation refinement simulation method, characterized in that: The following steps are involved: S1. Obtain tunnel design data and geological condition data; S2. Establishing a refined numerical model of tunnel excavation based on the tunnel design data and geological condition data of step S1; S3. Obtain the vibration displacement of the boom tunnel boring machine in the three directions of X (drilling direction), Y (horizontal direction), and Z (vertical direction) during construction under different working conditions; S4, using wavelet transform to reduce noise and extract vibration trend terms, decomposing rigid body displacement and vibration waves; S5. Obtain the construction conditions, and adjust the excavation process of the numerical model in step S2 according to the milling path of the construction conditions, and load the vibration wave in step S4 to obtain the deformation result of the tunnel excavation.

2. The vibration-considered cantilever roadheader excavation refinement simulation method according to claim 1, characterized in that: In step S1, the tunnel design data and geological condition data include excavation section size, tunnel length, stratum distribution, surrounding rock mechanical parameters, excavation method and support parameters.

3. The vibration-considered cantilever roadheader excavation refinement simulation method according to claim 1, characterized in that: In step S2, a refined numerical model of tunnel excavation is established, including the following sub-steps: S21, establishing a geometric model based on the tunnel design data and geological condition data in S1; S22. Determine the refined block excavation area of ​​the model within the analysis step according to the actual excavation method and divide the grid; S23, assign material parameters and define boundary conditions; S24. Apply gravity to perform initial ground stress balance.

4. The vibration-considered cantilever roadheader excavation refinement simulation method according to claim 1, characterized in that: The different working conditions in step S3 can be simplified into a combination of three reference working conditions, including: (1) drilling perpendicular to the tunnel face; (2) horizontal milling; and (3) vertical downward milling.

5. The vibration-considered cantilever roadheader excavation refinement simulation method according to claim 1, characterized in that: In step S3, a vibration sensor is installed on the cantilever tunnel boring machine to collect data and obtain the vibration displacement of the cantilever tunnel boring machine during construction under different working conditions.

6. The vibration-considered cantilever roadheader excavation refinement simulation method according to claim 1, characterized in that: The wavelet transform in step S4 provides a time-frequency window that changes with frequency. The signal is gradually subjected to multi-scale refinement analysis through the scaling and translation operations of the wavelet basis, completing the decomposition of high- and low-frequency signals. By taking advantage of the fact that the scaling factor increases or decreases with frequency, the window is enlarged or reduced to achieve adaptive analysis of high-frequency signals with high resolution and low-frequency signals with low resolution. In the wavelet decomposition process, the decomposition result of each layer is to decompose the low-frequency signal obtained by the previous layer into two parts: low-frequency and high-frequency. The signal x(t) is decomposed into: The function cluster composed of orthogonal wavelet basis is used to approximate the target time signal sequence, where the function cluster ψ a,τ The expression of (t) and wavelet basis ψ(t): Right now: Where: τ is the time factor, a is the scale factor; Performing integral transformation on the function cluster, we can obtain the wavelet transform approximation expression of the original signal: Where: WT x (a,τ) is the approximate expression of wavelet transform; Adaptive soft threshold function is used to process high frequency coefficients: Where: cD1 is the detail coefficient of the first layer decomposition, N is the data length, and j is the decomposition level; During wavelet transform, the effects of different wavelet bases vary greatly. Therefore, the most commonly used Daubechies wavelets DB1 to DB10 are used to perform a three-layer wavelet transform, and the wavelet base is optimized for each set of data. The denoising effect of wavelet transform depends on the selection of wavelet base and the setting of denoising threshold. Since the noise component of the denoised sequence cannot be identified, in order to avoid distortion, it is generally believed that under the same threshold condition, the closer the selected wavelet base is to the original sequence (that is, the smaller the root mean square error and the smaller the degree of distortion), the better. The root mean square error calculation formula is as follows: Where, is the wavelet transform value, y i is the true value, and n is the number of samples.

7. The vibration-considered cantilever roadheader excavation refinement simulation method according to claim 1, characterized in that: In step S4, using wavelet transform to reduce noise and extract vibration trend items, and decompose rigid body displacement and vibration waves, includes the following sub-steps: S41, calculating the wavelet basis function ψ(t), translating to achieve full signal coverage, and scaling the scale factor a of the wavelet basis function; Step S41 includes the following sub-steps: S411, sequentially selecting wavelet basis functions ψ(t) from DB1 to DB10, and aligning the starting point of ψ(t) with the measured signal x(t); S412, calculating the inner product of the wavelet basis function ψ(t) and x(t) to obtain the wavelet transform coefficient; S413. Shift ψ(t) rightward by τ to obtain ψ(t-τ), and repeat steps S411 and S412 to achieve full signal coverage. S414, scaling the scale factor a of the wavelet basis function, and repeating steps S411 to S413; S42, calculating the RMSE value, and selecting a wavelet basis function according to the RMSE value, outputting the optimal wavelet basis, and completing the wavelet transform; S43, decomposition of rigid body displacement and vibration waves; The rigid body displacement in step S43 is calculated by using the amplitude mean of the amplitude load curve, and the vibration wave is calculated by subtracting the rigid body displacement from the amplitude load curve.

8. The vibration-considered cantilever roadheader excavation refinement simulation method according to claim 1, characterized in that: Step S5 includes the following sub-steps: S51, applying the vibration wave obtained in step S4 in the form of displacement by inputting boundary conditions, specifically: applying vibration displacement in the corresponding axis direction to the surface of each excavation block with the X, Y, and Z axes as normal directions, and performing dynamic calculations through an implicit dynamic analysis step; S52, use the static general analysis step to "kill" the corresponding blocks and complete the excavation; S53, repeat S51 and S52 until all excavation blocks are excavated; S54. Export the displacement of the pre-buried measuring points.

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